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However, this also carries with it major challenges: improving the policy beyond the", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 632, + 505, + 645 + ], + "spans": [ + { + "bbox": [ + 105, + 632, + 505, + 645 + ], + "score": 1.0, + "content": "level of the behavior policy that collected the data requires estimating values for actions other than", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 644, + 505, + 655 + ], + "spans": [ + { + "bbox": [ + 106, + 644, + 505, + 655 + ], + "score": 1.0, + "content": "those that were seen in the dataset, and this, in turn, requires trading off policy improvement against", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "score": 1.0, + "content": "distributional shift, since the values of actions that are too different from those in the data are unlikely", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 666, + 505, + 677 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 505, + 677 + ], + "score": 1.0, + "content": "to be estimated accurately. Prior methods generally address this by either constraining the policy to", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 675, + 506, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 675, + 506, + 689 + ], + "score": 1.0, + "content": "limit how far it deviates from the behavior policy (Fujimoto et al., 2019; Wu et al., 2019; Fujimoto", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 687, + 506, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 506, + 700 + ], + "score": 1.0, + "content": "& Gu, 2021; Kumar et al., 2019; Nair et al., 2020; Wang et al., 2020), or by regularizing the learned", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 699, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 505, + 712 + ], + "score": 1.0, + "content": "value functions to assign low values to out-of-distribution actions (Kumar et al., 2020; Kostrikov", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "et al., 2021). Nevertheless, this imposes a trade-off between how much the policy improves and how", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 720, + 505, + 731 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 505, + 731 + ], + "score": 1.0, + "content": "vulnerable it is to misestimation due to distributional shift. Can we devise an offline RL method that", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 40.5 + } + ], + "page_idx": 0, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 25, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 25, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2022", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 303, + 751, + 308, + 760 + ], + "lines": [ + { + "bbox": [ + 302, + 751, + 308, + 761 + ], + "spans": [ + { + "bbox": [ + 302, + 751, + 308, + 761 + ], + "score": 1.0, + "content": "1", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 107, + 79, + 388, + 117 + ], + "lines": [ + { + "bbox": [ + 106, + 78, + 389, + 97 + ], + "spans": [ + { + "bbox": [ + 106, + 78, + 389, + 97 + ], + "score": 1.0, + "content": "OFFLINE REINFORCEMENT LEARNING", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 97, + 324, + 119 + ], + "spans": [ + { + "bbox": [ + 106, + 97, + 324, + 119 + ], + "score": 1.0, + "content": "WITH IMPLICIT Q-LEARNING", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "list", + "bbox": [ + 113, + 137, + 465, + 183 + ], + "lines": [ + { + "bbox": [ + 111, + 137, + 305, + 150 + ], + "spans": [ + { + "bbox": [ + 111, + 137, + 305, + 150 + ], + "score": 1.0, + "content": "Ilya Kostrikov, Ashvin Nair & Sergey Levine", + "type": "text" + } + ], + "index": 2, + "is_list_start_line": true + }, + { + "bbox": [ + 111, + 148, + 357, + 162 + ], + "spans": [ + { + "bbox": [ + 111, + 148, + 357, + 162 + ], + "score": 1.0, + "content": "Department of Electrical Engineering and Computer Science", + "type": "text" + } + ], + "index": 3, + "is_list_start_line": true + }, + { + "bbox": [ + 111, + 160, + 250, + 172 + ], + "spans": [ + { + "bbox": [ + 111, + 160, + 250, + 172 + ], + "score": 1.0, + "content": "University of California, Berkeley", + "type": "text" + } + ], + "index": 4, + "is_list_start_line": true + }, + { + "bbox": [ + 112, + 170, + 464, + 183 + ], + "spans": [ + { + "bbox": [ + 112, + 170, + 464, + 183 + ], + "score": 1.0, + "content": "kostrikov,anair17 @berkeley.edu, svlevine@eecs.berkeley.edu", + "type": "text" + } + ], + "index": 5, + "is_list_start_line": true + } + ], + "index": 3.5, + "bbox_fs": [ + 111, + 137, + 464, + 183 + ] + }, + { + "type": "title", + "bbox": [ + 278, + 211, + 333, + 223 + ], + "lines": [ + { + "bbox": [ + 276, + 210, + 336, + 225 + ], + "spans": [ + { + "bbox": [ + 276, + 210, + 336, + 225 + ], + "score": 1.0, + "content": "ABSTRACT", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 6 + }, + { + "type": "text", + "bbox": [ + 142, + 239, + 468, + 523 + ], + "lines": [ + { + "bbox": [ + 142, + 237, + 469, + 252 + ], + "spans": [ + { + "bbox": [ + 142, + 237, + 469, + 252 + ], + "score": 1.0, + "content": "Offline reinforcement learning requires reconciling two conflicting aims: learning", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 141, + 249, + 470, + 262 + ], + "spans": [ + { + "bbox": [ + 141, + 249, + 470, + 262 + ], + "score": 1.0, + "content": "a policy that improves over the behavior policy that collected the dataset, while at", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 141, + 260, + 469, + 273 + ], + "spans": [ + { + "bbox": [ + 141, + 260, + 469, + 273 + ], + "score": 1.0, + "content": "the same time minimizing the deviation from the behavior policy so as to avoid", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 141, + 271, + 470, + 284 + ], + "spans": [ + { + "bbox": [ + 141, + 271, + 470, + 284 + ], + "score": 1.0, + "content": "errors due to distributional shift. This trade-off is critical, because most current", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 142, + 282, + 469, + 295 + ], + "spans": [ + { + "bbox": [ + 142, + 282, + 469, + 295 + ], + "score": 1.0, + "content": "offline reinforcement learning methods need to query the value of unseen actions", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 142, + 294, + 469, + 306 + ], + "spans": [ + { + "bbox": [ + 142, + 294, + 469, + 306 + ], + "score": 1.0, + "content": "during training to improve the policy, and therefore need to either constrain these", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 141, + 305, + 469, + 317 + ], + "spans": [ + { + "bbox": [ + 141, + 305, + 469, + 317 + ], + "score": 1.0, + "content": "actions to be in-distribution, or else regularize their values. We propose a new", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 141, + 315, + 470, + 327 + ], + "spans": [ + { + "bbox": [ + 141, + 315, + 470, + 327 + ], + "score": 1.0, + "content": "offline RL method that never needs to evaluate actions outside of the dataset, but", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 141, + 326, + 470, + 339 + ], + "spans": [ + { + "bbox": [ + 141, + 326, + 470, + 339 + ], + "score": 1.0, + "content": "still enables the learned policy to improve substantially over the best behavior in", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 141, + 337, + 470, + 349 + ], + "spans": [ + { + "bbox": [ + 141, + 337, + 470, + 349 + ], + "score": 1.0, + "content": "the data through generalization. The main insight in our work is that, instead of", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 141, + 348, + 469, + 361 + ], + "spans": [ + { + "bbox": [ + 141, + 348, + 469, + 361 + ], + "score": 1.0, + "content": "evaluating unseen actions from the latest policy, we can approximate the policy", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 141, + 360, + 469, + 371 + ], + "spans": [ + { + "bbox": [ + 141, + 360, + 469, + 371 + ], + "score": 1.0, + "content": "improvement step implicitly by treating the state value function as a random vari-", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 141, + 370, + 469, + 383 + ], + "spans": [ + { + "bbox": [ + 141, + 370, + 469, + 383 + ], + "score": 1.0, + "content": "able, with randomness determined by the action (while still integrating over the", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 141, + 381, + 470, + 394 + ], + "spans": [ + { + "bbox": [ + 141, + 381, + 470, + 394 + ], + "score": 1.0, + "content": "dynamics to avoid excessive optimism), and then taking a state conditional upper", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 141, + 392, + 470, + 404 + ], + "spans": [ + { + "bbox": [ + 141, + 392, + 470, + 404 + ], + "score": 1.0, + "content": "expectile of this random variable to estimate the value of the best actions in that", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 141, + 404, + 469, + 415 + ], + "spans": [ + { + "bbox": [ + 141, + 404, + 469, + 415 + ], + "score": 1.0, + "content": "state. This leverages the generalization capacity of the function approximator to", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 141, + 414, + 469, + 427 + ], + "spans": [ + { + "bbox": [ + 141, + 414, + 469, + 427 + ], + "score": 1.0, + "content": "estimate the value of the best available action at a given state without ever directly", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 141, + 425, + 470, + 437 + ], + "spans": [ + { + "bbox": [ + 141, + 425, + 470, + 437 + ], + "score": 1.0, + "content": "querying a Q-function with this unseen action. Our algorithm alternates between", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 141, + 436, + 469, + 448 + ], + "spans": [ + { + "bbox": [ + 141, + 436, + 469, + 448 + ], + "score": 1.0, + "content": "fitting this upper expectile value function and backing it up into a Q-function,", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 141, + 446, + 470, + 460 + ], + "spans": [ + { + "bbox": [ + 141, + 446, + 470, + 460 + ], + "score": 1.0, + "content": "without any explicit policy. Then, we extract the policy via advantage-weighted", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 141, + 457, + 470, + 470 + ], + "spans": [ + { + "bbox": [ + 141, + 457, + 470, + 470 + ], + "score": 1.0, + "content": "behavioral cloning, which also avoids querying out-of-sample actions. We dub", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 141, + 469, + 469, + 482 + ], + "spans": [ + { + "bbox": [ + 141, + 469, + 469, + 482 + ], + "score": 1.0, + "content": "our method implicit Q-learning (IQL). IQL is easy to implement, computationally", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 142, + 480, + 469, + 492 + ], + "spans": [ + { + "bbox": [ + 142, + 480, + 469, + 492 + ], + "score": 1.0, + "content": "efficient, and only requires fitting an additional critic with an asymmetric L2 loss.", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 142, + 492, + 469, + 502 + ], + "spans": [ + { + "bbox": [ + 142, + 492, + 469, + 502 + ], + "score": 1.0, + "content": "IQL demonstrates the state-of-the-art performance on D4RL, a standard bench-", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 141, + 502, + 469, + 514 + ], + "spans": [ + { + "bbox": [ + 141, + 502, + 469, + 514 + ], + "score": 1.0, + "content": "mark for offline reinforcement learning. We also demonstrate that IQL achieves", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 141, + 513, + 469, + 525 + ], + "spans": [ + { + "bbox": [ + 141, + 513, + 469, + 525 + ], + "score": 1.0, + "content": "strong performance fine-tuning using online interaction after offline initialization.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 19.5, + "bbox_fs": [ + 141, + 237, + 470, + 525 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 551, + 206, + 563 + ], + "lines": [ + { + "bbox": [ + 105, + 549, + 208, + 567 + ], + "spans": [ + { + "bbox": [ + 105, + 549, + 208, + 567 + ], + "score": 1.0, + "content": "1 INTRODUCTION", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 33 + }, + { + "type": "text", + "bbox": [ + 107, + 578, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 577, + 505, + 590 + ], + "spans": [ + { + "bbox": [ + 105, + 577, + 505, + 590 + ], + "score": 1.0, + "content": "Offline reinforcement learning (RL) addresses the problem of learning effective policies entirely", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 587, + 502, + 601 + ], + "spans": [ + { + "bbox": [ + 105, + 587, + 502, + 601 + ], + "score": 1.0, + "content": "from previously collected data, without online interaction (Fujimoto et al., 2019; Lange et al., 2012).", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 600, + 505, + 613 + ], + "spans": [ + { + "bbox": [ + 105, + 600, + 505, + 613 + ], + "score": 1.0, + "content": "This is very appealing in a range of real-world domains, from robotics to logistics and operations", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 611, + 505, + 623 + ], + "spans": [ + { + "bbox": [ + 106, + 611, + 505, + 623 + ], + "score": 1.0, + "content": "research, where real-world exploration with untrained policies is costly or dangerous, but prior data", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 622, + 505, + 633 + ], + "spans": [ + { + "bbox": [ + 105, + 622, + 505, + 633 + ], + "score": 1.0, + "content": "is available. However, this also carries with it major challenges: improving the policy beyond the", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 632, + 505, + 645 + ], + "spans": [ + { + "bbox": [ + 105, + 632, + 505, + 645 + ], + "score": 1.0, + "content": "level of the behavior policy that collected the data requires estimating values for actions other than", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 644, + 505, + 655 + ], + "spans": [ + { + "bbox": [ + 106, + 644, + 505, + 655 + ], + "score": 1.0, + "content": "those that were seen in the dataset, and this, in turn, requires trading off policy improvement against", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "score": 1.0, + "content": "distributional shift, since the values of actions that are too different from those in the data are unlikely", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 666, + 505, + 677 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 505, + 677 + ], + "score": 1.0, + "content": "to be estimated accurately. Prior methods generally address this by either constraining the policy to", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 675, + 506, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 675, + 506, + 689 + ], + "score": 1.0, + "content": "limit how far it deviates from the behavior policy (Fujimoto et al., 2019; Wu et al., 2019; Fujimoto", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 687, + 506, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 506, + 700 + ], + "score": 1.0, + "content": "& Gu, 2021; Kumar et al., 2019; Nair et al., 2020; Wang et al., 2020), or by regularizing the learned", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 699, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 505, + 712 + ], + "score": 1.0, + "content": "value functions to assign low values to out-of-distribution actions (Kumar et al., 2020; Kostrikov", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "et al., 2021). Nevertheless, this imposes a trade-off between how much the policy improves and how", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 720, + 505, + 731 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 505, + 731 + ], + "score": 1.0, + "content": "vulnerable it is to misestimation due to distributional shift. Can we devise an offline RL method that", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "avoids this issue by never needing to directly query or estimate values for actions that were not seen", + "type": "text", + "cross_page": true + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 94, + 155, + 105 + ], + "spans": [ + { + "bbox": [ + 106, + 94, + 155, + 105 + ], + "score": 1.0, + "content": "in the data?", + "type": "text", + "cross_page": true + } + ], + "index": 1 + } + ], + "index": 40.5, + "bbox_fs": [ + 105, + 577, + 506, + 731 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 82, + 504, + 105 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "avoids this issue by never needing to directly query or estimate values for actions that were not seen", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 94, + 155, + 105 + ], + "spans": [ + { + "bbox": [ + 106, + 94, + 155, + 105 + ], + "score": 1.0, + "content": "in the data?", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "text", + "bbox": [ + 106, + 110, + 505, + 254 + ], + "lines": [ + { + "bbox": [ + 106, + 111, + 505, + 122 + ], + "spans": [ + { + "bbox": [ + 106, + 111, + 505, + 122 + ], + "score": 1.0, + "content": "In this work, we start from an observation that in-distribution constraints widely used in prior work", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 121, + 505, + 133 + ], + "spans": [ + { + "bbox": [ + 106, + 121, + 505, + 133 + ], + "score": 1.0, + "content": "might not be sufficient to avoid value function extrapolation, and we ask whether it is possible to", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 131, + 506, + 145 + ], + "spans": [ + { + "bbox": [ + 105, + 131, + 506, + 145 + ], + "score": 1.0, + "content": "learn an optimal policy with in-sample learning, without ever querying the values of any unseen", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 143, + 506, + 156 + ], + "spans": [ + { + "bbox": [ + 106, + 143, + 506, + 156 + ], + "score": 1.0, + "content": "actions. The key idea in our method is to approximate an upper expectile of the distribution over", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 153, + 505, + 167 + ], + "spans": [ + { + "bbox": [ + 106, + 153, + 505, + 167 + ], + "score": 1.0, + "content": "values with respect to the distribution of dataset actions for each state. We alternate between fitting", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 165, + 505, + 177 + ], + "spans": [ + { + "bbox": [ + 106, + 165, + 505, + 177 + ], + "score": 1.0, + "content": "this value function with expectile regression, and then using it to compute Bellman backups for", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 176, + 506, + 188 + ], + "spans": [ + { + "bbox": [ + 106, + 176, + 155, + 188 + ], + "score": 1.0, + "content": "training the", + "type": "text" + }, + { + "bbox": [ + 156, + 176, + 165, + 187 + ], + "score": 0.84, + "content": "Q", + "type": "inline_equation" + }, + { + "bbox": [ + 165, + 176, + 506, + 188 + ], + "score": 1.0, + "content": "-function. We show that we can do this simply by modifying the loss function in a", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 187, + 505, + 200 + ], + "spans": [ + { + "bbox": [ + 105, + 187, + 491, + 200 + ], + "score": 1.0, + "content": "SARSA-style TD backup, without ever using out-of-sample actions in the target value. Once this", + "type": "text" + }, + { + "bbox": [ + 491, + 187, + 501, + 199 + ], + "score": 0.78, + "content": "Q", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 187, + 505, + 200 + ], + "score": 1.0, + "content": "-", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 197, + 506, + 211 + ], + "spans": [ + { + "bbox": [ + 105, + 197, + 506, + 211 + ], + "score": 1.0, + "content": "function has converged, we extract the corresponding policy using advantage-weighted behavioral", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 209, + 505, + 222 + ], + "spans": [ + { + "bbox": [ + 106, + 209, + 505, + 222 + ], + "score": 1.0, + "content": "cloning. This approach does not require explicit constraints or explicit regularization of out-of-", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 219, + 505, + 232 + ], + "spans": [ + { + "bbox": [ + 106, + 219, + 505, + 232 + ], + "score": 1.0, + "content": "distribution actions during value function training, though our policy extraction step does implicitly", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 231, + 504, + 244 + ], + "spans": [ + { + "bbox": [ + 105, + 231, + 504, + 244 + ], + "score": 1.0, + "content": "enforce a constraint, as discussed in prior work on advantage-weighted regression (Peters & Schaal,", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 241, + 348, + 255 + ], + "spans": [ + { + "bbox": [ + 106, + 241, + 348, + 255 + ], + "score": 1.0, + "content": "2007; Peng et al., 2019; Nair et al., 2020; Wang et al., 2020).", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 8 + }, + { + "type": "text", + "bbox": [ + 106, + 258, + 505, + 358 + ], + "lines": [ + { + "bbox": [ + 106, + 259, + 505, + 271 + ], + "spans": [ + { + "bbox": [ + 106, + 259, + 505, + 271 + ], + "score": 1.0, + "content": "Our main contribution is implicit Q-learning (IQL), a new offline RL algorithm that avoids ever", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 269, + 505, + 283 + ], + "spans": [ + { + "bbox": [ + 105, + 269, + 505, + 283 + ], + "score": 1.0, + "content": "querying values of unseen actions while still being able to perform multi-step dynamic program-", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 281, + 505, + 293 + ], + "spans": [ + { + "bbox": [ + 105, + 281, + 505, + 293 + ], + "score": 1.0, + "content": "ming updates. Our method is easy to implement by making a small change to the loss function in", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 292, + 505, + 304 + ], + "spans": [ + { + "bbox": [ + 105, + 292, + 505, + 304 + ], + "score": 1.0, + "content": "a simple SARSA-like TD update and is computationally very efficient. Furthermore, our approach", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 303, + 505, + 316 + ], + "spans": [ + { + "bbox": [ + 106, + 303, + 505, + 316 + ], + "score": 1.0, + "content": "demonstrates the state-of-the-art performance on D4RL, a popular benchmark for offline reinforce-", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 313, + 506, + 327 + ], + "spans": [ + { + "bbox": [ + 105, + 313, + 506, + 327 + ], + "score": 1.0, + "content": "ment learning. In particular, our approach significantly improves over the prior state-of-the-art on", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 324, + 506, + 338 + ], + "spans": [ + { + "bbox": [ + 105, + 324, + 506, + 338 + ], + "score": 1.0, + "content": "challenging Ant Maze tasks that require to “stitch” several sub-optimal trajectories. Finally, we", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 335, + 506, + 348 + ], + "spans": [ + { + "bbox": [ + 105, + 335, + 506, + 348 + ], + "score": 1.0, + "content": "demonstrate that our approach is suitable for finetuning; after initialization from offline RL, IQL is", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 347, + 403, + 360 + ], + "spans": [ + { + "bbox": [ + 106, + 347, + 403, + 360 + ], + "score": 1.0, + "content": "capable of improving policy performance utilizing additional interactions.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 19 + }, + { + "type": "title", + "bbox": [ + 108, + 374, + 209, + 386 + ], + "lines": [ + { + "bbox": [ + 104, + 372, + 211, + 388 + ], + "spans": [ + { + "bbox": [ + 104, + 372, + 211, + 388 + ], + "score": 1.0, + "content": "2 RELATED WORK", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 24 + }, + { + "type": "text", + "bbox": [ + 106, + 397, + 505, + 583 + ], + "lines": [ + { + "bbox": [ + 105, + 395, + 505, + 410 + ], + "spans": [ + { + "bbox": [ + 105, + 395, + 505, + 410 + ], + "score": 1.0, + "content": "A significant portion of recently proposed offline RL methods are based on either constrained or reg-", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 408, + 504, + 419 + ], + "spans": [ + { + "bbox": [ + 106, + 408, + 504, + 419 + ], + "score": 1.0, + "content": "ularized approximate dynamic programming (e.g., Q-learning or actor-critic methods), with the con-", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 419, + 504, + 430 + ], + "spans": [ + { + "bbox": [ + 106, + 419, + 504, + 430 + ], + "score": 1.0, + "content": "straint or regularizer serving to limit deviation from the behavior policy. We will refer to these meth-", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 429, + 505, + 442 + ], + "spans": [ + { + "bbox": [ + 105, + 429, + 505, + 442 + ], + "score": 1.0, + "content": "ods as “multi-step dynamic programming” algorithms, since they perform true dynamic program-", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 440, + 506, + 452 + ], + "spans": [ + { + "bbox": [ + 105, + 440, + 506, + 452 + ], + "score": 1.0, + "content": "ming for multiple iterations, and therefore can in principle recover the optimal policy if provided", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 450, + 507, + 465 + ], + "spans": [ + { + "bbox": [ + 105, + 450, + 507, + 465 + ], + "score": 1.0, + "content": "with high-coverage data. The constraints can be implemented via an explicit density model (Wu", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 462, + 506, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 462, + 506, + 475 + ], + "score": 1.0, + "content": "et al., 2019; Fujimoto et al., 2019; Kumar et al., 2019; Ghasemipour et al., 2021), implicit divergence", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 473, + 506, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 473, + 506, + 486 + ], + "score": 1.0, + "content": "constraints (Nair et al., 2020; Wang et al., 2020; Peters & Schaal, 2007; Peng et al., 2019; Siegel", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 485, + 505, + 497 + ], + "spans": [ + { + "bbox": [ + 106, + 485, + 505, + 497 + ], + "score": 1.0, + "content": "et al., 2020), or by adding a supervised learning term to the policy improvement objective (Fujimoto", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 494, + 505, + 508 + ], + "spans": [ + { + "bbox": [ + 106, + 495, + 160, + 508 + ], + "score": 1.0, + "content": "& Gu, 2021)", + "type": "text" + }, + { + "bbox": [ + 165, + 494, + 505, + 507 + ], + "score": 1.0, + "content": "Several works have also proposed to directly regularize the Q-function to produce", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 505, + 504, + 520 + ], + "spans": [ + { + "bbox": [ + 106, + 505, + 504, + 520 + ], + "score": 1.0, + "content": "low values for out-of-distribution actions (Kostrikov et al., 2021; Kumar et al., 2020; Fakoor et al.,", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 516, + 506, + 530 + ], + "spans": [ + { + "bbox": [ + 105, + 516, + 131, + 530 + ], + "score": 0.46, + "content": "\\boxed { 2 0 2 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 135, + 516, + 506, + 530 + ], + "score": 1.0, + "content": "Our method is also a multi-step dynamic programming algorithm. However, in contrast to", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 528, + 506, + 541 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 506, + 541 + ], + "score": 1.0, + "content": "prior works, our method completely avoids directly querying the learned Q-function with unseen", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 539, + 505, + 551 + ], + "spans": [ + { + "bbox": [ + 105, + 539, + 505, + 551 + ], + "score": 1.0, + "content": "actions during training, removing the need for any constraint during this stage, though the subse-", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 104, + 550, + 506, + 563 + ], + "spans": [ + { + "bbox": [ + 104, + 550, + 506, + 563 + ], + "score": 1.0, + "content": "quent policy extraction, which is based on advantage-weighted regression (Peng et al., 2019; Nair", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 561, + 506, + 574 + ], + "spans": [ + { + "bbox": [ + 105, + 561, + 506, + 574 + ], + "score": 1.0, + "content": "et al., 2020), does apply an implicit constraint. However, this policy does not actually influence", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 571, + 203, + 586 + ], + "spans": [ + { + "bbox": [ + 105, + 571, + 203, + 586 + ], + "score": 1.0, + "content": "value function training.", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 33 + }, + { + "type": "text", + "bbox": [ + 106, + 589, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 589, + 504, + 601 + ], + "spans": [ + { + "bbox": [ + 106, + 589, + 504, + 601 + ], + "score": 1.0, + "content": "In contrast to multi-step dynamic programming methods, several recent works have proposed meth-", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 600, + 506, + 613 + ], + "spans": [ + { + "bbox": [ + 106, + 600, + 506, + 613 + ], + "score": 1.0, + "content": "ods that rely either on a single step of policy iteration, fitting the value function or Q-function of", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 610, + 506, + 624 + ], + "spans": [ + { + "bbox": [ + 105, + 610, + 506, + 624 + ], + "score": 1.0, + "content": "the behavior policy and then extracting the corresponding greedy policy (Peng et al., 2019; Brand-", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 621, + 506, + 634 + ], + "spans": [ + { + "bbox": [ + 105, + 621, + 506, + 634 + ], + "score": 1.0, + "content": "fonbrener et al., 2021; Gulcehre et al., 2021), or else avoid value functions completely and utilize", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 633, + 505, + 646 + ], + "spans": [ + { + "bbox": [ + 105, + 633, + 505, + 646 + ], + "score": 1.0, + "content": "behavioral cloning-style objectives (Chen et al., 2021). We collectively refer to these as “single-step”", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 644, + 506, + 657 + ], + "spans": [ + { + "bbox": [ + 106, + 644, + 506, + 657 + ], + "score": 1.0, + "content": "approaches. These methods avoid needing to query unseen actions as well, since they either use no", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 655, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 505, + 667 + ], + "score": 1.0, + "content": "value function at all, or learn the value function of the behavior policy. Although these methods are", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "score": 1.0, + "content": "simple to implement and effective on the MuJoCo locomotion tasks in D4RL, we show that such", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 106, + 677, + 504, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 504, + 689 + ], + "score": 1.0, + "content": "single-step methods perform very poorly on more complex datasets in D4RL, which require combin-", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 106, + 687, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 106, + 687, + 505, + 700 + ], + "score": 1.0, + "content": "ing parts of suboptimal trajectories (“stitching”). Prior multi-step dynamic programming methods", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 105, + 699, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 505, + 711 + ], + "score": 1.0, + "content": "perform much better in such settings, as does our method. We discuss this distinction in more detail", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 106, + 707, + 506, + 724 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 149, + 721 + ], + "score": 1.0, + "content": "in Section", + "type": "text" + }, + { + "bbox": [ + 149, + 709, + 167, + 722 + ], + "score": 0.28, + "content": "5 . 1 .", + "type": "inline_equation" + }, + { + "bbox": [ + 168, + 707, + 506, + 724 + ], + "score": 1.0, + "content": "Our method also shares the simplicity and computational efficiency of single-step", + "type": "text" + } + ], + "index": 53 + }, + { + "bbox": [ + 105, + 720, + 470, + 732 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 470, + 732 + ], + "score": 1.0, + "content": "approaches, providing an appealing combination of the strengths of both types of methods.", + "type": "text" + } + ], + "index": 54 + } + ], + "index": 48 + } + ], + "page_idx": 1, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2022", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 309, + 760 + ], + "lines": [ + { + "bbox": [ + 301, + 750, + 310, + 763 + ], + "spans": [ + { + "bbox": [ + 301, + 750, + 310, + 763 + ], + "score": 1.0, + "content": "2", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 82, + 504, + 105 + ], + "lines": [], + "index": 0.5, + "bbox_fs": [ + 106, + 82, + 505, + 105 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 106, + 110, + 505, + 254 + ], + "lines": [ + { + "bbox": [ + 106, + 111, + 505, + 122 + ], + "spans": [ + { + "bbox": [ + 106, + 111, + 505, + 122 + ], + "score": 1.0, + "content": "In this work, we start from an observation that in-distribution constraints widely used in prior work", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 121, + 505, + 133 + ], + "spans": [ + { + "bbox": [ + 106, + 121, + 505, + 133 + ], + "score": 1.0, + "content": "might not be sufficient to avoid value function extrapolation, and we ask whether it is possible to", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 131, + 506, + 145 + ], + "spans": [ + { + "bbox": [ + 105, + 131, + 506, + 145 + ], + "score": 1.0, + "content": "learn an optimal policy with in-sample learning, without ever querying the values of any unseen", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 143, + 506, + 156 + ], + "spans": [ + { + "bbox": [ + 106, + 143, + 506, + 156 + ], + "score": 1.0, + "content": "actions. The key idea in our method is to approximate an upper expectile of the distribution over", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 153, + 505, + 167 + ], + "spans": [ + { + "bbox": [ + 106, + 153, + 505, + 167 + ], + "score": 1.0, + "content": "values with respect to the distribution of dataset actions for each state. 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We show that we can do this simply by modifying the loss function in a", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 187, + 505, + 200 + ], + "spans": [ + { + "bbox": [ + 105, + 187, + 491, + 200 + ], + "score": 1.0, + "content": "SARSA-style TD backup, without ever using out-of-sample actions in the target value. 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This approach does not require explicit constraints or explicit regularization of out-of-", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 219, + 505, + 232 + ], + "spans": [ + { + "bbox": [ + 106, + 219, + 505, + 232 + ], + "score": 1.0, + "content": "distribution actions during value function training, though our policy extraction step does implicitly", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 231, + 504, + 244 + ], + "spans": [ + { + "bbox": [ + 105, + 231, + 504, + 244 + ], + "score": 1.0, + "content": "enforce a constraint, as discussed in prior work on advantage-weighted regression (Peters & Schaal,", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 241, + 348, + 255 + ], + "spans": [ + { + "bbox": [ + 106, + 241, + 348, + 255 + ], + "score": 1.0, + "content": "2007; Peng et al., 2019; Nair et al., 2020; Wang et al., 2020).", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 8, + "bbox_fs": [ + 105, + 111, + 506, + 255 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 258, + 505, + 358 + ], + "lines": [ + { + "bbox": [ + 106, + 259, + 505, + 271 + ], + "spans": [ + { + "bbox": [ + 106, + 259, + 505, + 271 + ], + "score": 1.0, + "content": "Our main contribution is implicit Q-learning (IQL), a new offline RL algorithm that avoids ever", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 269, + 505, + 283 + ], + "spans": [ + { + "bbox": [ + 105, + 269, + 505, + 283 + ], + "score": 1.0, + "content": "querying values of unseen actions while still being able to perform multi-step dynamic program-", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 281, + 505, + 293 + ], + "spans": [ + { + "bbox": [ + 105, + 281, + 505, + 293 + ], + "score": 1.0, + "content": "ming updates. Our method is easy to implement by making a small change to the loss function in", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 292, + 505, + 304 + ], + "spans": [ + { + "bbox": [ + 105, + 292, + 505, + 304 + ], + "score": 1.0, + "content": "a simple SARSA-like TD update and is computationally very efficient. Furthermore, our approach", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 303, + 505, + 316 + ], + "spans": [ + { + "bbox": [ + 106, + 303, + 505, + 316 + ], + "score": 1.0, + "content": "demonstrates the state-of-the-art performance on D4RL, a popular benchmark for offline reinforce-", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 313, + 506, + 327 + ], + "spans": [ + { + "bbox": [ + 105, + 313, + 506, + 327 + ], + "score": 1.0, + "content": "ment learning. In particular, our approach significantly improves over the prior state-of-the-art on", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 324, + 506, + 338 + ], + "spans": [ + { + "bbox": [ + 105, + 324, + 506, + 338 + ], + "score": 1.0, + "content": "challenging Ant Maze tasks that require to “stitch” several sub-optimal trajectories. Finally, we", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 335, + 506, + 348 + ], + "spans": [ + { + "bbox": [ + 105, + 335, + 506, + 348 + ], + "score": 1.0, + "content": "demonstrate that our approach is suitable for finetuning; after initialization from offline RL, IQL is", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 347, + 403, + 360 + ], + "spans": [ + { + "bbox": [ + 106, + 347, + 403, + 360 + ], + "score": 1.0, + "content": "capable of improving policy performance utilizing additional interactions.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 19, + "bbox_fs": [ + 105, + 259, + 506, + 360 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 374, + 209, + 386 + ], + "lines": [ + { + "bbox": [ + 104, + 372, + 211, + 388 + ], + "spans": [ + { + "bbox": [ + 104, + 372, + 211, + 388 + ], + "score": 1.0, + "content": "2 RELATED WORK", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 24 + }, + { + "type": "text", + "bbox": [ + 106, + 397, + 505, + 583 + ], + "lines": [ + { + "bbox": [ + 105, + 395, + 505, + 410 + ], + "spans": [ + { + "bbox": [ + 105, + 395, + 505, + 410 + ], + "score": 1.0, + "content": "A significant portion of recently proposed offline RL methods are based on either constrained or reg-", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 408, + 504, + 419 + ], + "spans": [ + { + "bbox": [ + 106, + 408, + 504, + 419 + ], + "score": 1.0, + "content": "ularized approximate dynamic programming (e.g., Q-learning or actor-critic methods), with the con-", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 419, + 504, + 430 + ], + "spans": [ + { + "bbox": [ + 106, + 419, + 504, + 430 + ], + "score": 1.0, + "content": "straint or regularizer serving to limit deviation from the behavior policy. We will refer to these meth-", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 429, + 505, + 442 + ], + "spans": [ + { + "bbox": [ + 105, + 429, + 505, + 442 + ], + "score": 1.0, + "content": "ods as “multi-step dynamic programming” algorithms, since they perform true dynamic program-", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 440, + 506, + 452 + ], + "spans": [ + { + "bbox": [ + 105, + 440, + 506, + 452 + ], + "score": 1.0, + "content": "ming for multiple iterations, and therefore can in principle recover the optimal policy if provided", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 450, + 507, + 465 + ], + "spans": [ + { + "bbox": [ + 105, + 450, + 507, + 465 + ], + "score": 1.0, + "content": "with high-coverage data. The constraints can be implemented via an explicit density model (Wu", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 462, + 506, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 462, + 506, + 475 + ], + "score": 1.0, + "content": "et al., 2019; Fujimoto et al., 2019; Kumar et al., 2019; Ghasemipour et al., 2021), implicit divergence", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 473, + 506, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 473, + 506, + 486 + ], + "score": 1.0, + "content": "constraints (Nair et al., 2020; Wang et al., 2020; Peters & Schaal, 2007; Peng et al., 2019; Siegel", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 485, + 505, + 497 + ], + "spans": [ + { + "bbox": [ + 106, + 485, + 505, + 497 + ], + "score": 1.0, + "content": "et al., 2020), or by adding a supervised learning term to the policy improvement objective (Fujimoto", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 494, + 505, + 508 + ], + "spans": [ + { + "bbox": [ + 106, + 495, + 160, + 508 + ], + "score": 1.0, + "content": "& Gu, 2021)", + "type": "text" + }, + { + "bbox": [ + 165, + 494, + 505, + 507 + ], + "score": 1.0, + "content": "Several works have also proposed to directly regularize the Q-function to produce", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 505, + 504, + 520 + ], + "spans": [ + { + "bbox": [ + 106, + 505, + 504, + 520 + ], + "score": 1.0, + "content": "low values for out-of-distribution actions (Kostrikov et al., 2021; Kumar et al., 2020; Fakoor et al.,", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 516, + 506, + 530 + ], + "spans": [ + { + "bbox": [ + 105, + 516, + 131, + 530 + ], + "score": 0.46, + "content": "\\boxed { 2 0 2 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 135, + 516, + 506, + 530 + ], + "score": 1.0, + "content": "Our method is also a multi-step dynamic programming algorithm. However, in contrast to", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 528, + 506, + 541 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 506, + 541 + ], + "score": 1.0, + "content": "prior works, our method completely avoids directly querying the learned Q-function with unseen", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 539, + 505, + 551 + ], + "spans": [ + { + "bbox": [ + 105, + 539, + 505, + 551 + ], + "score": 1.0, + "content": "actions during training, removing the need for any constraint during this stage, though the subse-", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 104, + 550, + 506, + 563 + ], + "spans": [ + { + "bbox": [ + 104, + 550, + 506, + 563 + ], + "score": 1.0, + "content": "quent policy extraction, which is based on advantage-weighted regression (Peng et al., 2019; Nair", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 561, + 506, + 574 + ], + "spans": [ + { + "bbox": [ + 105, + 561, + 506, + 574 + ], + "score": 1.0, + "content": "et al., 2020), does apply an implicit constraint. However, this policy does not actually influence", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 571, + 203, + 586 + ], + "spans": [ + { + "bbox": [ + 105, + 571, + 203, + 586 + ], + "score": 1.0, + "content": "value function training.", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 33, + "bbox_fs": [ + 104, + 395, + 507, + 586 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 589, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 589, + 504, + 601 + ], + "spans": [ + { + "bbox": [ + 106, + 589, + 504, + 601 + ], + "score": 1.0, + "content": "In contrast to multi-step dynamic programming methods, several recent works have proposed meth-", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 600, + 506, + 613 + ], + "spans": [ + { + "bbox": [ + 106, + 600, + 506, + 613 + ], + "score": 1.0, + "content": "ods that rely either on a single step of policy iteration, fitting the value function or Q-function of", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 610, + 506, + 624 + ], + "spans": [ + { + "bbox": [ + 105, + 610, + 506, + 624 + ], + "score": 1.0, + "content": "the behavior policy and then extracting the corresponding greedy policy (Peng et al., 2019; Brand-", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 621, + 506, + 634 + ], + "spans": [ + { + "bbox": [ + 105, + 621, + 506, + 634 + ], + "score": 1.0, + "content": "fonbrener et al., 2021; Gulcehre et al., 2021), or else avoid value functions completely and utilize", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 633, + 505, + 646 + ], + "spans": [ + { + "bbox": [ + 105, + 633, + 505, + 646 + ], + "score": 1.0, + "content": "behavioral cloning-style objectives (Chen et al., 2021). We collectively refer to these as “single-step”", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 644, + 506, + 657 + ], + "spans": [ + { + "bbox": [ + 106, + 644, + 506, + 657 + ], + "score": 1.0, + "content": "approaches. These methods avoid needing to query unseen actions as well, since they either use no", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 655, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 505, + 667 + ], + "score": 1.0, + "content": "value function at all, or learn the value function of the behavior policy. Although these methods are", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "score": 1.0, + "content": "simple to implement and effective on the MuJoCo locomotion tasks in D4RL, we show that such", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 106, + 677, + 504, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 504, + 689 + ], + "score": 1.0, + "content": "single-step methods perform very poorly on more complex datasets in D4RL, which require combin-", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 106, + 687, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 106, + 687, + 505, + 700 + ], + "score": 1.0, + "content": "ing parts of suboptimal trajectories (“stitching”). Prior multi-step dynamic programming methods", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 105, + 699, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 505, + 711 + ], + "score": 1.0, + "content": "perform much better in such settings, as does our method. We discuss this distinction in more detail", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 106, + 707, + 506, + 724 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 149, + 721 + ], + "score": 1.0, + "content": "in Section", + "type": "text" + }, + { + "bbox": [ + 149, + 709, + 167, + 722 + ], + "score": 0.28, + "content": "5 . 1 .", + "type": "inline_equation" + }, + { + "bbox": [ + 168, + 707, + 506, + 724 + ], + "score": 1.0, + "content": "Our method also shares the simplicity and computational efficiency of single-step", + "type": "text" + } + ], + "index": 53 + }, + { + "bbox": [ + 105, + 720, + 470, + 732 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 470, + 732 + ], + "score": 1.0, + "content": "approaches, providing an appealing combination of the strengths of both types of methods.", + "type": "text" + } + ], + "index": 54 + } + ], + "index": 48, + "bbox_fs": [ + 105, + 589, + 506, + 732 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 82, + 505, + 214 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 505, + 94 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 505, + 94 + ], + "score": 1.0, + "content": "Our method is based on estimating the characteristics of a random variable. Several recent works", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 93, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 106, + 93, + 505, + 106 + ], + "score": 1.0, + "content": "involve approximating statistical quantities of the value function distribution. 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Although our method is related, in that we perform expectile regression, our aim is", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 137, + 504, + 148 + ], + "spans": [ + { + "bbox": [ + 105, + 137, + 504, + 148 + ], + "score": 1.0, + "content": "not to estimate the distribution of values that results from stochastic transitions, but rather estimate", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 148, + 505, + 160 + ], + "spans": [ + { + "bbox": [ + 105, + 148, + 505, + 160 + ], + "score": 1.0, + "content": "expectiles of the state value function with respect to random actions. This is a very different statistic:", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 160, + 505, + 171 + ], + "spans": [ + { + "bbox": [ + 106, + 160, + 254, + 171 + ], + "score": 1.0, + "content": "our aim is not to determine how the", + "type": "text" + }, + { + "bbox": [ + 254, + 160, + 263, + 171 + ], + "score": 0.86, + "content": "Q", + "type": "inline_equation" + }, + { + "bbox": [ + 264, + 160, + 505, + 171 + ], + "score": 1.0, + "content": "-value can vary with different future outcomes, but how the", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 170, + 505, + 182 + ], + "spans": [ + { + "bbox": [ + 106, + 171, + 116, + 182 + ], + "score": 0.83, + "content": "Q", + "type": "inline_equation" + }, + { + "bbox": [ + 116, + 170, + 505, + 182 + ], + "score": 1.0, + "content": "-value can vary with different actions while averaging together future outcomes due to stochastic", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 181, + 505, + 192 + ], + "spans": [ + { + "bbox": [ + 105, + 181, + 505, + 192 + ], + "score": 1.0, + "content": "dynamics. 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In our method, which we derive next, we retain the benefits of using this SARSA-like", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 361, + 506, + 374 + ], + "spans": [ + { + "bbox": [ + 106, + 361, + 506, + 374 + ], + "score": 1.0, + "content": "objective, but modify it so that it allows us to perform multi-step dynamic programming and learn a", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 371, + 209, + 384 + ], + "spans": [ + { + "bbox": [ + 105, + 371, + 209, + 384 + ], + "score": 1.0, + "content": "near-optimal Q-function.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 12.5 + }, + { + "type": "text", + "bbox": [ + 106, + 387, + 505, + 433 + ], + "lines": [ + { + "bbox": [ + 106, + 388, + 506, + 401 + ], + "spans": [ + { + "bbox": [ + 106, + 388, + 219, + 401 + ], + "score": 1.0, + "content": "Our method will perform a", + "type": "text" + }, + { + "bbox": [ + 219, + 388, + 228, + 400 + ], + "score": 0.85, + "content": "Q", + "type": "inline_equation" + }, + { + "bbox": [ + 228, + 388, + 359, + 401 + ], + "score": 1.0, + "content": "-function update similar to Eqn.", + "type": "text" + }, + { + "bbox": [ + 360, + 388, + 372, + 401 + ], + "score": 0.74, + "content": "\\mathbb { Q }", + "type": "inline_equation" + }, + { + "bbox": [ + 372, + 388, + 506, + 401 + ], + "score": 1.0, + "content": ", but we will aim to estimate the", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 399, + 505, + 411 + ], + "spans": [ + { + "bbox": [ + 105, + 399, + 150, + 411 + ], + "score": 1.0, + "content": "maximum", + "type": "text" + }, + { + "bbox": [ + 150, + 400, + 159, + 411 + ], + "score": 0.85, + "content": "Q", + "type": "inline_equation" + }, + { + "bbox": [ + 159, + 399, + 505, + 411 + ], + "score": 1.0, + "content": "-value over actions that are in the support of the data distribution. Crucially, we will", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 410, + 505, + 423 + ], + "spans": [ + { + "bbox": [ + 105, + 410, + 387, + 423 + ], + "score": 1.0, + "content": "show that it is possible to do this without ever querying the learned", + "type": "text" + }, + { + "bbox": [ + 387, + 411, + 396, + 421 + ], + "score": 0.68, + "content": "Q", + "type": "inline_equation" + }, + { + "bbox": [ + 396, + 410, + 505, + 423 + ], + "score": 1.0, + "content": "-function on out-of-sample", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 422, + 498, + 434 + ], + "spans": [ + { + "bbox": [ + 106, + 422, + 498, + 434 + ], + "score": 1.0, + "content": "actions by utilizing expectile regression. 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To this end, we propose to fit", + "type": "text" + }, + { + "bbox": [ + 457, + 484, + 492, + 496 + ], + "score": 0.93, + "content": "Q _ { \\theta } ( s , a )", + "type": "inline_equation" + }, + { + "bbox": [ + 493, + 484, + 505, + 497 + ], + "score": 1.0, + "content": "to", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 494, + 505, + 508 + ], + "spans": [ + { + "bbox": [ + 105, + 494, + 505, + 508 + ], + "score": 1.0, + "content": "estimate state-conditional expectiles of the target values, and show that specific expectiles approxi-", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 504, + 505, + 520 + ], + "spans": [ + { + "bbox": [ + 106, + 504, + 300, + 520 + ], + "score": 1.0, + "content": "mate the maximization defined above. In Section", + "type": "text" + }, + { + "bbox": [ + 300, + 505, + 317, + 518 + ], + "score": 0.77, + "content": "\\boxed { 4 . 4 }", + "type": "inline_equation" + }, + { + "bbox": [ + 317, + 504, + 505, + 520 + ], + "score": 1.0, + "content": "we show that this approach performs multi-step", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 517, + 456, + 529 + ], + "spans": [ + { + "bbox": [ + 106, + 517, + 298, + 529 + ], + "score": 1.0, + "content": "dynamic programming in theory, and in Section", + "type": "text" + }, + { + "bbox": [ + 298, + 518, + 315, + 529 + ], + "score": 0.65, + "content": "\\underline { { \\boldsymbol { \\mathsf { F . 1 } } } }", + "type": "inline_equation" + }, + { + "bbox": [ + 315, + 517, + 456, + 529 + ], + "score": 1.0, + "content": "we show that it does so in practice.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 25 + }, + { + "type": "title", + "bbox": [ + 107, + 540, + 238, + 551 + ], + "lines": [ + { + "bbox": [ + 106, + 540, + 238, + 551 + ], + "spans": [ + { + "bbox": [ + 106, + 540, + 238, + 551 + ], + "score": 1.0, + "content": "4.1 EXPECTILE REGRESSION", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 28 + }, + { + "type": "text", + "bbox": [ + 106, + 560, + 505, + 594 + ], + "lines": [ + { + "bbox": [ + 106, + 560, + 505, + 572 + ], + "spans": [ + { + "bbox": [ + 106, + 560, + 505, + 572 + ], + "score": 1.0, + "content": "Practical methods for estimating various statistics of a random variable have been thoroughly studies", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 571, + 505, + 583 + ], + "spans": [ + { + "bbox": [ + 105, + 571, + 288, + 583 + ], + "score": 1.0, + "content": "in applied statistics and econometrics. 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It provides unbiased", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 149, + 412, + 163 + ], + "spans": [ + { + "bbox": [ + 105, + 149, + 412, + 163 + ], + "score": 1.0, + "content": "gradients and is easy to implement with standard machine learning libraries.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 3 + }, + { + "type": "title", + "bbox": [ + 107, + 174, + 411, + 186 + ], + "lines": [ + { + "bbox": [ + 105, + 173, + 413, + 188 + ], + "spans": [ + { + "bbox": [ + 105, + 173, + 413, + 188 + ], + "score": 1.0, + "content": "4.2 LEARNING THE VALUE FUNCTION WITH EXPECTILE REGRESSION", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 5 + }, + { + "type": "text", + "bbox": [ + 106, + 195, + 505, + 251 + ], + "lines": [ + { + "bbox": [ + 106, + 195, + 505, + 208 + ], + "spans": [ + { + "bbox": [ + 106, + 195, + 505, + 208 + ], + "score": 1.0, + "content": "Expectile regression provides us with a powerful framework to estimate statistics of a random vari-", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 205, + 505, + 219 + ], + "spans": [ + { + "bbox": [ + 105, + 205, + 505, + 219 + ], + "score": 1.0, + "content": "able beyond mean regression. We can use expectile regression to modify the policy evaluation", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 217, + 505, + 231 + ], + "spans": [ + { + "bbox": [ + 106, + 217, + 176, + 231 + ], + "score": 1.0, + "content": "objective in Eqn.", + "type": "text" + }, + { + "bbox": [ + 177, + 218, + 189, + 228 + ], + "score": 0.67, + "content": "\\textcircled { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 189, + 217, + 505, + 231 + ], + "score": 1.0, + "content": "to predict an upper expectile of the TD targets that approximates the maximum", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 227, + 506, + 243 + ], + "spans": [ + { + "bbox": [ + 105, + 227, + 118, + 242 + ], + "score": 1.0, + "content": "of", + "type": "text" + }, + { + "bbox": [ + 118, + 228, + 203, + 241 + ], + "score": 0.9, + "content": "\\dot { r } ( s , a ) + \\gamma \\bar { Q } _ { \\hat { \\theta } } ( s ^ { \\prime } , a ^ { \\prime } )", + "type": "inline_equation" + }, + { + "bbox": [ + 203, + 227, + 255, + 242 + ], + "score": 1.0, + "content": "over actions", + "type": "text" + }, + { + "bbox": [ + 255, + 228, + 264, + 238 + ], + "score": 0.85, + "content": "a ^ { \\prime }", + "type": "inline_equation" + }, + { + "bbox": [ + 265, + 227, + 444, + 242 + ], + "score": 1.0, + "content": "constrained to the dataset actions, as in Eqn.", + "type": "text" + }, + { + "bbox": [ + 445, + 227, + 457, + 243 + ], + "score": 0.6, + "content": "( 4 )", + "type": "inline_equation" + }, + { + "bbox": [ + 458, + 227, + 506, + 242 + ], + "score": 1.0, + "content": ". This leads", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 239, + 295, + 253 + ], + "spans": [ + { + "bbox": [ + 106, + 239, + 295, + 253 + ], + "score": 1.0, + "content": "to the following expectile regression objective:", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 8 + }, + { + "type": "interline_equation", + "bbox": [ + 181, + 256, + 429, + 271 + ], + "lines": [ + { + "bbox": [ + 181, + 256, + 429, + 271 + ], + "spans": [ + { + "bbox": [ + 181, + 256, + 429, + 271 + ], + "score": 0.89, + "content": "L ( \\theta ) = \\mathbb { E } _ { ( s , a , s ^ { \\prime } , a ^ { \\prime } ) \\sim \\mathcal { D } } [ L _ { 2 } ^ { \\tau } ( r ( s , a ) + \\gamma Q _ { \\hat { \\theta } } ( s ^ { \\prime } , a ^ { \\prime } ) - Q _ { \\theta } ( s , a ) ) ] .", + "type": "interline_equation", + "image_path": "3d3b988ed2174b94e9b117094923a46074ff5d84d7df3dae95b6373b08418442.jpg" + } + ] + } + ], + "index": 11, + "virtual_lines": [ + { + "bbox": [ + 181, + 256, + 429, + 271 + ], + "spans": [], + "index": 11 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 276, + 505, + 343 + ], + "lines": [ + { + "bbox": [ + 106, + 277, + 504, + 288 + ], + "spans": [ + { + "bbox": [ + 106, + 277, + 504, + 288 + ], + "score": 1.0, + "content": "However, this formulation has a significant drawback. Instead of estimating expectiles just with", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 288, + 505, + 299 + ], + "spans": [ + { + "bbox": [ + 106, + 288, + 505, + 299 + ], + "score": 1.0, + "content": "respect to the actions in the support of the data, it also incorporates stochasticity that comes from the", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 298, + 506, + 311 + ], + "spans": [ + { + "bbox": [ + 105, + 298, + 201, + 311 + ], + "score": 1.0, + "content": "environment dynamics", + "type": "text" + }, + { + "bbox": [ + 201, + 298, + 257, + 310 + ], + "score": 0.93, + "content": "s ^ { \\prime } \\sim p ( \\cdot | s , a )", + "type": "inline_equation" + }, + { + "bbox": [ + 257, + 298, + 506, + 311 + ], + "score": 1.0, + "content": ". Therefore, a large target value might not necessarily reflect", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 309, + 505, + 321 + ], + "spans": [ + { + "bbox": [ + 106, + 309, + 505, + 321 + ], + "score": 1.0, + "content": "the existence of a single action that achieves that value, but rather a “lucky” sample that happened", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 320, + 506, + 333 + ], + "spans": [ + { + "bbox": [ + 105, + 320, + 506, + 333 + ], + "score": 1.0, + "content": "to have transitioned into a good state. We resolve this by introducing a separate value function that", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 330, + 505, + 344 + ], + "spans": [ + { + "bbox": [ + 105, + 330, + 505, + 344 + ], + "score": 1.0, + "content": "approximates an expectile only with respect to the action distribution, leading to the following loss:", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 14.5 + }, + { + "type": "interline_equation", + "bbox": [ + 214, + 348, + 396, + 363 + ], + "lines": [ + { + "bbox": [ + 214, + 348, + 396, + 363 + ], + "spans": [ + { + "bbox": [ + 214, + 348, + 396, + 363 + ], + "score": 0.92, + "content": "L _ { V } ( \\psi ) = \\mathbb { E } _ { ( s , a ) \\sim \\mathcal { D } } [ L _ { 2 } ^ { \\tau } ( Q _ { \\hat { \\theta } } ( s , a ) - V _ { \\psi } ( s ) ) ] .", + "type": "interline_equation", + "image_path": "51ad350ad0c80c36aed365b48e63fd15832c814ad84056536d15345bd65d3ba7.jpg" + } + ] + } + ], + "index": 18, + "virtual_lines": [ + { + "bbox": [ + 214, + 348, + 396, + 363 + ], + "spans": [], + "index": 18 + } + ] + }, + { + "type": "text", + "bbox": [ + 105, + 367, + 503, + 390 + ], + "lines": [ + { + "bbox": [ + 106, + 366, + 505, + 380 + ], + "spans": [ + { + "bbox": [ + 106, + 366, + 279, + 380 + ], + "score": 1.0, + "content": "We can then use this estimate to update the", + "type": "text" + }, + { + "bbox": [ + 279, + 368, + 288, + 379 + ], + "score": 0.87, + "content": "Q", + "type": "inline_equation" + }, + { + "bbox": [ + 288, + 366, + 505, + 380 + ], + "score": 1.0, + "content": "-functions with the MSE loss, which averages over the", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 379, + 459, + 390 + ], + "spans": [ + { + "bbox": [ + 106, + 379, + 459, + 390 + ], + "score": 1.0, + "content": "stochasticity from the transitions and avoids the “lucky” sample issue mentioned above:", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 19.5 + }, + { + "type": "interline_equation", + "bbox": [ + 190, + 394, + 420, + 410 + ], + "lines": [ + { + "bbox": [ + 190, + 394, + 420, + 410 + ], + "spans": [ + { + "bbox": [ + 190, + 394, + 420, + 410 + ], + "score": 0.91, + "content": "L _ { Q } ( \\theta ) = \\mathbb { E } _ { ( s , a , s ^ { \\prime } ) \\sim \\mathcal { D } } [ ( r ( s , a ) + \\gamma V _ { \\psi } ( s ^ { \\prime } ) - Q _ { \\theta } ( s , a ) ) ^ { 2 } ] .", + "type": "interline_equation", + "image_path": "9fd38717e672bc56176e7593227ca23400d3e15e817605fa21388e1e9a68855d.jpg" + } + ] + } + ], + "index": 21, + "virtual_lines": [ + { + "bbox": [ + 190, + 394, + 420, + 410 + ], + "spans": [], + "index": 21 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 415, + 505, + 482 + ], + "lines": [ + { + "bbox": [ + 105, + 415, + 506, + 428 + ], + "spans": [ + { + "bbox": [ + 105, + 415, + 506, + 428 + ], + "score": 1.0, + "content": "Note that these losses do not use any explicit policy, and only utilize actions from the dataset for", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 425, + 505, + 439 + ], + "spans": [ + { + "bbox": [ + 105, + 425, + 395, + 438 + ], + "score": 1.0, + "content": "both objectives, similarly to SARSA-style policy evaluation. In Section", + "type": "text" + }, + { + "bbox": [ + 395, + 425, + 412, + 439 + ], + "score": 0.83, + "content": "^ { 4 . 4 , }", + "type": "inline_equation" + }, + { + "bbox": [ + 413, + 425, + 505, + 438 + ], + "score": 1.0, + "content": "we will show that this", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 437, + 506, + 450 + ], + "spans": [ + { + "bbox": [ + 105, + 437, + 506, + 450 + ], + "score": 1.0, + "content": "procedure recovers the optimal Q-function under some assumptions. Also, even though only one", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 448, + 505, + 460 + ], + "spans": [ + { + "bbox": [ + 106, + 448, + 505, + 460 + ], + "score": 1.0, + "content": "action is available for every state in the dataset for continuous action spaces, due to neural network", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 104, + 458, + 506, + 471 + ], + "spans": [ + { + "bbox": [ + 104, + 458, + 506, + 471 + ], + "score": 1.0, + "content": "generalization, the expectile regression does not result in SARSA-style policy evaluation as shown", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 469, + 165, + 481 + ], + "spans": [ + { + "bbox": [ + 105, + 469, + 148, + 481 + ], + "score": 1.0, + "content": "in Section", + "type": "text" + }, + { + "bbox": [ + 148, + 469, + 165, + 480 + ], + "score": 0.36, + "content": "5 . 2 .", + "type": "inline_equation" + } + ], + "index": 27 + } + ], + "index": 24.5 + }, + { + "type": "title", + "bbox": [ + 107, + 495, + 349, + 507 + ], + "lines": [ + { + "bbox": [ + 106, + 495, + 350, + 507 + ], + "spans": [ + { + "bbox": [ + 106, + 495, + 350, + 507 + ], + "score": 1.0, + "content": "4.3 POLICY EXTRACTION AND ALGORITHM SUMMARY", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 28 + }, + { + "type": "text", + "bbox": [ + 107, + 515, + 356, + 649 + ], + "lines": [ + { + "bbox": [ + 106, + 514, + 357, + 529 + ], + "spans": [ + { + "bbox": [ + 106, + 514, + 357, + 529 + ], + "score": 1.0, + "content": "While our modified TD learning procedure learns an approx-", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 525, + 357, + 540 + ], + "spans": [ + { + "bbox": [ + 105, + 525, + 357, + 540 + ], + "score": 1.0, + "content": "imation to the optimal Q-function, it does not explicitly rep-", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 537, + 356, + 550 + ], + "spans": [ + { + "bbox": [ + 105, + 537, + 356, + 550 + ], + "score": 1.0, + "content": "resent the corresponding policy, and therefore requires a sep-", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 549, + 356, + 561 + ], + "spans": [ + { + "bbox": [ + 106, + 549, + 356, + 561 + ], + "score": 1.0, + "content": "arate policy extraction step. While one can consider any tech-", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 560, + 357, + 572 + ], + "spans": [ + { + "bbox": [ + 106, + 560, + 357, + 572 + ], + "score": 1.0, + "content": "nique for policy extraction that constrains the learned policy to", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 571, + 356, + 582 + ], + "spans": [ + { + "bbox": [ + 106, + 571, + 356, + 582 + ], + "score": 1.0, + "content": "stay close to the dataset actions, we aim for a simple method", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 582, + 357, + 594 + ], + "spans": [ + { + "bbox": [ + 106, + 582, + 357, + 594 + ], + "score": 1.0, + "content": "for policy extraction. As before, we aim to avoid using out-", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 592, + 357, + 604 + ], + "spans": [ + { + "bbox": [ + 106, + 592, + 357, + 604 + ], + "score": 1.0, + "content": "of-samples actions. 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This step can be seen", + "type": "text" + } + ], + "index": 55 + }, + { + "bbox": [ + 106, + 721, + 362, + 732 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 362, + 732 + ], + "score": 1.0, + "content": "as selecting and cloning the most optimal actions in the dataset.", + "type": "text" + } + ], + "index": 56 + } + ], + "index": 55 + } + ], + "page_idx": 4, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 26, + 293, + 38 + ], + "lines": [ + { + "bbox": [ + 106, + 25, + 294, + 39 + ], + "spans": [ + { + "bbox": [ + 106, + 25, + 294, + 39 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2022", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 309, + 760 + ], + "lines": [ + { + "bbox": [ + 301, + 750, + 310, + 762 + ], + "spans": [ + { + "bbox": [ + 301, + 750, + 310, + 762 + ], + "score": 1.0, + "content": "5", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 105, + 82, + 437, + 94 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 438, + 96 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 438, + 96 + ], + "score": 1.0, + "content": "We can also use this formulation to predict expectiles of a conditional distribution:", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0, + "bbox_fs": [ + 106, + 82, + 438, + 96 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 232, + 99, + 378, + 122 + ], + "lines": [ + { + "bbox": [ + 232, + 99, + 378, + 122 + ], + "spans": [ + { + "bbox": [ + 232, + 99, + 378, + 122 + ], + "score": 0.92, + "content": "\\operatorname * { a r g m i n } _ { m _ { \\tau } ( x ) } \\mathbb { E } _ { ( x , y ) \\sim \\mathcal { D } } [ L _ { 2 } ^ { \\tau } ( y - m _ { \\tau } ( x ) ) ] .", + "type": "interline_equation", + "image_path": "9d6565d4be234184cf027b8fd1a9db8abd350bc957b0249ab61c4a630e553387.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 232, + 99, + 378, + 122 + ], + "spans": [], + "index": 1 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 127, + 505, + 161 + ], + "lines": [ + { + "bbox": [ + 105, + 127, + 504, + 141 + ], + "spans": [ + { + "bbox": [ + 105, + 127, + 504, + 141 + ], + "score": 1.0, + "content": "Fig. 1 (right) illustrates conditional expectile regression on a simple two-dimensional distribution.", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 139, + 505, + 151 + ], + "spans": [ + { + "bbox": [ + 106, + 139, + 505, + 151 + ], + "score": 1.0, + "content": "Note that we can optimize this objective with stochastic gradient descent. It provides unbiased", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 149, + 412, + 163 + ], + "spans": [ + { + "bbox": [ + 105, + 149, + 412, + 163 + ], + "score": 1.0, + "content": "gradients and is easy to implement with standard machine learning libraries.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 3, + "bbox_fs": [ + 105, + 127, + 505, + 163 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 174, + 411, + 186 + ], + "lines": [ + { + "bbox": [ + 105, + 173, + 413, + 188 + ], + "spans": [ + { + "bbox": [ + 105, + 173, + 413, + 188 + ], + "score": 1.0, + "content": "4.2 LEARNING THE VALUE FUNCTION WITH EXPECTILE REGRESSION", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 5 + }, + { + "type": "text", + "bbox": [ + 106, + 195, + 505, + 251 + ], + "lines": [ + { + "bbox": [ + 106, + 195, + 505, + 208 + ], + "spans": [ + { + "bbox": [ + 106, + 195, + 505, + 208 + ], + "score": 1.0, + "content": "Expectile regression provides us with a powerful framework to estimate statistics of a random vari-", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 205, + 505, + 219 + ], + "spans": [ + { + "bbox": [ + 105, + 205, + 505, + 219 + ], + "score": 1.0, + "content": "able beyond mean regression. 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Instead of estimating expectiles just with", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 288, + 505, + 299 + ], + "spans": [ + { + "bbox": [ + 106, + 288, + 505, + 299 + ], + "score": 1.0, + "content": "respect to the actions in the support of the data, it also incorporates stochasticity that comes from the", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 298, + 506, + 311 + ], + "spans": [ + { + "bbox": [ + 105, + 298, + 201, + 311 + ], + "score": 1.0, + "content": "environment dynamics", + "type": "text" + }, + { + "bbox": [ + 201, + 298, + 257, + 310 + ], + "score": 0.93, + "content": "s ^ { \\prime } \\sim p ( \\cdot | s , a )", + "type": "inline_equation" + }, + { + "bbox": [ + 257, + 298, + 506, + 311 + ], + "score": 1.0, + "content": ". 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In Section", + "type": "text" + }, + { + "bbox": [ + 395, + 425, + 412, + 439 + ], + "score": 0.83, + "content": "^ { 4 . 4 , }", + "type": "inline_equation" + }, + { + "bbox": [ + 413, + 425, + 505, + 438 + ], + "score": 1.0, + "content": "we will show that this", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 437, + 506, + 450 + ], + "spans": [ + { + "bbox": [ + 105, + 437, + 506, + 450 + ], + "score": 1.0, + "content": "procedure recovers the optimal Q-function under some assumptions. 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We summarize our", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 124, + 506, + 140 + ], + "spans": [ + { + "bbox": [ + 104, + 124, + 212, + 140 + ], + "score": 1.0, + "content": "final method in Algorithm", + "type": "text" + }, + { + "bbox": [ + 213, + 126, + 223, + 139 + ], + "score": 0.73, + "content": "^ { 1 . }", + "type": "inline_equation" + }, + { + "bbox": [ + 223, + 124, + 506, + 140 + ], + "score": 1.0, + "content": "Note that the policy does not influence the value function in any way,", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 138, + 505, + 149 + ], + "spans": [ + { + "bbox": [ + 106, + 138, + 505, + 149 + ], + "score": 1.0, + "content": "and therefore extraction could be performed either concurrently or after TD learning. 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Let", + "type": "text" + }, + { + "bbox": [ + 170, + 228, + 181, + 238 + ], + "score": 0.64, + "content": "X", + "type": "inline_equation" + }, + { + "bbox": [ + 181, + 226, + 504, + 240 + ], + "score": 1.0, + "content": "be a real-valued random variable with a bounded support and supremum of the", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 239, + 189, + 251 + ], + "spans": [ + { + "bbox": [ + 105, + 239, + 148, + 251 + ], + "score": 1.0, + "content": "support is", + "type": "text" + }, + { + "bbox": [ + 149, + 239, + 159, + 249 + ], + "score": 0.84, + "content": "x ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 160, + 239, + 189, + 251 + ], + "score": 1.0, + "content": ". Then,", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 11.5 + }, + { + "type": "interline_equation", + "bbox": [ + 276, + 243, + 334, + 261 + ], + "lines": [ + { + "bbox": [ + 276, + 243, + 334, + 261 + ], + "spans": [ + { + "bbox": [ + 276, + 243, + 334, + 261 + ], + "score": 0.91, + "content": "\\operatorname* { l i m } _ { \\tau 1 } m _ { \\tau } = x ^ { \\ast }", + "type": "interline_equation", + "image_path": "3123e0d4150d1a44dc8737af054373b26472ac0c1bb7be9f8801d27960f877f4.jpg" + } + ] + } + ], + "index": 13, + "virtual_lines": [ + { + "bbox": [ + 276, + 243, + 334, + 261 + ], + "spans": [], + "index": 13 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 266, + 505, + 300 + ], + "lines": [ + { + "bbox": [ + 108, + 266, + 505, + 278 + ], + "spans": [ + { + "bbox": [ + 108, + 266, + 489, + 278 + ], + "score": 1.0, + "content": "Proof Sketch. One can show that expectiles of a random variable have the same supremum", + "type": "text" + }, + { + "bbox": [ + 490, + 267, + 501, + 276 + ], + "score": 0.86, + "content": "x ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 266, + 505, + 278 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 276, + 506, + 290 + ], + "spans": [ + { + "bbox": [ + 105, + 276, + 176, + 290 + ], + "score": 1.0, + "content": "Moreover, for all", + "type": "text" + }, + { + "bbox": [ + 176, + 279, + 186, + 288 + ], + "score": 0.85, + "content": "\\tau _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 187, + 276, + 204, + 290 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 205, + 279, + 215, + 288 + ], + "score": 0.85, + "content": "\\tau _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 215, + 276, + 254, + 290 + ], + "score": 1.0, + "content": "such that", + "type": "text" + }, + { + "bbox": [ + 254, + 278, + 286, + 288 + ], + "score": 0.91, + "content": "\\tau _ { 1 } < \\tau _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 286, + 276, + 318, + 290 + ], + "score": 1.0, + "content": ", we get", + "type": "text" + }, + { + "bbox": [ + 318, + 277, + 366, + 289 + ], + "score": 0.92, + "content": "m _ { \\tau _ { 1 } } \\leq m _ { \\tau _ { 2 } }", + "type": "inline_equation" + }, + { + "bbox": [ + 367, + 276, + 506, + 290 + ], + "score": 1.0, + "content": ". Therefore, the limit follows from", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 289, + 505, + 300 + ], + "spans": [ + { + "bbox": [ + 106, + 289, + 376, + 300 + ], + "score": 1.0, + "content": "the properties of bounded monotonically non-decreasing functions.", + "type": "text" + }, + { + "bbox": [ + 495, + 289, + 505, + 298 + ], + "score": 0.999, + "content": "□", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 15 + }, + { + "type": "text", + "bbox": [ + 107, + 311, + 505, + 356 + ], + "lines": [ + { + "bbox": [ + 105, + 311, + 505, + 324 + ], + "spans": [ + { + "bbox": [ + 105, + 311, + 505, + 324 + ], + "score": 1.0, + "content": "In the following theorems, we show that under certain assumptions, our method indeed approximates", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 322, + 505, + 335 + ], + "spans": [ + { + "bbox": [ + 106, + 322, + 227, + 335 + ], + "score": 1.0, + "content": "the optimal state-action value", + "type": "text" + }, + { + "bbox": [ + 227, + 322, + 241, + 334 + ], + "score": 0.9, + "content": "Q ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 241, + 322, + 505, + 335 + ], + "score": 1.0, + "content": "and performs multi-step dynamical programming. We first prove", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 334, + 505, + 345 + ], + "spans": [ + { + "bbox": [ + 105, + 334, + 505, + 345 + ], + "score": 1.0, + "content": "a technical lemma relating different expectiles of the Q-function, and then derive our main result", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 345, + 267, + 356 + ], + "spans": [ + { + "bbox": [ + 105, + 345, + 267, + 356 + ], + "score": 1.0, + "content": "regarding the optimality of our method.", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 18.5 + }, + { + "type": "text", + "bbox": [ + 106, + 361, + 505, + 396 + ], + "lines": [ + { + "bbox": [ + 104, + 359, + 507, + 375 + ], + "spans": [ + { + "bbox": [ + 104, + 359, + 446, + 375 + ], + "score": 1.0, + "content": "For the sake of simplicity, we introduce the following notation for our analysis. Let", + "type": "text" + }, + { + "bbox": [ + 447, + 361, + 484, + 373 + ], + "score": 0.92, + "content": "\\mathbb { E } _ { x \\sim X } ^ { \\tau } [ x ]", + "type": "inline_equation" + }, + { + "bbox": [ + 484, + 359, + 507, + 375 + ], + "score": 1.0, + "content": "be a", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 371, + 506, + 386 + ], + "spans": [ + { + "bbox": [ + 106, + 372, + 119, + 383 + ], + "score": 0.86, + "content": "\\tau ^ { \\mathrm { { t h } } }", + "type": "inline_equation" + }, + { + "bbox": [ + 120, + 371, + 171, + 386 + ], + "score": 1.0, + "content": "expectile of", + "type": "text" + }, + { + "bbox": [ + 171, + 374, + 181, + 383 + ], + "score": 0.81, + "content": "X", + "type": "inline_equation" + }, + { + "bbox": [ + 181, + 371, + 205, + 386 + ], + "score": 1.0, + "content": "(e.g.,", + "type": "text" + }, + { + "bbox": [ + 205, + 372, + 224, + 384 + ], + "score": 0.86, + "content": "\\mathbb { E } ^ { 0 . 5 }", + "type": "inline_equation" + }, + { + "bbox": [ + 224, + 371, + 462, + 386 + ], + "score": 1.0, + "content": "corresponds to the standard expectation). Then, we define", + "type": "text" + }, + { + "bbox": [ + 462, + 374, + 487, + 385 + ], + "score": 0.91, + "content": "V _ { \\tau } ( s )", + "type": "inline_equation" + }, + { + "bbox": [ + 487, + 371, + 506, + 386 + ], + "score": 1.0, + "content": "and", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 107, + 383, + 496, + 398 + ], + "spans": [ + { + "bbox": [ + 107, + 384, + 142, + 396 + ], + "score": 0.92, + "content": "Q _ { \\tau } ( s , \\bar { a } )", + "type": "inline_equation" + }, + { + "bbox": [ + 143, + 383, + 332, + 398 + ], + "score": 1.0, + "content": ", which correspond to optimal solutions of Eqn.", + "type": "text" + }, + { + "bbox": [ + 333, + 383, + 342, + 397 + ], + "score": 0.66, + "content": "5", + "type": "inline_equation" + }, + { + "bbox": [ + 343, + 383, + 357, + 398 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 357, + 383, + 367, + 397 + ], + "score": 0.61, + "content": "\\boxed { 6 }", + "type": "inline_equation" + }, + { + "bbox": [ + 367, + 383, + 496, + 398 + ], + "score": 1.0, + "content": "correspondingly, recursively as:", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 22 + }, + { + "type": "interline_equation", + "bbox": [ + 230, + 397, + 351, + 412 + ], + "lines": [ + { + "bbox": [ + 230, + 397, + 351, + 412 + ], + "spans": [ + { + "bbox": [ + 230, + 397, + 351, + 412 + ], + "score": 0.83, + "content": "V _ { \\tau } ( s ) = \\mathbb { E } _ { a \\sim \\pi _ { \\beta } ( \\cdot | s ) } ^ { \\tau } [ Q _ { \\tau } ( s , a ) ] ,", + "type": "interline_equation", + "image_path": "d4d196c6eee6179125e817c92a26bad2713c3abd84c57a0771427528202a265b.jpg" + } + ] + } + ], + "index": 24, + "virtual_lines": [ + { + "bbox": [ + 230, + 397, + 351, + 412 + ], + "spans": [], + "index": 24 + } + ] + }, + { + "type": "interline_equation", + "bbox": [ + 217, + 414, + 391, + 427 + ], + "lines": [ + { + "bbox": [ + 217, + 414, + 391, + 427 + ], + "spans": [ + { + "bbox": [ + 217, + 414, + 391, + 427 + ], + "score": 0.82, + "content": "Q _ { \\tau } ( s , a ) = r ( s , a ) + \\gamma \\mathbb { E } _ { s ^ { \\prime } \\sim p ( \\cdot \\vert s , a ) } [ V _ { \\tau } ( s ^ { \\prime } ) ] .", + "type": "interline_equation", + "image_path": "9d2daf2c2bf3ae508a2be34242fed7dc8cce8bd1542f8cf25b8bd49cd72ebc14.jpg" + } + ] + } + ], + "index": 25, + "virtual_lines": [ + { + "bbox": [ + 217, + 414, + 391, + 427 + ], + "spans": [], + "index": 25 + } + ] + }, + { + "type": "text", + "bbox": [ + 108, + 428, + 401, + 441 + ], + "lines": [ + { + "bbox": [ + 106, + 427, + 400, + 442 + ], + "spans": [ + { + "bbox": [ + 106, + 427, + 183, + 442 + ], + "score": 1.0, + "content": "Lemma 2. For all", + "type": "text" + }, + { + "bbox": [ + 184, + 431, + 189, + 438 + ], + "score": 0.33, + "content": "s", + "type": "inline_equation" + }, + { + "bbox": [ + 190, + 427, + 192, + 442 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 193, + 430, + 203, + 439 + ], + "score": 0.72, + "content": "\\tau _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 203, + 427, + 222, + 442 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 222, + 430, + 232, + 439 + ], + "score": 0.85, + "content": "\\tau _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 232, + 427, + 271, + 442 + ], + "score": 1.0, + "content": "such that", + "type": "text" + }, + { + "bbox": [ + 272, + 430, + 304, + 440 + ], + "score": 0.9, + "content": "\\tau _ { 1 } < \\tau _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 304, + 427, + 333, + 442 + ], + "score": 1.0, + "content": "we get", + "type": "text" + }, + { + "bbox": [ + 334, + 428, + 400, + 441 + ], + "score": 0.91, + "content": "V _ { \\tau _ { 1 } } ( s ) \\leq V _ { \\tau _ { 2 } } ( s )", + "type": "inline_equation" + } + ], + "index": 26 + } + ], + "index": 26 + }, + { + "type": "text", + "bbox": [ + 107, + 451, + 498, + 474 + ], + "lines": [ + { + "bbox": [ + 105, + 449, + 502, + 466 + ], + "spans": [ + { + "bbox": [ + 105, + 449, + 502, + 466 + ], + "score": 1.0, + "content": "Proof. The proof follows the policy improvement proof (Sutton & Barto, 2018). See Appendix A.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 27 + }, + { + "type": "text", + "bbox": [ + 106, + 482, + 506, + 523 + ], + "lines": [ + { + "bbox": [ + 106, + 481, + 506, + 495 + ], + "spans": [ + { + "bbox": [ + 106, + 481, + 203, + 495 + ], + "score": 1.0, + "content": "Corollary 2.1. For any", + "type": "text" + }, + { + "bbox": [ + 204, + 485, + 210, + 492 + ], + "score": 0.7, + "content": "\\tau", + "type": "inline_equation" + }, + { + "bbox": [ + 211, + 481, + 271, + 495 + ], + "score": 1.0, + "content": "and s we have", + "type": "text" + }, + { + "bbox": [ + 272, + 482, + 411, + 495 + ], + "score": 0.67, + "content": "V _ { \\tau } ( s ) \\leq \\mathrm { m a x } \\qquad a \\in \\mathcal { A } \\quad \\ldots \\ : Q ^ { * } ( s , a )", + "type": "inline_equation" + }, + { + "bbox": [ + 412, + 482, + 439, + 495 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 439, + 482, + 463, + 495 + ], + "score": 0.91, + "content": "V _ { \\tau } ( s )", + "type": "inline_equation" + }, + { + "bbox": [ + 464, + 482, + 506, + 495 + ], + "score": 1.0, + "content": "is defined", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 324, + 492, + 375, + 503 + ], + "spans": [ + { + "bbox": [ + 324, + 492, + 337, + 503 + ], + "score": 1.0, + "content": "s.t.", + "type": "text" + }, + { + "bbox": [ + 337, + 493, + 375, + 502 + ], + "score": 0.53, + "content": "\\pi _ { \\beta } ( a | s ) { > } 0", + "type": "inline_equation" + } + ], + "index": 29 + }, + { + "bbox": [ + 104, + 499, + 506, + 515 + ], + "spans": [ + { + "bbox": [ + 104, + 499, + 165, + 515 + ], + "score": 1.0, + "content": "as above and", + "type": "text" + }, + { + "bbox": [ + 166, + 501, + 201, + 513 + ], + "score": 0.93, + "content": "Q ^ { * } ( s , a )", + "type": "inline_equation" + }, + { + "bbox": [ + 202, + 499, + 506, + 515 + ], + "score": 1.0, + "content": "is an optimal state-action value function constrained to the dataset and", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 512, + 150, + 524 + ], + "spans": [ + { + "bbox": [ + 106, + 512, + 150, + 524 + ], + "score": 1.0, + "content": "defined as", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 29.5 + }, + { + "type": "interline_equation", + "bbox": [ + 178, + 511, + 432, + 555 + ], + "lines": [ + { + "bbox": [ + 178, + 511, + 432, + 555 + ], + "spans": [ + { + "bbox": [ + 178, + 511, + 432, + 555 + ], + "score": 0.87, + "content": "Q ^ { * } ( s , a ) = r ( s , a ) + \\gamma \\mathbb { E } _ { s ^ { \\prime } \\sim p ( \\cdot \\vert s , a ) } \\left[ \\operatorname* { m a x } _ { a ^ { \\prime } \\in \\mathcal { A } } Q ^ { * } ( s ^ { \\prime } , a ^ { \\prime } ) \\right] .", + "type": "interline_equation", + "image_path": "4c5ae9c24a7029782ab98fde56e7b1a143f8fbb59a6ca98af99b4691a803ab12.jpg" + } + ] + } + ], + "index": 33, + "virtual_lines": [ + { + "bbox": [ + 178, + 511, + 432, + 525.6666666666666 + ], + "spans": [], + "index": 32 + }, + { + "bbox": [ + 178, + 525.6666666666666, + 432, + 540.3333333333333 + ], + "spans": [], + "index": 33 + }, + { + "bbox": [ + 178, + 540.3333333333333, + 432, + 554.9999999999999 + ], + "spans": [], + "index": 34 + } + ] + }, + { + "type": "text", + "bbox": [ + 104, + 554, + 505, + 575 + ], + "lines": [ + { + "bbox": [ + 106, + 552, + 505, + 566 + ], + "spans": [ + { + "bbox": [ + 106, + 552, + 505, + 566 + ], + "score": 1.0, + "content": "Proof. The proof follows from the observation that convex combination is smaller than maximum.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 35 + }, + { + "type": "text", + "bbox": [ + 107, + 581, + 156, + 593 + ], + "lines": [ + { + "bbox": [ + 106, + 581, + 159, + 594 + ], + "spans": [ + { + "bbox": [ + 106, + 581, + 159, + 594 + ], + "score": 1.0, + "content": "Theorem 3.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 36 + }, + { + "type": "interline_equation", + "bbox": [ + 234, + 591, + 377, + 618 + ], + "lines": [ + { + "bbox": [ + 234, + 591, + 377, + 618 + ], + "spans": [ + { + "bbox": [ + 234, + 591, + 377, + 618 + ], + "score": 0.9, + "content": "\\operatorname* { l i m } _ { \\tau 1 } V _ { \\tau } ( s ) = \\operatorname* { m a x } _ { a \\in \\mathcal { A } \\atop s . t . \\pi _ { \\beta } ( a \\mid s ) > 0 } Q ^ { \\ast } ( s , a ) .", + "type": "interline_equation", + "image_path": "7f438634fee57f50fd80523cd44198b33013cdb29936c44ecab10361c0f20413.jpg" + } + ] + } + ], + "index": 37.5, + "virtual_lines": [ + { + "bbox": [ + 234, + 591, + 377, + 604.5 + ], + "spans": [], + "index": 37 + }, + { + "bbox": [ + 234, + 604.5, + 377, + 618.0 + ], + "spans": [], + "index": 38 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 620, + 352, + 633 + ], + "lines": [ + { + "bbox": [ + 105, + 618, + 352, + 634 + ], + "spans": [ + { + "bbox": [ + 105, + 618, + 352, + 634 + ], + "score": 1.0, + "content": "Proof. Follows from combining Lemma 1 and Corollary 2.1.", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 39 + }, + { + "type": "text", + "bbox": [ + 106, + 643, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 643, + 506, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 643, + 231, + 657 + ], + "score": 1.0, + "content": "Therefore, for a larger value of", + "type": "text" + }, + { + "bbox": [ + 232, + 644, + 256, + 654 + ], + "score": 0.89, + "content": "\\tau < 1", + "type": "inline_equation" + }, + { + "bbox": [ + 257, + 643, + 506, + 657 + ], + "score": 1.0, + "content": ", we get a better approximation of the maximum. On the other", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 654, + 505, + 668 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 425, + 668 + ], + "score": 1.0, + "content": "hand, it also becomes a more challenging optimization problem. Thus, we treat", + "type": "text" + }, + { + "bbox": [ + 426, + 657, + 433, + 665 + ], + "score": 0.74, + "content": "\\tau", + "type": "inline_equation" + }, + { + "bbox": [ + 433, + 654, + 505, + 668 + ], + "score": 1.0, + "content": "as a hyperparam-", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 666, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 106, + 666, + 303, + 678 + ], + "score": 1.0, + "content": "eter. Due to the property discussed in Theorem", + "type": "text" + }, + { + "bbox": [ + 303, + 666, + 313, + 678 + ], + "score": 0.81, + "content": "\\bigtriangledown", + "type": "inline_equation" + }, + { + "bbox": [ + 313, + 666, + 505, + 678 + ], + "score": 1.0, + "content": "we dub our method implicit Q-learning (IQL).", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "score": 1.0, + "content": "We also emphasize that our value learning method defines the entire spectrum of methods between", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 688, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 106, + 688, + 144, + 700 + ], + "score": 1.0, + "content": "SARSA", + "type": "text" + }, + { + "bbox": [ + 144, + 688, + 179, + 699 + ], + "score": 0.84, + "content": "\\tau = 0 . 5", + "type": "inline_equation" + }, + { + "bbox": [ + 179, + 688, + 250, + 700 + ], + "score": 1.0, + "content": ") and Q-Learning", + "type": "text" + }, + { + "bbox": [ + 251, + 688, + 279, + 698 + ], + "score": 0.84, + "content": "( \\tau 1 )", + "type": "inline_equation" + }, + { + "bbox": [ + 280, + 688, + 505, + 700 + ], + "score": 1.0, + "content": "). Note that in contrast to other multi-step methods, IQL", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 699, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 505, + 711 + ], + "score": 1.0, + "content": "absorbs the policy improvement step into value learning. Therefore, fitting Q-function corresponds", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 709, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 505, + 723 + ], + "score": 1.0, + "content": "to the policy evaluation step, while fitting the value function with IQL corresponds to implicit policy", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 721, + 164, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 164, + 733 + ], + "score": 1.0, + "content": "improvement.", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 43.5 + } + ], + "page_idx": 5, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2022", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 495, + 621, + 504, + 631 + ], + "lines": [ + { + "bbox": [ + 496, + 622, + 504, + 631 + ], + "spans": [ + { + "bbox": [ + 496, + 622, + 504, + 631 + ], + "score": 0.999, + "content": "□", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 309, + 760 + ], + "lines": [ + { + "bbox": [ + 302, + 750, + 310, + 761 + ], + "spans": [ + { + "bbox": [ + 302, + 750, + 310, + 761 + ], + "score": 1.0, + "content": "6", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 495, + 565, + 504, + 574 + ], + "lines": [ + { + "bbox": [ + 495, + 565, + 505, + 576 + ], + "spans": [ + { + "bbox": [ + 495, + 565, + 505, + 576 + ], + "score": 0.994, + "content": "□", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 493, + 451, + 504, + 473 + ], + "lines": [] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 82, + 505, + 160 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 415, + 95 + ], + "score": 1.0, + "content": "Our final algorithm consists of two stages. First, we fit the value function and", + "type": "text" + }, + { + "bbox": [ + 415, + 83, + 424, + 94 + ], + "score": 0.82, + "content": "Q", + "type": "inline_equation" + }, + { + "bbox": [ + 424, + 82, + 505, + 95 + ], + "score": 1.0, + "content": ", performing a num-", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 506, + 107 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 299, + 107 + ], + "score": 1.0, + "content": "ber of gradient updates alternating between Eqn.", + "type": "text" + }, + { + "bbox": [ + 300, + 93, + 312, + 106 + ], + "score": 0.67, + "content": "( 5 )", + "type": "inline_equation" + }, + { + "bbox": [ + 313, + 93, + 329, + 107 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 330, + 93, + 342, + 106 + ], + "score": 0.55, + "content": "( 6 )", + "type": "inline_equation" + }, + { + "bbox": [ + 343, + 93, + 506, + 107 + ], + "score": 1.0, + "content": ". Second, we perform stochastic gradient", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 104, + 504, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 104, + 172, + 118 + ], + "score": 1.0, + "content": "descent on Eqn.", + "type": "text" + }, + { + "bbox": [ + 173, + 104, + 185, + 118 + ], + "score": 0.81, + "content": "\\overset { \\cdot } { ( 7 ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 186, + 104, + 438, + 118 + ], + "score": 1.0, + "content": ". For both steps, we use a version of clipped double Q-learning", + "type": "text" + }, + { + "bbox": [ + 438, + 104, + 504, + 117 + ], + "score": 0.27, + "content": "( { \\overline { { \\mathbb { F } { \\mathrm { u j i m o t o ~ e t ~ a l . } } } } } , )", + "type": "inline_equation" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 504, + 128 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 131, + 128 + ], + "score": 0.85, + "content": "\\underline { { 2 0 1 8 } } )", + "type": "inline_equation" + }, + { + "bbox": [ + 132, + 116, + 237, + 127 + ], + "score": 1.0, + "content": ", taking a minimum of two", + "type": "text" + }, + { + "bbox": [ + 237, + 116, + 246, + 127 + ], + "score": 0.85, + "content": "Q", + "type": "inline_equation" + }, + { + "bbox": [ + 246, + 116, + 301, + 127 + ], + "score": 1.0, + "content": "-functions for", + "type": "text" + }, + { + "bbox": [ + 302, + 115, + 311, + 125 + ], + "score": 0.79, + "content": "V", + "type": "inline_equation" + }, + { + "bbox": [ + 311, + 116, + 504, + 127 + ], + "score": 1.0, + "content": "-function and policy updates. We summarize our", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 124, + 506, + 140 + ], + "spans": [ + { + "bbox": [ + 104, + 124, + 212, + 140 + ], + "score": 1.0, + "content": "final method in Algorithm", + "type": "text" + }, + { + "bbox": [ + 213, + 126, + 223, + 139 + ], + "score": 0.73, + "content": "^ { 1 . }", + "type": "inline_equation" + }, + { + "bbox": [ + 223, + 124, + 506, + 140 + ], + "score": 1.0, + "content": "Note that the policy does not influence the value function in any way,", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 138, + 505, + 149 + ], + "spans": [ + { + "bbox": [ + 106, + 138, + 505, + 149 + ], + "score": 1.0, + "content": "and therefore extraction could be performed either concurrently or after TD learning. Concurrent", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 148, + 457, + 160 + ], + "spans": [ + { + "bbox": [ + 106, + 149, + 439, + 160 + ], + "score": 1.0, + "content": "learning provides a way to use IQL with online finetuning, as we discuss in Section", + "type": "text" + }, + { + "bbox": [ + 440, + 148, + 457, + 160 + ], + "score": 0.52, + "content": "{ \\bar { 5 . 3 } } .", + "type": "inline_equation" + } + ], + "index": 6 + } + ], + "index": 3, + "bbox_fs": [ + 104, + 82, + 506, + 160 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 172, + 176, + 183 + ], + "lines": [ + { + "bbox": [ + 105, + 171, + 177, + 185 + ], + "spans": [ + { + "bbox": [ + 105, + 171, + 177, + 185 + ], + "score": 1.0, + "content": "4.4 ANALYSIS", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 7 + }, + { + "type": "text", + "bbox": [ + 108, + 192, + 504, + 226 + ], + "lines": [ + { + "bbox": [ + 106, + 193, + 505, + 205 + ], + "spans": [ + { + "bbox": [ + 106, + 193, + 505, + 205 + ], + "score": 1.0, + "content": "In this section, we will show that IQL can recover the optimal value function under the dataset", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 204, + 505, + 216 + ], + "spans": [ + { + "bbox": [ + 106, + 204, + 505, + 216 + ], + "score": 1.0, + "content": "support constraints. First, we prove a simple lemma that we will then use to show how our approach", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 215, + 296, + 227 + ], + "spans": [ + { + "bbox": [ + 106, + 215, + 296, + 227 + ], + "score": 1.0, + "content": "can enable learning the optimal value function.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 9, + "bbox_fs": [ + 106, + 193, + 505, + 227 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 227, + 502, + 250 + ], + "lines": [ + { + "bbox": [ + 105, + 226, + 504, + 240 + ], + "spans": [ + { + "bbox": [ + 105, + 226, + 170, + 240 + ], + "score": 1.0, + "content": "Lemma 1. Let", + "type": "text" + }, + { + "bbox": [ + 170, + 228, + 181, + 238 + ], + "score": 0.64, + "content": "X", + "type": "inline_equation" + }, + { + "bbox": [ + 181, + 226, + 504, + 240 + ], + "score": 1.0, + "content": "be a real-valued random variable with a bounded support and supremum of the", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 239, + 189, + 251 + ], + "spans": [ + { + "bbox": [ + 105, + 239, + 148, + 251 + ], + "score": 1.0, + "content": "support is", + "type": "text" + }, + { + "bbox": [ + 149, + 239, + 159, + 249 + ], + "score": 0.84, + "content": "x ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 160, + 239, + 189, + 251 + ], + "score": 1.0, + "content": ". Then,", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 11.5, + "bbox_fs": [ + 105, + 226, + 504, + 251 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 276, + 243, + 334, + 261 + ], + "lines": [ + { + "bbox": [ + 276, + 243, + 334, + 261 + ], + "spans": [ + { + "bbox": [ + 276, + 243, + 334, + 261 + ], + "score": 0.91, + "content": "\\operatorname* { l i m } _ { \\tau 1 } m _ { \\tau } = x ^ { \\ast }", + "type": "interline_equation", + "image_path": "3123e0d4150d1a44dc8737af054373b26472ac0c1bb7be9f8801d27960f877f4.jpg" + } + ] + } + ], + "index": 13, + "virtual_lines": [ + { + "bbox": [ + 276, + 243, + 334, + 261 + ], + "spans": [], + "index": 13 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 266, + 505, + 300 + ], + "lines": [ + { + "bbox": [ + 108, + 266, + 505, + 278 + ], + "spans": [ + { + "bbox": [ + 108, + 266, + 489, + 278 + ], + "score": 1.0, + "content": "Proof Sketch. One can show that expectiles of a random variable have the same supremum", + "type": "text" + }, + { + "bbox": [ + 490, + 267, + 501, + 276 + ], + "score": 0.86, + "content": "x ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 266, + 505, + 278 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 276, + 506, + 290 + ], + "spans": [ + { + "bbox": [ + 105, + 276, + 176, + 290 + ], + "score": 1.0, + "content": "Moreover, for all", + "type": "text" + }, + { + "bbox": [ + 176, + 279, + 186, + 288 + ], + "score": 0.85, + "content": "\\tau _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 187, + 276, + 204, + 290 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 205, + 279, + 215, + 288 + ], + "score": 0.85, + "content": "\\tau _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 215, + 276, + 254, + 290 + ], + "score": 1.0, + "content": "such that", + "type": "text" + }, + { + "bbox": [ + 254, + 278, + 286, + 288 + ], + "score": 0.91, + "content": "\\tau _ { 1 } < \\tau _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 286, + 276, + 318, + 290 + ], + "score": 1.0, + "content": ", we get", + "type": "text" + }, + { + "bbox": [ + 318, + 277, + 366, + 289 + ], + "score": 0.92, + "content": "m _ { \\tau _ { 1 } } \\leq m _ { \\tau _ { 2 } }", + "type": "inline_equation" + }, + { + "bbox": [ + 367, + 276, + 506, + 290 + ], + "score": 1.0, + "content": ". 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We first prove", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 334, + 505, + 345 + ], + "spans": [ + { + "bbox": [ + 105, + 334, + 505, + 345 + ], + "score": 1.0, + "content": "a technical lemma relating different expectiles of the Q-function, and then derive our main result", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 345, + 267, + 356 + ], + "spans": [ + { + "bbox": [ + 105, + 345, + 267, + 356 + ], + "score": 1.0, + "content": "regarding the optimality of our method.", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 18.5, + "bbox_fs": [ + 105, + 311, + 505, + 356 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 361, + 505, + 396 + ], + "lines": [ + { + "bbox": [ + 104, + 359, + 507, + 375 + ], + "spans": [ + { + "bbox": [ + 104, + 359, + 446, + 375 + ], + "score": 1.0, + "content": "For the sake of simplicity, we introduce the following notation for our analysis. Let", + "type": "text" + }, + { + "bbox": [ + 447, + 361, + 484, + 373 + ], + "score": 0.92, + "content": "\\mathbb { E } _ { x \\sim X } ^ { \\tau } [ x ]", + "type": "inline_equation" + }, + { + "bbox": [ + 484, + 359, + 507, + 375 + ], + "score": 1.0, + "content": "be a", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 371, + 506, + 386 + ], + "spans": [ + { + "bbox": [ + 106, + 372, + 119, + 383 + ], + "score": 0.86, + "content": "\\tau ^ { \\mathrm { { t h } } }", + "type": "inline_equation" + }, + { + "bbox": [ + 120, + 371, + 171, + 386 + ], + "score": 1.0, + "content": "expectile of", + "type": "text" + }, + { + "bbox": [ + 171, + 374, + 181, + 383 + ], + "score": 0.81, + "content": "X", + "type": "inline_equation" + }, + { + "bbox": [ + 181, + 371, + 205, + 386 + ], + "score": 1.0, + "content": "(e.g.,", + "type": "text" + }, + { + "bbox": [ + 205, + 372, + 224, + 384 + ], + "score": 0.86, + "content": "\\mathbb { E } ^ { 0 . 5 }", + "type": "inline_equation" + }, + { + "bbox": [ + 224, + 371, + 462, + 386 + ], + "score": 1.0, + "content": "corresponds to the standard expectation). Then, we define", + "type": "text" + }, + { + "bbox": [ + 462, + 374, + 487, + 385 + ], + "score": 0.91, + "content": "V _ { \\tau } ( s )", + "type": "inline_equation" + }, + { + "bbox": [ + 487, + 371, + 506, + 386 + ], + "score": 1.0, + "content": "and", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 107, + 383, + 496, + 398 + ], + "spans": [ + { + "bbox": [ + 107, + 384, + 142, + 396 + ], + "score": 0.92, + "content": "Q _ { \\tau } ( s , \\bar { a } )", + "type": "inline_equation" + }, + { + "bbox": [ + 143, + 383, + 332, + 398 + ], + "score": 1.0, + "content": ", which correspond to optimal solutions of Eqn.", + "type": "text" + }, + { + "bbox": [ + 333, + 383, + 342, + 397 + ], + "score": 0.66, + "content": "5", + "type": "inline_equation" + }, + { + "bbox": [ + 343, + 383, + 357, + 398 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 357, + 383, + 367, + 397 + ], + "score": 0.61, + "content": "\\boxed { 6 }", + "type": "inline_equation" + }, + { + "bbox": [ + 367, + 383, + 496, + 398 + ], + "score": 1.0, + "content": "correspondingly, recursively as:", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 22, + "bbox_fs": [ + 104, + 359, + 507, + 398 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 230, + 397, + 351, + 412 + ], + "lines": [ + { + "bbox": [ + 230, + 397, + 351, + 412 + ], + "spans": [ + { + "bbox": [ + 230, + 397, + 351, + 412 + ], + "score": 0.83, + "content": "V _ { \\tau } ( s ) = \\mathbb { E } _ { a \\sim \\pi _ { \\beta } ( \\cdot | s ) } ^ { \\tau } [ Q _ { \\tau } ( s , a ) ] ,", + "type": "interline_equation", + "image_path": "d4d196c6eee6179125e817c92a26bad2713c3abd84c57a0771427528202a265b.jpg" + } + ] + } + ], + "index": 24, + "virtual_lines": [ + { + "bbox": [ + 230, + 397, + 351, + 412 + ], + "spans": [], + "index": 24 + } + ] + }, + { + "type": "interline_equation", + "bbox": [ + 217, + 414, + 391, + 427 + ], + "lines": [ + { + "bbox": [ + 217, + 414, + 391, + 427 + ], + "spans": [ + { + "bbox": [ + 217, + 414, + 391, + 427 + ], + "score": 0.82, + "content": "Q _ { \\tau } ( s , a ) = r ( s , a ) + \\gamma \\mathbb { E } _ { s ^ { \\prime } \\sim p ( \\cdot \\vert s , a ) } [ V _ { \\tau } ( s ^ { \\prime } ) ] .", + "type": "interline_equation", + "image_path": "9d2daf2c2bf3ae508a2be34242fed7dc8cce8bd1542f8cf25b8bd49cd72ebc14.jpg" + } + ] + } + ], + "index": 25, + "virtual_lines": [ + { + "bbox": [ + 217, + 414, + 391, + 427 + ], + "spans": [], + "index": 25 + } + ] + }, + { + "type": "text", + "bbox": [ + 108, + 428, + 401, + 441 + ], + "lines": [ + { + "bbox": [ + 106, + 427, + 400, + 442 + ], + "spans": [ + { + "bbox": [ + 106, + 427, + 183, + 442 + ], + "score": 1.0, + "content": "Lemma 2. For all", + "type": "text" + }, + { + "bbox": [ + 184, + 431, + 189, + 438 + ], + "score": 0.33, + "content": "s", + "type": "inline_equation" + }, + { + "bbox": [ + 190, + 427, + 192, + 442 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 193, + 430, + 203, + 439 + ], + "score": 0.72, + "content": "\\tau _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 203, + 427, + 222, + 442 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 222, + 430, + 232, + 439 + ], + "score": 0.85, + "content": "\\tau _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 232, + 427, + 271, + 442 + ], + "score": 1.0, + "content": "such that", + "type": "text" + }, + { + "bbox": [ + 272, + 430, + 304, + 440 + ], + "score": 0.9, + "content": "\\tau _ { 1 } < \\tau _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 304, + 427, + 333, + 442 + ], + "score": 1.0, + "content": "we get", + "type": "text" + }, + { + "bbox": [ + 334, + 428, + 400, + 441 + ], + "score": 0.91, + "content": "V _ { \\tau _ { 1 } } ( s ) \\leq V _ { \\tau _ { 2 } } ( s )", + "type": "inline_equation" + } + ], + "index": 26 + } + ], + "index": 26, + "bbox_fs": [ + 106, + 427, + 400, + 442 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 451, + 498, + 474 + ], + "lines": [ + { + "bbox": [ + 105, + 449, + 502, + 466 + ], + "spans": [ + { + "bbox": [ + 105, + 449, + 502, + 466 + ], + "score": 1.0, + "content": "Proof. The proof follows the policy improvement proof (Sutton & Barto, 2018). See Appendix A.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 27, + "bbox_fs": [ + 105, + 449, + 502, + 466 + ] + }, + { + "type": "list", + "bbox": [ + 106, + 482, + 506, + 523 + ], + "lines": [ + { + "bbox": [ + 106, + 481, + 506, + 495 + ], + "spans": [ + { + "bbox": [ + 106, + 481, + 203, + 495 + ], + "score": 1.0, + "content": "Corollary 2.1. For any", + "type": "text" + }, + { + "bbox": [ + 204, + 485, + 210, + 492 + ], + "score": 0.7, + "content": "\\tau", + "type": "inline_equation" + }, + { + "bbox": [ + 211, + 481, + 271, + 495 + ], + "score": 1.0, + "content": "and s we have", + "type": "text" + }, + { + "bbox": [ + 272, + 482, + 411, + 495 + ], + "score": 0.67, + "content": "V _ { \\tau } ( s ) \\leq \\mathrm { m a x } \\qquad a \\in \\mathcal { A } \\quad \\ldots \\ : Q ^ { * } ( s , a )", + "type": "inline_equation" + }, + { + "bbox": [ + 412, + 482, + 439, + 495 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 439, + 482, + 463, + 495 + ], + "score": 0.91, + "content": "V _ { \\tau } ( s )", + "type": "inline_equation" + }, + { + "bbox": [ + 464, + 482, + 506, + 495 + ], + "score": 1.0, + "content": "is defined", + "type": "text" + } + ], + "index": 28, + "is_list_start_line": true + }, + { + "bbox": [ + 324, + 492, + 375, + 503 + ], + "spans": [ + { + "bbox": [ + 324, + 492, + 337, + 503 + ], + "score": 1.0, + "content": "s.t.", + "type": "text" + }, + { + "bbox": [ + 337, + 493, + 375, + 502 + ], + "score": 0.53, + "content": "\\pi _ { \\beta } ( a | s ) { > } 0", + "type": "inline_equation" + } + ], + "index": 29, + "is_list_end_line": true + }, + { + "bbox": [ + 104, + 499, + 506, + 515 + ], + "spans": [ + { + "bbox": [ + 104, + 499, + 165, + 515 + ], + "score": 1.0, + "content": "as above and", + "type": "text" + }, + { + "bbox": [ + 166, + 501, + 201, + 513 + ], + "score": 0.93, + "content": "Q ^ { * } ( s , a )", + "type": "inline_equation" + }, + { + "bbox": [ + 202, + 499, + 506, + 515 + ], + "score": 1.0, + "content": "is an optimal state-action value function constrained to the dataset and", + "type": "text" + } + ], + "index": 30, + "is_list_start_line": true + }, + { + "bbox": [ + 106, + 512, + 150, + 524 + ], + "spans": [ + { + "bbox": [ + 106, + 512, + 150, + 524 + ], + "score": 1.0, + "content": "defined as", + "type": "text" + } + ], + "index": 31, + "is_list_start_line": true, + "is_list_end_line": true + } + ], + "index": 29.5, + "bbox_fs": [ + 104, + 481, + 506, + 524 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 178, + 511, + 432, + 555 + ], + "lines": [ + { + "bbox": [ + 178, + 511, + 432, + 555 + ], + "spans": [ + { + "bbox": [ + 178, + 511, + 432, + 555 + ], + "score": 0.87, + "content": "Q ^ { * } ( s , a ) = r ( s , a ) + \\gamma \\mathbb { E } _ { s ^ { \\prime } \\sim p ( \\cdot \\vert s , a ) } \\left[ \\operatorname* { m a x } _ { a ^ { \\prime } \\in \\mathcal { A } } Q ^ { * } ( s ^ { \\prime } , a ^ { \\prime } ) \\right] .", + "type": "interline_equation", + "image_path": "4c5ae9c24a7029782ab98fde56e7b1a143f8fbb59a6ca98af99b4691a803ab12.jpg" + } + ] + } + ], + "index": 33, + "virtual_lines": [ + { + "bbox": [ + 178, + 511, + 432, + 525.6666666666666 + ], + "spans": [], + "index": 32 + }, + { + "bbox": [ + 178, + 525.6666666666666, + 432, + 540.3333333333333 + ], + "spans": [], + "index": 33 + }, + { + "bbox": [ + 178, + 540.3333333333333, + 432, + 554.9999999999999 + ], + "spans": [], + "index": 34 + } + ] + }, + { + "type": "text", + "bbox": [ + 104, + 554, + 505, + 575 + ], + "lines": [ + { + "bbox": [ + 106, + 552, + 505, + 566 + ], + "spans": [ + { + "bbox": [ + 106, + 552, + 505, + 566 + ], + "score": 1.0, + "content": "Proof. The proof follows from the observation that convex combination is smaller than maximum.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 35, + "bbox_fs": [ + 106, + 552, + 505, + 566 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 581, + 156, + 593 + ], + "lines": [ + { + "bbox": [ + 106, + 581, + 159, + 594 + ], + "spans": [ + { + "bbox": [ + 106, + 581, + 159, + 594 + ], + "score": 1.0, + "content": "Theorem 3.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 36, + "bbox_fs": [ + 106, + 581, + 159, + 594 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 234, + 591, + 377, + 618 + ], + "lines": [ + { + "bbox": [ + 234, + 591, + 377, + 618 + ], + "spans": [ + { + "bbox": [ + 234, + 591, + 377, + 618 + ], + "score": 0.9, + "content": "\\operatorname* { l i m } _ { \\tau 1 } V _ { \\tau } ( s ) = \\operatorname* { m a x } _ { a \\in \\mathcal { A } \\atop s . t . \\pi _ { \\beta } ( a \\mid s ) > 0 } Q ^ { \\ast } ( s , a ) .", + "type": "interline_equation", + "image_path": "7f438634fee57f50fd80523cd44198b33013cdb29936c44ecab10361c0f20413.jpg" + } + ] + } + ], + "index": 37.5, + "virtual_lines": [ + { + "bbox": [ + 234, + 591, + 377, + 604.5 + ], + "spans": [], + "index": 37 + }, + { + "bbox": [ + 234, + 604.5, + 377, + 618.0 + ], + "spans": [], + "index": 38 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 620, + 352, + 633 + ], + "lines": [ + { + "bbox": [ + 105, + 618, + 352, + 634 + ], + "spans": [ + { + "bbox": [ + 105, + 618, + 352, + 634 + ], + "score": 1.0, + "content": "Proof. Follows from combining Lemma 1 and Corollary 2.1.", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 39, + "bbox_fs": [ + 105, + 618, + 352, + 634 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 643, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 643, + 506, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 643, + 231, + 657 + ], + "score": 1.0, + "content": "Therefore, for a larger value of", + "type": "text" + }, + { + "bbox": [ + 232, + 644, + 256, + 654 + ], + "score": 0.89, + "content": "\\tau < 1", + "type": "inline_equation" + }, + { + "bbox": [ + 257, + 643, + 506, + 657 + ], + "score": 1.0, + "content": ", we get a better approximation of the maximum. On the other", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 654, + 505, + 668 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 425, + 668 + ], + "score": 1.0, + "content": "hand, it also becomes a more challenging optimization problem. Thus, we treat", + "type": "text" + }, + { + "bbox": [ + 426, + 657, + 433, + 665 + ], + "score": 0.74, + "content": "\\tau", + "type": "inline_equation" + }, + { + "bbox": [ + 433, + 654, + 505, + 668 + ], + "score": 1.0, + "content": "as a hyperparam-", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 666, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 106, + 666, + 303, + 678 + ], + "score": 1.0, + "content": "eter. Due to the property discussed in Theorem", + "type": "text" + }, + { + "bbox": [ + 303, + 666, + 313, + 678 + ], + "score": 0.81, + "content": "\\bigtriangledown", + "type": "inline_equation" + }, + { + "bbox": [ + 313, + 666, + 505, + 678 + ], + "score": 1.0, + "content": "we dub our method implicit Q-learning (IQL).", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "score": 1.0, + "content": "We also emphasize that our value learning method defines the entire spectrum of methods between", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 688, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 106, + 688, + 144, + 700 + ], + "score": 1.0, + "content": "SARSA", + "type": "text" + }, + { + "bbox": [ + 144, + 688, + 179, + 699 + ], + "score": 0.84, + "content": "\\tau = 0 . 5", + "type": "inline_equation" + }, + { + "bbox": [ + 179, + 688, + 250, + 700 + ], + "score": 1.0, + "content": ") and Q-Learning", + "type": "text" + }, + { + "bbox": [ + 251, + 688, + 279, + 698 + ], + "score": 0.84, + "content": "( \\tau 1 )", + "type": "inline_equation" + }, + { + "bbox": [ + 280, + 688, + 505, + 700 + ], + "score": 1.0, + "content": "). Note that in contrast to other multi-step methods, IQL", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 699, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 505, + 711 + ], + "score": 1.0, + "content": "absorbs the policy improvement step into value learning. Therefore, fitting Q-function corresponds", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 709, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 505, + 723 + ], + "score": 1.0, + "content": "to the policy evaluation step, while fitting the value function with IQL corresponds to implicit policy", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 721, + 164, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 164, + 733 + ], + "score": 1.0, + "content": "improvement.", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 43.5, + "bbox_fs": [ + 105, + 643, + 506, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 115, + 80, + 493, + 166 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 115, + 80, + 493, + 166 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 115, + 80, + 493, + 166 + ], + "spans": [ + { + "bbox": [ + 115, + 80, + 493, + 166 + ], + "score": 0.966, + "type": "image", + "image_path": "38d9e8ba0505f1fcda3e8c36c5bd6166024a05cfac64e3433ec793f149d35e0d.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 115, + 80, + 493, + 108.66666666666667 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 115, + 108.66666666666667, + 493, + 137.33333333333334 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 115, + 137.33333333333334, + 493, + 166.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 175, + 506, + 241 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 175, + 506, + 187 + ], + "spans": [ + { + "bbox": [ + 105, + 175, + 506, + 187 + ], + "score": 1.0, + "content": "Figure 2: Evaluation of our algorithm on a toy umaze environment (a). When the static dataset", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 185, + 506, + 199 + ], + "spans": [ + { + "bbox": [ + 105, + 185, + 506, + 199 + ], + "score": 1.0, + "content": "is heavily corrupted by suboptimal actions, one-step policy evaluation results in a value function", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 196, + 506, + 210 + ], + "spans": [ + { + "bbox": [ + 105, + 196, + 506, + 210 + ], + "score": 1.0, + "content": "that degrades to zero far from the rewarding states too quickly (c). Our algorithm aims to learn", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 208, + 506, + 220 + ], + "spans": [ + { + "bbox": [ + 105, + 208, + 506, + 220 + ], + "score": 1.0, + "content": "a near-optimal value function, combining the best properties of SARSA-style evaluation with the", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 218, + 506, + 232 + ], + "spans": [ + { + "bbox": [ + 105, + 218, + 506, + 232 + ], + "score": 1.0, + "content": "ability to perform multi-step dynamic programming, leading to value functions that are much closer", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 230, + 380, + 243 + ], + "spans": [ + { + "bbox": [ + 105, + 230, + 380, + 243 + ], + "score": 1.0, + "content": "to optimality (shown in (b)) and producing a much better policy (d).", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 5.5 + } + ], + "index": 3.25 + }, + { + "type": "title", + "bbox": [ + 109, + 264, + 277, + 276 + ], + "lines": [ + { + "bbox": [ + 105, + 262, + 279, + 278 + ], + "spans": [ + { + "bbox": [ + 105, + 262, + 279, + 278 + ], + "score": 1.0, + "content": "5 EXPERIMENTAL EVALUATION", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 9 + }, + { + "type": "text", + "bbox": [ + 106, + 279, + 505, + 399 + ], + "lines": [ + { + "bbox": [ + 105, + 279, + 505, + 290 + ], + "spans": [ + { + "bbox": [ + 105, + 279, + 505, + 290 + ], + "score": 1.0, + "content": "Our experiments aim to evaluate our method comparatively, in contrast to prior offline RL meth-", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 290, + 505, + 302 + ], + "spans": [ + { + "bbox": [ + 106, + 290, + 505, + 302 + ], + "score": 1.0, + "content": "ods, and in particular to understand how our approach compares both to single-step methods and", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 104, + 298, + 506, + 315 + ], + "spans": [ + { + "bbox": [ + 104, + 298, + 506, + 315 + ], + "score": 1.0, + "content": "multi-step dynamic programming approaches. We will first demonstrate the benefits of multi-step", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 312, + 505, + 324 + ], + "spans": [ + { + "bbox": [ + 106, + 312, + 505, + 324 + ], + "score": 1.0, + "content": "dynamic programming methods, such as ours, in contrast to single-step methods, showing that on", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 322, + 505, + 335 + ], + "spans": [ + { + "bbox": [ + 105, + 322, + 505, + 335 + ], + "score": 1.0, + "content": "some problems this difference can be extremely large. We will then compare IQL with state-of-the-", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 332, + 505, + 346 + ], + "spans": [ + { + "bbox": [ + 105, + 332, + 328, + 346 + ], + "score": 1.0, + "content": "art single-step and multi-step algorithms on the D4RL", + "type": "text" + }, + { + "bbox": [ + 329, + 333, + 394, + 346 + ], + "score": 0.63, + "content": "\\mathrm { ( F u ~ e t ~ a l . , } \\mathbb { 2 0 2 0 } )", + "type": "inline_equation" + }, + { + "bbox": [ + 394, + 332, + 505, + 346 + ], + "score": 1.0, + "content": "benchmark tasks, studying", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 344, + 505, + 357 + ], + "spans": [ + { + "bbox": [ + 106, + 344, + 505, + 357 + ], + "score": 1.0, + "content": "the degree to which we can learn effective policies using only the actions in the dataset. We examine", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 356, + 505, + 368 + ], + "spans": [ + { + "bbox": [ + 106, + 356, + 505, + 368 + ], + "score": 1.0, + "content": "domains that contain near-optimal trajectories, where single-step methods perform well, as well as", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 365, + 505, + 380 + ], + "spans": [ + { + "bbox": [ + 105, + 365, + 505, + 380 + ], + "score": 1.0, + "content": "domains with no optimal trajectories at all, which require multi-step dynamic programming. Finally,", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 377, + 506, + 391 + ], + "spans": [ + { + "bbox": [ + 105, + 377, + 506, + 391 + ], + "score": 1.0, + "content": "we will study how IQL compares to prior methods when finetuning with online RL starting from an", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 388, + 205, + 399 + ], + "spans": [ + { + "bbox": [ + 106, + 388, + 205, + 399 + ], + "score": 1.0, + "content": "offline RL initialization.", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 15 + }, + { + "type": "title", + "bbox": [ + 107, + 409, + 444, + 421 + ], + "lines": [ + { + "bbox": [ + 105, + 408, + 444, + 423 + ], + "spans": [ + { + "bbox": [ + 105, + 408, + 444, + 423 + ], + "score": 1.0, + "content": "5.1 THE DIFFERENCE BETWEEN ONE-STEP POLICY IMPROVEMENT AND IQL", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 21 + }, + { + "type": "text", + "bbox": [ + 107, + 425, + 505, + 491 + ], + "lines": [ + { + "bbox": [ + 106, + 424, + 505, + 438 + ], + "spans": [ + { + "bbox": [ + 106, + 424, + 505, + 438 + ], + "score": 1.0, + "content": "We first use a simple maze environment to illustrate the importance of multi-step dynamic program-", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 436, + 500, + 449 + ], + "spans": [ + { + "bbox": [ + 105, + 436, + 500, + 449 + ], + "score": 1.0, + "content": "ming for offline RL. The maze has a u-shape, a single start state, and a single goal state (see Fig. 2a)", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 447, + 505, + 460 + ], + "spans": [ + { + "bbox": [ + 106, + 447, + 505, + 460 + ], + "score": 1.0, + "content": "The agent receives a reward of 10 for entering the goal state and zero reward for all other transitions.", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 458, + 505, + 470 + ], + "spans": [ + { + "bbox": [ + 105, + 458, + 505, + 470 + ], + "score": 1.0, + "content": "With a probability of 0.25, the agent transitions to a random state, and otherwise to the commanded", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 470, + 504, + 481 + ], + "spans": [ + { + "bbox": [ + 106, + 470, + 504, + 481 + ], + "score": 1.0, + "content": "state. The dataset consists of 1 optimal trajectory and 99 trajectories with uniform random actions.", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 480, + 329, + 492 + ], + "spans": [ + { + "bbox": [ + 105, + 480, + 291, + 492 + ], + "score": 1.0, + "content": "Due to a short horizon of the problem, we use", + "type": "text" + }, + { + "bbox": [ + 291, + 480, + 325, + 492 + ], + "score": 0.91, + "content": "\\gamma = 0 . 9", + "type": "inline_equation" + }, + { + "bbox": [ + 325, + 480, + 329, + 492 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 24.5 + }, + { + "type": "text", + "bbox": [ + 106, + 497, + 505, + 585 + ], + "lines": [ + { + "bbox": [ + 106, + 496, + 505, + 510 + ], + "spans": [ + { + "bbox": [ + 106, + 496, + 123, + 509 + ], + "score": 1.0, + "content": "Fig.", + "type": "text" + }, + { + "bbox": [ + 124, + 496, + 133, + 510 + ], + "score": 0.27, + "content": "2", + "type": "inline_equation" + }, + { + "bbox": [ + 134, + 496, + 414, + 509 + ], + "score": 1.0, + "content": "(c, d) illustrates the difference between single-step methods which fit", + "type": "text" + }, + { + "bbox": [ + 414, + 497, + 450, + 508 + ], + "score": 0.91, + "content": "Q ^ { \\pi } ( s , a )", + "type": "inline_equation" + }, + { + "bbox": [ + 451, + 496, + 505, + 509 + ], + "score": 1.0, + "content": "via SARSA-", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 508, + 502, + 520 + ], + "spans": [ + { + "bbox": [ + 106, + 508, + 427, + 520 + ], + "score": 1.0, + "content": "style objective, in this case represented by Onepstep RL (Brandfonbrener et al.,", + "type": "text" + }, + { + "bbox": [ + 428, + 508, + 453, + 520 + ], + "score": 0.34, + "content": "\\boxed { 2 0 2 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 453, + 508, + 502, + 520 + ], + "score": 1.0, + "content": "Wang et al.,", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 518, + 505, + 531 + ], + "spans": [ + { + "bbox": [ + 105, + 518, + 131, + 531 + ], + "score": 0.27, + "content": "\\dot { \\boxed { 2 0 1 8 } } ;", + "type": "inline_equation" + }, + { + "bbox": [ + 131, + 519, + 272, + 531 + ], + "score": 1.0, + "content": "Gulcehre et al., 2021) and IQL with", + "type": "text" + }, + { + "bbox": [ + 273, + 519, + 310, + 529 + ], + "score": 0.89, + "content": "\\tau = 0 . 9 5", + "type": "inline_equation" + }, + { + "bbox": [ + 311, + 519, + 505, + 531 + ], + "score": 1.0, + "content": ". Note that these methods represent a special case", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 530, + 505, + 542 + ], + "spans": [ + { + "bbox": [ + 106, + 530, + 187, + 542 + ], + "score": 1.0, + "content": "of our method with", + "type": "text" + }, + { + "bbox": [ + 187, + 531, + 222, + 540 + ], + "score": 0.87, + "content": "\\bar { \\tau } = 0 . 5", + "type": "inline_equation" + }, + { + "bbox": [ + 223, + 530, + 505, + 542 + ], + "score": 1.0, + "content": ". Although states closer to the high reward state will still have higher", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 541, + 505, + 552 + ], + "spans": [ + { + "bbox": [ + 106, + 541, + 505, + 552 + ], + "score": 1.0, + "content": "values, these values decay much faster as we move further away than they would for the optimal", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 552, + 505, + 564 + ], + "spans": [ + { + "bbox": [ + 106, + 552, + 505, + 564 + ], + "score": 1.0, + "content": "value function, and the resulting policy is highly suboptimal. Since IQL (d) performs iterative", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 563, + 506, + 575 + ], + "spans": [ + { + "bbox": [ + 105, + 563, + 506, + 575 + ], + "score": 1.0, + "content": "dynamic programming, it correctly propagates the signal, and the values are no longer dominated", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 573, + 468, + 586 + ], + "spans": [ + { + "bbox": [ + 105, + 573, + 468, + 586 + ], + "score": 1.0, + "content": "by noise. The resulting value function closely matches the true optimal value function (b).", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 31.5 + }, + { + "type": "title", + "bbox": [ + 107, + 595, + 329, + 606 + ], + "lines": [ + { + "bbox": [ + 105, + 594, + 330, + 608 + ], + "spans": [ + { + "bbox": [ + 105, + 594, + 330, + 608 + ], + "score": 1.0, + "content": "5.2 COMPARISONS ON OFFLINE RL BENCHMARKS", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 36 + }, + { + "type": "text", + "bbox": [ + 106, + 611, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 611, + 505, + 623 + ], + "spans": [ + { + "bbox": [ + 106, + 611, + 505, + 623 + ], + "score": 1.0, + "content": "Next, we evaluate our approach on the D4RL benchmark in comparison to prior methods (see Ta-", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 619, + 506, + 636 + ], + "spans": [ + { + "bbox": [ + 106, + 619, + 120, + 636 + ], + "score": 1.0, + "content": "ble", + "type": "text" + }, + { + "bbox": [ + 121, + 622, + 132, + 635 + ], + "score": 0.47, + "content": "\\bigstar \\bigstar \\bigstar \\bigstar", + "type": "inline_equation" + }, + { + "bbox": [ + 132, + 619, + 506, + 636 + ], + "score": 1.0, + "content": ". The MuJoCo tasks in D4RL consist of the Gym locomotion tasks, the Ant Maze tasks,", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 632, + 505, + 646 + ], + "spans": [ + { + "bbox": [ + 105, + 632, + 505, + 646 + ], + "score": 1.0, + "content": "and the Adroit and Kitchen robotic manipulation environments. Some prior works, particularly", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 644, + 505, + 656 + ], + "spans": [ + { + "bbox": [ + 106, + 644, + 505, + 656 + ], + "score": 1.0, + "content": "those proposing one-step methods, focus entirely on the Gym locomotion tasks. However, these", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 655, + 506, + 667 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 506, + 667 + ], + "score": 1.0, + "content": "tasks include a significant fraction of near-optimal trajectories in the dataset. In contrast, the Ant", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 665, + 506, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 506, + 678 + ], + "score": 1.0, + "content": "Maze tasks, especially the medium and large ones, contain very few or no near-optimal trajectories,", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 677, + 506, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 506, + 689 + ], + "score": 1.0, + "content": "making them very challenging for one-step methods. These domains require “stitching” parts of", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 687, + 506, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 506, + 700 + ], + "score": 1.0, + "content": "suboptimal trajectories that travel between different states to find a path from the start to the goal of", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 698, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 698, + 145, + 711 + ], + "score": 1.0, + "content": "the maze", + "type": "text" + }, + { + "bbox": [ + 146, + 698, + 211, + 711 + ], + "score": 0.82, + "content": "\\mathtt { ( F u ~ e t ~ a l . } ] \\mathtt { ( E 0 2 0 ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 211, + 698, + 505, + 711 + ], + "score": 1.0, + "content": ". As we will show, multi-step dynamic programming is essential in these", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 709, + 506, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 506, + 722 + ], + "score": 1.0, + "content": "domains. The Adroit and Kitchen tasks are comparatively less discriminating, and we found that", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 721, + 501, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 501, + 733 + ], + "score": 1.0, + "content": "most RL methods perform similarly to imitation learning in these domains (Florence et al., 2021)", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 42 + } + ], + "page_idx": 6, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 25, + 294, + 39 + ], + "spans": [ + { + "bbox": [ + 106, + 25, + 294, + 39 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2022", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 309, + 759 + ], + "lines": [ + { + "bbox": [ + 302, + 750, + 309, + 762 + ], + "spans": [ + { + "bbox": [ + 302, + 750, + 309, + 762 + ], + "score": 1.0, + "content": "7", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "image", + "bbox": [ + 115, + 80, + 493, + 166 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 115, + 80, + 493, + 166 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 115, + 80, + 493, + 166 + ], + "spans": [ + { + "bbox": [ + 115, + 80, + 493, + 166 + ], + "score": 0.966, + "type": "image", + "image_path": "38d9e8ba0505f1fcda3e8c36c5bd6166024a05cfac64e3433ec793f149d35e0d.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 115, + 80, + 493, + 108.66666666666667 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 115, + 108.66666666666667, + 493, + 137.33333333333334 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 115, + 137.33333333333334, + 493, + 166.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 175, + 506, + 241 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 175, + 506, + 187 + ], + "spans": [ + { + "bbox": [ + 105, + 175, + 506, + 187 + ], + "score": 1.0, + "content": "Figure 2: Evaluation of our algorithm on a toy umaze environment (a). When the static dataset", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 185, + 506, + 199 + ], + "spans": [ + { + "bbox": [ + 105, + 185, + 506, + 199 + ], + "score": 1.0, + "content": "is heavily corrupted by suboptimal actions, one-step policy evaluation results in a value function", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 196, + 506, + 210 + ], + "spans": [ + { + "bbox": [ + 105, + 196, + 506, + 210 + ], + "score": 1.0, + "content": "that degrades to zero far from the rewarding states too quickly (c). Our algorithm aims to learn", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 208, + 506, + 220 + ], + "spans": [ + { + "bbox": [ + 105, + 208, + 506, + 220 + ], + "score": 1.0, + "content": "a near-optimal value function, combining the best properties of SARSA-style evaluation with the", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 218, + 506, + 232 + ], + "spans": [ + { + "bbox": [ + 105, + 218, + 506, + 232 + ], + "score": 1.0, + "content": "ability to perform multi-step dynamic programming, leading to value functions that are much closer", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 230, + 380, + 243 + ], + "spans": [ + { + "bbox": [ + 105, + 230, + 380, + 243 + ], + "score": 1.0, + "content": "to optimality (shown in (b)) and producing a much better policy (d).", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 5.5 + } + ], + "index": 3.25 + }, + { + "type": "title", + "bbox": [ + 109, + 264, + 277, + 276 + ], + "lines": [ + { + "bbox": [ + 105, + 262, + 279, + 278 + ], + "spans": [ + { + "bbox": [ + 105, + 262, + 279, + 278 + ], + "score": 1.0, + "content": "5 EXPERIMENTAL EVALUATION", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 9 + }, + { + "type": "text", + "bbox": [ + 106, + 279, + 505, + 399 + ], + "lines": [ + { + "bbox": [ + 105, + 279, + 505, + 290 + ], + "spans": [ + { + "bbox": [ + 105, + 279, + 505, + 290 + ], + "score": 1.0, + "content": "Our experiments aim to evaluate our method comparatively, in contrast to prior offline RL meth-", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 290, + 505, + 302 + ], + "spans": [ + { + "bbox": [ + 106, + 290, + 505, + 302 + ], + "score": 1.0, + "content": "ods, and in particular to understand how our approach compares both to single-step methods and", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 104, + 298, + 506, + 315 + ], + "spans": [ + { + "bbox": [ + 104, + 298, + 506, + 315 + ], + "score": 1.0, + "content": "multi-step dynamic programming approaches. We will first demonstrate the benefits of multi-step", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 312, + 505, + 324 + ], + "spans": [ + { + "bbox": [ + 106, + 312, + 505, + 324 + ], + "score": 1.0, + "content": "dynamic programming methods, such as ours, in contrast to single-step methods, showing that on", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 322, + 505, + 335 + ], + "spans": [ + { + "bbox": [ + 105, + 322, + 505, + 335 + ], + "score": 1.0, + "content": "some problems this difference can be extremely large. We will then compare IQL with state-of-the-", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 332, + 505, + 346 + ], + "spans": [ + { + "bbox": [ + 105, + 332, + 328, + 346 + ], + "score": 1.0, + "content": "art single-step and multi-step algorithms on the D4RL", + "type": "text" + }, + { + "bbox": [ + 329, + 333, + 394, + 346 + ], + "score": 0.63, + "content": "\\mathrm { ( F u ~ e t ~ a l . , } \\mathbb { 2 0 2 0 } )", + "type": "inline_equation" + }, + { + "bbox": [ + 394, + 332, + 505, + 346 + ], + "score": 1.0, + "content": "benchmark tasks, studying", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 344, + 505, + 357 + ], + "spans": [ + { + "bbox": [ + 106, + 344, + 505, + 357 + ], + "score": 1.0, + "content": "the degree to which we can learn effective policies using only the actions in the dataset. We examine", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 356, + 505, + 368 + ], + "spans": [ + { + "bbox": [ + 106, + 356, + 505, + 368 + ], + "score": 1.0, + "content": "domains that contain near-optimal trajectories, where single-step methods perform well, as well as", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 365, + 505, + 380 + ], + "spans": [ + { + "bbox": [ + 105, + 365, + 505, + 380 + ], + "score": 1.0, + "content": "domains with no optimal trajectories at all, which require multi-step dynamic programming. Finally,", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 377, + 506, + 391 + ], + "spans": [ + { + "bbox": [ + 105, + 377, + 506, + 391 + ], + "score": 1.0, + "content": "we will study how IQL compares to prior methods when finetuning with online RL starting from an", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 388, + 205, + 399 + ], + "spans": [ + { + "bbox": [ + 106, + 388, + 205, + 399 + ], + "score": 1.0, + "content": "offline RL initialization.", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 15, + "bbox_fs": [ + 104, + 279, + 506, + 399 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 409, + 444, + 421 + ], + "lines": [ + { + "bbox": [ + 105, + 408, + 444, + 423 + ], + "spans": [ + { + "bbox": [ + 105, + 408, + 444, + 423 + ], + "score": 1.0, + "content": "5.1 THE DIFFERENCE BETWEEN ONE-STEP POLICY IMPROVEMENT AND IQL", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 21 + }, + { + "type": "text", + "bbox": [ + 107, + 425, + 505, + 491 + ], + "lines": [ + { + "bbox": [ + 106, + 424, + 505, + 438 + ], + "spans": [ + { + "bbox": [ + 106, + 424, + 505, + 438 + ], + "score": 1.0, + "content": "We first use a simple maze environment to illustrate the importance of multi-step dynamic program-", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 436, + 500, + 449 + ], + "spans": [ + { + "bbox": [ + 105, + 436, + 500, + 449 + ], + "score": 1.0, + "content": "ming for offline RL. The maze has a u-shape, a single start state, and a single goal state (see Fig. 2a)", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 447, + 505, + 460 + ], + "spans": [ + { + "bbox": [ + 106, + 447, + 505, + 460 + ], + "score": 1.0, + "content": "The agent receives a reward of 10 for entering the goal state and zero reward for all other transitions.", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 458, + 505, + 470 + ], + "spans": [ + { + "bbox": [ + 105, + 458, + 505, + 470 + ], + "score": 1.0, + "content": "With a probability of 0.25, the agent transitions to a random state, and otherwise to the commanded", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 470, + 504, + 481 + ], + "spans": [ + { + "bbox": [ + 106, + 470, + 504, + 481 + ], + "score": 1.0, + "content": "state. The dataset consists of 1 optimal trajectory and 99 trajectories with uniform random actions.", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 480, + 329, + 492 + ], + "spans": [ + { + "bbox": [ + 105, + 480, + 291, + 492 + ], + "score": 1.0, + "content": "Due to a short horizon of the problem, we use", + "type": "text" + }, + { + "bbox": [ + 291, + 480, + 325, + 492 + ], + "score": 0.91, + "content": "\\gamma = 0 . 9", + "type": "inline_equation" + }, + { + "bbox": [ + 325, + 480, + 329, + 492 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 24.5, + "bbox_fs": [ + 105, + 424, + 505, + 492 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 497, + 505, + 585 + ], + "lines": [ + { + "bbox": [ + 106, + 496, + 505, + 510 + ], + "spans": [ + { + "bbox": [ + 106, + 496, + 123, + 509 + ], + "score": 1.0, + "content": "Fig.", + "type": "text" + }, + { + "bbox": [ + 124, + 496, + 133, + 510 + ], + "score": 0.27, + "content": "2", + "type": "inline_equation" + }, + { + "bbox": [ + 134, + 496, + 414, + 509 + ], + "score": 1.0, + "content": "(c, d) illustrates the difference between single-step methods which fit", + "type": "text" + }, + { + "bbox": [ + 414, + 497, + 450, + 508 + ], + "score": 0.91, + "content": "Q ^ { \\pi } ( s , a )", + "type": "inline_equation" + }, + { + "bbox": [ + 451, + 496, + 505, + 509 + ], + "score": 1.0, + "content": "via SARSA-", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 508, + 502, + 520 + ], + "spans": [ + { + "bbox": [ + 106, + 508, + 427, + 520 + ], + "score": 1.0, + "content": "style objective, in this case represented by Onepstep RL (Brandfonbrener et al.,", + "type": "text" + }, + { + "bbox": [ + 428, + 508, + 453, + 520 + ], + "score": 0.34, + "content": "\\boxed { 2 0 2 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 453, + 508, + 502, + 520 + ], + "score": 1.0, + "content": "Wang et al.,", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 518, + 505, + 531 + ], + "spans": [ + { + "bbox": [ + 105, + 518, + 131, + 531 + ], + "score": 0.27, + "content": "\\dot { \\boxed { 2 0 1 8 } } ;", + "type": "inline_equation" + }, + { + "bbox": [ + 131, + 519, + 272, + 531 + ], + "score": 1.0, + "content": "Gulcehre et al., 2021) and IQL with", + "type": "text" + }, + { + "bbox": [ + 273, + 519, + 310, + 529 + ], + "score": 0.89, + "content": "\\tau = 0 . 9 5", + "type": "inline_equation" + }, + { + "bbox": [ + 311, + 519, + 505, + 531 + ], + "score": 1.0, + "content": ". Note that these methods represent a special case", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 530, + 505, + 542 + ], + "spans": [ + { + "bbox": [ + 106, + 530, + 187, + 542 + ], + "score": 1.0, + "content": "of our method with", + "type": "text" + }, + { + "bbox": [ + 187, + 531, + 222, + 540 + ], + "score": 0.87, + "content": "\\bar { \\tau } = 0 . 5", + "type": "inline_equation" + }, + { + "bbox": [ + 223, + 530, + 505, + 542 + ], + "score": 1.0, + "content": ". Although states closer to the high reward state will still have higher", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 541, + 505, + 552 + ], + "spans": [ + { + "bbox": [ + 106, + 541, + 505, + 552 + ], + "score": 1.0, + "content": "values, these values decay much faster as we move further away than they would for the optimal", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 552, + 505, + 564 + ], + "spans": [ + { + "bbox": [ + 106, + 552, + 505, + 564 + ], + "score": 1.0, + "content": "value function, and the resulting policy is highly suboptimal. Since IQL (d) performs iterative", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 563, + 506, + 575 + ], + "spans": [ + { + "bbox": [ + 105, + 563, + 506, + 575 + ], + "score": 1.0, + "content": "dynamic programming, it correctly propagates the signal, and the values are no longer dominated", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 573, + 468, + 586 + ], + "spans": [ + { + "bbox": [ + 105, + 573, + 468, + 586 + ], + "score": 1.0, + "content": "by noise. The resulting value function closely matches the true optimal value function (b).", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 31.5, + "bbox_fs": [ + 105, + 496, + 506, + 586 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 595, + 329, + 606 + ], + "lines": [ + { + "bbox": [ + 105, + 594, + 330, + 608 + ], + "spans": [ + { + "bbox": [ + 105, + 594, + 330, + 608 + ], + "score": 1.0, + "content": "5.2 COMPARISONS ON OFFLINE RL BENCHMARKS", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 36 + }, + { + "type": "text", + "bbox": [ + 106, + 611, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 611, + 505, + 623 + ], + "spans": [ + { + "bbox": [ + 106, + 611, + 505, + 623 + ], + "score": 1.0, + "content": "Next, we evaluate our approach on the D4RL benchmark in comparison to prior methods (see Ta-", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 619, + 506, + 636 + ], + "spans": [ + { + "bbox": [ + 106, + 619, + 120, + 636 + ], + "score": 1.0, + "content": "ble", + "type": "text" + }, + { + "bbox": [ + 121, + 622, + 132, + 635 + ], + "score": 0.47, + "content": "\\bigstar \\bigstar \\bigstar \\bigstar", + "type": "inline_equation" + }, + { + "bbox": [ + 132, + 619, + 506, + 636 + ], + "score": 1.0, + "content": ". The MuJoCo tasks in D4RL consist of the Gym locomotion tasks, the Ant Maze tasks,", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 632, + 505, + 646 + ], + "spans": [ + { + "bbox": [ + 105, + 632, + 505, + 646 + ], + "score": 1.0, + "content": "and the Adroit and Kitchen robotic manipulation environments. Some prior works, particularly", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 644, + 505, + 656 + ], + "spans": [ + { + "bbox": [ + 106, + 644, + 505, + 656 + ], + "score": 1.0, + "content": "those proposing one-step methods, focus entirely on the Gym locomotion tasks. However, these", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 655, + 506, + 667 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 506, + 667 + ], + "score": 1.0, + "content": "tasks include a significant fraction of near-optimal trajectories in the dataset. In contrast, the Ant", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 665, + 506, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 506, + 678 + ], + "score": 1.0, + "content": "Maze tasks, especially the medium and large ones, contain very few or no near-optimal trajectories,", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 677, + 506, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 506, + 689 + ], + "score": 1.0, + "content": "making them very challenging for one-step methods. These domains require “stitching” parts of", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 687, + 506, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 506, + 700 + ], + "score": 1.0, + "content": "suboptimal trajectories that travel between different states to find a path from the start to the goal of", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 698, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 698, + 145, + 711 + ], + "score": 1.0, + "content": "the maze", + "type": "text" + }, + { + "bbox": [ + 146, + 698, + 211, + 711 + ], + "score": 0.82, + "content": "\\mathtt { ( F u ~ e t ~ a l . } ] \\mathtt { ( E 0 2 0 ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 211, + 698, + 505, + 711 + ], + "score": 1.0, + "content": ". As we will show, multi-step dynamic programming is essential in these", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 709, + 506, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 506, + 722 + ], + "score": 1.0, + "content": "domains. The Adroit and Kitchen tasks are comparatively less discriminating, and we found that", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 721, + 501, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 501, + 733 + ], + "score": 1.0, + "content": "most RL methods perform similarly to imitation learning in these domains (Florence et al., 2021)", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 42, + "bbox_fs": [ + 105, + 611, + 506, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 106, + 122, + 524, + 295 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 106, + 80, + 523, + 113 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 79, + 523, + 93 + ], + "spans": [ + { + "bbox": [ + 105, + 79, + 523, + 93 + ], + "score": 1.0, + "content": "Table 1: Averaged normalized scores on MuJoCo locomotion and Ant Maze tasks. Our method outper-", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 92, + 523, + 104 + ], + "spans": [ + { + "bbox": [ + 106, + 92, + 523, + 104 + ], + "score": 1.0, + "content": "forms prior methods on the challenging Ant Maze tasks, which require dynamic programming, and is", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 103, + 367, + 114 + ], + "spans": [ + { + "bbox": [ + 105, + 103, + 367, + 114 + ], + "score": 1.0, + "content": "competitive with the best prior methods on the locomotion tasks.", + "type": "text" + } + ], + "index": 2 + } + ], + "index": 1 + }, + { + "type": "table_body", + "bbox": [ + 106, + 122, + 524, + 295 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 122, + 524, + 295 + ], + "spans": [ + { + "bbox": [ + 106, + 122, + 524, + 295 + ], + "score": 0.984, + "html": "
DatasetBC10%BCBCQDTABMAWACOnestep RLTD3+BCCQLIQL (Ours)
halfcheetah-m-v242.642.547.042.6±0.153.643.548.4±0.148.3±0.344.0±5.447.4±0.2
hopper-m-v252.956.956.767.6±1.00.757.059.6±2.559.3±4.258.5±2.166.2±5.7
walker2d-m-v275.375.072.674.0±1.40.572.481.8±2.283.7±2.172.5±0.878.3±8.7
halfcheetah-m-r-v236.640.640.436.6±0.850.540.538.1±1.344.6±0.545.5±0.544.2±1.2
hopper-m-r-v218.175.953.382.7±7.049.637.297.5±0.760.9±18.895.0±6.494.7±8.6
walker2d-m-r-v226.062.552.166.6±3.053.827.049.5±12.081.8±5.577.2±5.573.8±7.1
halfcheetah-m-e-v255.292.989.186.8±1.318.542.893.4±1.690.7±4.391.6±2.886.7±5.3
hopper-m-e-v252.5110.981.8107.6±1.80.755.8103.3±1.998.0±9.4105.4±6.891.5±14.3
walker2d-m-e-v2107.5109.0109.5108.1±0.23.574.5113.0±0.4110.1±0.5108.8±0.7109.6±1.0
locomotion-v2 total466.7666.2602.5672.6±16.6231.4450.7684.6±22.7677.4±44.5698.5±31.0692.4±52.1
antmaze-u-v054.662.889.859.259.956.764.378.674.087.5±2.6
antmaze-u-d-v045.650.283.053.048.749.360.771.484.062.2 ±13.8
antmaze-m-p-v00.05.415.00.00.00.00.310.661.271.2 ± 7.3
antmaze-m-d-v00.09.80.00.00.50.70.03.053.770.0±10.9
antmaze-l-p-v0 antmaze-l-d-v00.0 0.00.0 6.00.00.00.0.00.00.215.839.6±5.8
antmaze-vO total100.2134.20.0 187.80.00.01.00.00.014.947.5±9.5
112.2109.1107.7125.3163.8303.6378.0±49.9
total566.9800.4790.3784.8340.5558.4809.9841.21002.11070.4±102.0
kitchen-v0 total adroit-vO total154.5 104.5-------144.6159.8±22.6
：=--=--93.6118.1±30.7
total+kitchen+adroit825.9-------1240.31348.3±155.3
runtime10m10m960m20m20m*20m80m20m
", + "type": "table", + "image_path": "bb09557cf0cbff7d1dcd4a1b20f72d15f5f16db0fc8c59692121e513818de2cc.jpg" + } + ] + } + ], + "index": 4, + "virtual_lines": [ + { + "bbox": [ + 106, + 122, + 524, + 179.66666666666666 + ], + "spans": [], + "index": 3 + }, + { + "bbox": [ + 106, + 179.66666666666666, + 524, + 237.33333333333331 + ], + "spans": [], + "index": 4 + }, + { + "bbox": [ + 106, + 237.33333333333331, + 524, + 295.0 + ], + "spans": [], + "index": 5 + } + ] + }, + { + "type": "table_footnote", + "bbox": [ + 105, + 296, + 523, + 311 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 292, + 522, + 307 + ], + "spans": [ + { + "bbox": [ + 106, + 292, + 369, + 307 + ], + "score": 1.0, + "content": "⇤: Note that it is challenging to compare one-step and multi-step methods directly. Also, Brandfonbrener et al.", + "type": "text" + }, + { + "bbox": [ + 369, + 295, + 387, + 304 + ], + "score": 0.26, + "content": "\\boxed { ( 2 0 2 1 ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 387, + 292, + 522, + 307 + ], + "score": 1.0, + "content": "reports results for a set of hyperparameters, such as batch", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 303, + 520, + 311 + ], + "spans": [ + { + "bbox": [ + 106, + 303, + 520, + 311 + ], + "score": 1.0, + "content": "and network size, that is significantly different from other methods. We report results for the original hyperparameters and runtime for a comparable set of hyperparameters.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 6.5 + } + ], + "index": 4 + }, + { + "type": "text", + "bbox": [ + 105, + 332, + 504, + 355 + ], + "lines": [ + { + "bbox": [ + 106, + 331, + 505, + 344 + ], + "spans": [ + { + "bbox": [ + 106, + 331, + 505, + 344 + ], + "score": 1.0, + "content": "We therefore focus our analysis on the Gym locomotion and Ant Maze domains, but include full", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 343, + 348, + 356 + ], + "spans": [ + { + "bbox": [ + 106, + 343, + 348, + 356 + ], + "score": 1.0, + "content": "Adroit and Kitchen results in Appendix B for completeness.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 8.5 + }, + { + "type": "text", + "bbox": [ + 107, + 357, + 296, + 598 + ], + "lines": [ + { + "bbox": [ + 107, + 357, + 297, + 369 + ], + "spans": [ + { + "bbox": [ + 107, + 357, + 297, + 369 + ], + "score": 1.0, + "content": "Comparisons and baselines. We compare to", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 368, + 296, + 379 + ], + "spans": [ + { + "bbox": [ + 106, + 368, + 296, + 379 + ], + "score": 1.0, + "content": "methods that are representative of both multi-", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 379, + 296, + 391 + ], + "spans": [ + { + "bbox": [ + 106, + 379, + 296, + 391 + ], + "score": 1.0, + "content": "step dynamic programming and one-step ap-", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 390, + 298, + 402 + ], + "spans": [ + { + "bbox": [ + 105, + 390, + 298, + 402 + ], + "score": 1.0, + "content": "proaches. In the former category, we compare", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 400, + 298, + 414 + ], + "spans": [ + { + "bbox": [ + 105, + 400, + 235, + 414 + ], + "score": 1.0, + "content": "to CQL (Kumar et al., 2020),", + "type": "text" + }, + { + "bbox": [ + 236, + 401, + 275, + 411 + ], + "score": 0.78, + "content": "\\mathrm { T D } 3 { + } \\mathrm { B C }", + "type": "inline_equation" + }, + { + "bbox": [ + 275, + 400, + 298, + 414 + ], + "score": 1.0, + "content": "(Fu-", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 411, + 295, + 424 + ], + "spans": [ + { + "bbox": [ + 106, + 411, + 295, + 424 + ], + "score": 1.0, + "content": "jimoto & Gu, 2021), and AWAC (Nair et al.,", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 423, + 297, + 435 + ], + "spans": [ + { + "bbox": [ + 106, + 423, + 136, + 435 + ], + "score": 1.0, + "content": "2020).", + "type": "text" + }, + { + "bbox": [ + 141, + 423, + 297, + 435 + ], + "score": 1.0, + "content": "In the latter category, we compare", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 433, + 296, + 446 + ], + "spans": [ + { + "bbox": [ + 105, + 433, + 296, + 446 + ], + "score": 1.0, + "content": "to Onestep RL (Brandfonbrener et al., 2021)", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 444, + 295, + 457 + ], + "spans": [ + { + "bbox": [ + 106, + 444, + 295, + 457 + ], + "score": 1.0, + "content": "and Decision Transformers (Chen et al., 2021).", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 456, + 297, + 466 + ], + "spans": [ + { + "bbox": [ + 106, + 456, + 297, + 466 + ], + "score": 1.0, + "content": "We obtained the Decision Transformers results", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 466, + 297, + 478 + ], + "spans": [ + { + "bbox": [ + 105, + 466, + 297, + 478 + ], + "score": 1.0, + "content": "on Ant Maze subsets of D4RL tasks using", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 477, + 297, + 489 + ], + "spans": [ + { + "bbox": [ + 106, + 477, + 297, + 489 + ], + "score": 1.0, + "content": "the author-provided implementation2 and fol-", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 489, + 298, + 500 + ], + "spans": [ + { + "bbox": [ + 106, + 489, + 298, + 500 + ], + "score": 1.0, + "content": "lowing authors instructions communicated over", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 500, + 297, + 510 + ], + "spans": [ + { + "bbox": [ + 106, + 500, + 239, + 510 + ], + "score": 1.0, + "content": "email. We obtained results for", + "type": "text" + }, + { + "bbox": [ + 239, + 500, + 279, + 510 + ], + "score": 0.86, + "content": "\\mathrm { T D } 3 { + } \\mathrm { B C }", + "type": "inline_equation" + }, + { + "bbox": [ + 279, + 500, + 297, + 510 + ], + "score": 1.0, + "content": "and", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 107, + 511, + 297, + 521 + ], + "spans": [ + { + "bbox": [ + 107, + 511, + 297, + 521 + ], + "score": 1.0, + "content": "Onestep RL (Exp. Weight) directly from the au-", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 521, + 297, + 533 + ], + "spans": [ + { + "bbox": [ + 106, + 521, + 297, + 533 + ], + "score": 1.0, + "content": "thors. Note that Chen et al. (2021) and Brand-", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 532, + 298, + 545 + ], + "spans": [ + { + "bbox": [ + 106, + 532, + 169, + 545 + ], + "score": 1.0, + "content": "fonbrener et al.", + "type": "text" + }, + { + "bbox": [ + 169, + 532, + 196, + 545 + ], + "score": 0.73, + "content": "\\textcircled { 2 0 2 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 196, + 532, + 298, + 545 + ], + "score": 1.0, + "content": "incorrectly report results", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 543, + 297, + 555 + ], + "spans": [ + { + "bbox": [ + 106, + 543, + 297, + 555 + ], + "score": 1.0, + "content": "for some prior methods, such as CQL, using the", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 552, + 298, + 568 + ], + "spans": [ + { + "bbox": [ + 105, + 552, + 298, + 568 + ], + "score": 1.0, + "content": "“-v0” environments. These generally produce", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 565, + 297, + 576 + ], + "spans": [ + { + "bbox": [ + 106, + 565, + 297, + 576 + ], + "score": 1.0, + "content": "lower scores than the “-v2” environments that", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 577, + 297, + 588 + ], + "spans": [ + { + "bbox": [ + 106, + 577, + 297, + 588 + ], + "score": 1.0, + "content": "these papers use for their own methods. 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DatasetBC10%BCBCQDTABMAWACOnestep RLTD3+BCCQLIQL (Ours)
halfcheetah-m-v242.642.547.042.6±0.153.643.548.4±0.148.3±0.344.0±5.447.4±0.2
hopper-m-v252.956.956.767.6±1.00.757.059.6±2.559.3±4.258.5±2.166.2±5.7
walker2d-m-v275.375.072.674.0±1.40.572.481.8±2.283.7±2.172.5±0.878.3±8.7
halfcheetah-m-r-v236.640.640.436.6±0.850.540.538.1±1.344.6±0.545.5±0.544.2±1.2
hopper-m-r-v218.175.953.382.7±7.049.637.297.5±0.760.9±18.895.0±6.494.7±8.6
walker2d-m-r-v226.062.552.166.6±3.053.827.049.5±12.081.8±5.577.2±5.573.8±7.1
halfcheetah-m-e-v255.292.989.186.8±1.318.542.893.4±1.690.7±4.391.6±2.886.7±5.3
hopper-m-e-v252.5110.981.8107.6±1.80.755.8103.3±1.998.0±9.4105.4±6.891.5±14.3
walker2d-m-e-v2107.5109.0109.5108.1±0.23.574.5113.0±0.4110.1±0.5108.8±0.7109.6±1.0
locomotion-v2 total466.7666.2602.5672.6±16.6231.4450.7684.6±22.7677.4±44.5698.5±31.0692.4±52.1
antmaze-u-v054.662.889.859.259.956.764.378.674.087.5±2.6
antmaze-u-d-v045.650.283.053.048.749.360.771.484.062.2 ±13.8
antmaze-m-p-v00.05.415.00.00.00.00.310.661.271.2 ± 7.3
antmaze-m-d-v00.09.80.00.00.50.70.03.053.770.0±10.9
antmaze-l-p-v0 antmaze-l-d-v00.0 0.00.0 6.00.00.00.0.00.00.215.839.6±5.8
antmaze-vO total100.2134.20.0 187.80.00.01.00.00.014.947.5±9.5
112.2109.1107.7125.3163.8303.6378.0±49.9
total566.9800.4790.3784.8340.5558.4809.9841.21002.11070.4±102.0
kitchen-v0 total adroit-vO total154.5 104.5-------144.6159.8±22.6
：=--=--93.6118.1±30.7
total+kitchen+adroit825.9-------1240.31348.3±155.3
runtime10m10m960m20m20m*20m80m20m
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We report results for the original hyperparameters and runtime for a comparable set of hyperparameters.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 6.5 + } + ], + "index": 4 + }, + { + "type": "text", + "bbox": [ + 105, + 332, + 504, + 355 + ], + "lines": [ + { + "bbox": [ + 106, + 331, + 505, + 344 + ], + "spans": [ + { + "bbox": [ + 106, + 331, + 505, + 344 + ], + "score": 1.0, + "content": "We therefore focus our analysis on the Gym locomotion and Ant Maze domains, but include full", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 343, + 348, + 356 + ], + "spans": [ + { + "bbox": [ + 106, + 343, + 348, + 356 + ], + "score": 1.0, + "content": "Adroit and Kitchen results in Appendix B for completeness.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 8.5, + "bbox_fs": [ + 106, + 331, + 505, + 356 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 357, + 296, + 598 + ], + "lines": [ + { + "bbox": [ + 107, + 357, + 297, + 369 + ], + "spans": [ + { + "bbox": [ + 107, + 357, + 297, + 369 + ], + "score": 1.0, + "content": "Comparisons and baselines. We compare to", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 368, + 296, + 379 + ], + "spans": [ + { + "bbox": [ + 106, + 368, + 296, + 379 + ], + "score": 1.0, + "content": "methods that are representative of both multi-", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 379, + 296, + 391 + ], + "spans": [ + { + "bbox": [ + 106, + 379, + 296, + 391 + ], + "score": 1.0, + "content": "step dynamic programming and one-step ap-", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 390, + 298, + 402 + ], + "spans": [ + { + "bbox": [ + 105, + 390, + 298, + 402 + ], + "score": 1.0, + "content": "proaches. In the former category, we compare", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 400, + 298, + 414 + ], + "spans": [ + { + "bbox": [ + 105, + 400, + 235, + 414 + ], + "score": 1.0, + "content": "to CQL (Kumar et al., 2020),", + "type": "text" + }, + { + "bbox": [ + 236, + 401, + 275, + 411 + ], + "score": 0.78, + "content": "\\mathrm { T D } 3 { + } \\mathrm { B C }", + "type": "inline_equation" + }, + { + "bbox": [ + 275, + 400, + 298, + 414 + ], + "score": 1.0, + "content": "(Fu-", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 411, + 295, + 424 + ], + "spans": [ + { + "bbox": [ + 106, + 411, + 295, + 424 + ], + "score": 1.0, + "content": "jimoto & Gu, 2021), and AWAC (Nair et al.,", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 423, + 297, + 435 + ], + "spans": [ + { + "bbox": [ + 106, + 423, + 136, + 435 + ], + "score": 1.0, + "content": "2020).", + "type": "text" + }, + { + "bbox": [ + 141, + 423, + 297, + 435 + ], + "score": 1.0, + "content": "In the latter category, we compare", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 433, + 296, + 446 + ], + "spans": [ + { + "bbox": [ + 105, + 433, + 296, + 446 + ], + "score": 1.0, + "content": "to Onestep RL (Brandfonbrener et al., 2021)", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 444, + 295, + 457 + ], + "spans": [ + { + "bbox": [ + 106, + 444, + 295, + 457 + ], + "score": 1.0, + "content": "and Decision Transformers (Chen et al., 2021).", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 456, + 297, + 466 + ], + "spans": [ + { + "bbox": [ + 106, + 456, + 297, + 466 + ], + "score": 1.0, + "content": "We obtained the Decision Transformers results", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 466, + 297, + 478 + ], + "spans": [ + { + "bbox": [ + 105, + 466, + 297, + 478 + ], + "score": 1.0, + "content": "on Ant Maze subsets of D4RL tasks using", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 477, + 297, + 489 + ], + "spans": [ + { + "bbox": [ + 106, + 477, + 297, + 489 + ], + "score": 1.0, + "content": "the author-provided implementation2 and fol-", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 489, + 298, + 500 + ], + "spans": [ + { + "bbox": [ + 106, + 489, + 298, + 500 + ], + "score": 1.0, + "content": "lowing authors instructions communicated over", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 500, + 297, + 510 + ], + "spans": [ + { + "bbox": [ + 106, + 500, + 239, + 510 + ], + "score": 1.0, + "content": "email. We obtained results for", + "type": "text" + }, + { + "bbox": [ + 239, + 500, + 279, + 510 + ], + "score": 0.86, + "content": "\\mathrm { T D } 3 { + } \\mathrm { B C }", + "type": "inline_equation" + }, + { + "bbox": [ + 279, + 500, + 297, + 510 + ], + "score": 1.0, + "content": "and", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 107, + 511, + 297, + 521 + ], + "spans": [ + { + "bbox": [ + 107, + 511, + 297, + 521 + ], + "score": 1.0, + "content": "Onestep RL (Exp. Weight) directly from the au-", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 521, + 297, + 533 + ], + "spans": [ + { + "bbox": [ + 106, + 521, + 297, + 533 + ], + "score": 1.0, + "content": "thors. Note that Chen et al. 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These generally produce", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 565, + 297, + 576 + ], + "spans": [ + { + "bbox": [ + 106, + 565, + 297, + 576 + ], + "score": 1.0, + "content": "lower scores than the “-v2” environments that", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 577, + 297, + 588 + ], + "spans": [ + { + "bbox": [ + 106, + 577, + 297, + 588 + ], + "score": 1.0, + "content": "these papers use for their own methods. 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Because of this fix, our reported CQL", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 608, + 506, + 622 + ], + "spans": [ + { + "bbox": [ + 105, + 608, + 406, + 622 + ], + "score": 1.0, + "content": "scores are higher than all other prior methods. We obtained results for", + "type": "text" + }, + { + "bbox": [ + 406, + 609, + 430, + 620 + ], + "score": 0.31, + "content": "\\mathbf { \\tilde { \\mu } } ^ { 6 6 } \\mathbf { - v } 2 \\mathbf { \\ w } ^ { 5 }", + "type": "inline_equation" + }, + { + "bbox": [ + 431, + 608, + 506, + 622 + ], + "score": 1.0, + "content": "datasets using an", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 105, + 618, + 505, + 633 + ], + "spans": [ + { + "bbox": [ + 105, + 618, + 505, + 633 + ], + "score": 1.0, + "content": "author-suggested implementation.3 On the Gym locomotion tasks (halfcheetah, hopper, walker2d),", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 105, + 631, + 505, + 644 + ], + "spans": [ + { + "bbox": [ + 105, + 631, + 505, + 644 + ], + "score": 1.0, + "content": "we find that IQL performs comparably to the best performing prior method, CQL. On the more", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 104, + 640, + 505, + 655 + ], + "spans": [ + { + "bbox": [ + 104, + 640, + 505, + 655 + ], + "score": 1.0, + "content": "challenging Ant Maze task, IQL outperforms CQL, and outperforms the one-step methods by a very", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 105, + 653, + 162, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 653, + 162, + 667 + ], + "score": 1.0, + "content": "large margin.", + "type": "text" + } + ], + "index": 53 + } + ], + "index": 50.5, + "bbox_fs": [ + 104, + 597, + 506, + 667 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 667, + 505, + 701 + ], + "lines": [ + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "score": 1.0, + "content": "Runtime. Our approach is also computationally faster than the baselines (see Table 1). For the", + "type": "text" + } + ], + "index": 54 + }, + { + "bbox": [ + 105, + 676, + 504, + 691 + ], + "spans": [ + { + "bbox": [ + 105, + 676, + 504, + 691 + ], + "score": 1.0, + "content": "baselines, we measure runtime for our reimplementations of the methods in JAX (Bradbury et al.,", + "type": "text" + } + ], + "index": 55 + }, + { + "bbox": [ + 105, + 689, + 504, + 702 + ], + "spans": [ + { + "bbox": [ + 105, + 689, + 299, + 702 + ], + "score": 1.0, + "content": "2018) built on top of JAXRL (Kostrikov, 2021),", + "type": "text" + }, + { + "bbox": [ + 299, + 689, + 504, + 701 + ], + "score": 1.0, + "content": "which are typically faster than the original imple-", + "type": "text" + } + ], + "index": 56 + }, + { + "bbox": [ + 106, + 83, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 83, + 505, + 95 + ], + "score": 1.0, + "content": "mentations. For example, the original implementation of CQL takes more than 4 hours to perform", + "type": "text", + "cross_page": true + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 93, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 106, + 93, + 433, + 106 + ], + "score": 1.0, + "content": "1M updates, while ours takes only 80 minutes. Even so, IQL still requires about", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 434, + 94, + 446, + 104 + ], + "score": 0.51, + "content": "4 \\mathbf { x }", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 446, + 93, + 505, + 106 + ], + "score": 1.0, + "content": "less time than", + "type": "text", + "cross_page": true + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 104, + 505, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 104, + 505, + 118 + ], + "score": 1.0, + "content": "our reimplementation of CQL on average, and is comparable to the fastest prior one-step methods.", + "type": "text", + "cross_page": true + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 114, + 505, + 128 + ], + "spans": [ + { + "bbox": [ + 105, + 114, + 505, + 128 + ], + "score": 1.0, + "content": "We did not reimplement Decision Transformers due to their complexity and report runtime of the", + "type": "text", + "cross_page": true + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 127, + 207, + 139 + ], + "spans": [ + { + "bbox": [ + 106, + 127, + 207, + 139 + ], + "score": 1.0, + "content": "original implementation.", + "type": "text", + "cross_page": true + } + ], + "index": 4 + } + ], + "index": 55, + "bbox_fs": [ + 105, + 666, + 505, + 702 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 505, + 138 + ], + "lines": [ + { + "bbox": [ + 106, + 83, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 83, + 505, + 95 + ], + "score": 1.0, + "content": "mentations. For example, the original implementation of CQL takes more than 4 hours to perform", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 93, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 106, + 93, + 433, + 106 + ], + "score": 1.0, + "content": "1M updates, while ours takes only 80 minutes. Even so, IQL still requires about", + "type": "text" + }, + { + "bbox": [ + 434, + 94, + 446, + 104 + ], + "score": 0.51, + "content": "4 \\mathbf { x }", + "type": "inline_equation" + }, + { + "bbox": [ + 446, + 93, + 505, + 106 + ], + "score": 1.0, + "content": "less time than", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 104, + 505, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 104, + 505, + 118 + ], + "score": 1.0, + "content": "our reimplementation of CQL on average, and is comparable to the fastest prior one-step methods.", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 114, + 505, + 128 + ], + "spans": [ + { + "bbox": [ + 105, + 114, + 505, + 128 + ], + "score": 1.0, + "content": "We did not reimplement Decision Transformers due to their complexity and report runtime of the", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 127, + 207, + 139 + ], + "spans": [ + { + "bbox": [ + 106, + 127, + 207, + 139 + ], + "score": 1.0, + "content": "original implementation.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 2 + }, + { + "type": "text", + "bbox": [ + 107, + 143, + 505, + 209 + ], + "lines": [ + { + "bbox": [ + 106, + 143, + 505, + 154 + ], + "spans": [ + { + "bbox": [ + 106, + 143, + 145, + 154 + ], + "score": 1.0, + "content": "Effect of", + "type": "text" + }, + { + "bbox": [ + 146, + 145, + 153, + 153 + ], + "score": 0.7, + "content": "\\tau", + "type": "inline_equation" + }, + { + "bbox": [ + 153, + 143, + 505, + 154 + ], + "score": 1.0, + "content": "hyperparameter. We also demonstrate that it is crucial to compute a larger expectile", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 153, + 505, + 167 + ], + "spans": [ + { + "bbox": [ + 105, + 153, + 469, + 167 + ], + "score": 1.0, + "content": "on tasks that require “stitching” (see Fig. 3). We provide complete results in Appendix", + "type": "text" + }, + { + "bbox": [ + 467, + 154, + 482, + 166 + ], + "score": 1.0, + "content": "B.", + "type": "text" + }, + { + "bbox": [ + 481, + 154, + 505, + 165 + ], + "score": 1.0, + "content": "With", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 164, + 505, + 176 + ], + "spans": [ + { + "bbox": [ + 106, + 164, + 173, + 176 + ], + "score": 1.0, + "content": "larger values of", + "type": "text" + }, + { + "bbox": [ + 173, + 167, + 180, + 175 + ], + "score": 0.75, + "content": "\\tau", + "type": "inline_equation" + }, + { + "bbox": [ + 181, + 164, + 292, + 176 + ], + "score": 1.0, + "content": ", our method approximates", + "type": "text" + }, + { + "bbox": [ + 293, + 165, + 302, + 176 + ], + "score": 0.84, + "content": "Q", + "type": "inline_equation" + }, + { + "bbox": [ + 302, + 164, + 505, + 176 + ], + "score": 1.0, + "content": "-learning better, leading to better performance on", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 176, + 505, + 188 + ], + "spans": [ + { + "bbox": [ + 105, + 176, + 505, + 188 + ], + "score": 1.0, + "content": "the Ant Maze tasks. 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Finally,", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 198, + 424, + 210 + ], + "spans": [ + { + "bbox": [ + 106, + 198, + 388, + 210 + ], + "score": 1.0, + "content": "clipped double Q-Learning is crucial for estimating values for a larger", + "type": "text" + }, + { + "bbox": [ + 388, + 198, + 421, + 208 + ], + "score": 0.89, + "content": "\\tau = 0 . 9", + "type": "inline_equation" + }, + { + "bbox": [ + 421, + 198, + 424, + 210 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 7.5 + }, + { + "type": "title", + "bbox": [ + 107, + 217, + 312, + 228 + ], + "lines": [ + { + "bbox": [ + 105, + 216, + 313, + 230 + ], + "spans": [ + { + "bbox": [ + 105, + 216, + 313, + 230 + ], + "score": 1.0, + "content": "5.3 ONLINE FINE-TUNING AFTER OFFLINE RL", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 11 + }, + { + "type": "text", + "bbox": [ + 107, + 231, + 237, + 439 + ], + "lines": [ + { + "bbox": [ + 105, + 231, + 237, + 244 + ], + "spans": [ + { + "bbox": [ + 105, + 231, + 237, + 244 + ], + "score": 1.0, + "content": "The policies obtained by offline", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 242, + 238, + 254 + ], + "spans": [ + { + "bbox": [ + 105, + 242, + 238, + 254 + ], + "score": 1.0, + "content": "RL can often be improved with a", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 253, + 237, + 266 + ], + "spans": [ + { + "bbox": [ + 105, + 253, + 237, + 266 + ], + "score": 1.0, + "content": "small amount of online interac-", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 263, + 238, + 277 + ], + "spans": [ + { + "bbox": [ + 105, + 263, + 238, + 277 + ], + "score": 1.0, + "content": "tion. IQL is well-suited for on-", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 275, + 238, + 289 + ], + "spans": [ + { + "bbox": [ + 105, + 275, + 238, + 289 + ], + "score": 1.0, + "content": "line fine-tuning for two reasons.", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 285, + 238, + 299 + ], + "spans": [ + { + "bbox": [ + 105, + 285, + 238, + 299 + ], + "score": 1.0, + "content": "First, IQL has strong offline per-", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 297, + 238, + 310 + ], + "spans": [ + { + "bbox": [ + 105, + 297, + 238, + 310 + ], + "score": 1.0, + "content": "formance, as shown in the pre-", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 309, + 238, + 320 + ], + "spans": [ + { + "bbox": [ + 106, + 309, + 238, + 320 + ], + "score": 1.0, + "content": "vious section, which provides a", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 319, + 238, + 331 + ], + "spans": [ + { + "bbox": [ + 105, + 319, + 238, + 331 + ], + "score": 1.0, + "content": "good initialization. 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DatasetAWACCQLIQL (Ours)
antmaze-umaze-vO antmaze-umaze-diverse-v056.7 →59.0 49.3 →49.070.1 →99.4 31.1 →99.488.0 →96.3 67.0 →49.0
antmaze-medium-play-v00.0 →0.023.0 →0.069.0 →89.2
antmaze-medium-diverse-v00.7 →0.323.0 →32.371.8 →91.4
antmaze-large-play-v00.0 →0.01.0 →0.036.8 →51.8
antmaze-large-diverse-v01.0 →0.01.0 →0.042.2 →59.8
antmaze-vO total107.7 →108.3151.5 →231.1374.8 →437.5
pen-binary-v044.6 →70.331.2 →9.937.4 →60.7
door-binary-v01.3 →30.10.2 →0.00.7 →32.3
relocate-binary-v00.8 →2.70.1 →0.00.0 →31.0
hand-vO total46.7 →103.131.5 →9.938.1 →124.0
total154.4→211.4182.8→241.0412.9561.5
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In all tasks, IQL is able to finetune to a significantly", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 244, + 396, + 506, + 408 + ], + "spans": [ + { + "bbox": [ + 244, + 396, + 506, + 408 + ], + "score": 1.0, + "content": "higher performance than the offline initialization, with final per-", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 244, + 407, + 505, + 418 + ], + "spans": [ + { + "bbox": [ + 244, + 407, + 505, + 418 + ], + "score": 1.0, + "content": "formance that is comparable to or better than the best of either", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 244, + 417, + 446, + 430 + ], + "spans": [ + { + "bbox": [ + 244, + 417, + 446, + 430 + ], + "score": 1.0, + "content": "AWAC or CQL on all tasks except pen-binary-v0.", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 36.5 + }, + { + "type": "text", + "bbox": [ + 106, + 440, + 505, + 561 + ], + "lines": [ + { + "bbox": [ + 106, + 439, + 506, + 452 + ], + "spans": [ + { + "bbox": [ + 106, + 439, + 506, + 452 + ], + "score": 1.0, + "content": "dataset, then run 1M steps of online RL, and then report the final performance. We compare to", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 450, + 506, + 464 + ], + "spans": [ + { + "bbox": [ + 106, + 450, + 181, + 464 + ], + "score": 1.0, + "content": "AWAC (Nair et al.,", + "type": "text" + }, + { + "bbox": [ + 182, + 451, + 207, + 463 + ], + "score": 0.4, + "content": "\\boxed { 2 0 2 0 }", + "type": "inline_equation" + }, + { + "bbox": [ + 207, + 450, + 484, + 464 + ], + "score": 1.0, + "content": ", which has been proposed specifically for online finetuning, and CQL", + "type": "text" + }, + { + "bbox": [ + 484, + 451, + 506, + 464 + ], + "score": 0.63, + "content": "\\underline { { \\mathbb { K u } } } - \\rfloor", + "type": "inline_equation" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 462, + 506, + 474 + ], + "spans": [ + { + "bbox": [ + 106, + 462, + 149, + 474 + ], + "score": 1.0, + "content": "mar et al.,", + "type": "text" + }, + { + "bbox": [ + 149, + 462, + 174, + 474 + ], + "score": 0.64, + "content": "\\overline { { \\boxed { 2 0 2 0 } } }", + "type": "inline_equation" + }, + { + "bbox": [ + 175, + 462, + 506, + 474 + ], + "score": 1.0, + "content": ", which showed the best performance among prior methods in our experiments in", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 104, + 471, + 505, + 487 + ], + "spans": [ + { + "bbox": [ + 104, + 471, + 398, + 487 + ], + "score": 1.0, + "content": "the previous section. Exact experimental details are provided in Appendix", + "type": "text" + }, + { + "bbox": [ + 399, + 472, + 411, + 486 + ], + "score": 0.53, + "content": "\\mathbf { C } .", + "type": "inline_equation" + }, + { + "bbox": [ + 411, + 471, + 505, + 487 + ], + "score": 1.0, + "content": "We use the challenging", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 482, + 505, + 497 + ], + "spans": [ + { + "bbox": [ + 105, + 482, + 212, + 497 + ], + "score": 1.0, + "content": "Ant Maze D4RL domains", + "type": "text" + }, + { + "bbox": [ + 212, + 483, + 277, + 495 + ], + "score": 0.51, + "content": "\\mathtt { ( F u ) e t a l . } \\mathtt { / } 2 0 2 0 \\rVert", + "type": "inline_equation" + }, + { + "bbox": [ + 277, + 482, + 505, + 497 + ], + "score": 1.0, + "content": ", as well as the high-dimensional dexterous manipulation", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 494, + 505, + 508 + ], + "spans": [ + { + "bbox": [ + 106, + 494, + 255, + 508 + ], + "score": 1.0, + "content": "environments from Rajeswaran et al.", + "type": "text" + }, + { + "bbox": [ + 255, + 495, + 282, + 507 + ], + "score": 0.55, + "content": "\\overline { { \\left( \\frac { 2 0 1 8 } { \\it 1 8 } \\right) } }", + "type": "inline_equation" + }, + { + "bbox": [ + 282, + 494, + 355, + 508 + ], + "score": 1.0, + "content": ", which Nair et al.", + "type": "text" + }, + { + "bbox": [ + 356, + 495, + 383, + 507 + ], + "score": 0.76, + "content": "\\underline { { ( 2 0 2 0 ) } }", + "type": "inline_equation" + }, + { + "bbox": [ + 383, + 494, + 505, + 508 + ], + "score": 1.0, + "content": "propose to use to study online", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 506, + 505, + 519 + ], + "spans": [ + { + "bbox": [ + 106, + 506, + 312, + 518 + ], + "score": 1.0, + "content": "adaptation with AWAC. Results are shown in Table", + "type": "text" + }, + { + "bbox": [ + 312, + 506, + 322, + 519 + ], + "score": 0.46, + "content": "\\boxed { 5 }", + "type": "inline_equation" + }, + { + "bbox": [ + 323, + 506, + 505, + 518 + ], + "score": 1.0, + "content": "On the Ant Maze domains, IQL significantly", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 517, + 505, + 528 + ], + "spans": [ + { + "bbox": [ + 106, + 517, + 505, + 528 + ], + "score": 1.0, + "content": "outperforms both prior methods after online finetuning. CQL attains the second best score, while", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 527, + 505, + 540 + ], + "spans": [ + { + "bbox": [ + 105, + 527, + 505, + 540 + ], + "score": 1.0, + "content": "AWAC performs comparatively worse due to much weaker offline initialization. On the dexterous", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 538, + 505, + 551 + ], + "spans": [ + { + "bbox": [ + 105, + 538, + 505, + 551 + ], + "score": 1.0, + "content": "hand tasks, IQL performs significantly better than AWAC on relocate-binary-v0, comparably on", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 106, + 549, + 430, + 562 + ], + "spans": [ + { + "bbox": [ + 106, + 549, + 430, + 562 + ], + "score": 1.0, + "content": "door-binary-v0, and slightly worse on pen-binary-v0, with the best overall score.", + "type": "text" + } + ], + "index": 50 + } + ], + "index": 45 + }, + { + "type": "title", + "bbox": [ + 107, + 572, + 195, + 584 + ], + "lines": [ + { + "bbox": [ + 105, + 569, + 198, + 587 + ], + "spans": [ + { + "bbox": [ + 105, + 569, + 198, + 587 + ], + "score": 1.0, + "content": "6 CONCLUSION", + "type": "text" + } + ], + "index": 51 + } + ], + "index": 51 + }, + { + "type": "text", + "bbox": [ + 106, + 591, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 106, + 590, + 505, + 604 + ], + "spans": [ + { + "bbox": [ + 106, + 590, + 505, + 604 + ], + "score": 1.0, + "content": "We presented implicit Q-Learning (IQL), a general algorithm for offline RL that completely avoids", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 105, + 601, + 504, + 614 + ], + "spans": [ + { + "bbox": [ + 105, + 601, + 504, + 614 + ], + "score": 1.0, + "content": "any queries to values of out-of-sample actions during training while still enabling multi-step dy-", + "type": "text" + } + ], + "index": 53 + }, + { + "bbox": [ + 106, + 613, + 505, + 625 + ], + "spans": [ + { + "bbox": [ + 106, + 613, + 505, + 625 + ], + "score": 1.0, + "content": "namic programming. To our knowledge, this is the first method that combines both of these fea-", + "type": "text" + } + ], + "index": 54 + }, + { + "bbox": [ + 106, + 624, + 505, + 636 + ], + "spans": [ + { + "bbox": [ + 106, + 624, + 505, + 636 + ], + "score": 1.0, + "content": "tures. This has a number of important benefits. First, our algorithm is computationally efficient:", + "type": "text" + } + ], + "index": 55 + }, + { + "bbox": [ + 105, + 635, + 505, + 647 + ], + "spans": [ + { + "bbox": [ + 105, + 635, + 505, + 647 + ], + "score": 1.0, + "content": "we can perform 1M updates on one GTX1080 GPU in less than 20 minutes. 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Finally, despite the simplicity and efficiency of this method, we show that it at-", + "type": "text" + } + ], + "index": 59 + }, + { + "bbox": [ + 106, + 679, + 505, + 691 + ], + "spans": [ + { + "bbox": [ + 106, + 679, + 505, + 691 + ], + "score": 1.0, + "content": "tains excellent performance across all of the tasks in the D4RL benchmark, matching the best prior", + "type": "text" + } + ], + "index": 60 + }, + { + "bbox": [ + 106, + 690, + 505, + 702 + ], + "spans": [ + { + "bbox": [ + 106, + 690, + 505, + 702 + ], + "score": 1.0, + "content": "methods on the MuJoCo locomotion tasks, and exceeding the state-of-the-art performance on the", + "type": "text" + } + ], + "index": 61 + }, + { + "bbox": [ + 105, + 699, + 506, + 713 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 506, + 713 + ], + "score": 1.0, + "content": "challenging ant maze environments, where multi-step dynamic programming is essential for good", + "type": "text" + } + ], + "index": 62 + }, + { + "bbox": [ + 106, + 712, + 162, + 724 + ], + "spans": [ + { + "bbox": [ + 106, + 712, + 162, + 724 + ], + "score": 1.0, + "content": "performance.", + "type": "text" + } + ], + "index": 63 + } + ], + "index": 57.5 + } + ], + "page_idx": 8, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2022", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 308, + 759 + ], + "lines": [ + { + "bbox": [ + 302, + 751, + 309, + 762 + ], + "spans": [ + { + "bbox": [ + 302, + 751, + 309, + 762 + ], + "score": 1.0, + "content": "9", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 505, + 138 + ], + "lines": [], + "index": 2, + "bbox_fs": [ + 105, + 83, + 505, + 139 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 107, + 143, + 505, + 209 + ], + "lines": [ + { + "bbox": [ + 106, + 143, + 505, + 154 + ], + "spans": [ + { + "bbox": [ + 106, + 143, + 145, + 154 + ], + "score": 1.0, + "content": "Effect of", + "type": "text" + }, + { + "bbox": [ + 146, + 145, + 153, + 153 + ], + "score": 0.7, + "content": "\\tau", + "type": "inline_equation" + }, + { + "bbox": [ + 153, + 143, + 505, + 154 + ], + "score": 1.0, + "content": "hyperparameter. We also demonstrate that it is crucial to compute a larger expectile", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 153, + 505, + 167 + ], + "spans": [ + { + "bbox": [ + 105, + 153, + 469, + 167 + ], + "score": 1.0, + "content": "on tasks that require “stitching” (see Fig. 3). 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IQL is well-suited for on-", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 275, + 238, + 289 + ], + "spans": [ + { + "bbox": [ + 105, + 275, + 238, + 289 + ], + "score": 1.0, + "content": "line fine-tuning for two reasons.", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 285, + 238, + 299 + ], + "spans": [ + { + "bbox": [ + 105, + 285, + 238, + 299 + ], + "score": 1.0, + "content": "First, IQL has strong offline per-", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 297, + 238, + 310 + ], + "spans": [ + { + "bbox": [ + 105, + 297, + 238, + 310 + ], + "score": 1.0, + "content": "formance, as shown in the pre-", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 309, + 238, + 320 + ], + "spans": [ + { + "bbox": [ + 106, + 309, + 238, + 320 + ], + "score": 1.0, + "content": "vious section, which provides a", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 319, + 238, + 331 + ], + "spans": [ + { + "bbox": [ + 105, + 319, + 238, + 331 + ], + "score": 1.0, + "content": "good initialization. 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DatasetAWACCQLIQL (Ours)
antmaze-umaze-vO antmaze-umaze-diverse-v056.7 →59.0 49.3 →49.070.1 →99.4 31.1 →99.488.0 →96.3 67.0 →49.0
antmaze-medium-play-v00.0 →0.023.0 →0.069.0 →89.2
antmaze-medium-diverse-v00.7 →0.323.0 →32.371.8 →91.4
antmaze-large-play-v00.0 →0.01.0 →0.036.8 →51.8
antmaze-large-diverse-v01.0 →0.01.0 →0.042.2 →59.8
antmaze-vO total107.7 →108.3151.5 →231.1374.8 →437.5
pen-binary-v044.6 →70.331.2 →9.937.4 →60.7
door-binary-v01.3 →30.10.2 →0.00.7 →32.3
relocate-binary-v00.8 →2.70.1 →0.00.0 →31.0
hand-vO total46.7 →103.131.5 →9.938.1 →124.0
total154.4→211.4182.8→241.0412.9561.5
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Exact experimental details are provided in Appendix", + "type": "text" + }, + { + "bbox": [ + 399, + 472, + 411, + 486 + ], + "score": 0.53, + "content": "\\mathbf { C } .", + "type": "inline_equation" + }, + { + "bbox": [ + 411, + 471, + 505, + 487 + ], + "score": 1.0, + "content": "We use the challenging", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 482, + 505, + 497 + ], + "spans": [ + { + "bbox": [ + 105, + 482, + 212, + 497 + ], + "score": 1.0, + "content": "Ant Maze D4RL domains", + "type": "text" + }, + { + "bbox": [ + 212, + 483, + 277, + 495 + ], + "score": 0.51, + "content": "\\mathtt { ( F u ) e t a l . } \\mathtt { / } 2 0 2 0 \\rVert", + "type": "inline_equation" + }, + { + "bbox": [ + 277, + 482, + 505, + 497 + ], + "score": 1.0, + "content": ", as well as the high-dimensional dexterous manipulation", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 494, + 505, + 508 + ], + "spans": [ + { + "bbox": [ + 106, + 494, + 255, + 508 + ], + "score": 1.0, + "content": "environments from Rajeswaran et al.", + "type": "text" + }, + { + "bbox": [ + 255, + 495, + 282, + 507 + ], + "score": 0.55, + "content": "\\overline { { \\left( \\frac { 2 0 1 8 } { \\it 1 8 } \\right) } }", + "type": "inline_equation" + }, + { + "bbox": [ + 282, + 494, + 355, + 508 + ], + "score": 1.0, + "content": ", which Nair et al.", + "type": "text" + }, + { + "bbox": [ + 356, + 495, + 383, + 507 + ], + "score": 0.76, + "content": "\\underline { { ( 2 0 2 0 ) } }", + "type": "inline_equation" + }, + { + "bbox": [ + 383, + 494, + 505, + 508 + ], + "score": 1.0, + "content": "propose to use to study online", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 506, + 505, + 519 + ], + "spans": [ + { + "bbox": [ + 106, + 506, + 312, + 518 + ], + "score": 1.0, + "content": "adaptation with AWAC. Results are shown in Table", + "type": "text" + }, + { + "bbox": [ + 312, + 506, + 322, + 519 + ], + "score": 0.46, + "content": "\\boxed { 5 }", + "type": "inline_equation" + }, + { + "bbox": [ + 323, + 506, + 505, + 518 + ], + "score": 1.0, + "content": "On the Ant Maze domains, IQL significantly", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 517, + 505, + 528 + ], + "spans": [ + { + "bbox": [ + 106, + 517, + 505, + 528 + ], + "score": 1.0, + "content": "outperforms both prior methods after online finetuning. CQL attains the second best score, while", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 527, + 505, + 540 + ], + "spans": [ + { + "bbox": [ + 105, + 527, + 505, + 540 + ], + "score": 1.0, + "content": "AWAC performs comparatively worse due to much weaker offline initialization. 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DatasetBC10%BCBCQDTABMAWACOnestep RLTD3+BCCQLIQL (Ours)
halfcheetah-m-v242.642.547.042.6±0.153.643.548.4±0.148.3±0.344.0±5.447.4±0.2
hopper-m-v252.956.956.767.6±1.00.757.059.6±2.559.3±4.258.5±2.166.2±5.7
walker2d-m-v275.375.072.674.0±1.40.572.481.8±2.283.7±2.172.5±0.878.3±8.7
halfcheetah-m-r-v236.640.640.436.6±0.850.540.538.1±1.344.6±0.545.5±0.544.2±1.2
hopper-m-r-v218.175.953.382.7±7.049.637.297.5±0.760.9±18.895.0±6.494.7±8.6
walker2d-m-r-v226.062.552.166.6±3.053.827.049.5±12.081.8±5.577.2±5.573.8±7.1
halfcheetah-m-e-v255.292.989.186.8±1.318.542.893.4±1.690.7±4.391.6±2.886.7±5.3
hopper-m-e-v252.5110.981.8107.6±1.80.755.8103.3±1.998.0±9.4105.4±6.891.5±14.3
walker2d-m-e-v2107.5109.0109.5108.1±0.23.574.5113.0±0.4110.1±0.5108.8±0.7109.6±1.0
locomotion-v2 total466.7666.2602.5672.6±16.6231.4450.7684.6±22.7677.4±44.5698.5±31.0692.4±52.1
antmaze-u-v054.662.889.859.259.956.764.378.674.087.5±2.6
antmaze-u-d-v045.650.283.053.048.749.360.771.484.062.2 ±13.8
antmaze-m-p-v00.05.415.00.00.00.00.310.661.271.2 ± 7.3
antmaze-m-d-v00.09.80.00.00.50.70.03.053.770.0±10.9
antmaze-l-p-v0 antmaze-l-d-v00.0 0.00.0 6.00.00.00.0.00.00.215.839.6±5.8
antmaze-vO total100.2134.20.0 187.80.00.01.00.00.014.947.5±9.5
112.2109.1107.7125.3163.8303.6378.0±49.9
total566.9800.4790.3784.8340.5558.4809.9841.21002.11070.4±102.0
kitchen-v0 total adroit-vO total154.5 104.5-------144.6159.8±22.6
：=--=--93.6118.1±30.7
total+kitchen+adroit825.9-------1240.31348.3±155.3
runtime10m10m960m20m20m*20m80m20m
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DatasetAWACCQLIQL (Ours)
antmaze-umaze-vO antmaze-umaze-diverse-v056.7 →59.0 49.3 →49.070.1 →99.4 31.1 →99.488.0 →96.3 67.0 →49.0
antmaze-medium-play-v00.0 →0.023.0 →0.069.0 →89.2
antmaze-medium-diverse-v00.7 →0.323.0 →32.371.8 →91.4
antmaze-large-play-v00.0 →0.01.0 →0.036.8 →51.8
antmaze-large-diverse-v01.0 →0.01.0 →0.042.2 →59.8
antmaze-vO total107.7 →108.3151.5 →231.1374.8 →437.5
pen-binary-v044.6 →70.331.2 →9.937.4 →60.7
door-binary-v01.3 →30.10.2 →0.00.7 →32.3
relocate-binary-v00.8 →2.70.1 →0.00.0 →31.0
hand-vO total46.7 →103.131.5 →9.938.1 →124.0
total154.4→211.4182.8→241.0412.9561.5
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However, most language models", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 601, + 505, + 615 + ], + "spans": [ + { + "bbox": [ + 105, + 601, + 505, + 615 + ], + "score": 1.0, + "content": "are trained without direct signals of human preference, with supervised target strings serving as (a", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 612, + 506, + 626 + ], + "spans": [ + { + "bbox": [ + 105, + 612, + 506, + 626 + ], + "score": 1.0, + "content": "sometimes crude) proxy. 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Allen School of Computer Science, University of Washington", + "type": "text" + } + ], + "index": 7, + "is_list_end_line": true + }, + { + "bbox": [ + 112, + 221, + 342, + 234 + ], + "spans": [ + { + "bbox": [ + 112, + 221, + 342, + 234 + ], + "score": 1.0, + "content": "rajkumar.ramamurthy@iais.fraunhofer.de", + "type": "text" + } + ], + "index": 8, + "is_list_start_line": true, + "is_list_end_line": true + }, + { + "bbox": [ + 112, + 232, + 365, + 245 + ], + "spans": [ + { + "bbox": [ + 112, + 232, + 365, + 245 + ], + "score": 1.0, + "content": "{raja,jackh}@allenai.org; kdb82@cornell.edu", + "type": "text" + } + ], + "index": 9, + "is_list_start_line": true, + "is_list_end_line": true + } + ], + "index": 6.5, + "bbox_fs": [ + 111, + 173, + 514, + 245 + ] + }, + { + "type": "title", + "bbox": [ + 278, + 272, + 333, + 284 + ], + "lines": [ + { + "bbox": [ + 276, + 271, + 336, + 286 + ], + "spans": [ + { + "bbox": [ + 276, + 271, + 336, + 286 + ], + "score": 1.0, + "content": "ABSTRACT", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 10 + }, + { + "type": "text", + "bbox": [ + 143, + 298, + 469, + 375 + ], + "lines": [ + { + "bbox": [ + 141, + 298, + 469, + 311 + ], + "spans": [ + { + "bbox": [ + 141, + 298, + 469, + 311 + ], + "score": 1.0, + "content": "We tackle the problem of aligning pre-trained large language models (LMs) with", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 141, + 308, + 469, + 322 + ], + "spans": [ + { + "bbox": [ + 141, + 308, + 469, + 322 + ], + "score": 1.0, + "content": "human preferences. If we view text generation as a sequential decision-making", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 142, + 321, + 470, + 333 + ], + "spans": [ + { + "bbox": [ + 142, + 321, + 470, + 333 + ], + "score": 1.0, + "content": "problem, reinforcement learning (RL) appears to be a natural conceptual framework.", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 141, + 330, + 470, + 344 + ], + "spans": [ + { + "bbox": [ + 141, + 330, + 470, + 344 + ], + "score": 1.0, + "content": "However, using RL for LM-based generation faces empirical challenges, including", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 141, + 342, + 470, + 355 + ], + "spans": [ + { + "bbox": [ + 141, + 342, + 470, + 355 + ], + "score": 1.0, + "content": "training instability due to the combinatorial action space, as well as a lack of open-", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 141, + 353, + 469, + 365 + ], + "spans": [ + { + "bbox": [ + 141, + 353, + 469, + 365 + ], + "score": 1.0, + "content": "source libraries and benchmarks customized for LM alignment. Thus, a question", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 141, + 364, + 425, + 376 + ], + "spans": [ + { + "bbox": [ + 141, + 364, + 425, + 376 + ], + "score": 1.0, + "content": "rises in the research community: is RL a practical paradigm for NLP?", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 14, + "bbox_fs": [ + 141, + 298, + 470, + 376 + ] + }, + { + "type": "text", + "bbox": [ + 142, + 378, + 469, + 541 + ], + "lines": [ + { + "bbox": [ + 140, + 376, + 470, + 390 + ], + "spans": [ + { + "bbox": [ + 140, + 376, + 470, + 390 + ], + "score": 1.0, + "content": "To help answer this, we first introduce an open-source modular library, RL4LMs1,2", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 140, + 387, + 471, + 402 + ], + "spans": [ + { + "bbox": [ + 140, + 387, + 471, + 402 + ], + "score": 1.0, + "content": "for optimizing language generators with RL. The library consists of on-policy RL", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 141, + 399, + 469, + 411 + ], + "spans": [ + { + "bbox": [ + 141, + 399, + 469, + 411 + ], + "score": 1.0, + "content": "algorithms that can be used to train any encoder or encoder-decoder LM in the", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 141, + 411, + 470, + 423 + ], + "spans": [ + { + "bbox": [ + 141, + 411, + 470, + 423 + ], + "score": 1.0, + "content": "HuggingFace library (Wolf et al., 2020) with an arbitrary reward function. Next, we", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 141, + 421, + 470, + 434 + ], + "spans": [ + { + "bbox": [ + 141, + 421, + 470, + 434 + ], + "score": 1.0, + "content": "present the GRUE (General Reinforced-language Understanding Evaluation)", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 141, + 432, + 469, + 445 + ], + "spans": [ + { + "bbox": [ + 141, + 432, + 469, + 445 + ], + "score": 1.0, + "content": "benchmark, a set of 6 language generation tasks which are supervised not by target", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 142, + 444, + 469, + 456 + ], + "spans": [ + { + "bbox": [ + 142, + 444, + 469, + 456 + ], + "score": 1.0, + "content": "strings, but by reward functions which capture automated measures of human", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 141, + 454, + 470, + 466 + ], + "spans": [ + { + "bbox": [ + 141, + 454, + 470, + 466 + ], + "score": 1.0, + "content": "preference. GRUE is the first leaderboard-style evaluation of RL algorithms for", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 141, + 464, + 469, + 477 + ], + "spans": [ + { + "bbox": [ + 141, + 464, + 469, + 477 + ], + "score": 1.0, + "content": "NLP tasks. Finally, we introduce an easy-to-use, performant RL algorithm, NLPO", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 141, + 475, + 470, + 489 + ], + "spans": [ + { + "bbox": [ + 141, + 475, + 470, + 489 + ], + "score": 1.0, + "content": "(Natural Language Policy Optimization) that learns to effectively reduce the", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 141, + 487, + 470, + 500 + ], + "spans": [ + { + "bbox": [ + 141, + 487, + 470, + 500 + ], + "score": 1.0, + "content": "combinatorial action space in language generation. We show 1) that RL techniques", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 141, + 498, + 470, + 511 + ], + "spans": [ + { + "bbox": [ + 141, + 498, + 470, + 511 + ], + "score": 1.0, + "content": "are generally better than supervised methods at aligning LMs to human preferences;", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 141, + 508, + 470, + 522 + ], + "spans": [ + { + "bbox": [ + 141, + 508, + 470, + 522 + ], + "score": 1.0, + "content": "and 2) that NLPO exhibits greater stability and performance than previous policy", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 141, + 520, + 469, + 532 + ], + "spans": [ + { + "bbox": [ + 141, + 520, + 469, + 532 + ], + "score": 1.0, + "content": "gradient methods (e.g., PPO (Schulman et al., 2017)), based on both automatic and", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 142, + 531, + 222, + 543 + ], + "spans": [ + { + "bbox": [ + 142, + 531, + 222, + 543 + ], + "score": 1.0, + "content": "human evaluations.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 25, + "bbox_fs": [ + 140, + 376, + 471, + 543 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 565, + 206, + 577 + ], + "lines": [ + { + "bbox": [ + 105, + 564, + 208, + 581 + ], + "spans": [ + { + "bbox": [ + 105, + 564, + 208, + 581 + ], + "score": 1.0, + "content": "1 INTRODUCTION", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 33 + }, + { + "type": "text", + "bbox": [ + 106, + 590, + 505, + 689 + ], + "lines": [ + { + "bbox": [ + 106, + 591, + 505, + 603 + ], + "spans": [ + { + "bbox": [ + 106, + 591, + 505, + 603 + ], + "score": 1.0, + "content": "The ultimate aim of language technology is to interact with humans. However, most language models", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 601, + 505, + 615 + ], + "spans": [ + { + "bbox": [ + 105, + 601, + 505, + 615 + ], + "score": 1.0, + "content": "are trained without direct signals of human preference, with supervised target strings serving as (a", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 612, + 506, + 626 + ], + "spans": [ + { + "bbox": [ + 105, + 612, + 506, + 626 + ], + "score": 1.0, + "content": "sometimes crude) proxy. One option to incorporate user feedback is via human-in-the-loop, i.e., a", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 624, + 504, + 635 + ], + "spans": [ + { + "bbox": [ + 106, + 624, + 504, + 635 + ], + "score": 1.0, + "content": "user would be expected to provide feedback for each sample online as the model trains, but this", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 633, + 505, + 648 + ], + "spans": [ + { + "bbox": [ + 105, + 633, + 505, + 648 + ], + "score": 1.0, + "content": "degree of dense supervision is often prohibitive and inefficient. Automated metrics offer a promising", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 646, + 506, + 658 + ], + "spans": [ + { + "bbox": [ + 106, + 646, + 506, + 658 + ], + "score": 1.0, + "content": "compromise: models of human preference like pairwise learned preference models (Ouyang et al.,", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 656, + 506, + 669 + ], + "spans": [ + { + "bbox": [ + 106, + 656, + 506, + 669 + ], + "score": 1.0, + "content": "2022), BERTScore (Zhang et al., 2019), BLEURT (Sellam et al., 2020) have significantly improved", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 666, + 505, + 681 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 505, + 681 + ], + "score": 1.0, + "content": "correlation with human judgment compared to earlier metrics (BLEU, METEOR, etc.), and are cheap", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 678, + 506, + 691 + ], + "spans": [ + { + "bbox": [ + 105, + 678, + 506, + 691 + ], + "score": 1.0, + "content": "to evaluate. But — these functions are usually not per-token differentiable: like humans, metrics", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 376, + 506, + 389 + ], + "spans": [ + { + "bbox": [ + 105, + 376, + 506, + 389 + ], + "score": 1.0, + "content": "can only offer quality estimates for full generations. Reinforcement Learning (RL) offers a natural", + "type": "text", + "cross_page": true + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 387, + 506, + 400 + ], + "spans": [ + { + "bbox": [ + 105, + 387, + 506, + 400 + ], + "score": 1.0, + "content": "path forward for optimizing non-differentiable, scalar objectives for LM-based generation when it", + "type": "text", + "cross_page": true + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 398, + 506, + 412 + ], + "spans": [ + { + "bbox": [ + 105, + 398, + 506, + 412 + ], + "score": 1.0, + "content": "is cast as a sequential decision-making problem. However, Goodhart’s Law3 looms: particularly", + "type": "text", + "cross_page": true + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 410, + 505, + 421 + ], + "spans": [ + { + "bbox": [ + 105, + 410, + 505, + 421 + ], + "score": 1.0, + "content": "in the case of imperfect metrics that use neural networks, it is easy to find nonsense samples that", + "type": "text", + "cross_page": true + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 421, + 505, + 433 + ], + "spans": [ + { + "bbox": [ + 105, + 421, + 505, + 433 + ], + "score": 1.0, + "content": "achieve high-quality estimates. 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GRUE challenges models to optimize these reward functions while", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 558, + 506, + 572 + ], + "spans": [ + { + "bbox": [ + 105, + 558, + 506, + 572 + ], + "score": 1.0, + "content": "remaining fluent language generators. We train language models via RL—both with and without", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 569, + 505, + 581 + ], + "spans": [ + { + "bbox": [ + 106, + 569, + 505, + 581 + ], + "score": 1.0, + "content": "task specific supervised pre-training—to optimize rewards. Finally, beyond existing RL methods, we", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 580, + 505, + 592 + ], + "spans": [ + { + "bbox": [ + 106, + 580, + 505, + 592 + ], + "score": 1.0, + "content": "introduce a novel on-policy RL algorithm called NLPO (Natural Language Policy Optimization),", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 591, + 497, + 604 + ], + "spans": [ + { + "bbox": [ + 106, + 591, + 497, + 604 + ], + "score": 1.0, + "content": "that dynamically learns task-specific constraints over the distribution of language at a token level.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 26, + "bbox_fs": [ + 105, + 480, + 506, + 604 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 607, + 505, + 707 + ], + "lines": [ + { + "bbox": [ + 105, + 606, + 506, + 621 + ], + "spans": [ + { + "bbox": [ + 105, + 606, + 506, + 621 + ], + "score": 1.0, + "content": "ttExperiments on GRUE and human evaluations show that NLPO better balances learning preference", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 619, + 505, + 631 + ], + "spans": [ + { + "bbox": [ + 106, + 619, + 505, + 631 + ], + "score": 1.0, + "content": "rewards while maintaining language fluency compared to alternatives, including PPO (Figure 1). We", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 627, + 506, + 644 + ], + "spans": [ + { + "bbox": [ + 105, + 627, + 506, + 644 + ], + "score": 1.0, + "content": "find that using RL to learn from scalar reward feedback can be more: (1) data efficient than using", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 640, + 506, + 654 + ], + "spans": [ + { + "bbox": [ + 105, + 640, + 506, + 654 + ], + "score": 1.0, + "content": "additional expert demonstrations via supervised learning (though a combination of both is best)—a", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 652, + 505, + 664 + ], + "spans": [ + { + "bbox": [ + 106, + 652, + 505, + 664 + ], + "score": 1.0, + "content": "learned reward function enables greater performance when used as a signal for an RL method than", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 663, + 505, + 675 + ], + "spans": [ + { + "bbox": [ + 105, + 663, + 505, + 675 + ], + "score": 1.0, + "content": "a supervised method trained with 5 times more data, and (2) parameter efficient—enabling a 220", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 673, + 505, + 686 + ], + "spans": [ + { + "bbox": [ + 105, + 673, + 505, + 686 + ], + "score": 1.0, + "content": "million parameter model trained with a combination of supervision and NLPO to outperform a 3", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 684, + 505, + 697 + ], + "spans": [ + { + "bbox": [ + 106, + 684, + 505, + 697 + ], + "score": 1.0, + "content": "billion supervised model. We hope that the benchmarks, baselines, and building blocks we release", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 695, + 389, + 708 + ], + "spans": [ + { + "bbox": [ + 106, + 695, + 389, + 708 + ], + "score": 1.0, + "content": "serve to drive forward research in aligning LMs to human preferences.", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 36, + "bbox_fs": [ + 105, + 606, + 506, + 708 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 108, + 81, + 210, + 93 + ], + "lines": [ + { + "bbox": [ + 104, + 79, + 213, + 96 + ], + "spans": [ + { + "bbox": [ + 104, + 79, + 213, + 96 + ], + "score": 1.0, + "content": "2 RELATED WORK", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 107, + 106, + 505, + 183 + ], + "lines": [ + { + "bbox": [ + 105, + 105, + 507, + 119 + ], + "spans": [ + { + "bbox": [ + 105, + 105, + 507, + 119 + ], + "score": 1.0, + "content": "Imitation learning for NLP. Algorithms such as Schedule Sampling (SS) (Bengio et al., 2015),", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 117, + 506, + 129 + ], + "spans": [ + { + "bbox": [ + 105, + 117, + 506, + 129 + ], + "score": 1.0, + "content": "Parallel SS (Duckworth et al., 2019), SS for Transformers (Mihaylova & Martins, 2019), Diffential SS", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 128, + 506, + 141 + ], + "spans": [ + { + "bbox": [ + 106, + 128, + 506, + 141 + ], + "score": 1.0, + "content": "(Goyal et al., 2017), LOLS (Lampouras & Vlachos, 2016; Chang et al., 2015), TextGAIL (Wu et al.,", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 138, + 506, + 152 + ], + "spans": [ + { + "bbox": [ + 105, + 138, + 506, + 152 + ], + "score": 1.0, + "content": "2021b), and SEARNN (Leblond et al., 2017), have been inspired by DAGGER (Ross et al., 2011)", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 150, + 505, + 162 + ], + "spans": [ + { + "bbox": [ + 106, + 150, + 505, + 162 + ], + "score": 1.0, + "content": "and SEARN (Daumé et al., 2009). However, these algorithms are known to suffer from exposure bias", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 160, + 507, + 174 + ], + "spans": [ + { + "bbox": [ + 105, + 160, + 507, + 174 + ], + "score": 1.0, + "content": "in generation (Chiang & Chen, 2021; Arora et al., 2022) and the cliff MDP problem (Huszár, 2015;", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 172, + 277, + 185 + ], + "spans": [ + { + "bbox": [ + 105, + 172, + 277, + 185 + ], + "score": 1.0, + "content": "Agarwal et al., 2019; Swamy et al., 2021).", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 4 + }, + { + "type": "text", + "bbox": [ + 107, + 189, + 505, + 255 + ], + "lines": [ + { + "bbox": [ + 105, + 188, + 505, + 202 + ], + "spans": [ + { + "bbox": [ + 105, + 188, + 505, + 202 + ], + "score": 1.0, + "content": "RL for Large Action Spaces. MIXER (Ranzato et al., 2016) combined ideas from schedule sampling", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 200, + 506, + 212 + ], + "spans": [ + { + "bbox": [ + 105, + 200, + 506, + 212 + ], + "score": 1.0, + "content": "and REINFORCE (Williams, 1992). Bahdanau et al. (2016) proposed an actor-critic algorithm to", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 210, + 506, + 223 + ], + "spans": [ + { + "bbox": [ + 105, + 210, + 506, + 223 + ], + "score": 1.0, + "content": "address the variance/large action space problems when using REINFORCE for language generation;", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 222, + 506, + 234 + ], + "spans": [ + { + "bbox": [ + 105, + 222, + 506, + 234 + ], + "score": 1.0, + "content": "follow-up works such as KG-A2C (Ammanabrolu & Hausknecht, 2020), TrufLL (Martin et al., 2022),", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 231, + 506, + 246 + ], + "spans": [ + { + "bbox": [ + 105, + 231, + 506, + 246 + ], + "score": 1.0, + "content": "AE-DQN (Zahavy et al., 2018), and GALAD (Ammanabrolu et al., 2022) addressed similar issues by", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 244, + 392, + 257 + ], + "spans": [ + { + "bbox": [ + 105, + 244, + 392, + 257 + ], + "score": 1.0, + "content": "attempting to eliminate and reduce the action space during exploration.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 10.5 + }, + { + "type": "text", + "bbox": [ + 107, + 261, + 505, + 415 + ], + "lines": [ + { + "bbox": [ + 105, + 260, + 505, + 273 + ], + "spans": [ + { + "bbox": [ + 105, + 260, + 505, + 273 + ], + "score": 1.0, + "content": "RL for NLP. RL, often in the form of bandit learning, has been used to improve models in machine", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 271, + 505, + 284 + ], + "spans": [ + { + "bbox": [ + 106, + 271, + 505, + 284 + ], + "score": 1.0, + "content": "translation (Wu et al., 2016; Nguyen et al., 2017; Kiegeland & Kreutzer, 2021), summarization", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 282, + 506, + 295 + ], + "spans": [ + { + "bbox": [ + 105, + 282, + 506, + 295 + ], + "score": 1.0, + "content": "(Stiennon et al., 2020; Paulus et al., 2017), dialogue (Li et al., 2016; Zhou et al., 2017; Jaques et al.,", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 292, + 507, + 307 + ], + "spans": [ + { + "bbox": [ + 105, + 292, + 507, + 307 + ], + "score": 1.0, + "content": "2020), image captioning (Rennie et al., 2017), question generation (Pang & He, 2021), text-games", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 304, + 506, + 317 + ], + "spans": [ + { + "bbox": [ + 106, + 304, + 506, + 317 + ], + "score": 1.0, + "content": "(Narasimhan et al., 2015; Hausknecht et al., 2020), and more (Ranzato et al., 2016; Snell et al., 2022).", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 104, + 313, + 506, + 329 + ], + "spans": [ + { + "bbox": [ + 104, + 313, + 506, + 329 + ], + "score": 1.0, + "content": "Lu et al. (2022) adapt reward-conditioned transformers (Chen et al., 2021) for several language", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 104, + 326, + 506, + 339 + ], + "spans": [ + { + "bbox": [ + 104, + 326, + 506, + 339 + ], + "score": 1.0, + "content": "generation tasks. RL has been the focus of efforts to align LMs with human preferences (Stiennon", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 336, + 505, + 351 + ], + "spans": [ + { + "bbox": [ + 105, + 336, + 505, + 351 + ], + "score": 1.0, + "content": "et al., 2020; Wu et al., 2021a; Nakano et al., 2021; Ziegler et al., 2019), e.g., Ouyang et al. (2022)", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 348, + 506, + 361 + ], + "spans": [ + { + "bbox": [ + 105, + 348, + 506, + 361 + ], + "score": 1.0, + "content": "fine-tuned large language model with PPO Schulman et al. (2017) to align with models of human", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 359, + 506, + 371 + ], + "spans": [ + { + "bbox": [ + 105, + 359, + 506, + 371 + ], + "score": 1.0, + "content": "preference, but their non-public dataset doesn’t enable comparison. Though RL has been successful", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 370, + 505, + 383 + ], + "spans": [ + { + "bbox": [ + 105, + 370, + 505, + 383 + ], + "score": 1.0, + "content": "in some of the use cases described above, it has simultaneously been critiqued for being significantly", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 380, + 505, + 394 + ], + "spans": [ + { + "bbox": [ + 105, + 380, + 505, + 394 + ], + "score": 1.0, + "content": "less stable than supervised LM training (Choshen et al., 2020). As a result, there is relatively", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 391, + 505, + 406 + ], + "spans": [ + { + "bbox": [ + 105, + 391, + 505, + 406 + ], + "score": 1.0, + "content": "little consensus if RL is a worthwhile consideration for training LMs compared to, say, collecting", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 403, + 215, + 416 + ], + "spans": [ + { + "bbox": [ + 106, + 403, + 215, + 416 + ], + "score": 1.0, + "content": "additional supervised data.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 20.5 + }, + { + "type": "title", + "bbox": [ + 108, + 430, + 397, + 443 + ], + "lines": [ + { + "bbox": [ + 105, + 430, + 399, + 445 + ], + "spans": [ + { + "bbox": [ + 105, + 430, + 399, + 445 + ], + "score": 1.0, + "content": "3 RL4LMS: A LIBRARY FOR TRAINING LMS WITH RL", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 28 + }, + { + "type": "text", + "bbox": [ + 107, + 455, + 506, + 566 + ], + "lines": [ + { + "bbox": [ + 105, + 454, + 506, + 469 + ], + "spans": [ + { + "bbox": [ + 105, + 454, + 506, + 469 + ], + "score": 1.0, + "content": "We introduce RL4LMs, an open-source library with building blocks for fine-tuning and evaluating", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 466, + 505, + 478 + ], + "spans": [ + { + "bbox": [ + 106, + 466, + 505, + 478 + ], + "score": 1.0, + "content": "RL algorithms on LM-based generation. The library is built on HuggingFace (Wolf et al., 2020)", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 478, + 507, + 491 + ], + "spans": [ + { + "bbox": [ + 106, + 478, + 507, + 491 + ], + "score": 1.0, + "content": "and stable-baselines-3 (Raffin et al., 2021), combining important components from their interfaces.", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 104, + 487, + 506, + 502 + ], + "spans": [ + { + "bbox": [ + 104, + 487, + 506, + 502 + ], + "score": 1.0, + "content": "RL4LMs can be used to train any decoder only or encoder-decoder transformer models from Hug-", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 500, + 506, + 512 + ], + "spans": [ + { + "bbox": [ + 105, + 500, + 506, + 512 + ], + "score": 1.0, + "content": "gingFace with any on-policy RL algorithm from stable-baselines-3. Furthermore, we provide reliable", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 511, + 506, + 523 + ], + "spans": [ + { + "bbox": [ + 106, + 511, + 506, + 523 + ], + "score": 1.0, + "content": "implementations of popular on-policy RL algorithms that are tailored for LM fine-tuning such as", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 520, + 505, + 533 + ], + "spans": [ + { + "bbox": [ + 105, + 520, + 505, + 533 + ], + "score": 1.0, + "content": "PPO (Schulman et al., 2017), TRPO (Schulman et al., 2015a), A2C (Mnih et al., 2016), and our own", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 532, + 506, + 545 + ], + "spans": [ + { + "bbox": [ + 105, + 532, + 506, + 545 + ], + "score": 1.0, + "content": "NLPO (§4). The library is modular, which enables users to plug-in customized environments, reward", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 543, + 507, + 556 + ], + "spans": [ + { + "bbox": [ + 105, + 543, + 507, + 556 + ], + "score": 1.0, + "content": "functions, metrics, and algorithms. 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Similarly, the value network", + "type": "text" + }, + { + "bbox": [ + 338, + 383, + 351, + 395 + ], + "score": 0.88, + "content": "V _ { \\phi }", + "type": "inline_equation" + }, + { + "bbox": [ + 351, + 383, + 506, + 396 + ], + "score": 1.0, + "content": "used to estimate the value function is", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 393, + 506, + 406 + ], + "spans": [ + { + "bbox": [ + 105, + 393, + 186, + 406 + ], + "score": 1.0, + "content": "also initialized from", + "type": "text" + }, + { + "bbox": [ + 187, + 396, + 198, + 405 + ], + "score": 0.85, + "content": "\\pi _ { 0 }", + "type": "inline_equation" + }, + { + "bbox": [ + 199, + 393, + 506, + 406 + ], + "score": 1.0, + "content": "except for the final layer which is randomly initialized to output a single scalar", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 404, + 511, + 443 + ], + "spans": [ + { + "bbox": [ + 106, + 415, + 248, + 430 + ], + "score": 0.85, + "content": "\\begin{array} { r } { V _ { t } ^ { \\pi } = \\mathbb { E } _ { a _ { t } \\sim \\pi } [ \\sum _ { \\tau = t } ^ { T } \\gamma R ( \\mathbf { \\bar { s } } _ { \\tau } , a _ { \\tau } , \\pmb { y } ) ] } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 241, + 417, + 463, + 430 + ], + "score": 0.66, + "content": ") ] , Q _ { t } ^ { \\pi } ( s _ { t } , a _ { t } ) = R ( s _ { t } , a _ { t } , \\pmb { y } ) + \\gamma \\mathbb { E } _ { s _ { t + 1 } \\sim P } [ V _ { t + 1 } ^ { \\pi } ( \\pmb { s } _ { t + 1 } ) ]", + "type": "inline_equation" + }, + { + "bbox": [ + 464, + 404, + 511, + 443 + ], + "score": 1.0, + "content": "nctions asleading tog stability,", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 271, + 429, + 383, + 441 + ], + "spans": [ + { + "bbox": [ + 271, + 429, + 383, + 441 + ], + "score": 0.88, + "content": "A _ { t } ^ { \\pi } ( \\pmb { \\mathscr { s } } , \\alpha ) = Q _ { t } ^ { \\pi } ( \\pmb { \\mathscr { s } } , \\alpha ) - V _ { t } ^ { \\pi }", + "type": "inline_equation" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 440, + 481, + 452 + ], + "spans": [ + { + "bbox": [ + 105, + 440, + 481, + 452 + ], + "score": 1.0, + "content": "advantage is appoximated using Generalized Advantage Estimation (Schulman et al., 2015b).", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 22.5 + }, + { + "type": "text", + "bbox": [ + 106, + 456, + 505, + 501 + ], + "lines": [ + { + "bbox": [ + 106, + 456, + 506, + 470 + ], + "spans": [ + { + "bbox": [ + 106, + 456, + 212, + 470 + ], + "score": 1.0, + "content": "Given an input-output pair", + "type": "text" + }, + { + "bbox": [ + 212, + 457, + 237, + 468 + ], + "score": 0.92, + "content": "( { \\pmb x } , { \\pmb y } )", + "type": "inline_equation" + }, + { + "bbox": [ + 238, + 456, + 506, + 470 + ], + "score": 1.0, + "content": "and generation predictions from our agent; because the environment", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 468, + 505, + 480 + ], + "spans": [ + { + "bbox": [ + 106, + 468, + 505, + 480 + ], + "score": 1.0, + "content": "rewards are sequence-level and sparse, following Wu et al. (2021a) we regularize the reward function", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 479, + 505, + 492 + ], + "spans": [ + { + "bbox": [ + 106, + 479, + 505, + 492 + ], + "score": 1.0, + "content": "using a token-level KL penalty for all on-policy algorithms, to prevent the model from deviating too", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 490, + 412, + 501 + ], + "spans": [ + { + "bbox": [ + 106, + 490, + 216, + 501 + ], + "score": 1.0, + "content": "far from the initialized LM", + "type": "text" + }, + { + "bbox": [ + 216, + 491, + 227, + 500 + ], + "score": 0.82, + "content": "\\pi _ { 0 }", + "type": "inline_equation" + }, + { + "bbox": [ + 228, + 490, + 412, + 501 + ], + "score": 1.0, + "content": ". 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We hypothesize that the size of the action", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 627, + 506, + 639 + ], + "spans": [ + { + "bbox": [ + 105, + 627, + 506, + 639 + ], + "score": 1.0, + "content": "space is a core cause of instability when training LMs with existing RL methods. To address this issue,", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 638, + 505, + 651 + ], + "spans": [ + { + "bbox": [ + 105, + 638, + 505, + 651 + ], + "score": 1.0, + "content": "we introduce NLPO (Natural Language Policy Optimization), which is inspired by work on action", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 648, + 506, + 662 + ], + "spans": [ + { + "bbox": [ + 105, + 648, + 506, + 662 + ], + "score": 1.0, + "content": "elimination/invalid-action masking (Zahavy et al., 2018; Huang & Ontañón, 2020; Ammanabrolu", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 660, + 506, + 672 + ], + "spans": [ + { + "bbox": [ + 105, + 660, + 506, + 672 + ], + "score": 1.0, + "content": "& Hausknecht, 2020). 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This abstraction allows", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 93, + 460, + 106 + ], + "spans": [ + { + "bbox": [ + 106, + 93, + 460, + 106 + ], + "score": 1.0, + "content": "for new tasks to be added quickly with compatibility across all implemented algorithms.", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5, + "bbox_fs": [ + 105, + 82, + 505, + 106 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 117, + 344, + 129 + ], + "lines": [ + { + "bbox": [ + 105, + 117, + 345, + 130 + ], + "spans": [ + { + "bbox": [ + 105, + 117, + 345, + 130 + ], + "score": 1.0, + "content": "3.2 REWARD FUNCTIONS AND EVALUATION METRICS", + "type": "text" + } + ], + "index": 2 + } + ], + "index": 2 + }, + { + "type": "text", + "bbox": [ + 106, + 138, + 505, + 292 + ], + "lines": [ + { + "bbox": [ + 105, + 138, + 506, + 152 + ], + "spans": [ + { + "bbox": [ + 105, + 138, + 506, + 152 + ], + "score": 1.0, + "content": "Because RL4LMs provides a generic interface for per-token or per-sequence generation rewards, it", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 149, + 506, + 162 + ], + "spans": [ + { + "bbox": [ + 105, + 149, + 506, + 162 + ], + "score": 1.0, + "content": "is possible to quickly apply a wide array of RL algorithms to a similarly diverse range of textual", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 160, + 505, + 173 + ], + "spans": [ + { + "bbox": [ + 105, + 160, + 505, + 173 + ], + "score": 1.0, + "content": "metrics-as-rewards. 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Our", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 371, + 506, + 384 + ], + "spans": [ + { + "bbox": [ + 105, + 371, + 403, + 384 + ], + "score": 1.0, + "content": "benchmark experiments focus on fine-tuning a pre-trained LM denoted as", + "type": "text" + }, + { + "bbox": [ + 403, + 374, + 415, + 383 + ], + "score": 0.85, + "content": "\\pi _ { 0 }", + "type": "inline_equation" + }, + { + "bbox": [ + 415, + 371, + 506, + 384 + ], + "score": 1.0, + "content": "from which we initial", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 383, + 506, + 396 + ], + "spans": [ + { + "bbox": [ + 105, + 383, + 181, + 396 + ], + "score": 1.0, + "content": "our agent’s policy", + "type": "text" + }, + { + "bbox": [ + 182, + 384, + 216, + 394 + ], + "score": 0.89, + "content": "\\pi _ { \\theta } = \\pi _ { 0 }", + "type": "inline_equation" + }, + { + "bbox": [ + 217, + 383, + 338, + 396 + ], + "score": 1.0, + "content": ". 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(2021a) we regularize the reward function", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 479, + 505, + 492 + ], + "spans": [ + { + "bbox": [ + 106, + 479, + 505, + 492 + ], + "score": 1.0, + "content": "using a token-level KL penalty for all on-policy algorithms, to prevent the model from deviating too", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 490, + 412, + 501 + ], + "spans": [ + { + "bbox": [ + 106, + 490, + 216, + 501 + ], + "score": 1.0, + "content": "far from the initialized LM", + "type": "text" + }, + { + "bbox": [ + 216, + 491, + 227, + 500 + ], + "score": 0.82, + "content": "\\pi _ { 0 }", + "type": "inline_equation" + }, + { + "bbox": [ + 228, + 490, + 412, + 501 + ], + "score": 1.0, + "content": ". 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We hypothesize that the size of the action", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 627, + 506, + 639 + ], + "spans": [ + { + "bbox": [ + 105, + 627, + 506, + 639 + ], + "score": 1.0, + "content": "space is a core cause of instability when training LMs with existing RL methods. To address this issue,", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 638, + 505, + 651 + ], + "spans": [ + { + "bbox": [ + 105, + 638, + 505, + 651 + ], + "score": 1.0, + "content": "we introduce NLPO (Natural Language Policy Optimization), which is inspired by work on action", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 648, + 506, + 662 + ], + "spans": [ + { + "bbox": [ + 105, + 648, + 506, + 662 + ], + "score": 1.0, + "content": "elimination/invalid-action masking (Zahavy et al., 2018; Huang & Ontañón, 2020; Ammanabrolu", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 660, + 506, + 672 + ], + "spans": [ + { + "bbox": [ + 105, + 660, + 506, + 672 + ], + "score": 1.0, + "content": "& Hausknecht, 2020). 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To combat reward hacking for any single metric,", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 555, + 507, + 569 + ], + "spans": [ + { + "bbox": [ + 105, + 555, + 507, + 569 + ], + "score": 1.0, + "content": "each task is evaluated at test time according to a task-specific mix of metrics, detailed in Table 1.", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 568, + 505, + 580 + ], + "spans": [ + { + "bbox": [ + 106, + 568, + 505, + 580 + ], + "score": 1.0, + "content": "The metrics span two categories. Task preference metrics capture how well the models produce", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 577, + 506, + 591 + ], + "spans": [ + { + "bbox": [ + 105, + 577, + 506, + 591 + ], + "score": 1.0, + "content": "generations that satisfy the desiderata of the specific generation task, e.g., for Commongen, if the", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 589, + 506, + 602 + ], + "spans": [ + { + "bbox": [ + 105, + 589, + 506, + 602 + ], + "score": 1.0, + "content": "generations contain all the required words, or for IMDB, how positive the generated completions", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 600, + 505, + 613 + ], + "spans": [ + { + "bbox": [ + 106, + 600, + 505, + 613 + ], + "score": 1.0, + "content": "are. 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At training time, there are no special restrictions: models are free to use the supervised", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 623, + 506, + 635 + ], + "spans": [ + { + "bbox": [ + 106, + 623, + 506, + 635 + ], + "score": 1.0, + "content": "data, compute metrics on intermediate generations, etc. Train/val/test splits follow the original works.", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 633, + 471, + 646 + ], + "spans": [ + { + "bbox": [ + 105, + 633, + 471, + 646 + ], + "score": 1.0, + "content": "All results are averaged over multiple seeds, with exact counts being found in Appendix B.", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 34, + "bbox_fs": [ + 105, + 545, + 507, + 646 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 650, + 504, + 673 + ], + "lines": [ + { + "bbox": [ + 106, + 649, + 506, + 663 + ], + "spans": [ + { + "bbox": [ + 106, + 649, + 506, + 663 + ], + "score": 1.0, + "content": "Experimental Setup. We use RL4LMs to test a large range of algorithms on the GRUE benchmark.", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 661, + 505, + 673 + ], + "spans": [ + { + "bbox": [ + 106, + 661, + 505, + 673 + ], + "score": 1.0, + "content": "Specifically: We compare 3 algorithms for direct fine-tuning — Supervised, PPO,5 and NLPO. In", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 305, + 505, + 320 + ], + "spans": [ + { + "bbox": [ + 105, + 305, + 505, + 320 + ], + "score": 1.0, + "content": "addition, we consider a hybrid approach of supervised learning and our RL methods by applying", + "type": "text", + "cross_page": true + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 317, + 505, + 330 + ], + "spans": [ + { + "bbox": [ + 105, + 317, + 505, + 330 + ], + "score": 1.0, + "content": "PPO and NLPO on checkpoints that have been fine-tuned in a supervised fashion—we call these", + "type": "text", + "cross_page": true + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 327, + 505, + 342 + ], + "spans": [ + { + "bbox": [ + 105, + 327, + 152, + 342 + ], + "score": 1.0, + "content": "Supervised", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 152, + 329, + 177, + 339 + ], + "score": 0.28, + "content": "+ \\mathrm { P P O }", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 178, + 327, + 505, + 342 + ], + "score": 1.0, + "content": ", Supervised+NLPO. 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DatasetTaskInputOutputTask Preference Metrics(s)Naturalness Metrics(s)
IMDB (Maas et al., 2011)Text Continua- tionPartial Movie ReviewA positive completion of the movie review.Learned Sentiment ClassifierPerplexity (GPT-2)
CommonGEN (Lin et al., 2020)Generative CommonsenseConcept SetA sentence coherently using all input concepts.CIDER; ROUGE-2,L; BLEU-3,4; METEOR; CoverageSPICE
CNN Daily Mail (Hermann et al.,2015) SummarizationNews ArticleSummarized article.SummaCZS; ROUGE-1,2,L,LSum; METEOR; BLEUBertScore
ToTTo (Parikh et al.,2020)Data to TextHighlighted Wiki TableFactually accurate text describing the information.SacreBLEU; PARENTBLEURT
WMT-16 (en-de) (Bojar et al., 2016)Machine Trans- lationText (English)Translated text (German).TER; cHRF;ROUGE-1,2,L,LSum, METEOR; SacreBLEU,BLEUBertScore
NarrativeQA (Kocisky et al.,2018)Question An- sweringQuestion Context (a Story)Abstractive answer to the question.ROUGE-1,2,L,LSum,LMax; METEOR; BLEU; SacreBLEUBertScore
DailyDialog (Li et al., 2017)Chitchat Dia- logueDialogue HistoryA conversational responseMETEOR; Learned Intent ClassfierBertScore
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We note that we test RL algorithms on these tasks for a wider range of possible", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 273, + 479, + 287 + ], + "spans": [ + { + "bbox": [ + 106, + 273, + 479, + 287 + ], + "score": 1.0, + "content": "rewards than just the task specific ones shown here. Unless specified, datasets are in English.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4 + } + ], + "index": 2.5 + }, + { + "type": "text", + "bbox": [ + 107, + 306, + 505, + 362 + ], + "lines": [ + { + "bbox": [ + 105, + 305, + 505, + 320 + ], + "spans": [ + { + "bbox": [ + 105, + 305, + 505, + 320 + ], + "score": 1.0, + "content": "addition, we consider a hybrid approach of supervised learning and our RL methods by applying", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 317, + 505, + 330 + ], + "spans": [ + { + "bbox": [ + 105, + 317, + 505, + 330 + ], + "score": 1.0, + "content": "PPO and NLPO on checkpoints that have been fine-tuned in a supervised fashion—we call these", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 327, + 505, + 342 + ], + "spans": [ + { + "bbox": [ + 105, + 327, + 152, + 342 + ], + "score": 1.0, + "content": "Supervised", + "type": "text" + }, + { + "bbox": [ + 152, + 329, + 177, + 339 + ], + "score": 0.28, + "content": "+ \\mathrm { P P O }", + "type": "inline_equation" + }, + { + "bbox": [ + 178, + 327, + 505, + 342 + ], + "score": 1.0, + "content": ", Supervised+NLPO. As an additional baseline, we additionally run zero-shot", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 339, + 505, + 353 + ], + "spans": [ + { + "bbox": [ + 105, + 339, + 505, + 353 + ], + "score": 1.0, + "content": "evaluations where we design prompts which aim to elicit task-specific generations, but with no", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 351, + 247, + 363 + ], + "spans": [ + { + "bbox": [ + 106, + 351, + 247, + 363 + ], + "score": 1.0, + "content": "training data or parameter updates.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 8 + }, + { + "type": "text", + "bbox": [ + 107, + 367, + 505, + 455 + ], + "lines": [ + { + "bbox": [ + 105, + 367, + 506, + 380 + ], + "spans": [ + { + "bbox": [ + 105, + 367, + 506, + 380 + ], + "score": 1.0, + "content": "For each task, to isolate the effect of training method, we select a single pre-trained LM backbone.", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 378, + 506, + 390 + ], + "spans": [ + { + "bbox": [ + 105, + 378, + 285, + 390 + ], + "score": 1.0, + "content": "For IMDB text continuation we use GPT-2 (", + "type": "text" + }, + { + "bbox": [ + 286, + 379, + 309, + 389 + ], + "score": 0.55, + "content": "1 1 7 \\mathrm { m }", + "type": "inline_equation" + }, + { + "bbox": [ + 310, + 378, + 506, + 390 + ], + "score": 1.0, + "content": "parameters), and for the rest of the tasks we use", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 389, + 506, + 402 + ], + "spans": [ + { + "bbox": [ + 105, + 389, + 143, + 402 + ], + "score": 1.0, + "content": "T5-base", + "type": "text" + }, + { + "bbox": [ + 143, + 389, + 167, + 400 + ], + "score": 0.49, + "content": "2 2 0 \\mathrm { m }", + "type": "inline_equation" + }, + { + "bbox": [ + 168, + 389, + 506, + 402 + ], + "score": 1.0, + "content": "parameters). For our RL models (PPO, NLPO, Supervised+PPO, Supervised+NLPO),", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 401, + 506, + 412 + ], + "spans": [ + { + "bbox": [ + 106, + 401, + 506, + 412 + ], + "score": 1.0, + "content": "for a thorough investigation of how reward-hacking might interplay with GRUE, we run a separate set", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 411, + 506, + 425 + ], + "spans": [ + { + "bbox": [ + 105, + 411, + 506, + 425 + ], + "score": 1.0, + "content": "of experiments optimizing multiple task rewards for each task independently, e.g., for Commongen", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 421, + 506, + 435 + ], + "spans": [ + { + "bbox": [ + 105, + 421, + 506, + 435 + ], + "score": 1.0, + "content": "which has 6 task rewards (CIDER, ROUGE-2, ROUGE-L, BLEU-3, BLEU-4, METEOR) we run 6", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 433, + 506, + 446 + ], + "spans": [ + { + "bbox": [ + 105, + 433, + 506, + 446 + ], + "score": 1.0, + "content": "different experiments optimizing each metric independently and report all possible metrics seen in", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 443, + 390, + 456 + ], + "spans": [ + { + "bbox": [ + 105, + 443, + 390, + 456 + ], + "score": 1.0, + "content": "Table 1 regardless of which individual metric was being optimized for.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 14.5 + }, + { + "type": "text", + "bbox": [ + 106, + 461, + 505, + 571 + ], + "lines": [ + { + "bbox": [ + 105, + 459, + 507, + 474 + ], + "spans": [ + { + "bbox": [ + 105, + 459, + 507, + 474 + ], + "score": 1.0, + "content": "Human Participant Study. We gather human judgments for five of the tasks in GRUE. In doing so,", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 472, + 506, + 484 + ], + "spans": [ + { + "bbox": [ + 105, + 472, + 506, + 484 + ], + "score": 1.0, + "content": "our goals are 1) to validate that the automated metrics we selected for GRUE correlate with human", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 483, + 506, + 495 + ], + "spans": [ + { + "bbox": [ + 105, + 483, + 506, + 495 + ], + "score": 1.0, + "content": "judgments with respect to relative ranking between models; and 2) to provide additional empirical", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 493, + 506, + 507 + ], + "spans": [ + { + "bbox": [ + 105, + 493, + 506, + 507 + ], + "score": 1.0, + "content": "comparisons regarding NLPO vs. PPO, ablations to study the effects of the KL naturalness penalty,", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 505, + 506, + 518 + ], + "spans": [ + { + "bbox": [ + 106, + 505, + 506, + 518 + ], + "score": 1.0, + "content": "etc. We specifically consider IMDB, Commongen, ToTTo, DailyDialog, and CNN Daily Mail. For", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 516, + 506, + 528 + ], + "spans": [ + { + "bbox": [ + 106, + 516, + 506, + 528 + ], + "score": 1.0, + "content": "each individual sample in a task, we ask 3 unique human raters to provide Likert judgments of 1)", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 526, + 506, + 540 + ], + "spans": [ + { + "bbox": [ + 105, + 526, + 506, + 540 + ], + "score": 1.0, + "content": "quality, i.e., for the specific task, how correct/appropriate is the generation, given the context, and", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 537, + 506, + 550 + ], + "spans": [ + { + "bbox": [ + 106, + 537, + 506, + 550 + ], + "score": 1.0, + "content": "2) fluency, i.e., how well-written is the generation. We used Amazon Mechanical Turk, and paid", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 549, + 505, + 560 + ], + "spans": [ + { + "bbox": [ + 106, + 549, + 228, + 560 + ], + "score": 1.0, + "content": "crowdworkers a minimum of", + "type": "text" + }, + { + "bbox": [ + 228, + 549, + 256, + 560 + ], + "score": 0.9, + "content": "\\$ 15/\\mathrm { h r }", + "type": "inline_equation" + }, + { + "bbox": [ + 257, + 549, + 505, + 560 + ], + "score": 1.0, + "content": ". More details, including qualification information, interface", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 560, + 404, + 572 + ], + "spans": [ + { + "bbox": [ + 105, + 560, + 404, + 572 + ], + "score": 1.0, + "content": "screenshots, instructions, etc. are given in the corresponding Appendicies.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 23.5 + }, + { + "type": "text", + "bbox": [ + 107, + 584, + 503, + 595 + ], + "lines": [ + { + "bbox": [ + 105, + 583, + 506, + 597 + ], + "spans": [ + { + "bbox": [ + 105, + 583, + 506, + 597 + ], + "score": 1.0, + "content": "5.1 RESULTS ON GRUE: WHICH ALGORITHM SHOULD BE USED TO LEARN PREFERENCES?", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 29 + }, + { + "type": "text", + "bbox": [ + 107, + 604, + 504, + 660 + ], + "lines": [ + { + "bbox": [ + 106, + 605, + 505, + 617 + ], + "spans": [ + { + "bbox": [ + 106, + 605, + 505, + 617 + ], + "score": 1.0, + "content": "Figures 2(a), 2(b) present the results on GRUE, split into task metrics and naturalness metrics, and", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 615, + 506, + 629 + ], + "spans": [ + { + "bbox": [ + 105, + 615, + 506, + 629 + ], + "score": 1.0, + "content": "Tables 2, 3 highlight key results via ablation studies. Full results are available in Appendix B. For text", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 626, + 506, + 640 + ], + "spans": [ + { + "bbox": [ + 105, + 626, + 506, + 640 + ], + "score": 1.0, + "content": "continuation and summarization, with non-trivial zero-shot performance, RL tends to perform better", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 638, + 505, + 650 + ], + "spans": [ + { + "bbox": [ + 106, + 638, + 505, + 650 + ], + "score": 1.0, + "content": "than supervised training, but for tasks like Commongen and ToTTo, which have very low zero-shot", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 649, + 495, + 662 + ], + "spans": [ + { + "bbox": [ + 105, + 649, + 495, + 662 + ], + "score": 1.0, + "content": "performance, supervised training performs best—with both approaches outperforming zero-shot.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 32 + }, + { + "type": "text", + "bbox": [ + 107, + 666, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "score": 1.0, + "content": "However, using RL+Supervised learning in conjunction works best; NLPO+supervised and", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 677, + 506, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 506, + 690 + ], + "score": 1.0, + "content": "PPO+supervised usually always outperforms NLPO/PPO (or supervised in isolation) across both task", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 686, + 506, + 702 + ], + "spans": [ + { + "bbox": [ + 105, + 686, + 506, + 702 + ], + "score": 1.0, + "content": "metrics and naturalness metrics. Supervised warm-starting is particularly effective for Commongen", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 699, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 505, + 712 + ], + "score": 1.0, + "content": "and ToTTo, which our results suggest are more prone to reward hacking. The one exception to this", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 428, + 722 + ], + "score": 1.0, + "content": "trend is DailyDialog where the RL models outperform warm-started Supervised", + "type": "text" + }, + { + "bbox": [ + 428, + 710, + 447, + 720 + ], + "score": 0.26, + "content": "+ \\mathrm { R L }", + "type": "inline_equation" + }, + { + "bbox": [ + 448, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "models likely", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 719, + 506, + 735 + ], + "spans": [ + { + "bbox": [ + 105, + 719, + 506, + 735 + ], + "score": 1.0, + "content": "due to the low performance of the Supervised models. We note that Supervised+NLPO using a", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 37.5 + } + ], + "page_idx": 5, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2023", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 752, + 308, + 760 + ], + "lines": [ + { + "bbox": [ + 302, + 751, + 309, + 762 + ], + "spans": [ + { + "bbox": [ + 302, + 751, + 309, + 762 + ], + "score": 1.0, + "content": "6", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "table", + "bbox": [ + 117, + 79, + 494, + 239 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 117, + 79, + 494, + 239 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 117, + 79, + 494, + 239 + ], + "spans": [ + { + "bbox": [ + 117, + 79, + 494, + 239 + ], + "score": 0.981, + "html": "
DatasetTaskInputOutputTask Preference Metrics(s)Naturalness Metrics(s)
IMDB (Maas et al., 2011)Text Continua- tionPartial Movie ReviewA positive completion of the movie review.Learned Sentiment ClassifierPerplexity (GPT-2)
CommonGEN (Lin et al., 2020)Generative CommonsenseConcept SetA sentence coherently using all input concepts.CIDER; ROUGE-2,L; BLEU-3,4; METEOR; CoverageSPICE
CNN Daily Mail (Hermann et al.,2015) SummarizationNews ArticleSummarized article.SummaCZS; ROUGE-1,2,L,LSum; METEOR; BLEUBertScore
ToTTo (Parikh et al.,2020)Data to TextHighlighted Wiki TableFactually accurate text describing the information.SacreBLEU; PARENTBLEURT
WMT-16 (en-de) (Bojar et al., 2016)Machine Trans- lationText (English)Translated text (German).TER; cHRF;ROUGE-1,2,L,LSum, METEOR; SacreBLEU,BLEUBertScore
NarrativeQA (Kocisky et al.,2018)Question An- sweringQuestion Context (a Story)Abstractive answer to the question.ROUGE-1,2,L,LSum,LMax; METEOR; BLEU; SacreBLEUBertScore
DailyDialog (Li et al., 2017)Chitchat Dia- logueDialogue HistoryA conversational responseMETEOR; Learned Intent ClassfierBertScore
", + "type": "table", + "image_path": "b056917381bc657590cb3031471d4d34e3db23d5329b8f101b006857917f8164.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 117, + 79, + 494, + 132.33333333333334 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 117, + 132.33333333333334, + 494, + 185.66666666666669 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 117, + 185.66666666666669, + 494, + 239.00000000000003 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "table_caption", + "bbox": [ + 109, + 252, + 503, + 285 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 251, + 505, + 265 + ], + "spans": [ + { + "bbox": [ + 106, + 251, + 505, + 265 + ], + "score": 1.0, + "content": "Table 1: GRUE Benchmark using RL4LMs showing the various tasks, input and output types, and", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 107, + 263, + 505, + 275 + ], + "spans": [ + { + "bbox": [ + 107, + 263, + 505, + 275 + ], + "score": 1.0, + "content": "the metrics used. We note that we test RL algorithms on these tasks for a wider range of possible", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 273, + 479, + 287 + ], + "spans": [ + { + "bbox": [ + 106, + 273, + 479, + 287 + ], + "score": 1.0, + "content": "rewards than just the task specific ones shown here. Unless specified, datasets are in English.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4 + } + ], + "index": 2.5 + }, + { + "type": "text", + "bbox": [ + 107, + 306, + 505, + 362 + ], + "lines": [], + "index": 8, + "bbox_fs": [ + 105, + 305, + 505, + 363 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 107, + 367, + 505, + 455 + ], + "lines": [ + { + "bbox": [ + 105, + 367, + 506, + 380 + ], + "spans": [ + { + "bbox": [ + 105, + 367, + 506, + 380 + ], + "score": 1.0, + "content": "For each task, to isolate the effect of training method, we select a single pre-trained LM backbone.", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 378, + 506, + 390 + ], + "spans": [ + { + "bbox": [ + 105, + 378, + 285, + 390 + ], + "score": 1.0, + "content": "For IMDB text continuation we use GPT-2 (", + "type": "text" + }, + { + "bbox": [ + 286, + 379, + 309, + 389 + ], + "score": 0.55, + "content": "1 1 7 \\mathrm { m }", + "type": "inline_equation" + }, + { + "bbox": [ + 310, + 378, + 506, + 390 + ], + "score": 1.0, + "content": "parameters), and for the rest of the tasks we use", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 389, + 506, + 402 + ], + "spans": [ + { + "bbox": [ + 105, + 389, + 143, + 402 + ], + "score": 1.0, + "content": "T5-base", + "type": "text" + }, + { + "bbox": [ + 143, + 389, + 167, + 400 + ], + "score": 0.49, + "content": "2 2 0 \\mathrm { m }", + "type": "inline_equation" + }, + { + "bbox": [ + 168, + 389, + 506, + 402 + ], + "score": 1.0, + "content": "parameters). For our RL models (PPO, NLPO, Supervised+PPO, Supervised+NLPO),", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 401, + 506, + 412 + ], + "spans": [ + { + "bbox": [ + 106, + 401, + 506, + 412 + ], + "score": 1.0, + "content": "for a thorough investigation of how reward-hacking might interplay with GRUE, we run a separate set", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 411, + 506, + 425 + ], + "spans": [ + { + "bbox": [ + 105, + 411, + 506, + 425 + ], + "score": 1.0, + "content": "of experiments optimizing multiple task rewards for each task independently, e.g., for Commongen", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 421, + 506, + 435 + ], + "spans": [ + { + "bbox": [ + 105, + 421, + 506, + 435 + ], + "score": 1.0, + "content": "which has 6 task rewards (CIDER, ROUGE-2, ROUGE-L, BLEU-3, BLEU-4, METEOR) we run 6", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 433, + 506, + 446 + ], + "spans": [ + { + "bbox": [ + 105, + 433, + 506, + 446 + ], + "score": 1.0, + "content": "different experiments optimizing each metric independently and report all possible metrics seen in", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 443, + 390, + 456 + ], + "spans": [ + { + "bbox": [ + 105, + 443, + 390, + 456 + ], + "score": 1.0, + "content": "Table 1 regardless of which individual metric was being optimized for.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 14.5, + "bbox_fs": [ + 105, + 367, + 506, + 456 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 461, + 505, + 571 + ], + "lines": [ + { + "bbox": [ + 105, + 459, + 507, + 474 + ], + "spans": [ + { + "bbox": [ + 105, + 459, + 507, + 474 + ], + "score": 1.0, + "content": "Human Participant Study. We gather human judgments for five of the tasks in GRUE. In doing so,", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 472, + 506, + 484 + ], + "spans": [ + { + "bbox": [ + 105, + 472, + 506, + 484 + ], + "score": 1.0, + "content": "our goals are 1) to validate that the automated metrics we selected for GRUE correlate with human", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 483, + 506, + 495 + ], + "spans": [ + { + "bbox": [ + 105, + 483, + 506, + 495 + ], + "score": 1.0, + "content": "judgments with respect to relative ranking between models; and 2) to provide additional empirical", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 493, + 506, + 507 + ], + "spans": [ + { + "bbox": [ + 105, + 493, + 506, + 507 + ], + "score": 1.0, + "content": "comparisons regarding NLPO vs. PPO, ablations to study the effects of the KL naturalness penalty,", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 505, + 506, + 518 + ], + "spans": [ + { + "bbox": [ + 106, + 505, + 506, + 518 + ], + "score": 1.0, + "content": "etc. We specifically consider IMDB, Commongen, ToTTo, DailyDialog, and CNN Daily Mail. For", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 516, + 506, + 528 + ], + "spans": [ + { + "bbox": [ + 106, + 516, + 506, + 528 + ], + "score": 1.0, + "content": "each individual sample in a task, we ask 3 unique human raters to provide Likert judgments of 1)", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 526, + 506, + 540 + ], + "spans": [ + { + "bbox": [ + 105, + 526, + 506, + 540 + ], + "score": 1.0, + "content": "quality, i.e., for the specific task, how correct/appropriate is the generation, given the context, and", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 537, + 506, + 550 + ], + "spans": [ + { + "bbox": [ + 106, + 537, + 506, + 550 + ], + "score": 1.0, + "content": "2) fluency, i.e., how well-written is the generation. We used Amazon Mechanical Turk, and paid", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 549, + 505, + 560 + ], + "spans": [ + { + "bbox": [ + 106, + 549, + 228, + 560 + ], + "score": 1.0, + "content": "crowdworkers a minimum of", + "type": "text" + }, + { + "bbox": [ + 228, + 549, + 256, + 560 + ], + "score": 0.9, + "content": "\\$ 15/\\mathrm { h r }", + "type": "inline_equation" + }, + { + "bbox": [ + 257, + 549, + 505, + 560 + ], + "score": 1.0, + "content": ". More details, including qualification information, interface", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 560, + 404, + 572 + ], + "spans": [ + { + "bbox": [ + 105, + 560, + 404, + 572 + ], + "score": 1.0, + "content": "screenshots, instructions, etc. are given in the corresponding Appendicies.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 23.5, + "bbox_fs": [ + 105, + 459, + 507, + 572 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 584, + 503, + 595 + ], + "lines": [ + { + "bbox": [ + 105, + 583, + 506, + 597 + ], + "spans": [ + { + "bbox": [ + 105, + 583, + 506, + 597 + ], + "score": 1.0, + "content": "5.1 RESULTS ON GRUE: WHICH ALGORITHM SHOULD BE USED TO LEARN PREFERENCES?", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 29, + "bbox_fs": [ + 105, + 583, + 506, + 597 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 604, + 504, + 660 + ], + "lines": [ + { + "bbox": [ + 106, + 605, + 505, + 617 + ], + "spans": [ + { + "bbox": [ + 106, + 605, + 505, + 617 + ], + "score": 1.0, + "content": "Figures 2(a), 2(b) present the results on GRUE, split into task metrics and naturalness metrics, and", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 615, + 506, + 629 + ], + "spans": [ + { + "bbox": [ + 105, + 615, + 506, + 629 + ], + "score": 1.0, + "content": "Tables 2, 3 highlight key results via ablation studies. Full results are available in Appendix B. For text", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 626, + 506, + 640 + ], + "spans": [ + { + "bbox": [ + 105, + 626, + 506, + 640 + ], + "score": 1.0, + "content": "continuation and summarization, with non-trivial zero-shot performance, RL tends to perform better", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 638, + 505, + 650 + ], + "spans": [ + { + "bbox": [ + 106, + 638, + 505, + 650 + ], + "score": 1.0, + "content": "than supervised training, but for tasks like Commongen and ToTTo, which have very low zero-shot", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 649, + 495, + 662 + ], + "spans": [ + { + "bbox": [ + 105, + 649, + 495, + 662 + ], + "score": 1.0, + "content": "performance, supervised training performs best—with both approaches outperforming zero-shot.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 32, + "bbox_fs": [ + 105, + 605, + 506, + 662 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 666, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 505, + 678 + ], + "score": 1.0, + "content": "However, using RL+Supervised learning in conjunction works best; NLPO+supervised and", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 677, + 506, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 506, + 690 + ], + "score": 1.0, + "content": "PPO+supervised usually always outperforms NLPO/PPO (or supervised in isolation) across both task", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 686, + 506, + 702 + ], + "spans": [ + { + "bbox": [ + 105, + 686, + 506, + 702 + ], + "score": 1.0, + "content": "metrics and naturalness metrics. 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The one exception to this", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 428, + 722 + ], + "score": 1.0, + "content": "trend is DailyDialog where the RL models outperform warm-started Supervised", + "type": "text" + }, + { + "bbox": [ + 428, + 710, + 447, + 720 + ], + "score": 0.26, + "content": "+ \\mathrm { R L }", + "type": "inline_equation" + }, + { + "bbox": [ + 448, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "models likely", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 719, + 506, + 735 + ], + "spans": [ + { + "bbox": [ + 105, + 719, + 506, + 735 + ], + "score": 1.0, + "content": "due to the low performance of the Supervised models. 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Test", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 433, + 374, + 444 + ], + "spans": [ + { + "bbox": [ + 105, + 433, + 374, + 444 + ], + "score": 1.0, + "content": "results are averaged over all the respective metrics seen in Table 1.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4 + } + ], + "index": 2.5 + }, + { + "type": "table", + "bbox": [ + 108, + 471, + 344, + 531 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 108, + 471, + 344, + 531 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 108, + 471, + 344, + 531 + ], + "spans": [ + { + "bbox": [ + 108, + 471, + 344, + 531 + ], + "score": 0.965, + "html": "
QuestionsTasks
IMDBCommonGen CNN/DMToTTOWMT16NarQA Dialog
Needs Warm StartXX√X√
Easily reward hackable?XXXX
RL >Sup (auto)?XXXXX
RL > Sup (human)？XXX
Sup+RL > Sup (auto)?√
Sup+RL > Sup (human)?XX
Sup+NLPO >Sup+PPO (auto)?
Sup+NLPO > Sup+PPO (human)?
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AblationSentimentPerplexity
Zero Shot Supervised PPO NLPO0.489 0.539 0.60232.171 35.472 33.816 33.832
Warm Starting (Sec.5.1)0.611
PPO+Supervised0.62635.049
NLPO+Supervised0.62034.816
DataBudget (Rewardtrained on10%of data,Sec.5.3)
PPO0.59835.929
NLPO0.59933.536
Removing NLPO Top-p Constraints (Sec.5.2) (p =1 is equivalent to PPO, p = 0.9 is NLPO)
NLPO p = 0.10.57932.451
NLPO p = 0.50.58832.447
Removing KL Constraints (Sec.5.2) PPO-no-KL
NLPO-no-KL0.838 0.85841.897 41.429
Discount Ablations (γ= 1) (Sec.5.4)
PPO0.65141.035
NLPO0.62443.720
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QuestionsTasks
IMDBCommonGen CNN/DMToTTOWMT16NarQA Dialog
Needs Warm StartXX√X√
Easily reward hackable?XXXX
RL >Sup (auto)?XXXXX
RL > Sup (human)？XXX
Sup+RL > Sup (auto)?√
Sup+RL > Sup (human)?XX
Sup+NLPO >Sup+PPO (auto)?
Sup+NLPO > Sup+PPO (human)?
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AblationSentimentPerplexity
Zero Shot Supervised PPO NLPO0.489 0.539 0.60232.171 35.472 33.816 33.832
Warm Starting (Sec.5.1)0.611
PPO+Supervised0.62635.049
NLPO+Supervised0.62034.816
DataBudget (Rewardtrained on10%of data,Sec.5.3)
PPO0.59835.929
NLPO0.59933.536
Removing NLPO Top-p Constraints (Sec.5.2) (p =1 is equivalent to PPO, p = 0.9 is NLPO)
NLPO p = 0.10.57932.451
NLPO p = 0.50.58832.447
Removing KL Constraints (Sec.5.2) PPO-no-KL
NLPO-no-KL0.838 0.85841.897 41.429
Discount Ablations (γ= 1) (Sec.5.4)
PPO0.65141.035
NLPO0.62443.720
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As human judgments can be noisy, we run additional", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 104, + 92, + 507, + 108 + ], + "spans": [ + { + "bbox": [ + 104, + 92, + 507, + 108 + ], + "score": 1.0, + "content": "statistical analysis such as measuring inter-annotator agreement, via Krippendorf’s alpha score,", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 105, + 505, + 117 + ], + "spans": [ + { + "bbox": [ + 105, + 105, + 505, + 117 + ], + "score": 1.0, + "content": "and using a one-way ANOVA followed by a post-hoc Tukey HSD test to measure if differences in", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 505, + 128 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 505, + 128 + ], + "score": 1.0, + "content": "means of average scores between pairs of models are significant. We find that trends in our human", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 126, + 506, + 140 + ], + "spans": [ + { + "bbox": [ + 105, + 126, + 506, + 140 + ], + "score": 1.0, + "content": "evaluations generally match those seen in the automated metrics for both task and naturalness metrics", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 137, + 504, + 150 + ], + "spans": [ + { + "bbox": [ + 106, + 137, + 461, + 150 + ], + "score": 1.0, + "content": "(see Figures 2(c), 2(d) which summarize Appendix Tables 10,15,21,26, 35—Supervised", + "type": "text" + }, + { + "bbox": [ + 461, + 137, + 504, + 148 + ], + "score": 0.34, + "content": "+ \\mathrm { N L P O } >", + "type": "inline_equation" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 148, + 506, + 161 + ], + "spans": [ + { + "bbox": [ + 106, + 148, + 153, + 161 + ], + "score": 1.0, + "content": "Supervised", + "type": "text" + }, + { + "bbox": [ + 154, + 149, + 164, + 159 + ], + "score": 0.8, + "content": "\\geq", + "type": "inline_equation" + }, + { + "bbox": [ + 164, + 148, + 211, + 161 + ], + "score": 1.0, + "content": "Supervised", + "type": "text" + }, + { + "bbox": [ + 212, + 149, + 325, + 159 + ], + "score": 0.47, + "content": "+ { \\mathrm { P P O } } > { \\mathrm { N L P O } } \\geq { \\mathrm { P P O } } > Z", + "type": "inline_equation" + }, + { + "bbox": [ + 325, + 148, + 506, + 161 + ], + "score": 1.0, + "content": "ero-shot—with the exception of Supervised", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 159, + 506, + 171 + ], + "spans": [ + { + "bbox": [ + 105, + 159, + 214, + 171 + ], + "score": 1.0, + "content": "outperforming Supervised", + "type": "text" + }, + { + "bbox": [ + 214, + 160, + 240, + 170 + ], + "score": 0.3, + "content": "+ \\mathrm { P P O }", + "type": "inline_equation" + }, + { + "bbox": [ + 240, + 159, + 506, + 171 + ], + "score": 1.0, + "content": "on 2 out of 5 tasks when automated metrics would indicate that", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 171, + 506, + 182 + ], + "spans": [ + { + "bbox": [ + 106, + 171, + 152, + 182 + ], + "score": 1.0, + "content": "Supervised", + "type": "text" + }, + { + "bbox": [ + 152, + 171, + 178, + 181 + ], + "score": 0.45, + "content": "+ \\mathrm { P P O }", + "type": "inline_equation" + }, + { + "bbox": [ + 178, + 171, + 506, + 182 + ], + "score": 1.0, + "content": "outperforms Supervised on all of the tasks. We draw two conclusions from this:", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 181, + 504, + 193 + ], + "spans": [ + { + "bbox": [ + 106, + 181, + 504, + 193 + ], + "score": 1.0, + "content": "(1) if the generated text is above a certain threshold of naturalness, the automated metrics usually", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 192, + 506, + 205 + ], + "spans": [ + { + "bbox": [ + 105, + 192, + 506, + 205 + ], + "score": 1.0, + "content": "correlate with human judgements; (2) usually but not always as seen in the relative performance of", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 203, + 505, + 217 + ], + "spans": [ + { + "bbox": [ + 105, + 203, + 218, + 217 + ], + "score": 1.0, + "content": "Supervised and Supervised", + "type": "text" + }, + { + "bbox": [ + 218, + 203, + 243, + 214 + ], + "score": 0.26, + "content": "+ \\mathrm { P P O }", + "type": "inline_equation" + }, + { + "bbox": [ + 243, + 203, + 505, + 217 + ], + "score": 1.0, + "content": ", potentially indicating reward hacking behaviors undetected by", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 214, + 353, + 226 + ], + "spans": [ + { + "bbox": [ + 106, + 214, + 353, + 226 + ], + "score": 1.0, + "content": "automated metrics but caught by human preference feedback.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 6 + }, + { + "type": "title", + "bbox": [ + 108, + 242, + 399, + 253 + ], + "lines": [ + { + "bbox": [ + 105, + 241, + 400, + 255 + ], + "spans": [ + { + "bbox": [ + 105, + 241, + 400, + 255 + ], + "score": 1.0, + "content": "5.2 PREFERENCE REWARD LEARNING, SELECTION, AND HACKING", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 13 + }, + { + "type": "text", + "bbox": [ + 107, + 264, + 505, + 319 + ], + "lines": [ + { + "bbox": [ + 106, + 263, + 505, + 277 + ], + "spans": [ + { + "bbox": [ + 106, + 263, + 505, + 277 + ], + "score": 1.0, + "content": "While the GRUE benchmark’s metric for each task is an average over several measures, the RL", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 274, + 505, + 288 + ], + "spans": [ + { + "bbox": [ + 105, + 274, + 505, + 288 + ], + "score": 1.0, + "content": "models we trained optimized only a single metric independently. Thus, we can empirically investigate", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 287, + 505, + 299 + ], + "spans": [ + { + "bbox": [ + 106, + 287, + 505, + 299 + ], + "score": 1.0, + "content": "which metric for which GRUE produces the best results. We observe that many possible single metric", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 298, + 505, + 309 + ], + "spans": [ + { + "bbox": [ + 106, + 298, + 505, + 309 + ], + "score": 1.0, + "content": "rewards provide task performance gains over supervised methods (results shown in Fig. 3(a), 2(c) are", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 308, + 506, + 320 + ], + "spans": [ + { + "bbox": [ + 105, + 308, + 506, + 320 + ], + "score": 1.0, + "content": "averaged across these reward functions) with the condition that the text is also coherent and natural.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 16 + }, + { + "type": "text", + "bbox": [ + 107, + 325, + 505, + 435 + ], + "lines": [ + { + "bbox": [ + 105, + 324, + 506, + 338 + ], + "spans": [ + { + "bbox": [ + 105, + 324, + 506, + 338 + ], + "score": 1.0, + "content": "Which constraints best prevent reward hacking? The reward function in Equation 1 balances a", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 336, + 505, + 348 + ], + "spans": [ + { + "bbox": [ + 106, + 336, + 505, + 348 + ], + "score": 1.0, + "content": "task-specific reward with a KL constraint — models are penalized from straying too far from a base", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 348, + 505, + 359 + ], + "spans": [ + { + "bbox": [ + 105, + 348, + 505, + 359 + ], + "score": 1.0, + "content": "LM in their pursuit of high reward (Table 3 and Appendix Table 5) clearly show that if KL constraints", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 104, + 358, + 506, + 370 + ], + "spans": [ + { + "bbox": [ + 104, + 358, + 506, + 370 + ], + "score": 1.0, + "content": "are removed entirely, models reward hack). But which model works best as a base regularizing LM?", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 369, + 506, + 382 + ], + "spans": [ + { + "bbox": [ + 105, + 369, + 506, + 382 + ], + "score": 1.0, + "content": "When the initial policy (i.e., the raw, pretrained model) has low performance on the task, the KL", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 380, + 506, + 393 + ], + "spans": [ + { + "bbox": [ + 105, + 380, + 506, + 393 + ], + "score": 1.0, + "content": "penalty pushes the policy towards nonsense, e.g. on Commongen and ToTTo the trained policy learns", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 390, + 506, + 404 + ], + "spans": [ + { + "bbox": [ + 105, + 390, + 506, + 404 + ], + "score": 1.0, + "content": "to simply repeat portions of the input (as seen in Tables B.4.5, B.6.4). This behavior is mitigated", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 104, + 401, + 505, + 415 + ], + "spans": [ + { + "bbox": [ + 104, + 401, + 505, + 415 + ], + "score": 1.0, + "content": "if the base regularizing LM is the supervised model—the reward encourages the policy to balance", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 413, + 505, + 425 + ], + "spans": [ + { + "bbox": [ + 105, + 413, + 505, + 425 + ], + "score": 1.0, + "content": "the task-specific reward and a more reasonable regularization term. Deriving KL penalties from", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 424, + 385, + 436 + ], + "spans": [ + { + "bbox": [ + 105, + 424, + 385, + 436 + ], + "score": 1.0, + "content": "warm-started initial policies is critical for performance on such tasks.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 23.5 + }, + { + "type": "text", + "bbox": [ + 107, + 441, + 505, + 540 + ], + "lines": [ + { + "bbox": [ + 105, + 440, + 505, + 453 + ], + "spans": [ + { + "bbox": [ + 105, + 440, + 505, + 453 + ], + "score": 1.0, + "content": "PPO vs. NLPO. Figure 2 shows that NLPO generally outperforms PPO and supervised, especially", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 452, + 505, + 464 + ], + "spans": [ + { + "bbox": [ + 106, + 452, + 505, + 464 + ], + "score": 1.0, + "content": "when applied after supervised training. We hypothesize that the primary reason for NLPO’s improved", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 463, + 506, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 463, + 506, + 475 + ], + "score": 1.0, + "content": "performance and stability is because the masking policy provides an additional constraint for the", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 473, + 506, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 473, + 506, + 486 + ], + "score": 1.0, + "content": "current policy. This constraint is not based on the initial untuned policy like the KL penalty but of", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 484, + 505, + 498 + ], + "spans": [ + { + "bbox": [ + 105, + 484, + 171, + 498 + ], + "score": 1.0, + "content": "the policy from", + "type": "text" + }, + { + "bbox": [ + 171, + 486, + 179, + 496 + ], + "score": 0.81, + "content": "\\mu", + "type": "inline_equation" + }, + { + "bbox": [ + 179, + 484, + 505, + 498 + ], + "score": 1.0, + "content": "iterations ago and likely contains more task-relevant information learned during", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 495, + 505, + 508 + ], + "spans": [ + { + "bbox": [ + 105, + 495, + 505, + 508 + ], + "score": 1.0, + "content": "RL training. Table 3 (and Appendix Table 8) shows how performance increases up to a point and", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 505, + 505, + 520 + ], + "spans": [ + { + "bbox": [ + 105, + 505, + 177, + 520 + ], + "score": 1.0, + "content": "then decreases as", + "type": "text" + }, + { + "bbox": [ + 177, + 508, + 184, + 518 + ], + "score": 0.81, + "content": "p", + "type": "inline_equation" + }, + { + "bbox": [ + 185, + 505, + 211, + 520 + ], + "score": 1.0, + "content": "in top-", + "type": "text" + }, + { + "bbox": [ + 212, + 508, + 218, + 518 + ], + "score": 0.77, + "content": "p", + "type": "inline_equation" + }, + { + "bbox": [ + 218, + 505, + 505, + 520 + ], + "score": 1.0, + "content": "sampling is increased for the masking policy, relaxing the constraint by", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 517, + 505, + 530 + ], + "spans": [ + { + "bbox": [ + 105, + 517, + 505, + 530 + ], + "score": 1.0, + "content": "eliminating less tokens at each step, implying that there is a balance to be found in how much the", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 528, + 303, + 542 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 303, + 542 + ], + "score": 1.0, + "content": "model should be constrained during RL training.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 33 + }, + { + "type": "text", + "bbox": [ + 107, + 545, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 545, + 505, + 558 + ], + "spans": [ + { + "bbox": [ + 105, + 545, + 505, + 558 + ], + "score": 1.0, + "content": "Human Preference Reward Learning. To this point, our experiments have largely focused on", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 556, + 506, + 569 + ], + "spans": [ + { + "bbox": [ + 105, + 556, + 506, + 569 + ], + "score": 1.0, + "content": "optimizing evaluation metrics that correlate with human judgments, e.g., METEOR. Here: we", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 566, + 506, + 581 + ], + "spans": [ + { + "bbox": [ + 105, + 566, + 506, + 581 + ], + "score": 1.0, + "content": "additionally test how well preferences can be learned from direct human feedback. For this, we focus", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 577, + 506, + 592 + ], + "spans": [ + { + "bbox": [ + 105, + 577, + 506, + 592 + ], + "score": 1.0, + "content": "on Commongen — a GRUE dataset well-suited for displaying differences due to human preferences.", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 589, + 506, + 602 + ], + "spans": [ + { + "bbox": [ + 105, + 589, + 506, + 602 + ], + "score": 1.0, + "content": "First, we randomly select prompts from the Commongen train dataset and sample a single completion", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 599, + 506, + 613 + ], + "spans": [ + { + "bbox": [ + 105, + 599, + 506, + 613 + ], + "score": 1.0, + "content": "from both the Supervised and Supervised+NLPO models. We then present the prompt and the two", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 611, + 505, + 624 + ], + "spans": [ + { + "bbox": [ + 105, + 611, + 505, + 624 + ], + "score": 1.0, + "content": "completion candidates to 3 unique crowdworkers and ask them to select which one they prefer with", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 622, + 506, + 635 + ], + "spans": [ + { + "bbox": [ + 105, + 622, + 387, + 635 + ], + "score": 1.0, + "content": "respect to commonsense/fluency for 417 unique pairs (Krippendorf", + "type": "text" + }, + { + "bbox": [ + 388, + 622, + 425, + 632 + ], + "score": 0.82, + "content": "\\alpha = . 2 8", + "type": "inline_equation" + }, + { + "bbox": [ + 425, + 622, + 506, + 635 + ], + "score": 1.0, + "content": "). We use this data", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 633, + 506, + 645 + ], + "spans": [ + { + "bbox": [ + 105, + 633, + 506, + 645 + ], + "score": 1.0, + "content": "to train a reward model, T5-11B Raffel et al. (2020), on the balanced binary classification task of", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 643, + 505, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 643, + 505, + 657 + ], + "score": 1.0, + "content": "predicting which of the pair was preferred by a majority of 3 annotators, conditioned on the prompt", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 654, + 505, + 669 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 505, + 669 + ], + "score": 1.0, + "content": "and completion. The resulting model achieved 69.5 test ROC AUC suggesting it indeed captures", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 104, + 665, + 505, + 679 + ], + "spans": [ + { + "bbox": [ + 104, + 665, + 505, + 679 + ], + "score": 1.0, + "content": "average human preferences. Additional details on this process are found in Appendix B.4.4. We train", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 105, + 676, + 505, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 676, + 152, + 690 + ], + "score": 1.0, + "content": "Supervised", + "type": "text" + }, + { + "bbox": [ + 152, + 677, + 172, + 687 + ], + "score": 0.61, + "content": "+ \\mathrm { R L }", + "type": "inline_equation" + }, + { + "bbox": [ + 172, + 676, + 505, + 690 + ], + "score": 1.0, + "content": "with a METEOR-only reward as a baseline, and compare it to a reward function", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "score": 1.0, + "content": "that uses the fine-tuned T5-11B model. Finally, we rerun the same pairwise preference collection", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 105, + 699, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 505, + 712 + ], + "score": 1.0, + "content": "procedure—this time sampling from Commongen test—with human participants to compare the", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 105, + 709, + 507, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 507, + 723 + ], + "score": 1.0, + "content": "generations from a preference optimized RL policy to the previously best Supervised+NLPO policy.", + "type": "text" + } + ], + "index": 53 + }, + { + "bbox": [ + 106, + 720, + 505, + 734 + ], + "spans": [ + { + "bbox": [ + 106, + 720, + 505, + 734 + ], + "score": 1.0, + "content": "Comparing the METEOR-only to the preference model, the generations produced by the human", + "type": "text" + } + ], + "index": 54 + } + ], + "index": 46 + } + ], + "page_idx": 7, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2023", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 752, + 308, + 759 + ], + "lines": [ + { + "bbox": [ + 302, + 750, + 309, + 761 + ], + "spans": [ + { + "bbox": [ + 302, + 750, + 309, + 761 + ], + "score": 1.0, + "content": "8", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 83, + 505, + 225 + ], + "lines": [ + { + "bbox": [ + 106, + 83, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 83, + 505, + 95 + ], + "score": 1.0, + "content": "Human agreement with automated metrics. As human judgments can be noisy, we run additional", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 104, + 92, + 507, + 108 + ], + "spans": [ + { + "bbox": [ + 104, + 92, + 507, + 108 + ], + "score": 1.0, + "content": "statistical analysis such as measuring inter-annotator agreement, via Krippendorf’s alpha score,", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 105, + 505, + 117 + ], + "spans": [ + { + "bbox": [ + 105, + 105, + 505, + 117 + ], + "score": 1.0, + "content": "and using a one-way ANOVA followed by a post-hoc Tukey HSD test to measure if differences in", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 505, + 128 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 505, + 128 + ], + "score": 1.0, + "content": "means of average scores between pairs of models are significant. We find that trends in our human", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 126, + 506, + 140 + ], + "spans": [ + { + "bbox": [ + 105, + 126, + 506, + 140 + ], + "score": 1.0, + "content": "evaluations generally match those seen in the automated metrics for both task and naturalness metrics", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 137, + 504, + 150 + ], + "spans": [ + { + "bbox": [ + 106, + 137, + 461, + 150 + ], + "score": 1.0, + "content": "(see Figures 2(c), 2(d) which summarize Appendix Tables 10,15,21,26, 35—Supervised", + "type": "text" + }, + { + "bbox": [ + 461, + 137, + 504, + 148 + ], + "score": 0.34, + "content": "+ \\mathrm { N L P O } >", + "type": "inline_equation" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 148, + 506, + 161 + ], + "spans": [ + { + "bbox": [ + 106, + 148, + 153, + 161 + ], + "score": 1.0, + "content": "Supervised", + "type": "text" + }, + { + "bbox": [ + 154, + 149, + 164, + 159 + ], + "score": 0.8, + "content": "\\geq", + "type": "inline_equation" + }, + { + "bbox": [ + 164, + 148, + 211, + 161 + ], + "score": 1.0, + "content": "Supervised", + "type": "text" + }, + { + "bbox": [ + 212, + 149, + 325, + 159 + ], + "score": 0.47, + "content": "+ { \\mathrm { P P O } } > { \\mathrm { N L P O } } \\geq { \\mathrm { P P O } } > Z", + "type": "inline_equation" + }, + { + "bbox": [ + 325, + 148, + 506, + 161 + ], + "score": 1.0, + "content": "ero-shot—with the exception of Supervised", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 159, + 506, + 171 + ], + "spans": [ + { + "bbox": [ + 105, + 159, + 214, + 171 + ], + "score": 1.0, + "content": "outperforming Supervised", + "type": "text" + }, + { + "bbox": [ + 214, + 160, + 240, + 170 + ], + "score": 0.3, + "content": "+ \\mathrm { P P O }", + "type": "inline_equation" + }, + { + "bbox": [ + 240, + 159, + 506, + 171 + ], + "score": 1.0, + "content": "on 2 out of 5 tasks when automated metrics would indicate that", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 171, + 506, + 182 + ], + "spans": [ + { + "bbox": [ + 106, + 171, + 152, + 182 + ], + "score": 1.0, + "content": "Supervised", + "type": "text" + }, + { + "bbox": [ + 152, + 171, + 178, + 181 + ], + "score": 0.45, + "content": "+ \\mathrm { P P O }", + "type": "inline_equation" + }, + { + "bbox": [ + 178, + 171, + 506, + 182 + ], + "score": 1.0, + "content": "outperforms Supervised on all of the tasks. We draw two conclusions from this:", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 181, + 504, + 193 + ], + "spans": [ + { + "bbox": [ + 106, + 181, + 504, + 193 + ], + "score": 1.0, + "content": "(1) if the generated text is above a certain threshold of naturalness, the automated metrics usually", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 192, + 506, + 205 + ], + "spans": [ + { + "bbox": [ + 105, + 192, + 506, + 205 + ], + "score": 1.0, + "content": "correlate with human judgements; (2) usually but not always as seen in the relative performance of", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 203, + 505, + 217 + ], + "spans": [ + { + "bbox": [ + 105, + 203, + 218, + 217 + ], + "score": 1.0, + "content": "Supervised and Supervised", + "type": "text" + }, + { + "bbox": [ + 218, + 203, + 243, + 214 + ], + "score": 0.26, + "content": "+ \\mathrm { P P O }", + "type": "inline_equation" + }, + { + "bbox": [ + 243, + 203, + 505, + 217 + ], + "score": 1.0, + "content": ", potentially indicating reward hacking behaviors undetected by", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 214, + 353, + 226 + ], + "spans": [ + { + "bbox": [ + 106, + 214, + 353, + 226 + ], + "score": 1.0, + "content": "automated metrics but caught by human preference feedback.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 6, + "bbox_fs": [ + 104, + 83, + 507, + 226 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 242, + 399, + 253 + ], + "lines": [ + { + "bbox": [ + 105, + 241, + 400, + 255 + ], + "spans": [ + { + "bbox": [ + 105, + 241, + 400, + 255 + ], + "score": 1.0, + "content": "5.2 PREFERENCE REWARD LEARNING, SELECTION, AND HACKING", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 13 + }, + { + "type": "text", + "bbox": [ + 107, + 264, + 505, + 319 + ], + "lines": [ + { + "bbox": [ + 106, + 263, + 505, + 277 + ], + "spans": [ + { + "bbox": [ + 106, + 263, + 505, + 277 + ], + "score": 1.0, + "content": "While the GRUE benchmark’s metric for each task is an average over several measures, the RL", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 274, + 505, + 288 + ], + "spans": [ + { + "bbox": [ + 105, + 274, + 505, + 288 + ], + "score": 1.0, + "content": "models we trained optimized only a single metric independently. Thus, we can empirically investigate", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 287, + 505, + 299 + ], + "spans": [ + { + "bbox": [ + 106, + 287, + 505, + 299 + ], + "score": 1.0, + "content": "which metric for which GRUE produces the best results. We observe that many possible single metric", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 298, + 505, + 309 + ], + "spans": [ + { + "bbox": [ + 106, + 298, + 505, + 309 + ], + "score": 1.0, + "content": "rewards provide task performance gains over supervised methods (results shown in Fig. 3(a), 2(c) are", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 308, + 506, + 320 + ], + "spans": [ + { + "bbox": [ + 105, + 308, + 506, + 320 + ], + "score": 1.0, + "content": "averaged across these reward functions) with the condition that the text is also coherent and natural.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 16, + "bbox_fs": [ + 105, + 263, + 506, + 320 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 325, + 505, + 435 + ], + "lines": [ + { + "bbox": [ + 105, + 324, + 506, + 338 + ], + "spans": [ + { + "bbox": [ + 105, + 324, + 506, + 338 + ], + "score": 1.0, + "content": "Which constraints best prevent reward hacking? The reward function in Equation 1 balances a", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 336, + 505, + 348 + ], + "spans": [ + { + "bbox": [ + 106, + 336, + 505, + 348 + ], + "score": 1.0, + "content": "task-specific reward with a KL constraint — models are penalized from straying too far from a base", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 348, + 505, + 359 + ], + "spans": [ + { + "bbox": [ + 105, + 348, + 505, + 359 + ], + "score": 1.0, + "content": "LM in their pursuit of high reward (Table 3 and Appendix Table 5) clearly show that if KL constraints", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 104, + 358, + 506, + 370 + ], + "spans": [ + { + "bbox": [ + 104, + 358, + 506, + 370 + ], + "score": 1.0, + "content": "are removed entirely, models reward hack). But which model works best as a base regularizing LM?", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 369, + 506, + 382 + ], + "spans": [ + { + "bbox": [ + 105, + 369, + 506, + 382 + ], + "score": 1.0, + "content": "When the initial policy (i.e., the raw, pretrained model) has low performance on the task, the KL", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 380, + 506, + 393 + ], + "spans": [ + { + "bbox": [ + 105, + 380, + 506, + 393 + ], + "score": 1.0, + "content": "penalty pushes the policy towards nonsense, e.g. on Commongen and ToTTo the trained policy learns", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 390, + 506, + 404 + ], + "spans": [ + { + "bbox": [ + 105, + 390, + 506, + 404 + ], + "score": 1.0, + "content": "to simply repeat portions of the input (as seen in Tables B.4.5, B.6.4). This behavior is mitigated", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 104, + 401, + 505, + 415 + ], + "spans": [ + { + "bbox": [ + 104, + 401, + 505, + 415 + ], + "score": 1.0, + "content": "if the base regularizing LM is the supervised model—the reward encourages the policy to balance", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 413, + 505, + 425 + ], + "spans": [ + { + "bbox": [ + 105, + 413, + 505, + 425 + ], + "score": 1.0, + "content": "the task-specific reward and a more reasonable regularization term. Deriving KL penalties from", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 424, + 385, + 436 + ], + "spans": [ + { + "bbox": [ + 105, + 424, + 385, + 436 + ], + "score": 1.0, + "content": "warm-started initial policies is critical for performance on such tasks.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 23.5, + "bbox_fs": [ + 104, + 324, + 506, + 436 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 441, + 505, + 540 + ], + "lines": [ + { + "bbox": [ + 105, + 440, + 505, + 453 + ], + "spans": [ + { + "bbox": [ + 105, + 440, + 505, + 453 + ], + "score": 1.0, + "content": "PPO vs. NLPO. Figure 2 shows that NLPO generally outperforms PPO and supervised, especially", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 452, + 505, + 464 + ], + "spans": [ + { + "bbox": [ + 106, + 452, + 505, + 464 + ], + "score": 1.0, + "content": "when applied after supervised training. We hypothesize that the primary reason for NLPO’s improved", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 463, + 506, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 463, + 506, + 475 + ], + "score": 1.0, + "content": "performance and stability is because the masking policy provides an additional constraint for the", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 473, + 506, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 473, + 506, + 486 + ], + "score": 1.0, + "content": "current policy. This constraint is not based on the initial untuned policy like the KL penalty but of", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 484, + 505, + 498 + ], + "spans": [ + { + "bbox": [ + 105, + 484, + 171, + 498 + ], + "score": 1.0, + "content": "the policy from", + "type": "text" + }, + { + "bbox": [ + 171, + 486, + 179, + 496 + ], + "score": 0.81, + "content": "\\mu", + "type": "inline_equation" + }, + { + "bbox": [ + 179, + 484, + 505, + 498 + ], + "score": 1.0, + "content": "iterations ago and likely contains more task-relevant information learned during", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 495, + 505, + 508 + ], + "spans": [ + { + "bbox": [ + 105, + 495, + 505, + 508 + ], + "score": 1.0, + "content": "RL training. Table 3 (and Appendix Table 8) shows how performance increases up to a point and", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 505, + 505, + 520 + ], + "spans": [ + { + "bbox": [ + 105, + 505, + 177, + 520 + ], + "score": 1.0, + "content": "then decreases as", + "type": "text" + }, + { + "bbox": [ + 177, + 508, + 184, + 518 + ], + "score": 0.81, + "content": "p", + "type": "inline_equation" + }, + { + "bbox": [ + 185, + 505, + 211, + 520 + ], + "score": 1.0, + "content": "in top-", + "type": "text" + }, + { + "bbox": [ + 212, + 508, + 218, + 518 + ], + "score": 0.77, + "content": "p", + "type": "inline_equation" + }, + { + "bbox": [ + 218, + 505, + 505, + 520 + ], + "score": 1.0, + "content": "sampling is increased for the masking policy, relaxing the constraint by", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 517, + 505, + 530 + ], + "spans": [ + { + "bbox": [ + 105, + 517, + 505, + 530 + ], + "score": 1.0, + "content": "eliminating less tokens at each step, implying that there is a balance to be found in how much the", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 528, + 303, + 542 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 303, + 542 + ], + "score": 1.0, + "content": "model should be constrained during RL training.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 33, + "bbox_fs": [ + 105, + 440, + 506, + 542 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 545, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 545, + 505, + 558 + ], + "spans": [ + { + "bbox": [ + 105, + 545, + 505, + 558 + ], + "score": 1.0, + "content": "Human Preference Reward Learning. To this point, our experiments have largely focused on", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 556, + 506, + 569 + ], + "spans": [ + { + "bbox": [ + 105, + 556, + 506, + 569 + ], + "score": 1.0, + "content": "optimizing evaluation metrics that correlate with human judgments, e.g., METEOR. Here: we", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 566, + 506, + 581 + ], + "spans": [ + { + "bbox": [ + 105, + 566, + 506, + 581 + ], + "score": 1.0, + "content": "additionally test how well preferences can be learned from direct human feedback. For this, we focus", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 577, + 506, + 592 + ], + "spans": [ + { + "bbox": [ + 105, + 577, + 506, + 592 + ], + "score": 1.0, + "content": "on Commongen — a GRUE dataset well-suited for displaying differences due to human preferences.", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 589, + 506, + 602 + ], + "spans": [ + { + "bbox": [ + 105, + 589, + 506, + 602 + ], + "score": 1.0, + "content": "First, we randomly select prompts from the Commongen train dataset and sample a single completion", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 599, + 506, + 613 + ], + "spans": [ + { + "bbox": [ + 105, + 599, + 506, + 613 + ], + "score": 1.0, + "content": "from both the Supervised and Supervised+NLPO models. We then present the prompt and the two", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 611, + 505, + 624 + ], + "spans": [ + { + "bbox": [ + 105, + 611, + 505, + 624 + ], + "score": 1.0, + "content": "completion candidates to 3 unique crowdworkers and ask them to select which one they prefer with", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 622, + 506, + 635 + ], + "spans": [ + { + "bbox": [ + 105, + 622, + 387, + 635 + ], + "score": 1.0, + "content": "respect to commonsense/fluency for 417 unique pairs (Krippendorf", + "type": "text" + }, + { + "bbox": [ + 388, + 622, + 425, + 632 + ], + "score": 0.82, + "content": "\\alpha = . 2 8", + "type": "inline_equation" + }, + { + "bbox": [ + 425, + 622, + 506, + 635 + ], + "score": 1.0, + "content": "). We use this data", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 633, + 506, + 645 + ], + "spans": [ + { + "bbox": [ + 105, + 633, + 506, + 645 + ], + "score": 1.0, + "content": "to train a reward model, T5-11B Raffel et al. (2020), on the balanced binary classification task of", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 643, + 505, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 643, + 505, + 657 + ], + "score": 1.0, + "content": "predicting which of the pair was preferred by a majority of 3 annotators, conditioned on the prompt", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 654, + 505, + 669 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 505, + 669 + ], + "score": 1.0, + "content": "and completion. The resulting model achieved 69.5 test ROC AUC suggesting it indeed captures", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 104, + 665, + 505, + 679 + ], + "spans": [ + { + "bbox": [ + 104, + 665, + 505, + 679 + ], + "score": 1.0, + "content": "average human preferences. Additional details on this process are found in Appendix B.4.4. We train", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 105, + 676, + 505, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 676, + 152, + 690 + ], + "score": 1.0, + "content": "Supervised", + "type": "text" + }, + { + "bbox": [ + 152, + 677, + 172, + 687 + ], + "score": 0.61, + "content": "+ \\mathrm { R L }", + "type": "inline_equation" + }, + { + "bbox": [ + 172, + 676, + 505, + 690 + ], + "score": 1.0, + "content": "with a METEOR-only reward as a baseline, and compare it to a reward function", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "score": 1.0, + "content": "that uses the fine-tuned T5-11B model. Finally, we rerun the same pairwise preference collection", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 105, + 699, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 505, + 712 + ], + "score": 1.0, + "content": "procedure—this time sampling from Commongen test—with human participants to compare the", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 105, + 709, + 507, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 507, + 723 + ], + "score": 1.0, + "content": "generations from a preference optimized RL policy to the previously best Supervised+NLPO policy.", + "type": "text" + } + ], + "index": 53 + }, + { + "bbox": [ + 106, + 720, + 505, + 734 + ], + "spans": [ + { + "bbox": [ + 106, + 720, + 505, + 734 + ], + "score": 1.0, + "content": "Comparing the METEOR-only to the preference model, the generations produced by the human", + "type": "text" + } + ], + "index": 54 + }, + { + "bbox": [ + 105, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "feedback model are preferred in 682 cases, compared to the METEOR-only model which is preferred", + "type": "text", + "cross_page": true + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 92, + 506, + 107 + ], + "spans": [ + { + "bbox": [ + 105, + 92, + 159, + 107 + ], + "score": 1.0, + "content": "in 587 cases", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 160, + 94, + 198, + 105 + ], + "score": 0.88, + "content": "\\mathit { p } < 0 . 0 1", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 198, + 92, + 506, + 107 + ], + "score": 1.0, + "content": "the models are equally preferred). This implies that this pipeline of collecting", + "type": "text", + "cross_page": true + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 105, + 506, + 117 + ], + "spans": [ + { + "bbox": [ + 106, + 105, + 506, + 117 + ], + "score": 1.0, + "content": "preferences, training a reward, and further tuning the policy improves alignment to human preferences.", + "type": "text", + "cross_page": true + } + ], + "index": 2 + } + ], + "index": 46, + "bbox_fs": [ + 104, + 545, + 507, + 734 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 506, + 116 + ], + "lines": [ + { + "bbox": [ + 105, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "feedback model are preferred in 682 cases, compared to the METEOR-only model which is preferred", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 92, + 506, + 107 + ], + "spans": [ + { + "bbox": [ + 105, + 92, + 159, + 107 + ], + "score": 1.0, + "content": "in 587 cases", + "type": "text" + }, + { + "bbox": [ + 160, + 94, + 198, + 105 + ], + "score": 0.88, + "content": "\\mathit { p } < 0 . 0 1", + "type": "inline_equation" + }, + { + "bbox": [ + 198, + 92, + 506, + 107 + ], + "score": 1.0, + "content": "the models are equally preferred). This implies that this pipeline of collecting", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 105, + 506, + 117 + ], + "spans": [ + { + "bbox": [ + 106, + 105, + 506, + 117 + ], + "score": 1.0, + "content": "preferences, training a reward, and further tuning the policy improves alignment to human preferences.", + "type": "text" + } + ], + "index": 2 + } + ], + "index": 1 + }, + { + "type": "text", + "bbox": [ + 106, + 129, + 471, + 141 + ], + "lines": [ + { + "bbox": [ + 105, + 129, + 473, + 142 + ], + "spans": [ + { + "bbox": [ + 105, + 129, + 473, + 142 + ], + "score": 1.0, + "content": "5.3 DATA BUDGET: IMPROVE YOUR REWARD OR GATHER MORE DEMONSTRATION?", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 3 + }, + { + "type": "text", + "bbox": [ + 107, + 150, + 505, + 238 + ], + "lines": [ + { + "bbox": [ + 106, + 150, + 505, + 163 + ], + "spans": [ + { + "bbox": [ + 106, + 150, + 505, + 163 + ], + "score": 1.0, + "content": "Given a fixed data collection budget, is it more efficient to gather feedback to improve a learned", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 161, + 506, + 173 + ], + "spans": [ + { + "bbox": [ + 105, + 161, + 506, + 173 + ], + "score": 1.0, + "content": "reward function or to gather more expert demonstrations? We use the IMDB text continuation task as", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 173, + 506, + 185 + ], + "spans": [ + { + "bbox": [ + 105, + 173, + 506, + 185 + ], + "score": 1.0, + "content": "a case study. In the IMDB task, a model is given a partial movie review as a prompt, and is asked to", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 183, + 506, + 195 + ], + "spans": [ + { + "bbox": [ + 105, + 183, + 506, + 195 + ], + "score": 1.0, + "content": "continue it as positively as possible (even if the prompt was negative). The original dataset consists of", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 194, + 506, + 206 + ], + "spans": [ + { + "bbox": [ + 105, + 194, + 506, + 206 + ], + "score": 1.0, + "content": "movie reviews and sentiment labels of positive, negative, or neutral. A DistilBERT (Sanh et al., 2019)", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 204, + 505, + 218 + ], + "spans": [ + { + "bbox": [ + 105, + 204, + 505, + 218 + ], + "score": 1.0, + "content": "classifier is trained on these labels and used to provide sentiment scores on how positive a given piece", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 215, + 506, + 228 + ], + "spans": [ + { + "bbox": [ + 105, + 215, + 506, + 228 + ], + "score": 1.0, + "content": "of text is, which serves as the task reward. The trade-off is between gathering more: 1) sentiment", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 226, + 491, + 240 + ], + "spans": [ + { + "bbox": [ + 105, + 226, + 491, + 240 + ], + "score": 1.0, + "content": "labels (improving the reward); or 2) positive sentiment reviews (improving supervised training).", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 7.5 + }, + { + "type": "text", + "bbox": [ + 107, + 244, + 505, + 364 + ], + "lines": [ + { + "bbox": [ + 105, + 243, + 501, + 257 + ], + "spans": [ + { + "bbox": [ + 105, + 243, + 501, + 257 + ], + "score": 1.0, + "content": "We train a classifier on varying amounts of training data and evaluate on the held out test dataset—", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 254, + 505, + 267 + ], + "spans": [ + { + "bbox": [ + 105, + 254, + 505, + 267 + ], + "score": 1.0, + "content": "finding as expected that more training data improves test accuracy and so results in a higher quality", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 104, + 264, + 506, + 280 + ], + "spans": [ + { + "bbox": [ + 104, + 264, + 506, + 280 + ], + "score": 1.0, + "content": "reward. We then use each of these rewards of varying quality during RL training, and evaluate using", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 277, + 506, + 288 + ], + "spans": [ + { + "bbox": [ + 106, + 277, + 506, + 288 + ], + "score": 1.0, + "content": "the same metric as GRUE (i.e., a classifier trained with the entire training set). As seen in Table 3,", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 288, + 506, + 300 + ], + "spans": [ + { + "bbox": [ + 106, + 288, + 506, + 300 + ], + "score": 1.0, + "content": "we find that improving the reward quality improves LM performance as well. Further, we trained a", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 298, + 506, + 311 + ], + "spans": [ + { + "bbox": [ + 105, + 298, + 506, + 311 + ], + "score": 1.0, + "content": "supervised model with at least as many samples used to train each of these reward classifiers. We find", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 309, + 506, + 322 + ], + "spans": [ + { + "bbox": [ + 106, + 309, + 506, + 322 + ], + "score": 1.0, + "content": "that a learned reward function enables greater performance when used as a signal for an RL", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 318, + 506, + 334 + ], + "spans": [ + { + "bbox": [ + 105, + 318, + 506, + 334 + ], + "score": 1.0, + "content": "method than a supervised method trained with 5 times more data. This implies that improving", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 331, + 506, + 343 + ], + "spans": [ + { + "bbox": [ + 105, + 331, + 506, + 343 + ], + "score": 1.0, + "content": "reward models can be more data efficient than collection expert demonstrations for a task—and that’s", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 343, + 505, + 355 + ], + "spans": [ + { + "bbox": [ + 105, + 343, + 505, + 355 + ], + "score": 1.0, + "content": "not accounting for the fact that assigning sentiment labels is likely a simpler task than writing full", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 354, + 424, + 365 + ], + "spans": [ + { + "bbox": [ + 106, + 354, + 424, + 365 + ], + "score": 1.0, + "content": "demonstrations. Further details on this ablation are found in Appendix Table 7.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 17 + }, + { + "type": "text", + "bbox": [ + 106, + 378, + 490, + 390 + ], + "lines": [ + { + "bbox": [ + 106, + 378, + 491, + 390 + ], + "spans": [ + { + "bbox": [ + 106, + 378, + 491, + 390 + ], + "score": 1.0, + "content": "5.4 PRACTICAL CONSIDERATIONS: WHICH IMPLEMENTATION DETAILS MATTER MOST?", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 23 + }, + { + "type": "text", + "bbox": [ + 107, + 399, + 505, + 530 + ], + "lines": [ + { + "bbox": [ + 106, + 399, + 505, + 410 + ], + "spans": [ + { + "bbox": [ + 106, + 399, + 505, + 410 + ], + "score": 1.0, + "content": "Generation as a token-level MDP, not a bandit environment. Most recent works that tune LMs", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 408, + 506, + 423 + ], + "spans": [ + { + "bbox": [ + 105, + 408, + 506, + 423 + ], + "score": 1.0, + "content": "using RL do so by calculating a reward for all the tokens in the sentence (Wu et al., 2021a; Ouyang", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 421, + 505, + 433 + ], + "spans": [ + { + "bbox": [ + 105, + 421, + 505, + 433 + ], + "score": 1.0, + "content": "et al., 2022; Lu et al., 2022). This setting is equivalent to a bandit feedback environment where the", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 432, + 506, + 444 + ], + "spans": [ + { + "bbox": [ + 105, + 432, + 506, + 444 + ], + "score": 1.0, + "content": "action space is the space of all possible generations for the task (Sutton & Barto, 2018). This type of", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 442, + 506, + 456 + ], + "spans": [ + { + "bbox": [ + 105, + 442, + 444, + 456 + ], + "score": 1.0, + "content": "environment can be simulated within our RL formulation by setting the discount factor", + "type": "text" + }, + { + "bbox": [ + 444, + 443, + 470, + 454 + ], + "score": 0.91, + "content": "\\gamma = 1", + "type": "inline_equation" + }, + { + "bbox": [ + 470, + 442, + 506, + 456 + ], + "score": 1.0, + "content": ". Table 3", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 453, + 506, + 467 + ], + "spans": [ + { + "bbox": [ + 105, + 453, + 506, + 467 + ], + "score": 1.0, + "content": "(and Appendix Table 6) shows that this causes instability in training with respect to naturalness", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 465, + 505, + 477 + ], + "spans": [ + { + "bbox": [ + 105, + 465, + 346, + 477 + ], + "score": 1.0, + "content": "in both PPO and NLPO for IMDB. Our standard setting is", + "type": "text" + }, + { + "bbox": [ + 347, + 465, + 385, + 476 + ], + "score": 0.9, + "content": "\\gamma = 0 . 9 5", + "type": "inline_equation" + }, + { + "bbox": [ + 385, + 465, + 505, + 477 + ], + "score": 1.0, + "content": "when calculating discounted", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 475, + 506, + 488 + ], + "spans": [ + { + "bbox": [ + 105, + 475, + 506, + 488 + ], + "score": 1.0, + "content": "rewards-to-go in the token-level MDP formulation, which reduces the magnitude of the reward that is", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 486, + 506, + 500 + ], + "spans": [ + { + "bbox": [ + 105, + 486, + 506, + 500 + ], + "score": 1.0, + "content": "applied to tokens selected at the beginning. The sentiment scores are approximately the same between", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 496, + 505, + 511 + ], + "spans": [ + { + "bbox": [ + 105, + 496, + 505, + 511 + ], + "score": 1.0, + "content": "both settings but the naturalness of language in the bandit setting is significantly less—indicating", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 508, + 505, + 521 + ], + "spans": [ + { + "bbox": [ + 105, + 508, + 227, + 521 + ], + "score": 1.0, + "content": "that discounting rewards with", + "type": "text" + }, + { + "bbox": [ + 227, + 509, + 253, + 520 + ], + "score": 0.91, + "content": "\\gamma < 1", + "type": "inline_equation" + }, + { + "bbox": [ + 253, + 508, + 505, + 521 + ], + "score": 1.0, + "content": "via a token-level MDP formulation is at least sometimes more", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 520, + 242, + 532 + ], + "spans": [ + { + "bbox": [ + 106, + 520, + 242, + 532 + ], + "score": 1.0, + "content": "effective for language generation.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 29.5 + }, + { + "type": "text", + "bbox": [ + 107, + 536, + 505, + 624 + ], + "lines": [ + { + "bbox": [ + 105, + 536, + 506, + 549 + ], + "spans": [ + { + "bbox": [ + 105, + 536, + 506, + 549 + ], + "score": 1.0, + "content": "Dropout and Sampling. We found two other implementation details to be critical for stability of", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 547, + 505, + 560 + ], + "spans": [ + { + "bbox": [ + 105, + 547, + 505, + 560 + ], + "score": 1.0, + "content": "RL training. The first is dropout, which in its standard form was found to cause instability in policy", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 558, + 506, + 571 + ], + "spans": [ + { + "bbox": [ + 105, + 558, + 506, + 571 + ], + "score": 1.0, + "content": "gradient methods in continuous control settings by Hausknecht & Wagener (2022). We find a similar", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 568, + 506, + 582 + ], + "spans": [ + { + "bbox": [ + 105, + 568, + 506, + 582 + ], + "score": 1.0, + "content": "effect when using dropout when RL training LMs as well, with training loss often diverging for", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 580, + 505, + 593 + ], + "spans": [ + { + "bbox": [ + 105, + 580, + 139, + 593 + ], + "score": 1.0, + "content": "dropout", + "type": "text" + }, + { + "bbox": [ + 140, + 581, + 157, + 591 + ], + "score": 0.86, + "content": "> 0", + "type": "inline_equation" + }, + { + "bbox": [ + 158, + 580, + 505, + 593 + ], + "score": 1.0, + "content": "in training. The second important detail, particularly affecting the machine translation", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 591, + 505, + 604 + ], + "spans": [ + { + "bbox": [ + 105, + 591, + 505, + 604 + ], + "score": 1.0, + "content": "task, is sampling methods. We find that using the same sampling methods during exploration and", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 602, + 505, + 615 + ], + "spans": [ + { + "bbox": [ + 105, + 602, + 505, + 615 + ], + "score": 1.0, + "content": "inference is critical to translating training performance to test performance–else the model exhibits", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 613, + 264, + 625 + ], + "spans": [ + { + "bbox": [ + 106, + 613, + 264, + 625 + ], + "score": 1.0, + "content": "high train rewards but low test metrics.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 39.5 + }, + { + "type": "title", + "bbox": [ + 108, + 640, + 201, + 653 + ], + "lines": [ + { + "bbox": [ + 104, + 638, + 203, + 656 + ], + "spans": [ + { + "bbox": [ + 104, + 638, + 203, + 656 + ], + "score": 1.0, + "content": "6 CONCLUSIONS", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 44 + }, + { + "type": "text", + "bbox": [ + 107, + 665, + 505, + 731 + ], + "lines": [ + { + "bbox": [ + 105, + 664, + 505, + 679 + ], + "spans": [ + { + "bbox": [ + 105, + 664, + 505, + 679 + ], + "score": 1.0, + "content": "We’re hopeful that the GRUE benchmark and the RL4LMs library can push progress in aligning", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 677, + 506, + 690 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 506, + 690 + ], + "score": 1.0, + "content": "language models to human preferences via RL methods by providing the community with a standard", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 688, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 106, + 688, + 505, + 700 + ], + "score": 1.0, + "content": "means of comparing methods. Furthermore, we’re optimistic that, as the stability and consistency of", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 106, + 699, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 506, + 712 + ], + "score": 1.0, + "content": "training improves, our methods provide a path towards iterative improvement of language technolo-", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 709, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 506, + 723 + ], + "score": 1.0, + "content": "gies, with deployment, user feedback collection, and re-optimization enabling better user experiences", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 106, + 721, + 272, + 732 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 272, + 732 + ], + "score": 1.0, + "content": "when interacting with generative models.", + "type": "text" + } + ], + "index": 50 + } + ], + "index": 47.5 + } + ], + "page_idx": 8, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2023", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 308, + 759 + ], + "lines": [ + { + "bbox": [ + 302, + 751, + 309, + 762 + ], + "spans": [ + { + "bbox": [ + 302, + 751, + 309, + 762 + ], + "score": 1.0, + "content": "9", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 506, + 116 + ], + "lines": [], + "index": 1, + "bbox_fs": [ + 105, + 82, + 506, + 117 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 106, + 129, + 471, + 141 + ], + "lines": [ + { + "bbox": [ + 105, + 129, + 473, + 142 + ], + "spans": [ + { + "bbox": [ + 105, + 129, + 473, + 142 + ], + "score": 1.0, + "content": "5.3 DATA BUDGET: IMPROVE YOUR REWARD OR GATHER MORE DEMONSTRATION?", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 3, + "bbox_fs": [ + 105, + 129, + 473, + 142 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 150, + 505, + 238 + ], + "lines": [ + { + "bbox": [ + 106, + 150, + 505, + 163 + ], + "spans": [ + { + "bbox": [ + 106, + 150, + 505, + 163 + ], + "score": 1.0, + "content": "Given a fixed data collection budget, is it more efficient to gather feedback to improve a learned", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 161, + 506, + 173 + ], + "spans": [ + { + "bbox": [ + 105, + 161, + 506, + 173 + ], + "score": 1.0, + "content": "reward function or to gather more expert demonstrations? We use the IMDB text continuation task as", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 173, + 506, + 185 + ], + "spans": [ + { + "bbox": [ + 105, + 173, + 506, + 185 + ], + "score": 1.0, + "content": "a case study. In the IMDB task, a model is given a partial movie review as a prompt, and is asked to", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 183, + 506, + 195 + ], + "spans": [ + { + "bbox": [ + 105, + 183, + 506, + 195 + ], + "score": 1.0, + "content": "continue it as positively as possible (even if the prompt was negative). The original dataset consists of", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 194, + 506, + 206 + ], + "spans": [ + { + "bbox": [ + 105, + 194, + 506, + 206 + ], + "score": 1.0, + "content": "movie reviews and sentiment labels of positive, negative, or neutral. A DistilBERT (Sanh et al., 2019)", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 204, + 505, + 218 + ], + "spans": [ + { + "bbox": [ + 105, + 204, + 505, + 218 + ], + "score": 1.0, + "content": "classifier is trained on these labels and used to provide sentiment scores on how positive a given piece", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 215, + 506, + 228 + ], + "spans": [ + { + "bbox": [ + 105, + 215, + 506, + 228 + ], + "score": 1.0, + "content": "of text is, which serves as the task reward. The trade-off is between gathering more: 1) sentiment", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 226, + 491, + 240 + ], + "spans": [ + { + "bbox": [ + 105, + 226, + 491, + 240 + ], + "score": 1.0, + "content": "labels (improving the reward); or 2) positive sentiment reviews (improving supervised training).", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 7.5, + "bbox_fs": [ + 105, + 150, + 506, + 240 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 244, + 505, + 364 + ], + "lines": [ + { + "bbox": [ + 105, + 243, + 501, + 257 + ], + "spans": [ + { + "bbox": [ + 105, + 243, + 501, + 257 + ], + "score": 1.0, + "content": "We train a classifier on varying amounts of training data and evaluate on the held out test dataset—", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 254, + 505, + 267 + ], + "spans": [ + { + "bbox": [ + 105, + 254, + 505, + 267 + ], + "score": 1.0, + "content": "finding as expected that more training data improves test accuracy and so results in a higher quality", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 104, + 264, + 506, + 280 + ], + "spans": [ + { + "bbox": [ + 104, + 264, + 506, + 280 + ], + "score": 1.0, + "content": "reward. We then use each of these rewards of varying quality during RL training, and evaluate using", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 277, + 506, + 288 + ], + "spans": [ + { + "bbox": [ + 106, + 277, + 506, + 288 + ], + "score": 1.0, + "content": "the same metric as GRUE (i.e., a classifier trained with the entire training set). As seen in Table 3,", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 288, + 506, + 300 + ], + "spans": [ + { + "bbox": [ + 106, + 288, + 506, + 300 + ], + "score": 1.0, + "content": "we find that improving the reward quality improves LM performance as well. Further, we trained a", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 298, + 506, + 311 + ], + "spans": [ + { + "bbox": [ + 105, + 298, + 506, + 311 + ], + "score": 1.0, + "content": "supervised model with at least as many samples used to train each of these reward classifiers. We find", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 309, + 506, + 322 + ], + "spans": [ + { + "bbox": [ + 106, + 309, + 506, + 322 + ], + "score": 1.0, + "content": "that a learned reward function enables greater performance when used as a signal for an RL", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 318, + 506, + 334 + ], + "spans": [ + { + "bbox": [ + 105, + 318, + 506, + 334 + ], + "score": 1.0, + "content": "method than a supervised method trained with 5 times more data. This implies that improving", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 331, + 506, + 343 + ], + "spans": [ + { + "bbox": [ + 105, + 331, + 506, + 343 + ], + "score": 1.0, + "content": "reward models can be more data efficient than collection expert demonstrations for a task—and that’s", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 343, + 505, + 355 + ], + "spans": [ + { + "bbox": [ + 105, + 343, + 505, + 355 + ], + "score": 1.0, + "content": "not accounting for the fact that assigning sentiment labels is likely a simpler task than writing full", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 354, + 424, + 365 + ], + "spans": [ + { + "bbox": [ + 106, + 354, + 424, + 365 + ], + "score": 1.0, + "content": "demonstrations. Further details on this ablation are found in Appendix Table 7.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 17, + "bbox_fs": [ + 104, + 243, + 506, + 365 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 378, + 490, + 390 + ], + "lines": [ + { + "bbox": [ + 106, + 378, + 491, + 390 + ], + "spans": [ + { + "bbox": [ + 106, + 378, + 491, + 390 + ], + "score": 1.0, + "content": "5.4 PRACTICAL CONSIDERATIONS: WHICH IMPLEMENTATION DETAILS MATTER MOST?", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 23, + "bbox_fs": [ + 106, + 378, + 491, + 390 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 399, + 505, + 530 + ], + "lines": [ + { + "bbox": [ + 106, + 399, + 505, + 410 + ], + "spans": [ + { + "bbox": [ + 106, + 399, + 505, + 410 + ], + "score": 1.0, + "content": "Generation as a token-level MDP, not a bandit environment. Most recent works that tune LMs", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 408, + 506, + 423 + ], + "spans": [ + { + "bbox": [ + 105, + 408, + 506, + 423 + ], + "score": 1.0, + "content": "using RL do so by calculating a reward for all the tokens in the sentence (Wu et al., 2021a; Ouyang", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 421, + 505, + 433 + ], + "spans": [ + { + "bbox": [ + 105, + 421, + 505, + 433 + ], + "score": 1.0, + "content": "et al., 2022; Lu et al., 2022). This setting is equivalent to a bandit feedback environment where the", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 432, + 506, + 444 + ], + "spans": [ + { + "bbox": [ + 105, + 432, + 506, + 444 + ], + "score": 1.0, + "content": "action space is the space of all possible generations for the task (Sutton & Barto, 2018). This type of", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 442, + 506, + 456 + ], + "spans": [ + { + "bbox": [ + 105, + 442, + 444, + 456 + ], + "score": 1.0, + "content": "environment can be simulated within our RL formulation by setting the discount factor", + "type": "text" + }, + { + "bbox": [ + 444, + 443, + 470, + 454 + ], + "score": 0.91, + "content": "\\gamma = 1", + "type": "inline_equation" + }, + { + "bbox": [ + 470, + 442, + 506, + 456 + ], + "score": 1.0, + "content": ". Table 3", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 453, + 506, + 467 + ], + "spans": [ + { + "bbox": [ + 105, + 453, + 506, + 467 + ], + "score": 1.0, + "content": "(and Appendix Table 6) shows that this causes instability in training with respect to naturalness", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 465, + 505, + 477 + ], + "spans": [ + { + "bbox": [ + 105, + 465, + 346, + 477 + ], + "score": 1.0, + "content": "in both PPO and NLPO for IMDB. Our standard setting is", + "type": "text" + }, + { + "bbox": [ + 347, + 465, + 385, + 476 + ], + "score": 0.9, + "content": "\\gamma = 0 . 9 5", + "type": "inline_equation" + }, + { + "bbox": [ + 385, + 465, + 505, + 477 + ], + "score": 1.0, + "content": "when calculating discounted", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 475, + 506, + 488 + ], + "spans": [ + { + "bbox": [ + 105, + 475, + 506, + 488 + ], + "score": 1.0, + "content": "rewards-to-go in the token-level MDP formulation, which reduces the magnitude of the reward that is", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 486, + 506, + 500 + ], + "spans": [ + { + "bbox": [ + 105, + 486, + 506, + 500 + ], + "score": 1.0, + "content": "applied to tokens selected at the beginning. The sentiment scores are approximately the same between", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 496, + 505, + 511 + ], + "spans": [ + { + "bbox": [ + 105, + 496, + 505, + 511 + ], + "score": 1.0, + "content": "both settings but the naturalness of language in the bandit setting is significantly less—indicating", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 508, + 505, + 521 + ], + "spans": [ + { + "bbox": [ + 105, + 508, + 227, + 521 + ], + "score": 1.0, + "content": "that discounting rewards with", + "type": "text" + }, + { + "bbox": [ + 227, + 509, + 253, + 520 + ], + "score": 0.91, + "content": "\\gamma < 1", + "type": "inline_equation" + }, + { + "bbox": [ + 253, + 508, + 505, + 521 + ], + "score": 1.0, + "content": "via a token-level MDP formulation is at least sometimes more", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 520, + 242, + 532 + ], + "spans": [ + { + "bbox": [ + 106, + 520, + 242, + 532 + ], + "score": 1.0, + "content": "effective for language generation.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 29.5, + "bbox_fs": [ + 105, + 399, + 506, + 532 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 536, + 505, + 624 + ], + "lines": [ + { + "bbox": [ + 105, + 536, + 506, + 549 + ], + "spans": [ + { + "bbox": [ + 105, + 536, + 506, + 549 + ], + "score": 1.0, + "content": "Dropout and Sampling. We found two other implementation details to be critical for stability of", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 547, + 505, + 560 + ], + "spans": [ + { + "bbox": [ + 105, + 547, + 505, + 560 + ], + "score": 1.0, + "content": "RL training. The first is dropout, which in its standard form was found to cause instability in policy", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 558, + 506, + 571 + ], + "spans": [ + { + "bbox": [ + 105, + 558, + 506, + 571 + ], + "score": 1.0, + "content": "gradient methods in continuous control settings by Hausknecht & Wagener (2022). We find a similar", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 568, + 506, + 582 + ], + "spans": [ + { + "bbox": [ + 105, + 568, + 506, + 582 + ], + "score": 1.0, + "content": "effect when using dropout when RL training LMs as well, with training loss often diverging for", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 580, + 505, + 593 + ], + "spans": [ + { + "bbox": [ + 105, + 580, + 139, + 593 + ], + "score": 1.0, + "content": "dropout", + "type": "text" + }, + { + "bbox": [ + 140, + 581, + 157, + 591 + ], + "score": 0.86, + "content": "> 0", + "type": "inline_equation" + }, + { + "bbox": [ + 158, + 580, + 505, + 593 + ], + "score": 1.0, + "content": "in training. The second important detail, particularly affecting the machine translation", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 591, + 505, + 604 + ], + "spans": [ + { + "bbox": [ + 105, + 591, + 505, + 604 + ], + "score": 1.0, + "content": "task, is sampling methods. We find that using the same sampling methods during exploration and", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 602, + 505, + 615 + ], + "spans": [ + { + "bbox": [ + 105, + 602, + 505, + 615 + ], + "score": 1.0, + "content": "inference is critical to translating training performance to test performance–else the model exhibits", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 613, + 264, + 625 + ], + "spans": [ + { + "bbox": [ + 106, + 613, + 264, + 625 + ], + "score": 1.0, + "content": "high train rewards but low test metrics.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 39.5, + "bbox_fs": [ + 105, + 536, + 506, + 625 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 640, + 201, + 653 + ], + "lines": [ + { + "bbox": [ + 104, + 638, + 203, + 656 + ], + "spans": [ + { + "bbox": [ + 104, + 638, + 203, + 656 + ], + "score": 1.0, + "content": "6 CONCLUSIONS", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 44 + }, + { + "type": "text", + "bbox": [ + 107, + 665, + 505, + 731 + ], + "lines": [ + { + "bbox": [ + 105, + 664, + 505, + 679 + ], + "spans": [ + { + "bbox": [ + 105, + 664, + 505, + 679 + ], + "score": 1.0, + "content": "We’re hopeful that the GRUE benchmark and the RL4LMs library can push progress in aligning", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 677, + 506, + 690 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 506, + 690 + ], + "score": 1.0, + "content": "language models to human preferences via RL methods by providing the community with a standard", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 688, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 106, + 688, + 505, + 700 + ], + "score": 1.0, + "content": "means of comparing methods. 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In addition, we used a timing script to estimate hourly wages to ensure our target", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 296, + 505, + 308 + ], + "spans": [ + { + "bbox": [ + 105, + 296, + 117, + 308 + ], + "score": 1.0, + "content": "of", + "type": "text" + }, + { + "bbox": [ + 118, + 297, + 146, + 307 + ], + "score": 0.88, + "content": "\\$ 15/\\mathrm { h r }", + "type": "inline_equation" + }, + { + "bbox": [ + 146, + 296, + 505, + 308 + ], + "score": 1.0, + "content": "was met. In cases where this minimum hourly rate was not met, we manually assigned", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 307, + 144, + 320 + ], + "spans": [ + { + "bbox": [ + 105, + 307, + 144, + 320 + ], + "score": 1.0, + "content": "bonuses.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 13.5, + "bbox_fs": [ + 105, + 273, + 506, + 320 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 344, + 252, + 356 + ], + "lines": [ + { + "bbox": [ + 106, + 344, + 253, + 357 + ], + "spans": [ + { + "bbox": [ + 106, + 344, + 253, + 357 + ], + "score": 1.0, + "content": "B.2 GRUE EXPERIMENT SETUP", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 16 + }, + { + "type": "text", + "bbox": [ + 106, + 370, + 506, + 459 + ], + "lines": [ + { + "bbox": [ + 105, + 369, + 507, + 384 + ], + "spans": [ + { + "bbox": [ + 105, + 369, + 507, + 384 + ], + "score": 1.0, + "content": "We benchmark 5 training algorithms on 6 tasks (see Table 1) using either an encoder model (eg.", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 381, + 506, + 394 + ], + "spans": [ + { + "bbox": [ + 105, + 381, + 506, + 394 + ], + "score": 1.0, + "content": "GPT-2) or encoder-decoder model (eg. 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We use two separate LM models as actor and critics networks (i.e. no", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 425, + 505, + 437 + ], + "spans": [ + { + "bbox": [ + 106, + 425, + 505, + 437 + ], + "score": 1.0, + "content": "shared layers) in which the critic network has an additional linear layer mapping last token’s hidden", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 437, + 506, + 448 + ], + "spans": [ + { + "bbox": [ + 105, + 437, + 506, + 448 + ], + "score": 1.0, + "content": "representation to a scalar value. We use AdamW optimizer Loshchilov & Hutter (2017) with fixed", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 447, + 236, + 461 + ], + "spans": [ + { + "bbox": [ + 105, + 447, + 236, + 461 + ], + "score": 1.0, + "content": "learning rate and no scheduling.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 20.5, + "bbox_fs": [ + 105, + 369, + 507, + 461 + ] + }, + { + "type": "image", + "bbox": [ + 123, + 484, + 488, + 643 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 123, + 484, + 488, + 643 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 123, + 484, + 488, + 643 + ], + "spans": [ + { + "bbox": [ + 123, + 484, + 488, + 643 + ], + "score": 0.972, + "type": "image", + "image_path": "08bfe192984398ccb8f27c21aa1a4508e0aee43f386d8e7407f5edd912b24b86.jpg" + } + ] + } + ], + "index": 26, + "virtual_lines": [ + { + "bbox": [ + 123, + 484, + 488, + 537.0 + ], + "spans": [], + "index": 25 + }, + { + "bbox": [ + 123, + 537.0, + 488, + 590.0 + ], + "spans": [], + "index": 26 + }, + { + "bbox": [ + 123, + 590.0, + 488, + 643.0 + ], + "spans": [], + "index": 27 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 656, + 505, + 712 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 657, + 505, + 668 + ], + "spans": [ + { + "bbox": [ + 106, + 657, + 505, + 668 + ], + "score": 1.0, + "content": "Figure 3: Summarized results via automated metrics across all 7 GRUE tasks for each of the 5", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 667, + 505, + 679 + ], + "spans": [ + { + "bbox": [ + 106, + 667, + 505, + 679 + ], + "score": 1.0, + "content": "algorithms we consider, and human participant studies for the 5 tasks suitable for human studies. We", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 677, + 506, + 691 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 506, + 691 + ], + "score": 1.0, + "content": "break up the metrics into task-specific, e.g. average positive sentiment for IMDB task, and naturalness", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 689, + 505, + 701 + ], + "spans": [ + { + "bbox": [ + 105, + 689, + 505, + 701 + ], + "score": 1.0, + "content": "metrics, such as perplexity and human perceived coherence for the human rated metrics. 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Model Paramsvalue
supervisedbatch size: 64 epochs: 10 learning rate: 0.00001
pposteps per update: 1280 total number of steps: 64000 batch size: 64 epochs per update: 5 learning rate: 0.000001 discount factor: 0.99 gae lambda: 0.95 clip ratio: 0.2 value function coeff: 0.5
nlposteps per update:1280 total number of steps: 64000 batch size: 64 epochs per update: 5 learning rate: 0.000001 discount factor: 0.99 gae lambda: 0.95 clip ratio: 0.2 top mask ratio: 0.9
decodingtarget update iterations: 5 sampling: true top k: 50 min length: 48 max new tokens: 48
tokenizerpadding side: left truncation side: left max length: 64
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The dataset consists", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 523, + 505, + 534 + ], + "spans": [ + { + "bbox": [ + 106, + 523, + 117, + 534 + ], + "score": 1.0, + "content": "of", + "type": "text" + }, + { + "bbox": [ + 118, + 523, + 135, + 533 + ], + "score": 0.5, + "content": "2 5 \\mathrm { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 135, + 523, + 246, + 534 + ], + "score": 1.0, + "content": "training, 5k validation and", + "type": "text" + }, + { + "bbox": [ + 246, + 523, + 258, + 533 + ], + "score": 0.3, + "content": "5 \\mathrm { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 259, + 523, + 505, + 534 + ], + "score": 1.0, + "content": "test examples of movie review text with sentiment labels of", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 104, + 533, + 506, + 546 + ], + "spans": [ + { + "bbox": [ + 104, + 533, + 506, + 546 + ], + "score": 1.0, + "content": "positive and negative. The input to the model is a partial movie review text (upto 64 tokens) that", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 104, + 543, + 506, + 558 + ], + "spans": [ + { + "bbox": [ + 104, + 543, + 506, + 558 + ], + "score": 1.0, + "content": "needs to be completed (generating 48 tokens) by the model with a positive sentiment while retaining", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 556, + 505, + 567 + ], + "spans": [ + { + "bbox": [ + 106, + 556, + 505, + 567 + ], + "score": 1.0, + "content": "fluency. For RL methods, we use a sentiment classifier Sanh et al. (2019) that is trained on pairs of", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 566, + 505, + 579 + ], + "spans": [ + { + "bbox": [ + 106, + 566, + 505, + 579 + ], + "score": 1.0, + "content": "text and labels as a reward model which provides sentiment scores indicating how positive a given", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 577, + 506, + 589 + ], + "spans": [ + { + "bbox": [ + 105, + 577, + 506, + 589 + ], + "score": 1.0, + "content": "piece of text is. For supervised Seq2Seq baselines, we consider only the examples with positive labels.", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 587, + 506, + 601 + ], + "spans": [ + { + "bbox": [ + 105, + 587, + 506, + 601 + ], + "score": 1.0, + "content": "We chose GPT-2 as LM for this task as it is more suited for text continuation than encoder-decoder", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 598, + 506, + 612 + ], + "spans": [ + { + "bbox": [ + 105, + 598, + 212, + 612 + ], + "score": 1.0, + "content": "LMs (eg. T5). We use top-", + "type": "text" + }, + { + "bbox": [ + 212, + 600, + 219, + 609 + ], + "score": 0.53, + "content": "\\mathbf { \\nabla } \\cdot \\mathbf { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 219, + 598, + 278, + 612 + ], + "score": 1.0, + "content": "sampling with", + "type": "text" + }, + { + "bbox": [ + 278, + 599, + 312, + 609 + ], + "score": 0.9, + "content": "K = 5 0", + "type": "inline_equation" + }, + { + "bbox": [ + 312, + 598, + 506, + 612 + ], + "score": 1.0, + "content": "as the decoding method and for fair comparison,", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 610, + 506, + 623 + ], + "spans": [ + { + "bbox": [ + 105, + 610, + 417, + 623 + ], + "score": 1.0, + "content": "we keep this setting for all methods. For PPO and NLPO models, we train for", + "type": "text" + }, + { + "bbox": [ + 417, + 610, + 434, + 621 + ], + "score": 0.81, + "content": "6 4 k", + "type": "inline_equation" + }, + { + "bbox": [ + 435, + 610, + 506, + 623 + ], + "score": 1.0, + "content": "steps in total and", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 621, + 506, + 634 + ], + "spans": [ + { + "bbox": [ + 106, + 621, + 506, + 634 + ], + "score": 1.0, + "content": "update policy and value networks every 1280 steps with a mini-batch size of 64 and epochs of 5 per", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 632, + 506, + 645 + ], + "spans": [ + { + "bbox": [ + 106, + 632, + 506, + 645 + ], + "score": 1.0, + "content": "update. We apply adaptive KL controllers with different target KLs of 0.02, 0.05, 0.1, inf with an", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 642, + 506, + 656 + ], + "spans": [ + { + "bbox": [ + 105, + 642, + 205, + 656 + ], + "score": 1.0, + "content": "initial KL co-efficient of", + "type": "text" + }, + { + "bbox": [ + 205, + 643, + 239, + 654 + ], + "score": 0.91, + "content": "\\beta = 0 . 1", + "type": "inline_equation" + }, + { + "bbox": [ + 239, + 642, + 506, + 656 + ], + "score": 1.0, + "content": ". 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It is seen that higher target", + "type": "text" + }, + { + "bbox": [ + 239, + 721, + 253, + 731 + ], + "score": 0.33, + "content": "\\mathrm { K L }", + "type": "inline_equation" + }, + { + "bbox": [ + 253, + 721, + 505, + 733 + ], + "score": 1.0, + "content": "of 0.1 is desired to achieve higher rewards but results in drifting", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 45 + } + ], + "page_idx": 19, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2023", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 751, + 311, + 760 + ], + "lines": [ + { + "bbox": [ + 298, + 750, + 313, + 764 + ], + "spans": [ + { + "bbox": [ + 298, + 750, + 313, + 764 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 14, + "width": 15 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "table", + "bbox": [ + 207, + 79, + 403, + 428 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 207, + 79, + 403, + 428 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 207, + 79, + 403, + 428 + ], + "spans": [ + { + "bbox": [ + 207, + 79, + 403, + 428 + ], + "score": 0.975, + "html": "
Model Paramsvalue
supervisedbatch size: 64 epochs: 10 learning rate: 0.00001
pposteps per update: 1280 total number of steps: 64000 batch size: 64 epochs per update: 5 learning rate: 0.000001 discount factor: 0.99 gae lambda: 0.95 clip ratio: 0.2 value function coeff: 0.5
nlposteps per update:1280 total number of steps: 64000 batch size: 64 epochs per update: 5 learning rate: 0.000001 discount factor: 0.99 gae lambda: 0.95 clip ratio: 0.2 top mask ratio: 0.9
decodingtarget update iterations: 5 sampling: true top k: 50 min length: 48 max new tokens: 48
tokenizerpadding side: left truncation side: left max length: 64
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The dataset consists", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 523, + 505, + 534 + ], + "spans": [ + { + "bbox": [ + 106, + 523, + 117, + 534 + ], + "score": 1.0, + "content": "of", + "type": "text" + }, + { + "bbox": [ + 118, + 523, + 135, + 533 + ], + "score": 0.5, + "content": "2 5 \\mathrm { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 135, + 523, + 246, + 534 + ], + "score": 1.0, + "content": "training, 5k validation and", + "type": "text" + }, + { + "bbox": [ + 246, + 523, + 258, + 533 + ], + "score": 0.3, + "content": "5 \\mathrm { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 259, + 523, + 505, + 534 + ], + "score": 1.0, + "content": "test examples of movie review text with sentiment labels of", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 104, + 533, + 506, + 546 + ], + "spans": [ + { + "bbox": [ + 104, + 533, + 506, + 546 + ], + "score": 1.0, + "content": "positive and negative. The input to the model is a partial movie review text (upto 64 tokens) that", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 104, + 543, + 506, + 558 + ], + "spans": [ + { + "bbox": [ + 104, + 543, + 506, + 558 + ], + "score": 1.0, + "content": "needs to be completed (generating 48 tokens) by the model with a positive sentiment while retaining", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 556, + 505, + 567 + ], + "spans": [ + { + "bbox": [ + 106, + 556, + 505, + 567 + ], + "score": 1.0, + "content": "fluency. For RL methods, we use a sentiment classifier Sanh et al. (2019) that is trained on pairs of", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 566, + 505, + 579 + ], + "spans": [ + { + "bbox": [ + 106, + 566, + 505, + 579 + ], + "score": 1.0, + "content": "text and labels as a reward model which provides sentiment scores indicating how positive a given", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 577, + 506, + 589 + ], + "spans": [ + { + "bbox": [ + 105, + 577, + 506, + 589 + ], + "score": 1.0, + "content": "piece of text is. For supervised Seq2Seq baselines, we consider only the examples with positive labels.", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 587, + 506, + 601 + ], + "spans": [ + { + "bbox": [ + 105, + 587, + 506, + 601 + ], + "score": 1.0, + "content": "We chose GPT-2 as LM for this task as it is more suited for text continuation than encoder-decoder", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 598, + 506, + 612 + ], + "spans": [ + { + "bbox": [ + 105, + 598, + 212, + 612 + ], + "score": 1.0, + "content": "LMs (eg. T5). We use top-", + "type": "text" + }, + { + "bbox": [ + 212, + 600, + 219, + 609 + ], + "score": 0.53, + "content": "\\mathbf { \\nabla } \\cdot \\mathbf { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 219, + 598, + 278, + 612 + ], + "score": 1.0, + "content": "sampling with", + "type": "text" + }, + { + "bbox": [ + 278, + 599, + 312, + 609 + ], + "score": 0.9, + "content": "K = 5 0", + "type": "inline_equation" + }, + { + "bbox": [ + 312, + 598, + 506, + 612 + ], + "score": 1.0, + "content": "as the decoding method and for fair comparison,", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 610, + 506, + 623 + ], + "spans": [ + { + "bbox": [ + 105, + 610, + 417, + 623 + ], + "score": 1.0, + "content": "we keep this setting for all methods. For PPO and NLPO models, we train for", + "type": "text" + }, + { + "bbox": [ + 417, + 610, + 434, + 621 + ], + "score": 0.81, + "content": "6 4 k", + "type": "inline_equation" + }, + { + "bbox": [ + 435, + 610, + 506, + 623 + ], + "score": 1.0, + "content": "steps in total and", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 621, + 506, + 634 + ], + "spans": [ + { + "bbox": [ + 106, + 621, + 506, + 634 + ], + "score": 1.0, + "content": "update policy and value networks every 1280 steps with a mini-batch size of 64 and epochs of 5 per", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 632, + 506, + 645 + ], + "spans": [ + { + "bbox": [ + 106, + 632, + 506, + 645 + ], + "score": 1.0, + "content": "update. We apply adaptive KL controllers with different target KLs of 0.02, 0.05, 0.1, inf with an", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 642, + 506, + 656 + ], + "spans": [ + { + "bbox": [ + 105, + 642, + 205, + 656 + ], + "score": 1.0, + "content": "initial KL co-efficient of", + "type": "text" + }, + { + "bbox": [ + 205, + 643, + 239, + 654 + ], + "score": 0.91, + "content": "\\beta = 0 . 1", + "type": "inline_equation" + }, + { + "bbox": [ + 239, + 642, + 506, + 656 + ], + "score": 1.0, + "content": ". Table 4 provides an in-depth summary of all hyperparameters and", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 654, + 225, + 666 + ], + "spans": [ + { + "bbox": [ + 106, + 654, + 225, + 666 + ], + "score": 1.0, + "content": "other implementation details.", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 35.5, + "bbox_fs": [ + 104, + 511, + 506, + 666 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 678, + 257, + 690 + ], + "lines": [ + { + "bbox": [ + 106, + 678, + 259, + 691 + ], + "spans": [ + { + "bbox": [ + 106, + 678, + 259, + 691 + ], + "score": 1.0, + "content": "B.3.2 RESULTS AND DISCUSSION", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 43 + }, + { + "type": "text", + "bbox": [ + 108, + 699, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "score": 1.0, + "content": "Target KL ablation Fig 4 shows learning curves for PPO and NLPO in terms of episodic training", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 710, + 505, + 721 + ], + "spans": [ + { + "bbox": [ + 106, + 710, + 505, + 721 + ], + "score": 1.0, + "content": "reward, corpus level sentiment scores and perplexity scores on validation set averaged for 5 random", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 721, + 505, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 239, + 733 + ], + "score": 1.0, + "content": "seeds. It is seen that higher target", + "type": "text" + }, + { + "bbox": [ + 239, + 721, + 253, + 731 + ], + "score": 0.33, + "content": "\\mathrm { K L }", + "type": "inline_equation" + }, + { + "bbox": [ + 253, + 721, + 505, + 733 + ], + "score": 1.0, + "content": "of 0.1 is desired to achieve higher rewards but results in drifting", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 45, + "bbox_fs": [ + 105, + 698, + 506, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 119, + 86, + 492, + 308 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 119, + 86, + 492, + 308 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 119, + 86, + 492, + 308 + ], + "spans": [ + { + "bbox": [ + 119, + 86, + 492, + 308 + ], + "score": 0.977, + "type": "image", + "image_path": "0753251ba9a44636d15902153834bc0948325a9d58b74e36e838964b8174ce75.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 119, + 86, + 492, + 160.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 119, + 160.0, + 492, + 234.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 119, + 234.0, + 492, + 308.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 321, + 506, + 410 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 320, + 506, + 334 + ], + "spans": [ + { + "bbox": [ + 105, + 320, + 506, + 334 + ], + "score": 1.0, + "content": "Figure 4: Learning Curves: Averaged learning curves over 5 different runs by varying target", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 331, + 506, + 345 + ], + "spans": [ + { + "bbox": [ + 105, + 331, + 506, + 345 + ], + "score": 1.0, + "content": "KL, shaded regions indicate one standard deviation. (a) shows the rollout episodic total reward", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 343, + 506, + 356 + ], + "spans": [ + { + "bbox": [ + 106, + 343, + 506, + 356 + ], + "score": 1.0, + "content": "during training (b) shows evolution of sentiment scores on the validation split (c) shows evolution of", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 354, + 506, + 367 + ], + "spans": [ + { + "bbox": [ + 105, + 354, + 506, + 367 + ], + "score": 1.0, + "content": "perplexity on the validation split. From (a) and (b), it is seen that higher target KL (0.1) is desired to", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 365, + 506, + 377 + ], + "spans": [ + { + "bbox": [ + 105, + 365, + 506, + 377 + ], + "score": 1.0, + "content": "achieve higher rewards. However, this setting drifts away from the original LM too much and loses", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 376, + 506, + 388 + ], + "spans": [ + { + "bbox": [ + 105, + 376, + 506, + 388 + ], + "score": 1.0, + "content": "fluency. Therefore a lower target KL (0.02 or 0.05) is required to keep the model closer to original", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 387, + 506, + 399 + ], + "spans": [ + { + "bbox": [ + 105, + 387, + 506, + 399 + ], + "score": 1.0, + "content": "LM. Similar trends hold for NLPO but when compared to PPO, it retains lower perplexities and is", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 398, + 269, + 411 + ], + "spans": [ + { + "bbox": [ + 105, + 398, + 269, + 411 + ], + "score": 1.0, + "content": "more stable even with higher KL targets", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 6.5 + } + ], + "index": 3.75 + }, + { + "type": "table", + "bbox": [ + 109, + 435, + 496, + 576 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 109, + 435, + 496, + 576 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 109, + 435, + 496, + 576 + ], + "spans": [ + { + "bbox": [ + 109, + 435, + 496, + 576 + ], + "score": 0.938, + "html": "
Target-KLSemantic and Fluency MetricsDiversity Metrics
Sentiment Score ↑Perplexity ↓MSTTRDistinct1Distinct2H1H2Unique1Unique2
Zero-Shot0.489 ± 0.00632.171 ± 0.1370.682 ± 0.0010.042 ± 0.0010.294 ± 0.0018.656 ± 0.00413.716 ± 0.0035063 ± 14.83247620±238
Supervised0.539 ± 0.00435.472 ± 0.0740.682 ± 0.0010.047 ± 0.0010.312 ± 0.0028.755± 0.01213.806 ± 0.0165601±5751151± 345
PPO
0.020.546 ± 0.02233.127 ± 0.0920.680 ± 0.0030.044 ± 0.0010.297 ± 0.0048.665 ± 0.02913.685 ± 0.0765332 ± 18448380 ± 733
0.050.594 ± 0.02233.765 ± 0.3670.671 ± 0.0050.043 ± 0.0010.286 ± 0.0098.588 ± 0.06613.519 ± 0.1035171 ± 19046336 ± 1872
0.1 inf0.602 ± 0.01233.816 ± 0.2330.664 ± 0.0070.042 ± 0.0010.278 ± 0.0058.529 ± 0.03713.366 ± 0.1195108± 20445158 ± 961
0.838 ± 0.06141.897 ± 1.8060.577 ± 0.0590.034 ± 0.0030.197 ± 0.0367.737 ± 0.51411.866 ± 0.9934214± 26031181± 5524
PPO+supervised
0.10.626 ± 0.01435.049 ± 0.3470.668 ± 0.0040.048 ± 0.0020.307 ± 0.0088.704 ± 0.05313.656 ± 0.0665757± 32450522 ± 1514
inf0.796 ± 0.00442.916 ± 1.7160.617 ± 0.0170.038 ± 0.0030.233 ± 0.0178.149 ± 0.18312.733 ± 0.3164563 ± 32737040 ± 2507
NLPO
0.020.564 ± 0.04333.477 ± 0.5780.679 ± 0.0020.043 ± 0.0010.294 ± 0.0018.649 ± 0.00713.688 ± 0.045232±9647732 ± 184
0.050.582 ± 0.03733.470 ± 0.4530.675 ± 0.0030.043 ± 0.0010.293 ± 0.0048.63 ± 0.03313.656 ± 0.0855200 ± 10147484 ± 822
0.1 inf0.611 ± 0.023 0.858 ± 0.02933.832 ± 0.2830.670 ± 0.0020.043 ± 0.0020.286 ± 0.0068.602 ± 0.04913.53 ± 0.0765179 ± 19646294 ± 1072
41.429 ± 1.8250.575 ± 0.0480.035 ± 0.0050.201 ± 0.0287.755 ± 0.37911.862 ± 0.8084389 ± 60931714 ± 4500
NLPO+supervised8.725 ± 0.09
0.1 inf0.620 ± 0.01434.816 ± 0.3400.672 ± 0.0060.048 ± 0.0020.31 ± 0.01213.709 ± 0.1745589 ±14050734 ± 1903
0.777 ± 0.04241.035 ± 0.6010.636 ± 0.0230.043 ± 0.0050.265 ± 0.0348.373 ± 0.26912.947 ± 0.3595173 ± 58943342 ± 6828
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It is seen from perplexity", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 104, + 607, + 506, + 620 + ], + "spans": [ + { + "bbox": [ + 104, + 607, + 506, + 620 + ], + "score": 1.0, + "content": "scores that a lower target KL constraint is desired to keep the model closer to the original model. On", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 617, + 505, + 632 + ], + "spans": [ + { + "bbox": [ + 105, + 617, + 505, + 632 + ], + "score": 1.0, + "content": "the otherhand, a higher target KL yields higher sentiment scores at the cost of fluency. inf KL penalty", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 629, + 505, + 642 + ], + "spans": [ + { + "bbox": [ + 106, + 629, + 505, + 642 + ], + "score": 1.0, + "content": "(target KL of inf), model simply learns to generate positive phrases (eg: \"I highly recommend this", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 639, + 506, + 653 + ], + "spans": [ + { + "bbox": [ + 105, + 639, + 506, + 653 + ], + "score": 1.0, + "content": "movie to all!\", \"worth watching\") regardless of the context. NLPO achieves better sentiment and", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 652, + 219, + 663 + ], + "spans": [ + { + "bbox": [ + 105, + 652, + 219, + 663 + ], + "score": 1.0, + "content": "perplexity scores than PPO.", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 17 + }, + { + "type": "text", + "bbox": [ + 108, + 699, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 698, + 506, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 711 + ], + "score": 1.0, + "content": "away from pre-trained LM and loses fluency. Therefore, a lower target KL (0.02 or 0.05) is required", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "to keep the LM closer to original LM. 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(a) shows the rollout episodic total reward", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 343, + 506, + 356 + ], + "spans": [ + { + "bbox": [ + 106, + 343, + 506, + 356 + ], + "score": 1.0, + "content": "during training (b) shows evolution of sentiment scores on the validation split (c) shows evolution of", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 354, + 506, + 367 + ], + "spans": [ + { + "bbox": [ + 105, + 354, + 506, + 367 + ], + "score": 1.0, + "content": "perplexity on the validation split. From (a) and (b), it is seen that higher target KL (0.1) is desired to", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 365, + 506, + 377 + ], + "spans": [ + { + "bbox": [ + 105, + 365, + 506, + 377 + ], + "score": 1.0, + "content": "achieve higher rewards. However, this setting drifts away from the original LM too much and loses", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 376, + 506, + 388 + ], + "spans": [ + { + "bbox": [ + 105, + 376, + 506, + 388 + ], + "score": 1.0, + "content": "fluency. Therefore a lower target KL (0.02 or 0.05) is required to keep the model closer to original", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 387, + 506, + 399 + ], + "spans": [ + { + "bbox": [ + 105, + 387, + 506, + 399 + ], + "score": 1.0, + "content": "LM. Similar trends hold for NLPO but when compared to PPO, it retains lower perplexities and is", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 398, + 269, + 411 + ], + "spans": [ + { + "bbox": [ + 105, + 398, + 269, + 411 + ], + "score": 1.0, + "content": "more stable even with higher KL targets", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 6.5 + } + ], + "index": 3.75 + }, + { + "type": "table", + "bbox": [ + 109, + 435, + 496, + 576 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 109, + 435, + 496, + 576 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 109, + 435, + 496, + 576 + ], + "spans": [ + { + "bbox": [ + 109, + 435, + 496, + 576 + ], + "score": 0.938, + "html": "
Target-KLSemantic and Fluency MetricsDiversity Metrics
Sentiment Score ↑Perplexity ↓MSTTRDistinct1Distinct2H1H2Unique1Unique2
Zero-Shot0.489 ± 0.00632.171 ± 0.1370.682 ± 0.0010.042 ± 0.0010.294 ± 0.0018.656 ± 0.00413.716 ± 0.0035063 ± 14.83247620±238
Supervised0.539 ± 0.00435.472 ± 0.0740.682 ± 0.0010.047 ± 0.0010.312 ± 0.0028.755± 0.01213.806 ± 0.0165601±5751151± 345
PPO
0.020.546 ± 0.02233.127 ± 0.0920.680 ± 0.0030.044 ± 0.0010.297 ± 0.0048.665 ± 0.02913.685 ± 0.0765332 ± 18448380 ± 733
0.050.594 ± 0.02233.765 ± 0.3670.671 ± 0.0050.043 ± 0.0010.286 ± 0.0098.588 ± 0.06613.519 ± 0.1035171 ± 19046336 ± 1872
0.1 inf0.602 ± 0.01233.816 ± 0.2330.664 ± 0.0070.042 ± 0.0010.278 ± 0.0058.529 ± 0.03713.366 ± 0.1195108± 20445158 ± 961
0.838 ± 0.06141.897 ± 1.8060.577 ± 0.0590.034 ± 0.0030.197 ± 0.0367.737 ± 0.51411.866 ± 0.9934214± 26031181± 5524
PPO+supervised
0.10.626 ± 0.01435.049 ± 0.3470.668 ± 0.0040.048 ± 0.0020.307 ± 0.0088.704 ± 0.05313.656 ± 0.0665757± 32450522 ± 1514
inf0.796 ± 0.00442.916 ± 1.7160.617 ± 0.0170.038 ± 0.0030.233 ± 0.0178.149 ± 0.18312.733 ± 0.3164563 ± 32737040 ± 2507
NLPO
0.020.564 ± 0.04333.477 ± 0.5780.679 ± 0.0020.043 ± 0.0010.294 ± 0.0018.649 ± 0.00713.688 ± 0.045232±9647732 ± 184
0.050.582 ± 0.03733.470 ± 0.4530.675 ± 0.0030.043 ± 0.0010.293 ± 0.0048.63 ± 0.03313.656 ± 0.0855200 ± 10147484 ± 822
0.1 inf0.611 ± 0.023 0.858 ± 0.02933.832 ± 0.2830.670 ± 0.0020.043 ± 0.0020.286 ± 0.0068.602 ± 0.04913.53 ± 0.0765179 ± 19646294 ± 1072
41.429 ± 1.8250.575 ± 0.0480.035 ± 0.0050.201 ± 0.0287.755 ± 0.37911.862 ± 0.8084389 ± 60931714 ± 4500
NLPO+supervised8.725 ± 0.09
0.1 inf0.620 ± 0.01434.816 ± 0.3400.672 ± 0.0060.048 ± 0.0020.31 ± 0.01213.709 ± 0.1745589 ±14050734 ± 1903
0.777 ± 0.04241.035 ± 0.6010.636 ± 0.0230.043 ± 0.0050.265 ± 0.0348.373 ± 0.26912.947 ± 0.3595173 ± 58943342 ± 6828
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It is seen from perplexity", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 104, + 607, + 506, + 620 + ], + "spans": [ + { + "bbox": [ + 104, + 607, + 506, + 620 + ], + "score": 1.0, + "content": "scores that a lower target KL constraint is desired to keep the model closer to the original model. On", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 617, + 505, + 632 + ], + "spans": [ + { + "bbox": [ + 105, + 617, + 505, + 632 + ], + "score": 1.0, + "content": "the otherhand, a higher target KL yields higher sentiment scores at the cost of fluency. inf KL penalty", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 629, + 505, + 642 + ], + "spans": [ + { + "bbox": [ + 106, + 629, + 505, + 642 + ], + "score": 1.0, + "content": "(target KL of inf), model simply learns to generate positive phrases (eg: \"I highly recommend this", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 639, + 506, + 653 + ], + "spans": [ + { + "bbox": [ + 105, + 639, + 506, + 653 + ], + "score": 1.0, + "content": "movie to all!\", \"worth watching\") regardless of the context. NLPO achieves better sentiment and", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 652, + 219, + 663 + ], + "spans": [ + { + "bbox": [ + 105, + 652, + 219, + 663 + ], + "score": 1.0, + "content": "perplexity scores than PPO.", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 17, + "bbox_fs": [ + 104, + 585, + 506, + 663 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 699, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 698, + 506, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 711 + ], + "score": 1.0, + "content": "away from pre-trained LM and loses fluency. Therefore, a lower target KL (0.02 or 0.05) is required", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "to keep the LM closer to original LM. 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GammaSemantic and Fluency MetricsDiversity Metrics
Sentiment Score ↑Perplexity↓MSTTRDistinct1Distinct2HH2Unique1Unique2
Zero-Shot0.489 ± 0.00632.371 ± 0.1370.682 ± 0.0010.042 ± 0.0010.294 ± 0.0018.656 ± 0.00413.716 ± 0.0035063 ± 14.83247620 ± 238
PPO
0.50.511 ± 0.02335.945 ± 0.920.69 ± 0.0010.044 ± 0.0020.304 ± 0.0078.726 ± 0.04113.793 ± 0.0555304 ±28549668± 1496
0.950.605 ± 0.02333.497 ± 0.4470.666 ± 0.0130.043 ± 0.0020.287 ± 0.0088.575 ± 0.07313.484 ± 0.2445230 ±36346483 ± 1318
1.00.651 ± 0.0541.035 ± 2.8850.691 ± 0.0170.042 ± 0.0040.295 ± 0.0318.697 ± 0.23713.563 ± 0.3965127 ± 46048319 ± 5650
NLPO
0.50.49 ± 0.0137.279 ± 5.1370.688 ± 0.010.045 ± 0.0020.312 ± 0.0168.746 ± 0.11313.873 ± 0.255395±19250828 ± 2506
0.950.637 ± 0.01332.667 ± 0.6310.677 ± 0.0140.044 ± 0.0020.288 ± 0.0108.588 ±0.10013.484 ± 0.2365205 ±18946344 ± 2688
1.00.624 ± 0.03943.72 ± 2.4750.662 ± 0.0190.05 ± 0.0070.3 ± 0.0388.624 ±0.27713.360 ± 0.5376337 ±92149441 ± 6520
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Perc Data (size)Semantic and Fluency MetricsDiversity Metrics
Sentiment Score↑Perplexity ↓MSTTRDistinct1Distinct2HH2Unique1Unique2
Zero-Shot0.489 ± 0.00632.371 ± 0.1370.682 ± 0.0010.042 ± 0.0010.294 ± 0.0018.656 ± 0.00413.716 ± 0.0035063 ± 14.83247620 ± 238
Supervised
0.0 (0k)0.489 ± 0.00632.371 ± 0.1370.682 ± 0.0010.042 ± 0.0010.294 ± 0.0018.656 ± 0.00413.716 ± 0.0035063 ± 1447620 ± 238
0.1 (1k)0.531 ± 0.00534.846 ± 0.1230.685 ± 0.0010.045 ± 0.0010.313 ± 0.0048.775 ±0.02313.854 ± 0.0325215±6251125 ±685
0.5 (5k)0.536 ± 0.00635.008 ± 0.2290.684 ± 0.0010.047 ± 0.0000.314 ± 0.0028.764 ± 0.01013.837 ± 0.01785489± 4451284 ±576
1.0 (10k)0.539 ± 0.00435.472 ± 0.0740.682 ± 0.0010.047 ± 0.0010.312 ± 0.0028.755 ± 0.01213.806 ± 0.0165601±5751151 ±345
PPO
0.0 (0k)0.492 ± 0.0133.57 ± 0.3230.69 ± 0.020.047 ± 0.0010.321 ± 0.0158.816 ± 0.14913.866 ± 0.365629 ± 24052911 ± 1786
0.1 (2k)0.598 ± 0.01735.929 ± 1.3970.698 ± 0.0090.051 ± 0.0030.339 ± 0.0128.968 ± 0.08314.013 ± 0.1586173 ± 36055918 ± 2641
0.5 (10k)0.593 ± 0.02635.95± 2.1770.666 ± 0.0730.049 ± 0.0030.314 ± 0.0468.635 ± 0.63413.432 ± 1.1735882 ± 35651403 ± 9297
1.0 (20k)0.605 ± 0.02333.497 ± 0.4470.666 ± 0.0130.043 ± 0.0020.287 ± 0.0088.575 ± 0.07313.484 ± 0.2445230 ± 36346483 ± 1318
NLPO
0.0 (0k)0.487 ± 0.0132.572 ± 0.1650.685 ± 0.0030.043 ± 0.0010.299 ± 0.0038.691 ± 0.02313.787 ± 0.0345126 ± 17748475 ± 491
0.1 (2k)0.599 ± 0.00733.536 ± 0.3780.67 ± 0.010.043 ± 0.0010.289 ± 0.0098.608 ± 0.06113.576 ± 0.1925125± 22046755 ± 1449
0.5 (10k)0.617 ± 0.02133.409 ± 0.3540.668 ± 0.0050.041 ± 0.0010.281 ± 0.0068.552 ± 0.04413.533 ± 0.0914926± 18345256 ± 1022
1.0 (20k)0.637 ± 0.01332.667 ± 0.6310.677 ± 0.0140.044 ± 0.0020.288 ± 0.0108.588 ± 0.10013.484 ± 0.2365205± 18946344 ± 2688
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GammaSemantic and Fluency MetricsDiversity Metrics
Sentiment Score ↑Perplexity↓MSTTRDistinct1Distinct2HH2Unique1Unique2
Zero-Shot0.489 ± 0.00632.371 ± 0.1370.682 ± 0.0010.042 ± 0.0010.294 ± 0.0018.656 ± 0.00413.716 ± 0.0035063 ± 14.83247620 ± 238
PPO
0.50.511 ± 0.02335.945 ± 0.920.69 ± 0.0010.044 ± 0.0020.304 ± 0.0078.726 ± 0.04113.793 ± 0.0555304 ±28549668± 1496
0.950.605 ± 0.02333.497 ± 0.4470.666 ± 0.0130.043 ± 0.0020.287 ± 0.0088.575 ± 0.07313.484 ± 0.2445230 ±36346483 ± 1318
1.00.651 ± 0.0541.035 ± 2.8850.691 ± 0.0170.042 ± 0.0040.295 ± 0.0318.697 ± 0.23713.563 ± 0.3965127 ± 46048319 ± 5650
NLPO
0.50.49 ± 0.0137.279 ± 5.1370.688 ± 0.010.045 ± 0.0020.312 ± 0.0168.746 ± 0.11313.873 ± 0.255395±19250828 ± 2506
0.950.637 ± 0.01332.667 ± 0.6310.677 ± 0.0140.044 ± 0.0020.288 ± 0.0108.588 ±0.10013.484 ± 0.2365205 ±18946344 ± 2688
1.00.624 ± 0.03943.72 ± 2.4750.662 ± 0.0190.05 ± 0.0070.3 ± 0.0388.624 ±0.27713.360 ± 0.5376337 ±92149441 ± 6520
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Perc Data (size)Semantic and Fluency MetricsDiversity Metrics
Sentiment Score↑Perplexity ↓MSTTRDistinct1Distinct2HH2Unique1Unique2
Zero-Shot0.489 ± 0.00632.371 ± 0.1370.682 ± 0.0010.042 ± 0.0010.294 ± 0.0018.656 ± 0.00413.716 ± 0.0035063 ± 14.83247620 ± 238
Supervised
0.0 (0k)0.489 ± 0.00632.371 ± 0.1370.682 ± 0.0010.042 ± 0.0010.294 ± 0.0018.656 ± 0.00413.716 ± 0.0035063 ± 1447620 ± 238
0.1 (1k)0.531 ± 0.00534.846 ± 0.1230.685 ± 0.0010.045 ± 0.0010.313 ± 0.0048.775 ±0.02313.854 ± 0.0325215±6251125 ±685
0.5 (5k)0.536 ± 0.00635.008 ± 0.2290.684 ± 0.0010.047 ± 0.0000.314 ± 0.0028.764 ± 0.01013.837 ± 0.01785489± 4451284 ±576
1.0 (10k)0.539 ± 0.00435.472 ± 0.0740.682 ± 0.0010.047 ± 0.0010.312 ± 0.0028.755 ± 0.01213.806 ± 0.0165601±5751151 ±345
PPO
0.0 (0k)0.492 ± 0.0133.57 ± 0.3230.69 ± 0.020.047 ± 0.0010.321 ± 0.0158.816 ± 0.14913.866 ± 0.365629 ± 24052911 ± 1786
0.1 (2k)0.598 ± 0.01735.929 ± 1.3970.698 ± 0.0090.051 ± 0.0030.339 ± 0.0128.968 ± 0.08314.013 ± 0.1586173 ± 36055918 ± 2641
0.5 (10k)0.593 ± 0.02635.95± 2.1770.666 ± 0.0730.049 ± 0.0030.314 ± 0.0468.635 ± 0.63413.432 ± 1.1735882 ± 35651403 ± 9297
1.0 (20k)0.605 ± 0.02333.497 ± 0.4470.666 ± 0.0130.043 ± 0.0020.287 ± 0.0088.575 ± 0.07313.484 ± 0.2445230 ± 36346483 ± 1318
NLPO
0.0 (0k)0.487 ± 0.0132.572 ± 0.1650.685 ± 0.0030.043 ± 0.0010.299 ± 0.0038.691 ± 0.02313.787 ± 0.0345126 ± 17748475 ± 491
0.1 (2k)0.599 ± 0.00733.536 ± 0.3780.67 ± 0.010.043 ± 0.0010.289 ± 0.0098.608 ± 0.06113.576 ± 0.1925125± 22046755 ± 1449
0.5 (10k)0.617 ± 0.02133.409 ± 0.3540.668 ± 0.0050.041 ± 0.0010.281 ± 0.0068.552 ± 0.04413.533 ± 0.0914926± 18345256 ± 1022
1.0 (20k)0.637 ± 0.01332.667 ± 0.6310.677 ± 0.0140.044 ± 0.0020.288 ± 0.0108.588 ± 0.10013.484 ± 0.2365205± 18946344 ± 2688
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HyperparamsSemantic and Fluency MetricsDiversity Metrics
Sentiment Score ↑Perplexity↓MSTTRDistinct1Distinct2HH2Unique1Unique2
Target Update Iterations μ
10.594 ± 0.01832.671 ± 0.2010.669 ± 0.0080.042 ± 0.0020.284 ± 0.0078.575 ± 0.06413.503 ± 0.1814986 ± 26545916± 1168
100.622 ± 0.01432.729 ± 0.5670.659 ± 0.0190.042 ± 0.0020.274 ± 0.0078.489 ± 0.10613.31 ± 0.2725138±38543989 ± 1120
200.637 ± 0.01332.667 ± 0.6310.677 ± 0.0140.044 ± 0.0020.288 ± 0.0108.588 ± 0.10013.484 ± 0.2365205 ±18946344 ± 2688
500.603 ± 0.01533.397 ±0.3250.67 ± 0.0060.043 ± 0.0010.287 ±0.0048.605 ± 0.04113.54 ± 0.1165228 ± 11346418 ± 685
Top-p mask
0.10.579 ± 0.02132.451 ± 0.2430.67 ± 0.0080.042 ± 0.0010.283 ± 0.018.569 ± 0.08413.515 ± 0.1955018 ± 4745760 ±1579
0.30.588 ± 0.01932.451 ± 0.3030.666 ± 0.0070.043 ± 0.0010.285 ± 0.0048.568 ± 0.03213.482 ± 0.1725201 ± 24746357± 539
0.50.588 ± 0.0132.447 ± 0.3930.669 ± 0.0010.044 ± 0.0030.291 ± 0.0088.614 ± 0.05313.535 ± 0.065305± 38447251 ± 1226
0.70.619 ± 0.01332.373 ±0.3290.663 ± 0.0080.043 ± 0.0010.28 ± 0.0068.533 ± 0.04313.366 ± 0.1295186 ± 21645149 ± 1452
0.90.637 ± 0.01332.667 ± 0.6310.677 ± 0.0140.044 ± 0.0020.288 ± 0.0108.588 ± 0.10013.484 ± 0.2365205± 18946344± 2688
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AlgorithmUnique NCoherenceSentiment
ValueAlphaSkewValueAlphaSkew
NLPO with KL3.490.1963.4973.610.23.601
NLPO without KL273.160.213.1584.410.1584.403
PPO without KL273.160.173.1634.360.1964.363
PPO with KL293.460.1243.4623.580.1163.575
Zero Shot283.60.1623.5913.10.133.097
Supervised293.510.1923.5123.430.23.428
Human274.130.1594.1283.010.313.017
Supervised+PPO223.450.2113.1473.640.213.161
Supervised+NLPO223.480.1813.2263.730.223.047
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HyperparamsSemantic and Fluency MetricsDiversity Metrics
Sentiment Score ↑Perplexity↓MSTTRDistinct1Distinct2HH2Unique1Unique2
Target Update Iterations μ
10.594 ± 0.01832.671 ± 0.2010.669 ± 0.0080.042 ± 0.0020.284 ± 0.0078.575 ± 0.06413.503 ± 0.1814986 ± 26545916± 1168
100.622 ± 0.01432.729 ± 0.5670.659 ± 0.0190.042 ± 0.0020.274 ± 0.0078.489 ± 0.10613.31 ± 0.2725138±38543989 ± 1120
200.637 ± 0.01332.667 ± 0.6310.677 ± 0.0140.044 ± 0.0020.288 ± 0.0108.588 ± 0.10013.484 ± 0.2365205 ±18946344 ± 2688
500.603 ± 0.01533.397 ±0.3250.67 ± 0.0060.043 ± 0.0010.287 ±0.0048.605 ± 0.04113.54 ± 0.1165228 ± 11346418 ± 685
Top-p mask
0.10.579 ± 0.02132.451 ± 0.2430.67 ± 0.0080.042 ± 0.0010.283 ± 0.018.569 ± 0.08413.515 ± 0.1955018 ± 4745760 ±1579
0.30.588 ± 0.01932.451 ± 0.3030.666 ± 0.0070.043 ± 0.0010.285 ± 0.0048.568 ± 0.03213.482 ± 0.1725201 ± 24746357± 539
0.50.588 ± 0.0132.447 ± 0.3930.669 ± 0.0010.044 ± 0.0030.291 ± 0.0088.614 ± 0.05313.535 ± 0.065305± 38447251 ± 1226
0.70.619 ± 0.01332.373 ±0.3290.663 ± 0.0080.043 ± 0.0010.28 ± 0.0068.533 ± 0.04313.366 ± 0.1295186 ± 21645149 ± 1452
0.90.637 ± 0.01332.667 ± 0.6310.677 ± 0.0140.044 ± 0.0020.288 ± 0.0108.588 ± 0.10013.484 ± 0.2365205± 18946344± 2688
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AlgorithmUnique NCoherenceSentiment
ValueAlphaSkewValueAlphaSkew
NLPO with KL3.490.1963.4973.610.23.601
NLPO without KL273.160.213.1584.410.1584.403
PPO without KL273.160.173.1634.360.1964.363
PPO with KL293.460.1243.4623.580.1163.575
Zero Shot283.60.1623.5913.10.133.097
Supervised293.510.1923.5123.430.23.428
Human274.130.1594.1283.010.313.017
Supervised+PPO223.450.2113.1473.640.213.161
Supervised+NLPO223.480.1813.2263.730.223.047
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Your job is to rate the the", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 119, + 253, + 186, + 259 + ], + "spans": [ + { + "bbox": [ + 119, + 253, + 186, + 259 + ], + "score": 0.99, + "content": "system generation across 2 axes:", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 10 + }, + { + "type": "text", + "bbox": [ + 125, + 263, + 293, + 281 + ], + "lines": [ + { + "bbox": [ + 125, + 262, + 293, + 270 + ], + "spans": [ + { + "bbox": [ + 125, + 262, + 293, + 270 + ], + "score": 0.957, + "content": "·Coherence/Quality:/s thesystem's generation grammatical,easy-to-read anddoes it", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 130, + 269, + 178, + 275 + ], + "spans": [ + { + "bbox": [ + 130, + 269, + 178, + 275 + ], + "score": 0.975, + "content": "follow fromtheprompt?", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 125, + 274, + 249, + 282 + ], + "spans": [ + { + "bbox": [ + 125, + 274, + 249, + 282 + ], + "score": 0.956, + "content": "·Sentiment:Justconsidering the completion,how positiveisit?", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 13 + }, + { + "type": "text", + "bbox": [ + 122, + 286, + 287, + 298 + ], + "lines": [ + { + "bbox": [ + 120, + 285, + 287, + 292 + ], + "spans": [ + { + "bbox": [ + 120, + 285, + 287, + 292 + ], + "score": 0.986, + "content": "You will be able to rate each of the three axes on a scale from 1 to 5, with 1 being the", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 120, + 291, + 238, + 298 + ], + "spans": [ + { + "bbox": [ + 120, + 291, + 238, + 298 + ], + "score": 0.996, + "content": "lowest/worst and 5 the highest/best. The specific scales are:", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 15.5 + }, + { + "type": "title", + "bbox": [ + 126, + 303, + 172, + 308 + ], + "lines": [ + { + "bbox": [ + 126, + 303, + 172, + 308 + ], + "spans": [], + "index": 17 + } + ], + "index": 17 + }, + { + "type": "text", + "bbox": [ + 136, + 309, + 291, + 371 + ], + "lines": [ + { + "bbox": [ + 136, + 309, + 289, + 315 + ], + "spans": [ + { + "bbox": [ + 136, + 309, + 289, + 315 + ], + "score": 0.98, + "content": "○5/5 (excellent): The completion follows effortlessly from the prompt,and is", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 140, + 315, + 214, + 321 + ], + "spans": [ + { + "bbox": [ + 140, + 315, + 214, + 321 + ], + "score": 0.999, + "content": "grammatical, fluent, and reasonable.", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 136, + 321, + 291, + 327 + ], + "spans": [ + { + "bbox": [ + 136, + 321, + 291, + 327 + ], + "score": 0.982, + "content": "○ 4/5 (good): The completion makes sense given the input, but there are minor", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 140, + 326, + 282, + 335 + ], + "spans": [ + { + "bbox": [ + 140, + 326, + 282, + 335 + ], + "score": 0.966, + "content": "grammatical errorsortopicalshiftsthatdon't makeforthebestwriting.", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 136, + 334, + 291, + 340 + ], + "spans": [ + { + "bbox": [ + 136, + 334, + 291, + 340 + ], + "score": 0.989, + "content": "o 3/5 (okay): I can see why this continued from the input, and it's readable, but", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 141, + 340, + 222, + 346 + ], + "spans": [ + { + "bbox": [ + 141, + 340, + 222, + 346 + ], + "score": 0.992, + "content": "there are problems that can't be ignored", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 135, + 345, + 289, + 353 + ], + "spans": [ + { + "bbox": [ + 135, + 345, + 289, + 353 + ], + "score": 0.988, + 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Ithink this", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 328, + 245, + 477, + 251 + ], + "spans": [ + { + "bbox": [ + 328, + 245, + 477, + 251 + ], + "score": 0.99, + "content": "small misstep is the result of a producer hampering her excellent creativity.", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 328, + 251, + 481, + 258 + ], + "spans": [ + { + "bbox": [ + 328, + 251, + 481, + 258 + ], + "score": 0.997, + "content": "There are some shining moments that show her expertise, and Ilook forward", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 328, + 257, + 386, + 263 + ], + "spans": [ + { + "bbox": [ + 328, + 257, + 386, + 263 + ], + "score": 0.99, + "content": "to the director's future films!", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 40.5 + }, + { + "type": "text", + "bbox": [ + 322, + 278, + 491, + 316 + ], + "lines": [ + { + "bbox": [ + 326, + 277, + 491, + 285 + ], + "spans": [ + { + "bbox": [ + 326, + 277, + 491, + 285 + ], + "score": 0.983, + "content": "Coherence/Quality: 4/5 Why?The completion recognizes that this movie isnt good", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 327, + 284, + 488, + 290 + ], + "spans": [ + { + "bbox": [ + 327, + 284, + 488, + 290 + ], + "score": 0.996, + "content": "(as described in the prompt),and makes a reasonable pivot towards talking about", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 327, + 290, + 486, + 297 + ], + "spans": [ + { + "bbox": [ + 327, + 290, + 486, + 297 + ], + "score": 0.979, + "content": "the director's other works. 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"type": "title", + "bbox": [ + 316, + 160, + 355, + 168 + ], + "lines": [ + { + "bbox": [ + 315, + 158, + 358, + 170 + ], + "spans": [ + { + "bbox": [ + 315, + 158, + 358, + 170 + ], + "score": 0.994, + "content": "Example 1:", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 1 + }, + { + "type": "text", + "bbox": [ + 317, + 171, + 337, + 177 + ], + "lines": [ + { + "bbox": [ + 317, + 171, + 337, + 177 + ], + "spans": [], + "index": 2 + } + ], + "index": 2, + "bbox_fs": [ + 317, + 171, + 337, + 177 + ] + }, + { + "type": "text", + "bbox": [ + 328, + 185, + 472, + 216 + ], + "lines": [ + { + "bbox": [ + 328, + 185, + 474, + 191 + ], + "spans": [ + { + "bbox": [ + 328, + 185, + 474, + 191 + ], + "score": 0.98, + "content": "I cannot BELIEVE anyone is giving this film a good rating. In addition to the", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 328, + 191, + 470, + 198 + ], + "spans": [ + { + "bbox": [ + 328, + 191, + 470, + 198 + ], + "score": 0.98, + "content": "terrible acting, thin (nonexistent?) plot line and sloooooooow pace, this", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 328, + 198, + 471, + 204 + ], + "spans": [ + { + "bbox": [ + 328, + 198, + 471, + 204 + ], + "score": 0.977, + "content": "would be the movie to watch if you were really TRYING to fall asleep. The", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 329, + 204, + 463, + 210 + ], + "spans": [ + { + "bbox": [ + 329, + 204, + 463, + 210 + ], + "score": 0.985, + "content": "writer's and director's brains must have been fried eggs to ever have", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 329, + 210, + 443, + 216 + ], + "spans": [ + { + "bbox": [ + 329, + 210, + 443, + 216 + ], + "score": 0.983, + "content": "concocted something as abominable as this. Based on the", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 5, + "bbox_fs": [ + 328, + 185, + 474, + 216 + ] + }, + { + "type": "title", + "bbox": [ + 123, + 223, + 181, + 229 + ], + "lines": [ + { + "bbox": [ + 123, + 222, + 182, + 230 + ], + "spans": [ + { + "bbox": [ + 123, + 222, + 182, + 230 + ], + "score": 0.999, + "content": "Instructions (click to expand)", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 8 + }, + { + "type": "text", + "bbox": [ + 119, + 240, + 293, + 258 + ], + "lines": [ + { + "bbox": [ + 120, + 240, + 291, + 246 + ], + "spans": [ + { + "bbox": [ + 120, + 240, + 291, + 246 + ], + "score": 0.983, + "content": "In this HIT you wil be presented with a partial movie review that acts as a prompt and a", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 120, + 246, + 294, + 252 + ], + "spans": [ + { + "bbox": [ + 120, + 246, + 294, + 252 + ], + "score": 0.992, + "content": "system's automatically-generated continuation of that excerpt. Your job is to rate the the", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 119, + 253, + 186, + 259 + ], + "spans": [ + { + "bbox": [ + 119, + 253, + 186, + 259 + ], + "score": 0.99, + "content": "system generation across 2 axes:", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 10, + "bbox_fs": [ + 119, + 240, + 294, + 259 + ] + }, + { + "type": "text", + "bbox": [ + 125, + 263, + 293, + 281 + ], + "lines": [ + { + "bbox": [ + 125, + 262, + 293, + 270 + ], + "spans": [ + { + "bbox": [ + 125, + 262, + 293, + 270 + ], + "score": 0.957, + "content": "·Coherence/Quality:/s thesystem's generation grammatical,easy-to-read anddoes it", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 130, + 269, + 178, + 275 + ], + "spans": [ + { + "bbox": [ + 130, + 269, + 178, + 275 + ], + "score": 0.975, + "content": "follow fromtheprompt?", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 125, + 274, + 249, + 282 + ], + "spans": [ + { + "bbox": [ + 125, + 274, + 249, + 282 + ], + "score": 0.956, + "content": "·Sentiment:Justconsidering the completion,how positiveisit?", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 13, + "bbox_fs": [ + 125, + 262, + 293, + 282 + ] + }, + { + "type": "text", + "bbox": [ + 122, + 286, + 287, + 298 + ], + "lines": [ + { + "bbox": [ + 120, + 285, + 287, + 292 + ], + "spans": [ + { + "bbox": [ + 120, + 285, + 287, + 292 + ], + "score": 0.986, + "content": "You will be able to rate each of the three axes on a scale from 1 to 5, with 1 being the", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 120, + 291, + 238, + 298 + ], + "spans": [ + { + "bbox": [ + 120, + 291, + 238, + 298 + ], + "score": 0.996, + "content": "lowest/worst and 5 the highest/best. The specific scales are:", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 15.5, + "bbox_fs": [ + 120, + 285, + 287, + 298 + ] + }, + { + "type": "title", + "bbox": [ + 126, + 303, + 172, + 308 + ], + "lines": [ + { + "bbox": [ + 126, + 303, + 172, + 308 + ], + "spans": [], + "index": 17 + } + ], + "index": 17 + }, + { + "type": "list", + "bbox": [ + 136, + 309, + 291, + 371 + ], + "lines": [ + { + "bbox": [ + 136, + 309, + 289, + 315 + ], + "spans": [ + { + "bbox": [ + 136, + 309, + 289, + 315 + ], + "score": 0.98, + "content": "○5/5 (excellent): The completion follows effortlessly from the prompt,and is", + "type": "text" + } + ], + "index": 18, + "is_list_start_line": true + }, + { + "bbox": [ + 140, + 315, + 214, + 321 + ], + "spans": [ + { + "bbox": [ + 140, + 315, + 214, + 321 + ], + "score": 0.999, + "content": "grammatical, fluent, and reasonable.", + "type": "text" + } + ], + "index": 19, + "is_list_end_line": true + }, + { + "bbox": [ + 136, + 321, + 291, + 327 + ], + "spans": [ + { + "bbox": [ + 136, + 321, + 291, + 327 + ], + "score": 0.982, + "content": "○ 4/5 (good): The completion makes sense given the input, but there are minor", + "type": "text" + } + ], + "index": 20, + "is_list_start_line": true + }, + { + "bbox": [ + 140, + 326, + 282, + 335 + ], + "spans": [ + { + "bbox": [ + 140, + 326, + 282, + 335 + ], + "score": 0.966, + "content": "grammatical errorsortopicalshiftsthatdon't makeforthebestwriting.", + "type": "text" + } + ], + "index": 21, + "is_list_end_line": true + }, + { + "bbox": [ + 136, + 334, + 291, + 340 + ], + "spans": [ + { + "bbox": [ + 136, + 334, + 291, + 340 + ], + "score": 0.989, + "content": "o 3/5 (okay): I can see why this continued from the input, and it's readable, but", + "type": "text" + } + ], + "index": 22, + "is_list_start_line": true + }, + { + "bbox": [ + 141, + 340, + 222, + 346 + ], + "spans": [ + { + "bbox": [ + 141, + 340, + 222, + 346 + ], + "score": 0.992, + "content": "there are problems that can't be ignored", + "type": "text" + } + ], + "index": 23, + "is_list_end_line": true + }, + { + "bbox": [ + 135, + 345, + 289, + 353 + ], + "spans": [ + { + "bbox": [ + 135, + 345, + 289, + 353 + ], + "score": 0.988, + "content": "2/5 (poor): Some parts of the completion might make sense given the input,", + "type": "text" + } + ], + "index": 24, + "is_list_start_line": true + }, + { + "bbox": [ + 140, + 352, + 237, + 359 + ], + "spans": [ + { + "bbox": [ + 140, + 352, + 237, + 359 + ], + "score": 0.985, + "content": "but it's unnatural, illogical, or quite hard to read.", + "type": "text" + } + ], + "index": 25, + "is_list_end_line": true + }, + { + "bbox": [ + 137, + 358, + 287, + 366 + ], + "spans": [ + { + "bbox": [ + 137, + 358, + 287, + 366 + ], + "score": 0.976, + "content": "○ 1/5 (terible): The completion completely ignores or contradicts the input,", + "type": "text" + } + ], + "index": 26, + "is_list_start_line": true + }, + { + "bbox": [ + 140, + 364, + 258, + 372 + ], + "spans": [ + { + "bbox": [ + 140, + 364, + 258, + 372 + ], + "score": 0.993, + "content": "and/or there are severe errors in grammaticality or fluency.", + "type": "text" + } + ], + "index": 27, + "is_list_end_line": true + } + ], + "index": 22.5, + "bbox_fs": [ + 135, + 309, + 291, + 372 + ] + }, + { + "type": "title", + "bbox": [ + 126, + 376, + 154, + 381 + ], + "lines": [ + { + "bbox": [ + 126, + 375, + 154, + 381 + ], + "spans": [ + { + "bbox": [ + 126, + 375, + 154, + 381 + ], + "score": 0.995, + "content": "·Sentiment", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 28 + }, + { + "type": "text", + "bbox": [ + 135, + 382, + 290, + 426 + ], + "lines": [ + { + "bbox": [ + 136, + 381, + 253, + 388 + ], + "spans": [ + { + "bbox": [ + 136, + 381, + 253, + 388 + ], + "score": 0.979, + "content": "○ 5/5 (very positive): The completion is glowingly positive.", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 136, + 387, + 288, + 394 + ], + "spans": [ + { + 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+ "bbox": [ + 136, + 412, + 277, + 420 + ], + "score": 0.975, + "content": "○2/5 (mostly negative): Most of what's expressed here is very negative.", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 135, + 418, + 292, + 426 + ], + "spans": [ + { + "bbox": [ + 135, + 418, + 292, + 426 + ], + "score": 0.987, + "content": "1/5(scathingly negative):Thecompletion ofersa strongly negative opinion", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 32, + "bbox_fs": [ + 135, + 381, + 292, + 426 + ] + }, + { + "type": "text", + "bbox": [ + 120, + 436, + 274, + 442 + ], + "lines": [ + { + "bbox": [ + 119, + 435, + 275, + 443 + ], + "spans": [ + { + "bbox": [ + 119, + 435, + 275, + 443 + ], + "score": 0.969, + "content": "Note: forrating sentiment, only consider the completion,and not the prompt itself!", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 36, + "bbox_fs": [ + 119, + 435, + 275, + 443 + ] + }, + { + "type": "text", + "bbox": [ + 123, + 453, + 176, + 459 + ], + "lines": [ + { + "bbox": [ + 123, + 452, + 177, + 459 + ], + "spans": [ + { + "bbox": [ + 123, + 452, + 177, + 459 + ], + "score": 0.994, + "content": "Examples (click to expand)", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 37, + "bbox_fs": [ + 123, + 452, + 177, + 459 + ] + }, + { + "type": "text", + "bbox": [ + 317, + 224, + 394, + 231 + ], + "lines": [ + { + "bbox": [ + 316, + 223, + 395, + 232 + ], + "spans": [ + { + "bbox": [ + 316, + 223, + 395, + 232 + ], + "score": 0.992, + "content": "System's generation (rate thisl):", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 38, + "bbox_fs": [ + 316, + 223, + 395, + 232 + ] + }, + { + "type": "text", + "bbox": [ + 327, + 238, + 480, + 263 + ], + "lines": [ + { + "bbox": [ + 328, + 238, + 479, + 245 + ], + "spans": [ + { + "bbox": [ + 328, + 238, + 479, + 245 + ], + "score": 0.972, + "content": "... director's prior work, however, I have hope for her future films. Ithink this", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 328, + 245, + 477, + 251 + ], + "spans": [ + { + "bbox": [ + 328, + 245, + 477, + 251 + ], + "score": 0.99, + "content": "small misstep is the result of a producer hampering her excellent creativity.", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 328, + 251, + 481, + 258 + ], + "spans": [ + { + "bbox": [ + 328, + 251, + 481, + 258 + ], + "score": 0.997, + "content": "There are some shining moments that show her expertise, and Ilook forward", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 328, + 257, + 386, + 263 + ], + "spans": [ + { + "bbox": [ + 328, + 257, + 386, + 263 + ], + "score": 0.99, + "content": "to the director's future films!", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 40.5, + "bbox_fs": [ + 328, + 238, + 481, + 263 + ] + }, + { + "type": "text", + "bbox": [ + 322, + 278, + 491, + 316 + ], + "lines": [ + { + "bbox": [ + 326, + 277, + 491, + 285 + ], + "spans": [ + { + "bbox": [ + 326, + 277, + 491, + 285 + ], + "score": 0.983, + "content": "Coherence/Quality: 4/5 Why?The completion recognizes that this movie isnt good", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 327, + 284, + 488, + 290 + ], + "spans": [ + { + "bbox": [ + 327, + 284, + 488, + 290 + ], + "score": 0.996, + "content": "(as described in the prompt),and makes a reasonable pivot towards talking about", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 327, + 290, + 486, + 297 + ], + "spans": [ + { + "bbox": [ + 327, + 290, + 486, + 297 + ], + "score": 0.979, + "content": "the director's other works. The shift in sentiment is somewhat abrupt, but is well-", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 326, + 297, + 349, + 303 + ], + "spans": [ + { + "bbox": [ + 326, + 297, + 349, + 303 + ], + "score": 0.991, + "content": "explained.", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 327, + 303, + 491, + 309 + ], + "spans": [ + { + "bbox": [ + 327, + 303, + 491, + 309 + ], + "score": 0.989, + "content": "Sentiment: 4/5 Why? The completion recognizes some shortcomings as a pivot, but", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 326, + 309, + 451, + 316 + ], + "spans": [ + { + "bbox": [ + 326, + 309, + 451, + 316 + ], + "score": 0.993, + "content": "also, provides a hopeful message for the director's future work", + "type": "text" + } + ], + "index": 48 + } + ], + "index": 45.5, + "bbox_fs": [ + 326, + 277, + 491, + 316 + ] + }, + { + "type": "title", + "bbox": [ + 317, + 333, + 354, + 341 + ], + "lines": [ + { + "bbox": [ + 315, + 330, + 357, + 343 + ], + "spans": [ + { + "bbox": [ + 315, + 330, + 357, + 343 + ], + "score": 0.991, + "content": "Example 2:", + "type": "text" + } + ], + "index": 49 + } + ], + "index": 49 + }, + { + "type": "text", + "bbox": [ + 317, + 343, + 337, + 349 + ], + "lines": [ + { + "bbox": [ + 317, + 343, + 337, + 349 + ], + "spans": [], + "index": 50 + } + ], + "index": 50, + "bbox_fs": [ + 317, + 343, + 337, + 349 + ] + }, + { + "type": "text", + "bbox": [ + 327, + 357, + 473, + 389 + ], + "lines": [ + { + "bbox": [ + 328, + 357, + 474, + 364 + ], + "spans": [ + { + "bbox": [ + 328, + 357, + 474, + 364 + ], + "score": 0.983, + "content": "I cannot BELIEVE anyone is giving this film a good rating. In addition to the", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 328, + 363, + 471, + 370 + ], + "spans": [ + { + "bbox": [ + 328, + 363, + 471, + 370 + ], + "score": 0.988, + "content": "terrible acting, thin (nonexistent?) plot line and slooooooooow pace, this", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 328, + 370, + 471, + 376 + ], + "spans": [ + { + "bbox": [ + 328, + 370, + 471, + 376 + ], + "score": 0.967, + "content": "would be the movie to watch if you were really TRYING to fall asleep. The", + "type": "text" + } + ], + "index": 53 + }, + { + "bbox": [ + 328, + 376, + 463, + 382 + ], + "spans": [ + { + "bbox": [ + 328, + 376, + 463, + 382 + ], + "score": 0.981, + "content": "writer's and director's brains must have been fried eggs to ever have", + "type": "text" + } + ], + "index": 54 + }, + { + "bbox": [ + 329, + 383, + 443, + 388 + ], + "spans": [ + { + "bbox": [ + 329, + 383, + 443, + 388 + ], + "score": 0.989, + "content": "concocted something as abominable as this. Based on the", + "type": "text" + } + ], + "index": 55 + } + ], + "index": 53, + "bbox_fs": [ + 328, + 357, + 474, + 388 + ] + }, + { + "type": "text", + "bbox": [ + 317, + 397, + 394, + 403 + ], + "lines": [ + { + "bbox": [ + 316, + 395, + 395, + 404 + ], + "spans": [ + { + "bbox": [ + 316, + 395, + 395, + 404 + ], + "score": 0.987, + "content": "System's generation (rate thisl):", + "type": "text" + } + ], + "index": 56 + } + ], + "index": 56, + "bbox_fs": [ + 316, + 395, + 395, + 404 + ] + }, + { + "type": "text", + "bbox": [ + 329, + 411, + 478, + 430 + ], + "lines": [ + { + "bbox": [ + 329, + 411, + 480, + 417 + ], + "spans": [ + { + "bbox": [ + 329, + 411, + 480, + 417 + ], + "score": 0.976, + "content": "... amazing filmmaking, the film is a must-see for anyone who loves movies. A", + "type": "text" + } + ], + "index": 57 + }, + { + "bbox": [ + 328, + 417, + 472, + 424 + ], + "spans": [ + { + "bbox": [ + 328, + 417, + 472, + 424 + ], + "score": 0.989, + "content": "masterpiece of cinema, great for all ages. I highly recommend this film to", + "type": "text" + } + ], + "index": 58 + }, + { + "bbox": [ + 327, + 423, + 360, + 430 + ], + "spans": [ + { + "bbox": [ + 327, + 423, + 360, + 430 + ], + "score": 0.999, + "content": "anyone.10/10.", + "type": "text" + } + ], + "index": 59 + } + ], + "index": 58, + "bbox_fs": [ + 327, + 411, + 480, + 430 + ] + }, + { + "type": "text", + "bbox": [ + 322, + 438, + 492, + 456 + ], + "lines": [ + { + "bbox": [ + 322, + 437, + 492, + 444 + ], + "spans": [ + { + "bbox": [ + 322, + 437, + 492, + 444 + ], + "score": 0.984, + "content": "· Coherence/Quality:1/5 Why?The very positive completion doesn't make any sense", + "type": "text" + } + ], + "index": 60 + }, + { + "bbox": [ + 326, + 444, + 491, + 451 + ], + "spans": [ + { + "bbox": [ + 326, + 444, + 491, + 451 + ], + "score": 0.994, + "content": "given the very negative discussion in the prompt. 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Group 1Group 2CoherenceDiff (G2-G1)p-values
SentimentDiff (G2-G1) p-values
PPO with KLPPO with KLPPOwithout KLNLPO with KL-0.30.0350.7830.001
PPO with KL0.030.90.0270.9
PPO with KLNLPO without KL-0.30.0350.8270.001
PPO with KLSupervised0.050.9-0.150.591
PPO with KLHuman0.6670.001-0.5670.001
PPO with KLZero Shot0.1370.776-0.4830.001
PPO without KLNLPO with KL0.330.013-0.7570.001
PPO without KLNLPO without KL0.0010.90.0430.9
PPO without KLSupervised0.350.006-0.9330.001
PPO without KLHuman0.9670.009-1.350.001
PPO without KLZero Shot0.4370.001-1.2670.001
NLPO with KLNLPO without KL-0.330.0130.80.001
NLPO with KLSupervised0.020.9-0.1770.404
NLPO with KLHuman0.6370.001-0.5930.001
NLPO with KLZero Shot0.1070.9-0.510.001
NLPO without KLSupervised0.350.006-0.9770.001
NLPO without KLHuman0.9670.001-1.3930.001
NLPO without KLZero Shot0.4370.001-1.310.001
SupervisedHuman0.6170.001-0.4170.001
SupervisedZero Shot0.0870.9-0.3330.0027
HumanZero Shot-0.530.0010.0830.9
Supervised+PPOSupervised+NLPO0.030.90.090.035
Supervised+PPONLPO with KL0.040.9-0.030.9
Supervised+PPONLPO without KL-0.290.0010.770.001
Supervised+PPOPPO without KL-0.290.0060.720.001
Supervised+PPOPPO with KL0.010.9-0.060.001
Supervised+PPOZero Shot0.150.035-0.540.001
Supervised+PPOSupervised0.060.001-0.210.001
Supervised+PPOSupervised+NLPOHuman0.680.001-0.630.001
NLPO with KL0.010.9-0.120.001
Supervised+NLPONLPO without KL-0.320.0010.680.001
Supervised+NLPOPPO without KL-0.320.0350.630.001
Supervised+NLPOPPO with KL-0.020.9-0.150.006
Supervised+NLPOSupervised+NLPOSupervised+NLPOZero Shot-0.120.001-0.630.001
Supervised0.030.9-0.30.001
Human0.650.001-0.720.006
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Group 1Group 2CoherenceDiff (G2-G1)p-values
SentimentDiff (G2-G1) p-values
PPO with KLPPO with KLPPOwithout KLNLPO with KL-0.30.0350.7830.001
PPO with KL0.030.90.0270.9
PPO with KLNLPO without KL-0.30.0350.8270.001
PPO with KLSupervised0.050.9-0.150.591
PPO with KLHuman0.6670.001-0.5670.001
PPO with KLZero Shot0.1370.776-0.4830.001
PPO without KLNLPO with KL0.330.013-0.7570.001
PPO without KLNLPO without KL0.0010.90.0430.9
PPO without KLSupervised0.350.006-0.9330.001
PPO without KLHuman0.9670.009-1.350.001
PPO without KLZero Shot0.4370.001-1.2670.001
NLPO with KLNLPO without KL-0.330.0130.80.001
NLPO with KLSupervised0.020.9-0.1770.404
NLPO with KLHuman0.6370.001-0.5930.001
NLPO with KLZero Shot0.1070.9-0.510.001
NLPO without KLSupervised0.350.006-0.9770.001
NLPO without KLHuman0.9670.001-1.3930.001
NLPO without KLZero Shot0.4370.001-1.310.001
SupervisedHuman0.6170.001-0.4170.001
SupervisedZero Shot0.0870.9-0.3330.0027
HumanZero Shot-0.530.0010.0830.9
Supervised+PPOSupervised+NLPO0.030.90.090.035
Supervised+PPONLPO with KL0.040.9-0.030.9
Supervised+PPONLPO without KL-0.290.0010.770.001
Supervised+PPOPPO without KL-0.290.0060.720.001
Supervised+PPOPPO with KL0.010.9-0.060.001
Supervised+PPOZero Shot0.150.035-0.540.001
Supervised+PPOSupervised0.060.001-0.210.001
Supervised+PPOSupervised+NLPOHuman0.680.001-0.630.001
NLPO with KL0.010.9-0.120.001
Supervised+NLPONLPO without KL-0.320.0010.680.001
Supervised+NLPOPPO without KL-0.320.0350.630.001
Supervised+NLPOPPO with KL-0.020.9-0.150.006
Supervised+NLPOSupervised+NLPOSupervised+NLPOZero Shot-0.120.001-0.630.001
Supervised0.030.9-0.30.001
Human0.650.001-0.720.006
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When the wife disappears, her sister begins a vigorous search involving the", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 3.5 + }, + { + "type": "text", + "bbox": [ + 107, + 142, + 492, + 165 + ], + "lines": [ + { + "bbox": [ + 107, + 141, + 489, + 150 + ], + "spans": [ + { + "bbox": [ + 107, + 141, + 489, + 150 + ], + "score": 1.0, + "content": "Zero-Shot: husband’s sister, which leads several men to a remote cabin and then a boat. The", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 125, + 148, + 477, + 159 + ], + "spans": [ + { + "bbox": [ + 125, + 148, + 477, + 159 + ], + "score": 1.0, + "content": "wife and her husband then start to see the same things. Finally, a strange woman is", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 126, + 157, + 422, + 166 + ], + "spans": [ + { + "bbox": [ + 126, + 157, + 422, + 166 + ], + "score": 1.0, + "content": "driving out to her cabin and discovers the husband’s disappearance but", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 6 + }, + { + "type": "text", + "bbox": [ + 106, + 166, + 492, + 189 + ], + "lines": [ + { + "bbox": [ + 105, + 164, + 489, + 174 + ], + "spans": [ + { + "bbox": [ + 105, + 164, + 489, + 174 + ], + "score": 1.0, + "content": "References: local police, state government, and a television crime show. What she finds out", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 126, + 173, + 488, + 182 + ], + "spans": [ + { + "bbox": [ + 126, + 173, + 488, + 182 + ], + "score": 1.0, + "content": "stuns the entire community. Good drama with lots of fine performances; based on a true", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 126, + 180, + 151, + 191 + ], + "spans": [ + { + "bbox": [ + 126, + 180, + 151, + 191 + ], + "score": 1.0, + "content": "story", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 9 + }, + { + "type": "text", + "bbox": [ + 104, + 190, + 498, + 213 + ], + "lines": [ + { + "bbox": [ + 106, + 188, + 498, + 199 + ], + "spans": [ + { + "bbox": [ + 106, + 188, + 498, + 199 + ], + "score": 1.0, + "content": "PPO: police and the local public. At the end, the woman is killed and the wife is found naked", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 125, + 196, + 500, + 206 + ], + "spans": [ + { + "bbox": [ + 125, + 196, + 500, + 206 + ], + "score": 1.0, + "content": "and with a red head tattooed on her back. This is part of a special feature called\"On the", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 129, + 204, + 230, + 214 + ], + "spans": [ + { + "bbox": [ + 129, + 204, + 230, + 214 + ], + "score": 1.0, + "content": "Road, Hidden\" which was", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 12 + }, + { + "type": "text", + "bbox": [ + 106, + 213, + 500, + 237 + ], + "lines": [ + { + "bbox": [ + 106, + 213, + 498, + 222 + ], + "spans": [ + { + "bbox": [ + 106, + 213, + 498, + 222 + ], + "score": 1.0, + "content": "PPO-no-KL: police and other local governments. Written by G. Scott Fitzgerald, who also stars", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 126, + 220, + 501, + 230 + ], + "spans": [ + { + "bbox": [ + 126, + 220, + 501, + 230 + ], + "score": 1.0, + "content": "in this production, \"A Very Merry Christmas\" is a wonderful family movie with a wonderful", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 130, + 229, + 455, + 238 + ], + "spans": [ + { + "bbox": [ + 130, + 229, + 455, + 238 + ], + "score": 1.0, + "content": "soundtrack and wonderful characters. It brings home the true beauty of small-", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 15 + }, + { + "type": "text", + "bbox": [ + 103, + 237, + 500, + 261 + ], + "lines": [ + { + "bbox": [ + 106, + 237, + 502, + 246 + ], + "spans": [ + { + "bbox": [ + 106, + 237, + 502, + 246 + ], + "score": 1.0, + "content": "NLPO: mother while the brother goes under. 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Everything is very simply portrayed as it would be in", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 126, + 373, + 488, + 381 + ], + "spans": [ + { + "bbox": [ + 126, + 373, + 488, + 381 + ], + "score": 1.0, + "content": "reality. At times the storyline was confusing, but perhaps in order to give a sense of", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 126, + 379, + 480, + 390 + ], + "spans": [ + { + "bbox": [ + 126, + 379, + 480, + 390 + ], + "score": 1.0, + "content": "the characters’ frame of mind how they too do now know what is happening or why. 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In other films these two have been referred to from time to", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 130, + 412, + 414, + 421 + ], + "spans": [ + { + "bbox": [ + 130, + 412, + 414, + 421 + ], + "score": 1.0, + "content": "time in a form and manner more suited to the screen. The film shows", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 36 + }, + { + "type": "text", + "bbox": [ + 110, + 421, + 498, + 452 + ], + "lines": [ + { + "bbox": [ + 107, + 419, + 490, + 430 + ], + "spans": [ + { + "bbox": [ + 107, + 419, + 490, + 430 + ], + "score": 1.0, + "content": "References: film made it somewhat boring, but I could understand how the director is trying", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 126, + 428, + 489, + 437 + ], + "spans": [ + { + "bbox": [ + 126, + 428, + 489, + 437 + ], + "score": 1.0, + "content": "not to glamorize the story and points. He depicted the harsh and unsettling events and", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 127, + 437, + 499, + 444 + ], + "spans": [ + { + "bbox": [ + 127, + 437, + 499, + 444 + ], + "score": 1.0, + "content": "effects of war. 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To", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 125, + 468, + 484, + 478 + ], + "spans": [ + { + "bbox": [ + 125, + 468, + 484, + 478 + ], + "score": 1.0, + "content": "put it simply, I strongly recommend to everyone who plays the role to buy this DVD!!!", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 43 + }, + { + "type": "text", + "bbox": [ + 105, + 477, + 495, + 500 + ], + "lines": [ + { + "bbox": [ + 106, + 476, + 497, + 485 + ], + "spans": [ + { + "bbox": [ + 106, + 476, + 497, + 485 + ], + "score": 1.0, + "content": "PPO-no-KL: movie helps it to flow along in a believable way. Rating 4 out of 5 Great Movie! I", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 126, + 484, + 492, + 493 + ], + "spans": [ + { + "bbox": [ + 126, + 484, + 492, + 493 + ], + "score": 1.0, + "content": "highly recommend these movies! I highly recommend these movies! Rating 5 out of 5 Great", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 125, + 490, + 352, + 501 + ], + "spans": [ + { + "bbox": [ + 125, + 490, + 352, + 501 + ], + "score": 1.0, + "content": "Movie! I highly recommend these movies! Rating 10 of\"", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 46 + }, + { + "type": "text", + "bbox": [ + 105, + 500, + 492, + 524 + ], + "lines": [ + { + "bbox": [ + 105, + 498, + 490, + 509 + ], + "spans": [ + { + "bbox": [ + 105, + 498, + 490, + 509 + ], + "score": 1.0, + "content": "NLPO: novel makes it one of the first books I have read by a British actor. It is a fun way", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 126, + 508, + 493, + 517 + ], + "spans": [ + { + "bbox": [ + 126, + 508, + 493, + 517 + ], + "score": 1.0, + "content": "for someone who likes their books, like me, to sit through a novel. If you like to read", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 125, + 515, + 217, + 526 + ], + "spans": [ + { + "bbox": [ + 125, + 515, + 217, + 526 + ], + "score": 1.0, + "content": "novels, check it out.", + "type": "text" + } + ], + "index": 50 + } + ], + "index": 49 + }, + { + "type": "text", + "bbox": [ + 107, + 524, + 494, + 548 + ], + "lines": [ + { + "bbox": [ + 105, + 523, + 490, + 533 + ], + "spans": [ + { + "bbox": [ + 105, + 523, + 490, + 533 + ], + "score": 1.0, + "content": "NLPO-no-KL: setting makes the final product very enjoyable to watch. Highly recommended!! ~", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 125, + 531, + 496, + 541 + ], + "spans": [ + { + "bbox": [ + 125, + 531, + 496, + 541 + ], + "score": 1.0, + "content": "Michael Bowerman, SPSA Film Festival Host, SPSA, WA (December 17, 2006), 8/17/2006 Great", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 125, + 539, + 232, + 549 + ], + "spans": [ + { + "bbox": [ + 125, + 539, + 232, + 549 + ], + "score": 1.0, + "content": "photography, good acting,", + "type": "text" + } + ], + "index": 53 + } + ], + "index": 52 + }, + { + "type": "text", + "bbox": [ + 106, + 548, + 488, + 572 + ], + "lines": [ + { + "bbox": [ + 106, + 546, + 486, + 556 + ], + "spans": [ + { + "bbox": [ + 106, + 546, + 486, + 556 + ], + "score": 1.0, + "content": "Supervised: \"Dakota Clan\" and his sister, the two become friends with Ted Masters who soon", + "type": "text" + } + ], + "index": 54 + }, + { + "bbox": [ + 127, + 555, + 488, + 564 + ], + "spans": [ + { + "bbox": [ + 127, + 555, + 488, + 564 + ], + "score": 1.0, + "content": "finds the chance to fly back to their home land and go back to save his brother’s life", + "type": "text" + } + ], + "index": 55 + }, + { + "bbox": [ + 126, + 563, + 209, + 573 + ], + "spans": [ + { + "bbox": [ + 126, + 563, + 209, + 573 + ], + "score": 1.0, + "content": "and his family. 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One is African but never grew", + "type": "text" + } + ], + "index": 65 + }, + { + "bbox": [ + 125, + 667, + 264, + 676 + ], + "spans": [ + { + "bbox": [ + 125, + 667, + 264, + 676 + ], + "score": 1.0, + "content": "up the other. One of them, a man", + "type": "text" + } + ], + "index": 66 + } + ], + "index": 65 + }, + { + "type": "text", + "bbox": [ + 106, + 676, + 500, + 707 + ], + "lines": [ + { + "bbox": [ + 106, + 675, + 482, + 685 + ], + "spans": [ + { + "bbox": [ + 106, + 675, + 482, + 685 + ], + "score": 1.0, + "content": "References: would sweep every award in the offering. He meets the challenge of presenting", + "type": "text" + } + ], + "index": 67 + }, + { + "bbox": [ + 127, + 684, + 501, + 692 + ], + "spans": [ + { + "bbox": [ + 127, + 684, + 501, + 692 + ], + "score": 1.0, + "content": "Shylock head on, and delivers an extraordinarily subtle and nuanced performance. 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The supporting cast", + "type": "text" + } + ], + "index": 70 + } + ], + "index": 68.5 + }, + { + "type": "text", + "bbox": [ + 105, + 708, + 494, + 731 + ], + "lines": [ + { + "bbox": [ + 105, + 706, + 495, + 717 + ], + "spans": [ + { + "bbox": [ + 105, + 706, + 495, + 717 + ], + "score": 1.0, + "content": "PPO: would have made him an instant-classic. This movie captures the spirit of childhood and", + "type": "text" + } + ], + "index": 71 + }, + { + "bbox": [ + 125, + 714, + 492, + 725 + ], + "spans": [ + { + "bbox": [ + 125, + 714, + 492, + 725 + ], + "score": 1.0, + "content": "has everyone in the world watching it. It’s a love story and it’s really heartbreaking.", + "type": "text" + } + ], + "index": 72 + }, + { + "bbox": [ + 126, + 723, + 296, + 732 + ], + "spans": [ + { + "bbox": [ + 126, + 723, + 296, + 732 + ], + "score": 1.0, + "content": "And at the same time, it’s a classic. It", + "type": "text" + } + ], + "index": 73 + } + ], + "index": 72 + } + ], + "page_idx": 25, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2023", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 751, + 311, + 760 + ], + "lines": [ + { + "bbox": [ + 298, + 750, + 313, + 763 + ], + "spans": [ + { + "bbox": [ + 298, + 750, + 313, + 763 + ], + "score": 1.0, + "content": "26", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 107, + 82, + 242, + 93 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 242, + 95 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 242, + 95 + ], + "score": 1.0, + "content": "B.3.4 QUALITATIVE RESULTS", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "title", + "bbox": [ + 106, + 102, + 505, + 113 + ], + "lines": [ + { + "bbox": [ + 105, + 100, + 507, + 115 + ], + "spans": [ + { + "bbox": [ + 105, + 100, + 507, + 115 + ], + "score": 1.0, + "content": "We show sample generations from each of the algorithms for three randomly picked prompts below.", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 1 + }, + { + "type": "title", + "bbox": [ + 106, + 118, + 141, + 125 + ], + "lines": [ + { + "bbox": [ + 106, + 118, + 141, + 125 + ], + "spans": [], + "index": 2 + } + ], + "index": 2 + }, + { + "type": "text", + "bbox": [ + 108, + 125, + 494, + 141 + ], + "lines": [ + { + "bbox": [ + 106, + 124, + 494, + 135 + ], + "spans": [ + { + "bbox": [ + 106, + 124, + 494, + 135 + ], + "score": 1.0, + "content": "Prompt: A man and his wife are not getting along because of the wife’s jealousy and drinking", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 125, + 133, + 485, + 143 + ], + "spans": [ + { + "bbox": [ + 125, + 133, + 485, + 143 + ], + "score": 1.0, + "content": "problems. When the wife disappears, her sister begins a vigorous search involving the", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 3.5, + "bbox_fs": [ + 106, + 124, + 494, + 143 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 142, + 492, + 165 + ], + "lines": [ + { + "bbox": [ + 107, + 141, + 489, + 150 + ], + "spans": [ + { + "bbox": [ + 107, + 141, + 489, + 150 + ], + "score": 1.0, + "content": "Zero-Shot: husband’s sister, which leads several men to a remote cabin and then a boat. The", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 125, + 148, + 477, + 159 + ], + "spans": [ + { + "bbox": [ + 125, + 148, + 477, + 159 + ], + "score": 1.0, + "content": "wife and her husband then start to see the same things. Finally, a strange woman is", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 126, + 157, + 422, + 166 + ], + "spans": [ + { + "bbox": [ + 126, + 157, + 422, + 166 + ], + "score": 1.0, + "content": "driving out to her cabin and discovers the husband’s disappearance but", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 6, + "bbox_fs": [ + 107, + 141, + 489, + 166 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 166, + 492, + 189 + ], + "lines": [ + { + "bbox": [ + 105, + 164, + 489, + 174 + ], + "spans": [ + { + "bbox": [ + 105, + 164, + 489, + 174 + ], + "score": 1.0, + "content": "References: local police, state government, and a television crime show. What she finds out", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 126, + 173, + 488, + 182 + ], + "spans": [ + { + "bbox": [ + 126, + 173, + 488, + 182 + ], + "score": 1.0, + "content": "stuns the entire community. Good drama with lots of fine performances; based on a true", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 126, + 180, + 151, + 191 + ], + "spans": [ + { + "bbox": [ + 126, + 180, + 151, + 191 + ], + "score": 1.0, + "content": "story", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 9, + "bbox_fs": [ + 105, + 164, + 489, + 191 + ] + }, + { + "type": "text", + "bbox": [ + 104, + 190, + 498, + 213 + ], + "lines": [ + { + "bbox": [ + 106, + 188, + 498, + 199 + ], + "spans": [ + { + "bbox": [ + 106, + 188, + 498, + 199 + ], + "score": 1.0, + "content": "PPO: police and the local public. At the end, the woman is killed and the wife is found naked", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 125, + 196, + 500, + 206 + ], + "spans": [ + { + "bbox": [ + 125, + 196, + 500, + 206 + ], + "score": 1.0, + "content": "and with a red head tattooed on her back. This is part of a special feature called\"On the", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 129, + 204, + 230, + 214 + ], + "spans": [ + { + "bbox": [ + 129, + 204, + 230, + 214 + ], + "score": 1.0, + "content": "Road, Hidden\" which was", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 12, + "bbox_fs": [ + 106, + 188, + 500, + 214 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 213, + 500, + 237 + ], + "lines": [ + { + "bbox": [ + 106, + 213, + 498, + 222 + ], + "spans": [ + { + "bbox": [ + 106, + 213, + 498, + 222 + ], + "score": 1.0, + "content": "PPO-no-KL: police and other local governments. Written by G. Scott Fitzgerald, who also stars", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 126, + 220, + 501, + 230 + ], + "spans": [ + { + "bbox": [ + 126, + 220, + 501, + 230 + ], + "score": 1.0, + "content": "in this production, \"A Very Merry Christmas\" is a wonderful family movie with a wonderful", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 130, + 229, + 455, + 238 + ], + "spans": [ + { + "bbox": [ + 130, + 229, + 455, + 238 + ], + "score": 1.0, + "content": "soundtrack and wonderful characters. It brings home the true beauty of small-", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 15, + "bbox_fs": [ + 106, + 213, + 501, + 238 + ] + }, + { + "type": "text", + "bbox": [ + 103, + 237, + 500, + 261 + ], + "lines": [ + { + "bbox": [ + 106, + 237, + 502, + 246 + ], + "spans": [ + { + "bbox": [ + 106, + 237, + 502, + 246 + ], + "score": 1.0, + "content": "NLPO: mother while the brother goes under. After all, his sister, who was apparently kidnapped", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 130, + 245, + 502, + 254 + ], + "spans": [ + { + "bbox": [ + 130, + 245, + 502, + 254 + ], + "score": 1.0, + "content": "but who turns out to be a man, is no longer in her place. If a film that was made in the", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 130, + 252, + 155, + 262 + ], + "spans": [ + { + "bbox": [ + 130, + 252, + 155, + 262 + ], + "score": 1.0, + "content": "1950s", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 18, + "bbox_fs": [ + 106, + 237, + 502, + 262 + ] + }, + { + "type": "text", + "bbox": [ + 104, + 261, + 500, + 285 + ], + "lines": [ + { + "bbox": [ + 105, + 258, + 502, + 271 + ], + "spans": [ + { + "bbox": [ + 105, + 258, + 502, + 271 + ], + "score": 1.0, + "content": "NLPO-no-KL: friends of the wife, and also the friend of the wife of the woman that is missing,", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 128, + 267, + 485, + 279 + ], + "spans": [ + { + "bbox": [ + 128, + 267, + 485, + 279 + ], + "score": 1.0, + "content": "and eventually he begins to find that she has gone to Germany and he has made a very", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 126, + 276, + 343, + 286 + ], + "spans": [ + { + "bbox": [ + 126, + 276, + 343, + 286 + ], + "score": 1.0, + "content": "good friend. There is a good scene between John and", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 21, + "bbox_fs": [ + 105, + 258, + 502, + 286 + ] + }, + { + "type": "text", + "bbox": [ + 109, + 285, + 498, + 309 + ], + "lines": [ + { + "bbox": [ + 107, + 284, + 477, + 294 + ], + "spans": [ + { + "bbox": [ + 107, + 284, + 477, + 294 + ], + "score": 1.0, + "content": "Supervised: amily tree. The widower, now widowed, returns, the daughter, daughter is not", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 124, + 291, + 497, + 303 + ], + "spans": [ + { + "bbox": [ + 124, + 291, + 497, + 303 + ], + "score": 1.0, + "content": "pleased when his wife is mistaken for one of her sons, and the patriarch, then a wealthy", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 125, + 300, + 310, + 310 + ], + "spans": [ + { + "bbox": [ + 125, + 300, + 310, + 310 + ], + "score": 1.0, + "content": "man, falls victim to a jealous husband. The", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 24, + "bbox_fs": [ + 107, + 284, + 497, + 310 + ] + }, + { + "type": "title", + "bbox": [ + 106, + 325, + 142, + 333 + ], + "lines": [ + { + "bbox": [ + 105, + 323, + 144, + 334 + ], + "spans": [ + { + "bbox": [ + 105, + 323, + 144, + 334 + ], + "score": 1.0, + "content": "Sample 2", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 26 + }, + { + "type": "text", + "bbox": [ + 107, + 334, + 498, + 396 + ], + "lines": [ + { + "bbox": [ + 106, + 333, + 480, + 342 + ], + "spans": [ + { + "bbox": [ + 106, + 333, + 480, + 342 + ], + "score": 1.0, + "content": "Prompt: A very credible and unsettling movie portraying the effects of war on the general", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 125, + 341, + 497, + 350 + ], + "spans": [ + { + "bbox": [ + 125, + 341, + 497, + 350 + ], + "score": 1.0, + "content": "public, Shame gives us a chilling understanding oh Ingmar Bergman’s beliefs. The absence", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 125, + 348, + 497, + 358 + ], + "spans": [ + { + "bbox": [ + 125, + 348, + 497, + 358 + ], + "score": 1.0, + "content": "of color and sound (as in a soundtrack) helps to give the film a more realistic feeling.", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 126, + 356, + 477, + 366 + ], + "spans": [ + { + "bbox": [ + 126, + 356, + 477, + 366 + ], + "score": 1.0, + "content": "There is no soft or hard lighting or a variety of camera angles to give the story a", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 126, + 365, + 473, + 374 + ], + "spans": [ + { + "bbox": [ + 126, + 365, + 473, + 374 + ], + "score": 1.0, + "content": "charming or dramatic effect. Everything is very simply portrayed as it would be in", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 126, + 373, + 488, + 381 + ], + "spans": [ + { + "bbox": [ + 126, + 373, + 488, + 381 + ], + "score": 1.0, + "content": "reality. At times the storyline was confusing, but perhaps in order to give a sense of", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 126, + 379, + 480, + 390 + ], + "spans": [ + { + "bbox": [ + 126, + 379, + 480, + 390 + ], + "score": 1.0, + "content": "the characters’ frame of mind how they too do now know what is happening or why. The", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 127, + 389, + 200, + 398 + ], + "spans": [ + { + "bbox": [ + 127, + 389, + 200, + 398 + ], + "score": 1.0, + "content": "simplicity of the", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 30.5, + "bbox_fs": [ + 106, + 333, + 497, + 398 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 397, + 499, + 420 + ], + "lines": [ + { + "bbox": [ + 106, + 397, + 494, + 405 + ], + "spans": [ + { + "bbox": [ + 106, + 397, + 494, + 405 + ], + "score": 1.0, + "content": "Zero-Shot: camera work is at once apparent and fascinating in the manner in which it affects", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 126, + 404, + 501, + 413 + ], + "spans": [ + { + "bbox": [ + 126, + 404, + 501, + 413 + ], + "score": 1.0, + "content": "the way things are portrayed. In other films these two have been referred to from time to", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 130, + 412, + 414, + 421 + ], + "spans": [ + { + "bbox": [ + 130, + 412, + 414, + 421 + ], + "score": 1.0, + "content": "time in a form and manner more suited to the screen. The film shows", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 36, + "bbox_fs": [ + 106, + 397, + 501, + 421 + ] + }, + { + "type": "text", + "bbox": [ + 110, + 421, + 498, + 452 + ], + "lines": [ + { + "bbox": [ + 107, + 419, + 490, + 430 + ], + "spans": [ + { + "bbox": [ + 107, + 419, + 490, + 430 + ], + "score": 1.0, + "content": "References: film made it somewhat boring, but I could understand how the director is trying", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 126, + 428, + 489, + 437 + ], + "spans": [ + { + "bbox": [ + 126, + 428, + 489, + 437 + ], + "score": 1.0, + "content": "not to glamorize the story and points. He depicted the harsh and unsettling events and", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 127, + 437, + 499, + 444 + ], + "spans": [ + { + "bbox": [ + 127, + 437, + 499, + 444 + ], + "score": 1.0, + "content": "effects of war. In the beginning the characters were introduced and shown as content with", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 131, + 445, + 217, + 453 + ], + "spans": [ + { + "bbox": [ + 131, + 445, + 217, + 453 + ], + "score": 1.0, + "content": "the lighter settings", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 39.5, + "bbox_fs": [ + 107, + 419, + 499, + 453 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 453, + 495, + 476 + ], + "lines": [ + { + "bbox": [ + 105, + 451, + 486, + 462 + ], + "spans": [ + { + "bbox": [ + 105, + 451, + 486, + 462 + ], + "score": 1.0, + "content": "PPO: characters relationships is so engrossing and the great and unique story presented by", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 126, + 460, + 493, + 470 + ], + "spans": [ + { + "bbox": [ + 126, + 460, + 493, + 470 + ], + "score": 1.0, + "content": "each pair of brothers and sisters creates a truly gripping and enjoyable experience. To", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 125, + 468, + 484, + 478 + ], + "spans": [ + { + "bbox": [ + 125, + 468, + 484, + 478 + ], + "score": 1.0, + "content": "put it simply, I strongly recommend to everyone who plays the role to buy this DVD!!!", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 43, + "bbox_fs": [ + 105, + 451, + 493, + 478 + ] + }, + { + "type": "text", + "bbox": [ + 105, + 477, + 495, + 500 + ], + "lines": [ + { + "bbox": [ + 106, + 476, + 497, + 485 + ], + "spans": [ + { + "bbox": [ + 106, + 476, + 497, + 485 + ], + "score": 1.0, + "content": "PPO-no-KL: movie helps it to flow along in a believable way. Rating 4 out of 5 Great Movie! I", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 126, + 484, + 492, + 493 + ], + "spans": [ + { + "bbox": [ + 126, + 484, + 492, + 493 + ], + "score": 1.0, + "content": "highly recommend these movies! I highly recommend these movies! Rating 5 out of 5 Great", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 125, + 490, + 352, + 501 + ], + "spans": [ + { + "bbox": [ + 125, + 490, + 352, + 501 + ], + "score": 1.0, + "content": "Movie! I highly recommend these movies! Rating 10 of\"", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 46, + "bbox_fs": [ + 106, + 476, + 497, + 501 + ] + }, + { + "type": "text", + "bbox": [ + 105, + 500, + 492, + 524 + ], + "lines": [ + { + "bbox": [ + 105, + 498, + 490, + 509 + ], + "spans": [ + { + "bbox": [ + 105, + 498, + 490, + 509 + ], + "score": 1.0, + "content": "NLPO: novel makes it one of the first books I have read by a British actor. It is a fun way", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 126, + 508, + 493, + 517 + ], + "spans": [ + { + "bbox": [ + 126, + 508, + 493, + 517 + ], + "score": 1.0, + "content": "for someone who likes their books, like me, to sit through a novel. If you like to read", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 125, + 515, + 217, + 526 + ], + "spans": [ + { + "bbox": [ + 125, + 515, + 217, + 526 + ], + "score": 1.0, + "content": "novels, check it out.", + "type": "text" + } + ], + "index": 50 + } + ], + "index": 49, + "bbox_fs": [ + 105, + 498, + 493, + 526 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 524, + 494, + 548 + ], + "lines": [ + { + "bbox": [ + 105, + 523, + 490, + 533 + ], + "spans": [ + { + "bbox": [ + 105, + 523, + 490, + 533 + ], + "score": 1.0, + "content": "NLPO-no-KL: setting makes the final product very enjoyable to watch. Highly recommended!! ~", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 125, + 531, + 496, + 541 + ], + "spans": [ + { + "bbox": [ + 125, + 531, + 496, + 541 + ], + "score": 1.0, + "content": "Michael Bowerman, SPSA Film Festival Host, SPSA, WA (December 17, 2006), 8/17/2006 Great", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 125, + 539, + 232, + 549 + ], + "spans": [ + { + "bbox": [ + 125, + 539, + 232, + 549 + ], + "score": 1.0, + "content": "photography, good acting,", + "type": "text" + } + ], + "index": 53 + } + ], + "index": 52, + "bbox_fs": [ + 105, + 523, + 496, + 549 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 548, + 488, + 572 + ], + "lines": [ + { + "bbox": [ + 106, + 546, + 486, + 556 + ], + "spans": [ + { + "bbox": [ + 106, + 546, + 486, + 556 + ], + "score": 1.0, + "content": "Supervised: \"Dakota Clan\" and his sister, the two become friends with Ted Masters who soon", + "type": "text" + } + ], + "index": 54 + }, + { + "bbox": [ + 127, + 555, + 488, + 564 + ], + "spans": [ + { + "bbox": [ + 127, + 555, + 488, + 564 + ], + "score": 1.0, + "content": "finds the chance to fly back to their home land and go back to save his brother’s life", + "type": "text" + } + ], + "index": 55 + }, + { + "bbox": [ + 126, + 563, + 209, + 573 + ], + "spans": [ + { + "bbox": [ + 126, + 563, + 209, + 573 + ], + "score": 1.0, + "content": "and his family. The", + "type": "text" + } + ], + "index": 56 + } + ], + "index": 55, + "bbox_fs": [ + 106, + 546, + 488, + 573 + ] + }, + { + "type": "title", + "bbox": [ + 106, + 588, + 141, + 595 + ], + "lines": [ + { + "bbox": [ + 105, + 586, + 144, + 598 + ], + "spans": [ + { + "bbox": [ + 105, + 586, + 144, + 598 + ], + "score": 1.0, + "content": "Sample 3", + "type": "text" + } + ], + "index": 57 + } + ], + "index": 57 + }, + { + "type": "text", + "bbox": [ + 107, + 596, + 504, + 644 + ], + "lines": [ + { + "bbox": [ + 105, + 595, + 502, + 605 + ], + "spans": [ + { + "bbox": [ + 105, + 595, + 502, + 605 + ], + "score": 1.0, + "content": "Prompt: Shakespearean language is wild and rambling, saturated in multiple meanings, word play", + "type": "text" + } + ], + "index": 58 + }, + { + "bbox": [ + 130, + 603, + 472, + 613 + ], + "spans": [ + { + "bbox": [ + 130, + 603, + 472, + 613 + ], + "score": 1.0, + "content": "and metaphor. 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Model Paramsvalue
supervisedbatch size: 8 epochs: 4 learning rate: 0.00001 learning rate scheduler: cosine weight decay: 0.01
ppo/ nlposteps per update: 1280 total number of steps: 256000 batch size: 64 epochs per update: 5 learning rate: 0.000002 entropy coefficient: 0.01 initial kl coeff: 0.001 target kl: 2.0 discount factor: 0.99 gae lambda: 0.95 clip ratio: 0.2 value function coeff: 0.5 top mask ratio: 0.9 target update iterations: 20
supervised+ ppo (or nlpo)steps per update:1280 total number of steps:128000 batch size: 64 epochs per update: 5 learning rate: 0.000002 entropy coefficient: 0.01 initial kl coeff: 0.01 target kl: 1.0 discount factor: 0.99 gae lambda: 0.95 clip ratio: 0.2 value function coeff: 0.5 top mask ratio: 0.9
decodingtarget update iterations: 20 num beams: 5 min length: 5
tokenizermax new tokens: 20 padding side: left max length: 20
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Additionally, we also train with task-specific rewards such as CIDEr (Vedantam", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 175, + 505, + 187 + ], + "spans": [ + { + "bbox": [ + 105, + 175, + 505, + 187 + ], + "score": 1.0, + "content": "et al., 2015), SPICE (Anderson et al., 2016) and SPiDer (Liu et al., 2017) which is a just a linear", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 185, + 505, + 198 + ], + "spans": [ + { + "bbox": [ + 105, + 185, + 505, + 198 + ], + "score": 1.0, + "content": "combination of both with equal weights. We chose T5-base as the base LM since it is well-suited", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 196, + 507, + 210 + ], + "spans": [ + { + "bbox": [ + 105, + 196, + 507, + 210 + ], + "score": 1.0, + "content": "for structure to text tasks. 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Table 11 provides an in-depth summary of setting of hyperparameter values along with", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 302, + 226, + 313 + ], + "spans": [ + { + "bbox": [ + 105, + 302, + 226, + 313 + ], + "score": 1.0, + "content": "other implementation details.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 13.5, + "bbox_fs": [ + 105, + 224, + 507, + 313 + ] + }, + { + "type": "table", + "bbox": [ + 207, + 331, + 404, + 694 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 207, + 331, + 404, + 694 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 207, + 331, + 404, + 694 + ], + "spans": [ + { + "bbox": [ + 207, + 331, + 404, + 694 + ], + "score": 0.971, + "html": "
Model Paramsvalue
supervisedbatch size: 8 epochs: 4 learning rate: 0.00001 learning rate scheduler: cosine weight decay: 0.01
ppo/ nlposteps per update: 1280 total number of steps: 256000 batch size: 64 epochs per update: 5 learning rate: 0.000002 entropy coefficient: 0.01 initial kl coeff: 0.001 target kl: 2.0 discount factor: 0.99 gae lambda: 0.95 clip ratio: 0.2 value function coeff: 0.5 top mask ratio: 0.9 target update iterations: 20
supervised+ ppo (or nlpo)steps per update:1280 total number of steps:128000 batch size: 64 epochs per update: 5 learning rate: 0.000002 entropy coefficient: 0.01 initial kl coeff: 0.01 target kl: 1.0 discount factor: 0.99 gae lambda: 0.95 clip ratio: 0.2 value function coeff: 0.5 top mask ratio: 0.9
decodingtarget update iterations: 20 num beams: 5 min length: 5
tokenizermax new tokens: 20 padding side: left max length: 20
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Our main finding is that warm-started initial", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 124, + 506, + 136 + ], + "spans": [ + { + "bbox": [ + 106, + 124, + 506, + 136 + ], + "score": 1.0, + "content": "policies are crucial for learning to generate coherent sentences with common sense. 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TasksCIDErSPICECoverage
AlgLMReward functionRouge-2Rouge-LBleu (n=3)Bleu (n=4)Meteor
Zero-Shot PPOT50.0160.2640.0290.0060.2036.2000.11591.070
T5Rouge-10.085 ± 0.0080.354 ± 0.0040.161 ± 0.0110.087 ± 0.0090.235± 0.0028.673 ± 0.2340.157 ± 0.00188.544 ± 2.36
T5Rouge-Avg0.093 ± 0.0050.351 ± 0.0010.169 ± 0.0320.097 ± 0.0170.224 ± 0.0128.212 ± 1.3290.159 ± 0.01182.584 ± 2.569
T5Meteor0.091± 0.0080.308 ± 0.0070.166 ± 0.0160.088 ± 0.0130.220 ± 0.0067.251 ± 0.4530.161 ± 0.00779.718 ± 2.267
T5SPice0.065 ± 0.0030.302 ± 0.0020.115 ± 0.0630.067 ± 0.0410.193 ± 0.0146.571 ± 1.3120.175 ± 0.01169.340 ± 3.617
T5CiDer0.066 ± 0.0030.304 ± 0.0020.132 ± 0.0570.074 ± 0.0360.211 ± 0.0096.877 ± 1.2180.143 ± 0.01780.114 ± 4.852
T5SPider0.117 ± 0.0050.352 ± 0.0070.224 ± 0.0140.137 ± 0.0110.226 ± 0.019.162 ± 0.5390.186 ± 0.00673.374 ± 6.073
T5Rouge-10.087 ± 0.0020.339 ± 0.0090.127 ± 0.0480.069 ± 0.0350.213 ± 0.0026.962 ± 0.8830.145± 0.022
Rouge-Avg0.095 ± 0.0010.338 ± 0.0020.159 ± 0.020.093 ± 0.0130.216 ± 0.0097.55 ± 0.6880.153 ± 0.00880.89 ± 9.544 77.944 ± 2.770
T5 T5Meteor0.110 ± 0.0050.332 ± 0.0030.214 ± 0.0070.124 ± 0.0070.235 ± 0.0048.669 ± 0.1640.173 ± 0.00282.007 ± 1.012
CommonGenT5 T5SPice0.014 ± 0.0060.242 ± 0.0010.037 ± 0.0110.018 ± 0.0070.156 ± 0.0074.685 ± 0.2830.168 ± 0.00856.998 ± 3.548
CiDer0.046 ± 0.0010.241 ± 0.0030.078 ± 0.0280.043 ± 0.0160.143 ± 0.0183.964 ± 0.7920.103 ± 0.01249.606 ± 7.971
SPider0.060 ± 0.0060.258 ± 0.0010.090 ± 0.0080.056 ± 0.0050.151 ± 0.0224.411 ± 0.8370.123 ± 0.02249.230 ± 10.468
SupervisedT50.215 ± 0.0010.438 ± 0.0010.444 ± 0.0010.329 ± 0.0010.321 ± 0.00116.385 ± 0.0460.299 ± 0.00194.476 ± 0.172
Supervised + PPORouge-10.232 ± 0.0020.453 ± 0.0020.454 ± 0.0060.338 ± 0.0060.320 ± 0.00216.233 ± 0.1590.288 ± 0.00496.412 ± 0.424
T5Rouge-Avg0.230 ± 0.0010.450 ± 0.0010.448 ± 0.0050.334 ± 0.0050.319 ± 0.00116.069 ± 0.1670.287 ± 0.00396.116 ± 0.679
T5 T5Meteor0.234 ± 0.0020.450 ± 0.0030.462 ± 0.0070.342 ± 0.0070.327 ± 0.00116.797 ± 0.1520.295 ± 0.00197.690 ± 0.371
T5SPice0.227 ± 0.0040.447 ± 0.0030.450 ± 0.0070.336 ± 0.0080.319 ± 0.00216.208 ± 0.2490.288 ± 0.00396.492 ± 0.29
T5CiDer0.224 ± 0.0030.446 ± 0.0030.427 ± 0.0120.309 ± 0.010.316 ± 0.00415.497 ± 0.4280.283 ± 0.00496.344 ± 0.547
T5SPider0.226 ± 0.0030.448 ± 0.0020.436 ± 0.0050.319 ± 0.0040.317 ± 0.00315.678 ± 0.1920.281 ± 0.00396.154 ± 0.426
T5Rouge-10.229 ±0.0020.450 ± 0.0010.454± 0.0050.338 ± 0.0040.320± 0.00316.206 ± 0.1750.289±0.00296.342 ± 0.572
Supervised + NLPOT5Rouge-Avg0.232 ± 0.0030.451 ± 0.0020.458 ± 0.010.342 ± 0.0090.321 ± 0.00316.351 ± 0.3350.290 ± 0.00595.998 ± 0.496
Meteor0.231 ± 0.0030.449 ± 0.0020.454 ± 0.0070.334 ± 0.0080.326 ± 0.00216.574 ± 0.2690.292 ± 0.00397.374 ± 0.457
T5 T5SPice0.223 ± 0.0020.442 ± 0.0010.435 ± 0.0110.321 ± 0.0100.315 ± 0.00415.747 ± 0.4010.283 ± 0.00596.25 ± 0.313
T5CiDer0.226 ± 0.0020.447 ± 0.0040.433 ± 0.0070.315 ± 0.0080.318 ± 0.00315.741 ± 0.1700.285 ± 0.00196.354 ± 0.971
SPider0.226 ± 0.0040.447 ± 0.0030.434 ± 0.0060.316 ± 0.0060.319 ± 0.00215.739 ± 0.3110.284 ± 0.00396.333 ± 0.644
T5
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The most important result is that RL fine-tuning on a supervised model yields", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 388, + 505, + 402 + ], + "spans": [ + { + "bbox": [ + 105, + 388, + 505, + 402 + ], + "score": 1.0, + "content": "better performance across most metrics especially Coverage which indicates the ratio of concepts", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 400, + 213, + 412 + ], + "spans": [ + { + "bbox": [ + 105, + 400, + 213, + 412 + ], + "score": 1.0, + "content": "covered in generated texts", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 12.5 + } + ], + "index": 10.75 + } + ], + "page_idx": 28, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2023", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 751, + 311, + 760 + ], + "lines": [ + { + "bbox": [ + 298, + 750, + 313, + 764 + ], + "spans": [ + { + "bbox": [ + 298, + 750, + 313, + 764 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 14, + "width": 15 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 108, + 82, + 257, + 94 + ], + "lines": [ + { + "bbox": [ + 105, + 81, + 259, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 81, + 259, + 95 + ], + "score": 1.0, + "content": "B.4.2 RESULTS AND DISCUSSION", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 106, + 101, + 505, + 179 + ], + "lines": [ + { + "bbox": [ + 105, + 101, + 505, + 114 + ], + "spans": [ + { + "bbox": [ + 105, + 101, + 505, + 114 + ], + "score": 1.0, + "content": "Tables 13, 12 presents our benchmarking results with 6 reward functions along with supervised", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 113, + 505, + 125 + ], + "spans": [ + { + "bbox": [ + 106, + 113, + 505, + 125 + ], + "score": 1.0, + "content": "baseline performances on dev and test sets respectively. Our main finding is that warm-started initial", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 124, + 506, + 136 + ], + "spans": [ + { + "bbox": [ + 106, + 124, + 506, + 136 + ], + "score": 1.0, + "content": "policies are crucial for learning to generate coherent sentences with common sense. Without warm-", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 136, + 504, + 147 + ], + "spans": [ + { + "bbox": [ + 106, + 136, + 504, + 147 + ], + "score": 1.0, + "content": "start, policies suffer from reward hacking despite application of repetition penalty and task-specific", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 144, + 505, + 159 + ], + "spans": [ + { + "bbox": [ + 105, + 144, + 505, + 159 + ], + "score": 1.0, + "content": "metrics such as CIDer etc. Further, we find that RL fine-tuned models obtain very high concept", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 157, + 505, + 169 + ], + "spans": [ + { + "bbox": [ + 106, + 157, + 505, + 169 + ], + "score": 1.0, + "content": "coverage which is also seen in Table B.4.5. 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TasksCIDErSPICECoverage
AlgLMReward functionRouge-2Rouge-LBleu (n=3)Bleu (n=4)Meteor
Zero-Shot PPOT50.0160.2640.0290.0060.2036.2000.11591.070
T5Rouge-10.085 ± 0.0080.354 ± 0.0040.161 ± 0.0110.087 ± 0.0090.235± 0.0028.673 ± 0.2340.157 ± 0.00188.544 ± 2.36
T5Rouge-Avg0.093 ± 0.0050.351 ± 0.0010.169 ± 0.0320.097 ± 0.0170.224 ± 0.0128.212 ± 1.3290.159 ± 0.01182.584 ± 2.569
T5Meteor0.091± 0.0080.308 ± 0.0070.166 ± 0.0160.088 ± 0.0130.220 ± 0.0067.251 ± 0.4530.161 ± 0.00779.718 ± 2.267
T5SPice0.065 ± 0.0030.302 ± 0.0020.115 ± 0.0630.067 ± 0.0410.193 ± 0.0146.571 ± 1.3120.175 ± 0.01169.340 ± 3.617
T5CiDer0.066 ± 0.0030.304 ± 0.0020.132 ± 0.0570.074 ± 0.0360.211 ± 0.0096.877 ± 1.2180.143 ± 0.01780.114 ± 4.852
T5SPider0.117 ± 0.0050.352 ± 0.0070.224 ± 0.0140.137 ± 0.0110.226 ± 0.019.162 ± 0.5390.186 ± 0.00673.374 ± 6.073
T5Rouge-10.087 ± 0.0020.339 ± 0.0090.127 ± 0.0480.069 ± 0.0350.213 ± 0.0026.962 ± 0.8830.145± 0.022
Rouge-Avg0.095 ± 0.0010.338 ± 0.0020.159 ± 0.020.093 ± 0.0130.216 ± 0.0097.55 ± 0.6880.153 ± 0.00880.89 ± 9.544 77.944 ± 2.770
T5 T5Meteor0.110 ± 0.0050.332 ± 0.0030.214 ± 0.0070.124 ± 0.0070.235 ± 0.0048.669 ± 0.1640.173 ± 0.00282.007 ± 1.012
CommonGenT5 T5SPice0.014 ± 0.0060.242 ± 0.0010.037 ± 0.0110.018 ± 0.0070.156 ± 0.0074.685 ± 0.2830.168 ± 0.00856.998 ± 3.548
CiDer0.046 ± 0.0010.241 ± 0.0030.078 ± 0.0280.043 ± 0.0160.143 ± 0.0183.964 ± 0.7920.103 ± 0.01249.606 ± 7.971
SPider0.060 ± 0.0060.258 ± 0.0010.090 ± 0.0080.056 ± 0.0050.151 ± 0.0224.411 ± 0.8370.123 ± 0.02249.230 ± 10.468
SupervisedT50.215 ± 0.0010.438 ± 0.0010.444 ± 0.0010.329 ± 0.0010.321 ± 0.00116.385 ± 0.0460.299 ± 0.00194.476 ± 0.172
Supervised + PPORouge-10.232 ± 0.0020.453 ± 0.0020.454 ± 0.0060.338 ± 0.0060.320 ± 0.00216.233 ± 0.1590.288 ± 0.00496.412 ± 0.424
T5Rouge-Avg0.230 ± 0.0010.450 ± 0.0010.448 ± 0.0050.334 ± 0.0050.319 ± 0.00116.069 ± 0.1670.287 ± 0.00396.116 ± 0.679
T5 T5Meteor0.234 ± 0.0020.450 ± 0.0030.462 ± 0.0070.342 ± 0.0070.327 ± 0.00116.797 ± 0.1520.295 ± 0.00197.690 ± 0.371
T5SPice0.227 ± 0.0040.447 ± 0.0030.450 ± 0.0070.336 ± 0.0080.319 ± 0.00216.208 ± 0.2490.288 ± 0.00396.492 ± 0.29
T5CiDer0.224 ± 0.0030.446 ± 0.0030.427 ± 0.0120.309 ± 0.010.316 ± 0.00415.497 ± 0.4280.283 ± 0.00496.344 ± 0.547
T5SPider0.226 ± 0.0030.448 ± 0.0020.436 ± 0.0050.319 ± 0.0040.317 ± 0.00315.678 ± 0.1920.281 ± 0.00396.154 ± 0.426
T5Rouge-10.229 ±0.0020.450 ± 0.0010.454± 0.0050.338 ± 0.0040.320± 0.00316.206 ± 0.1750.289±0.00296.342 ± 0.572
Supervised + NLPOT5Rouge-Avg0.232 ± 0.0030.451 ± 0.0020.458 ± 0.010.342 ± 0.0090.321 ± 0.00316.351 ± 0.3350.290 ± 0.00595.998 ± 0.496
Meteor0.231 ± 0.0030.449 ± 0.0020.454 ± 0.0070.334 ± 0.0080.326 ± 0.00216.574 ± 0.2690.292 ± 0.00397.374 ± 0.457
T5 T5SPice0.223 ± 0.0020.442 ± 0.0010.435 ± 0.0110.321 ± 0.0100.315 ± 0.00415.747 ± 0.4010.283 ± 0.00596.25 ± 0.313
T5CiDer0.226 ± 0.0020.447 ± 0.0040.433 ± 0.0070.315 ± 0.0080.318 ± 0.00315.741 ± 0.1700.285 ± 0.00196.354 ± 0.971
SPider0.226 ± 0.0040.447 ± 0.0030.434 ± 0.0060.316 ± 0.0060.319 ± 0.00215.739 ± 0.3110.284 ± 0.00396.333 ± 0.644
T5
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TasksAlgReward FunctionTop k LMRouge-1Rouge-2 Rouge-LRouge-LSumLexical and Semantic Metrics MeteorBLEUBertScoreCiderSpiceMSTTRDistinct1Distinct2 H1Diversity Metrics H2Unique1UniqueMean Output Length
0.415
Zero-Shot PPORouge-1T5 50 T50.537 ± 0.0040.016 0.093 ± 0.0120.2700.270 0.1790.0 0.380 ± 0.0060.380 ± 0.0060.235 ± 0.0050.016 ± 0.0020.854 0.896 ± 0.0010.6400.231 0.950 ±0.0150.318 ± 0.0160.430 0.526 ± 0.0200.090 0.128 ± 0.0050.335 0.518 ± 0.0365.998 7.957 6.679 ± 0.132 10.572 ± 0.234345 437.4 ± 42.0171964 2418.8 ± 167.9478.797 7.214 ± 0.374
Rouge-Avg50 T50.519 ± 0.01850.102 ± 0.007 0.377 ± 0.0130.376 ± 0.0140.225 ± 0.0240.020 ± 0.0020.897 ± 0.0050.921 ± 0.1020.328 ± 0.0090.536 ± 0.0690.141 ± 0.0220.510 ± 0.056 6.777 ± 0.53910.348 ± 0.134458.6 ± 19.7342244.4 ± 162.8556.887 ± 1.006
Meteor50 T50.411 ± 0.0090.090 ± 0.0080.304 ± 0.0060.304 ± 0.0060.210 ± 0.0050.029 ± 0.0040.875 ± 0.0070.638 ± 0.0480.259 ± 0.0170.547 ± 0.0120.147 ± 0.0030.529 ± 0.0147.62 ± 0.127 11.464 ± 0.1511039.4 ± 63.2765197.2 ± 280.00413.660 ± 0.324
SPice50 T50.439 ± 0.0350.079 ± 0.045 0.323 ± 0.0360.323 ± 0.0360.183 ± 0.0220.012 ± 0.0090.891 ± 0.0050.777 ± 0.1400.400 ± 0.0120.546 ± 0.0540.149 ± 0.019 0.545 ± 0.0726.721 ± 0.44110.492 ± 0.330409.2 ± 41.6051878.4 ± 167.4925.706 ± 0.678
CiDer50 T50.453 ± 0.0380.081±0.0370.326 ±0.0330.326 ±00330.203±00220.017 ±0.0090.85±0.0080.770±0.1340.291 ±0.0360.597±080.195 ± 0.040 0.639 ± 0.1067.732 ± 0.68211.131 ± 0.502777.0 ± 144.6763350.8 ± 503.4197.393 ± 0.572
NLPOSPider50 T50.512 ± 0.0080.141 ± 0.0070.388 ± 0.002 0.388 ± 0.0030.242 ± 0.007 0.032 ± 0.0030.902 ± 0.0011.045 ± 0.0340.380 ± 0.0060.482 ± 0.0150.133 ± 0.003 0.472 ± 0.0216.372 ± 0.22110.303 ± 0.228502.6 ± 33.4222281.4 ± 252.4717.489 ± 0.358
Rouge-1 Rouge-Avg50 T50.499 ± 0.012 0.47 ± 0.010.089±0.0030.328±0.0070.328±0.0070.198±0.0020.01±0.0010.872±0.0050.815±0.0090.305±0.0080.559±0.010.148 ± 0.003 0.555 ± 0.0127.059 ± 0.06710.657 ± 0.105457.9 ± 11.1082349.6 ± 60.3456.586 ± 0.094
Meteor50 50T5 0.389 ± 0.0130.096±0.0040.12±00060.32±0.0060.202±0.0080.025±0.0020.843±00130.86±0.0260.299±00070.2±0.019 0.1 ± 0.0040.691 ± 0.040.266± 0.016 0.503± 0.0030.146 ± 0.0110.513 ± 0.0126.781 ± 0.1510.424 ± 0.156484.18 ± 17.3032357.54 ± 152.1137.131 ± 0.487
CommonGenSPiceT50.329 ± 0.0150.293 ±0.0080.293 ± 0.0080.226 ± 0.0240.035 ± 0.0040.832 ± 0.0180.132 ± 0.0050.471 ± 0.008 0.568 ± 0.0267.146 ± 0.19210.727 ± 0.313648.05 ± 33.9633536.0 ± 444.63811.062 ± 1.301
CiDer50 T50.036 ± 0.0080.247 ±0.0130.247 ± 0.0130.137 ± 0.0090.006 ± 0.0020.817 ± 0.0240.515 ± 0.0330.323 ±0021 0.282 ± 0.0090.543 ± 0.0230.174 ± 0.004 0.179 ± 0.0057.176 ± 0.21210.551 ± 0.216479.45 ± 19.772065.8 ± 288.8435.785 ± 0.431
SPider50 50T5 0.515 ± 0.0060.143 ± 0.0080.387±0.0060.308 ± 0.0060.19 ± 0.001 0.019 ± 0.0010.865 ± 0.0150.726 ± 0.0180.842 ±0.019 0.717 ± 0.0260.297 ± 0.0190.525 ±0.0240.55 ± 0.020.576 ± 0.0147.286 ± 0.12510.812 ± 0.089661.46 ± 21.776 2726.32 ± 71.2537.13 ± 0.223
T5 0.393 ± 0.0080.086 ± 0.012 0.175 ± 0.0010.297 ± 0.0070.297 ± 0.0070.183 ± 0.0070.02 ± 0.0030.167 ± 0.009 0.537 ± 0.0256.986 ± 0.26210.451 ± 0.171530.14 ± 16.8052263.4 ± 166.2216.687 ± 0.372
Supervised Supervised + PPOT50.503 ± 0.0010.411 ± 0.0010.411 ± 0.0010.309 ± 0.0010.069 ± 0.001 0.929 ± 0.0001.381 ± 0.0110.443 ± 0.0010.509 ± 0.0010.101 ± 0.0010.339 ± 0.001 6.531 ± 0.00610.079 ± 0.016503.600 ± 6.5302158.8 ± 24.51410.934 ± 0.020
Rouge-1 Rouge-Avg50 T50.537 ± 0.004 0.536 ± 0.0010.198 ± 0.0050.433 ± 0.002 0.433 ± 0.0020.314 ± 0.0030.070 ± 0.0020.930 ± 0.001 1.426 ± 0.0180.449 ± 0.0010.527 ± 0.0070.112 ± 0.001 0.114 ± 0.0020.393 ± 0.0046.680 ± 0.044 10.289 ± 0.040498.2 ± 8.9312317.0 ± 22.6099.667 ± 0.105
50T50.198 ± 0.002 0.433 ± 0.002 0.433 ± 0.002 0.311 ± 0.002 0.070 ± 0.002 0.929 ± 0.0011.421 ± 0.0280.446 ± 0.0040.526 ± 0.0040.395 ± 0.0056.682 ± 0.029710.274 ± 0.042506.4 ± 6.829 2326.4 ± 41.7789.614 ± 0.102
Meteor50T5 0.540 ± 0.0050.204 ± 0.0050.436 ± 0.0040.436 ± 0.0040.329 ± 0.0030.076± 0.0030.930 ± 0.0011.474 ± 0.0220.447 ± 0.0040.514 ± 0.004 0.105 ± 0.0020.378 ± 0.0086.631 ± 0.05310.270 ± 0.064507.0 ± 17.146 2424.6 ± 72.55010.551 ± 0.271
SPice50T5 0.532 ± 0.0060.194 ± 0.0070.430 ± 0.0050.430 ± 0.0050.311 ± 0.0040.068 ± 0.0030.929 ± 0.0011.415 ± 0.0290.458 ±0.00110.532±0.0080.113±0.00830.392 ±0.0096.736 ± 0.05810.338 ± 0.057507.4 ± 14.319 2313.8 ± 27.6949.742 ± 0.208
CiDer50T5 0.530 ± 0.0040.191 ± 0.003 0.197 ± 0.0020.427 ± 0.0040.427 ± 0.004 0.309 ± 0.0080.063 ± 0.0020.928 ± 0.001 0.928 ± 0.0011.337 ± 0.0400.444 ± 0.0020.518 ± 0.009 0.110 ± 0.0030.382 ± 0.0066.614 ± 0.082 6.673 ± 0.06610.166 ± 0.053 10.247 ± 0.066490.4 ± 9.4572295.4 ± 51.5549.838 ± 0.265
Supervised + NLPOSpiDer Rouge-150 T50.536 ± 0.002 0.545 ± 0.0020.432 ± 0.0010.430 ±0.0020.430±0.0020.313±0.002 0.31 ± 0.0020.064 ±0.0021.374 ±0.0180.445 ± 0.0030.524 ± 0.0070.112 ± 0.001 0.114 ± 0.0020.394 ± 0.004 0.399 ± 0.005504.8 ± 7.4402361.8 ± 20.856 2311.46 ± 3.4519.761 ± 0.121 9.463 ± 0.111
50T50.197 ± 0.0020.432 ± 0.0010.068 ± 0.0010.929 ± 0.01.41 ± 0.0120.449 ± 0.0010.529 ± 0.0026.705 ± 0.01810.301 ± 0.03498.86 ± 8.594
Rouge-Avg Meteor50 50 SPice 50 T5T5 0.541 ± 0.003 T5 0.537 ± 0.0030.2 ± 0.003 0.201 ± 0.0040.435 ± 0.002 0.435 ± 0.0020.313 ± 0.002 0.431 ± 0.0020.431 ± 0.0020.326 ± 0.0020.07 ± 0.002 0.074 ± 0.0030.93 ± 0.001 0.93 ± 0.01.424 ± 0.0230.447 ± 0.0031.464 ± 0.0250.448 ± 0.0020.516 ± 0.0060.53 ± 0.006 0.113 ± 0.002 0.106 ± 0.0020.396 ± 0.008 0.377 ± 0.0086.708 ± 0.05 6.634 ± 0.04410.318 ± 0.074 493.64 ± 10.068 10.26 ± 0.077 506.04 ± 3.502
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TasksAlgReward FunctionTop k LMRouge-1Rouge-2 Rouge-LRouge-LSumLexical and Semantic Metrics MeteorBLEUBertScoreCiderSpiceMSTTRDistinct1Distinct2 H1Diversity Metrics H2Unique1UniqueMean Output Length
0.415
Zero-Shot PPORouge-1T5 50 T50.537 ± 0.0040.016 0.093 ± 0.0120.2700.270 0.1790.0 0.380 ± 0.0060.380 ± 0.0060.235 ± 0.0050.016 ± 0.0020.854 0.896 ± 0.0010.6400.231 0.950 ±0.0150.318 ± 0.0160.430 0.526 ± 0.0200.090 0.128 ± 0.0050.335 0.518 ± 0.0365.998 7.957 6.679 ± 0.132 10.572 ± 0.234345 437.4 ± 42.0171964 2418.8 ± 167.9478.797 7.214 ± 0.374
Rouge-Avg50 T50.519 ± 0.01850.102 ± 0.007 0.377 ± 0.0130.376 ± 0.0140.225 ± 0.0240.020 ± 0.0020.897 ± 0.0050.921 ± 0.1020.328 ± 0.0090.536 ± 0.0690.141 ± 0.0220.510 ± 0.056 6.777 ± 0.53910.348 ± 0.134458.6 ± 19.7342244.4 ± 162.8556.887 ± 1.006
Meteor50 T50.411 ± 0.0090.090 ± 0.0080.304 ± 0.0060.304 ± 0.0060.210 ± 0.0050.029 ± 0.0040.875 ± 0.0070.638 ± 0.0480.259 ± 0.0170.547 ± 0.0120.147 ± 0.0030.529 ± 0.0147.62 ± 0.127 11.464 ± 0.1511039.4 ± 63.2765197.2 ± 280.00413.660 ± 0.324
SPice50 T50.439 ± 0.0350.079 ± 0.045 0.323 ± 0.0360.323 ± 0.0360.183 ± 0.0220.012 ± 0.0090.891 ± 0.0050.777 ± 0.1400.400 ± 0.0120.546 ± 0.0540.149 ± 0.019 0.545 ± 0.0726.721 ± 0.44110.492 ± 0.330409.2 ± 41.6051878.4 ± 167.4925.706 ± 0.678
CiDer50 T50.453 ± 0.0380.081±0.0370.326 ±0.0330.326 ±00330.203±00220.017 ±0.0090.85±0.0080.770±0.1340.291 ±0.0360.597±080.195 ± 0.040 0.639 ± 0.1067.732 ± 0.68211.131 ± 0.502777.0 ± 144.6763350.8 ± 503.4197.393 ± 0.572
NLPOSPider50 T50.512 ± 0.0080.141 ± 0.0070.388 ± 0.002 0.388 ± 0.0030.242 ± 0.007 0.032 ± 0.0030.902 ± 0.0011.045 ± 0.0340.380 ± 0.0060.482 ± 0.0150.133 ± 0.003 0.472 ± 0.0216.372 ± 0.22110.303 ± 0.228502.6 ± 33.4222281.4 ± 252.4717.489 ± 0.358
Rouge-1 Rouge-Avg50 T50.499 ± 0.012 0.47 ± 0.010.089±0.0030.328±0.0070.328±0.0070.198±0.0020.01±0.0010.872±0.0050.815±0.0090.305±0.0080.559±0.010.148 ± 0.003 0.555 ± 0.0127.059 ± 0.06710.657 ± 0.105457.9 ± 11.1082349.6 ± 60.3456.586 ± 0.094
Meteor50 50T5 0.389 ± 0.0130.096±0.0040.12±00060.32±0.0060.202±0.0080.025±0.0020.843±00130.86±0.0260.299±00070.2±0.019 0.1 ± 0.0040.691 ± 0.040.266± 0.016 0.503± 0.0030.146 ± 0.0110.513 ± 0.0126.781 ± 0.1510.424 ± 0.156484.18 ± 17.3032357.54 ± 152.1137.131 ± 0.487
CommonGenSPiceT50.329 ± 0.0150.293 ±0.0080.293 ± 0.0080.226 ± 0.0240.035 ± 0.0040.832 ± 0.0180.132 ± 0.0050.471 ± 0.008 0.568 ± 0.0267.146 ± 0.19210.727 ± 0.313648.05 ± 33.9633536.0 ± 444.63811.062 ± 1.301
CiDer50 T50.036 ± 0.0080.247 ±0.0130.247 ± 0.0130.137 ± 0.0090.006 ± 0.0020.817 ± 0.0240.515 ± 0.0330.323 ±0021 0.282 ± 0.0090.543 ± 0.0230.174 ± 0.004 0.179 ± 0.0057.176 ± 0.21210.551 ± 0.216479.45 ± 19.772065.8 ± 288.8435.785 ± 0.431
SPider50 50T5 0.515 ± 0.0060.143 ± 0.0080.387±0.0060.308 ± 0.0060.19 ± 0.001 0.019 ± 0.0010.865 ± 0.0150.726 ± 0.0180.842 ±0.019 0.717 ± 0.0260.297 ± 0.0190.525 ±0.0240.55 ± 0.020.576 ± 0.0147.286 ± 0.12510.812 ± 0.089661.46 ± 21.776 2726.32 ± 71.2537.13 ± 0.223
T5 0.393 ± 0.0080.086 ± 0.012 0.175 ± 0.0010.297 ± 0.0070.297 ± 0.0070.183 ± 0.0070.02 ± 0.0030.167 ± 0.009 0.537 ± 0.0256.986 ± 0.26210.451 ± 0.171530.14 ± 16.8052263.4 ± 166.2216.687 ± 0.372
Supervised Supervised + PPOT50.503 ± 0.0010.411 ± 0.0010.411 ± 0.0010.309 ± 0.0010.069 ± 0.001 0.929 ± 0.0001.381 ± 0.0110.443 ± 0.0010.509 ± 0.0010.101 ± 0.0010.339 ± 0.001 6.531 ± 0.00610.079 ± 0.016503.600 ± 6.5302158.8 ± 24.51410.934 ± 0.020
Rouge-1 Rouge-Avg50 T50.537 ± 0.004 0.536 ± 0.0010.198 ± 0.0050.433 ± 0.002 0.433 ± 0.0020.314 ± 0.0030.070 ± 0.0020.930 ± 0.001 1.426 ± 0.0180.449 ± 0.0010.527 ± 0.0070.112 ± 0.001 0.114 ± 0.0020.393 ± 0.0046.680 ± 0.044 10.289 ± 0.040498.2 ± 8.9312317.0 ± 22.6099.667 ± 0.105
50T50.198 ± 0.002 0.433 ± 0.002 0.433 ± 0.002 0.311 ± 0.002 0.070 ± 0.002 0.929 ± 0.0011.421 ± 0.0280.446 ± 0.0040.526 ± 0.0040.395 ± 0.0056.682 ± 0.029710.274 ± 0.042506.4 ± 6.829 2326.4 ± 41.7789.614 ± 0.102
Meteor50T5 0.540 ± 0.0050.204 ± 0.0050.436 ± 0.0040.436 ± 0.0040.329 ± 0.0030.076± 0.0030.930 ± 0.0011.474 ± 0.0220.447 ± 0.0040.514 ± 0.004 0.105 ± 0.0020.378 ± 0.0086.631 ± 0.05310.270 ± 0.064507.0 ± 17.146 2424.6 ± 72.55010.551 ± 0.271
SPice50T5 0.532 ± 0.0060.194 ± 0.0070.430 ± 0.0050.430 ± 0.0050.311 ± 0.0040.068 ± 0.0030.929 ± 0.0011.415 ± 0.0290.458 ±0.00110.532±0.0080.113±0.00830.392 ±0.0096.736 ± 0.05810.338 ± 0.057507.4 ± 14.319 2313.8 ± 27.6949.742 ± 0.208
CiDer50T5 0.530 ± 0.0040.191 ± 0.003 0.197 ± 0.0020.427 ± 0.0040.427 ± 0.004 0.309 ± 0.0080.063 ± 0.0020.928 ± 0.001 0.928 ± 0.0011.337 ± 0.0400.444 ± 0.0020.518 ± 0.009 0.110 ± 0.0030.382 ± 0.0066.614 ± 0.082 6.673 ± 0.06610.166 ± 0.053 10.247 ± 0.066490.4 ± 9.4572295.4 ± 51.5549.838 ± 0.265
Supervised + NLPOSpiDer Rouge-150 T50.536 ± 0.002 0.545 ± 0.0020.432 ± 0.0010.430 ±0.0020.430±0.0020.313±0.002 0.31 ± 0.0020.064 ±0.0021.374 ±0.0180.445 ± 0.0030.524 ± 0.0070.112 ± 0.001 0.114 ± 0.0020.394 ± 0.004 0.399 ± 0.005504.8 ± 7.4402361.8 ± 20.856 2311.46 ± 3.4519.761 ± 0.121 9.463 ± 0.111
50T50.197 ± 0.0020.432 ± 0.0010.068 ± 0.0010.929 ± 0.01.41 ± 0.0120.449 ± 0.0010.529 ± 0.0026.705 ± 0.01810.301 ± 0.03498.86 ± 8.594
Rouge-Avg Meteor50 50 SPice 50 T5T5 0.541 ± 0.003 T5 0.537 ± 0.0030.2 ± 0.003 0.201 ± 0.0040.435 ± 0.002 0.435 ± 0.0020.313 ± 0.002 0.431 ± 0.0020.431 ± 0.0020.326 ± 0.0020.07 ± 0.002 0.074 ± 0.0030.93 ± 0.001 0.93 ± 0.01.424 ± 0.0230.447 ± 0.0031.464 ± 0.0250.448 ± 0.0020.516 ± 0.0060.53 ± 0.006 0.113 ± 0.002 0.106 ± 0.0020.396 ± 0.008 0.377 ± 0.0086.708 ± 0.05 6.634 ± 0.04410.318 ± 0.074 493.64 ± 10.068 10.26 ± 0.077 506.04 ± 3.502
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AlgorithmUnique NCoherenceCommonsense
ValueAlphaSkewValueAlphaSkew
PPO+Supervised254.140.0734.1374.030.1374.023
NLPO+Supervised4.250.0364.2534.160.0024.163
Zero Shot2624242.150.3912.1542.290.3422.291
PPO2.840.162.8493.030.0813.027
Supervised234.390.1594.3874.210.2254.209
NLPO2420.3352.0032.130.2652.124
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Group 1Group 2CoherenceCommonsense
Diff (G2-G1)p-valuesDiff (G2-G1)p-values
NLPOPPO0.8470.0010.8970.001
NLPOSupervised2.3970.0012.0830.001
NLPONLPO+Supervised2.2570.0012.0330.001
NLPOPPO+Supervised2.1430.0011.8970.001
NLPOZero Shot0.1530.5150.1570.624
PPOSupervised1.5500.0011.1870.001
PPONLPO+Supervised1.4100.0011.1370.001
PPOPPO+Supervised1.2970.0011.0000.001
PPOZero Shot-0.6930.001-0.7400.001
SupervisedNLPO+Supervised-0.1400.601-0.0500.900
SupervisedPPO+Supervised-0.2530.050-0.1870.045
SupervisedZero Shot-2.2430.001-1.9270.001
NLPO+SupervisedPPO+Supervised-0.1130.008-0.1370.007
NLPO+SupervisedZero Shot-2.1030.001-1.8770.001
PPO+SupervisedZero Shot-1.9900.001-1.7400.001
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AlgorithmUnique NCoherenceCommonsense
ValueAlphaSkewValueAlphaSkew
PPO+Supervised254.140.0734.1374.030.1374.023
NLPO+Supervised4.250.0364.2534.160.0024.163
Zero Shot2624242.150.3912.1542.290.3422.291
PPO2.840.162.8493.030.0813.027
Supervised234.390.1594.3874.210.2254.209
NLPO2420.3352.0032.130.2652.124
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Group 1Group 2CoherenceCommonsense
Diff (G2-G1)p-valuesDiff (G2-G1)p-values
NLPOPPO0.8470.0010.8970.001
NLPOSupervised2.3970.0012.0830.001
NLPONLPO+Supervised2.2570.0012.0330.001
NLPOPPO+Supervised2.1430.0011.8970.001
NLPOZero Shot0.1530.5150.1570.624
PPOSupervised1.5500.0011.1870.001
PPONLPO+Supervised1.4100.0011.1370.001
PPOPPO+Supervised1.2970.0011.0000.001
PPOZero Shot-0.6930.001-0.7400.001
SupervisedNLPO+Supervised-0.1400.601-0.0500.900
SupervisedPPO+Supervised-0.2530.050-0.1870.045
SupervisedZero Shot-2.2430.001-1.9270.001
NLPO+SupervisedPPO+Supervised-0.1130.008-0.1370.007
NLPO+SupervisedZero Shot-2.1030.001-1.8770.001
PPO+SupervisedZero Shot-1.9900.001-1.7400.001
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Usually the generation", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 131, + 136, + 276, + 142 + ], + "spans": [ + { + "bbox": [ + 131, + 136, + 276, + 142 + ], + "score": 0.998, + "content": "will be only a single sentence. 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This sentence, even though it doesn't make", + "type": "text" + } + ], + "index": 28, + "is_list_start_line": true + }, + { + "bbox": [ + 322, + 227, + 414, + 234 + ], + "spans": [ + { + "bbox": [ + 322, + 227, + 414, + 234 + ], + "score": 0.985, + "content": "sense,is grammatically correct and easy to read.", + "type": "text" + } + ], + "index": 29, + "is_list_start_line": true, + "is_list_end_line": true + }, + { + "bbox": [ + 320, + 233, + 470, + 239 + ], + "spans": [ + { + "bbox": [ + 320, + 233, + 470, + 239 + ], + "score": 0.977, + "content": "· Commonsense: 2/5 Why? 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We then", + "type": "text" + } + ], + "index": 86 + }, + { + "bbox": [ + 105, + 721, + 505, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 721, + 505, + 733 + ], + "score": 1.0, + "content": "present the prompt and the two completion candidates to 3 unique crowdworkers and ask them to", + "type": "text" + } + ], + "index": 87 + } + ], + "index": 84, + "bbox_fs": [ + 105, + 654, + 506, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 181, + 92, + 268, + 100 + ], + "lines": [ + { + "bbox": [ + 180, + 91, + 269, + 101 + ], + "spans": [ + { + "bbox": [ + 180, + 91, + 269, + 101 + ], + "score": 0.996, + "content": "Instructions (click to expand)", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 175, + 117, + 444, + 155 + ], + "lines": [ + { + "bbox": [ + 175, + 117, + 329, + 127 + ], + "spans": [ + { + "bbox": [ + 175, + 117, + 329, + 127 + ], + "score": 0.993, + "content": "Thanks for your participation and work on this HIT!", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 174, + 126, + 444, + 136 + ], + "spans": [ + { + "bbox": [ + 174, + 126, + 444, + 136 + ], + "score": 0.98, + "content": " In this task you willbe presented with two sentences,each containing similar words.Your", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 174, + 136, + 444, + 147 + ], + "spans": [ + { + "bbox": [ + 174, + 136, + 444, + 147 + ], + "score": 0.992, + "content": " job is to pick the sentence that you prefer.While the judgment is ultimately subjective,", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 175, + 146, + 268, + 156 + ], + "spans": [ + { + "bbox": [ + 175, + 146, + 268, + 156 + ], + "score": 0.985, + "content": "consider the following factors:", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 2.5 + }, + { + "type": "text", + "bbox": [ + 183, + 162, + 421, + 191 + ], + "lines": [ + { + "bbox": [ + 184, + 162, + 422, + 171 + ], + "spans": [ + { + "bbox": [ + 184, + 162, + 422, + 171 + ], + "score": 0.987, + "content": "· Most important: Which sentence makes the most sense?Which describes a", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 191, + 172, + 393, + 181 + ], + "spans": [ + { + "bbox": [ + 191, + 172, + 393, + 181 + ], + "score": 0.989, + "content": "plausible, realistic, and commonsensical scenario more effectively?", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 184, + 181, + 387, + 191 + ], + "spans": [ + { + "bbox": [ + 184, + 181, + 387, + 191 + ], + "score": 0.978, + "content": "· Which generation is more grammatical, easy-to-read, and fluent?", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 6 + }, + { + "type": "text", + "bbox": [ + 176, + 198, + 439, + 235 + ], + "lines": [ + { + "bbox": [ + 175, + 198, + 430, + 207 + ], + "spans": [ + { + "bbox": [ + 175, + 198, + 430, + 207 + ], + "score": 0.975, + "content": "In general, be forgiving of slight grammatical errors. If one conceptually makes much", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 175, + 207, + 423, + 217 + ], + "spans": [ + { + "bbox": [ + 175, + 207, + 423, + 217 + ], + "score": 0.98, + "content": "more sense than the other, you should prefer it even if there are slight issues with", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 175, + 216, + 439, + 227 + ], + "spans": [ + { + "bbox": [ + 175, + 216, + 439, + 227 + ], + "score": 0.979, + "content": "readability. However,if there are severe readability issues that effect comprehensibility,", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 175, + 226, + 281, + 235 + ], + "spans": [ + { + "bbox": [ + 175, + 226, + 281, + 235 + ], + "score": 0.998, + "content": "feel free to select the other option.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 9.5 + }, + { + "type": "text", + "bbox": [ + 176, + 236, + 334, + 245 + ], + "lines": [ + { + "bbox": [ + 175, + 235, + 335, + 246 + ], + "spans": [ + { + "bbox": [ + 175, + 235, + 335, + 246 + ], + "score": 0.968, + "content": "Thanks again for your efforts,we appreciate your work!", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 12 + }, + { + "type": "text", + "bbox": [ + 167, + 286, + 436, + 305 + ], + "lines": [ + { + "bbox": [ + 167, + 286, + 433, + 296 + ], + "spans": [ + { + "bbox": [ + 167, + 286, + 433, + 296 + ], + "score": 0.987, + "content": "Please take a moment to read both choices.Select the more commonsensical, complete,", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 166, + 295, + 437, + 306 + ], + "spans": [ + { + "bbox": [ + 166, + 295, + 437, + 306 + ], + "score": 0.981, + "content": "and grammatical option.If they are both bad, still do your best to pick the one you prefer.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 13.5 + }, + { + "type": "image", + "bbox": [ + 168, + 318, + 441, + 373 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 168, + 318, + 441, + 373 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 168, + 318, + 441, + 373 + ], + "spans": [ + { + "bbox": [ + 168, + 318, + 441, + 373 + ], + "score": 0.941, + "type": "image", + "image_path": "7f2a8a298f263da5f6a0a8833823ee3de319ba6c62964e711cabe4cb928836cf.jpg" + } + ] + } + ], + "index": 16, + "virtual_lines": [ + { + "bbox": [ + 168, + 318, + 441, + 336.3333333333333 + ], + "spans": [], + "index": 15 + }, + { + "bbox": [ + 168, + 336.3333333333333, + 441, + 354.66666666666663 + ], + "spans": [], + "index": 16 + }, + { + "bbox": [ + 168, + 354.66666666666663, + 441, + 372.99999999999994 + ], + "spans": [], + "index": 17 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 163, + 384, + 445, + 396 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 163, + 383, + 447, + 397 + ], + "spans": [ + { + "bbox": [ + 163, + 383, + 447, + 397 + ], + "score": 1.0, + "content": "Figure 7: Instructions and interface for the pairwise Commongen HIT.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 18 + } + ], + "index": 17.0 + }, + { + "type": "text", + "bbox": [ + 106, + 416, + 506, + 604 + ], + "lines": [ + { + "bbox": [ + 105, + 417, + 506, + 430 + ], + "spans": [ + { + "bbox": [ + 105, + 417, + 506, + 430 + ], + "score": 1.0, + "content": "select which one they prefer with respect to commonsense/fluency; We gathered 3 annotations on", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 428, + 505, + 440 + ], + "spans": [ + { + "bbox": [ + 105, + 428, + 199, + 440 + ], + "score": 1.0, + "content": "417 pairs (Krippendorf", + "type": "text" + }, + { + "bbox": [ + 199, + 429, + 234, + 439 + ], + "score": 0.88, + "content": "\\alpha = . 2 8", + "type": "inline_equation" + }, + { + "bbox": [ + 234, + 428, + 505, + 440 + ], + "score": 1.0, + "content": "), and split into 60/20/20 train/val/test split. We then trained a reward", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 104, + 438, + 506, + 452 + ], + "spans": [ + { + "bbox": [ + 104, + 438, + 506, + 452 + ], + "score": 1.0, + "content": "model, T5-11B Raffel et al. (2020), on the balanced binary classification task of predicting which", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 450, + 506, + 462 + ], + "spans": [ + { + "bbox": [ + 105, + 450, + 506, + 462 + ], + "score": 1.0, + "content": "of the pair was preferred by a majority of 3 annotators, conditioned on the prompt and completion.", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 460, + 506, + 474 + ], + "spans": [ + { + "bbox": [ + 105, + 460, + 506, + 474 + ], + "score": 1.0, + "content": "The resulting model achieved 69.5 test ROC AUC suggesting it indeed captures average human", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 471, + 507, + 484 + ], + "spans": [ + { + "bbox": [ + 105, + 471, + 414, + 484 + ], + "score": 1.0, + "content": "preferences. The model is then used as a reward function. We train Supervised", + "type": "text" + }, + { + "bbox": [ + 414, + 472, + 433, + 482 + ], + "score": 0.53, + "content": "+ \\mathrm { R L }", + "type": "inline_equation" + }, + { + "bbox": [ + 433, + 471, + 507, + 484 + ], + "score": 1.0, + "content": "with a METEOR-", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 483, + 506, + 494 + ], + "spans": [ + { + "bbox": [ + 106, + 483, + 506, + 494 + ], + "score": 1.0, + "content": "only reward as a baseline, and compare it to a reward function that uses the fine-tuned T5-11B model.", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 493, + 505, + 507 + ], + "spans": [ + { + "bbox": [ + 105, + 493, + 365, + 507 + ], + "score": 1.0, + "content": "We design the reward function based on the preference model as", + "type": "text" + }, + { + "bbox": [ + 365, + 494, + 505, + 506 + ], + "score": 0.9, + "content": "r = m e t e o r + p r e f / ( 1 + | m i s s | )", + "type": "inline_equation" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 505, + 506, + 517 + ], + "spans": [ + { + "bbox": [ + 106, + 505, + 506, + 517 + ], + "score": 1.0, + "content": "where miss is a set of concepts not covered in the generated text, in an attempt to mimic the data", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 516, + 505, + 528 + ], + "spans": [ + { + "bbox": [ + 106, + 516, + 505, + 528 + ], + "score": 1.0, + "content": "collection process that humans are instructed to follow. 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If one conceptually makes much", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 175, + 207, + 423, + 217 + ], + "spans": [ + { + "bbox": [ + 175, + 207, + 423, + 217 + ], + "score": 0.98, + "content": "more sense than the other, you should prefer it even if there are slight issues with", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 175, + 216, + 439, + 227 + ], + "spans": [ + { + "bbox": [ + 175, + 216, + 439, + 227 + ], + "score": 0.979, + "content": "readability. However,if there are severe readability issues that effect comprehensibility,", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 175, + 226, + 281, + 235 + ], + "spans": [ + { + "bbox": [ + 175, + 226, + 281, + 235 + ], + "score": 0.998, + "content": "feel free to select the other option.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 9.5, + "bbox_fs": [ + 175, + 198, + 439, + 235 + ] + }, + { + "type": "text", + "bbox": [ + 176, + 236, + 334, + 245 + ], + "lines": [ + { + "bbox": [ + 175, + 235, + 335, + 246 + ], + "spans": [ + { + "bbox": [ + 175, + 235, + 335, + 246 + ], + "score": 0.968, + "content": "Thanks again for your efforts,we appreciate your work!", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 12, + "bbox_fs": [ + 175, + 235, + 335, + 246 + ] + }, + { + "type": "text", + "bbox": [ + 167, + 286, + 436, + 305 + ], + "lines": [ + { + "bbox": [ + 167, + 286, + 433, + 296 + ], + "spans": [ + { + "bbox": [ + 167, + 286, + 433, + 296 + ], + "score": 0.987, + "content": "Please take a moment to read both choices.Select the more commonsensical, complete,", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 166, + 295, + 437, + 306 + ], + "spans": [ + { + "bbox": [ + 166, + 295, + 437, + 306 + ], + "score": 0.981, + "content": "and grammatical option.If they are both bad, still do your best to pick the one you prefer.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 13.5, + "bbox_fs": [ + 166, + 286, + 437, + 306 + ] + }, + { + "type": "image", + "bbox": [ + 168, + 318, + 441, + 373 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 168, + 318, + 441, + 373 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 168, + 318, + 441, + 373 + ], + "spans": [ + { + "bbox": [ + 168, + 318, + 441, + 373 + ], + "score": 0.941, + "type": "image", + "image_path": "7f2a8a298f263da5f6a0a8833823ee3de319ba6c62964e711cabe4cb928836cf.jpg" + } + ] + } + ], + "index": 16, + "virtual_lines": [ + { + "bbox": [ + 168, + 318, + 441, + 336.3333333333333 + ], + "spans": [], + "index": 15 + }, + { + "bbox": [ + 168, + 336.3333333333333, + 441, + 354.66666666666663 + ], + "spans": [], + "index": 16 + }, + { + "bbox": [ + 168, + 354.66666666666663, + 441, + 372.99999999999994 + ], + "spans": [], + "index": 17 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 163, + 384, + 445, + 396 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 163, + 383, + 447, + 397 + ], + "spans": [ + { + "bbox": [ + 163, + 383, + 447, + 397 + ], + "score": 1.0, + "content": "Figure 7: Instructions and interface for the pairwise Commongen HIT.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 18 + } + ], + "index": 17.0 + }, + { + "type": "text", + "bbox": [ + 106, + 416, + 506, + 604 + ], + "lines": [ + { + "bbox": [ + 105, + 417, + 506, + 430 + ], + "spans": [ + { + "bbox": [ + 105, + 417, + 506, + 430 + ], + "score": 1.0, + "content": "select which one they prefer with respect to commonsense/fluency; We gathered 3 annotations on", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 428, + 505, + 440 + ], + "spans": [ + { + "bbox": [ + 105, + 428, + 199, + 440 + ], + "score": 1.0, + "content": "417 pairs (Krippendorf", + "type": "text" + }, + { + "bbox": [ + 199, + 429, + 234, + 439 + ], + "score": 0.88, + "content": "\\alpha = . 2 8", + "type": "inline_equation" + }, + { + "bbox": [ + 234, + 428, + 505, + 440 + ], + "score": 1.0, + "content": "), and split into 60/20/20 train/val/test split. We then trained a reward", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 104, + 438, + 506, + 452 + ], + "spans": [ + { + "bbox": [ + 104, + 438, + 506, + 452 + ], + "score": 1.0, + "content": "model, T5-11B Raffel et al. (2020), on the balanced binary classification task of predicting which", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 450, + 506, + 462 + ], + "spans": [ + { + "bbox": [ + 105, + 450, + 506, + 462 + ], + "score": 1.0, + "content": "of the pair was preferred by a majority of 3 annotators, conditioned on the prompt and completion.", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 460, + 506, + 474 + ], + "spans": [ + { + "bbox": [ + 105, + 460, + 506, + 474 + ], + "score": 1.0, + "content": "The resulting model achieved 69.5 test ROC AUC suggesting it indeed captures average human", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 471, + 507, + 484 + ], + "spans": [ + { + "bbox": [ + 105, + 471, + 414, + 484 + ], + "score": 1.0, + "content": "preferences. The model is then used as a reward function. We train Supervised", + "type": "text" + }, + { + "bbox": [ + 414, + 472, + 433, + 482 + ], + "score": 0.53, + "content": "+ \\mathrm { R L }", + "type": "inline_equation" + }, + { + "bbox": [ + 433, + 471, + 507, + 484 + ], + "score": 1.0, + "content": "with a METEOR-", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 483, + 506, + 494 + ], + "spans": [ + { + "bbox": [ + 106, + 483, + 506, + 494 + ], + "score": 1.0, + "content": "only reward as a baseline, and compare it to a reward function that uses the fine-tuned T5-11B model.", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 493, + 505, + 507 + ], + "spans": [ + { + "bbox": [ + 105, + 493, + 365, + 507 + ], + "score": 1.0, + "content": "We design the reward function based on the preference model as", + "type": "text" + }, + { + "bbox": [ + 365, + 494, + 505, + 506 + ], + "score": 0.9, + "content": "r = m e t e o r + p r e f / ( 1 + | m i s s | )", + "type": "inline_equation" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 505, + 506, + 517 + ], + "spans": [ + { + "bbox": [ + 106, + 505, + 506, + 517 + ], + "score": 1.0, + "content": "where miss is a set of concepts not covered in the generated text, in an attempt to mimic the data", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 516, + 505, + 528 + ], + "spans": [ + { + "bbox": [ + 106, + 516, + 505, + 528 + ], + "score": 1.0, + "content": "collection process that humans are instructed to follow. This reward function accounts for both", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 527, + 505, + 539 + ], + "spans": [ + { + "bbox": [ + 106, + 527, + 505, + 539 + ], + "score": 1.0, + "content": "the task of using all concepts and also human’s preferences for how a sentence should look within", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 537, + 505, + 550 + ], + "spans": [ + { + "bbox": [ + 106, + 537, + 505, + 550 + ], + "score": 1.0, + "content": "the constraints stipulated by the task. Finally, we rerun the same pairwise preference collection", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 549, + 505, + 561 + ], + "spans": [ + { + "bbox": [ + 106, + 549, + 505, + 561 + ], + "score": 1.0, + "content": "procedure—this time sampling from Commongen test—with human participants to compare the", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 559, + 506, + 573 + ], + "spans": [ + { + "bbox": [ + 105, + 559, + 506, + 573 + ], + "score": 1.0, + "content": "generations from a preference optimized RL policy to the previously best Supervised+NLPO policy.", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 570, + 505, + 583 + ], + "spans": [ + { + "bbox": [ + 106, + 570, + 505, + 583 + ], + "score": 1.0, + "content": "Comparing the METEOR-only to the preference model head-to-head, the generations produced by", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 581, + 506, + 594 + ], + "spans": [ + { + "bbox": [ + 105, + 581, + 506, + 594 + ], + "score": 1.0, + "content": "the human feedback model are preferred in 682 cases, compared to the METEOR-only model which", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 592, + 384, + 605 + ], + "spans": [ + { + "bbox": [ + 105, + 592, + 209, + 605 + ], + "score": 1.0, + "content": "is preferred in 587 cases (", + "type": "text" + }, + { + "bbox": [ + 209, + 593, + 246, + 604 + ], + "score": 0.88, + "content": "p < 0 . 0 1", + "type": "inline_equation" + }, + { + "bbox": [ + 246, + 592, + 384, + 605 + ], + "score": 1.0, + "content": "the models are equally preferred).", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 27, + "bbox_fs": [ + 104, + 417, + 507, + 605 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 616, + 246, + 627 + ], + "lines": [ + { + "bbox": [ + 105, + 614, + 248, + 629 + ], + "spans": [ + { + "bbox": [ + 105, + 614, + 248, + 629 + ], + "score": 1.0, + "content": "B.4.5 QUALITATIVE ANALYSIS", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 36 + }, + { + "type": "text", + "bbox": [ + 106, + 635, + 504, + 646 + ], + "lines": [ + { + "bbox": [ + 105, + 633, + 506, + 649 + ], + "spans": [ + { + "bbox": [ + 105, + 633, + 506, + 649 + ], + "score": 1.0, + "content": "This section shows sample generations from different algorithms for three randomly picked prompts.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 37, + "bbox_fs": [ + 105, + 633, + 506, + 649 + ] + }, + { + "type": "list", + "bbox": [ + 106, + 651, + 434, + 716 + ], + "lines": [ + { + "bbox": [ + 106, + 651, + 142, + 660 + ], + "spans": [ + { + "bbox": [ + 106, + 651, + 142, + 660 + ], + "score": 1.0, + "content": "Sample 1", + "type": "text" + } + ], + "index": 38, + "is_list_end_line": true + }, + { + "bbox": [ + 105, + 658, + 373, + 669 + ], + "spans": [ + { + "bbox": [ + 105, + 658, + 373, + 669 + ], + "score": 1.0, + "content": "Prompt: generate a sentence with: apron cut hat kitchen sausage", + "type": "text" + } + ], + "index": 39, + "is_list_start_line": true, + "is_list_end_line": true + }, + { + "bbox": [ + 106, + 667, + 388, + 676 + ], + "spans": [ + { + "bbox": [ + 106, + 667, + 388, + 676 + ], + "score": 1.0, + "content": "Zero-Shot: generate a sentence with: apron cut hat kitchen sausage.", + "type": "text" + } + ], + "index": 40, + "is_list_start_line": true, + "is_list_end_line": true + }, + { + "bbox": [ + 105, + 675, + 276, + 685 + ], + "spans": [ + { + "bbox": [ + 105, + 675, + 276, + 685 + ], + "score": 1.0, + "content": "PPO: sausage in the kitchen on an apron.", + "type": "text" + } + ], + "index": 41, + "is_list_start_line": true, + "is_list_end_line": true + }, + { + "bbox": [ + 105, + 683, + 339, + 692 + ], + "spans": [ + { + "bbox": [ + 105, + 683, + 339, + 692 + ], + "score": 1.0, + "content": "NLPO: sausage cut hat cut hat cut hat cut apron cut hat", + "type": "text" + } + ], + "index": 42, + "is_list_start_line": true, 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Model Paramsvalue
supervisedbatch size: 16 epochs: 2 learning rate: 0.0001 learning rate scheduler: cosine weight decay: 0.1 steps per update: 5120
ppo/ nlpototal number of steps: 512000 batch size: 64 epochs per update: 5 learning rate: 0.000002 entropy coefficient: 0.0 initial kl coeff: 0.001 target kl: 0.2 discount factor: 0.99 gae lambda: 0.95 clip ratio: 0.2 value function coeff: 0.5 rollouts top k: sweep of (50,100) top mask ratio: 0.9 target update iterations: sweep of (10, 20, 30)
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decodingsampling: True temperature: 0.7 min length: 50
tokenizermax new tokens: 100 padding side: left truncation side:right max length: 512
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For decoding, we use multinomial", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 177, + 324, + 189 + ], + "spans": [ + { + "bbox": [ + 105, + 177, + 324, + 189 + ], + "score": 1.0, + "content": "sampling with a temperature of 0.7 for all the models.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 4.5, + "bbox_fs": [ + 104, + 121, + 507, + 189 + ] + }, + { + "type": "table", + "bbox": [ + 207, + 198, + 403, + 537 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 207, + 198, + 403, + 537 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 207, + 198, + 403, + 537 + ], + "spans": [ + { + "bbox": [ + 207, + 198, + 403, + 537 + ], + "score": 0.968, + "html": "
Model Paramsvalue
supervisedbatch size: 16 epochs: 2 learning rate: 0.0001 learning rate scheduler: cosine weight decay: 0.1 steps per update: 5120
ppo/ nlpototal number of steps: 512000 batch size: 64 epochs per update: 5 learning rate: 0.000002 entropy coefficient: 0.0 initial kl coeff: 0.001 target kl: 0.2 discount factor: 0.99 gae lambda: 0.95 clip ratio: 0.2 value function coeff: 0.5 rollouts top k: sweep of (50,100) top mask ratio: 0.9 target update iterations: sweep of (10, 20, 30)
total number of steps: 256000 batch size: 64 epochs per update: 5 learning rate: 0.000002 entropy coefficient: 0.0 initial kl coeff: 0.01 target kl: 0.2 discount factor: 0.99 gae lambda: 0.95 clip ratio: 0.2 value function coeff: 0.5
decodingsampling: True temperature: 0.7 min length: 50
tokenizermax new tokens: 100 padding side: left truncation side:right max length: 512
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As baselines, we report lead-3 which selects first three", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 617, + 505, + 629 + ], + "spans": [ + { + "bbox": [ + 106, + 617, + 505, + 629 + ], + "score": 1.0, + "content": "sentences as the summary, Zero-Shot and a supervised model. PPO and NLPO models are on par with", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 627, + 506, + 641 + ], + "spans": [ + { + "bbox": [ + 105, + 627, + 506, + 641 + ], + "score": 1.0, + "content": "supervised performance on several metrics including Rouge-2, Rouge-L, and Bleu. On fine-tuning", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 639, + 506, + 651 + ], + "spans": [ + { + "bbox": [ + 105, + 639, + 506, + 651 + ], + "score": 1.0, + "content": "on top of supervised model, performance improves consistently on all metrics indicating that RL", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 650, + 505, + 662 + ], + "spans": [ + { + "bbox": [ + 106, + 650, + 505, + 662 + ], + "score": 1.0, + "content": "fine-tuning is beneficial. Another interesting finding is that, RL fine-tuned models are factually", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 661, + 505, + 673 + ], + "spans": [ + { + "bbox": [ + 106, + 661, + 505, + 673 + ], + "score": 1.0, + "content": "consistent as measured by SummaCZS metric. For ablations on PPO params, NLPO params, we refer", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 672, + 172, + 683 + ], + "spans": [ + { + "bbox": [ + 106, + 672, + 172, + 683 + ], + "score": 1.0, + "content": "to Tables 18,19.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 39.5, + "bbox_fs": [ + 104, + 594, + 507, + 683 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 83, + 199, + 685, + 357 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 83, + 199, + 685, + 357 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 83, + 199, + 685, + 357 + ], + "spans": [ + { + "bbox": [ + 83, + 199, + 685, + 357 + ], + "score": 0.973, + "html": "
TasksAlgReward FunctionLM|Rouge-1Rouge-2Rouge-LLexical and Semantic Metrics Rouge-LSumMeteorBLEUBertScoreFactual Consistency SummaCZs|MSTTRDistinct1Distinct2 HDiversity Metrics HUniqueUnique2Mean Output Length
Lead-30.4010.1750.2500.3630.3330.099 0.8740.9930.7500.0482 0.38610.48116.6312146527315384
Zero-Shot PPOT5 T50.372 0.1450.2470.3110.256 0.0770.8640.6540.725 0.061 0.7600.41410.28516.1831911319399955
Rouge-10.4100.1820.2830.3490.276 0.0950.8760.6220.0680.46410.66116.4371818919138347
Rouge-AvgT50.3960.1760.2730.3380.270 0.0950.8740.6220.773 0.0710.49010.83016.6641947820914048
MeteorT50.4080.1780.2760.3420.301 0.1090.8730.5270.765 0.0600.44710.69916.6882052823438661
NLPORouge-1T50.4040.180 0.2780.3440.275 0.0960.8750.6360.7710.0690.48010.78916.6181867720197148
Rouge-AvgT50.4040.1770.2790.3440.274 0.0940.8740.5860.765 0.0660.47610.74416.6201817920636850
MeteorT50.4050.1800.2770.3430.292 0.1080.8720.5780.772 0.0640.47110.80216.7662021223103856
SupervisedT50.4110.1770.2760.3430.309 0.1080.8760.6540.7270.0570.40110.45916.4102109623034368
Supervised + PPORouge-1T50.4170.1890.2940.3580.278 0.1010.8820.7220.7500.0700.45910.59516.3891818418422046
Rouge-AvgT50.425 0.1940.2970.3630.296 0.1140.8820.7280.7470.0660.44510.58916.4581893920061752
MeteorT50.4260.1940.2930.3610.3160.1250.8800.7260.7410.0590.42010.532 16.4912039522443263
Supervised + NLPOT5 0.4210.1930.2970.3610.2870.1080.8820.7400.7480.0670.44610.52816.3131820418556148
Rouge-1Rouge-AvgT5 0.4240.1930.2960.3630.2950.1150.8820.7430.7440.0650.44310.57016.4441874720170553
MeteorT50.4290.1940.2930.3610.3190.1240.8800.7430.7450.0590.42210.57416.5162035822680163
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TasksAlgReward FunctionLM|Rouge-1Rouge-2Rouge-LLexical and Semantic Metrics Rouge-LSumMeteorBLEUBertScoreFactual Consistency SummaCZs|MSTTRDistinct1Distinct2 HDiversity Metrics HUniqueUnique2Mean Output Length
Lead-30.4010.1750.2500.3630.3330.099 0.8740.9930.7500.0482 0.38610.48116.6312146527315384
Zero-Shot PPOT5 T50.372 0.1450.2470.3110.256 0.0770.8640.6540.725 0.061 0.7600.41410.28516.1831911319399955
Rouge-10.4100.1820.2830.3490.276 0.0950.8760.6220.0680.46410.66116.4371818919138347
Rouge-AvgT50.3960.1760.2730.3380.270 0.0950.8740.6220.773 0.0710.49010.83016.6641947820914048
MeteorT50.4080.1780.2760.3420.301 0.1090.8730.5270.765 0.0600.44710.69916.6882052823438661
NLPORouge-1T50.4040.180 0.2780.3440.275 0.0960.8750.6360.7710.0690.48010.78916.6181867720197148
Rouge-AvgT50.4040.1770.2790.3440.274 0.0940.8740.5860.765 0.0660.47610.74416.6201817920636850
MeteorT50.4050.1800.2770.3430.292 0.1080.8720.5780.772 0.0640.47110.80216.7662021223103856
SupervisedT50.4110.1770.2760.3430.309 0.1080.8760.6540.7270.0570.40110.45916.4102109623034368
Supervised + PPORouge-1T50.4170.1890.2940.3580.278 0.1010.8820.7220.7500.0700.45910.59516.3891818418422046
Rouge-AvgT50.425 0.1940.2970.3630.296 0.1140.8820.7280.7470.0660.44510.58916.4581893920061752
MeteorT50.4260.1940.2930.3610.3160.1250.8800.7260.7410.0590.42010.532 16.4912039522443263
Supervised + NLPOT5 0.4210.1930.2970.3610.2870.1080.8820.7400.7480.0670.44610.52816.3131820418556148
Rouge-1Rouge-AvgT5 0.4240.1930.2960.3630.2950.1150.8820.7430.7440.0650.44310.57016.4441874720170553
MeteorT50.4290.1940.2930.3610.3190.1240.8800.7430.7450.0590.42210.57416.5162035822680163
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AlgReward FunctionLexical and Semantic Metrics
Top kRouge-1Rouge-2Rouge-LRouge-LSumMeteorBLEUBertScore
Rouge-1
50 1000.404 0.4120.181 0.1860.280 0.2860.346 0.3540.273 0.2760.095 0.0940.874 0.876
Rouge-Avg
PPO50 1000.401 0.3990.177 0.1790.2760.342 0.3420.2710.0920.873
0.2750.2700.0940.874
Meteor500.4130.1820.2790.3480.3010.1100.873
1000.4090.1790.2760.3450.2960.1080.871
Rouge-1500.4140.1900.2930.3580.2720.0970.881
1000.4200.1930.2950.3620.2770.1000.881
Supervised+PPORouge-Avg500.4260.1960.2980.3660.2940.1140.881
1000.4270.1960.2980.3660.2940.1130.881
Meteor50 1000.429 0.4320.197 0.1990.297 0.2970.367 0.3670.306 0.3170.122 0.1310.881 0.879
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AlgReward FunctionTop k (rollout)Top p (Action mask)target update n;ter sRouge-1Rouge-2Lexical and Semantic Metrics Rouge-L Rouge-LSumMeteorBLEUBertScore
Rouge-1500.910 200.400 0.3960.178 0.1730.275 0.2740.343 0.3400.269 0.2570.094 0.0820.872 0.873
300.3960.1740.2730.3390.2650.0910.872
1000.9100.4070.1770.2790.3470.2650.0850.875
200.4060.1820.2810.3470.2730.0940.874
300.4050.1800.2790.3470.2690.0910.875
Rouge-Avg0.9
5010 200.400 0.3490.180 0.1470.276 0.2410.343 0.2980.271 0.2370.096 0.0780.873 0.858
NLPO300.3930.1730.2720.3360.2670.0920.870
1000.9100.3960.1740.2740.3390.2650.0880.872
200.4060.1790.2800.3470.2720.0920.874
300.4000.1780.2790.3440.2660.0870.874
Meteor500.9100.4040.1770.2740.872
200.4060.1800.2760.343 0.3430.286 0.2920.102 0.1070.871
300.4010.1720.2710.3370.2880.0990.870
1000.9100.4050.1780.2760.3430.2940.1070.870
200.4060.1760.2760.3430.2910.1060.872
300.4090.1840.2800.3480.2910.1080.873
Rouge-1500.9100.4250.1960.2990.3660.2850.1060.882
200.4170.1910.2950.3600.2760.1000.881
300.4180.1920.2960.3610.2780.1010.881
1000.9100.4240.1960.2990.3660.2860.1060.882
200.4230.1960.2990.3650.2890.1100.881
300.4200.1930.2960.3620.2790.1020.881
Rouge-Avg500.9100.4260.1970.2980.3670.2940.1150.881
200.4250.1960.2980.3660.2920.1120.881
0.9300.4240.1940.2970.3650.2870.1070.881
Supervised + NLPO10010 200.424 0.4280.196 0.1980.298 0.3000.365 0.3680.291 0.2960.113 0.1150.881 0.882
0.9300.4290.1990.3000.3690.2960.1160.882
Meteor50100.4300.1970.2940.3640.3200.1300.879
200.4320.1980.2970.3670.3180.1300.880
300.4230.1910.2930.3610.2970.1160.879
1000.9100.4350.2000.2980.3690.3200.1310.881
200.4330.1980.297 0.2970.3680.3190.130 0.1320.879 0.879
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AlgReward FunctionLexical and Semantic Metrics
Top kRouge-1Rouge-2Rouge-LRouge-LSumMeteorBLEUBertScore
Rouge-1
50 1000.404 0.4120.181 0.1860.280 0.2860.346 0.3540.273 0.2760.095 0.0940.874 0.876
Rouge-Avg
PPO50 1000.401 0.3990.177 0.1790.2760.342 0.3420.2710.0920.873
0.2750.2700.0940.874
Meteor500.4130.1820.2790.3480.3010.1100.873
1000.4090.1790.2760.3450.2960.1080.871
Rouge-1500.4140.1900.2930.3580.2720.0970.881
1000.4200.1930.2950.3620.2770.1000.881
Supervised+PPORouge-Avg500.4260.1960.2980.3660.2940.1140.881
1000.4270.1960.2980.3660.2940.1130.881
Meteor50 1000.429 0.4320.197 0.1990.297 0.2970.367 0.3670.306 0.3170.122 0.1310.881 0.879
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AlgReward FunctionTop k (rollout)Top p (Action mask)target update n;ter sRouge-1Rouge-2Lexical and Semantic Metrics Rouge-L Rouge-LSumMeteorBLEUBertScore
Rouge-1500.910 200.400 0.3960.178 0.1730.275 0.2740.343 0.3400.269 0.2570.094 0.0820.872 0.873
300.3960.1740.2730.3390.2650.0910.872
1000.9100.4070.1770.2790.3470.2650.0850.875
200.4060.1820.2810.3470.2730.0940.874
300.4050.1800.2790.3470.2690.0910.875
Rouge-Avg0.9
5010 200.400 0.3490.180 0.1470.276 0.2410.343 0.2980.271 0.2370.096 0.0780.873 0.858
NLPO300.3930.1730.2720.3360.2670.0920.870
1000.9100.3960.1740.2740.3390.2650.0880.872
200.4060.1790.2800.3470.2720.0920.874
300.4000.1780.2790.3440.2660.0870.874
Meteor500.9100.4040.1770.2740.872
200.4060.1800.2760.343 0.3430.286 0.2920.102 0.1070.871
300.4010.1720.2710.3370.2880.0990.870
1000.9100.4050.1780.2760.3430.2940.1070.870
200.4060.1760.2760.3430.2910.1060.872
300.4090.1840.2800.3480.2910.1080.873
Rouge-1500.9100.4250.1960.2990.3660.2850.1060.882
200.4170.1910.2950.3600.2760.1000.881
300.4180.1920.2960.3610.2780.1010.881
1000.9100.4240.1960.2990.3660.2860.1060.882
200.4230.1960.2990.3650.2890.1100.881
300.4200.1930.2960.3620.2790.1020.881
Rouge-Avg500.9100.4260.1970.2980.3670.2940.1150.881
200.4250.1960.2980.3660.2920.1120.881
0.9300.4240.1940.2970.3650.2870.1070.881
Supervised + NLPO10010 200.424 0.4280.196 0.1980.298 0.3000.365 0.3680.291 0.2960.113 0.1150.881 0.882
0.9300.4290.1990.3000.3690.2960.1160.882
Meteor50100.4300.1970.2940.3640.3200.1300.879
200.4320.1980.2970.3670.3180.1300.880
300.4230.1910.2930.3610.2970.1160.879
1000.9100.4350.2000.2980.3690.3200.1310.881
200.4330.1980.297 0.2970.3680.3190.130 0.1320.879 0.879
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AlgorithmUnique NCoherenceQuality
ValueAlphaSkewValueAlphaSkew
PPO+Supervised224.210.1984.2243.970.2563.98
NLPO+Supervised194.30.264.3083.980.0894
Zero Shot173.730.13.7573.690.253.722
Supervised194.250.1164.2413.990.23.986
NLPO174.030.134.0423.830.1913.832
PPO213.940.1113.9453.760.1293.767
Human193.890.2773.9023.770.0293.769
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Group 1Group 2CoherenceDiff (G2-G1) p-valuesQualityDiff (G2-G1) p-values
HumanHumanNLPO0.1470.7550.0600.900
HumanNLPO+Supervised0.4130.0010.2130.047
HumanHumanPPO0.0530.900-0.007
PPO+Supervised0.3270.0240.2000.544
HumanSupervised0.3600.0080.2200.043
HumanZero Shot-0.1600.679-0.0800.900
NLPONLPO+Supervised0.2670.0120.1530.008
NLPONLPOPPO-0.0930.900-0.067
PPO+Supervised0.1800.5640.1400.860
NLPOSupervised0.2130.3610.1600.754
NLPOZero Shot-0.3070.044-0.1400.860
NLPO+SupervisedPPO-0.3600.008-0.2200.043
NLPO+SupervisedPPO+Supervised-0.0870.009-0.0130.009
NLPO+SupervisedSupervised-0.0530.0090.0070.900
NLPO+SupervisedZero Shot-0.5730.001-0.2930.012
PPOPPOPPO+Supervised0.2730.1060.2070.508
Supervised0.3070.0440.2270.394
PPOZero Shot-0.2130.361-0.0730.900
PPO+SupervisedPPO+SupervisedSupervisedSupervised0.0330.9000.0200.900
Zero Shot-0.4870.001-0.2800.155
Zero Shot-0.5200.001-0.3000.101
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AlgorithmUnique NCoherenceQuality
ValueAlphaSkewValueAlphaSkew
PPO+Supervised224.210.1984.2243.970.2563.98
NLPO+Supervised194.30.264.3083.980.0894
Zero Shot173.730.13.7573.690.253.722
Supervised194.250.1164.2413.990.23.986
NLPO174.030.134.0423.830.1913.832
PPO213.940.1113.9453.760.1293.767
Human193.890.2773.9023.770.0293.769
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Group 1Group 2CoherenceDiff (G2-G1) p-valuesQualityDiff (G2-G1) p-values
HumanHumanNLPO0.1470.7550.0600.900
HumanNLPO+Supervised0.4130.0010.2130.047
HumanHumanPPO0.0530.900-0.007
PPO+Supervised0.3270.0240.2000.544
HumanSupervised0.3600.0080.2200.043
HumanZero Shot-0.1600.679-0.0800.900
NLPONLPO+Supervised0.2670.0120.1530.008
NLPONLPOPPO-0.0930.900-0.067
PPO+Supervised0.1800.5640.1400.860
NLPOSupervised0.2130.3610.1600.754
NLPOZero Shot-0.3070.044-0.1400.860
NLPO+SupervisedPPO-0.3600.008-0.2200.043
NLPO+SupervisedPPO+Supervised-0.0870.009-0.0130.009
NLPO+SupervisedSupervised-0.0530.0090.0070.900
NLPO+SupervisedZero Shot-0.5730.001-0.2930.012
PPOPPOPPO+Supervised0.2730.1060.2070.508
Supervised0.3070.0440.2270.394
PPOZero Shot-0.2130.361-0.0730.900
PPO+SupervisedPPO+SupervisedSupervisedSupervised0.0330.9000.0200.900
Zero Shot-0.4870.001-0.2800.155
Zero Shot-0.5200.001-0.3000.101
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Tables 20, 21 show averaged", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 475, + 505, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 475, + 505, + 486 + ], + "score": 1.0, + "content": "results, annotator agreement, and the results of statistical significance tests to determine which models", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 486, + 303, + 498 + ], + "spans": [ + { + "bbox": [ + 105, + 486, + 303, + 498 + ], + "score": 1.0, + "content": "output better generations when rated by humans.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 7 + }, + { + "type": "title", + "bbox": [ + 108, + 510, + 246, + 521 + ], + "lines": [ + { + "bbox": [ + 105, + 508, + 248, + 523 + ], + "spans": [ + { + "bbox": [ + 105, + 508, + 248, + 523 + ], + "score": 1.0, + "content": "B.5.4 QUALITATIVE ANALYSIS", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 10 + }, + { + "type": "title", + "bbox": [ + 106, + 529, + 504, + 541 + ], + "lines": [ + { + "bbox": [ + 106, + 527, + 506, + 543 + ], + "spans": [ + { + "bbox": [ + 106, + 527, + 506, + 543 + ], + "score": 1.0, + "content": "We show sample generations from each of the algorithms for three randomly picked prompts below.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 11 + }, + { + "type": "title", + "bbox": [ + 106, + 546, + 141, + 554 + ], + "lines": [ + { + "bbox": [ + 105, + 544, + 144, + 556 + ], + "spans": [ + { + "bbox": [ + 105, + 544, + 144, + 556 + ], + "score": 1.0, + "content": "Sample 1", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 12 + }, + { + "type": "text", + "bbox": [ + 112, + 555, + 502, + 731 + ], + "lines": [ + { + "bbox": [ + 109, + 554, + 486, + 566 + ], + "spans": [ + { + "bbox": [ + 109, + 554, + 486, + 566 + ], + "score": 1.0, + "content": "Prompt: Manchester City are confident UEFAâ˘A´Zs punishment for breaching financial fairplay", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 126, + 563, + 489, + 572 + ], + "spans": [ + { + "bbox": [ + 126, + 563, + 489, + 572 + ], + "score": 1.0, + "content": "regulations will be lifted this summer which would allow them to bid for stellar names", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 126, + 571, + 485, + 581 + ], + "spans": [ + { + "bbox": [ + 126, + 571, + 485, + 581 + ], + "score": 1.0, + "content": "like Raheem Sterling, Gareth Bale, Kevin de Bruyne and Ross Barkley. City boss Manuel", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 126, + 578, + 468, + 588 + ], + "spans": [ + { + "bbox": [ + 126, + 578, + 468, + 588 + ], + "score": 1.0, + "content": "Pellegrini has been hampered over the past year by UEFA restricting them to a net", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 126, + 588, + 497, + 598 + ], + "spans": [ + { + "bbox": [ + 126, + 588, + 497, + 598 + ], + "score": 1.0, + "content": "transfer spend of 49million in each window and keeping the clubâ˘A´Zs overall wage bill to", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 125, + 596, + 489, + 608 + ], + "spans": [ + { + "bbox": [ + 125, + 596, + 489, + 608 + ], + "score": 1.0, + "content": "its current level of 205million-a-year. 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It has cost City on the pitch.", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 126, + 247, + 501, + 257 + ], + "spans": [ + { + "bbox": [ + 126, + 247, + 501, + 257 + ], + "score": 1.0, + "content": "Even if they win their remaining eight Premier League fixtures their points tally will be", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 129, + 256, + 476, + 266 + ], + "spans": [ + { + "bbox": [ + 129, + 256, + 476, + 266 + ], + "score": 1.0, + "content": "lower than last season and they crashed out once again at the last-16 stage of the", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 127, + 264, + 493, + 273 + ], + "spans": [ + { + "bbox": [ + 127, + 264, + 493, + 273 + ], + "score": 1.0, + "content": "Champions League. Pellegrini and director of football Txiki Begiristain both accept the", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 127, + 272, + 500, + 281 + ], + "spans": [ + { + "bbox": [ + 127, + 272, + 500, + 281 + ], + "score": 1.0, + "content": "squad needs replenishing and they want to be in the market for the top available players.", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 129, + 279, + 502, + 289 + ], + "spans": [ + { + "bbox": [ + 129, + 279, + 502, + 289 + ], + "score": 1.0, + "content": "Manchester City have been heavily linked with a move for former Chelsea midfielder Kevin", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 129, + 288, + 492, + 297 + ], + "spans": [ + { + "bbox": [ + 129, + 288, + 492, + 297 + ], + "score": 1.0, + "content": "de Bruyne . The club also want to be involved in any race for Liverpool contract rebel", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 126, + 296, + 480, + 305 + ], + "spans": [ + { + "bbox": [ + 126, + 296, + 480, + 305 + ], + "score": 1.0, + "content": "Raheem Sterling . They have been strongly linked with former Chelsea winger Kevin de", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 126, + 303, + 480, + 313 + ], + "spans": [ + { + "bbox": [ + 126, + 303, + 480, + 313 + ], + "score": 1.0, + "content": "Bruyne who has been one of the best players in the Bundesliga with Wolfsburg. And if", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 126, + 311, + 489, + 321 + ], + "spans": [ + { + "bbox": [ + 126, + 311, + 489, + 321 + ], + "score": 1.0, + "content": "Liverpool do allow Sterling to leave, City want to be involved in the chase for one of", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 125, + 319, + 488, + 331 + ], + "spans": [ + { + "bbox": [ + 125, + 319, + 488, + 331 + ], + "score": 1.0, + "content": "Englandâ˘A´Zs most outstanding talents to help fit in with quotas for homegrown players.", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 125, + 327, + 482, + 339 + ], + "spans": [ + { + "bbox": [ + 125, + 327, + 482, + 339 + ], + "score": 1.0, + "content": "â˘AŸIf you are the manager or a player of a big tem, you are always open to criticism", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 124, + 336, + 502, + 347 + ], + "spans": [ + { + "bbox": [ + 124, + 336, + 502, + 347 + ], + "score": 1.0, + "content": "because everyone expects a high level of performance,â˘A´Z he said. â˘AŸThe major issue with", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 129, + 345, + 480, + 355 + ], + "spans": [ + { + "bbox": [ + 129, + 345, + 480, + 355 + ], + "score": 1.0, + "content": "our team always seems to be the money but this season I think we were the team that", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 126, + 353, + 498, + 363 + ], + "spans": [ + { + "bbox": [ + 126, + 353, + 498, + 363 + ], + "score": 1.0, + "content": "spent less than any other team. That is the weird thing. â˘AŸFor this club trying to be a", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 124, + 362, + 489, + 372 + ], + "spans": [ + { + "bbox": [ + 124, + 362, + 489, + 372 + ], + "score": 1.0, + "content": "big team in so few years, maybe we are paying the cost for that.â˘A´Z Since the transfer", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 125, + 370, + 502, + 380 + ], + "spans": [ + { + "bbox": [ + 125, + 370, + 502, + 380 + ], + "score": 1.0, + "content": "penalties were introduced, City have spent 91million on players in the last two windows (", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 124, + 378, + 481, + 388 + ], + "spans": [ + { + "bbox": [ + 124, + 378, + 481, + 388 + ], + "score": 1.0, + "content": "Net spend 68million). That compares to Manchester United 145.5million, Liverpool 113", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 126, + 387, + 501, + 395 + ], + "spans": [ + { + "bbox": [ + 126, + 387, + 501, + 395 + ], + "score": 1.0, + "content": "million, Arsenal 92.5million and Chelsea 82.6million. Over the same time period Barcelona", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 129, + 394, + 485, + 404 + ], + "spans": [ + { + "bbox": [ + 129, + 394, + 485, + 404 + ], + "score": 1.0, + "content": "spent 118.3million on players and Real Madrid 81.2million though they also broke the", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 126, + 402, + 371, + 412 + ], + "spans": [ + { + "bbox": [ + 126, + 402, + 371, + 412 + ], + "score": 1.0, + "content": "world transfer record for Gareth Bale the previous summer.", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 23.5, + "bbox_fs": [ + 116, + 151, + 502, + 412 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 411, + 501, + 435 + ], + "lines": [ + { + "bbox": [ + 105, + 410, + 477, + 421 + ], + "spans": [ + { + "bbox": [ + 105, + 410, + 477, + 421 + ], + "score": 1.0, + "content": "Zero-Shot: manuel Pellegrini hoping UEFAâ˘A´Zs punishment for breaching financial fairplay", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 126, + 419, + 502, + 429 + ], + "spans": [ + { + "bbox": [ + 126, + 419, + 502, + 429 + ], + "score": 1.0, + "content": "regulations will be lifted this summer. city have been restricted to a net transfer spend", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 129, + 426, + 471, + 437 + ], + "spans": [ + { + "bbox": [ + 129, + 426, + 471, + 437 + ], + "score": 1.0, + "content": "of 49million in each window. a total of 23million has been lost in the last year.", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 41, + "bbox_fs": [ + 105, + 410, + 502, + 437 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 436, + 500, + 475 + ], + "lines": [ + { + "bbox": [ + 106, + 435, + 493, + 443 + ], + "spans": [ + { + "bbox": [ + 106, + 435, + 493, + 443 + ], + "score": 1.0, + "content": "References: Manchester City have been restricted to a net transfer spend of 49m .Club’s also", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 126, + 443, + 493, + 453 + ], + "spans": [ + { + "bbox": [ + 126, + 443, + 493, + 453 + ], + "score": 1.0, + "content": "had to keep overall wage bill to its current level of 205m .Punishments imposed by UEFA", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 126, + 450, + 481, + 461 + ], + "spans": [ + { + "bbox": [ + 126, + 450, + 481, + 461 + ], + "score": 1.0, + "content": "for breaching Financial Fair Play rules .The spending restrictions were set for this", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 126, + 459, + 484, + 469 + ], + "spans": [ + { + "bbox": [ + 126, + 459, + 484, + 469 + ], + "score": 1.0, + "content": "season and the next one .But City are confident they will be lifted early after their", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 126, + 467, + 176, + 476 + ], + "spans": [ + { + "bbox": [ + 126, + 467, + 176, + 476 + ], + "score": 1.0, + "content": "compliance .", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 45, + "bbox_fs": [ + 106, + 435, + 493, + 476 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 476, + 500, + 508 + ], + "lines": [ + { + "bbox": [ + 106, + 475, + 489, + 485 + ], + "spans": [ + { + "bbox": [ + 106, + 475, + 489, + 485 + ], + "score": 1.0, + "content": "PPO: Manuel Pellegrini is hoping UEFAâ˘A´Zs punishment for breaching financial fairplay rules", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 126, + 484, + 501, + 493 + ], + "spans": [ + { + "bbox": [ + 126, + 484, + 501, + 493 + ], + "score": 1.0, + "content": "will be lifted this summer. Manchester City have been limited to a net spend of 49million", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 130, + 493, + 496, + 501 + ], + "spans": [ + { + "bbox": [ + 130, + 493, + 496, + 501 + ], + "score": 1.0, + "content": "in each transfer window. the club also keep the club’s overall wage bill to its current", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 126, + 500, + 242, + 510 + ], + "spans": [ + { + "bbox": [ + 126, + 500, + 242, + 510 + ], + "score": 1.0, + "content": "level of 205million-a-year.", + "type": "text" + } + ], + "index": 51 + } + ], + "index": 49.5, + "bbox_fs": [ + 106, + 475, + 501, + 510 + ] + }, + { + "type": "text", + "bbox": [ + 104, + 509, + 488, + 533 + ], + "lines": [ + { + "bbox": [ + 105, + 507, + 477, + 519 + ], + "spans": [ + { + "bbox": [ + 105, + 507, + 477, + 519 + ], + "score": 1.0, + "content": "NLPO: Manchester City are confident UEFAâ˘A´Zs punishment for breaching financial fairplay", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 126, + 517, + 488, + 526 + ], + "spans": [ + { + "bbox": [ + 126, + 517, + 488, + 526 + ], + "score": 1.0, + "content": "regulations will be lifted this summer. that would allow them to bid for stellar names", + "type": "text" + } + ], + "index": 53 + }, + { + "bbox": [ + 126, + 523, + 359, + 534 + ], + "spans": [ + { + "bbox": [ + 126, + 523, + 359, + 534 + ], + "score": 1.0, + "content": "like Raheem Sterling, Kevin de Bruyne and Ross Barkley.", + "type": "text" + } + ], + "index": 54 + } + ], + "index": 53, + "bbox_fs": [ + 105, + 507, + 488, + 534 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 533, + 495, + 572 + ], + "lines": [ + { + "bbox": [ + 106, + 533, + 486, + 542 + ], + "spans": [ + { + "bbox": [ + 106, + 533, + 486, + 542 + ], + "score": 1.0, + "content": "Supervised: Manchester City have been limited to a net transfer spend of 49million in each", + "type": "text" + } + ], + "index": 55 + }, + { + "bbox": [ + 126, + 540, + 493, + 551 + ], + "spans": [ + { + "bbox": [ + 126, + 540, + 493, + 551 + ], + "score": 1.0, + "content": "window. City’s overall wage bill is 205m-a-year due to a breach of UEFA rules. City are", + "type": "text" + } + ], + "index": 56 + }, + { + "bbox": [ + 126, + 549, + 493, + 558 + ], + "spans": [ + { + "bbox": [ + 126, + 549, + 493, + 558 + ], + "score": 1.0, + "content": "confident the financial restrictions will be lifted at the end of the current season in", + "type": "text" + } + ], + "index": 57 + }, + { + "bbox": [ + 126, + 556, + 481, + 567 + ], + "spans": [ + { + "bbox": [ + 126, + 556, + 481, + 567 + ], + "score": 1.0, + "content": "order to bid for stars such as Raheem Sterling. Manuel Pellegrini is hoping that the", + "type": "text" + } + ], + "index": 58 + }, + { + "bbox": [ + 126, + 564, + 422, + 574 + ], + "spans": [ + { + "bbox": [ + 126, + 564, + 422, + 574 + ], + "score": 1.0, + "content": "financial restrictions will be lifted at the end of the 2015/16 season", + "type": "text" + } + ], + "index": 59 + } + ], + "index": 57, + "bbox_fs": [ + 106, + 533, + 493, + 574 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 573, + 498, + 605 + ], + "lines": [ + { + "bbox": [ + 106, + 573, + 486, + 582 + ], + "spans": [ + { + "bbox": [ + 106, + 573, + 151, + 582 + ], + "score": 1.0, + "content": "Supervised", + "type": "text" + }, + { + "bbox": [ + 152, + 574, + 159, + 580 + ], + "score": 0.43, + "content": "^ +", + "type": "inline_equation" + }, + { + "bbox": [ + 159, + 573, + 486, + 582 + ], + "score": 1.0, + "content": "PPO: Manchester City have been restricted to a net spend of 49million in each", + "type": "text" + } + ], + "index": 60 + }, + { + "bbox": [ + 126, + 581, + 468, + 590 + ], + "spans": [ + { + "bbox": [ + 126, + 581, + 468, + 590 + ], + "score": 1.0, + "content": "window and kept their overall wage bill at 205m. Manuel Pellegrini believes these", + "type": "text" + } + ], + "index": 61 + }, + { + "bbox": [ + 126, + 589, + 500, + 597 + ], + "spans": [ + { + "bbox": [ + 126, + 589, + 500, + 597 + ], + "score": 1.0, + "content": "restrictions will be lifted at the end of the season. 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The club have been restricted to a net", + "type": "text" + } + ], + "index": 65 + }, + { + "bbox": [ + 126, + 622, + 481, + 631 + ], + "spans": [ + { + "bbox": [ + 126, + 622, + 481, + 631 + ], + "score": 1.0, + "content": "transfer spend of 49million over the past two window. They aim to bid for stars like", + "type": "text" + } + ], + "index": 66 + }, + { + "bbox": [ + 126, + 630, + 497, + 639 + ], + "spans": [ + { + "bbox": [ + 126, + 630, + 497, + 639 + ], + "score": 1.0, + "content": "Raheem Sterling, Gareth Bale and Kevin de Bruyne. City lost 23m on transfers in the last", + "type": "text" + } + ], + "index": 67 + }, + { + "bbox": [ + 126, + 637, + 405, + 646 + ], + "spans": [ + { + "bbox": [ + 126, + 637, + 405, + 646 + ], + "score": 1.0, + "content": "12 months due to financial restrictions imposed by UEFA for breach", + "type": "text" + } + ], + "index": 68 + } + ], + "index": 66, + "bbox_fs": [ + 106, + 605, + 501, + 646 + ] + }, + { + "type": "title", + "bbox": [ + 106, + 654, + 141, + 661 + ], + "lines": [ + { + "bbox": [ + 106, + 654, + 141, + 661 + ], + "spans": [], + "index": 69 + } + ], + "index": 69 + }, + { + "type": "text", + "bbox": [ + 108, + 662, + 504, + 726 + ], + "lines": [ + { + "bbox": [ + 106, + 661, + 491, + 671 + ], + "spans": [ + { + "bbox": [ + 106, + 661, + 491, + 671 + ], + "score": 1.0, + "content": "Prompt: (CNN)Larry Johnson remembers the fear and feeling of helplessness from being on the", + "type": "text" + } + ], + "index": 70 + }, + { + "bbox": [ + 125, + 669, + 493, + 679 + ], + "spans": [ + { + "bbox": [ + 125, + 669, + 493, + 679 + ], + "score": 1.0, + "content": "SkyWest Airlines flight that made an emergency landing in Buffalo, New York. \"I thought", + "type": "text" + } + ], + "index": 71 + }, + { + "bbox": [ + 125, + 677, + 489, + 688 + ], + "spans": [ + { + "bbox": [ + 125, + 677, + 489, + 688 + ], + "score": 1.0, + "content": "we were done,\" he said Thursday, one day later. \"There was no doubt in my mind that we", + "type": "text" + } + ], + "index": 72 + }, + { + "bbox": [ + 126, + 685, + 488, + 695 + ], + "spans": [ + { + "bbox": [ + 126, + 685, + 488, + 695 + ], + "score": 1.0, + "content": "weren’t going to land.\" Johnson was flying with his brother, his girlfriend and his 8-", + "type": "text" + } + ], + "index": 73 + }, + { + "bbox": [ + 125, + 693, + 489, + 703 + ], + "spans": [ + { + "bbox": [ + 125, + 693, + 489, + 703 + ], + "score": 1.0, + "content": "month-old son when he says a flight attendant came over the speaker asking for someone", + "type": "text" + } + ], + "index": 74 + }, + { + "bbox": [ + 125, + 701, + 502, + 711 + ], + "spans": [ + { + "bbox": [ + 125, + 701, + 502, + 711 + ], + "score": 1.0, + "content": "who was medically trained to help with a sick passenger. 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The", + "type": "text", + "cross_page": true + } + ], + "index": 0 + }, + { + "bbox": [ + 125, + 93, + 498, + 102 + ], + "spans": [ + { + "bbox": [ + 125, + 93, + 498, + 102 + ], + "score": 1.0, + "content": "Federal Aviation Administration on Wednesday initially reported a pressurization problem", + "type": "text", + "cross_page": true + } + ], + "index": 1 + }, + { + "bbox": [ + 126, + 101, + 501, + 110 + ], + "spans": [ + { + "bbox": [ + 126, + 101, + 501, + 110 + ], + "score": 1.0, + "content": "with SkyWest Flight 5622, and said it would investigate. It later issued a statement that", + "type": "text", + "cross_page": true + } + ], + "index": 2 + }, + { + "bbox": [ + 128, + 108, + 502, + 119 + ], + "spans": [ + { + "bbox": [ + 128, + 108, + 502, + 119 + ], + "score": 1.0, + "content": "did not reference any pressurization issues. \"It was like being trapped and you couldn’t", + "type": "text", + "cross_page": true + } + ], + "index": 3 + }, + { + "bbox": [ + 129, + 117, + 497, + 127 + ], + "spans": [ + { + "bbox": [ + 129, + 117, + 497, + 127 + ], + "score": 1.0, + "content": "do anything. You have no control over it. Your body just felt pressured,\" Johnson said.", + "type": "text", + "cross_page": true + } + ], + "index": 4 + }, + { + "bbox": [ + 125, + 124, + 501, + 135 + ], + "spans": [ + { + "bbox": [ + 125, + 124, + 501, + 135 + ], + "score": 1.0, + "content": "Johnson said his girlfriend was seeing spots and that \"when I was blinking, it was really", + "type": "text", + "cross_page": true + } + ], + "index": 5 + }, + { + "bbox": [ + 128, + 132, + 494, + 143 + ], + "spans": [ + { + "bbox": [ + 128, + 132, + 494, + 143 + ], + "score": 1.0, + "content": "bright. I could barely see.\" According to Marissa Snow, spokeswoman for SkyWest, three", + "type": "text", + "cross_page": true + } + ], + "index": 6 + }, + { + "bbox": [ + 124, + 140, + 498, + 151 + ], + "spans": [ + { + "bbox": [ + 124, + 140, + 498, + 151 + ], + "score": 1.0, + "content": "passengers reported a loss of consciousness while on the flight. Fifteen passengers were", + "type": "text", + "cross_page": true + } + ], + "index": 7 + }, + { + "bbox": [ + 126, + 149, + 492, + 158 + ], + "spans": [ + { + "bbox": [ + 126, + 149, + 492, + 158 + ], + "score": 1.0, + "content": "examined by medical personnel at the Buffalo airport, but no one was transported to the", + "type": "text", + "cross_page": true + } + ], + "index": 8 + }, + { + "bbox": [ + 126, + 156, + 493, + 167 + ], + "spans": [ + { + "bbox": [ + 126, + 156, + 493, + 167 + ], + "score": 1.0, + "content": "hospital, she said. The spokeswoman said that maintenance personnel found no indication", + "type": "text", + "cross_page": true + } + ], + "index": 9 + }, + { + "bbox": [ + 126, + 165, + 480, + 173 + ], + "spans": [ + { + "bbox": [ + 126, + 165, + 480, + 173 + ], + "score": 1.0, + "content": "of a pressurization problem with the aircraft, an Embraer E170, and that the airline", + "type": "text", + "cross_page": true + } + ], + "index": 10 + }, + { + "bbox": [ + 126, + 172, + 493, + 183 + ], + "spans": [ + { + "bbox": [ + 126, + 172, + 493, + 183 + ], + "score": 1.0, + "content": "continues to investigate the cause. An official with the National Transportation Safety", + "type": "text", + "cross_page": true + } + ], + "index": 11 + }, + { + "bbox": [ + 126, + 181, + 484, + 190 + ], + "spans": [ + { + "bbox": [ + 126, + 181, + 484, + 190 + ], + "score": 1.0, + "content": "Board told CNN that the agency is in communication with the FAA and SkyWest to gather", + "type": "text", + "cross_page": true + } + ], + "index": 12 + }, + { + "bbox": [ + 126, + 189, + 400, + 198 + ], + "spans": [ + { + "bbox": [ + 126, + 189, + 400, + 198 + ], + "score": 1.0, + "content": "information on the incident to better understand what took place.", + "type": "text", + "cross_page": true + } + ], + "index": 13 + } + ], + "index": 73.5, + "bbox_fs": [ + 106, + 661, + 504, + 727 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 124, + 85, + 501, + 196 + ], + "lines": [ + { + "bbox": [ + 126, + 85, + 489, + 95 + ], + "spans": [ + { + "bbox": [ + 126, + 85, + 489, + 95 + ], + "score": 1.0, + "content": "re not going to be able to breathe,\" Johnson recalled the flight attendant saying. The", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 125, + 93, + 498, + 102 + ], + "spans": [ + { + "bbox": [ + 125, + 93, + 498, + 102 + ], + "score": 1.0, + "content": "Federal Aviation Administration on Wednesday initially reported a pressurization problem", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 126, + 101, + 501, + 110 + ], + "spans": [ + { + "bbox": [ + 126, + 101, + 501, + 110 + ], + "score": 1.0, + "content": "with SkyWest Flight 5622, and said it would investigate. It later issued a statement that", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 128, + 108, + 502, + 119 + ], + "spans": [ + { + "bbox": [ + 128, + 108, + 502, + 119 + ], + "score": 1.0, + "content": "did not reference any pressurization issues. \"It was like being trapped and you couldn’t", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 129, + 117, + 497, + 127 + ], + "spans": [ + { + "bbox": [ + 129, + 117, + 497, + 127 + ], + "score": 1.0, + "content": "do anything. You have no control over it. Your body just felt pressured,\" Johnson said.", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 125, + 124, + 501, + 135 + ], + "spans": [ + { + "bbox": [ + 125, + 124, + 501, + 135 + ], + "score": 1.0, + "content": "Johnson said his girlfriend was seeing spots and that \"when I was blinking, it was really", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 128, + 132, + 494, + 143 + ], + "spans": [ + { + "bbox": [ + 128, + 132, + 494, + 143 + ], + "score": 1.0, + "content": "bright. I could barely see.\" According to Marissa Snow, spokeswoman for SkyWest, three", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 124, + 140, + 498, + 151 + ], + "spans": [ + { + "bbox": [ + 124, + 140, + 498, + 151 + ], + "score": 1.0, + "content": "passengers reported a loss of consciousness while on the flight. Fifteen passengers were", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 126, + 149, + 492, + 158 + ], + "spans": [ + { + "bbox": [ + 126, + 149, + 492, + 158 + ], + "score": 1.0, + "content": "examined by medical personnel at the Buffalo airport, but no one was transported to the", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 126, + 156, + 493, + 167 + ], + "spans": [ + { + "bbox": [ + 126, + 156, + 493, + 167 + ], + "score": 1.0, + "content": "hospital, she said. The spokeswoman said that maintenance personnel found no indication", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 126, + 165, + 480, + 173 + ], + "spans": [ + { + "bbox": [ + 126, + 165, + 480, + 173 + ], + "score": 1.0, + "content": "of a pressurization problem with the aircraft, an Embraer E170, and that the airline", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 126, + 172, + 493, + 183 + ], + "spans": [ + { + "bbox": [ + 126, + 172, + 493, + 183 + ], + "score": 1.0, + "content": "continues to investigate the cause. An official with the National Transportation Safety", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 126, + 181, + 484, + 190 + ], + "spans": [ + { + "bbox": [ + 126, + 181, + 484, + 190 + ], + "score": 1.0, + "content": "Board told CNN that the agency is in communication with the FAA and SkyWest to gather", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 126, + 189, + 400, + 198 + ], + "spans": [ + { + "bbox": [ + 126, + 189, + 400, + 198 + ], + "score": 1.0, + "content": "information on the incident to better understand what took place.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 6.5 + }, + { + "type": "text", + "bbox": [ + 109, + 198, + 501, + 331 + ], + "lines": [ + { + "bbox": [ + 107, + 196, + 499, + 206 + ], + "spans": [ + { + "bbox": [ + 107, + 196, + 499, + 206 + ], + "score": 1.0, + "content": "Mary Cunningham was the nurse on board who attended to the first sick passenger. \"There was a", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 126, + 205, + 489, + 214 + ], + "spans": [ + { + "bbox": [ + 126, + 205, + 489, + 214 + ], + "score": 1.0, + "content": "woman, very lethargic, very nauseous, turning gray, just not looking good,\" Cunningham", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 126, + 213, + 480, + 222 + ], + "spans": [ + { + "bbox": [ + 126, + 213, + 480, + 222 + ], + "score": 1.0, + "content": "said. After administering oxygen to the woman, Cunningham, a nurse at Yale-New Haven", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 126, + 221, + 476, + 230 + ], + "spans": [ + { + "bbox": [ + 126, + 221, + 476, + 230 + ], + "score": 1.0, + "content": "Hospital in Connecticut, returned to her seat. Soon after, Cunningham said, she was", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 126, + 229, + 485, + 237 + ], + "spans": [ + { + "bbox": [ + 126, + 229, + 485, + 237 + ], + "score": 1.0, + "content": "called up again by the flight attendant after another women near the first started to", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 126, + 237, + 497, + 246 + ], + "spans": [ + { + "bbox": [ + 126, + 237, + 497, + 246 + ], + "score": 1.0, + "content": "lose consciousness. \"It was something that was affecting oxygen in that area,\" which was", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 126, + 245, + 485, + 254 + ], + "spans": [ + { + "bbox": [ + 126, + 245, + 485, + 254 + ], + "score": 1.0, + "content": "near the middle of the plane, she said. Cunningham said she had to return to her seat", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 126, + 253, + 489, + 262 + ], + "spans": [ + { + "bbox": [ + 126, + 253, + 489, + 262 + ], + "score": 1.0, + "content": "after feeling lightheaded. There were 84 passengers on board the plane, including nine", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 126, + 261, + 474, + 270 + ], + "spans": [ + { + "bbox": [ + 126, + 261, + 474, + 270 + ], + "score": 1.0, + "content": "crew members. Flight 5622 was originally scheduled to fly from Chicago to Hartford,", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 126, + 269, + 481, + 277 + ], + "spans": [ + { + "bbox": [ + 126, + 269, + 481, + 277 + ], + "score": 1.0, + "content": "Connecticut. The plane descended 28,000 feet in three minutes. \"It would feel like a", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 126, + 276, + 489, + 285 + ], + "spans": [ + { + "bbox": [ + 126, + 276, + 489, + 285 + ], + "score": 1.0, + "content": "roller coaster -- when you’re coming over the top and you’re going down,\" CNN aviation", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 126, + 284, + 502, + 295 + ], + "spans": [ + { + "bbox": [ + 126, + 284, + 502, + 295 + ], + "score": 1.0, + "content": "analyst Mary Schiavo said, describing how such a descent would feel. \"You know that these", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 128, + 292, + 489, + 303 + ], + "spans": [ + { + "bbox": [ + 128, + 292, + 489, + 303 + ], + "score": 1.0, + "content": "pilots knew they were in a very grave and very serious situation.\" Johnson, flying to", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 126, + 300, + 485, + 309 + ], + "spans": [ + { + "bbox": [ + 126, + 300, + 485, + 309 + ], + "score": 1.0, + "content": "visit his parents with their only grandchild, was glad that roller coaster ride ended", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 126, + 308, + 488, + 318 + ], + "spans": [ + { + "bbox": [ + 126, + 308, + 488, + 318 + ], + "score": 1.0, + "content": "safely. \"It was a shaky ride. It wasn’t anything I would like to experience again,\" he", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 126, + 316, + 485, + 326 + ], + "spans": [ + { + "bbox": [ + 126, + 316, + 485, + 326 + ], + "score": 1.0, + "content": "said. CNN’s Jean Casarez, Josh Gaynor, Dana Ford and Stephanie Gallman contributed to", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 126, + 324, + 179, + 334 + ], + "spans": [ + { + "bbox": [ + 126, + 324, + 179, + 334 + ], + "score": 1.0, + "content": "this report.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 22 + }, + { + "type": "text", + "bbox": [ + 108, + 332, + 496, + 356 + ], + "lines": [ + { + "bbox": [ + 106, + 331, + 498, + 342 + ], + "spans": [ + { + "bbox": [ + 106, + 331, + 498, + 342 + ], + "score": 1.0, + "content": "Zero-Shot: \"you’re going to feel dizzy and woozy and lightheaded,\" Johnson says. \"it was like", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 126, + 339, + 493, + 350 + ], + "spans": [ + { + "bbox": [ + 126, + 339, + 493, + 350 + ], + "score": 1.0, + "content": "being trapped and you couldn’t do anything,\" Johnson says. \"the plane was trying to get", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 126, + 347, + 313, + 357 + ], + "spans": [ + { + "bbox": [ + 126, + 347, + 313, + 357 + ], + "score": 1.0, + "content": "back on the ground,\" passenger says of fear.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 32 + }, + { + "type": "text", + "bbox": [ + 108, + 357, + 493, + 372 + ], + "lines": [ + { + "bbox": [ + 106, + 356, + 495, + 366 + ], + "spans": [ + { + "bbox": [ + 106, + 356, + 495, + 366 + ], + "score": 1.0, + "content": "References: Three passengers report a loss of consciousness on SkyWest flight .But officials", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 125, + 363, + 355, + 373 + ], + "spans": [ + { + "bbox": [ + 125, + 363, + 355, + 373 + ], + "score": 1.0, + "content": "say there is no evidence of a pressurization problem .", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 34.5 + }, + { + "type": "text", + "bbox": [ + 107, + 372, + 500, + 396 + ], + "lines": [ + { + "bbox": [ + 106, + 372, + 486, + 380 + ], + "spans": [ + { + "bbox": [ + 106, + 372, + 486, + 380 + ], + "score": 1.0, + "content": "PPO: SkyWest flight 5312 made emergency landing in Buffalo, new york. passengers were told", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 126, + 380, + 501, + 390 + ], + "spans": [ + { + "bbox": [ + 126, + 380, + 501, + 390 + ], + "score": 1.0, + "content": "they were not going to be able to breathe, passenger recalls attendant. the faa initially", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 130, + 388, + 363, + 397 + ], + "spans": [ + { + "bbox": [ + 130, + 388, + 363, + 397 + ], + "score": 1.0, + "content": "reported a pressurization problem with the flight 5622.", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 37 + }, + { + "type": "text", + "bbox": [ + 107, + 396, + 497, + 420 + ], + "lines": [ + { + "bbox": [ + 105, + 394, + 478, + 405 + ], + "spans": [ + { + "bbox": [ + 105, + 394, + 478, + 405 + ], + "score": 1.0, + "content": "NLPO: SkyWest flight 5622 made emergency landing in buffalo, new york.Larry Johnson says", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 126, + 403, + 498, + 414 + ], + "spans": [ + { + "bbox": [ + 126, + 403, + 498, + 414 + ], + "score": 1.0, + "content": "flight attendant announced there was a pressurization problem. three passengers reported", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 127, + 412, + 421, + 421 + ], + "spans": [ + { + "bbox": [ + 127, + 412, + 421, + 421 + ], + "score": 1.0, + "content": "loss of consciousness while on flight; no one transported to hospital.", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 40 + }, + { + "type": "text", + "bbox": [ + 109, + 420, + 483, + 451 + ], + "lines": [ + { + "bbox": [ + 106, + 419, + 477, + 430 + ], + "spans": [ + { + "bbox": [ + 106, + 419, + 477, + 430 + ], + "score": 1.0, + "content": "Supervised: The FAA says it is investigating the cause of the emergency landing. SkyWest", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 125, + 427, + 485, + 437 + ], + "spans": [ + { + "bbox": [ + 125, + 427, + 485, + 437 + ], + "score": 1.0, + "content": "Flight 5622 made an emergency landing in Buffalo, New York. The flight was carrying a", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 126, + 435, + 477, + 444 + ], + "spans": [ + { + "bbox": [ + 126, + 435, + 477, + 444 + ], + "score": 1.0, + "content": "family of three people. The flight attendant told the passengers to prepare for the", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 126, + 442, + 162, + 453 + ], + "spans": [ + { + "bbox": [ + 126, + 442, + 162, + 453 + ], + "score": 1.0, + "content": "landing.", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 43.5 + }, + { + "type": "text", + "bbox": [ + 106, + 452, + 500, + 483 + ], + "lines": [ + { + "bbox": [ + 106, + 451, + 477, + 460 + ], + "spans": [ + { + "bbox": [ + 106, + 451, + 151, + 460 + ], + "score": 1.0, + "content": "Supervised", + "type": "text" + }, + { + "bbox": [ + 152, + 452, + 159, + 459 + ], + "score": 0.6, + "content": "^ +", + "type": "inline_equation" + }, + { + "bbox": [ + 159, + 451, + 477, + 460 + ], + "score": 1.0, + "content": "PPO: \"I thought we were done,\" the father of one passenger says. The flight", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 126, + 460, + 480, + 469 + ], + "spans": [ + { + "bbox": [ + 126, + 460, + 480, + 469 + ], + "score": 1.0, + "content": "attendant announced there was a pressurization problem. The flight made an emergency", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 125, + 466, + 498, + 477 + ], + "spans": [ + { + "bbox": [ + 125, + 466, + 498, + 477 + ], + "score": 1.0, + "content": "landing in Buffalo, New York. Three passengers reported a loss of consciousness while on", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 126, + 474, + 175, + 485 + ], + "spans": [ + { + "bbox": [ + 126, + 474, + 175, + 485 + ], + "score": 1.0, + "content": "the flight.", + "type": "text" + } + ], + "index": 49 + } + ], + "index": 47.5 + }, + { + "type": "text", + "bbox": [ + 107, + 484, + 498, + 515 + ], + "lines": [ + { + "bbox": [ + 106, + 483, + 498, + 493 + ], + "spans": [ + { + "bbox": [ + 106, + 483, + 152, + 493 + ], + "score": 1.0, + "content": "Supervised", + "type": "text" + }, + { + "bbox": [ + 152, + 484, + 159, + 491 + ], + "score": 0.45, + "content": "^ +", + "type": "inline_equation" + }, + { + "bbox": [ + 159, + 483, + 498, + 493 + ], + "score": 1.0, + "content": "NLPO: SkyWest Airlines flight made an emergency landing in Buffalo, New York, on", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 126, + 490, + 496, + 502 + ], + "spans": [ + { + "bbox": [ + 126, + 490, + 496, + 502 + ], + "score": 1.0, + "content": "Thursday. \"There was no doubt in my mind that we weren’t going to land,\" passenger says.", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 126, + 498, + 489, + 509 + ], + "spans": [ + { + "bbox": [ + 126, + 498, + 489, + 509 + ], + "score": 1.0, + "content": "\"You’re going to feel dizzy and woozy and lightheaded...you’re not going to be able to", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 126, + 507, + 208, + 516 + ], + "spans": [ + { + "bbox": [ + 126, + 507, + 208, + 516 + ], + "score": 1.0, + "content": "breathe,\" he says.\"", + "type": "text" + } + ], + "index": 53 + } + ], + "index": 51.5 + }, + { + "type": "title", + "bbox": [ + 107, + 524, + 141, + 532 + ], + "lines": [ + { + "bbox": [ + 105, + 522, + 144, + 533 + ], + "spans": [ + { + "bbox": [ + 105, + 522, + 144, + 533 + ], + "score": 1.0, + "content": "Sample 3", + "type": "text" + } + ], + "index": 54 + } + ], + "index": 54 + }, + { + "type": "text", + "bbox": [ + 117, + 532, + 504, + 731 + ], + "lines": [ + { + "bbox": [ + 115, + 531, + 497, + 542 + ], + "spans": [ + { + "bbox": [ + 115, + 531, + 497, + 542 + ], + "score": 1.0, + "content": "ompt: For Inverness the latest chapter in their remarkable story featured not one, but two,", + "type": "text" + } + ], + "index": 55 + }, + { + "bbox": [ + 125, + 539, + 473, + 549 + ], + "spans": [ + { + "bbox": [ + 125, + 539, + 473, + 549 + ], + "score": 1.0, + "content": "plot-changing twists. One featured penalty Celtic didn’t get for 2-0 in which Josh", + "type": "text" + } + ], + "index": 56 + }, + { + "bbox": [ + 126, + 547, + 504, + 557 + ], + "spans": [ + { + "bbox": [ + 126, + 547, + 504, + 557 + ], + "score": 1.0, + "content": "Meekings handball should have also led to a sending off. The other the spot kick they did,", + "type": "text" + } + ], + "index": 57 + }, + { + "bbox": [ + 129, + 555, + 469, + 565 + ], + "spans": [ + { + "bbox": [ + 129, + 555, + 469, + 565 + ], + "score": 1.0, + "content": "followed by a red card for Craig Gordon. ’I’ve not seen it yet, but going by the", + "type": "text" + } + ], + "index": 58 + }, + { + "bbox": [ + 126, + 563, + 498, + 574 + ], + "spans": [ + { + "bbox": [ + 126, + 563, + 498, + 574 + ], + "score": 1.0, + "content": "reaction of the Celtic players we got away with a penalty and a sending off and that was", + "type": "text" + } + ], + "index": 59 + }, + { + "bbox": [ + 125, + 571, + 489, + 582 + ], + "spans": [ + { + "bbox": [ + 125, + 571, + 489, + 582 + ], + "score": 1.0, + "content": "probably the turning point in the game,’ acknowledged Caley manager John Hughes after.", + "type": "text" + } + ], + "index": 60 + }, + { + "bbox": [ + 126, + 579, + 489, + 589 + ], + "spans": [ + { + "bbox": [ + 126, + 579, + 489, + 589 + ], + "score": 1.0, + "content": "Inverness’s Josh Meekings appears to get away with a handball on the line in their win", + "type": "text" + } + ], + "index": 61 + }, + { + "bbox": [ + 126, + 587, + 502, + 597 + ], + "spans": [ + { + "bbox": [ + 126, + 587, + 502, + 597 + ], + "score": 1.0, + "content": "over Celtic . Caley boss John Hughes says the break, which could have meant a penalty and", + "type": "text" + } + ], + "index": 62 + }, + { + "bbox": [ + 129, + 595, + 498, + 605 + ], + "spans": [ + { + "bbox": [ + 129, + 595, + 498, + 605 + ], + "score": 1.0, + "content": "red card, was a turning point . ’I’ve not spoken to Josh. I haven’t seen it - but going", + "type": "text" + } + ], + "index": 63 + }, + { + "bbox": [ + 125, + 603, + 489, + 613 + ], + "spans": [ + { + "bbox": [ + 125, + 603, + 489, + 613 + ], + "score": 1.0, + "content": "by the media it was definitely a hand ball. We look at the referee behind the line and", + "type": "text" + } + ], + "index": 64 + }, + { + "bbox": [ + 126, + 611, + 501, + 621 + ], + "spans": [ + { + "bbox": [ + 126, + 611, + 501, + 621 + ], + "score": 1.0, + "content": "all that and I know Ronny will feel aggrieved - because I certainly would. ’But it’s part", + "type": "text" + } + ], + "index": 65 + }, + { + "bbox": [ + 129, + 619, + 488, + 628 + ], + "spans": [ + { + "bbox": [ + 129, + 619, + 488, + 628 + ], + "score": 1.0, + "content": "and parcel of football and you need a wee bit of luck to beat Celtic. ’This was their", + "type": "text" + } + ], + "index": 66 + }, + { + "bbox": [ + 125, + 627, + 486, + 637 + ], + "spans": [ + { + "bbox": [ + 125, + 627, + 486, + 637 + ], + "score": 1.0, + "content": "biggest game of the season because they will go on and win the league and if they had", + "type": "text" + } + ], + "index": 67 + }, + { + "bbox": [ + 126, + 635, + 500, + 645 + ], + "spans": [ + { + "bbox": [ + 126, + 635, + 500, + 645 + ], + "score": 1.0, + "content": "beaten us today there was a good chance they would have gone on and won the Scottish Cup.", + "type": "text" + } + ], + "index": 68 + }, + { + "bbox": [ + 129, + 643, + 493, + 653 + ], + "spans": [ + { + "bbox": [ + 129, + 643, + 493, + 653 + ], + "score": 1.0, + "content": "’But when Marley Watkins was clipped by Craig Gordon and they were down to 10 men that", + "type": "text" + } + ], + "index": 69 + }, + { + "bbox": [ + 125, + 650, + 502, + 661 + ], + "spans": [ + { + "bbox": [ + 125, + 650, + 502, + 661 + ], + "score": 1.0, + "content": "was advantage Inverness. ’We weren’t going to give Celtic the ball back, they had to come", + "type": "text" + } + ], + "index": 70 + }, + { + "bbox": [ + 129, + 659, + 501, + 668 + ], + "spans": [ + { + "bbox": [ + 129, + 659, + 501, + 668 + ], + "score": 1.0, + "content": "and get it and we had to be patient. ’When big Edward put us into the lead we thought it", + "type": "text" + } + ], + "index": 71 + }, + { + "bbox": [ + 129, + 667, + 498, + 676 + ], + "spans": [ + { + "bbox": [ + 129, + 667, + 498, + 676 + ], + "score": 1.0, + "content": "was going to be our day on the back of things that had happened. ’Celtic equalised with", + "type": "text" + } + ], + "index": 72 + }, + { + "bbox": [ + 126, + 674, + 502, + 685 + ], + "spans": [ + { + "bbox": [ + 126, + 674, + 502, + 685 + ], + "score": 1.0, + "content": "another free kick but it’s typical of Inverness that we don’t do anything easy. ’We do it", + "type": "text" + } + ], + "index": 73 + }, + { + "bbox": [ + 129, + 684, + 492, + 693 + ], + "spans": [ + { + "bbox": [ + 129, + 684, + 492, + 693 + ], + "score": 1.0, + "content": "the hard way and we came up with the winner through David Raven.’ Hughes hauled Raven,", + "type": "text" + } + ], + "index": 74 + }, + { + "bbox": [ + 126, + 691, + 492, + 700 + ], + "spans": [ + { + "bbox": [ + 126, + 691, + 492, + 700 + ], + "score": 1.0, + "content": "his Scouse defender, from his backside as extra-time beckoned. Offended by the sight of", + "type": "text" + } + ], + "index": 75 + }, + { + "bbox": [ + 125, + 699, + 480, + 709 + ], + "spans": [ + { + "bbox": [ + 125, + 699, + 480, + 709 + ], + "score": 1.0, + "content": "one of his players resting he had a message to impart. Caley players celebrate after", + "type": "text" + } + ], + "index": 76 + }, + { + "bbox": [ + 126, + 707, + 488, + 717 + ], + "spans": [ + { + "bbox": [ + 126, + 707, + 488, + 717 + ], + "score": 1.0, + "content": "upsetting Celtic in a Scottish Cup semi-final 3-2 thriller . Celtic, depleted by games", + "type": "text" + } + ], + "index": 77 + }, + { + "bbox": [ + 126, + 715, + 480, + 725 + ], + "spans": [ + { + "bbox": [ + 126, + 715, + 480, + 725 + ], + "score": 1.0, + "content": "and absentees, were virtually on their knees after a relentless programme of midweek", + "type": "text" + } + ], + "index": 78 + }, + { + "bbox": [ + 125, + 723, + 501, + 732 + ], + "spans": [ + { + "bbox": [ + 125, + 723, + 501, + 732 + ], + "score": 1.0, + "content": "games. In last season’s League Cup Final Inverness had been passive and unambitious prior", + "type": "text" + } + ], + "index": 79 + } + ], + "index": 67 + } + ], + "page_idx": 40, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2023", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 752, + 310, + 760 + ], + "lines": [ + { + "bbox": [ + 298, + 750, + 312, + 764 + ], + "spans": [ + { + "bbox": [ + 298, + 750, + 312, + 764 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 14, + "width": 14 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 124, + 85, + 501, + 196 + ], + "lines": [], + "index": 6.5, + "bbox_fs": [ + 124, + 85, + 502, + 198 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 109, + 198, + 501, + 331 + ], + "lines": [ + { + "bbox": [ + 107, + 196, + 499, + 206 + ], + "spans": [ + { + "bbox": [ + 107, + 196, + 499, + 206 + ], + "score": 1.0, + "content": "Mary Cunningham was the nurse on board who attended to the first sick passenger. \"There was a", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 126, + 205, + 489, + 214 + ], + "spans": [ + { + "bbox": [ + 126, + 205, + 489, + 214 + ], + "score": 1.0, + "content": "woman, very lethargic, very nauseous, turning gray, just not looking good,\" Cunningham", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 126, + 213, + 480, + 222 + ], + "spans": [ + { + "bbox": [ + 126, + 213, + 480, + 222 + ], + "score": 1.0, + "content": "said. After administering oxygen to the woman, Cunningham, a nurse at Yale-New Haven", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 126, + 221, + 476, + 230 + ], + "spans": [ + { + "bbox": [ + 126, + 221, + 476, + 230 + ], + "score": 1.0, + "content": "Hospital in Connecticut, returned to her seat. Soon after, Cunningham said, she was", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 126, + 229, + 485, + 237 + ], + "spans": [ + { + "bbox": [ + 126, + 229, + 485, + 237 + ], + "score": 1.0, + "content": "called up again by the flight attendant after another women near the first started to", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 126, + 237, + 497, + 246 + ], + "spans": [ + { + "bbox": [ + 126, + 237, + 497, + 246 + ], + "score": 1.0, + "content": "lose consciousness. \"It was something that was affecting oxygen in that area,\" which was", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 126, + 245, + 485, + 254 + ], + "spans": [ + { + "bbox": [ + 126, + 245, + 485, + 254 + ], + "score": 1.0, + "content": "near the middle of the plane, she said. Cunningham said she had to return to her seat", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 126, + 253, + 489, + 262 + ], + "spans": [ + { + "bbox": [ + 126, + 253, + 489, + 262 + ], + "score": 1.0, + "content": "after feeling lightheaded. There were 84 passengers on board the plane, including nine", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 126, + 261, + 474, + 270 + ], + "spans": [ + { + "bbox": [ + 126, + 261, + 474, + 270 + ], + "score": 1.0, + "content": "crew members. Flight 5622 was originally scheduled to fly from Chicago to Hartford,", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 126, + 269, + 481, + 277 + ], + "spans": [ + { + "bbox": [ + 126, + 269, + 481, + 277 + ], + "score": 1.0, + "content": "Connecticut. The plane descended 28,000 feet in three minutes. \"It would feel like a", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 126, + 276, + 489, + 285 + ], + "spans": [ + { + "bbox": [ + 126, + 276, + 489, + 285 + ], + "score": 1.0, + "content": "roller coaster -- when you’re coming over the top and you’re going down,\" CNN aviation", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 126, + 284, + 502, + 295 + ], + "spans": [ + { + "bbox": [ + 126, + 284, + 502, + 295 + ], + "score": 1.0, + "content": "analyst Mary Schiavo said, describing how such a descent would feel. \"You know that these", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 128, + 292, + 489, + 303 + ], + "spans": [ + { + "bbox": [ + 128, + 292, + 489, + 303 + ], + "score": 1.0, + "content": "pilots knew they were in a very grave and very serious situation.\" Johnson, flying to", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 126, + 300, + 485, + 309 + ], + "spans": [ + { + "bbox": [ + 126, + 300, + 485, + 309 + ], + "score": 1.0, + "content": "visit his parents with their only grandchild, was glad that roller coaster ride ended", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 126, + 308, + 488, + 318 + ], + "spans": [ + { + "bbox": [ + 126, + 308, + 488, + 318 + ], + "score": 1.0, + "content": "safely. \"It was a shaky ride. It wasn’t anything I would like to experience again,\" he", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 126, + 316, + 485, + 326 + ], + "spans": [ + { + "bbox": [ + 126, + 316, + 485, + 326 + ], + "score": 1.0, + "content": "said. CNN’s Jean Casarez, Josh Gaynor, Dana Ford and Stephanie Gallman contributed to", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 126, + 324, + 179, + 334 + ], + "spans": [ + { + "bbox": [ + 126, + 324, + 179, + 334 + ], + "score": 1.0, + "content": "this report.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 22, + "bbox_fs": [ + 107, + 196, + 502, + 334 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 332, + 496, + 356 + ], + "lines": [ + { + "bbox": [ + 106, + 331, + 498, + 342 + ], + "spans": [ + { + "bbox": [ + 106, + 331, + 498, + 342 + ], + "score": 1.0, + "content": "Zero-Shot: \"you’re going to feel dizzy and woozy and lightheaded,\" Johnson says. \"it was like", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 126, + 339, + 493, + 350 + ], + "spans": [ + { + "bbox": [ + 126, + 339, + 493, + 350 + ], + "score": 1.0, + "content": "being trapped and you couldn’t do anything,\" Johnson says. \"the plane was trying to get", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 126, + 347, + 313, + 357 + ], + "spans": [ + { + "bbox": [ + 126, + 347, + 313, + 357 + ], + "score": 1.0, + "content": "back on the ground,\" passenger says of fear.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 32, + "bbox_fs": [ + 106, + 331, + 498, + 357 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 357, + 493, + 372 + ], + "lines": [ + { + "bbox": [ + 106, + 356, + 495, + 366 + ], + "spans": [ + { + "bbox": [ + 106, + 356, + 495, + 366 + ], + "score": 1.0, + "content": "References: Three passengers report a loss of consciousness on SkyWest flight .But officials", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 125, + 363, + 355, + 373 + ], + "spans": [ + { + "bbox": [ + 125, + 363, + 355, + 373 + ], + "score": 1.0, + "content": "say there is no evidence of a pressurization problem .", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 34.5, + "bbox_fs": [ + 106, + 356, + 495, + 373 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 372, + 500, + 396 + ], + "lines": [ + { + "bbox": [ + 106, + 372, + 486, + 380 + ], + "spans": [ + { + "bbox": [ + 106, + 372, + 486, + 380 + ], + "score": 1.0, + "content": "PPO: SkyWest flight 5312 made emergency landing in Buffalo, new york. passengers were told", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 126, + 380, + 501, + 390 + ], + "spans": [ + { + "bbox": [ + 126, + 380, + 501, + 390 + ], + "score": 1.0, + "content": "they were not going to be able to breathe, passenger recalls attendant. the faa initially", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 130, + 388, + 363, + 397 + ], + "spans": [ + { + "bbox": [ + 130, + 388, + 363, + 397 + ], + "score": 1.0, + "content": "reported a pressurization problem with the flight 5622.", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 37, + "bbox_fs": [ + 106, + 372, + 501, + 397 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 396, + 497, + 420 + ], + "lines": [ + { + "bbox": [ + 105, + 394, + 478, + 405 + ], + "spans": [ + { + "bbox": [ + 105, + 394, + 478, + 405 + ], + "score": 1.0, + "content": "NLPO: SkyWest flight 5622 made emergency landing in buffalo, new york.Larry Johnson says", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 126, + 403, + 498, + 414 + ], + "spans": [ + { + "bbox": [ + 126, + 403, + 498, + 414 + ], + "score": 1.0, + "content": "flight attendant announced there was a pressurization problem. three passengers reported", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 127, + 412, + 421, + 421 + ], + "spans": [ + { + "bbox": [ + 127, + 412, + 421, + 421 + ], + "score": 1.0, + "content": "loss of consciousness while on flight; no one transported to hospital.", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 40, + "bbox_fs": [ + 105, + 394, + 498, + 421 + ] + }, + { + "type": "text", + "bbox": [ + 109, + 420, + 483, + 451 + ], + "lines": [ + { + "bbox": [ + 106, + 419, + 477, + 430 + ], + "spans": [ + { + "bbox": [ + 106, + 419, + 477, + 430 + ], + "score": 1.0, + "content": "Supervised: The FAA says it is investigating the cause of the emergency landing. SkyWest", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 125, + 427, + 485, + 437 + ], + "spans": [ + { + "bbox": [ + 125, + 427, + 485, + 437 + ], + "score": 1.0, + "content": "Flight 5622 made an emergency landing in Buffalo, New York. The flight was carrying a", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 126, + 435, + 477, + 444 + ], + "spans": [ + { + "bbox": [ + 126, + 435, + 477, + 444 + ], + "score": 1.0, + "content": "family of three people. The flight attendant told the passengers to prepare for the", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 126, + 442, + 162, + 453 + ], + "spans": [ + { + "bbox": [ + 126, + 442, + 162, + 453 + ], + "score": 1.0, + "content": "landing.", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 43.5, + "bbox_fs": [ + 106, + 419, + 485, + 453 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 452, + 500, + 483 + ], + "lines": [ + { + "bbox": [ + 106, + 451, + 477, + 460 + ], + "spans": [ + { + "bbox": [ + 106, + 451, + 151, + 460 + ], + "score": 1.0, + "content": "Supervised", + "type": "text" + }, + { + "bbox": [ + 152, + 452, + 159, + 459 + ], + "score": 0.6, + "content": "^ +", + "type": "inline_equation" + }, + { + "bbox": [ + 159, + 451, + 477, + 460 + ], + "score": 1.0, + "content": "PPO: \"I thought we were done,\" the father of one passenger says. The flight", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 126, + 460, + 480, + 469 + ], + "spans": [ + { + "bbox": [ + 126, + 460, + 480, + 469 + ], + "score": 1.0, + "content": "attendant announced there was a pressurization problem. The flight made an emergency", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 125, + 466, + 498, + 477 + ], + "spans": [ + { + "bbox": [ + 125, + 466, + 498, + 477 + ], + "score": 1.0, + "content": "landing in Buffalo, New York. 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One featured penalty Celtic didn’t get for 2-0 in which Josh", + "type": "text" + } + ], + "index": 56 + }, + { + "bbox": [ + 126, + 547, + 504, + 557 + ], + "spans": [ + { + "bbox": [ + 126, + 547, + 504, + 557 + ], + "score": 1.0, + "content": "Meekings handball should have also led to a sending off. 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Model Paramsvalue
supervisedbatch size: 8 epochs: 4 learning rate: 0.0001 learning rate scheduler: constant with warm up weight decay: 0.1
ppo/nlposteps per update: 2560 total number of steps: 256000 batch size: 64 epochs per update: 5 learning rate: 0.000002 entropy coefficient: 0.0 initial kl coeff: 0.001 target kl: 2.0 discount factor: 0.99 gae lambda: 0.95 clip ratio: 0.2 rollouts top k : 0 value function coeff: 0.5 top mask ratio: 0.9 target update iterations: 20
batch size: 64 epochs per update: 5 learning rate: 0.0000005 entropy coefficient: 0.0 initial kl coeff: 0.01 target kl: 0.2 discount factor: 0.99 gae lambda: 0.95 clip ratio: 0.2 rollouts top k : 50
decodingtarget update iterations: 20 num beams: 5 min length: 10
tokenizermax new tokens: 50 padding side: left truncation side: right max length: 512
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Model Paramsvalue
supervisedbatch size: 8 epochs: 4 learning rate: 0.0001 learning rate scheduler: constant with warm up weight decay: 0.1
ppo/nlposteps per update: 2560 total number of steps: 256000 batch size: 64 epochs per update: 5 learning rate: 0.000002 entropy coefficient: 0.0 initial kl coeff: 0.001 target kl: 2.0 discount factor: 0.99 gae lambda: 0.95 clip ratio: 0.2 rollouts top k : 0 value function coeff: 0.5 top mask ratio: 0.9 target update iterations: 20
batch size: 64 epochs per update: 5 learning rate: 0.0000005 entropy coefficient: 0.0 initial kl coeff: 0.01 target kl: 0.2 discount factor: 0.99 gae lambda: 0.95 clip ratio: 0.2 rollouts top k : 50
decodingtarget update iterations: 20 num beams: 5 min length: 10
tokenizermax new tokens: 50 padding side: left truncation side: right max length: 512
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Similar to other tasks, our main finding is", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 586, + 505, + 600 + ], + "spans": [ + { + "bbox": [ + 105, + 586, + 505, + 600 + ], + "score": 1.0, + "content": "that warm-started initial policies are crucial for learning to generate descriptions from highlighted", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 597, + 505, + 610 + ], + "spans": [ + { + "bbox": [ + 105, + 597, + 505, + 610 + ], + "score": 1.0, + "content": "cells. Without warm-start, policies suffer from reward hacking and resulting in sub-optimal solutions", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 609, + 505, + 621 + ], + "spans": [ + { + "bbox": [ + 106, + 609, + 505, + 621 + ], + "score": 1.0, + "content": "despite application of task-specific metrics such as PARENT etc. We find that Supervised+NLPO", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 619, + 441, + 632 + ], + "spans": [ + { + "bbox": [ + 106, + 619, + 441, + 632 + ], + "score": 1.0, + "content": "method outperforms all models on ToTTo leaderboard in terms of PARENT metric.", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 35.5, + "bbox_fs": [ + 105, + 564, + 505, + 632 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 106, + 264, + 504, + 460 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 106, + 264, + 504, + 460 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 264, + 504, + 460 + ], + "spans": [ + { + "bbox": [ + 106, + 264, + 504, + 460 + ], + "score": 0.977, + "html": "
TasksAlgLMReward functionLexical and Semantic Metrics SacreBleuFactual Consistency PARENT
Zero-ShotT5OverallOverlapNon-OverlapOverallOverlapNon-OverlapOverallOverlapNon-Overlap
0.0360.0400.032-1.392-1.387-1.3970.1160.1190.112
PPOT5bleu0.0650.0670.063-1.074-1.045-1.0980.2460.2460.244
T5sacrebleu0.0860.0900.083-0.979-0.955-1.0030.2930.2920.294
T5meteor0.1440.1550.132-0.769-0.713-0.8260.3560.3610.351
T5parent0.1460.1530.128-0.721-0.688-0.7530.3360.3350.339
T5meteor + parent0.1610.1690.152-0.891-0.861-0.9220.3450.3420.348
NLPOT5bleu0.0620.0650.059-1.077-1.057-1.0970.2350.2360.233
T5sacrebleu0.0850.0880.083-0.945-0.917-0.9720.3140.3150.313
T5meteor0.1020.1080.097-1.044-1.009-1.0790.3290.3280.330
ToTToT5parent0.1590.1660.152-0.710-0.675-0.7450.3570.3510.363
T5meteor + parent0.1660.1750.158-0.704-0.668-0.7400.3650.3620.368
SupervisedT50.4570.5350.3770.2040.3270.0810.5830.6310.534
Supervised + PPOT5bleu0.4730.5480.3950.2000.3230.0780.5900.6380.542
T5sacrebleu0.4740.5570.3890.2090.3400.0770.5730.6200.525
T5meteor0.4680.5410.3920.2030.3250.0820.5900.6380.542
T5parent0.4690.5470.3880.1750.3000.0500.5950.6410.549
T5meteor + parent0.4730.5470.3920.1920.3140.0690.5950.6420.549
Supervised + NLPOT5bleu0.4750.5480.3990.2080.3300.0850.5930.6390.546
T5sacrebleu0.4750.5570.3920.2080.3350.0810.5770.6250.529
T5meteor0.4680.5410.3920.2010.3220.0790.5940.6410.546
T5parent0.4740.5500.3920.1920.3150.0680.5960.6430.550
T5meteor + parent0.4710.5460.3930.2040.3260.0810.5920.6400.544
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TasksAlgLMReward functionLexical and Semantic Metrics SacreBleuFactual Consistency PARENT
Zero-ShotT5OverallOverlapNon-OverlapOverallOverlapNon-OverlapOverallOverlapNon-Overlap
0.0360.0400.032-1.392-1.387-1.3970.1160.1190.112
PPOT5bleu0.0650.0670.063-1.074-1.045-1.0980.2460.2460.244
T5sacrebleu0.0860.0900.083-0.979-0.955-1.0030.2930.2920.294
T5meteor0.1440.1550.132-0.769-0.713-0.8260.3560.3610.351
T5parent0.1460.1530.128-0.721-0.688-0.7530.3360.3350.339
T5meteor + parent0.1610.1690.152-0.891-0.861-0.9220.3450.3420.348
NLPOT5bleu0.0620.0650.059-1.077-1.057-1.0970.2350.2360.233
T5sacrebleu0.0850.0880.083-0.945-0.917-0.9720.3140.3150.313
T5meteor0.1020.1080.097-1.044-1.009-1.0790.3290.3280.330
ToTToT5parent0.1590.1660.152-0.710-0.675-0.7450.3570.3510.363
T5meteor + parent0.1660.1750.158-0.704-0.668-0.7400.3650.3620.368
SupervisedT50.4570.5350.3770.2040.3270.0810.5830.6310.534
Supervised + PPOT5bleu0.4730.5480.3950.2000.3230.0780.5900.6380.542
T5sacrebleu0.4740.5570.3890.2090.3400.0770.5730.6200.525
T5meteor0.4680.5410.3920.2030.3250.0820.5900.6380.542
T5parent0.4690.5470.3880.1750.3000.0500.5950.6410.549
T5meteor + parent0.4730.5470.3920.1920.3140.0690.5950.6420.549
Supervised + NLPOT5bleu0.4750.5480.3990.2080.3300.0850.5930.6390.546
T5sacrebleu0.4750.5570.3920.2080.3350.0810.5770.6250.529
T5meteor0.4680.5410.3920.2010.3220.0790.5940.6410.546
T5parent0.4740.5500.3920.1920.3150.0680.5960.6430.550
T5meteor + parent0.4710.5460.3930.2040.3260.0810.5920.6400.544
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TasksAlgLM Reward functionRouge-1Rouge-2Rouge-LRouge-LSumMeteorBertScoreLexical and Semantic MetricsSacreBleuFactual Consistency PARENTDiversity Metrics
OverallOverlapNon-OverlapOverallOverlapNon-OverlapMSTTRDistinct1DistinctzHHUnique1Unique2Mean Output Length
Zero-ShotT50.1310.0550.1270.1270.0570.8050.0380.0420.0340.2386.7039.9338387
SupervisedT50.4100.2790.3880.3880.2230.9530.4580.3870.118 0.5860.119 0.6330.116 0.5400.428 0.7150.084 0.1620.5119.99514.4681516826490 5470619.964 17.791
PPObleu8740.138 0.1660.249 0.3000.249 0.3000.139 0.1650.844 0.85800680.0660.251 0.3000.250 0.2990.251 0.300800.091 0.1210.0810.659 11.07114.511 14.8807536 1013834232 4819528545
sacrebleu0.3220.1570.2860.2860.1730.8880.094 0.1470.086 0.1330.3580.3670.3500.6250.1360.48210.18914.910123465492521.484
meteor parent0.2680.1250.2510.2510.1190.8900.163 0.150 0.1580.1430.3370.3320.3420.7640.2020.64611.06814.988130683031313.035
meteor + parent0.2660.1280.2510.2510.1300.8860.165 0.1750.1550.3480.3460.3500.7020.1810.59410.09614.4321442215.354
NLPObleu0.2670.1340.240.240.1370.840.068 0.071 0.0890.0650.2380.2390.2370.4480.10.35911.25914.6239424720928.472
ToTTosacrebleu0.1680.297 0.2860.297 0.2860.1830.863 0.8880.093 0.1470.0850.320.3240.3170.494 0.6250.1110.37311.00715.03243379 5921.484
meteor parent120.2640.26400.8940.163 0.163 0.174 0.17100.358 0.360.367 0.3570.350 0.3640.824030.482 0.69110.189 11.49314.910 15.1271234614.204
meteor + parent0.2990.140.2760.2760.1420.8960.1810.1610.3690.3650.3720.7790.2140.67411.07215.275149395873715.141
Supervised + PPObleu0.4080.2830.3880.3880.2220.9540.5490.4050.5960.6440.5500.7220.1670.52510.08014.524152035472417.296
sacrebleu0.3950380.37880.9550.554 0.54088700.53587810.53910.08614.518148465232716.063
meteor0.410 0.4010.3890.954 0.9538477 0.5430.3940.5980.6470.547 0.5500.516 0.54510.037 10.20914.467 14.66015182.0 15379.054446 5542117.542
parent meteor + parent0.4060.2818830.95447 0.5440.3990.6000.6480.553878170.53210.14314.586153305521118
Supervised + NLPO0.4100.2830.3880.388830.9540.476 0.4770.644858720.1670.52410.07714.532152135494817.408
bleu sacrebleu0.3970.2760.380.380.9550010570.6280.1740.5410.12414.544149405298616.334
meteor0.4110.2830.3890.390.2240.9540.5470.4030.60.6490.5540.7270.1710.53610.15614.612153415529217.637
parent888.86038681909540.474 854708080.64585520.7160.16503110.019 10.15614.5 14.612153483479317093
T meteor + parent0.40504640.646
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TasksAlgLM Reward functionRouge-1Rouge-2Rouge-LRouge-LSumMeteorBertScoreLexical and Semantic MetricsSacreBleuFactual Consistency PARENTDiversity Metrics
OverallOverlapNon-OverlapOverallOverlapNon-OverlapMSTTRDistinct1DistinctzHHUnique1Unique2Mean Output Length
Zero-ShotT50.1310.0550.1270.1270.0570.8050.0380.0420.0340.2386.7039.9338387
SupervisedT50.4100.2790.3880.3880.2230.9530.4580.3870.118 0.5860.119 0.6330.116 0.5400.428 0.7150.084 0.1620.5119.99514.4681516826490 5470619.964 17.791
PPObleu8740.138 0.1660.249 0.3000.249 0.3000.139 0.1650.844 0.85800680.0660.251 0.3000.250 0.2990.251 0.300800.091 0.1210.0810.659 11.07114.511 14.8807536 1013834232 4819528545
sacrebleu0.3220.1570.2860.2860.1730.8880.094 0.1470.086 0.1330.3580.3670.3500.6250.1360.48210.18914.910123465492521.484
meteor parent0.2680.1250.2510.2510.1190.8900.163 0.150 0.1580.1430.3370.3320.3420.7640.2020.64611.06814.988130683031313.035
meteor + parent0.2660.1280.2510.2510.1300.8860.165 0.1750.1550.3480.3460.3500.7020.1810.59410.09614.4321442215.354
NLPObleu0.2670.1340.240.240.1370.840.068 0.071 0.0890.0650.2380.2390.2370.4480.10.35911.25914.6239424720928.472
ToTTosacrebleu0.1680.297 0.2860.297 0.2860.1830.863 0.8880.093 0.1470.0850.320.3240.3170.494 0.6250.1110.37311.00715.03243379 5921.484
meteor parent120.2640.26400.8940.163 0.163 0.174 0.17100.358 0.360.367 0.3570.350 0.3640.824030.482 0.69110.189 11.49314.910 15.1271234614.204
meteor + parent0.2990.140.2760.2760.1420.8960.1810.1610.3690.3650.3720.7790.2140.67411.07215.275149395873715.141
Supervised + PPObleu0.4080.2830.3880.3880.2220.9540.5490.4050.5960.6440.5500.7220.1670.52510.08014.524152035472417.296
sacrebleu0.3950380.37880.9550.554 0.54088700.53587810.53910.08614.518148465232716.063
meteor0.410 0.4010.3890.954 0.9538477 0.5430.3940.5980.6470.547 0.5500.516 0.54510.037 10.20914.467 14.66015182.0 15379.054446 5542117.542
parent meteor + parent0.4060.2818830.95447 0.5440.3990.6000.6480.553878170.53210.14314.586153305521118
Supervised + NLPO0.4100.2830.3880.388830.9540.476 0.4770.644858720.1670.52410.07714.532152135494817.408
bleu sacrebleu0.3970.2760.380.380.9550010570.6280.1740.5410.12414.544149405298616.334
meteor0.4110.2830.3890.390.2240.9540.5470.4030.60.6490.5540.7270.1710.53610.15614.612153415529217.637
parent888.86038681909540.474 854708080.64585520.7160.16503110.019 10.15614.5 14.612153483479317093
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AlgorithmUnique NCoherenceCorrectness
ValueAlphaSkewValueAlphaSkew
Zero Shot251.630.7181.6421.930.5031.946
PPO+Supervised4.570.2214.5794.480.0984.483
PPO2420282.750.4272.7533.230.2143.227
NLPO2.250.4012.2472.610.4192.613
Supervised244.590.1734.5924.540.1894.537
NLPO+Supervised264.580.2444.6014.570.1444.581
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Group 1Group 2CoherenceCorrectness
Diff (G2-G1)p-valuesDiff (G2-G1)p-values
PPONLPO-0.5070.001-0.6130.001
PPONLPO+Supervised1.8270.0011.3400.001
PPOSupervised1.8330.0011.3130.001
PPOPPO+Supervised1.8130.0011.2530.001
PPOZero Shot-1.1200.001-1.2930.001
NLPONLPO+Supervised2.3330.0011.9530.001
NLPOSupervised2.3400.0011.9270.001
NLPOPPO+Supervised2.3200.0011.8670.001
NLPOZero Shot-0.6130.001-0.6800.001
NLPO+SupervisedSupervised0.0070.9-0.0270.009
NLPO+SupervisedPPO+Supervised-0.0130.009-0.0870.009
NLPO+SupervisedZero Shot-2.9470.001-2.6330.001
SupervisedPPO+Supervised-0.0200.009-0.0600.009
SupervisedZero Shot-2.9530.001-2.6070.001
PPO+SupervisedZero Shot-2.9330.001-2.5470.001
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AlgorithmUnique NCoherenceCorrectness
ValueAlphaSkewValueAlphaSkew
Zero Shot251.630.7181.6421.930.5031.946
PPO+Supervised4.570.2214.5794.480.0984.483
PPO2420282.750.4272.7533.230.2143.227
NLPO2.250.4012.2472.610.4192.613
Supervised244.590.1734.5924.540.1894.537
NLPO+Supervised264.580.2444.6014.570.1444.581
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Group 1Group 2CoherenceCorrectness
Diff (G2-G1)p-valuesDiff (G2-G1)p-values
PPONLPO-0.5070.001-0.6130.001
PPONLPO+Supervised1.8270.0011.3400.001
PPOSupervised1.8330.0011.3130.001
PPOPPO+Supervised1.8130.0011.2530.001
PPOZero Shot-1.1200.001-1.2930.001
NLPONLPO+Supervised2.3330.0011.9530.001
NLPOSupervised2.3400.0011.9270.001
NLPOPPO+Supervised2.3200.0011.8670.001
NLPOZero Shot-0.6130.001-0.6800.001
NLPO+SupervisedSupervised0.0070.9-0.0270.009
NLPO+SupervisedPPO+Supervised-0.0130.009-0.0870.009
NLPO+SupervisedZero Shot-2.9470.001-2.6330.001
SupervisedPPO+Supervised-0.0200.009-0.0600.009
SupervisedZero Shot-2.9530.001-2.6070.001
PPO+SupervisedZero Shot-2.9330.001-2.5470.001
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Overall", + "type": "text" + }, + { + "bbox": [ + 370, + 630, + 376, + 639 + ], + "score": 0.79, + "content": "p", + "type": "inline_equation" + }, + { + "bbox": [ + 377, + 626, + 506, + 640 + ], + "score": 1.0, + "content": "-values showing that there is a", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 638, + 506, + 651 + ], + "spans": [ + { + "bbox": [ + 105, + 638, + 506, + 651 + ], + "score": 1.0, + "content": "significant difference in means between the models via a one-way ANOVA test are significant with", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 649, + 285, + 662 + ], + "spans": [ + { + "bbox": [ + 106, + 650, + 146, + 661 + ], + "score": 0.88, + "content": "p \\ll 0 . 0 5", + "type": "inline_equation" + }, + { + "bbox": [ + 146, + 649, + 285, + 662 + ], + "score": 1.0, + "content": "for both coherence and sentiment.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 12, + "bbox_fs": [ + 105, + 605, + 506, + 662 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 133, + 86, + 188, + 92 + ], + "lines": [ + { + "bbox": [ + 133, + 86, + 188, + 92 + ], + "spans": [], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 132, + 102, + 247, + 108 + ], + "lines": [ + { + "bbox": [ + 131, + 102, + 247, + 108 + ], + "spans": [ + { + "bbox": [ + 131, + 102, + 247, + 108 + ], + "score": 0.964, + "content": "Thank you for your particlpatlon In thls and other similar HITS!", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 1 + }, + { + "type": "text", + "bbox": [ + 131, + 112, + 283, + 124 + ], + "lines": [ + { + "bbox": [ + 130, + 111, + 267, + 119 + ], + "spans": [ + { + "bbox": [ + 130, + 111, + 267, + 119 + ], + "score": 0.949, + "content": "Please take a moment to familiarize yourself with this new HIT by reading the", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 130, + 118, + 284, + 124 + ], + "spans": [ + { + "bbox": [ + 130, + 118, + 284, + 124 + ], + "score": 0.972, + "content": "instructions/examples, because things have changed α bit. Thanks agaln for your work", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 2.5 + }, + { + "type": "text", + "bbox": [ + 130, + 128, + 297, + 157 + ], + "lines": [ + { + "bbox": [ + 130, + 128, + 294, + 134 + ], + "spans": [ + { + "bbox": [ + 130, + 128, + 294, + 134 + ], + "score": 0.985, + "content": " In this HIT you willbe presented with a table from Wikipedia, with a few cells highlighted", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 131, + 134, + 291, + 139 + ], + "spans": [ + { + "bbox": [ + 131, + 134, + 291, + 139 + ], + "score": 0.989, + "content": " in yellow. Along with the table, you will be provided some metadata like the title of the", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 130, + 139, + 295, + 146 + ], + "spans": [ + { + "bbox": [ + 130, + 139, + 295, + 146 + ], + "score": 0.992, + "content": "Wikipedia article/section. Based on this table, you willalso be given a system generation,", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 129, + 145, + 298, + 152 + ], + "spans": [ + { + "bbox": [ + 129, + 145, + 298, + 152 + ], + "score": 0.992, + "content": "which aims to capture/summarize/describe the Your job is to rate the generation across 2", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 130, + 152, + 142, + 158 + ], + "spans": [ + { + "bbox": [ + 130, + 152, + 142, + 158 + ], + "score": 0.987, + "content": "axes:", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 6 + }, + { + "type": "text", + "bbox": [ + 134, + 162, + 294, + 185 + ], + "lines": [ + { + "bbox": [ + 137, + 161, + 294, + 168 + ], + "spans": [ + { + "bbox": [ + 137, + 161, + 294, + 168 + ], + "score": 0.974, + "content": "·Fluency/Grammaticality: Is the system's generation grammatical,easy-to-read,and", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 140, + 167, + 155, + 174 + ], + "spans": [ + { + "bbox": [ + 140, + 167, + 155, + 174 + ], + "score": 0.976, + "content": "fluent?", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 139, + 172, + 294, + 180 + ], + "spans": [ + { + "bbox": [ + 139, + 172, + 294, + 180 + ], + "score": 0.946, + "content": "Correctness/Specificity: Does the generation correctlydescribeafact fromthe table", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 140, + 179, + 232, + 186 + ], + "spans": [ + { + "bbox": [ + 140, + 179, + 232, + 186 + ], + "score": 0.973, + "content": "and does that fact come from the highlighted cells?", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 10.5 + }, + { + "type": "text", + "bbox": [ + 132, + 189, + 289, + 201 + ], + "lines": [ + { + "bbox": [ + 131, + 189, + 289, + 196 + ], + "spans": [ + { + "bbox": [ + 131, + 189, + 289, + 196 + ], + "score": 0.986, + "content": "You will be able to rate each of the three axes on a scale from 1 to 5, with 1 belng the", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 13 + }, + { + "type": "title", + "bbox": [ + 135, + 205, + 190, + 210 + ], + "lines": [ + { + "bbox": [ + 135, + 204, + 192, + 212 + ], + "spans": [ + { + "bbox": [ + 135, + 204, + 192, + 212 + ], + "score": 0.965, + "content": "· Fluency/Grammaticality:", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 14 + }, + { + "type": "text", + "bbox": [ + 145, + 212, + 295, + 264 + ], + "lines": [ + { + "bbox": [ + 145, + 211, + 259, + 217 + ], + "spans": [ + { + "bbox": [ + 145, + 211, + 259, + 217 + ], + "score": 0.989, + "content": "○5/5 (excellent): The generation is grammatical and fluent.", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 145, + 216, + 284, + 223 + ], + "spans": [ + { + "bbox": [ + 145, + 216, + 284, + 223 + ], + "score": 0.977, + "content": "o4/5 (good): The sentence largely makes sense, but there are some small", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 149, + 222, + 285, + 230 + ], + "spans": [ + { + "bbox": [ + 149, + 222, + 285, + 230 + ], + "score": 0.994, + "content": "grammar Issues/out-of-place words that don't make for the best writing.", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 146, + 229, + 285, + 235 + ], + "spans": [ + { + "bbox": [ + 146, + 229, + 285, + 235 + ], + "score": 0.976, + "content": "○3/5 (okay): The grammar Is okay and it’s possible to read, but it definitely", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 150, + 235, + 219, + 240 + ], + "spans": [ + { + "bbox": [ + 150, + 235, + 219, + 240 + ], + "score": 0.971, + "content": "doesn't sound like a human wrote it.", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 145, + 240, + 294, + 246 + ], + "spans": [ + { + "bbox": [ + 145, + 240, + 294, + 246 + ], + "score": 0.967, + "content": "○ 2/5 (poor): Even though I can kind-of tell the meaning, it's dificult to read this", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 150, + 246, + 189, + 252 + ], + "spans": [ + { + "bbox": [ + 150, + 246, + 189, + 252 + ], + "score": 0.993, + "content": "unnatural sentence.", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 146, + 252, + 296, + 259 + ], + "spans": [ + { + "bbox": [ + 146, + 252, + 296, + 259 + ], + "score": 0.986, + "content": "○ 1/5 (terrible): The generation has severe errors in grammaticality/is almost or", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 150, + 258, + 195, + 265 + ], + "spans": [ + { + "bbox": [ + 150, + 258, + 195, + 265 + ], + "score": 0.982, + "content": "completely unreadable.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 19 + }, + { + "type": "title", + "bbox": [ + 135, + 269, + 188, + 274 + ], + "lines": [ + { + "bbox": [ + 135, + 267, + 189, + 275 + ], + "spans": [ + { + "bbox": [ + 135, + 268, + 140, + 273 + ], + "score": 0.28, + "content": "\\cdot", + "type": "inline_equation" + }, + { + "bbox": [ + 140, + 267, + 189, + 275 + ], + "score": 0.993, + "content": "Correctness/Specificity:", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 24 + }, + { + "type": "text", + "bbox": [ + 145, + 275, + 293, + 334 + ], + "lines": [ + { + "bbox": [ + 145, + 273, + 292, + 281 + ], + "spans": [ + { + "bbox": [ + 145, + 273, + 292, + 281 + ], + "score": 0.974, + "content": "○5/5 (correct and based on the highlighted cells): The generation correctly", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 150, + 280, + 261, + 286 + ], + "spans": [ + { + "bbox": [ + 150, + 280, + 261, + 286 + ], + "score": 0.995, + "content": "describes the information conveyed in the highlighted cells.", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 147, + 286, + 292, + 293 + ], + "spans": [ + { + "bbox": [ + 147, + 286, + 292, + 293 + ], + "score": 0.977, + "content": "o4/5(mostly reasonable): The generation mostly describes the Information in", + "type": "text" + } + ], + "index": 27 + }, + 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"Notes:", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 35 + }, + { + "type": "text", + "bbox": [ + 134, + 350, + 294, + 415 + ], + "lines": [ + { + "bbox": [ + 140, + 349, + 295, + 356 + ], + "spans": [ + { + "bbox": [ + 140, + 349, + 295, + 356 + ], + "score": 0.987, + "content": "For Fluency/Grammaticality_don't worry about correctness! There can be grammatical", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 140, + 355, + 281, + 362 + ], + "spans": [ + { + "bbox": [ + 140, + 355, + 281, + 362 + ], + "score": 0.985, + "content": " sentences that do not describe the assoclated table, and vice versa (see the", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 140, + 361, + 162, + 368 + ], + "spans": [ + { + "bbox": [ + 140, + 361, + 162, + 368 + ], + "score": 0.978, + "content": "examples).", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 140, + 367, + 288, + 374 + ], + "spans": [ + { + "bbox": [ + 140, + 367, + 288, + 374 + ], + "score": 0.972, + "content": "For Correctness/Specificity, consider both the correctness of the statement given the", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 140, + 373, + 290, + 380 + ], + "spans": [ + { + "bbox": [ + 140, + 373, + 290, + 380 + ], + "score": 0.976, + "content": "table,and also its specificity to the highlighted cels: don't give 5/5 if the generation", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 140, + 379, + 210, + 386 + ], + "spans": [ + { + "bbox": [ + 140, + 379, + 210, + 386 + ], + "score": 0.98, + "content": "applies better to unhighlighted cells.", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 140, + 385, + 291, + 392 + ], + "spans": [ + { + "bbox": [ + 140, + 385, + 291, + 392 + ], + "score": 0.963, + "content": "For Correctness/Specificity.it's okayifthe generation references the metadata like the", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 139, + 390, + 294, + 398 + ], + "spans": [ + { + "bbox": [ + 139, + 390, + 294, + 398 + ], + "score": 0.957, + "content": "title- polnts should be deducted for \"specificity\"Ifthere are other table cels that", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 140, + 397, + 196, + 403 + ], + "spans": [ + { + "bbox": [ + 140, + 397, + 196, + 403 + ], + "score": 0.987, + "content": "are referenced more dlrectly.", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 136, + 403, + 290, + 410 + ], + "spans": [ + { + "bbox": [ + 136, + 403, + 290, + 410 + ], + "score": 0.968, + "content": "•A handful oftables are quite largel Stillapply the same rating criterla, even if the", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 140, + 409, + 186, + 415 + ], + "spans": [ + { + "bbox": [ + 140, + 409, + 186, + 415 + ], + "score": 0.998, + "content": "tables have many rows.", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 41 + }, + { + "type": "table", + "bbox": [ + 324, + 206, + 469, + 356 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 315, + 187, + 365, + 203 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 314, + 186, + 351, + 196 + ], + "spans": [ + { + "bbox": [ + 314, + 186, + 351, + 196 + ], + "score": 0.994, + "content": "Example 2:", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 313, + 194, + 366, + 204 + ], + "spans": [ + { + "bbox": [ + 313, + 194, + 366, + 204 + ], + "score": 0.998, + "content": "Table from Wikipedia:", + "type": "text" + } + ], + "index": 48 + } + ], + "index": 47.5 + }, + { + "type": "table_body", + "bbox": [ + 324, + 206, + 469, + 356 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 324, + 206, + 469, + 356 + ], + "spans": [ + { + "bbox": [ + 324, + 206, + 469, + 356 + ], + "score": 0.693, + "html": "
Gerard Piqué Section Title: International goals
Table Section Text: None No. DateVenue SantiagoCapOpponentScore Result Competition
28 March 1 2009Bernabeu Stadium, Madrid, Spain'2Turkey1-01-02010 FIFA World Cup qualification
2 12 August 2009MacedoniaPhilip I Skopje, Arena,8North Macedonia2-23-2Friendly
5 3 September 2009Estadio Riazor, A Corufia, Spain9Belgium3-05-02010 FIFA World Cup qualification
14 4 October 2009HerzegovinaBilino Polje, Zenica, Bosnia and12Bosnia and Herzegovina1-05-2
513 June 2016Stadium Municipal, Toulouse, France78Czech Republic1-01-0UEFA Euro 2016
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Tables 25, 26 show averaged results, annotator agreement, and the results", + "type": "text" + } + ], + "index": 66 + }, + { + "bbox": [ + 105, + 707, + 505, + 721 + ], + "spans": [ + { + "bbox": [ + 105, + 707, + 505, + 721 + ], + "score": 1.0, + "content": "of statistical significance tests to determine which models output better generations when rated by", + "type": "text" + } + ], + "index": 67 + }, + { + "bbox": [ + 105, + 718, + 142, + 731 + ], + "spans": [ + { + "bbox": [ + 105, + 718, + 142, + 731 + ], + "score": 1.0, + "content": "humans.", + "type": "text" + } + ], + "index": 68 + } + ], + "index": 66 + } + ], + "page_idx": 46, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2023", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 751, + 310, + 759 + ], + "lines": [ + { + "bbox": [ + 298, + 750, + 312, + 763 + ], + "spans": [ + { + "bbox": [ + 298, + 750, + 312, + 763 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 13, + "width": 14 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 133, + 86, + 188, + 92 + ], + "lines": [ + { + "bbox": [ + 133, + 86, + 188, + 92 + ], + "spans": [], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 132, + 102, + 247, + 108 + ], + "lines": [ + { + "bbox": [ + 131, + 102, + 247, + 108 + ], + "spans": [ + { + "bbox": [ + 131, + 102, + 247, + 108 + ], + "score": 0.964, + "content": "Thank you for your particlpatlon In thls and other similar HITS!", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 1, + "bbox_fs": [ + 131, + 102, + 247, + 108 + ] + }, + { + "type": "text", + "bbox": [ + 131, + 112, + 283, + 124 + ], + "lines": [ + { + "bbox": [ + 130, + 111, + 267, + 119 + ], + "spans": [ + { + "bbox": [ + 130, + 111, + 267, + 119 + ], + "score": 0.949, + "content": "Please take a moment to familiarize yourself with this new HIT by reading the", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 130, + 118, + 284, + 124 + ], + "spans": [ + { + "bbox": [ + 130, + 118, + 284, + 124 + ], + "score": 0.972, + "content": "instructions/examples, because things have changed α bit. Thanks agaln for your work", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 130, + 128, + 294, + 134 + ], + "spans": [ + { + "bbox": [ + 130, + 128, + 294, + 134 + ], + "score": 0.985, + "content": " In this HIT you willbe presented with a table from Wikipedia, with a few cells highlighted", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 131, + 134, + 291, + 139 + ], + "spans": [ + { + "bbox": [ + 131, + 134, + 291, + 139 + ], + "score": 0.989, + "content": " in yellow. Along with the table, you will be provided some metadata like the title of the", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 130, + 139, + 295, + 146 + ], + "spans": [ + { + "bbox": [ + 130, + 139, + 295, + 146 + ], + "score": 0.992, + "content": "Wikipedia article/section. 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"score": 0.994, + "content": "the highlighted cells with only small deviations.", + "type": "text" + } + ], + "index": 28, + "is_list_end_line": true + }, + { + "bbox": [ + 147, + 298, + 290, + 305 + ], + "spans": [ + { + "bbox": [ + 147, + 298, + 290, + 305 + ], + "score": 0.982, + "content": "03/5 (neutral): The generation Is somewhat plausible/relevant, butit's not as", + "type": "text" + } + ], + "index": 29, + "is_list_start_line": true + }, + { + "bbox": [ + 150, + 304, + 254, + 310 + ], + "spans": [ + { + "bbox": [ + 150, + 304, + 254, + 310 + ], + "score": 0.974, + "content": " specific to the hlghlighted cells or correct as It could be.", + "type": "text" + } + ], + "index": 30, + "is_list_end_line": true + }, + { + "bbox": [ + 149, + 310, + 281, + 316 + ], + "spans": [ + { + "bbox": [ + 149, + 310, + 281, + 316 + ], + "score": 0.978, + "content": "2/5 (mostly unreasonable): I see why this could be generated given the", + "type": "text" + } + ], + "index": 31, + 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Gerard Piqué Section Title: International goals
Table Section Text: None No. DateVenue SantiagoCapOpponentScore Result Competition
28 March 1 2009Bernabeu Stadium, Madrid, Spain'2Turkey1-01-02010 FIFA World Cup qualification
2 12 August 2009MacedoniaPhilip I Skopje, Arena,8North Macedonia2-23-2Friendly
5 3 September 2009Estadio Riazor, A Corufia, Spain9Belgium3-05-02010 FIFA World Cup qualification
14 4 October 2009HerzegovinaBilino Polje, Zenica, Bosnia and12Bosnia and Herzegovina1-05-2
513 June 2016Stadium Municipal, Toulouse, France78Czech Republic1-01-0UEFA Euro 2016
", + "type": "table", + "image_path": "b4e26a630bab0a65a0f9ccf9c2d551d6935e314e36036d9f4a19465ac760f2c4.jpg" + } + ] + } + ], + "index": 49.5, + "virtual_lines": [ + { + "bbox": [ + 324, + 206, + 469, + 281.0 + ], + "spans": [], + "index": 49 + }, + { + "bbox": [ + 324, + 281.0, + 469, + 356.0 + ], + "spans": [], + "index": 50 + } + ] + } + ], + "index": 48.5 + }, + { + "type": "text", + "bbox": [ + 315, + 360, + 387, + 366 + ], + "lines": [ + { + "bbox": [ + 314, + 360, + 387, + 367 + ], + "spans": [ + { + "bbox": [ + 314, + 360, + 387, + 367 + ], + "score": 0.978, + "content": "System's generation (rate this!):", + "type": "text" + } + ], + "index": 51 + } + ], + "index": 51, + "bbox_fs": [ + 314, + 360, + 387, + 367 + ] + }, + { + "type": "text", + "bbox": [ + 327, + 374, + 429, + 379 + ], + "lines": [ + { + "bbox": [ + 326, + 374, + 429, + 380 + ], + "spans": [ + { + "bbox": [ + 326, + 374, + 429, + 380 + ], + "score": 0.979, + "content": "Plqué scored an Internatlonal goal at Stadlum Munlcipal.", + "type": "text" + } + ], + "index": 52 + } + ], + "index": 52, + "bbox_fs": [ + 326, + 374, + 429, + 380 + ] + }, + { + "type": "text", + "bbox": [ + 319, + 387, + 476, + 416 + ], + "lines": [ + { + "bbox": [ + 324, + 392, + 474, + 399 + ], + "spans": [ + { + "bbox": [ + 324, + 392, + 474, + 399 + ], + "score": 0.962, + "content": "the term \"International goal\" Is a bIt awkward -- \"a goal on the International stage\"", + "type": "text" + } + ], + "index": 53 + }, + { + "bbox": [ + 324, + 399, + 370, + 404 + ], + "spans": [ + { + "bbox": [ + 324, + 399, + 370, + 404 + ], + "score": 0.991, + "content": "would have been better.", + "type": "text" + } + ], + "index": 54 + }, + { + "bbox": [ + 320, + 405, + 477, + 410 + ], + "spans": [ + { + "bbox": [ + 320, + 405, + 477, + 410 + ], + "score": 0.981, + "content": "·Correctness/Specificity: 3/5 Why?It mlght be correct, but the focus of the sentence", + "type": "text" + } + ], + "index": 55 + }, + { + "bbox": [ + 324, + 410, + 459, + 416 + ], + "spans": [ + { + "bbox": [ + 324, + 410, + 459, + 416 + ], + "score": 0.981, + "content": "is the stadium where the player has scored, but that cell is not highlighted.", + "type": "text" + } + ], + "index": 56 + } + ], + "index": 54.5, + "bbox_fs": [ + 320, + 392, + 477, + 416 + ] + }, + { + "type": "image", + "bbox": [ + 131, + 449, + 482, + 613 + ], + "blocks": [ + { + "type": "image_caption", + "bbox": [ + 131, + 428, + 183, + 444 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 130, + 426, + 170, + 436 + ], + "spans": [ + { + "bbox": [ + 130, + 426, + 170, + 436 + ], + "score": 0.996, + "content": "Example 3:", + "type": "text" + } + ], + "index": 57 + }, + { + "bbox": [ + 130, + 435, + 185, + 444 + ], + "spans": [ + { + "bbox": [ + 130, + 435, + 185, + 444 + ], + "score": 0.998, + "content": "Table from Wikipedia:", + "type": "text" + } + ], + "index": 58 + } + ], + "index": 57.5 + }, + { + "type": "image_body", + "bbox": [ + 131, + 449, + 482, + 613 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 131, + 449, + 482, + 613 + ], + "spans": [ + { + "bbox": [ + 131, + 449, + 482, + 613 + ], + "score": 0.888, + "type": "image", + "image_path": "c685a697ec8ff3dc2caa09b027f2a8ade7135478b0985d2a7b1d38b63c2e34b9.jpg" + } + ] + } + ], + "index": 60, + "virtual_lines": [ + { + "bbox": [ + 131, + 449, + 482, + 503.6666666666667 + ], + "spans": [], + "index": 59 + }, + { + "bbox": [ + 131, + 503.6666666666667, + 482, + 558.3333333333334 + ], + "spans": [], + "index": 60 + }, + { + "bbox": [ + 131, + 558.3333333333334, + 482, + 613.0 + ], + "spans": [], + "index": 61 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 129, + 622, + 481, + 634 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 128, + 621, + 482, + 636 + ], + "spans": [ + { + "bbox": [ + 128, + 621, + 482, + 636 + ], + "score": 1.0, + "content": "Figure 9: Instructions, two examples, and interface for the ToTTo table description task.", + "type": "text" + } + ], + "index": 62 + } + ], + "index": 62 + } + ], + "index": 60 + }, + { + "type": "title", + "bbox": [ + 108, + 655, + 266, + 667 + ], + "lines": [ + { + "bbox": [ + 106, + 655, + 268, + 668 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 268, + 668 + ], + "score": 1.0, + "content": "B.6.3 HUMAN PARTICIPANT STUDY", + "type": "text" + } + ], + "index": 63 + } + ], + "index": 63 + }, + { + "type": "text", + "bbox": [ + 106, + 675, + 505, + 730 + ], + "lines": [ + { + "bbox": [ + 106, + 675, + 505, + 687 + ], + "spans": [ + { + "bbox": [ + 106, + 675, + 505, + 687 + ], + "score": 1.0, + "content": "Figure 9 shows the ToTTo instructions, example, and interface used for the human evaluation", + "type": "text" + } + ], + "index": 64 + }, + { + "bbox": [ + 104, + 685, + 505, + 698 + ], + "spans": [ + { + "bbox": [ + 104, + 685, + 505, + 698 + ], + "score": 1.0, + "content": "experiments. 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Model Params ppo/nlpovalue steps per update: 5120
total number of steps: 512000 batch size: 64 epochs per update: 5 learning rate: 0.000002 entropy coefficient: 0.0 initial kl coeff: 0.001 target kl: 1.0 discount factor: 0.99 gae lambda: 0.95 clip ratio: 0.2 rollouts top k : 50 value function coeff: 0.5 top mask ratio: 0.9 target update iterations: 20 steps per update:2560
supervised+ ppo (or nlpo)total number of steps: 512000 batch size: 64 epochs per update: 5 learning rate: 0.0000005 entropy coefficient: 0.0 initial kl coeff: 0.001 target kl: 0.2 discount factor: 0.99 gae lambda: 0.95 clip ratio: 0.2 rollouts top k : 50 value function coeff: 0.5 top mask ratio: 0.9
decodingtarget update iterations: 20 num beams: 4 max new tokens: 50
tokenizerpadding side: left truncation side:right max length: 512
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Model Params ppo/nlpovalue steps per update: 5120
total number of steps: 512000 batch size: 64 epochs per update: 5 learning rate: 0.000002 entropy coefficient: 0.0 initial kl coeff: 0.001 target kl: 1.0 discount factor: 0.99 gae lambda: 0.95 clip ratio: 0.2 rollouts top k : 50 value function coeff: 0.5 top mask ratio: 0.9 target update iterations: 20 steps per update:2560
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decodingtarget update iterations: 20 num beams: 4 max new tokens: 50
tokenizerpadding side: left truncation side:right max length: 512
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TasksAlgReward FunctionLM|Rouge-1Rouge-2 Rouge-LLexical and Semantic Metrics Rouge-LSumRouge-LMaxMeteorBLEUBertScoreMSTTRDistinct1Distinct2HDiversity Metrics HUnique1Unique2 Mean Output Length
NarQAZero ShotT50.0950.097
0.022 0.0250.0840.0840.1170.0950.0090.8350.4150.0269.64113.46818801149531.688
PPO Rouge Combined Rouge-L MaxT0.1010.1220.0990.837 0.8350.462 0.4390.03 0.0290.1259.759 13.78925221780632.352
T0.0990.08 8088080.1220.0998010.119 9.65313.61822921581631.479
NLPORouge Combined0.0230.080.118 0.1240.098 0.10.009 0.010.096 9.65213.528 13.75281983253
Rouge-L Max T50.0070.026 0.190 0.3670.3670.5810.0990.2098839 0.931018 0.60900250.1189.7763250
SupervisedRouge Combined0.378 0.380.177 0.3710.090.2290.9310.640.1560.5349.80713.657149954.923 4.353
Supervised + PPO0.3680.18 0.360.371 0.360.585 0.5850.0830.2390.9310.6410.174 0.1870.559 0.57610.132 10.20113.547 13.4523326 13785 3287 12436
Supervised + NLPORouge-L Max Rouge CombinedT T0.3980.3930.3730.5890.0960.240.9710.6790.1850.59510.304 13.6943371150673.913 4.728
0.3810.3830.3830.5880.0930.2430.9320.6450.1870.593287121713.889
Rouge-L Max0.19410.213.397
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TasksAlgReward FunctionLM|Rouge-1Rouge-2 Rouge-LLexical and Semantic Metrics Rouge-LSumRouge-LMaxMeteorBLEUBertScoreMSTTRDistinct1Distinct2HDiversity Metrics HUnique1Unique2 Mean Output Length
NarQAZero ShotT50.0950.097
0.022 0.0250.0840.0840.1170.0950.0090.8350.4150.0269.64113.46818801149531.688
PPO Rouge Combined Rouge-L MaxT0.1010.1220.0990.837 0.8350.462 0.4390.03 0.0290.1259.759 13.78925221780632.352
T0.0990.08 8088080.1220.0998010.119 9.65313.61822921581631.479
NLPORouge Combined0.0230.080.118 0.1240.098 0.10.009 0.010.096 9.65213.528 13.75281983253
Rouge-L Max T50.0070.026 0.190 0.3670.3670.5810.0990.2098839 0.931018 0.60900250.1189.7763250
SupervisedRouge Combined0.378 0.380.177 0.3710.090.2290.9310.640.1560.5349.80713.657149954.923 4.353
Supervised + PPO0.3680.18 0.360.371 0.360.585 0.5850.0830.2390.9310.6410.174 0.1870.559 0.57610.132 10.20113.547 13.4523326 13785 3287 12436
Supervised + NLPORouge-L Max Rouge CombinedT T0.3980.3930.3730.5890.0960.240.9710.6790.1850.59510.304 13.6943371150673.913 4.728
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Rouge-L Max0.19410.213.397
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Similar to other methods, our main finding is that warm-", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 124, + 506, + 137 + ], + "spans": [ + { + "bbox": [ + 105, + 124, + 506, + 137 + ], + "score": 1.0, + "content": "started initial policies are crucial for learning to generate answers that successfully use the input", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 136, + 141, + 146 + ], + "spans": [ + { + "bbox": [ + 105, + 136, + 141, + 146 + ], + "score": 1.0, + "content": "context.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 2.5 + }, + { + "type": "title", + "bbox": [ + 107, + 158, + 241, + 170 + ], + "lines": [ + { + "bbox": [ + 105, + 158, + 243, + 172 + ], + "spans": [ + { + "bbox": [ + 105, + 158, + 243, + 172 + ], + "score": 1.0, + "content": "B.7.3 QUALITATIVE RESULTS", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 5 + }, + { + "type": "title", + "bbox": [ + 106, + 178, + 504, + 190 + ], + "lines": [ 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+ "spans": [ + { + "bbox": [ + 124, + 210, + 498, + 221 + ], + "score": 1.0, + "content": "phoenix, arizona, starts an fm pirate radio station that broadcasts from the basement of", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 126, + 219, + 501, + 229 + ], + "spans": [ + { + "bbox": [ + 126, + 219, + 501, + 229 + ], + "score": 1.0, + "content": "his parents’ house. mark is a loner, an outsider, whose only outlet for his teenage angst", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 129, + 227, + 493, + 236 + ], + "spans": [ + { + "bbox": [ + 129, + 227, + 487, + 236 + ], + "score": 1.0, + "content": "and aggression is his unauthorized radio station. his pirate station’s theme song is", + "type": "text" + }, + { + "bbox": [ + 482, + 228, + 493, + 234 + ], + "score": 1.0, + "content": "\"", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 126, + 235, + 501, + 244 + ], + "spans": [ + { + "bbox": [ + 126, + 235, + 501, + 244 + ], + "score": 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443, + 500 + ], + "spans": [ + { + "bbox": [ + 130, + 490, + 443, + 500 + ], + "score": 1.0, + "content": "starts an fm pirate radio station that broadcasts from the basement of his", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 43.5, + "bbox_fs": [ + 106, + 483, + 502, + 500 + ] + }, + { + "type": "text", + "bbox": [ + 109, + 500, + 500, + 514 + ], + "lines": [ + { + "bbox": [ + 106, + 498, + 498, + 508 + ], + "spans": [ + { + "bbox": [ + 106, + 498, + 498, + 508 + ], + "score": 1.0, + "content": "References: he is a high school student in phoenix 2) loner and outsider student with a radio", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 126, + 506, + 159, + 516 + ], + "spans": [ + { + "bbox": [ + 126, + 506, + 159, + 516 + ], + "score": 1.0, + "content": "station", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 45.5, + "bbox_fs": [ + 106, + 498, + 498, + 516 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 515, + 500, + 530 + ], + 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"bbox": [ + 130, + 538, + 464, + 548 + ], + "spans": [ + { + "bbox": [ + 130, + 538, + 464, + 548 + ], + "score": 1.0, + "content": "fm pirate radio station that broadcasts from the basement of his parents’ house", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 106, + 546, + 246, + 556 + ], + "spans": [ + { + "bbox": [ + 106, + 546, + 246, + 556 + ], + "score": 1.0, + "content": "Supervised: a high school student", + "type": "text" + } + ], + "index": 51 + } + ], + "index": 50, + "bbox_fs": [ + 105, + 529, + 501, + 556 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 547, + 275, + 571 + ], + "lines": [ + { + "bbox": [ + 106, + 554, + 272, + 564 + ], + "spans": [ + { + "bbox": [ + 106, + 554, + 151, + 564 + ], + "score": 1.0, + "content": "Supervised", + "type": "text" + }, + { + "bbox": [ + 152, + 556, + 159, + 562 + ], + "score": 0.37, + "content": "^ +", + "type": "inline_equation" + }, + { + "bbox": [ + 159, + 554, + 272, + 564 + ], + "score": 1.0, + "content": "PPO: a high school student", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 106, + 563, + 276, + 572 + ], + "spans": [ + { + "bbox": [ + 106, + 563, + 151, + 572 + ], + "score": 1.0, + "content": "Supervised", + "type": "text" + }, + { + "bbox": [ + 152, + 564, + 159, + 570 + ], + "score": 0.44, + "content": "^ +", + "type": "inline_equation" + }, + { + "bbox": [ + 159, + 563, + 276, + 572 + ], + "score": 1.0, + "content": "NLPO: a high school student", + "type": "text" + } + ], + "index": 53 + } + ], + "index": 52.5, + "bbox_fs": [ + 106, + 554, + 276, + 572 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 579, + 141, + 586 + ], + "lines": [ + { + "bbox": [ + 105, + 577, + 144, + 589 + ], + "spans": [ + { + "bbox": [ + 105, + 577, + 144, + 589 + ], + "score": 1.0, + "content": "Sample 2", + "type": "text" + } + ], + "index": 54 + } + ], + "index": 54 + }, + { + "type": "text", + "bbox": [ + 111, + 586, + 504, + 731 + ], + "lines": [ + { + "bbox": [ + 110, + 587, + 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196, + 488, + 207 + ], + "score": 1.0, + "content": "their own future. the police step in and arrest mark and nora. as they are taken away,", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 124, + 203, + 497, + 214 + ], + "spans": [ + { + "bbox": [ + 124, + 203, + 497, + 214 + ], + "score": 1.0, + "content": "mark reminds the students to \"talk hard.\" as the film ends, the voices of other students", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 127, + 213, + 497, + 222 + ], + "spans": [ + { + "bbox": [ + 127, + 213, + 497, + 222 + ], + "score": 1.0, + "content": "(and even one of the teachers) speak as intros for their own independent stations, which", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 125, + 219, + 317, + 231 + ], + "spans": [ + { + "bbox": [ + 125, + 219, + 317, + 231 + ], + "score": 1.0, + "content": "can be heard broadcasting across the country.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 8.5 + }, + { + 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111, + 251, + 344, + 262 + ], + "score": 1.0, + "content": "eferences: 1) expelling them. 2) expelling the students", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 21 + }, + { + "type": "text", + "bbox": [ + 105, + 261, + 496, + 284 + ], + "lines": [ + { + "bbox": [ + 105, + 259, + 498, + 270 + ], + "spans": [ + { + "bbox": [ + 105, + 259, + 498, + 270 + ], + "score": 1.0, + "content": "PPO: mark hunter (slater) starts an fm pirate radio station that broadcasts from the basement", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 125, + 267, + 489, + 278 + ], + "spans": [ + { + "bbox": [ + 125, + 267, + 489, + 278 + ], + "score": 1.0, + "content": "of his parents’ house. mark is a loner, an outsider, whose only outlet for his teenage", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 126, + 276, + 141, + 285 + ], + "spans": [ + { + "bbox": [ + 126, + 276, + 141, + 285 + ], + "score": 1.0, + "content": "ang", + "type": "text" + } + ], + "index": 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], + "spans": [ + { + "bbox": [ + 106, + 308, + 346, + 318 + ], + "score": 1.0, + "content": "Supervised: he was taking them to a psychiatric hospital.", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 316, + 248, + 325 + ], + "spans": [ + { + "bbox": [ + 106, + 316, + 152, + 325 + ], + "score": 1.0, + "content": "Supervised", + "type": "text" + }, + { + "bbox": [ + 152, + 317, + 159, + 323 + ], + "score": 0.4, + "content": "^ +", + "type": "inline_equation" + }, + { + "bbox": [ + 159, + 316, + 248, + 325 + ], + "score": 1.0, + "content": "PPO: addressing them", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 324, + 276, + 333 + ], + "spans": [ + { + "bbox": [ + 106, + 324, + 151, + 333 + ], + "score": 1.0, + "content": "Supervised", + "type": "text" + }, + { + "bbox": [ + 152, + 325, + 159, + 331 + ], + "score": 0.44, + "content": "^ +", + "type": "inline_equation" + }, + { + "bbox": [ + 159, + 324, + 276, + 333 + ], + "score": 1.0, + 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Model Params supervisedvalue batch size: 64
ppo/nlpoepochs: 5 learning rate: 0.00001 learning rate scheduler: constant weight decay: 0.1 steps per update: 5120 total number of steps: 256000
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Model Params supervisedvalue batch size: 64
ppo/nlpoepochs: 5 learning rate: 0.00001 learning rate scheduler: constant weight decay: 0.1 steps per update: 5120 total number of steps: 256000
batch size: 64 epochs per update: 5 learning rate: 0.0.000001 entropy coefficient: 0.0 initial kl coeff: 0.001 target kl: 0.2 discount factor: 0.99 gae lambda: 0.95 clip ratio: 0.2 rollouts top k : 10 value function coeff: 0.5 top mask ratio: 0.5 target update iterations: 20
supervised+ ppo (or nlpo)steps per update:2560 total number of steps:256000 batch size: 64 epochs per update: 5 learning rate: 0.0000005 entropy coefficient: 0.0 initial kl coeff: 0.001 target kl: 0.2 discount factor: 0.99 gae lambda: 0.95 clip ratio: 0.2 rollouts top k :10 value function coeff: 0.5
decodingtop mask ratio: 0.5 target update iterations: 20 num beams: 4 length penalty: 0.6 max new tokens: 128
tokenizerpadding side: left truncation side:right max length: 128
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DatasetsAlgLMReward Function Rouge-1Rouge-2Rouge-LLexical and Semantic Metrics Rouge-LSumchRfTERBertScore
MeteorBLEUSacreBLEU
Zero-Shot PPOT5SacreBLEU0.635 0.6360.4140.5910.591 0.5910.483 0.4820.294 0.2940.3480.6130.5430.882
T5 T50.4150.5910.3480.614 0.5390.882
chRF TER0.6350.414 0.4160.591 0.5950.591 0.5940.4810.2910.3460.612 0.6160.540 0.5340.882
T5 T50.6380.4840.2940.3500.883
T5BertScore0.6370.4170.5930.5930.4790.2940.3470.6130.5340.882
NLPOSacreBLEU0.6350.4150.5920.5920.4840.2970.3520.6150.5420.882
T5 T5chRF TER0.6340.4130.590.590.4810.2910.3450.6120.5400.882
T5BertScore0.633 0.6220.412 0.3970.590.590.4770.2860.3410.6080.5400.881
Supervised0.6350.4110.58 0.5900.581 0.5900.458 0.4820.269 0.2940.323 0.3500.591 0.6170.546 0.5400.876 0.882
Supervised + PPOT5 T5 T5SacreBLEU chRF0.640 0.6400.4160.5950.5950.4870.2980.3550.6200.533 0.883
T5 T5TER0.416 0.4140.596 0.594 0.5930.596 0.594 0.5940.486 0.4830.298 0.295 0.2940.354 0.3520.6210.532 0.618 0.533 0.5330.883 0.882 0.882
Supervised + NLPOT5BertScore SacreBLEU0.637 0.637 0.6420.4130.4820.3500.616
chRF0.6360.4190.5960.5960.4970.2970.3550.621 0.5330.888
TER0.4120.5920.5920.4920.2930.3490.6170.534 0.5310.886
T50.6370.4140.5940.5940.4910.2920.3490.6150.886
T5BertScore0.640.4170.5980.5980.4990.2870.3490.620.5380.887
Zero-Shot PPO0.3860.588
T50.6190.5870.4450.2540.3080.5770.5730.870
T5SacreBLEU0.6210.3830.5870.5870.4480.2430.2960.5750.5830.869
T5 T5chRF TER0.6220.3850.5900.5900.4480.2480.3010.5780.5750.870
T5BertScore0.6230.3840.5910.5910.4430.2460.303 0.1740.5720.568 0.5730.869 0.839
NLPOSacreBLEU0.5330.3260.5070.5070.3210.1430.4060.578
T5 T5chRF0.6240.3850.590.590.450.2450.2990.5780.87 0.87
T5TER0.6240.3860.590.590.4510.248 0.2460.302 0.3030.581 0.5730.576 0.570.869
T5BertScore0.622 0.6110.384 0.3770.59 0.580.59 0.580.443 0.4250.2390.2910.5550.5730.866
Supervised0.6100.6090.4610.3370.538
Supervised + PPOT50.6380.4000.2800.5930.878
T5SacreBLEU0.4070.6100.6100.4650.2770.3320.5960.5420.877
T5chRF0.6400.4060.6090.6090.4640.2770.3310.5960.5430.877
T5 T5TER0.639 0.6370.4060.6090.6090.4570.2740.331 0.2910.5890.535 0.5590.876 0.867
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DatasetsAlgLMReward Function Rouge-1Rouge-2Rouge-LLexical and Semantic Metrics Rouge-LSumchRfTERBertScore
MeteorBLEUSacreBLEU
Zero-Shot PPOT5SacreBLEU0.635 0.6360.4140.5910.591 0.5910.483 0.4820.294 0.2940.3480.6130.5430.882
T5 T50.4150.5910.3480.614 0.5390.882
chRF TER0.6350.414 0.4160.591 0.5950.591 0.5940.4810.2910.3460.612 0.6160.540 0.5340.882
T5 T50.6380.4840.2940.3500.883
T5BertScore0.6370.4170.5930.5930.4790.2940.3470.6130.5340.882
NLPOSacreBLEU0.6350.4150.5920.5920.4840.2970.3520.6150.5420.882
T5 T5chRF TER0.6340.4130.590.590.4810.2910.3450.6120.5400.882
T5BertScore0.633 0.6220.412 0.3970.590.590.4770.2860.3410.6080.5400.881
Supervised0.6350.4110.58 0.5900.581 0.5900.458 0.4820.269 0.2940.323 0.3500.591 0.6170.546 0.5400.876 0.882
Supervised + PPOT5 T5 T5SacreBLEU chRF0.640 0.6400.4160.5950.5950.4870.2980.3550.6200.533 0.883
T5 T5TER0.416 0.4140.596 0.594 0.5930.596 0.594 0.5940.486 0.4830.298 0.295 0.2940.354 0.3520.6210.532 0.618 0.533 0.5330.883 0.882 0.882
Supervised + NLPOT5BertScore SacreBLEU0.637 0.637 0.6420.4130.4820.3500.616
chRF0.6360.4190.5960.5960.4970.2970.3550.621 0.5330.888
TER0.4120.5920.5920.4920.2930.3490.6170.534 0.5310.886
T50.6370.4140.5940.5940.4910.2920.3490.6150.886
T5BertScore0.640.4170.5980.5980.4990.2870.3490.620.5380.887
Zero-Shot PPO0.3860.588
T50.6190.5870.4450.2540.3080.5770.5730.870
T5SacreBLEU0.6210.3830.5870.5870.4480.2430.2960.5750.5830.869
T5 T5chRF TER0.6220.3850.5900.5900.4480.2480.3010.5780.5750.870
T5BertScore0.6230.3840.5910.5910.4430.2460.303 0.1740.5720.568 0.5730.869 0.839
NLPOSacreBLEU0.5330.3260.5070.5070.3210.1430.4060.578
T5 T5chRF0.6240.3850.590.590.450.2450.2990.5780.87 0.87
T5TER0.6240.3860.590.590.4510.248 0.2460.302 0.3030.581 0.5730.576 0.570.869
T5BertScore0.622 0.6110.384 0.3770.59 0.580.59 0.580.443 0.4250.2390.2910.5550.5730.866
Supervised0.6100.6090.4610.3370.538
Supervised + PPOT50.6380.4000.2800.5930.878
T5SacreBLEU0.4070.6100.6100.4650.2770.3320.5960.5420.877
T5chRF0.6400.4060.6090.6090.4640.2770.3310.5960.5430.877
T5 T5TER0.639 0.6370.4060.6090.6090.4570.2740.331 0.2910.5890.535 0.5590.876 0.867
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TasksAlgReward FunctionLMDistinct1
MSTTRDistinct2HHUnique1Unique2Mean Output Length
Zero-Shot72903369120.533
PPOT5SacreBLEU0.7380.1980.68710.16614.61375033414020.375
T5chRF0.7380.1960.68710.17514.61173763411620.337
T5TER0.7360.1960.68310.13214.58874473397720.356
T5BertScore0.7360.1950.68510.12914.574 72723347720.035
NLPOT5SacreBLEU0.7350.1930.6810.12514.592 73953427620.672
T5chRF0.7380.1960.68610.16414.60673993405620.351
WMT16T5 T5TER BertScore0.740.20.69410.20414.6375223423420.151
0.7390.20.69810.19414.60872033316919.482
SupervisedT50.7290.1900.66910.04814.53072053343020.622
Supervised + PPOT5 T5SacreBLEU chRF0.7320.1910.67410.08014.55272223372320.605
T5TER0.735 0.7320.1920.677 0.67610.09314.5697319 72653392320.586 20.441
T5BertScore0.7320.1920.67710.079 10.08214.553 14.55071873363520.305
0.19233385
Supervised + NLPOT5SacreBLEU0.7340.1910.67510.08914.56873083394120.686
T5 T5chRF TER0.7350.1940.68110.11214.57173723381420.348
T5BertScore0.737 0.7370.194 0.2270.68210.10514.56672433348220.159
0.74210.04214.17954382257412.63
Zero-ShotT50.6620.0970.47009.27614.52683125294718.739 19.069
PPOT5SacreBLEU0.6570.0950.4649.23014.498828553000
T5chRF0.6600.0960.4689.25314.52682435314218.912
T5 T5TER BertScore0.6590.0970.4749.24414.53681295191418.268
0.6730.1200.5419.28814.38866423726711.602
NLPOT5SacreBLEU0.6560.0940.4639.20714.48382405282219.043
T5chRF0.6580.0950.4649.23314.50282305316719.073
T5TER0.6610.0980.4769.27114.55282235243818.344
T5BertScore0.6670.1020.4919.3114.57681345074017.162
SupervisedT50.6550.0950.4679.21014.49279705143018.440
Supervised + PPOSacreBLEU0.6540.0940.4619.17614.46780615184018.803
T50.4649.20214.49780545219818.794
T5 T5chRF TER0.656 0.6580.094 0.0970.4759.23914.529 79695125518.048
T5BertScore0.6650.1020.4959.27014.524 74954762916.051
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TasksAlgReward FunctionLMDistinct1
MSTTRDistinct2HHUnique1Unique2Mean Output Length
Zero-Shot72903369120.533
PPOT5SacreBLEU0.7380.1980.68710.16614.61375033414020.375
T5chRF0.7380.1960.68710.17514.61173763411620.337
T5TER0.7360.1960.68310.13214.58874473397720.356
T5BertScore0.7360.1950.68510.12914.574 72723347720.035
NLPOT5SacreBLEU0.7350.1930.6810.12514.592 73953427620.672
T5chRF0.7380.1960.68610.16414.60673993405620.351
WMT16T5 T5TER BertScore0.740.20.69410.20414.6375223423420.151
0.7390.20.69810.19414.60872033316919.482
SupervisedT50.7290.1900.66910.04814.53072053343020.622
Supervised + PPOT5 T5SacreBLEU chRF0.7320.1910.67410.08014.55272223372320.605
T5TER0.735 0.7320.1920.677 0.67610.09314.5697319 72653392320.586 20.441
T5BertScore0.7320.1920.67710.079 10.08214.553 14.55071873363520.305
0.19233385
Supervised + NLPOT5SacreBLEU0.7340.1910.67510.08914.56873083394120.686
T5 T5chRF TER0.7350.1940.68110.11214.57173723381420.348
T5BertScore0.737 0.7370.194 0.2270.68210.10514.56672433348220.159
0.74210.04214.17954382257412.63
Zero-ShotT50.6620.0970.47009.27614.52683125294718.739 19.069
PPOT5SacreBLEU0.6570.0950.4649.23014.498828553000
T5chRF0.6600.0960.4689.25314.52682435314218.912
T5 T5TER BertScore0.6590.0970.4749.24414.53681295191418.268
0.6730.1200.5419.28814.38866423726711.602
NLPOT5SacreBLEU0.6560.0940.4639.20714.48382405282219.043
T5chRF0.6580.0950.4649.23314.50282305316719.073
T5TER0.6610.0980.4769.27114.55282235243818.344
T5BertScore0.6670.1020.4919.3114.57681345074017.162
SupervisedT50.6550.0950.4679.21014.49279705143018.440
Supervised + PPOSacreBLEU0.6540.0940.4619.17614.46780615184018.803
T50.4649.20214.49780545219818.794
T5 T5chRF TER0.656 0.6580.094 0.0970.4759.23914.529 79695125518.048
T5BertScore0.6650.1020.4959.27014.524 74954762916.051
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Model Params ppo/nlpovalue steps per update:1280
total number of steps:128000 batch size: 64 epochs per update: 5 learning rate: 0.000001 entropy coefficient: 0.0 initial kl coeff: 0.2 target kl: 0.5 discount factor: 0.99 gae lambda: 0.95 clip ratio: 0.2 rollouts top k : 20 value function coeff: 0.5 meteor coeff: 0.25 intent coeff: 0.75 top mask ratio: 0.9 target update iterations: 20
supervised+ ppo (or nlpo)steps per update:1280 total number of steps: 64000 batch size: 64 epochs per update: 5 learning rate: 0.000001 entropy coefficient: 0.0 initial kl coeff: 0.2 target kl: 0.5 discount factor: 0.99 gae lambda: 0.95 clip ratio: 0.2 rollouts top k : 20 value function coeff: 0.5 meteor coeff: 0.5 0.25 intent coeff: 0.5 0.75
decodingtop mask ratio: 0.9 target update iterations: 20 top k: 20 min length: 2 max new tokens: 50
tokenizerpadding side: left truncation side:right max length: 128
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For RL methods, we use a linear combination of meteor score and intent", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 210, + 505, + 222 + ], + "spans": [ + { + "bbox": [ + 106, + 210, + 505, + 222 + ], + "score": 1.0, + "content": "match score (whether the generated text’s intent matches with the reference’s intent) as the reward", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 220, + 506, + 233 + ], + "spans": [ + { + "bbox": [ + 105, + 220, + 506, + 233 + ], + "score": 1.0, + "content": "function. The coefficients for meteor and intent are chosen based on both lexical scores and intent", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 232, + 505, + 244 + ], + "spans": [ + { + "bbox": [ + 105, + 232, + 505, + 244 + ], + "score": 1.0, + "content": "accuracy on the validation set. For this purpose, we trained an intent classifier (fine-tuned RoBERTa", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 242, + 506, + 255 + ], + "spans": [ + { + "bbox": [ + 105, + 242, + 506, + 255 + ], + "score": 1.0, + "content": "(Liu et al., 2019)) that classifies given text into intent categories such as inform, question, directive", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 254, + 500, + 267 + ], + "spans": [ + { + "bbox": [ + 106, + 254, + 500, + 267 + ], + "score": 1.0, + "content": "and commisive, etc. Table 32 provides a summary of hyperparameters and implementation details.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 8, + "bbox_fs": [ + 105, + 121, + 507, + 267 + ] + }, + { + "type": "table", + "bbox": [ + 206, + 274, + 404, + 651 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 206, + 274, + 404, + 651 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 206, + 274, + 404, + 651 + ], + "spans": [ + { + "bbox": [ + 206, + 274, + 404, + 651 + ], + "score": 0.967, + "html": "
Model Params ppo/nlpovalue steps per update:1280
total number of steps:128000 batch size: 64 epochs per update: 5 learning rate: 0.000001 entropy coefficient: 0.0 initial kl coeff: 0.2 target kl: 0.5 discount factor: 0.99 gae lambda: 0.95 clip ratio: 0.2 rollouts top k : 20 value function coeff: 0.5 meteor coeff: 0.25 intent coeff: 0.75 top mask ratio: 0.9 target update iterations: 20
supervised+ ppo (or nlpo)steps per update:1280 total number of steps: 64000 batch size: 64 epochs per update: 5 learning rate: 0.000001 entropy coefficient: 0.0 initial kl coeff: 0.2 target kl: 0.5 discount factor: 0.99 gae lambda: 0.95 clip ratio: 0.2 rollouts top k : 20 value function coeff: 0.5 meteor coeff: 0.5 0.25 intent coeff: 0.5 0.75
decodingtop mask ratio: 0.9 target update iterations: 20 top k: 20 min length: 2 max new tokens: 50
tokenizerpadding side: left truncation side:right max length: 128
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TasksAlgReward FunctionLM|Rouge-1Rouge-2Rouge-LLexical and Semantic Metrics Rouge-LSumMeteor SacreBLEUBertScoreIntent AccuracyMSTTR Distinct1Distinct2HDiversity Metrics HUnique1Unique2Mean Output Length
Dialog0.131
Zero ShotGPT-2 0.1570.0120.131 0.1910.066 0.0640.854 0.8550.427 0.4370.6080.0550.3167.78711.83115741232718.685
SupervisedGPT-20.1620.0200.1380.1380.1860.635 0.0650.3428.05112.11919251395218.919
PPOMeteor + IntentGPT-20.1680.0120.1420.1420.2210.085 0.8610.4740.581 0.0580.3107.65311.43717191215618.538
NLPOMeteor + IntentGPT-20.1690.0130.1420.1420.2210.0870.8600.4900.568 0.0590.3097.63011.35117181194618.397
Supervised + PPOMeteor + IntentGPT-20.1690.0210.1440.1440.1980.0710.8570.4550.626 0.0680.3488.05612.01519831417018.829
Supervised + NLPOMeteor + IntentGPT-20.1710.0200.1460.1460.2050.074 0.8580.4540.6240.0700.3498.04411.99020511421318.763
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TasksAlgReward FunctionLM|Rouge-1Rouge-2Rouge-LLexical and Semantic Metrics Rouge-LSumMeteor SacreBLEUBertScoreIntent AccuracyMSTTR Distinct1Distinct2HDiversity Metrics HUnique1Unique2Mean Output Length
Dialog0.131
Zero ShotGPT-2 0.1570.0120.131 0.1910.066 0.0640.854 0.8550.427 0.4370.6080.0550.3167.78711.83115741232718.685
SupervisedGPT-20.1620.0200.1380.1380.1860.635 0.0650.3428.05112.11919251395218.919
PPOMeteor + IntentGPT-20.1680.0120.1420.1420.2210.085 0.8610.4740.581 0.0580.3107.65311.43717191215618.538
NLPOMeteor + IntentGPT-20.1690.0130.1420.1420.2210.0870.8600.4900.568 0.0590.3097.63011.35117181194618.397
Supervised + PPOMeteor + IntentGPT-20.1690.0210.1440.1440.1980.0710.8570.4550.626 0.0680.3488.05612.01519831417018.829
Supervised + NLPOMeteor + IntentGPT-20.1710.0200.1460.1460.2050.074 0.8580.4540.6240.0700.3498.04411.99020511421318.763
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AlgorithmUnique NCoherenceQuality
ValueAlphaSkewValueAlphaSkew
Zeroshot313.840.2254.1813.20.1253.352
NLPO304.180.1144.173.350.1593.318
PPO324.180.1124.0323.320.1633.478
Supervised+PPO313.990.1484.1333.480.1663.58
Supervised+NLPO314.130.1863.9533.580.1783.597
Supervised313.960.2493.8343.590.2363.196
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Group 1Group 2CoherenceDiff (G2-G1)p-valuesQualityDiff (G2-G1) p-values
NLPOPPO-0.0030.900-0.0300.900
NLPOSupervised-0.2270.0430.2380.020
NLPONLPOSupervised+NLPOSupervised+PPO-0.050-0.1940.9000.2340.022
0.0130.1270.803
NLPOZero Shot-0.3450.001-0.1540.655
PPOPPOPPOPPOSupervisedSupervised-0.2240.0490.2680.010
Supervised+NLPO-0.0470.9000.2640.011
Supervised+PPO-0.1910.1440.1570.636
Zero Shot-0.3410.001-0.1240.822
Supervised+NLPO0.1770.021-0.0030.900
SupervisedSupervised+PPO0.0330.900-0.1100.896
SupervisedZero Shot-0.1170.645-0.3910.002
Supervised+NLPOSupervised+PPO-0.1440.444-0.1070.009
Supervised+NLPOSupervised+PPOZero Shot-0.2940.002-0.3880.003
Zero Shot-0.1510.390-0.2810.008
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PPO324.180.1124.0323.320.1633.478
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Group 1Group 2CoherenceDiff (G2-G1)p-valuesQualityDiff (G2-G1) p-values
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NLPOSupervised-0.2270.0430.2380.020
NLPONLPOSupervised+NLPOSupervised+PPO-0.050-0.1940.9000.2340.022
0.0130.1270.803
NLPOZero Shot-0.3450.001-0.1540.655
PPOPPOPPOPPOSupervisedSupervised-0.2240.0490.2680.010
Supervised+NLPO-0.0470.9000.2640.011
Supervised+PPO-0.1910.1440.1570.636
Zero Shot-0.3410.001-0.1240.822
Supervised+NLPO0.1770.021-0.0030.900
SupervisedSupervised+PPO0.0330.900-0.1100.896
SupervisedZero Shot-0.1170.645-0.3910.002
Supervised+NLPOSupervised+PPO-0.1440.444-0.1070.009
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They couldn't find the", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 327, + 313, + 365, + 324 + ], + "spans": [ + { + "bbox": [ + 327, + 313, + 365, + 324 + ], + "score": 0.999, + "content": "problem.", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 39.5 + }, + { + "type": "title", + "bbox": [ + 230, + 361, + 371, + 389 + ], + "lines": [ + { + "bbox": [ + 229, + 360, + 372, + 375 + ], + "spans": [ + { + "bbox": [ + 229, + 360, + 372, + 375 + ], + "score": 0.994, + "content": " Fluency/Grammaticality:", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 228, + 376, + 252, + 391 + ], + "spans": [ + { + "bbox": [ + 228, + 376, + 252, + 391 + ], + "score": 1.0, + "content": "3/5", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 41.5 + }, + { + "type": "image", + "bbox": [ + 229, + 395, + 389, + 518 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 229, + 395, + 389, + 518 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 229, + 395, + 389, + 518 + ], + "spans": [ + { + "bbox": [ + 229, + 395, + 389, + 518 + ], + "score": 0.793, + "type": "image", + "image_path": "ad429a9c365687889223d1c83942b09252f4a8f788d27145620e353735be6fdd.jpg" + } + ] + } + ], + "index": 49, + "virtual_lines": [ + { + "bbox": [ + 229, + 395, + 389, + 404.46153846153845 + ], + "spans": [], + "index": 43 + }, + { + "bbox": [ + 229, + 404.46153846153845, + 389, + 413.9230769230769 + ], + "spans": [], + "index": 44 + }, + { + "bbox": [ + 229, + 413.9230769230769, + 389, + 423.38461538461536 + ], + "spans": [], + "index": 45 + }, + { + "bbox": [ + 229, + 423.38461538461536, + 389, + 432.8461538461538 + ], + "spans": [], + "index": 46 + }, + { + "bbox": [ + 229, + 432.8461538461538, + 389, + 442.30769230769226 + ], + "spans": [], + "index": 47 + }, + { + "bbox": [ + 229, + 442.30769230769226, + 389, + 451.7692307692307 + ], + "spans": [], + "index": 48 + }, + { + "bbox": [ + 229, + 451.7692307692307, + 389, + 461.23076923076917 + ], + "spans": [], + "index": 49 + }, + { + "bbox": [ + 229, + 461.23076923076917, + 389, + 470.6923076923076 + ], + "spans": [], + "index": 50 + }, + { + "bbox": [ + 229, + 470.6923076923076, + 389, + 480.1538461538461 + ], + "spans": [], + "index": 51 + }, + { + "bbox": [ + 229, + 480.1538461538461, + 389, + 489.6153846153845 + ], + "spans": [], + "index": 52 + }, + { + "bbox": [ + 229, + 489.6153846153845, + 389, + 499.076923076923 + ], + "spans": [], + "index": 53 + }, + { + "bbox": [ + 229, + 499.076923076923, + 389, + 508.53846153846143 + ], + "spans": [], + "index": 54 + }, + { + "bbox": [ + 229, + 508.53846153846143, + 389, + 517.9999999999999 + ], + "spans": [], + "index": 55 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 174, + 540, + 435, + 552 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 174, + 538, + 436, + 554 + ], + "spans": [ + { + "bbox": [ + 174, + 538, + 436, + 554 + ], + "score": 1.0, + "content": "Figure 10: Instructions and interface for the Daily Dialogue task.", + "type": "text" + } + ], + "index": 56 + } + ], + "index": 56 + } + ], + "index": 52.5 + }, + { + "type": "title", + "bbox": [ + 107, + 574, + 247, + 586 + ], + "lines": [ + { + "bbox": [ + 106, + 574, + 248, + 587 + ], + "spans": [ + { + "bbox": [ + 106, + 574, + 248, + 587 + ], + "score": 1.0, + "content": "B.9.4 QUALITATIVE ANALYSIS", + "type": "text" + } + ], + "index": 57 + } + ], + "index": 57 + }, + { + "type": "text", + "bbox": [ + 105, + 594, + 505, + 605 + ], + "lines": [ + { + "bbox": [ + 105, + 592, + 507, + 608 + ], + "spans": [ + { + "bbox": [ + 105, + 592, + 507, + 608 + ], + "score": 1.0, + "content": "We show sample generations from each of the algorithms for three randomly picked prompts below.", + "type": "text" + } + ], + "index": 58 + } + ], + "index": 58 + }, + { + "type": "title", + "bbox": [ + 106, + 612, + 141, + 619 + ], + "lines": [ + { + "bbox": [ + 106, + 612, + 141, + 619 + ], + "spans": [], + "index": 59 + } + ], + "index": 59 + }, + { + "type": "text", + "bbox": [ + 107, + 620, + 495, + 659 + ], + "lines": [ + { + "bbox": [ + 105, + 619, + 490, + 629 + ], + "spans": [ + { + "bbox": [ + 105, + 619, + 490, + 629 + ], + "score": 1.0, + "content": "Prompt: Right . And China is the homeland of tea . Yes , Chinese people love drinking", + "type": "text" + } + ], + "index": 60 + }, + { + "bbox": [ + 125, + 627, + 493, + 637 + ], + "spans": [ + { + "bbox": [ + 125, + 627, + 493, + 637 + ], + "score": 1.0, + "content": "tea so much . Some even claim they can’t live without tea . Do you know there are", + "type": "text" + } + ], + "index": 61 + }, + { + "bbox": [ + 126, + 635, + 489, + 645 + ], + "spans": [ + { + "bbox": [ + 126, + 635, + 489, + 645 + ], + "score": 1.0, + "content": "several catagories of Chinese tea ? Yes , I believe there are green teas , black", + "type": "text" + } + ], + "index": 62 + }, + { + "bbox": [ + 126, + 643, + 493, + 652 + ], + "spans": [ + { + "bbox": [ + 126, + 643, + 493, + 652 + ], + "score": 1.0, + "content": "teas and scented teas . Any Others ? Well , have you ever heard of Oulong tea and", + "type": "text" + } + ], + "index": 63 + }, + { + "bbox": [ + 126, + 651, + 221, + 660 + ], + "spans": [ + { + "bbox": [ + 126, + 651, + 221, + 660 + ], + "score": 1.0, + "content": "compressed tea ? ", + "type": "text" + } + ], + "index": 64 + } + ], + "index": 62 + }, + { + "type": "text", + "bbox": [ + 146, + 660, + 413, + 667 + ], + "lines": [ + { + "bbox": [ + 144, + 658, + 411, + 668 + ], + "spans": [ + { + "bbox": [ + 144, + 658, + 411, + 668 + ], + "score": 1.0, + "content": "s: Oh , yeah . Oulong tea is good for one’s health . isn’t it ?", + "type": "text" + } + ], + "index": 65 + } + ], + "index": 65 + }, + { + "type": "text", + "bbox": [ + 106, + 667, + 493, + 684 + ], + "lines": [ + { + "bbox": [ + 106, + 667, + 495, + 677 + ], + "spans": [ + { + "bbox": [ + 106, + 667, + 495, + 677 + ], + "score": 1.0, + "content": "Zero-Shot: I know that Oulong tea can be enjoyed with very few meals, and there are very few", + "type": "text" + } + ], + "index": 66 + }, + { + "bbox": [ + 105, + 674, + 318, + 685 + ], + "spans": [ + { + "bbox": [ + 105, + 674, + 318, + 685 + ], + "score": 1.0, + "content": "PPO: I have, but it’s not as strong as Oulong tea.", + "type": "text" + } + ], + "index": 67 + } + ], + "index": 66.5 + }, + { + "type": "text", + "bbox": [ + 107, + 684, + 251, + 691 + ], + "lines": [ + { + "bbox": [ + 106, + 682, + 250, + 693 + ], + "spans": [ + { + "bbox": [ + 106, + 682, + 250, + 693 + ], + "score": 1.0, + "content": "NLPO: I haven’t. I don’t have tea.", + "type": "text" + } + ], + "index": 68 + } + ], + "index": 68 + }, + { + "type": "text", + "bbox": [ + 106, + 692, + 474, + 716 + ], + "lines": [ + { + "bbox": [ + 106, + 691, + 448, + 701 + ], + "spans": [ + { + "bbox": [ + 106, + 691, + 448, + 701 + ], + "score": 1.0, + "content": "Supervised: Yes. I hear they do good. 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Thanks again for your wo", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 2.5, + "bbox_fs": [ + 113, + 118, + 280, + 132 + ] + }, + { + "type": "text", + "bbox": [ + 114, + 136, + 293, + 155 + ], + "lines": [ + { + "bbox": [ + 114, + 136, + 289, + 142 + ], + "spans": [ + { + "bbox": [ + 114, + 136, + 289, + 142 + ], + "score": 0.982, + "content": "In this HIT you will be presented with a dialogue consisting of a conversation between", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 114, + 142, + 294, + 149 + ], + "spans": [ + { + "bbox": [ + 114, + 142, + 294, + 149 + ], + "score": 0.979, + "content": " two people. 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The specific scales are:", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 10.5, + "bbox_fs": [ + 114, + 190, + 291, + 203 + ] + }, + { + "type": "title", + "bbox": [ + 120, + 208, + 181, + 213 + ], + "lines": [ + { + "bbox": [ + 118, + 206, + 182, + 215 + ], + "spans": [ + { + "bbox": [ + 118, + 206, + 182, + 215 + ], + "score": 0.996, + "content": "·Fluency/Grammaticality:", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 12 + }, + { + "type": "list", + "bbox": [ + 130, + 214, + 295, + 272 + ], + "lines": [ + { + "bbox": [ + 129, + 213, + 256, + 221 + ], + "spans": [ + { + "bbox": [ + 129, + 213, + 256, + 221 + ], + "score": 0.966, + "content": "05/5 (excelent): The generation is grammatical and fluent.", + "type": "text" + } + ], + "index": 13, + "is_list_start_line": true, + "is_list_end_line": true + }, + { + "bbox": [ + 130, + 221, + 283, + 228 + ], + "spans": [ + { + "bbox": [ + 130, + 221, + 283, + 228 + ], + "score": 0.98, + "content": "○4/5 (good): The sentence largely makes sense, but there are some smal", + "type": "text" + } + ], + "index": 14, + "is_list_start_line": true, + "is_list_end_line": true + }, + { + "bbox": [ + 135, + 227, + 285, + 235 + ], + "spans": [ + { + "bbox": [ + 135, + 227, + 285, + 235 + ], + "score": 0.991, + "content": "grammar issues/out-of-place words that don't make for the best writing.", + "type": "text" + } + ], + "index": 15, + "is_list_end_line": true + }, + { + "bbox": [ + 131, + 234, + 285, + 240 + ], + "spans": [ + { + "bbox": [ + 131, + 234, + 285, + 240 + ], + "score": 0.971, + "content": "o3/5 (okay): The grammar is okay and it's possible to read, but it definitely", + "type": "text" + } + ], + "index": 16, + "is_list_start_line": true, + "is_list_end_line": true + }, + { + "bbox": [ + 136, + 240, + 212, + 246 + ], + "spans": [ + { + "bbox": [ + 136, + 240, + 212, + 246 + ], + "score": 0.973, + "content": " doesn't sound like a human wrote it.", + "type": "text" + } + ], + "index": 17, + 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], + "score": 0.995, + "content": "Person 2: Did you call the repairman?", + "type": "text" + } + ], + "index": 25, + "is_list_start_line": true + }, + { + "bbox": [ + 328, + 245, + 403, + 256 + ], + "spans": [ + { + "bbox": [ + 328, + 245, + 403, + 256 + ], + "score": 0.992, + "content": "Person 1: Of course.", + "type": "text" + } + ], + "index": 26, + "is_list_end_line": true + } + ], + "index": 17, + "bbox_fs": [ + 129, + 213, + 297, + 273 + ] + }, + { + "type": "list", + "bbox": [ + 328, + 174, + 465, + 257 + ], + "lines": [], + "index": 24, + "bbox_fs": [ + 328, + 174, + 465, + 256 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 309, + 149, + 447, + 160 + ], + "lines": [ + { + "bbox": [ + 308, + 147, + 448, + 161 + ], + "spans": [ + { + "bbox": [ + 308, + 147, + 448, + 161 + ], + "score": 0.992, + "content": "Dialogue context (read me firstl):", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 27, + "bbox_fs": [ + 308, + 147, + 448, + 161 + ] + }, 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doesn't make", + "type": "text" + } + ], + "index": 34, + "is_list_start_line": true + }, + { + "bbox": [ + 136, + 324, + 164, + 329 + ], + "spans": [ + { + "bbox": [ + 136, + 324, + 164, + 329 + ], + "score": 0.968, + "content": "much sense.", + "type": "text" + } + ], + "index": 35, + "is_list_end_line": true + }, + { + "bbox": [ + 130, + 329, + 293, + 336 + ], + "spans": [ + { + "bbox": [ + 130, + 329, + 293, + 336 + ], + "score": 0.967, + "content": "○ 1/5 (wrong/nonsense/irrelevant): The generation doesn't seem to apply to", + "type": "text" + } + ], + "index": 36, + "is_list_start_line": true + }, + { + "bbox": [ + 135, + 335, + 231, + 343 + ], + "spans": [ + { + "bbox": [ + 135, + 335, + 231, + 343 + ], + "score": 0.975, + "content": "the dialogue at allor doesn't make any sense.", + "type": "text" + } + ], + "index": 37, + "is_list_end_line": true + } + ], + "index": 33, + "bbox_fs": [ + 129, + 283, + 293, + 343 + ] + }, + { + "type": "text", + "bbox": [ + 308, + 278, + 442, + 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And China is the homeland of tea . Yes , Chinese people love drinking", + "type": "text" + } + ], + "index": 60 + }, + { + "bbox": [ + 125, + 627, + 493, + 637 + ], + "spans": [ + { + "bbox": [ + 125, + 627, + 493, + 637 + ], + "score": 1.0, + "content": "tea so much . Some even claim they can’t live without tea . Do you know there are", + "type": "text" + } + ], + "index": 61 + }, + { + "bbox": [ + 126, + 635, + 489, + 645 + ], + "spans": [ + { + "bbox": [ + 126, + 635, + 489, + 645 + ], + "score": 1.0, + "content": "several catagories of Chinese tea ? Yes , I believe there are green teas , black", + "type": "text" + } + ], + "index": 62 + }, + { + "bbox": [ + 126, + 643, + 493, + 652 + ], + "spans": [ + { + "bbox": [ + 126, + 643, + 493, + 652 + ], + "score": 1.0, + "content": "teas and scented teas . Any Others ? 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I don’t have tea.", + "type": "text" + } + ], + "index": 68 + } + ], + "index": 68, + "bbox_fs": [ + 106, + 682, + 250, + 693 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 692, + 474, + 716 + ], + "lines": [ + { + "bbox": [ + 106, + 691, + 448, + 701 + ], + "spans": [ + { + "bbox": [ + 106, + 691, + 448, + 701 + ], + "score": 1.0, + "content": "Supervised: Yes. I hear they do good. And I heard this Taijiquan Tea is very good", + "type": "text" + } + ], + "index": 69 + }, + { + "bbox": [ + 106, + 699, + 477, + 709 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 152, + 709 + ], + "score": 1.0, + "content": "Supervised", + "type": "text" + }, + { + "bbox": [ + 152, + 700, + 159, + 706 + ], + "score": 0.51, + "content": "^ +", + "type": "inline_equation" + }, + { + "bbox": [ + 159, + 699, + 477, + 709 + ], + "score": 1.0, + "content": "PPO: Actually, I have had Oulong tea, but I haven’t had any for awhile now.", + "type": "text" + } + ], + "index": 70 + }, + { + "bbox": [ + 106, + 707, + 309, + 716 + ], + "spans": [ + { + "bbox": [ + 106, + 707, + 152, + 716 + ], + "score": 1.0, + "content": "Supervised", + "type": "text" + }, + { + "bbox": [ + 152, + 708, + 159, + 714 + ], + "score": 0.48, + "content": "^ +", + "type": "inline_equation" + }, + { + "bbox": [ + 159, + 707, + 309, + 716 + ], + "score": 1.0, + "content": "NLPO: No, I’ve never heard of that.", + "type": "text" + } + ], + "index": 71 + } + ], + "index": 70, + "bbox_fs": [ + 106, + 691, + 477, + 716 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 85, + 491, + 109 + ], + "lines": [ + { + "bbox": [ + 106, + 84, + 490, + 93 + ], + "spans": [ + { + "bbox": [ + 106, + 84, + 490, + 93 + ], + "score": 1.0, + "content": "Prompt: I think I might have a dahl . what’s in a dahl ? it’s got chickpeas and", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 126, + 92, + 485, + 102 + ], + "spans": [ + { + "bbox": [ + 126, + 92, + 485, + 102 + ], + "score": 1.0, + "content": "vegetables in a spicy curry sauce with rice . that sounds nice . Do you want to", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 127, + 100, + 434, + 109 + ], + "spans": [ + { + "bbox": [ + 127, + 100, + 434, + 109 + ], + "score": 1.0, + "content": "share some kebabs as well ? ok . How about some lamb kebabs ? ", + "type": "text" + } + ], + "index": 2 + } + ], + "index": 1 + }, + { + "type": "text", + "bbox": [ + 108, + 110, + 420, + 117 + ], + "lines": [ + { + "bbox": [ + 106, + 108, + 414, + 118 + ], + "spans": [ + { + "bbox": [ + 106, + 108, + 414, + 118 + ], + "score": 1.0, + "content": "References: that’s my favourite . Do you want to have some wine or beer ?", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 3 + }, + { + "type": "text", + "bbox": [ + 106, + 118, + 229, + 125 + ], + "lines": [ + { + "bbox": [ + 106, + 115, + 230, + 128 + ], + "spans": [ + { + "bbox": [ + 106, + 115, + 230, + 128 + ], + "score": 1.0, + "content": "Zero-Shot: they’re very salty", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 4 + }, + { + "type": "text", + "bbox": [ + 108, + 126, + 275, + 133 + ], + "lines": [ + { + "bbox": [ + 105, + 124, + 276, + 135 + ], + "spans": [ + { + "bbox": [ + 105, + 124, + 276, + 135 + ], + "score": 1.0, + "content": "PPO: well you might want to take a peek.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 5 + }, + { + "type": "text", + "bbox": [ + 107, + 134, + 199, + 141 + ], + "lines": [ + { + "bbox": [ + 106, + 133, + 200, + 141 + ], + "spans": [ + { + "bbox": [ + 106, + 133, + 200, + 141 + ], + "score": 1.0, + "content": "NLPO: well I like that", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 6 + }, + { + "type": "text", + "bbox": [ + 103, + 142, + 483, + 165 + ], + "lines": [ + { + "bbox": [ + 106, + 141, + 448, + 150 + ], + "spans": [ + { + "bbox": [ + 106, + 141, + 448, + 150 + ], + "score": 1.0, + "content": "Supervised: ok, here they are. I’m so thirsty. I can’t wait until the next bus to", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 148, + 486, + 158 + ], + "spans": [ + { + "bbox": [ + 106, + 148, + 151, + 158 + ], + "score": 1.0, + "content": "Supervised", + "type": "text" + }, + { + "bbox": [ + 152, + 150, + 159, + 156 + ], + "score": 0.48, + "content": "^ +", + "type": "inline_equation" + }, + { + "bbox": [ + 159, + 148, + 486, + 158 + ], + "score": 1.0, + "content": "PPO: I’ve tried that a few times, but they’re too dry and I don’t want any of", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 156, + 368, + 167 + ], + "spans": [ + { + "bbox": [ + 106, + 156, + 151, + 167 + ], + "score": 1.0, + "content": "Supervised", + "type": "text" + }, + { + "bbox": [ + 152, + 158, + 159, + 164 + ], + "score": 0.46, + "content": "^ +", + "type": "inline_equation" + }, + { + "bbox": [ + 159, + 156, + 368, + 167 + ], + "score": 1.0, + "content": "NLPO: oh, ok. That’s a good choice. I’ll take it.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 8 + }, + { + "type": "title", + "bbox": [ + 107, + 173, + 142, + 181 + ], + "lines": [ + { + "bbox": [ + 105, + 171, + 144, + 183 + ], + "spans": [ + { + "bbox": [ + 105, + 171, + 144, + 183 + ], + "score": 1.0, + "content": "Sample 3", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 10 + }, + { + "type": "text", + "bbox": [ + 107, + 181, + 503, + 236 + ], + "lines": [ + { + "bbox": [ + 106, + 180, + 494, + 189 + ], + "spans": [ + { + "bbox": [ + 106, + 180, + 494, + 189 + ], + "score": 1.0, + "content": "Prompt: Really ? Have you had an auto-reverse break before ? Yes , twice now . I think", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 126, + 188, + 497, + 199 + ], + "spans": [ + { + "bbox": [ + 126, + 188, + 497, + 199 + ], + "score": 1.0, + "content": "it’s too high-tech , and so it’s the first part that breaks . Hmm . You know , the", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 125, + 196, + 493, + 207 + ], + "spans": [ + { + "bbox": [ + 125, + 196, + 493, + 207 + ], + "score": 1.0, + "content": "problem might be dust . Did you clean the unit often ? Well . No , I didn’t clean", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 126, + 205, + 488, + 214 + ], + "spans": [ + { + "bbox": [ + 126, + 205, + 488, + 214 + ], + "score": 1.0, + "content": "it.But still , I only had the last one two months , and it broke . I don’t trust auto-", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 125, + 212, + 494, + 222 + ], + "spans": [ + { + "bbox": [ + 125, + 212, + 494, + 222 + ], + "score": 1.0, + "content": "reverse . Alright . Well . 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Are you sure about that?", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 20 + }, + { + "type": "text", + "bbox": [ + 107, + 261, + 292, + 268 + ], + "lines": [ + { + "bbox": [ + 105, + 259, + 293, + 270 + ], + "spans": [ + { + "bbox": [ + 105, + 259, + 293, + 270 + ], + "score": 1.0, + "content": "NLPO: Well. Well. I had no idea when it was,", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 21 + }, + { + "type": "text", + "bbox": [ + 108, + 269, + 275, + 276 + ], + "lines": [ + { + "bbox": [ + 106, + 267, + 276, + 278 + ], + "spans": [ + { + "bbox": [ + 106, + 267, + 276, + 278 + ], + "score": 1.0, + "content": "Supervised: Good.Well, what else I need?", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 22 + }, + { + "type": "text", + "bbox": [ + 113, + 277, + 451, + 285 + ], + "lines": [ + { + "bbox": [ + 110, + 275, + 452, + 285 + ], + "spans": [ + { + "bbox": [ + 110, + 275, + 152, + 285 + ], + "score": 1.0, + "content": "Supervised", + "type": "text" + }, + { + "bbox": [ + 152, + 277, + 159, + 283 + ], + "score": 0.49, + "content": "^ +", + "type": "inline_equation" + }, + { + "bbox": [ + 159, + 275, + 452, + 285 + ], + "score": 1.0, + "content": "PPO: But I think it lacks the CD player or its CD player accessories.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 23 + }, + { + "type": "text", + "bbox": [ + 111, + 285, + 337, + 292 + ], + "lines": [ + { + "bbox": [ + 109, + 284, + 339, + 293 + ], + "spans": [ + { + "bbox": [ + 109, + 284, + 152, + 293 + ], + "score": 1.0, + "content": "Supervised", + "type": "text" + }, + { + "bbox": [ + 152, + 285, + 159, + 291 + ], + "score": 0.53, + "content": "^ +", + "type": "inline_equation" + }, + { + "bbox": [ + 159, + 284, + 339, + 293 + ], + "score": 1.0, + "content": "NLPO: Cool! So what’s the trouble with it?", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 24 + } + ], + "page_idx": 60, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 300, + 752, + 310, + 760 + ], + "lines": [ + { + "bbox": [ + 298, + 750, + 312, + 763 + ], + "spans": [ + { + "bbox": [ + 298, + 750, + 312, + 763 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 13, + "width": 14 + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 107, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2023", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 85, + 491, + 109 + ], + "lines": [ + { + "bbox": [ + 106, + 84, + 490, + 93 + ], + "spans": [ + { + "bbox": [ + 106, + 84, + 490, + 93 + ], + "score": 1.0, + "content": "Prompt: I think I might have a dahl . what’s in a dahl ? it’s got chickpeas and", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 126, + 92, + 485, + 102 + ], + "spans": [ + { + "bbox": [ + 126, + 92, + 485, + 102 + ], + "score": 1.0, + "content": "vegetables in a spicy curry sauce with rice . that sounds nice . Do you want to", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 127, + 100, + 434, + 109 + ], + "spans": [ + { + "bbox": [ + 127, + 100, + 434, + 109 + ], + "score": 1.0, + "content": "share some kebabs as well ? ok . How about some lamb kebabs ? ", + "type": "text" + } + ], + "index": 2 + } + ], + "index": 1, + "bbox_fs": [ + 106, + 84, + 490, + 109 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 110, + 420, + 117 + ], + "lines": [ + { + "bbox": [ + 106, + 108, + 414, + 118 + ], + "spans": [ + { + "bbox": [ + 106, + 108, + 414, + 118 + ], + "score": 1.0, + "content": "References: that’s my favourite . Do you want to have some wine or beer ?", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 3, + "bbox_fs": [ + 106, + 108, + 414, + 118 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 118, + 229, + 125 + ], + "lines": [ + { + "bbox": [ + 106, + 115, + 230, + 128 + ], + "spans": [ + { + "bbox": [ + 106, + 115, + 230, + 128 + ], + "score": 1.0, + "content": "Zero-Shot: they’re very salty", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 4, + "bbox_fs": [ + 106, + 115, + 230, + 128 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 126, + 275, + 133 + ], + "lines": [ + { + "bbox": [ + 105, + 124, + 276, + 135 + ], + "spans": [ + { + "bbox": [ + 105, + 124, + 276, + 135 + ], + "score": 1.0, + "content": "PPO: well you might want to take a peek.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 5, + "bbox_fs": [ + 105, + 124, + 276, + 135 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 134, + 199, + 141 + ], + "lines": [ + { + "bbox": [ + 106, + 133, + 200, + 141 + ], + "spans": [ + { + "bbox": [ + 106, + 133, + 200, + 141 + ], + "score": 1.0, + "content": "NLPO: well I like that", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 6, + "bbox_fs": [ + 106, + 133, + 200, + 141 + ] + }, + { + "type": "text", + "bbox": [ + 103, + 142, + 483, + 165 + ], + "lines": [ + { + "bbox": [ + 106, + 141, + 448, + 150 + ], + "spans": [ + { + "bbox": [ + 106, + 141, + 448, + 150 + ], + "score": 1.0, + "content": "Supervised: ok, here they are. I’m so thirsty. I can’t wait until the next bus to", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 148, + 486, + 158 + ], + "spans": [ + { + "bbox": [ + 106, + 148, + 151, + 158 + ], + "score": 1.0, + "content": "Supervised", + "type": "text" + }, + { + "bbox": [ + 152, + 150, + 159, + 156 + ], + "score": 0.48, + "content": "^ +", + "type": "inline_equation" + }, + { + "bbox": [ + 159, + 148, + 486, + 158 + ], + "score": 1.0, + "content": "PPO: I’ve tried that a few times, but they’re too dry and I don’t want any of", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 156, + 368, + 167 + ], + "spans": [ + { + "bbox": [ + 106, + 156, + 151, + 167 + ], + "score": 1.0, + "content": "Supervised", + "type": "text" + }, + { + "bbox": [ + 152, + 158, + 159, + 164 + ], + "score": 0.46, + "content": "^ +", + "type": "inline_equation" + }, + { + "bbox": [ + 159, + 156, + 368, + 167 + ], + "score": 1.0, + "content": "NLPO: oh, ok. That’s a good choice. I’ll take it.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 8, + "bbox_fs": [ + 106, + 141, + 486, + 167 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 173, + 142, + 181 + ], + "lines": [ + { + "bbox": [ + 105, + 171, + 144, + 183 + ], + "spans": [ + { + "bbox": [ + 105, + 171, + 144, + 183 + ], + "score": 1.0, + "content": "Sample 3", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 10 + }, + { + "type": "text", + "bbox": [ + 107, + 181, + 503, + 236 + ], + "lines": [ + { + "bbox": [ + 106, + 180, + 494, + 189 + ], + "spans": [ + { + "bbox": [ + 106, + 180, + 494, + 189 + ], + "score": 1.0, + "content": "Prompt: Really ? Have you had an auto-reverse break before ? Yes , twice now . I think", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 126, + 188, + 497, + 199 + ], + "spans": [ + { + "bbox": [ + 126, + 188, + 497, + 199 + ], + "score": 1.0, + "content": "it’s too high-tech , and so it’s the first part that breaks . Hmm . You know , the", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 125, + 196, + 493, + 207 + ], + "spans": [ + { + "bbox": [ + 125, + 196, + 493, + 207 + ], + "score": 1.0, + "content": "problem might be dust . Did you clean the unit often ? Well . No , I didn’t clean", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 126, + 205, + 488, + 214 + ], + "spans": [ + { + "bbox": [ + 126, + 205, + 488, + 214 + ], + "score": 1.0, + "content": "it.But still , I only had the last one two months , and it broke . I don’t trust auto-", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 125, + 212, + 494, + 222 + ], + "spans": [ + { + "bbox": [ + 125, + 212, + 494, + 222 + ], + "score": 1.0, + "content": "reverse . Alright . Well . We have many units without auto-reverse.Here is a good", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 125, + 220, + 504, + 230 + ], + "spans": [ + { + "bbox": [ + 125, + 220, + 504, + 230 + ], + "score": 1.0, + "content": "unit . Very reliable.It has an AM / FM band , built-in microphone , recording capability ,", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 130, + 228, + 245, + 237 + ], + "spans": [ + { + "bbox": [ + 130, + 228, + 245, + 237 + ], + "score": 1.0, + "content": "and no auto-reverse . ", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 14, + "bbox_fs": [ + 106, + 180, + 504, + 237 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 237, + 225, + 244 + ], + "lines": [ + { + "bbox": [ + 106, + 236, + 227, + 245 + ], + "spans": [ + { + "bbox": [ + 106, + 236, + 227, + 245 + ], + "score": 1.0, + "content": "References: How much is it ?", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 18, + "bbox_fs": [ + 106, + 236, + 227, + 245 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 245, + 312, + 252 + ], + "lines": [ + { + "bbox": [ + 106, + 244, + 313, + 253 + ], + "spans": [ + { + "bbox": [ + 106, + 244, + 313, + 253 + ], + "score": 1.0, + "content": "Zero-Shot: Oh. So you don’t have the AM / FM band", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 19, + "bbox_fs": [ + 106, + 244, + 313, + 253 + ] + }, + { + "type": "text", + "bbox": [ + 109, + 253, + 307, + 261 + ], + "lines": [ + { + "bbox": [ + 108, + 252, + 305, + 261 + ], + "spans": [ + { + "bbox": [ + 108, + 252, + 305, + 261 + ], + "score": 1.0, + "content": "PPO: You said AM / FM. Are you sure about that?", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 20, + "bbox_fs": [ + 108, + 252, + 305, + 261 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 261, + 292, + 268 + ], + "lines": [ + { + "bbox": [ + 105, + 259, + 293, + 270 + ], + "spans": [ + { + "bbox": [ + 105, + 259, + 293, + 270 + ], + "score": 1.0, + "content": "NLPO: Well. Well. I had no idea when it was,", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 21, + "bbox_fs": [ + 105, + 259, + 293, + 270 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 269, + 275, + 276 + ], + "lines": [ + { + "bbox": [ + 106, + 267, + 276, + 278 + ], + "spans": [ + { + "bbox": [ + 106, + 267, + 276, + 278 + ], + "score": 1.0, + "content": "Supervised: Good.Well, what else I need?", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 22, + "bbox_fs": [ + 106, + 267, + 276, + 278 + ] + }, + { + "type": "text", + "bbox": [ + 113, + 277, + 451, + 285 + ], + "lines": [ + { + "bbox": [ + 110, + 275, + 452, + 285 + ], + "spans": [ + { + "bbox": [ + 110, + 275, + 152, + 285 + ], + "score": 1.0, + "content": "Supervised", + "type": "text" + }, + { + "bbox": [ + 152, + 277, + 159, + 283 + ], + "score": 0.49, + "content": "^ +", + "type": "inline_equation" + }, + { + "bbox": [ + 159, + 275, + 452, + 285 + ], + "score": 1.0, + "content": "PPO: But I think it lacks the CD player or its CD player accessories.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 23, + "bbox_fs": [ + 110, + 275, + 452, + 285 + ] + }, + { + "type": "text", + "bbox": [ + 111, + 285, + 337, + 292 + ], + "lines": [ + { + "bbox": [ + 109, + 284, + 339, + 293 + ], + "spans": [ + { + "bbox": [ + 109, + 284, + 152, + 293 + ], + "score": 1.0, + "content": "Supervised", + "type": "text" + }, + { + "bbox": [ + 152, + 285, + 159, + 291 + ], + "score": 0.53, + "content": "^ +", + "type": "inline_equation" + }, + { + "bbox": [ + 159, + 284, + 339, + 293 + ], + "score": 1.0, + "content": "NLPO: Cool! So what’s the trouble with it?", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 24, + "bbox_fs": [ + 109, + 284, + 339, + 293 + ] + } + ] + } + ], + "_backend": "pipeline", + "_version_name": "2.2.2" +} \ No newline at end of file diff --git a/parse/dev/CQsmMYmlP5T/CQsmMYmlP5T.md b/parse/dev/CQsmMYmlP5T/CQsmMYmlP5T.md new file mode 100644 index 0000000000000000000000000000000000000000..4d60916571be260addb159700d9886eb070b84b2 --- /dev/null +++ b/parse/dev/CQsmMYmlP5T/CQsmMYmlP5T.md @@ -0,0 +1,719 @@ +# GIT RE-BASIN: MERGING MODELS MODULO PERMUTATION SYMMETRIES + +Samuel K. Ainsworth, Jonathan Hayase, Siddhartha Srinivasa + +Paul G. Allen School of Computer Science and Engineering University of Washington {skainswo,jhayase,siddh}@cs.washington.edu + +# ABSTRACT + +The success of deep learning is due in large part to our ability to solve certain massive non-convex optimization problems with relative ease. Though non-convex optimization is NP-hard, simple algorithms – often variants of stochastic gradient descent – exhibit surprising effectiveness in fitting large neural networks in practice. We argue that neural network loss landscapes often contain (nearly) a single basin after accounting for all possible permutation symmetries of hidden units a la Entezari et al. (2021). We introduce three algorithms to permute the units of one model to bring them into alignment with a reference model in order to merge the two models in weight space. This transformation produces a functionally equivalent set of weights that lie in an approximately convex basin near the reference model. Experimentally, we demonstrate the single basin phenomenon across a variety of model architectures and datasets, including the first (to our knowledge) demonstration of zero-barrier linear mode connectivity between independently trained ResNet models on CIFAR-10. Additionally, we investigate intriguing phenomena relating model width and training time to mode connectivity. Finally, we discuss shortcomings of the linear mode connectivity hypothesis, including a counterexample to the single basin theory. + +# 1 INTRODUCTION + +We investigate the unreasonable effectiveness of stochastic gradient descent (SGD) algorithms on the high-dimensional non-convex optimization problems of deep learning. In particular, + +1. Why does SGD thrive in optimizing high-dimensional non-convex deep learning loss landscapes despite being noticeably less robust in other non-convex optimization settings, like policy learning (Ainsworth et al., 2021), trajectory optimization (Kelly, 2017), and recommender systems (Kang et al., 2016)? +2. What are all the local minima? When linearly interpolating between initialization and final trained weights, why does the loss smoothly and monotonically decrease (Goodfellow & Vinyals, 2015; Frankle, 2020; Lucas et al., 2021; Vlaar & Frankle, 2021)? +3. How can two independently trained models with different random initializations and data batch orders inevitably achieve nearly identical performance? Furthermore, why do their training loss curves often look identical? + +We posit that these phenomena point to the existence of some yet uncharacterized invariance(s) in the training dynamics causing independent training runs to exhibit similar characteristics. HechtNielsen (1990) noted the permutation symmetries of hidden units in neural networks; briefly, one can swap any two units of a hidden layer in a network and – assuming weights are adjusted accordingly – network functionality will not change. Recently, Benton et al. (2021) demonstrated that SGD solutions form a connected volume of low loss and Entezari et al. (2021) conjectured that this volume is convex modulo permutation symmetries. + +Conjecture 1 (Permutation invariance, informal (Entezari et al., 2021)). Most SGD solutions belong to a set whose elements can be permuted so that no barrier (as in Definition 2.2) exists on the linear interpolation between any two permuted elements. + +Table 1: Permutation symmetries of deep learning models vs. an upper estimate on the number of atoms in the known, observable universe. Deep learning loss landscapes contain incomprehensible amounts of geometric repetition. + +
ARCHITECTURENUM.PERMUTATIONSYMMETRIES
MLP (3 layers, 512 width)10 ^ 3498
VGG1610 ^ 35160
ResNet5010 ^ 55109
+ +Atoms in the observable universe 10 ∧ 82 + +We refer to such solutions as being linearly mode connected (LMC) (Frankle et al., 2020), an extension of mode connectivity (Garipov et al., 2018; Draxler et al., 2018). If true, Conjecture 1 will both materially expand our understanding of how SGD works in the context of deep learning and offer a credible explanation for the preceding phenomena, in particular. + +Contributions. In this paper, we attempt to uncover what invariances may be responsible for the phenomena cited above and the unreasonable effectiveness of SGD in deep learning. We make the following contributions: + +1. Matching methods. We propose three algorithms, grounded in concepts and techniques from combinatorial optimization, to align the weights of two independently trained models. Where appropriate, we prove hardness results for these problems and propose approximation algorithms. Our fastest method identifies permutations in mere seconds on current hardware. 2. Relationship to optimization algorithms. We demonstrate by means of counterexample that linear mode connectivity is an emergent property of training procedures, not of model architectures. We connect this result to prior work on the implicit biases of SGD. 3. Experiments, including zero-barrier LMC for ResNets. Empirically, we explore the existence of linear mode connectivity modulo permutation symmetries in experiments across MLPs, CNNs, and ResNets trained on MNIST, CIFAR-10, and CIFAR-100. We contribute the first-ever demonstration of zero-barrier LMC between two independently trained ResNets. We explore the relationship between LMC and model width as well as training time. Finally, we show evidence of our methods’ ability to combine models trained on independent datasets into a merged model that outperforms both input models in terms of test loss (but not accuracy) and is no more expensive in compute or memory than either input model. + +# 2 BACKGROUND + +Although our methods can be applied to arbitrary model architectures, we proceed with the multilayer perceptron (MLP) for its ease of presentation (Bishop, 2007). Consider an $L$ -layer MLP, + +$$ +f ( \pmb { x } ; \Theta ) = \pmb { z } _ { L + 1 } , \quad \pmb { z } _ { \ell + 1 } = \sigma ( \pmb { W } _ { \ell } \pmb { z } _ { \ell } + \pmb { b } _ { \ell } ) , \quad \pmb { z } _ { 1 } = \pmb { x } , +$$ + +where $\sigma$ denotes an element-wise nonlinear activation function. Furthermore, consider a loss, $\mathcal { L } ( \Theta )$ , that measures the suitability of a particular set of weights $\Theta$ towards some goal, e.g., fitting to a training dataset. + +Central to our investigation is the phenomenon of permutation symmetries of weight space. Given $\Theta$ , we can apply some permutation to the output features of any intermediate layer, $\ell$ , of the model, denoted by a permutation matrix $\pmb { P } \in S _ { d }$ ,1 + +$$ +z _ { \ell + 1 } = P ^ { \top } P z _ { \ell + 1 } = P ^ { \top } P \sigma ( W _ { \ell } z _ { \ell } + b _ { \ell } ) = P ^ { \top } \sigma ( P W _ { \ell } z _ { \ell } + P b _ { \ell } ) +$$ + +for $\sigma$ , an element-wise operator. It follows that as long as we reorder the input weights of layer $\ell + 1$ according to $P ^ { \top }$ , we will have a functionally equivalent model. To be precise, if we define $\Theta ^ { \prime }$ to be identical to $\Theta$ with the exception of + +$$ +\begin{array} { r } { { W } _ { \ell } ^ { \prime } = P { W } _ { \ell } , \quad { b } _ { \ell } ^ { \prime } = P { b } _ { \ell } , \quad { W } _ { \ell + 1 } ^ { \prime } = { W } _ { \ell + 1 } P ^ { \top } , } \end{array} +$$ + +then the two models are functionally equivalent: $f ( \pmb { x } ; \Theta ) = f ( \pmb { x } ; \Theta ^ { \prime } )$ for all inputs $_ { \textbf { \em x } }$ . This implies that for any trained weights $\Theta$ , there is an entire equivalence class of functionally equivalent weight assignments, not just one such $\Theta$ , and convergence to any one specific element of this equivalence class, as opposed to any others, is determined only by random seed. We denote a functionalitypreserving permutation of weights as $\pi ( \Theta )$ . + +Consider the task of reconciling the weights of two, independently trained models, $A$ and $B$ , with weights $\Theta _ { A }$ and $\Theta _ { B }$ , respectively, such that we can linearly interpolate between them. We assume that models $A$ and $B$ were trained with equivalent architectures but different random initializations, data orders, and potentially different hyperparameters or datasets, as well. Our central question is: Given $\Theta _ { A }$ and $\Theta _ { B }$ , can we identify some $\pi$ such that when linearly interpolating between $\Theta _ { A }$ and $\pi ( \Theta _ { B } )$ , all intermediate models enjoy performance similar to $\Theta _ { A }$ and $\Theta _ { B }$ ? + +![](images/b74fb2c8020c349d7fa616e0c2929d27002e3c9a4a43fd21b6f0a249ca20fdec.jpg) +Figure 1: Git Re-Basin merges models by teleporting solutions into a single basin. $\Theta _ { B }$ is permuted into functionally-equivalent $\pi ( \Theta _ { B } )$ so that it lies in the same basin as $\Theta _ { A }$ . + +We base any claims of loss landscape convexity on the usual definition of multi-dimensional convexity in terms of one-dimensional convexity per + +Definition 2.1 (Convexity). A function $f : \mathbb { R } ^ { D } \mathbb { R }$ is convex if every one-dimensional slice is convex, i.e., for all $x , y \in \mathbb { R } ^ { D }$ , the function $g ( \lambda ) = f ( ( 1 - \lambda ) x + \lambda y )$ is convex in $\lambda$ . + +Due to Definition 2.1, it suffices to show that arbitrary one-dimensional slices of a function are convex in order to reason about the convexity of complex, high-dimensional functions. In practice, we rarely observe perfect convexity but instead hope to approximate it as closely as possible. Following Frankle et al. (2020); Entezari et al. (2021); Draxler et al. (2018); Garipov et al. (2018) and others, we measure approximations to convexity via “barriers.” + +Definition 2.2 (Loss barrier (Frankle et al., 2020)). Given two points $\Theta _ { A } , \Theta _ { B }$ such that $\mathcal { L } ( \Theta _ { A } ) \approx$ $\mathcal { L } ( \Theta _ { B } )$ , the loss barrier is defined as $\begin{array} { r } { \operatorname* { m a x } _ { \lambda \in [ 0 , 1 ] } \mathcal { L } ( ( 1 - \lambda ) \Theta _ { A } + \lambda \Theta _ { B } ) - \frac { 1 } { 2 } ( \mathcal { L } ( \Theta _ { A } ) + \mathcal { L } ( \dot { \Theta } _ { B } ) \dot { ) } } \end{array}$ . + +Loss barriers are non-negative, with zero indicating an interpolation of flat or positive curvature. + +# 3 PERMUTATION SELECTION METHODS + +We introduce three methods of matching units between model $A$ and model $B$ . Further, we present an extension to simultaneously merging multiple models in Appendix A.10 and an appealing but failed method in Appendix A.11. + +# 3.1 MATCHING ACTIVATIONS + +Following the classic Hebbian mantra, “[neural network units] that fire together, wire together” (Hebb, 2005), we consider associating units across two models by performing regression between their activations. Matching activations between models is compelling since it captures the intuitive notion that two models must learn similar features to accomplish the same task (Li et al., 2016). Provided activations for each model, we aim to associate each unit in $A$ with a unit in $B$ . It stands to reason that a linear relationship may exist between the activations of the two models. We fit this into the regression framework by constraining ordinary least squares (OLS) to solutions in the set of permutation matrices, $S _ { d }$ . For activations of the $\ell ^ { \bullet }$ th layer, let $\mathbf { \bar { \chi } } _ { Z ^ { ( A ) } , Z ^ { ( B ) } } \in \mathbb { R } ^ { d \times n }$ denote the $d$ -dim. activations for all $n$ training data points in models $A$ and $B$ , respectively. Then, + +$$ +P _ { \ell } = \underset { P \in S _ { d } } { \arg \operatorname* { m i n } } \sum _ { i = 1 } ^ { n } \| Z _ { : , i } ^ { ( A ) } - P Z _ { : , i } ^ { ( B ) } \| ^ { 2 } = \underset { P \in S _ { d } } { \arg \operatorname* { m a x } } \langle P , Z ^ { ( A ) } ( Z ^ { ( B ) } ) ^ { \top } \rangle _ { F } , +$$ + +where $\begin{array} { r } { \langle { \boldsymbol A } , { \boldsymbol B } \rangle _ { F } = \sum _ { i , j } A _ { i , j } B _ { i , j } } \end{array}$ denotes the Frobenius inner product between real-valued matrices $\pmb { A }$ and $\textbf { { B } }$ . Conveniently, eq. (1) constitutes a “linear assignment problem” (LAP) (Bertsekas, 1998) for which efficient, practical algorithms are known. Having solved this assignment problem on each layer, we can then permute the weights of model $B$ to match model $A$ as closely as possible + +$$ +\pmb { W } _ { \ell } ^ { \prime } = \pmb { P } _ { \ell } \pmb { W } _ { \ell } ^ { ( B ) } \pmb { P } _ { \ell - 1 } ^ { \top } , \quad \pmb { b } _ { \ell } ^ { \prime } = \pmb { P } _ { \ell } \pmb { b } _ { \ell } ^ { ( B ) } +$$ + +for each layer $\ell$ , producing weights $\Theta ^ { \prime }$ with activations that align as closely possible with $\Theta _ { A }$ + +Computationally, this entire process is relatively lightweight: the $\pmb { Z } ^ { ( A ) }$ and ${ \pmb Z } ^ { ( B ) }$ matrices can be computed in a single pass over the training dataset, and, in practice, a full run through the training dataset may be unnecessary. Solving eq. (1) is possible due to well-established, polynomial-time algorithms for solving the linear assignment problem (Kuhn, 2010; Jonker & Volgenant, 1987; Crouse, 2016). Also, conveniently, the activation matching at each layer is independent of the matching at every other layer, resulting in a separable and straightforward optimization problem; this advantage will not be enjoyed by the following methods. + +Dispensing with regression, one could similarly associate units by matching against a matrix of cross-correlation coefficients in place of $Z ^ { ( A ) } ( \dot { Z } ^ { ( B ) } ) ^ { \top }$ . We observed correlation matching to work equally well but found OLS regression matching to be more principled and easier to implement. + +Activation matching has previously been studied for model merging in Tatro et al. (2020); Singh & Jaggi (2020); Li et al. (2016) albeit not from the perspective of OLS regression. + +# 3.2 MATCHING WEIGHTS + +Instead of associating units by their activations, we could alternatively inspect the weights of the model itself. Consider the first layer weights, $W _ { 1 }$ ; each row of $W _ { 1 }$ corresponds to a single feature. If two such rows were equal, they would compute exactly the same feature (ignoring bias terms for the time being). And, if $[ \pmb { W } _ { 1 } ^ { ( A ) } ] _ { i , : } \approx [ \pmb { W } _ { 1 } ^ { ( B ) } ] _ { j , : }$ , it stands to reason that units $i$ and $j$ should be associated. Extending this idea to every layer, we are inspired to pursue the optimization + +$$ +\underset { \pi } { \arg \operatorname* { m i n } } \ \| \mathrm { v e c } ( \Theta _ { A } ) - \mathrm { v e c } ( \pi ( \Theta _ { B } ) ) \| ^ { 2 } = \underset { \pi } { \arg \operatorname* { m a x } } \ \mathrm { v e c } ( \Theta _ { A } ) \cdot \mathrm { v e c } ( \pi ( \Theta _ { B } ) ) . +$$ + +We can re-express this in terms of the full weights, + +$$ +\operatorname * { a r g m a x } _ { \pi = \{ P _ { i } \} } \langle { \pmb W } _ { 1 } ^ { ( A ) } , { \pmb P } _ { 1 } { \pmb W } _ { 1 } ^ { ( B ) } \rangle _ { F } + \langle { \pmb W } _ { 2 } ^ { ( A ) } , { \pmb P } _ { 2 } { \pmb W } _ { 2 } ^ { ( B ) } { \pmb P } _ { 1 } ^ { \top } \rangle _ { F } + \cdot \cdot + \langle { \pmb W } _ { L } ^ { ( A ) } , { \pmb W } _ { L } ^ { ( B ) } { \pmb P } _ { L - 1 } ^ { \top } \rangle _ { F } , +$$ + +resulting in another matching problem. We term this formulation the “sum of bilinear assignments problem” (SOBLAP). Unfortunately, this matching problem is thornier than the classic linear assignment matching problem presented in eq. (1). Unlike LAP, we are interested in permuting both the rows and columns of $W _ { \ell } ^ { ( B ) }$ ) to match W (A)ℓ , which fundamentally differs from permuting only rows or only columns. We formalize this difficulty as follows. + +Lemma 1. The sum of a bilinear assignments problem (SOBLAP) is NP-hard and admits no polynomial-time constant-factor approximation scheme for $L > 2$ . + +Lemma 1 contrasts starkly with classical LAP, for which polynomial-time algorithms are known. + +Undeterred, we propose a approximation algorithm for SOBLAP. Looking at a single $P _ { \ell }$ while holding the others fixed, we observe that the problem can be reduced to a classic LAP, + +$$ +\begin{array} { r l } & { \underset { P _ { \ell } } { \arg \operatorname* { m a x } } \ \langle { \boldsymbol W } _ { \ell } ^ { ( A ) } , P _ { \ell } { \boldsymbol W } _ { \ell } ^ { ( B ) } { \boldsymbol P } _ { \ell - 1 } ^ { \top } \rangle _ { F } + \langle { \boldsymbol W } _ { \ell + 1 } ^ { ( A ) } , P _ { \ell + 1 } { \boldsymbol W } _ { \ell + 1 } ^ { ( B ) } { \boldsymbol P } _ { \ell } ^ { \top } \rangle _ { F } } \\ & { \qquad = \underset { P _ { \ell } } { \arg \operatorname* { m a x } } \ \langle P _ { \ell } , { \boldsymbol W } _ { \ell } ^ { ( A ) } { \boldsymbol P } _ { \ell - 1 } ( { \boldsymbol W } _ { \ell } ^ { ( B ) } ) ^ { \top } + ( { \boldsymbol W } _ { \ell + 1 } ^ { ( A ) } ) ^ { \top } P _ { \ell + 1 } { \boldsymbol W } _ { \ell + 1 } ^ { ( B ) } \rangle _ { F } . } \end{array} +$$ + +This leads to a convenient coordinate descent algorithm: go through each layer and greedily select its best $P _ { \ell }$ . Repeat until convergence. We present this in Algorithm 1. + +Although we present Algorithm 1 in terms of an MLP without bias terms, in practice our implementation can handle the weights of models of nearly arbitrary architectures, including bias terms, residual connections, convolutional layers, attention mechanisms, and so forth. We propose an extension of Algorithm 1 to merging more than two models at a time in Appendix A.10. + +![](images/6728305d713c85f40792a9007e2fd199d0797f18b8248371f77b8af3c0dced39.jpg) +Figure 2: Linear mode connectivity is possible after permuting. Loss landscapes when interpolating between models trained on MNIST, CIFAR-10, and ImageNet. In all cases we can significantly improve over na¨ıve interpolation. Straight-through estimator matching performs best but is very computationally expensive. Weight and activation matching perform similarly, although weight matching is orders of magnitude faster and does not rely on the input data distribution. We hypothesize that the ImageNet barrier could be reduced by increasing the model width as in Section 5.3. + +Algorithm 1: PERMUTATIONCOORDINATEDESCENT +Lemma 2. Algorithm 1 terminates. + +
AIgorIthmI:PERMUTATIONCOORDINATEDESCENT Given:Mode weigts A = {w(4),., [4)} and θB ={~w(B),.. W}
Result: A permutation π = {P1,...,PL-1} of OB such that vec(ΘA) · vec(π(OB)) is approximately maximized.
Initialize:Pl←I,...,PL-1 ←I
repeat
for l∈RANDOMPERMUTATION(1,...,L-1) do
P←SOLvELAP（W()P-1(W(B）+(W(）1W)）
end until convergence
+ +Our experiments showed this algorithm to be fast in terms of both iterations necessary for convergence and wall-clock time, generally on the order of seconds to a few minutes. + +Unlike the activation matching method presented in Section 3.1, weight matching ignores the data distribution entirely. Ignoring the input data distribution and therefore the loss landscape handicaps weight matching but allows it to be much faster. We therefore anticipate its potential application in fields such as finetuning (Devlin et al., 2019; Wortsman et al., 2022b;a), federated learning (McMahan et al., 2017; Konecnˇ y et al., 2016a;b), and model patching (Matena & Raffel, 2021; Sung et al.,´ 2021; Raffel, 2021). In practice, we found weight matching to be surprisingly competitive with data-aware methods. Section 5 studies this trade-off. + +# 3.3 LEARNING PERMUTATIONS WITH A STRAIGHT-THROUGH ESTIMATOR + +Inspired by the success of straight-through estimators (STEs) in other discrete optimization problems (Bengio et al., 2013; Kusupati et al., 2021; Rastegari et al., 2016; Courbariaux & Bengio, 2016), we attempt here to “learn” the ideal permutation of weights $\pi ( \Theta _ { B } )$ . Specifically, our goal is to optimize + +$$ +\operatorname* { m i n } _ { \hat { \Theta } _ { B } } \ { \mathcal { L } } \left( { \frac { 1 } { 2 } } \left( \Theta _ { A } + \mathrm { p r o j } \left( { \widetilde { \Theta } } _ { B } \right) \right) \right) , \qquad \mathrm { p r o j ( \Theta ) } \ { \overset { \triangle } { = } } \ \arg \operatorname* { m a x } _ { \pi } \ \mathrm { v e c } ( \Theta ) \cdot \mathrm { v e c } ( \pi ( \Theta _ { B } ) ) , +$$ + +where $\tilde { \Theta } _ { B }$ denotes an approximation of $\pi ( \Theta _ { B } )$ , allowing us to implicitly optimize $\pi$ . However, eq. (3) involves inconvenient non-differentiable projection operations, proj $( \cdot )$ , complicating the optimization. We overcome this via a “straight-through” estimator: we parameterize the problem in terms of a set of weights $\tilde { \Theta } _ { B } \approx \pi ( \Theta _ { B } )$ . In the forward pass, we project $\tilde { \Theta } _ { B }$ to the closest realizable $\pi ( \Theta _ { B } )$ . In the backwards pass, we then switch back to the unrestricted weights $\tilde { \Theta } _ { B }$ . In this way, we are guaranteed to stay true to the projection constraints in evaluating the loss but can still compute usable gradients at our current parameters, $\tilde { \Theta } _ { B }$ .2 + +![](images/66fdb92d5345a394d0ef2d04adc18349df134e93a47aae13eddad25cda8fb2bb.jpg) +Figure 3: Linear mode connectivity is challenging at initialization. We show loss barriers per training time for MLPs trained on MNIST (left) and CIFAR-10 (right). Loss interpolation plots are inlaid to highlight results in initial and later epochs. LMC manifests gradually throughout training. We hypothesize that the variance in CIFAR-10 training is higher due to our MLP architecture being under-powered relative to the dataset. (Y-axis scales differ in each inlaid plot.) + +Conveniently, we can re-purpose Algorithm 1 to solve proj $( { \tilde { \Theta } } _ { B } )$ . Furthermore, we found that initializing $\tilde { \Theta } _ { B } = \Theta _ { A }$ performed better than random initialization. This is to be expected immediately at initialization since the initial matching will be equivalent to the weight matching method of Section 3.1. However, it is not immediately clear why these solutions continue to outperform a random initialization asymptotically. + +Unlike the aforementioned methods, Algorithm 2 attempts to explicitly “learn” the best permutation $\pi$ using a conventional training loop. By initializing to the weight matching solution of Section 3.2 and leveraging the data distribution as in Section 3.1, it seeks to offer a best-of-both-worlds solution. However, this comes at a very steep computational cost relative to the other two methods. + +# 4 A COUNTEREXAMPLE TO UNIVERSAL LINEAR MODE CONNECTIVITY + +In this section we argue that common optimization algorithms, especially SGD and its relatives, are implicitly biased towards solutions admitting linear mode connectivity. In particular, we demonstrate – by way of a counterexample – that adversarial, non-SGD solutions exist in loss landscapes such that no permutation of units results in linear mode connectivity. We present this counterexample in complete detail in Appendix A.6. + +The existence of adversarial basins suggests that our ability to find LMC between independently trained models is thanks to inherent biases in optimization methods. We emphasize that this counterexample does not contradict Conjecture 1; rather, it illustrates the importance of the conjecture’s restriction to SGD solutions (Entezari et al., 2021). Characterizing the precise mechanism by which these solutions are biased towards LMC could be an exciting avenue for future work. + +We also note that there are invariances beyond permutation symmetries: It is possible to move features between layers, re-scale layers, and so forth. Prior works noted the feature/layer association (Nguyen et al., 2021) and re-scaling invariances (Ainsworth et al., 2018). The importance of these other symmetries and their interplay with optimization algorithms remains unclear. + +# 5 EXPERIMENTS + +Our base methodology is to separately train two models, $A$ and $B$ , starting from different random initializations and with different random batch orders, resulting in trained weights $\Theta _ { A }$ and $\Theta _ { B }$ , respectively. We then evaluate slices through the loss landscape, $\mathcal { L } ( ( 1 - \lambda ) \Theta _ { A } + \lambda \pi ( \Theta _ { B } ) )$ for $\lambda \in [ 0 , 1 ]$ , where $\pi$ is selected according to the methods presented in Section 3.3 Ideally, we seek a completely flat or even convex one-dimensional slice. As discussed in Section 2, the ability to exhibit this behavior for arbitrary $\Theta _ { A } , \Theta _ { B }$ empirically suggests that the loss landscape contains only a single basin modulo permutation symmetries. + +![](images/3e2b1e1ca8930ad7cb63f4865ef94b31090d2207fcd8a0648f4d185bd101dc14.jpg) +Figure 4: Wider models exhibit better linear mode connectivity. Training convolutional and ResNet architectures on CIFAR-10, we ablate their width and visualize loss barriers after weight matching. Notably, we achieve zero-barrier linear mode connectivity between ResNet models, the first such demonstration. + +We remark that a failure to find a $\pi$ such that linear mode connectivity holds cannot rule out the existence of a satisfactory permutation. Given the astronomical number of permutation symmetries, Conjecture 1 is essentially impossible to disprove for any realistically wide model architecture. + +# 5.1 LOSS LANDSCAPES BEFORE AND AFTER MATCHING + +We present results for models trained on MNIST (LeCun et al., 1998), CIFAR-10 (Krizhevsky, 2009), and ImageNet (Deng et al., 2009) in Figure 2. Na¨ıve interpolation $( \pi ( \Theta _ { B } ) = \Theta _ { B } )$ ) substantially degrades performance when interpolating. On the other hand, the methods introduced in Section 3 can achieve much better barriers. We achieve zero-barrier linear mode connectivity on MNIST with all three methods, although activation matching performs just slightly less favorably than weight matching and straight-through estimator (STE) matching. We especially note that the test loss landscape becomes convex after applying our weight matching and STE permutations! In other words, our interpolation actually yields a merged model that outperforms both models $A$ and $B$ . We elaborate on this phenomenon in Section 5.4 and Appendix A.10. + +On ImageNet we fall short of zero-barrier connections, although we do see a $67 \%$ decrease in barrier relative to na¨ıve interpolation. As we demonstrate in Section 5.3, we can achieve zero-barrier LMC on CIFAR-10 with large ResNet models. Therefore, we hypothesize that the presence of LMC depends on the model having sufficient capacity (esp. width) to capture the complexity of the input data distribution, and that ImageNet results could be improved by expanding model width. + +STE matching, the most expensive method, produces the best solutions. Somewhat surprising, however, is that the gap between STE and the other two methods is relatively small. In particular, it is remarkable how well Algorithm 1 performs without access to the input data at all. We found that weight matching offered a compelling balance between computational cost and performance: It runs in mere seconds (on current hardware) and produces high-quality solutions. + +# 5.2 ONSET OF MODE CONNECTIVITY + +Given the results of Section 5.1, it may be tempting to conclude that the entirety of weight space contains only a single basin modulo permutation symmetries. However, we found that linear mode connectivity is an emergent property of training, and we were unable to uncover it early in training. We explore the emergence of LMC in Figure 3. Concurrent to our work, Benzing et al. (2022) showed that LMC at initialization is possible using a permutation found at the end of training. + +Note that the final inlaid interpolation plot in Figure 3(right) demonstrates an important shortcoming of the loss barrier metric, i.e., the interpolation includes points with lower loss than either of the two models. However, the loss barrier is still positive due to non-negativity, as mentioned in Section 2. + +# 5.3 EFFECT OF MODEL WIDTH + +Conventional wisdom maintains that wider architectures are easier to optimize (Jacot et al., 2018; Lee et al., 2019). We now investigate whether they are also easier to linearly mode connect. We train VGG-16 (Simonyan & Zisserman, 2015) and ResNet20 (He et al., 2016) architectures of varying widths on the CIFAR-10 dataset. Results are presented in Figure 4.4 + +A clear relationship emerges between model width and linear mode connectivity, as measured by the loss barrier between solutions. Although $1 \times$ -sized models did not seem to exhibit linear mode connectivity, we found that larger width models decreased loss barriers all the way to zero. In Figure 4(right), we show what is to our knowledge the premiere demonstration of zero-barrier linear mode connectivity between two large ResNet models trained on a non-trivial dataset. + +We highlight that relatively thin models do not seem to obey linear mode connectivity yet still exhibit similarities in training dynamics. This suggests that either our permutation selection methods are failing to find satisfactory permutations on thinner models or that some form of invariance other than permutation symmetries must be at play in the thin model regime. + +# 5.4 MODEL PATCHING, SPLIT DATA TRAINING, AND IMPROVED CALIBRATION + +Inspired by work on finetuning (Wortsman et al., 2022a), model patching (Singh & Jaggi, 2020; Raffel, 2021), and federated learning (McMahan et al., 2017; Konecnˇ y et al., ´ 2016a;b), we study whether it is possible to synergistically merge the weights of two models trained on disjoint datasets. Consider, for example, an organization with multiple (possibly biased) datasets separated for regulatory (e.g., GDPR) or privacy (e.g., on-device data) considerations. Models can be trained on each dataset individually, but training in aggregate is not feasible. Can we combine separately trained models so that the merged model performs well on the entirety of the data? + +To address this question, we split the CIFAR100 dataset (Krizhevsky, 2009) into two disjoint subsets: dataset $A$ , containing $20 \%$ examples labelled 0-49 and $80 \%$ labelled 50-99, and dataset $B$ , vice versa. ResNet20 models $A$ and + +![](images/a40f48d35cd25ea9dc31ac529bdb2112216b0505ab81b6a1603e143e0e364bc6.jpg) +Figure 5: Models trained on disjoint datasets can be merged constructively. Algorithm 1 makes it possible for two ResNet models trained on disjoint, biased subsets of CIFAR-100 to be merged in weight space such that their combination outperforms both input models in terms of test loss on the combined dataset. + +$B$ were trained on their corresponding datasets. Privacy requirements mandate that we utilize a data-agnostic algorithm like Algorithm 1. Figure 5 shows the result of merging the two models with weight matching. For comparison, we benchmark na¨ıve weight interpolation, ensembling of the model logits, and full-data training. + +As expected, merging separately trained models did not match the performance of an omniscient model trained on the full dataset or an ensemble of the two models with twice the number of effective weights. On the other hand, we did manage to merge the two models in weight space, achieving an interpolated model that outperforms both input models in terms of test loss while using half the memory and compute required for ensembling. Furthermore, the merged model’s probability estimates are better calibrated than either of the input models as demonstrated in Figure 11. Accuracy results are presented in Figure 10. Algorithm 1 also vastly outperformed na¨ıve interpolation, the status quo for model combination in federated learning and distributed training. + +# 6 RELATED WORK + +(Linear) mode connectivity. Garipov et al. (2018); Draxler et al. (2018); Freeman & Bruna (2017) showed that different solutions in the neural network loss landscape could be connected by paths of near-constant loss, which Garipov et al. (2018) coined “mode connectivity.” Tatro et al. (2020) explored non-linear mode connectivity modulo permutation symmetries. Frankle et al. (2020) demonstrated a connection between linear mode connectivity and the lottery ticket hypothesis. Juneja et al. (2022) demonstrated that LMC does not always hold, even when fine-tuning. Hecht-Nielsen (1990); Chen et al. (1993) noted the existence of permutation symmetries, and Brea et al. (2019) implicated them as a source of saddle points in the loss landscape. Recently, the prescient work of Entezari et al. (2021) conjectured that SGD solutions could be linear mode connected modulo permutation symmetries and offered experiments buttressing this claim. Unlike previous works on LMC we accomplish zero-barrier paths between two independently-trained models with an algorithm that runs on the order of seconds. + +Loss landscapes and training dynamics. Li et al. (2016); Yosinski et al. (2014) investigated whether independently trained networks learn similar features, and to what extent they transfer. Jiang et al. (2021) argued that independently trained networks meaningfully differ in the features they learn in certain scenarios. Zhang et al. (2019) studied the relative importance of layers. Benton et al. (2021) argued that SGD solutions form a connected volume of low loss. Pittorino et al. (2022) proposed a toroidal topology of solutions and a set of algorithms for symmetry removal. On the theoretical front, Kawaguchi (2016) proved that deep linear networks contain no local minima. Boursier et al. (2022); Chizat & Bach (2018); Mei et al. (2018) characterized the training dynamics of one-hidden layer networks, proving that they converge to zero loss. Godfrey et al. (2022); Simsek et al. (2021) investigated the algebraic structure of symmetries in neural networks and how this structure manifests in loss landscape geometry. + +Federated learning and model merging. McMahan et al. (2017); Konecnˇ y et al. (2016a;b) in- ´ troduced the concept of “federated learning,” i.e., learning split across across multiple devices and datasets. Wang et al. (2020) proposed an exciting federated learning method in which model averaging is done after permuting units. Unlike this work, they merged smaller “child” models into a larger “main” model, and did so with a layer-wise algorithm that does not support residual connections or normalization layers. Raffel (2021); Matena & Raffel (2021); Sung et al. (2021) conceptualized the study of “model patching,” i.e., the idea that models should be easy to modify and submit changes to. Ilharco et al. (2022) investigated model patching for the fine-tuning of open-vocabulary vision models. Ashmore & Gashler (2015) first explored the use of matching algorithms for the alignment of network units. Singh & Jaggi (2020) proposed merging models by soft-aligning associations weights, inspired by optimal transport. Liu et al. (2022a); Uriot & Izzo (2020) further explored merging models taking possible permutations into account. Wortsman et al. (2022a) demonstrated state-of-the-art ImageNet performance by averaging the weights of many fine-tuned models. + +# 7 DISCUSSION AND FUTURE WORK + +We explore the role of permutation symmetries in the linear mode connectivity of SGD solutions. We present three algorithms to canonicalize independent neural network weights in order to make the loss landscape between them as flat as possible. In contrast to prior work, we linearly mode connect large ResNet models with no barrier in seconds to minutes. Despite presenting successes across multiple architectures and datasets, linear mode connectivity between thin models remains elusive. Therefore, we conjecture that permutation symmetries are a necessary piece, though not a complete picture, of the fundamental invariances at play in neural network training dynamics. In particular, we hypothesize that linear, possibly non-permutation, relationships connect the layerwise activations between models trained by SGD. In the infinite width limit, there exist satisfactory linear relationships that are also permutations. + +An expanded theory and empirical exploration of other invariances – such as cross-layer scaling or general linear relationships between activations – presents an intriguing avenue for future work. Ultimately, we anticipate that a lucid understanding of loss landscape geometry will not only advance the theory of deep learning but will also promote the development of better optimization, federated learning, and ensembling techniques. + +# ETHICS STATEMENT + +Merging models raises interesting ethical and technical questions about the resulting models. Do they inherit the same biases as their input models? Are rare examples forgotten when merging? Is it possible to gerrymander a subset of the dataset by splitting its elements across many shards? + +Deployment of any form of model merging ought to be paired with thorough auditing of the resulting model, investigating in particular whether the merged model is representative of the entirety of the data distribution. + +# REPRODUCIBILITY STATEMENT + +Our code is open sourced at https://github.com/samuela/git-re-basin. Our experimental logs and downloadable model checkpoints are fully open source at https://wandb.ai/ skainswo/git-re-basin. + +# ACKNOWLEDGMENTS + +We are grateful to Vivek Ramanujan, Mitchell Wortsman, Aditya Kusupati, Rahim Entezari, Jason Yosinski, Krishna Pillutla, Ofir Press, Matt Wallingford, Tim Dettmers, Raghav Somani, Gabriel Ilharco, Ludwig Schmidt, Sewoong Oh, and Kevin Jamieson for enlightening discussions. Thank you to John Thickstun and Sandy Kaplan for their thoughtful review of an earlier draft of this work and to Ofir Press and Tim Dettmers for their potent advice on framing and communicating this work. This work was (partially) funded by the National Science Foundation NRI (#2132848) & CHS (#2007011), DARPA RACER, the Office of Naval Research, Honda Research Institute, and Amazon. This work is supported in part by Microsoft and NSF grants DMS-2134012 and CCF2019844 as a part of NSF Institute for Foundations of Machine Learning (IFML). + +# REFERENCES + +Samuel K. 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URL http://arxiv.org/abs/1902.01996. + +# A APPENDIX + +# A.1 KNOWN FAILURE MODES + +We emphasize that none of the techniques presented in this paper are silver bullets. Here we list the failure cases that the authors are presently aware of, + +1. Models of insufficient width +2. Models in the initial stages of training +3. VGGs on MNIST +4. MNIST MLPs trained with SGD and too low of a learning rate, or Adam and too high of a learning rate +5. ConvNeXt architectures (Liu et al., 2022b), which have surprisingly few permutation symmetries due to extensive use of depth-wise convolutions + +Furthermore, we believe other failure modes certainly exist but have yet to be discovered. + +We are excited by the prospect of future work investigating these failure modes and improving our understanding of when and why model merging modulo permutation symmetries is feasible. + +# A.2 EXTENDED RELATED WORK + +Non-linear mode connectivity. A flourishing set of literature exists studying non-linear mode connectivity, including but not limited to Garipov et al. (2018); Draxler et al. (2018); Kuditipudi et al. (2019). This insightful line of work is inspirational to our own, however we take a strictly linear approach to mode connectivity as in Frankle et al. (2020); Juneja et al. (2022). Restricting ourselves to linear trajectories comes with the advantage of having direct implications for a single-basin theory. However, it comes at the cost of a more challenging, discrete optimization problem. In particular, we found that – in contrast to non-linear mode connectivity – linear mode connectivity becomes drastically harder with smaller width models. Note additionally that most pre-existing mode connectivity work does not account for permutation symmetries of weight space, a linchpin element of our work. A notable exception to this trend can be found in Tatro et al. (2020). + +To summarize: Freeman & Bruna (2017) introduced the notion of mode connectivity and proved that loss landscapes for single-hidden layer ReLU models contain only a single basin in the infinite width limit. Garipov et al. (2018) and Draxler et al. (2018) concurrently demonstrated that simple zero-barrier curves can be learned to connect the optima in weight space, thus reshaping our understanding of practical loss landscape geometries. Kuditipudi et al. (2019) proposes a theoretical explanation for the mode connectivity phenomenon. Benton et al. (2021) extends mode connectivity from one-dimensional paths to entire manifolds of low-loss, and show that these manifolds can be leveraged for state-of-the-art Bayesian ensembling of models. + +Relationship with Tatro et al. (2020). The impact of permutation symmetries on the non-linear mode connectivity of models is considered in Tatro et al. (2020). In particular, they independently propose an algorithm more-or-less equivalent to Section 3.1 but use it in conjunction with learned non-linear mode connecting curves. In contrast, we show that linear mode connectivity can be achieved without the need for learning non-linear paths between the aligned weights. Our derivation of Section 3.1 from the principle of least-squares regression is novel, to the best of our knowledge. + +Relationship with Singh & Jaggi (2020). Singh & Jaggi (2020) studies model merging with “soft matchings” between units from the perspective of optimal transport. We emphasize the following commonalities/differences with their work: + +• We focus on linear mode connectivity modulo permutation symmetries and its implications for a single-basin theory. On the other hand, Singh & Jaggi (2020) emphasizes “soft” (ie., non-permutation) matching of units via optimal transport. +• The activation matching method of Singh & Jaggi (2020) reduces to that of Section 3.1 when the optimal transport regularization term is set to zero and the unit “importance” values are set to uniform across all units on all layers. +• Our weight matching and straight-through estimator methods solve for an alignment across all layers jointly. In contrast, Singh & Jaggi (2020) executes greedy, single-pass matching looking only at weight information from the immediately previous layer when selecting permutations. Singh & Jaggi (2020) suggests jointly solving for alignments as an avenue for future work. +• The “wts” method of Singh & Jaggi (2020) is not run on models including bias terms, skip connections, or normalization layers. In contrast, our Algorithm 1 works with models of nearly arbitrary architecture. +• Our weight matching method (Algorithm 1) outperforms the “wts” method of Singh & Jaggi (2020). See Appendix A.7 for more information. +• Singh & Jaggi (2020) introduces a method for merging multiple models simultaneously, but only demonstrates results on at most 8 models at a time and performs continued training after merging. In contrast, our Algorithm 3 has been shown to work with as many as 32 models at a time and does not require continued training after merging. Our analysis of the calibration of the resulting merged models has no parallel in Singh & Jaggi (2020). + +Relationship with Entezari et al. (2021). Entezari et al. (2021) introduces the single-basin conjecture and provides the following evidence towards it: + +• Entezari et al. (2021) provides a statistical test which fails to detect a difference in barrier statistics between independently trained models and random permutations of the same model (Fig. 5 of Entezari et al. (2021)). Our work provides stronger support for the conjecture in that we give methods that can directly “unscramble” these permutations, proving that LMC can be found (Figures 4 and 5). Entezari et al. (2021)’s experimental protocol does not provide evidence for linear mode connectivity. Rather, their experimental results suggest that barriers resulting from independent training look like the barriers resulting from random permutations. But this result is consistent with a world in which all solutions have barriers between them – both between members of the same permutation equivalence class and between solutions in separate equivalence classes! In other words, there may still exist multiple equivalence classes of solutions. In contrast, we provide concrete evidence for a single-basin theory by developing algorithms that directly place independent solutions into the same basin (Figure 1). +• Although Entezari et al. (2021)’s conjecture is an important intellectual ancestor to our work, their demonstration of linear mode connectivity is limited to a single hidden-layer MLP on MNIST (Fig. 2 of Entezari et al. (2021)). However, this result for single hiddenlayer MLP models is preceded by Freeman & Bruna (2017); Uriot & Izzo (2020). On the other hand, we focus on larger models and datasets that are more closely aligned with models used in practice at the time of writing. +• Entezari et al. (2021) proposes a simulated annealing algorithm that yields modest reductions in barrier between independently trained models, yet requires multiple days to run. On the other hand, our weight matching algorithm (Algorithm 1) completely removes barriers between models for more challenging models and datasets (Figures 2 and 5), and runs in seconds (Appendix A.5). Moreover, our weight matching method does not require access to the training data, enabling its potential application in domains like federated learning and distributed training. + +In short, the work of Entezari et al. (2021) first proposed the “single-basin” conjecture. Our work is the first (to the best of our knowledge) to demonstrate that linear mode connectivity can be achieved between large models independently trained on challenging datasets. + +Differentiating through permutations. Akin to differentiable permutation learning, many prior works have studied differentiable sorting (Grover et al., 2019; Prillo & Eisenschlos, 2020; Cuturi et al., 2019; Petersen et al., 2022; 2021; Mena et al., 2018). Blondel et al. (2020) studied differentiable sorting and ranking with asymptotics that correspond to their non-differentiable versions. Fogel et al. (2015) explored recovering the linear orderings of items based on pairwise information, another form of permutation optimization. Bengio et al. (2013) introduced the straight-through estimator for differentiating through discrete projections that we utilize in Section 3.3. + +# A.3 EXPERIMENTAL DETAILS + +# A.3.1 MULTI-LAYER PERCEPTRON MODELS + +In these experiments we utilized networks with 3 hidden layers of 512 units each. ReLU activations were used between layers and no normalization was performed. Optimization was done with Adam and a learning rate of $1 e - 3$ . + +# A.3.2 VGG-16 AND RESNET MODELS ON CIFAR DATASETS + +We utilized the VGG-16 architecture of Simonyan & Zisserman (2015) with the exception that we used LayerNorm normalization in place of BatchNorm. Similarly we used the ResNet20 architecture of He et al. (2016) but with LayerNorms in place of BatchNorms. + +The following data augmentation was performed during training + +• Random resizes of the image between $0 . 8 \times - 1 . 2 \times$ +• Random $3 2 \times 3 2$ pixel crops +• Random horizontal flips +• Random rotations between $\pm 3 0 ^ { \circ }$ + +Optimization was done with SGD with momentum (momentum set to 0.9). A weight decay regularization term of $5 e - 4$ was applied. A single cosine decay schedule with linear warm-up was used. Learning rates were initialized at $1 e - 6$ and linearly increased to $1 e - 1$ over the span of an epoch. After that point a single cosine decay schedule (Loshchilov & Hutter, 2017) was used for the remainder of training. + +# A.3.3 RESNET50 MODELS ON IMAGENET-1K + +In this experiment we utilized pre-trained ResNet50 model available for download online, and one trained ourselves. These were standard ResNet50 models, including the use of BatchNorm. In line with prior work (Izmailov et al., 2018; Wortsman et al., 2021; Maddox et al., 2019; Wang et al., 2021), we recalculate BatchNorm statistics after performing weight interpolation. After our initial publication, the recalculation of BatchNorm statistics was suggested to us by the authors of Jordan et al. (2022). + +A.4 THE RELATIONSHIP BETWEEN PERMUTATION MATCHING AND NORMALIZATION LAYERS + +In this section we discuss the impact that different types of common normalization layers can have on the feasibility of model merging. + +• BatchNorm (Ioffe & Szegedy, 2015) generally breaks after interpolating between weights due to the so-called “variance collapse” problem (Jordan et al., 2022). Therefore, we recommend the recalculation of batch statistics after merging models (Izmailov et al., 2018; Wortsman et al., 2021; Maddox et al., 2019; Wang et al., 2021). +• LayerNorm (Ba et al., 2016) is invariant to permutations of units and we found that architectures with LayerNorm can be merged without issue. +• InstanceNorm (Ulyanov et al., 2016) also places no restrictions on unit order, and in principle does not present any issues, although we have not run any experiments with it. +• GroupNorm (Wu & He, 2020) relies on unit indexes to organize units into groups, and therefore is not invariant to permutations of units. In principle, permutation alignment methods would not work on architectures with GroupNorm, though we have not tested this. + +# A.5 ADDITIONAL INFORMATION ON ALGORITHM 1 + +On currently available hardware (p3.2xlarge AWS instance with an NVIDIA V100 GPU), we observed the following timing results with Algorithm 1, + +![](images/7474fc86a4fbae61576200d8c26d718ff3e25733e6249c884ee1b940a23fa88d.jpg) +Figure 6: A counterexample to universal LMC. There exist models such that no possible permutation of weights allows for linear mode connectivity. Left: performance of all possible linear interpolations between the two models. Right: A visualization of the prediction functions $f ( { \pmb x } )$ through each linear sweep. Each row corresponds to one of the four possible permutations, and each column corresponds to a value of $\lambda$ , the linear interpolant. The existence of such cases suggests that linear mode connectivity is an artifact of SGD. + +![](images/d73dcc4fd3766fed56337c441e5c222fb4aefcf416bd1863b89bdb0e3b81d36e.jpg) +Figure 7: The counterexample classification problem data. + +1. MLP (3 layers, 512 units each): 3 seconds +2. ResNet50 $1 \times$ width): 33 seconds +3. ResNet20 $3 2 \times$ width): 194 seconds + +In addition, we tested the ability of Algorithm 1 to recover a known, randomly selected permutation. In a handful of experiments we found that Algorithm 1 was able to exactly recover the known, random permutation in just 3-4 of passes over the layers. + +# A.6 COUNTEREXAMPLE DETAILS + +Consider a simple 2-dimensional classification task. Our data points are drawn $\textbf { \textit { x } } \sim$ Uniform $( [ - 1 , 1 ] ^ { 2 } )$ and $y = \mathbf { 1 } _ { x _ { 1 } < 0 }$ and $x _ { 2 } > 0$ . Figure 7 provides a visualization of a sample of such data. + +We utilize an MLP architecture consisting of two hidden layers, with two units each, and ReLU nonlinearities. Consider two weight assignments that both achieve a perfect fit to the data: + +$$ +\begin{array}{c} \begin{array} { r l } { f _ { A } ( \pmb { x } ) = [ - 1 } & { - 1 ] \sigma ( [ \begin{array} { l l } { - 1 } & { 0 } \\ { 0 } & { 1 } \end{array} ] \sigma ( [ \begin{array} { l l } { - 1 } & { 0 } \\ { 0 } & { - 1 } \end{array} ] \pmb { x } + [ 1 ] ) + [ \begin{array} { l } { 1 } \\ { 0 } \end{array} ] ) } \\ { f _ { B } ( \pmb { x } ) = [ - 1 } & { - 1 ] \sigma ( [ 1 } \\ { 0 } & { - 1 } \end{array} ] \sigma ( [ \begin{array} { l l } { 1 } & { 0 } \\ { 0 } & { 1 } \end{array} ] \pmb { x } + [ \begin{array} { l } { 0 } \\ { 1 } \end{array} ] ) + [ \begin{array} { l } { 0 } \\ { 1 } \end{array} ] ) . \end{array} +$$ + +We predict a positive label when $f ( { \pmb x } ) \geq 0$ and a negative label otherwise. + +Intuitively, these networks are organized such that each layer makes a classification whether $\mathbf { x } _ { 1 } < 0$ or $x _ { 2 } > 0$ . In model $A$ , the first layer tests whether $x _ { 2 } > 0$ , and the second layer tests whether $x _ { 1 } < 0$ , whereas in model $B$ the order is reversed. With a bit of algebra, it is possible to see that both $f _ { A }$ and $f _ { B }$ achieve perfect performance. However, no possible permutation of units results in linear mode connectivity between $f _ { A }$ and $f _ { B }$ . We visualize all possible permutations in Figure 6. + +We claim that this example, and the underlying trick, are simple enough to be embedded into larger models. For example, this could trivially be extended to ResNets where different subsets of layers could be set to identity functions. + +As discussed in Section 4, the existence of adversarial basins in the loss landscape has interesting consequences for our understanding of loss landscape geometry. In particular, we argue that this implies that common optimization algorithms are conveniently biased towards solutions that admit LMC. However, the precise connection between optimization algorithms and linear mode connectivity remains unclear. + +This counterexample does not constitute a contradiction of the conjecture in Entezari et al. (2021). To be more precise, Conjecture 1 of Entezari et al. (2021) proposes that there exists some subset, $s$ , of parameter space such that every pair of elements in $s$ can be linearly mode connected (after some permutation of units), and that with high probability SGD solutions are contained in $s$ . The example presented in this section does not contradict Entezari et al. (2021)’s conjecture, but instead illustrates that the restriction to SGD solutions is a “load-bearing” element of the conjecture. + +# A.7 ON THE FAILURES OF GREEDY UNI-DIRECTIONAL MATCHING + +In contrast to prior work (Pittorino et al., 2022; Singh & Jaggi, 2020; Wang et al., 2020), we eschew greedy uni-directional, single-pass matching between models. Instead we derive a weight matching algorithm from a principled, yet computationally infeasible optimization problem. In contrast to prior work, our method can be viewed as “bi-directional”: it selects unit associations based on weights in all relevant layers, not just in the immediately previous layer. In this section, we describe benefits of our holistic approach, including an example problem showing the failure modes of greedy uni-directional matching. We find that matching across all layers simultaneously allows our weight matching algorithm (Algorithm 1) to exploit units’ relationships with downstream weights in a way that greedy uni-directional matching cannot. + +Concretely, greedy uni-directional matching begins at the first layer and computes a matching, $P _ { 1 }$ , considering only ${ \bf \dot { W } } _ { 1 } ^ { ( A ) } , { \bf W } _ { 1 } ^ { ( B ) }$ . After matching, $P _ { 1 }$ is applied throughout the remainder of the network. Then, we proceed through the layers in order repeating this process. + +We compare our Algorithm 1 to greedy uni-directional matching experimentally in Appendix A.7.1 and present a theoretical counterexample that illustrates the advantages of our method in Appendix A.7.2. + +# A.7.1 EXPERIMENTAL COMPARISON + +In order to further evaluate our performance relative to prior work, and Pittorino et al. (2022); Singh & Jaggi (2020) in particular, we explored experimental comparisons with VGG11 models trained on CIFAR-10 and on ResNet50 models trained on ImageNet. + +VGG11 models trained on CIFAR-10. Following an exact reproduction of experiment from Table 1 of Singh & Jaggi (2020), we merged the model weights released along with their paper. We present results in Table 2. We found that our weight matching method outperforms the “wts” method of Singh & Jaggi (2020) in both implementation speed and model performance when reproducing their experiment with their trained model weights. + +ResNet50 models trained on ImageNet. We applied OT-Fusion (“wts”) to the ImageNet experiment that we consider in Section 5.1. We present results in Figure 8. We found the OT-Fusion method resulted in models with $1 . 3 8 \%$ top-1 accuracy on ImageNet, only marginally improving over na¨ıve averaging. On the other hand, we achieve $5 1 . 0 1 \%$ . + +BatchNorm statistics were recalculated after interpolation for all methods shown. + +Table 2: VGG11/CIFAR-10 performance relative to Singh & Jaggi (2020). We found that our weight matching method outperforms the “wts” method of Singh & Jaggi (2020) in both implementation speed and model performance when reproducing one of their experiments with their published model weights. Our implementation is $4 . 5 \times$ faster, and produces a solution with better model performance. + +
MethodTest accuracy (个)Run-time (↓)
OT-Fusion (Singh & Jaggi, 2020)85.98%2.86s
Weight matching (ours)86.57 %0.64s
+ +![](images/7d040064349a8c780e2a2137ffec0c52df8ab0f6cb815bd347b925660871158a.jpg) +Figure 8: ResNet50/ImageNet performance relative to Singh $\pmb { \& }$ Jaggi (2020). We found the OT-Fusion method resulted in models with $1 . 3 8 \%$ top-1 accuracy on ImageNet, only marginally improving over na¨ıve averaging. On the other hand, we achieve $5 1 . 0 1 \%$ . + +Although a number of factors may be responsible for the difference in performance between weight matching and OT-Fusion, we found the number of alignment passes made over the network layers to have a substantial impact. OT-Fusion is inherently limited to a single pass over the layers. On the other hand, we are not limited to any specific number of optimization passes and instead continue until convergence (convergence is guaranteed by Lemma 2). For comparison, if our weight matching algorithm is artificially handicapped to a single pass over the layers, we achieve a similarly low $\sim 7 \%$ top-1 accuracy. + +# A.7.2 AN EXAMPLE FAILURE CASE + +Consider two networks, $A$ and $B$ , with the objective that they capture the identity function $f ( x ) = x$ + +$$ +\begin{array} { r l } { f _ { \Theta _ { A } } ( x ) = [ 1 } & { 0 ] \left[ \begin{array} { l l } { 1 } & { 0 } \\ { 0 } & { \epsilon } \end{array} \right] \left[ \begin{array} { l } { 1 } \\ { 1 + \epsilon } \end{array} \right] x } \\ { f _ { \Theta _ { B } } ( x ) = [ 0 } & { 1 ] \left[ \begin{array} { l l } { 0 } & { 0 } \\ { 0 } & { 1 } \end{array} \right] \left[ \begin{array} { l } { 1 } \\ { 1 + \epsilon } \end{array} \right] x } \end{array} +$$ + +where $\epsilon > 0$ is some negligible constant. It can be seen that these reduce to $f _ { \Theta _ { A } } ( x ) = x$ and $f _ { \Theta _ { B } } ( x ) = ( 1 + \epsilon ) x$ . + +When aligning these models there are two possible opportunities for permutation, $\pi = \{ P _ { 1 } , P _ { 2 } \}$ The permuted model $B$ then has the form + +$$ +f _ { \pi ( \Theta _ { B } ) } ( x ) = \left( \left[ 0 \quad 1 \right] P _ { 2 } ^ { \top } \right) \left( P _ { 2 } \left[ 0 \quad 1 \right] P _ { 1 } ^ { \top } \right) \left( P _ { 1 } \left[ 1 + \epsilon \right] \right) x +$$ + +Now, aligning with greedy uni-directional matching will result in the alignment $\pi _ { g u d } = \{ P _ { 1 } =$ $I , P _ { 2 } = I \}$ . On the other hand, our weight matching method (Algorithm 1) results in $\pi _ { w m } =$ $\left\{ P _ { 1 } = { \left[ \begin{array} { l l } { 0 } & { 1 } \\ { 1 } & { 0 } \end{array} \right] } , P _ { 2 } = { \left[ \begin{array} { l l } { 0 } & { 1 } \\ { 1 } & { 0 } \end{array} \right] } \right\}$ , regardless of the algorithm’s execution order. + +![](images/eb18a76b62f58b2fd38376d589eefbb880fcd31b6f90836ee8b0a234fbc2f71a.jpg) +Figure 9: Top-1 accuracy results for the MNIST and CIFAR-10 models of Figure 2. + +![](images/b0d0655148ed913cf96a1339fad177b2df353b8cf4ccff993d21e89acadb5e92.jpg) +Figure 10: Accuracy results for the CIFAR-100 split data experiment. + +Interpolating these matched models at $\lambda = 0 . 5$ , we have + +$$ +\begin{array} { r l r l } & { f _ { \frac { 1 } { 2 } ( \Theta _ { A } + \pi _ { g u d } ( \Theta _ { B } ) ) } ( x ) = [ 0 . 5 } & { 0 . 5 ] [ 0 . 5 \qquad 0 } \\ & { f _ { \frac { 1 } { 2 } ( \Theta _ { A } + \pi _ { w m } ( \Theta _ { B } ) ) } ( x ) = [ 1 } & { 0 ] [ 0 \qquad \epsilon / 2 ] [ 1 + \epsilon / 2 ] x \qquad } & { = ( 0 . 5 + O ( \epsilon ) ) x } \\ & { f _ { \frac { 1 } { 2 } ( \Theta _ { A } + \pi _ { w m } ( \Theta _ { B } ) ) } ( x ) = [ 1 } & { 0 ] [ 0 \qquad \epsilon / 2 ] [ 1 + \epsilon / 2 ] x } & & { = ( 1 + \epsilon / 2 ) x } \end{array} +$$ + +Here we can see that the greedy uni-directional matching (Equation (9)) results in a merged model that fails to represent the input, identity-function models. On the other hand, our weight matching algorithm (Algorithm 1, Equation (10)) produces a merged model that accurately reflects both of the input models, and even improves performance over the $B$ model. 5 + +A.8 AUXILIARY PLOTS + +# A.9 STRAIGHT-THROUGH ESTIMATOR DETAILS + +See Algorithm 2 for a complete description of the straight-through estimator algorithm. + +A.10 MERGING MANY MODELS + +We propose Algorithm 3 to merge the weights of more than two models at a time. + +Following an argument similar to Lemma 2, it can be seen that Algorithm 3 terminates. + +In our limited testing, we found that this algorithm converges quickly to solutions that extrapolate better than individual models and results in a merged model with better probability estimate calibra + +![](images/f6f448ec9e78fac0fa4db3b8310a5ad096bbd940ab4553c98ec331efdb11f1d9.jpg) +Figure 11: Merging CIFAR-100 split data models results in superior probability calibration. Although our merged model is not competitive in terms of top-1 accuracy in the CIFAR-100 split data experiment, we find that it has far better calibrated probability estimates than either of the input models. In addition, we achieve calibration results on par with model ensembling while requiring $2 \times$ less memory and compute. + +![](images/eb946f43847ac0e8805093a9388e1a3823856bda647d54fba047b6b50c06be3d.jpg) +Figure 12: Accuracy results for merged ResNet50 $1 \times$ width) models on ImageNet. + +# Algorithm 2: Straight-through estimator training + +Given: Model weights $\Theta _ { A }$ , $\Theta _ { B }$ , and a learning rate $\eta$ + +Result: A permutation $\pi$ of $\Theta _ { B }$ such that $\begin{array} { r } { \mathcal { L } ( \frac { 1 } { 2 } ( \Theta _ { A } + \pi ( \Theta _ { B } ) ) ) } \end{array}$ is approximately minimized. + +Initialize: $\tilde { \Theta } _ { B } \Theta _ { A }$ + +# repeat + +$\pi ( \Theta _ { B } ) \mathrm { p r o j } ( \tilde { \Theta } _ { B } )$ using Algorithm 1. +Evaluate the loss of the midpoint, $\begin{array} { r } { \mathcal { L } ( \frac { 1 } { 2 } ( \Theta _ { A } + \pi ( \Theta _ { B } ) ) ) } \end{array}$ . +Evaluate the gradient, $\nabla \mathcal { L }$ , using $\tilde { \Theta } _ { B }$ in place of $\pi ( \Theta _ { B } )$ in the backwards pass. +Update parameters, $\tilde { \Theta } _ { B } \gets \tilde { \Theta } _ { B } - \eta \nabla \mathcal { L }$ . + +until convergence + +# Algorithm 3: MERGEMANY + +Given: Model weights $\Theta _ { 1 } , \dots , \Theta _ { N }$ + +Result: A merged set of parameters $\tilde { \Theta }$ . + +# repeat + +$$ +\Theta _ { i } \gets \pi ( \Theta _ { i } ) +$$ + +Table 3: Merging multiple models decreases test loss by $43 \%$ . We train five separate MLPs on MNIST. Using Algorithm 3 we merge all these models together simultaneously. This produces a model that appears to have better out-of-distribution performance than any of the input models, with superior test loss performance. We are excited by potential applications of this methodology in federated learning and ensembling, esp. along the lines of “model soups” (Wortsman et al., 2022a). + +
Train LossTrain Acc.Test LossTest Acc.
Seed 10.00001.00000.11530.9856
Seed 20.00001.00000.15310.9854
Seed 30.00001.00000.12290.9855
Seed 40.00001.00000.11080.9865
Seed 50.00001.00000.14430.9871
MERGEMANY0.01410.99520.07270.9831
+ +tion than any of the input models. For example, we present the results of this algorithm on MLPs trained on MNIST in Table A.10. + +In addition, we found that merging multiple models helps to calibrate the resulting model predictions. We present this effect in Figure 13. + +# A.11 FAILED IDEA: A METHOD FOR STEEPEST DESCENT + +Imagine standing in weight space at $\Theta _ { A }$ and trying to decide in which immediate direction to move in order to approach a $\Theta _ { B }$ -equivalent point. There are many, many possible permutations of $\Theta _ { B } -$ call them $\pi ^ { ( \bar { 1 } ) } ( \Theta _ { B } ) , \pi ^ { ( 2 ) } ( \Theta _ { B } ) , \dots - \mathrm { t }$ o aim for in the distance. Assuming that the loss landscape is in fact convex modulo these permutation symmetries, a natural choice would be to pick the $\pi ^ { ( i ) } ( \Theta _ { B } )$ that corresponds to the direction of steepest descent starting from $\Theta _ { A }$ since we expect $\pi ^ { ( i ) } ( \Theta _ { B } )$ to lie in the same basin as $\Theta _ { A }$ . In other words, + +$$ +\begin{array} { r l } { \operatorname* { m i n } _ { \pi } \left. \frac { d \mathcal { L } ( \Theta _ { A } + \lambda ( \pi ( \Theta _ { B } ) - \Theta _ { A } ) ) } { d \lambda } \right| _ { \lambda = 0 } } & { = \underset { \pi } { \operatorname* { m i n } } ~ \nabla \mathcal { L } ( \Theta _ { A } ) ^ { \top } ( \pi ( \Theta _ { B } ) - \Theta _ { A } ) } \\ & { = - \nabla \mathcal { L } ( \Theta _ { A } ) ^ { \top } \Theta _ { A } + \underset { \pi } { \operatorname* { m i n } } ~ \nabla \mathcal { L } ( \Theta _ { A } ) ^ { \top } \pi ( \Theta _ { B } ) } \end{array} +$$ + +Now, we are tenuously in a favorable situation: $\nabla { \mathcal { L } } ( \Theta _ { A } )$ is straightforward to compute, and picking the best $\pi$ reduces to a matching problem. In particular it is a SOBLAP matching problem of the same form as in Section 3.2. In addition, there is a fast, exact solution for the single intermediate layer case $\left( L = 2 \right.$ ). + +In practice, we found that this method can certainly find directions of steepest descent, but that they are accompanied by high barriers in between the initial dip and $\pi ( \Theta _ { B } )$ . + +![](images/20266c9cfdd50d6e3474dcffd5e8e32c8ed48138717b4cb24febf27fae82893d.jpg) +Figure 13: Merging multiple models results in superior calibration. Here we show the results of running Algorithm 3 on 32 MLP models trained on MNIST, with each model given access to a random $50 \%$ of the training dataset. The resulting merged model demonstrates substantively improved calibration of probability estimates on both the training and test datasets. MergeMany calibration results are competitive with model ensembling, despite requiring $3 2 \times$ less memory and compute. + +# A.12 PROOF OF LEMMA 1 + +To lighten notation we use $\langle \cdot , \cdot \rangle = \langle \cdot , \cdot \rangle _ { F }$ in this section. + +Lemma. Given $\pmb { A } , \pmb { B } \in \mathbb { R } ^ { d \times d }$ , + +$$ +\operatorname* { m i n } _ { P , Q p e r m . m a t r i c e s } \left. P A Q ^ { \top } , B \right. +$$ + +is strongly NP-hard and has no PTAS. + +Proof. We proceed by reduction from the quadratic assignment problem (QAP) (Koopmans & Beckmann, 1957; Cela, 2013). Consider a QAP, + +$$ +\operatorname* { m i n } _ { P \mathrm { \ p e r m . \ m a t r i x } } \left. P C P ^ { \top } , D \right. +$$ + +for $C , D \in \mathbb { R } ^ { d \times d }$ . + +Now, pick $A = C + \lambda I$ , $B = D - \lambda I$ . The we have, + +$$ +\begin{array} { r l } & { \underset { \boldsymbol { \sigma } , \boldsymbol { Q } } { \mathrm { n i n } } \left. P ( \boldsymbol { C } + \lambda \boldsymbol { I } ) \boldsymbol { Q } ^ { \top } , \boldsymbol { D } - \lambda \boldsymbol { I } \right. = \left. P C \boldsymbol { Q } ^ { \top } + \lambda P \boldsymbol { Q } ^ { \top } , \boldsymbol { D } - \lambda \boldsymbol { I } \right. } \\ & { \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad ( 1 3 ) } \\ & { \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad = \left. P C \boldsymbol { Q } ^ { \top } , \boldsymbol { D } \right. - \lambda \langle P C \boldsymbol { Q } ^ { \top } , \boldsymbol { I } \rangle + \lambda \langle P \boldsymbol { Q } ^ { \top } , \boldsymbol { D } \rangle - \lambda ^ { 2 } \langle P \boldsymbol { Q } ^ { \top } , \boldsymbol { I } \rangle } \\ & { \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad ( 1 4 ) } \\ & { \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad \quad = \left. P C \boldsymbol { Q } ^ { \top } , \boldsymbol { D } \right. - \lambda \langle P ^ { \top } \boldsymbol { Q } , \boldsymbol { C } \rangle + \lambda \langle P \boldsymbol { Q } ^ { \top } , \boldsymbol { D } \rangle - \lambda ^ { 2 } \mathrm { t r } ( P \boldsymbol { Q } ^ { \top } ) _ { - \lambda } \mathrm { t r } ( P \boldsymbol { Q } ^ { \top } ) _ { - \lambda } \mathrm { t r } ( P \boldsymbol { Q } ^ { \top } ) _ { - \lambda } , } \end{array} +$$ + +For sufficiently large $\lambda$ , the $\operatorname { t r } ( P Q ^ { \top } )$ term will dominate. Letting $\alpha \quad =$ max $\begin{array} { r } { ( \operatorname* { m a x } _ { i , j } | C _ { i , j } | , \operatorname* { m a x } _ { i , j } | D _ { i , j } | ) } \end{array}$ , we can bound the other terms, + +$$ +\begin{array} { r l r } { - d ^ { 2 } \alpha ^ { 2 } \le } & { \langle P C Q ^ { \top } , D \rangle \le d ^ { 2 } \alpha ^ { 2 } } & \\ { - \lambda d \alpha \le - \lambda \langle P ^ { \top } Q , C \rangle } & { \le \lambda d \alpha } & \\ { - \lambda d \alpha \le } & { \lambda \langle P Q ^ { \top } , D \rangle } & { \le \lambda d \alpha } \end{array} +$$ + +Now there are two classes of solutions: those where $P = Q$ and those where $P \neq Q$ . We seek to make the best (lowest) possible $P \neq Q$ solution to have worse (higher) objective value than the worst (highest) $P = Q$ solution. When $P = Q$ , the highest possible objective value is + +$$ +d ^ { 2 } \alpha ^ { 2 } + \lambda d \alpha + \lambda d \alpha - \lambda ^ { 2 } d +$$ + +and similarly, the lowest possible objective value when $P \neq Q$ is + +$$ +- d ^ { 2 } \alpha ^ { 2 } - \lambda d \alpha - \lambda d \alpha - \lambda ^ { 2 } d + \lambda ^ { 2 } +$$ + +where the final term is due to the fact that at least one entry of $P Q ^ { \top }$ must be 0. With some algebra, it can be seen that $\lambda > 5 d \alpha$ is sufficient to guarantee that all $P = Q$ solutions are superior to all $P \neq Q$ solutions. + +Now when $P = Q$ , all frivolous terms reduce to constants and we are left with the QAP objective: + +$$ +\begin{array} { r l r } & { } & { \underset { \pmb { P } } { \mathrm { m i n } } \ \langle \pmb { P } \pmb { C } \pmb { P } ^ { \top } , \pmb { D } \rangle - \lambda \langle \pmb { P } ^ { \top } \pmb { P } , \pmb { C } \rangle + \lambda \langle \pmb { P } \pmb { P } ^ { \top } , \pmb { D } \rangle - \lambda ^ { 2 } \mathrm { t r } ( \pmb { P } \pmb { P } ^ { \top } ) } \\ & { } & \\ & { } & { = - \lambda \mathrm { t r } ( \pmb { C } ) + \lambda \mathrm { t r } ( \pmb { D } ) - \lambda ^ { 2 } d + \underset { \pmb { P } } { \mathrm { m i n } } \ \langle \pmb { P } \pmb { C } \pmb { P } ^ { \top } , \pmb { D } \rangle } \end{array} +$$ + +completing the reduction. QAP is known to be strongly NP-hard (Koopmans & Beckmann, 1957; Sahni & Gonzalez, 1976) and MaxQAP is known to not admit any PTAS (Makarychev et al., 2014), thus completing the proof. □ + +# A.13 PROOF OF LEMMA 2 + +Lemma. Algorithm 1 terminates. + +Proof. We proceed by contradiction. + +Consider a graph with each possible permutation $\pi _ { i } = \left\{ P _ { 1 } , \ldots , P _ { L - 1 } \right\}$ as a vertex and directed edges $\pi _ { i } \pi _ { j }$ if $\pi _ { j }$ can be reached from $\pi _ { i }$ with a single $P _ { \ell }$ update, as in Algorithm 1. (Ignore those updates that result in no change to $P _ { \ell }$ in order to avoid $\pi _ { i } \pi _ { i }$ cycles.) Let $\rho ( \pi ) = \operatorname { v e c } ( \Theta _ { A } )$ · $\mathrm { v e c } ( \pi ( { \bar { \Theta } } _ { B } ) )$ denote the utility of a particular $\pi$ . Note that $\pi _ { i } \pi _ { j }$ implies $\rho ( \pi _ { i } ) < \rho ( \pi _ { j } )$ . There exist finitely many possible permutations $\pi _ { i }$ , meaning that a failure to terminate must involve a cycle in the graph $\pi _ { 1 } \to \cdot \cdot \cdot \to \pi _ { n } \to \pi _ { 1 }$ . However $\rho$ forms a total order on the vertices and therefore we have a contradiction. □ \ No newline at end of file diff --git a/parse/dev/CQsmMYmlP5T/CQsmMYmlP5T_content_list.json b/parse/dev/CQsmMYmlP5T/CQsmMYmlP5T_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..580c00ed9ca6797912a31f2b37c7d9144fc6a3ec --- /dev/null +++ b/parse/dev/CQsmMYmlP5T/CQsmMYmlP5T_content_list.json @@ -0,0 +1,3659 @@ +[ + { + "type": "text", + "text": "GIT RE-BASIN: MERGING MODELS MODULO PERMUTATION SYMMETRIES ", + "text_level": 1, + "bbox": [ + 174, + 98, + 820, + 146 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Samuel K. Ainsworth, Jonathan Hayase, Siddhartha Srinivasa ", + "bbox": [ + 183, + 170, + 619, + 185 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Paul G. Allen School of Computer Science and Engineering University of Washington {skainswo,jhayase,siddh}@cs.washington.edu ", + "bbox": [ + 184, + 185, + 591, + 227 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "ABSTRACT ", + "text_level": 1, + "bbox": [ + 454, + 262, + 544, + 277 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "The success of deep learning is due in large part to our ability to solve certain massive non-convex optimization problems with relative ease. Though non-convex optimization is NP-hard, simple algorithms – often variants of stochastic gradient descent – exhibit surprising effectiveness in fitting large neural networks in practice. We argue that neural network loss landscapes often contain (nearly) a single basin after accounting for all possible permutation symmetries of hidden units a la Entezari et al. (2021). We introduce three algorithms to permute the units of one model to bring them into alignment with a reference model in order to merge the two models in weight space. This transformation produces a functionally equivalent set of weights that lie in an approximately convex basin near the reference model. Experimentally, we demonstrate the single basin phenomenon across a variety of model architectures and datasets, including the first (to our knowledge) demonstration of zero-barrier linear mode connectivity between independently trained ResNet models on CIFAR-10. Additionally, we investigate intriguing phenomena relating model width and training time to mode connectivity. Finally, we discuss shortcomings of the linear mode connectivity hypothesis, including a counterexample to the single basin theory. ", + "bbox": [ + 233, + 292, + 764, + 527 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 INTRODUCTION ", + "text_level": 1, + "bbox": [ + 176, + 553, + 336, + 569 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We investigate the unreasonable effectiveness of stochastic gradient descent (SGD) algorithms on the high-dimensional non-convex optimization problems of deep learning. In particular, ", + "bbox": [ + 174, + 583, + 823, + 612 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1. Why does SGD thrive in optimizing high-dimensional non-convex deep learning loss landscapes despite being noticeably less robust in other non-convex optimization settings, like policy learning (Ainsworth et al., 2021), trajectory optimization (Kelly, 2017), and recommender systems (Kang et al., 2016)? \n2. What are all the local minima? When linearly interpolating between initialization and final trained weights, why does the loss smoothly and monotonically decrease (Goodfellow & Vinyals, 2015; Frankle, 2020; Lucas et al., 2021; Vlaar & Frankle, 2021)? \n3. How can two independently trained models with different random initializations and data batch orders inevitably achieve nearly identical performance? Furthermore, why do their training loss curves often look identical? ", + "bbox": [ + 199, + 622, + 825, + 770 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "We posit that these phenomena point to the existence of some yet uncharacterized invariance(s) in the training dynamics causing independent training runs to exhibit similar characteristics. HechtNielsen (1990) noted the permutation symmetries of hidden units in neural networks; briefly, one can swap any two units of a hidden layer in a network and – assuming weights are adjusted accordingly – network functionality will not change. Recently, Benton et al. (2021) demonstrated that SGD solutions form a connected volume of low loss and Entezari et al. (2021) conjectured that this volume is convex modulo permutation symmetries. ", + "bbox": [ + 174, + 781, + 825, + 878 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Conjecture 1 (Permutation invariance, informal (Entezari et al., 2021)). Most SGD solutions belong to a set whose elements can be permuted so that no barrier (as in Definition 2.2) exists on the linear interpolation between any two permuted elements. ", + "bbox": [ + 176, + 882, + 823, + 924 + ], + "page_idx": 0 + }, + { + "type": "table", + "img_path": "images/0bcd52f84cd857546638a85629ba832c80c4c331b2b27f2cf5493d4ff463ea44.jpg", + "table_caption": [ + "Table 1: Permutation symmetries of deep learning models vs. an upper estimate on the number of atoms in the known, observable universe. Deep learning loss landscapes contain incomprehensible amounts of geometric repetition. " + ], + "table_footnote": [ + "Atoms in the observable universe 10 ∧ 82 " + ], + "table_body": "
ARCHITECTURENUM.PERMUTATIONSYMMETRIES
MLP (3 layers, 512 width)10 ^ 3498
VGG1610 ^ 35160
ResNet5010 ^ 55109
", + "bbox": [ + 227, + 99, + 769, + 170 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "We refer to such solutions as being linearly mode connected (LMC) (Frankle et al., 2020), an extension of mode connectivity (Garipov et al., 2018; Draxler et al., 2018). If true, Conjecture 1 will both materially expand our understanding of how SGD works in the context of deep learning and offer a credible explanation for the preceding phenomena, in particular. ", + "bbox": [ + 174, + 260, + 825, + 315 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Contributions. In this paper, we attempt to uncover what invariances may be responsible for the phenomena cited above and the unreasonable effectiveness of SGD in deep learning. We make the following contributions: ", + "bbox": [ + 176, + 330, + 825, + 373 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "1. Matching methods. We propose three algorithms, grounded in concepts and techniques from combinatorial optimization, to align the weights of two independently trained models. Where appropriate, we prove hardness results for these problems and propose approximation algorithms. Our fastest method identifies permutations in mere seconds on current hardware. 2. Relationship to optimization algorithms. We demonstrate by means of counterexample that linear mode connectivity is an emergent property of training procedures, not of model architectures. We connect this result to prior work on the implicit biases of SGD. 3. Experiments, including zero-barrier LMC for ResNets. Empirically, we explore the existence of linear mode connectivity modulo permutation symmetries in experiments across MLPs, CNNs, and ResNets trained on MNIST, CIFAR-10, and CIFAR-100. We contribute the first-ever demonstration of zero-barrier LMC between two independently trained ResNets. We explore the relationship between LMC and model width as well as training time. Finally, we show evidence of our methods’ ability to combine models trained on independent datasets into a merged model that outperforms both input models in terms of test loss (but not accuracy) and is no more expensive in compute or memory than either input model. ", + "bbox": [ + 199, + 383, + 825, + 601 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "2 BACKGROUND ", + "text_level": 1, + "bbox": [ + 174, + 621, + 326, + 636 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Although our methods can be applied to arbitrary model architectures, we proceed with the multilayer perceptron (MLP) for its ease of presentation (Bishop, 2007). Consider an $L$ -layer MLP, ", + "bbox": [ + 174, + 651, + 823, + 680 + ], + "page_idx": 1 + }, + { + "type": "equation", + "img_path": "images/ea4a7bb0234af057a08957fdba69bda86b0847be0c1cd6ffac165c6b11e5158f.jpg", + "text": "$$\nf ( \\pmb { x } ; \\Theta ) = \\pmb { z } _ { L + 1 } , \\quad \\pmb { z } _ { \\ell + 1 } = \\sigma ( \\pmb { W } _ { \\ell } \\pmb { z } _ { \\ell } + \\pmb { b } _ { \\ell } ) , \\quad \\pmb { z } _ { 1 } = \\pmb { x } ,\n$$", + "text_format": "latex", + "bbox": [ + 316, + 684, + 679, + 702 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "where $\\sigma$ denotes an element-wise nonlinear activation function. Furthermore, consider a loss, $\\mathcal { L } ( \\Theta )$ , that measures the suitability of a particular set of weights $\\Theta$ towards some goal, e.g., fitting to a training dataset. ", + "bbox": [ + 176, + 705, + 825, + 747 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "Central to our investigation is the phenomenon of permutation symmetries of weight space. Given $\\Theta$ , we can apply some permutation to the output features of any intermediate layer, $\\ell$ , of the model, denoted by a permutation matrix $\\pmb { P } \\in S _ { d }$ ,1 ", + "bbox": [ + 176, + 753, + 823, + 796 + ], + "page_idx": 1 + }, + { + "type": "equation", + "img_path": "images/b923a70720a5d86225af5c2cb203679e7ba8d3becb1e46ef362c972d5c6abc43.jpg", + "text": "$$\nz _ { \\ell + 1 } = P ^ { \\top } P z _ { \\ell + 1 } = P ^ { \\top } P \\sigma ( W _ { \\ell } z _ { \\ell } + b _ { \\ell } ) = P ^ { \\top } \\sigma ( P W _ { \\ell } z _ { \\ell } + P b _ { \\ell } )\n$$", + "text_format": "latex", + "bbox": [ + 267, + 800, + 728, + 819 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "for $\\sigma$ , an element-wise operator. It follows that as long as we reorder the input weights of layer $\\ell + 1$ according to $P ^ { \\top }$ , we will have a functionally equivalent model. To be precise, if we define $\\Theta ^ { \\prime }$ to be identical to $\\Theta$ with the exception of ", + "bbox": [ + 173, + 823, + 826, + 866 + ], + "page_idx": 1 + }, + { + "type": "equation", + "img_path": "images/e6abd509c19d40e82533d1963bad757e97d3f5257da51fabd0250389599fa654.jpg", + "text": "$$\n\\begin{array} { r } { { W } _ { \\ell } ^ { \\prime } = P { W } _ { \\ell } , \\quad { b } _ { \\ell } ^ { \\prime } = P { b } _ { \\ell } , \\quad { W } _ { \\ell + 1 } ^ { \\prime } = { W } _ { \\ell + 1 } P ^ { \\top } , } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 331, + 869, + 665, + 888 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "then the two models are functionally equivalent: $f ( \\pmb { x } ; \\Theta ) = f ( \\pmb { x } ; \\Theta ^ { \\prime } )$ for all inputs $_ { \\textbf { \\em x } }$ . This implies that for any trained weights $\\Theta$ , there is an entire equivalence class of functionally equivalent weight assignments, not just one such $\\Theta$ , and convergence to any one specific element of this equivalence class, as opposed to any others, is determined only by random seed. We denote a functionalitypreserving permutation of weights as $\\pi ( \\Theta )$ . ", + "bbox": [ + 173, + 103, + 825, + 172 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Consider the task of reconciling the weights of two, independently trained models, $A$ and $B$ , with weights $\\Theta _ { A }$ and $\\Theta _ { B }$ , respectively, such that we can linearly interpolate between them. We assume that models $A$ and $B$ were trained with equivalent architectures but different random initializations, data orders, and potentially different hyperparameters or datasets, as well. Our central question is: Given $\\Theta _ { A }$ and $\\Theta _ { B }$ , can we identify some $\\pi$ such that when linearly interpolating between $\\Theta _ { A }$ and $\\pi ( \\Theta _ { B } )$ , all intermediate models enjoy performance similar to $\\Theta _ { A }$ and $\\Theta _ { B }$ ? ", + "bbox": [ + 174, + 180, + 485, + 361 + ], + "page_idx": 2 + }, + { + "type": "image", + "img_path": "images/b74fb2c8020c349d7fa616e0c2929d27002e3c9a4a43fd21b6f0a249ca20fdec.jpg", + "image_caption": [ + "Figure 1: Git Re-Basin merges models by teleporting solutions into a single basin. $\\Theta _ { B }$ is permuted into functionally-equivalent $\\pi ( \\Theta _ { B } )$ so that it lies in the same basin as $\\Theta _ { A }$ . " + ], + "image_footnote": [], + "bbox": [ + 516, + 174, + 810, + 342 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We base any claims of loss landscape convexity on the usual definition of multi-dimensional convexity in terms of one-dimensional convexity per ", + "bbox": [ + 173, + 367, + 483, + 424 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Definition 2.1 (Convexity). A function $f : \\mathbb { R } ^ { D } \\mathbb { R }$ is convex if every one-dimensional slice is convex, i.e., for all $x , y \\in \\mathbb { R } ^ { D }$ , the function $g ( \\lambda ) = f ( ( 1 - \\lambda ) x + \\lambda y )$ is convex in $\\lambda$ . ", + "bbox": [ + 169, + 428, + 823, + 458 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Due to Definition 2.1, it suffices to show that arbitrary one-dimensional slices of a function are convex in order to reason about the convexity of complex, high-dimensional functions. In practice, we rarely observe perfect convexity but instead hope to approximate it as closely as possible. Following Frankle et al. (2020); Entezari et al. (2021); Draxler et al. (2018); Garipov et al. (2018) and others, we measure approximations to convexity via “barriers.” ", + "bbox": [ + 174, + 469, + 825, + 540 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Definition 2.2 (Loss barrier (Frankle et al., 2020)). Given two points $\\Theta _ { A } , \\Theta _ { B }$ such that $\\mathcal { L } ( \\Theta _ { A } ) \\approx$ $\\mathcal { L } ( \\Theta _ { B } )$ , the loss barrier is defined as $\\begin{array} { r } { \\operatorname* { m a x } _ { \\lambda \\in [ 0 , 1 ] } \\mathcal { L } ( ( 1 - \\lambda ) \\Theta _ { A } + \\lambda \\Theta _ { B } ) - \\frac { 1 } { 2 } ( \\mathcal { L } ( \\Theta _ { A } ) + \\mathcal { L } ( \\dot { \\Theta } _ { B } ) \\dot { ) } } \\end{array}$ . ", + "bbox": [ + 173, + 545, + 820, + 575 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Loss barriers are non-negative, with zero indicating an interpolation of flat or positive curvature. ", + "bbox": [ + 171, + 587, + 802, + 602 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3 PERMUTATION SELECTION METHODS ", + "text_level": 1, + "bbox": [ + 176, + 623, + 519, + 640 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "We introduce three methods of matching units between model $A$ and model $B$ . Further, we present an extension to simultaneously merging multiple models in Appendix A.10 and an appealing but failed method in Appendix A.11. ", + "bbox": [ + 174, + 656, + 825, + 699 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3.1 MATCHING ACTIVATIONS ", + "text_level": 1, + "bbox": [ + 174, + 718, + 392, + 733 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "Following the classic Hebbian mantra, “[neural network units] that fire together, wire together” (Hebb, 2005), we consider associating units across two models by performing regression between their activations. Matching activations between models is compelling since it captures the intuitive notion that two models must learn similar features to accomplish the same task (Li et al., 2016). Provided activations for each model, we aim to associate each unit in $A$ with a unit in $B$ . It stands to reason that a linear relationship may exist between the activations of the two models. We fit this into the regression framework by constraining ordinary least squares (OLS) to solutions in the set of permutation matrices, $S _ { d }$ . For activations of the $\\ell ^ { \\bullet }$ th layer, let $\\mathbf { \\bar { \\chi } } _ { Z ^ { ( A ) } , Z ^ { ( B ) } } \\in \\mathbb { R } ^ { d \\times n }$ denote the $d$ -dim. activations for all $n$ training data points in models $A$ and $B$ , respectively. Then, ", + "bbox": [ + 173, + 744, + 825, + 872 + ], + "page_idx": 2 + }, + { + "type": "equation", + "img_path": "images/a87c0bf2847490baf13193ea5584e22cbc725116278f795011eac31182906029.jpg", + "text": "$$\nP _ { \\ell } = \\underset { P \\in S _ { d } } { \\arg \\operatorname* { m i n } } \\sum _ { i = 1 } ^ { n } \\| Z _ { : , i } ^ { ( A ) } - P Z _ { : , i } ^ { ( B ) } \\| ^ { 2 } = \\underset { P \\in S _ { d } } { \\arg \\operatorname* { m a x } } \\langle P , Z ^ { ( A ) } ( Z ^ { ( B ) } ) ^ { \\top } \\rangle _ { F } ,\n$$", + "text_format": "latex", + "bbox": [ + 251, + 880, + 745, + 922 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "where $\\begin{array} { r } { \\langle { \\boldsymbol A } , { \\boldsymbol B } \\rangle _ { F } = \\sum _ { i , j } A _ { i , j } B _ { i , j } } \\end{array}$ denotes the Frobenius inner product between real-valued matrices $\\pmb { A }$ and $\\textbf { { B } }$ . Conveniently, eq. (1) constitutes a “linear assignment problem” (LAP) (Bertsekas, 1998) for which efficient, practical algorithms are known. Having solved this assignment problem on each layer, we can then permute the weights of model $B$ to match model $A$ as closely as possible ", + "bbox": [ + 174, + 102, + 825, + 161 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/90dcbc589365f08bb72d967fdc8bec98acc4a2843edbc4b9db87e394e6ff63c6.jpg", + "text": "$$\n\\pmb { W } _ { \\ell } ^ { \\prime } = \\pmb { P } _ { \\ell } \\pmb { W } _ { \\ell } ^ { ( B ) } \\pmb { P } _ { \\ell - 1 } ^ { \\top } , \\quad \\pmb { b } _ { \\ell } ^ { \\prime } = \\pmb { P } _ { \\ell } \\pmb { b } _ { \\ell } ^ { ( B ) }\n$$", + "text_format": "latex", + "bbox": [ + 372, + 165, + 625, + 186 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "for each layer $\\ell$ , producing weights $\\Theta ^ { \\prime }$ with activations that align as closely possible with $\\Theta _ { A }$ ", + "bbox": [ + 179, + 189, + 787, + 205 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Computationally, this entire process is relatively lightweight: the $\\pmb { Z } ^ { ( A ) }$ and ${ \\pmb Z } ^ { ( B ) }$ matrices can be computed in a single pass over the training dataset, and, in practice, a full run through the training dataset may be unnecessary. Solving eq. (1) is possible due to well-established, polynomial-time algorithms for solving the linear assignment problem (Kuhn, 2010; Jonker & Volgenant, 1987; Crouse, 2016). Also, conveniently, the activation matching at each layer is independent of the matching at every other layer, resulting in a separable and straightforward optimization problem; this advantage will not be enjoyed by the following methods. ", + "bbox": [ + 173, + 212, + 825, + 310 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Dispensing with regression, one could similarly associate units by matching against a matrix of cross-correlation coefficients in place of $Z ^ { ( A ) } ( \\dot { Z } ^ { ( B ) } ) ^ { \\top }$ . We observed correlation matching to work equally well but found OLS regression matching to be more principled and easier to implement. ", + "bbox": [ + 174, + 316, + 825, + 361 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Activation matching has previously been studied for model merging in Tatro et al. (2020); Singh & Jaggi (2020); Li et al. (2016) albeit not from the perspective of OLS regression. ", + "bbox": [ + 171, + 367, + 823, + 396 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "3.2 MATCHING WEIGHTS", + "text_level": 1, + "bbox": [ + 176, + 411, + 364, + 426 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Instead of associating units by their activations, we could alternatively inspect the weights of the model itself. Consider the first layer weights, $W _ { 1 }$ ; each row of $W _ { 1 }$ corresponds to a single feature. If two such rows were equal, they would compute exactly the same feature (ignoring bias terms for the time being). And, if $[ \\pmb { W } _ { 1 } ^ { ( A ) } ] _ { i , : } \\approx [ \\pmb { W } _ { 1 } ^ { ( B ) } ] _ { j , : }$ , it stands to reason that units $i$ and $j$ should be associated. Extending this idea to every layer, we are inspired to pursue the optimization ", + "bbox": [ + 173, + 438, + 825, + 512 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/ccac0ad022d9b4a00fd7b103057d8e82de0d6151108ae319b214b4f742acf009.jpg", + "text": "$$\n\\underset { \\pi } { \\arg \\operatorname* { m i n } } \\ \\| \\mathrm { v e c } ( \\Theta _ { A } ) - \\mathrm { v e c } ( \\pi ( \\Theta _ { B } ) ) \\| ^ { 2 } = \\underset { \\pi } { \\arg \\operatorname* { m a x } } \\ \\mathrm { v e c } ( \\Theta _ { A } ) \\cdot \\mathrm { v e c } ( \\pi ( \\Theta _ { B } ) ) .\n$$", + "text_format": "latex", + "bbox": [ + 250, + 513, + 745, + 541 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "We can re-express this in terms of the full weights, ", + "bbox": [ + 174, + 544, + 508, + 559 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/58b834d3484224836a28b0db421ea6bad78e819bdbb2b79252c52a58a4367cd2.jpg", + "text": "$$\n\\operatorname * { a r g m a x } _ { \\pi = \\{ P _ { i } \\} } \\langle { \\pmb W } _ { 1 } ^ { ( A ) } , { \\pmb P } _ { 1 } { \\pmb W } _ { 1 } ^ { ( B ) } \\rangle _ { F } + \\langle { \\pmb W } _ { 2 } ^ { ( A ) } , { \\pmb P } _ { 2 } { \\pmb W } _ { 2 } ^ { ( B ) } { \\pmb P } _ { 1 } ^ { \\top } \\rangle _ { F } + \\cdot \\cdot + \\langle { \\pmb W } _ { L } ^ { ( A ) } , { \\pmb W } _ { L } ^ { ( B ) } { \\pmb P } _ { L - 1 } ^ { \\top } \\rangle _ { F } ,\n$$", + "text_format": "latex", + "bbox": [ + 189, + 561, + 787, + 595 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "resulting in another matching problem. We term this formulation the “sum of bilinear assignments problem” (SOBLAP). Unfortunately, this matching problem is thornier than the classic linear assignment matching problem presented in eq. (1). Unlike LAP, we are interested in permuting both the rows and columns of $W _ { \\ell } ^ { ( B ) }$ ) to match W (A)ℓ , which fundamentally differs from permuting only rows or only columns. We formalize this difficulty as follows. ", + "bbox": [ + 173, + 597, + 825, + 671 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Lemma 1. The sum of a bilinear assignments problem (SOBLAP) is NP-hard and admits no polynomial-time constant-factor approximation scheme for $L > 2$ . ", + "bbox": [ + 173, + 674, + 818, + 703 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Lemma 1 contrasts starkly with classical LAP, for which polynomial-time algorithms are known. ", + "bbox": [ + 173, + 713, + 805, + 728 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Undeterred, we propose a approximation algorithm for SOBLAP. Looking at a single $P _ { \\ell }$ while holding the others fixed, we observe that the problem can be reduced to a classic LAP, ", + "bbox": [ + 173, + 734, + 823, + 763 + ], + "page_idx": 3 + }, + { + "type": "equation", + "img_path": "images/4447cd1d6a13725ed51f953c610d4b3e8d0f89dee4f989f069596808c91fb38e.jpg", + "text": "$$\n\\begin{array} { r l } & { \\underset { P _ { \\ell } } { \\arg \\operatorname* { m a x } } \\ \\langle { \\boldsymbol W } _ { \\ell } ^ { ( A ) } , P _ { \\ell } { \\boldsymbol W } _ { \\ell } ^ { ( B ) } { \\boldsymbol P } _ { \\ell - 1 } ^ { \\top } \\rangle _ { F } + \\langle { \\boldsymbol W } _ { \\ell + 1 } ^ { ( A ) } , P _ { \\ell + 1 } { \\boldsymbol W } _ { \\ell + 1 } ^ { ( B ) } { \\boldsymbol P } _ { \\ell } ^ { \\top } \\rangle _ { F } } \\\\ & { \\qquad = \\underset { P _ { \\ell } } { \\arg \\operatorname* { m a x } } \\ \\langle P _ { \\ell } , { \\boldsymbol W } _ { \\ell } ^ { ( A ) } { \\boldsymbol P } _ { \\ell - 1 } ( { \\boldsymbol W } _ { \\ell } ^ { ( B ) } ) ^ { \\top } + ( { \\boldsymbol W } _ { \\ell + 1 } ^ { ( A ) } ) ^ { \\top } P _ { \\ell + 1 } { \\boldsymbol W } _ { \\ell + 1 } ^ { ( B ) } \\rangle _ { F } . } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 243, + 766, + 756, + 829 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "This leads to a convenient coordinate descent algorithm: go through each layer and greedily select its best $P _ { \\ell }$ . Repeat until convergence. We present this in Algorithm 1. ", + "bbox": [ + 173, + 832, + 820, + 861 + ], + "page_idx": 3 + }, + { + "type": "text", + "text": "Although we present Algorithm 1 in terms of an MLP without bias terms, in practice our implementation can handle the weights of models of nearly arbitrary architectures, including bias terms, residual connections, convolutional layers, attention mechanisms, and so forth. We propose an extension of Algorithm 1 to merging more than two models at a time in Appendix A.10. ", + "bbox": [ + 174, + 867, + 825, + 924 + ], + "page_idx": 3 + }, + { + "type": "image", + "img_path": "images/6728305d713c85f40792a9007e2fd199d0797f18b8248371f77b8af3c0dced39.jpg", + "image_caption": [ + "Figure 2: Linear mode connectivity is possible after permuting. Loss landscapes when interpolating between models trained on MNIST, CIFAR-10, and ImageNet. In all cases we can significantly improve over na¨ıve interpolation. Straight-through estimator matching performs best but is very computationally expensive. Weight and activation matching perform similarly, although weight matching is orders of magnitude faster and does not rely on the input data distribution. We hypothesize that the ImageNet barrier could be reduced by increasing the model width as in Section 5.3. " + ], + "image_footnote": [], + "bbox": [ + 184, + 102, + 812, + 188 + ], + "page_idx": 4 + }, + { + "type": "table", + "img_path": "images/3433ccab35bbbe356ec4ce2ae88f1f5b8c19fdd9f37263c6f1964bb9d1e4e9bf.jpg", + "table_caption": [ + "Algorithm 1: PERMUTATIONCOORDINATEDESCENT ", + "Lemma 2. Algorithm 1 terminates. " + ], + "table_footnote": [], + "table_body": "
AIgorIthmI:PERMUTATIONCOORDINATEDESCENT Given:Mode weigts A = {w(4),., [4)} and θB ={~w(B),.. W}
Result: A permutation π = {P1,...,PL-1} of OB such that vec(ΘA) · vec(π(OB)) is approximately maximized.
Initialize:Pl←I,...,PL-1 ←I
repeat
for l∈RANDOMPERMUTATION(1,...,L-1) do
P←SOLvELAP（W()P-1(W(B）+(W(）1W)）
end until convergence
", + "bbox": [ + 171, + 308, + 821, + 493 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Our experiments showed this algorithm to be fast in terms of both iterations necessary for convergence and wall-clock time, generally on the order of seconds to a few minutes. ", + "bbox": [ + 173, + 554, + 821, + 583 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Unlike the activation matching method presented in Section 3.1, weight matching ignores the data distribution entirely. Ignoring the input data distribution and therefore the loss landscape handicaps weight matching but allows it to be much faster. We therefore anticipate its potential application in fields such as finetuning (Devlin et al., 2019; Wortsman et al., 2022b;a), federated learning (McMahan et al., 2017; Konecnˇ y et al., 2016a;b), and model patching (Matena & Raffel, 2021; Sung et al.,´ 2021; Raffel, 2021). In practice, we found weight matching to be surprisingly competitive with data-aware methods. Section 5 studies this trade-off. ", + "bbox": [ + 173, + 589, + 825, + 688 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "3.3 LEARNING PERMUTATIONS WITH A STRAIGHT-THROUGH ESTIMATOR ", + "text_level": 1, + "bbox": [ + 174, + 708, + 694, + 723 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "Inspired by the success of straight-through estimators (STEs) in other discrete optimization problems (Bengio et al., 2013; Kusupati et al., 2021; Rastegari et al., 2016; Courbariaux & Bengio, 2016), we attempt here to “learn” the ideal permutation of weights $\\pi ( \\Theta _ { B } )$ . Specifically, our goal is to optimize ", + "bbox": [ + 174, + 734, + 825, + 791 + ], + "page_idx": 4 + }, + { + "type": "equation", + "img_path": "images/9c4d53a5a78947229bf57665e58624f496a7bee793953fb1bf65e3316787ae61.jpg", + "text": "$$\n\\operatorname* { m i n } _ { \\hat { \\Theta } _ { B } } \\ { \\mathcal { L } } \\left( { \\frac { 1 } { 2 } } \\left( \\Theta _ { A } + \\mathrm { p r o j } \\left( { \\widetilde { \\Theta } } _ { B } \\right) \\right) \\right) , \\qquad \\mathrm { p r o j ( \\Theta ) } \\ { \\overset { \\triangle } { = } } \\ \\arg \\operatorname* { m a x } _ { \\pi } \\ \\mathrm { v e c } ( \\Theta ) \\cdot \\mathrm { v e c } ( \\pi ( \\Theta _ { B } ) ) ,\n$$", + "text_format": "latex", + "bbox": [ + 218, + 801, + 776, + 837 + ], + "page_idx": 4 + }, + { + "type": "text", + "text": "where $\\tilde { \\Theta } _ { B }$ denotes an approximation of $\\pi ( \\Theta _ { B } )$ , allowing us to implicitly optimize $\\pi$ . However, eq. (3) involves inconvenient non-differentiable projection operations, proj $( \\cdot )$ , complicating the optimization. We overcome this via a “straight-through” estimator: we parameterize the problem in terms of a set of weights $\\tilde { \\Theta } _ { B } \\approx \\pi ( \\Theta _ { B } )$ . In the forward pass, we project $\\tilde { \\Theta } _ { B }$ to the closest realizable $\\pi ( \\Theta _ { B } )$ . In the backwards pass, we then switch back to the unrestricted weights $\\tilde { \\Theta } _ { B }$ . In this way, we are guaranteed to stay true to the projection constraints in evaluating the loss but can still compute usable gradients at our current parameters, $\\tilde { \\Theta } _ { B }$ .2 ", + "bbox": [ + 173, + 848, + 825, + 924 + ], + "page_idx": 4 + }, + { + "type": "image", + "img_path": "images/66fdb92d5345a394d0ef2d04adc18349df134e93a47aae13eddad25cda8fb2bb.jpg", + "image_caption": [ + "Figure 3: Linear mode connectivity is challenging at initialization. We show loss barriers per training time for MLPs trained on MNIST (left) and CIFAR-10 (right). Loss interpolation plots are inlaid to highlight results in initial and later epochs. LMC manifests gradually throughout training. We hypothesize that the variance in CIFAR-10 training is higher due to our MLP architecture being under-powered relative to the dataset. (Y-axis scales differ in each inlaid plot.) " + ], + "image_footnote": [], + "bbox": [ + 238, + 88, + 759, + 231 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 335, + 821, + 366 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Conveniently, we can re-purpose Algorithm 1 to solve proj $( { \\tilde { \\Theta } } _ { B } )$ . Furthermore, we found that initializing $\\tilde { \\Theta } _ { B } = \\Theta _ { A }$ performed better than random initialization. This is to be expected immediately at initialization since the initial matching will be equivalent to the weight matching method of Section 3.1. However, it is not immediately clear why these solutions continue to outperform a random initialization asymptotically. ", + "bbox": [ + 173, + 373, + 823, + 446 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Unlike the aforementioned methods, Algorithm 2 attempts to explicitly “learn” the best permutation $\\pi$ using a conventional training loop. By initializing to the weight matching solution of Section 3.2 and leveraging the data distribution as in Section 3.1, it seeks to offer a best-of-both-worlds solution. However, this comes at a very steep computational cost relative to the other two methods. ", + "bbox": [ + 174, + 453, + 825, + 508 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "4 A COUNTEREXAMPLE TO UNIVERSAL LINEAR MODE CONNECTIVITY ", + "text_level": 1, + "bbox": [ + 174, + 529, + 787, + 545 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "In this section we argue that common optimization algorithms, especially SGD and its relatives, are implicitly biased towards solutions admitting linear mode connectivity. In particular, we demonstrate – by way of a counterexample – that adversarial, non-SGD solutions exist in loss landscapes such that no permutation of units results in linear mode connectivity. We present this counterexample in complete detail in Appendix A.6. ", + "bbox": [ + 174, + 559, + 825, + 630 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "The existence of adversarial basins suggests that our ability to find LMC between independently trained models is thanks to inherent biases in optimization methods. We emphasize that this counterexample does not contradict Conjecture 1; rather, it illustrates the importance of the conjecture’s restriction to SGD solutions (Entezari et al., 2021). Characterizing the precise mechanism by which these solutions are biased towards LMC could be an exciting avenue for future work. ", + "bbox": [ + 174, + 637, + 823, + 707 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "We also note that there are invariances beyond permutation symmetries: It is possible to move features between layers, re-scale layers, and so forth. Prior works noted the feature/layer association (Nguyen et al., 2021) and re-scaling invariances (Ainsworth et al., 2018). The importance of these other symmetries and their interplay with optimization algorithms remains unclear. ", + "bbox": [ + 174, + 713, + 825, + 770 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "5 EXPERIMENTS ", + "text_level": 1, + "bbox": [ + 176, + 790, + 326, + 805 + ], + "page_idx": 5 + }, + { + "type": "text", + "text": "Our base methodology is to separately train two models, $A$ and $B$ , starting from different random initializations and with different random batch orders, resulting in trained weights $\\Theta _ { A }$ and $\\Theta _ { B }$ , respectively. We then evaluate slices through the loss landscape, $\\mathcal { L } ( ( 1 - \\lambda ) \\Theta _ { A } + \\lambda \\pi ( \\Theta _ { B } ) )$ for $\\lambda \\in [ 0 , 1 ]$ , where $\\pi$ is selected according to the methods presented in Section 3.3 Ideally, we seek a completely flat or even convex one-dimensional slice. As discussed in Section 2, the ability to exhibit this behavior for arbitrary $\\Theta _ { A } , \\Theta _ { B }$ empirically suggests that the loss landscape contains only a single basin modulo permutation symmetries. ", + "bbox": [ + 176, + 820, + 823, + 849 + ], + "page_idx": 5 + }, + { + "type": "image", + "img_path": "images/3e2b1e1ca8930ad7cb63f4865ef94b31090d2207fcd8a0648f4d185bd101dc14.jpg", + "image_caption": [ + "Figure 4: Wider models exhibit better linear mode connectivity. Training convolutional and ResNet architectures on CIFAR-10, we ablate their width and visualize loss barriers after weight matching. Notably, we achieve zero-barrier linear mode connectivity between ResNet models, the first such demonstration. " + ], + "image_footnote": [], + "bbox": [ + 238, + 88, + 759, + 231 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "", + "bbox": [ + 174, + 321, + 825, + 390 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We remark that a failure to find a $\\pi$ such that linear mode connectivity holds cannot rule out the existence of a satisfactory permutation. Given the astronomical number of permutation symmetries, Conjecture 1 is essentially impossible to disprove for any realistically wide model architecture. ", + "bbox": [ + 174, + 397, + 825, + 439 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.1 LOSS LANDSCAPES BEFORE AND AFTER MATCHING ", + "text_level": 1, + "bbox": [ + 174, + 457, + 580, + 470 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "We present results for models trained on MNIST (LeCun et al., 1998), CIFAR-10 (Krizhevsky, 2009), and ImageNet (Deng et al., 2009) in Figure 2. Na¨ıve interpolation $( \\pi ( \\Theta _ { B } ) = \\Theta _ { B } )$ ) substantially degrades performance when interpolating. On the other hand, the methods introduced in Section 3 can achieve much better barriers. We achieve zero-barrier linear mode connectivity on MNIST with all three methods, although activation matching performs just slightly less favorably than weight matching and straight-through estimator (STE) matching. We especially note that the test loss landscape becomes convex after applying our weight matching and STE permutations! In other words, our interpolation actually yields a merged model that outperforms both models $A$ and $B$ . We elaborate on this phenomenon in Section 5.4 and Appendix A.10. ", + "bbox": [ + 174, + 483, + 825, + 608 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "On ImageNet we fall short of zero-barrier connections, although we do see a $67 \\%$ decrease in barrier relative to na¨ıve interpolation. As we demonstrate in Section 5.3, we can achieve zero-barrier LMC on CIFAR-10 with large ResNet models. Therefore, we hypothesize that the presence of LMC depends on the model having sufficient capacity (esp. width) to capture the complexity of the input data distribution, and that ImageNet results could be improved by expanding model width. ", + "bbox": [ + 174, + 616, + 825, + 685 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "STE matching, the most expensive method, produces the best solutions. Somewhat surprising, however, is that the gap between STE and the other two methods is relatively small. In particular, it is remarkable how well Algorithm 1 performs without access to the input data at all. We found that weight matching offered a compelling balance between computational cost and performance: It runs in mere seconds (on current hardware) and produces high-quality solutions. ", + "bbox": [ + 174, + 691, + 825, + 762 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "5.2 ONSET OF MODE CONNECTIVITY ", + "text_level": 1, + "bbox": [ + 176, + 779, + 444, + 792 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Given the results of Section 5.1, it may be tempting to conclude that the entirety of weight space contains only a single basin modulo permutation symmetries. However, we found that linear mode connectivity is an emergent property of training, and we were unable to uncover it early in training. We explore the emergence of LMC in Figure 3. Concurrent to our work, Benzing et al. (2022) showed that LMC at initialization is possible using a permutation found at the end of training. ", + "bbox": [ + 174, + 804, + 825, + 875 + ], + "page_idx": 6 + }, + { + "type": "text", + "text": "Note that the final inlaid interpolation plot in Figure 3(right) demonstrates an important shortcoming of the loss barrier metric, i.e., the interpolation includes points with lower loss than either of the two models. However, the loss barrier is still positive due to non-negativity, as mentioned in Section 2. ", + "bbox": [ + 176, + 103, + 823, + 146 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.3 EFFECT OF MODEL WIDTH ", + "text_level": 1, + "bbox": [ + 176, + 162, + 401, + 178 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Conventional wisdom maintains that wider architectures are easier to optimize (Jacot et al., 2018; Lee et al., 2019). We now investigate whether they are also easier to linearly mode connect. We train VGG-16 (Simonyan & Zisserman, 2015) and ResNet20 (He et al., 2016) architectures of varying widths on the CIFAR-10 dataset. Results are presented in Figure 4.4 ", + "bbox": [ + 174, + 189, + 825, + 244 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "A clear relationship emerges between model width and linear mode connectivity, as measured by the loss barrier between solutions. Although $1 \\times$ -sized models did not seem to exhibit linear mode connectivity, we found that larger width models decreased loss barriers all the way to zero. In Figure 4(right), we show what is to our knowledge the premiere demonstration of zero-barrier linear mode connectivity between two large ResNet models trained on a non-trivial dataset. ", + "bbox": [ + 174, + 252, + 823, + 321 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "We highlight that relatively thin models do not seem to obey linear mode connectivity yet still exhibit similarities in training dynamics. This suggests that either our permutation selection methods are failing to find satisfactory permutations on thinner models or that some form of invariance other than permutation symmetries must be at play in the thin model regime. ", + "bbox": [ + 174, + 329, + 825, + 385 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "5.4 MODEL PATCHING, SPLIT DATA TRAINING, AND IMPROVED CALIBRATION ", + "text_level": 1, + "bbox": [ + 176, + 401, + 728, + 416 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "Inspired by work on finetuning (Wortsman et al., 2022a), model patching (Singh & Jaggi, 2020; Raffel, 2021), and federated learning (McMahan et al., 2017; Konecnˇ y et al., ´ 2016a;b), we study whether it is possible to synergistically merge the weights of two models trained on disjoint datasets. Consider, for example, an organization with multiple (possibly biased) datasets separated for regulatory (e.g., GDPR) or privacy (e.g., on-device data) considerations. Models can be trained on each dataset individually, but training in aggregate is not feasible. Can we combine separately trained models so that the merged model performs well on the entirety of the data? ", + "bbox": [ + 174, + 429, + 483, + 636 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "To address this question, we split the CIFAR100 dataset (Krizhevsky, 2009) into two disjoint subsets: dataset $A$ , containing $20 \\%$ examples labelled 0-49 and $80 \\%$ labelled 50-99, and dataset $B$ , vice versa. ResNet20 models $A$ and ", + "bbox": [ + 174, + 643, + 483, + 712 + ], + "page_idx": 7 + }, + { + "type": "image", + "img_path": "images/a40f48d35cd25ea9dc31ac529bdb2112216b0505ab81b6a1603e143e0e364bc6.jpg", + "image_caption": [ + "Figure 5: Models trained on disjoint datasets can be merged constructively. Algorithm 1 makes it possible for two ResNet models trained on disjoint, biased subsets of CIFAR-100 to be merged in weight space such that their combination outperforms both input models in terms of test loss on the combined dataset. " + ], + "image_footnote": [], + "bbox": [ + 524, + 433, + 794, + 585 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "$B$ were trained on their corresponding datasets. Privacy requirements mandate that we utilize a data-agnostic algorithm like Algorithm 1. Figure 5 shows the result of merging the two models with weight matching. For comparison, we benchmark na¨ıve weight interpolation, ensembling of the model logits, and full-data training. ", + "bbox": [ + 174, + 713, + 826, + 768 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "As expected, merging separately trained models did not match the performance of an omniscient model trained on the full dataset or an ensemble of the two models with twice the number of effective weights. On the other hand, we did manage to merge the two models in weight space, achieving an interpolated model that outperforms both input models in terms of test loss while using half the memory and compute required for ensembling. Furthermore, the merged model’s probability estimates are better calibrated than either of the input models as demonstrated in Figure 11. Accuracy results are presented in Figure 10. Algorithm 1 also vastly outperformed na¨ıve interpolation, the status quo for model combination in federated learning and distributed training. ", + "bbox": [ + 173, + 775, + 825, + 887 + ], + "page_idx": 7 + }, + { + "type": "text", + "text": "6 RELATED WORK ", + "text_level": 1, + "bbox": [ + 176, + 102, + 344, + 117 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "(Linear) mode connectivity. Garipov et al. (2018); Draxler et al. (2018); Freeman & Bruna (2017) showed that different solutions in the neural network loss landscape could be connected by paths of near-constant loss, which Garipov et al. (2018) coined “mode connectivity.” Tatro et al. (2020) explored non-linear mode connectivity modulo permutation symmetries. Frankle et al. (2020) demonstrated a connection between linear mode connectivity and the lottery ticket hypothesis. Juneja et al. (2022) demonstrated that LMC does not always hold, even when fine-tuning. Hecht-Nielsen (1990); Chen et al. (1993) noted the existence of permutation symmetries, and Brea et al. (2019) implicated them as a source of saddle points in the loss landscape. Recently, the prescient work of Entezari et al. (2021) conjectured that SGD solutions could be linear mode connected modulo permutation symmetries and offered experiments buttressing this claim. Unlike previous works on LMC we accomplish zero-barrier paths between two independently-trained models with an algorithm that runs on the order of seconds. ", + "bbox": [ + 174, + 133, + 825, + 300 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Loss landscapes and training dynamics. Li et al. (2016); Yosinski et al. (2014) investigated whether independently trained networks learn similar features, and to what extent they transfer. Jiang et al. (2021) argued that independently trained networks meaningfully differ in the features they learn in certain scenarios. Zhang et al. (2019) studied the relative importance of layers. Benton et al. (2021) argued that SGD solutions form a connected volume of low loss. Pittorino et al. (2022) proposed a toroidal topology of solutions and a set of algorithms for symmetry removal. On the theoretical front, Kawaguchi (2016) proved that deep linear networks contain no local minima. Boursier et al. (2022); Chizat & Bach (2018); Mei et al. (2018) characterized the training dynamics of one-hidden layer networks, proving that they converge to zero loss. Godfrey et al. (2022); Simsek et al. (2021) investigated the algebraic structure of symmetries in neural networks and how this structure manifests in loss landscape geometry. ", + "bbox": [ + 174, + 308, + 825, + 460 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "Federated learning and model merging. McMahan et al. (2017); Konecnˇ y et al. (2016a;b) in- ´ troduced the concept of “federated learning,” i.e., learning split across across multiple devices and datasets. Wang et al. (2020) proposed an exciting federated learning method in which model averaging is done after permuting units. Unlike this work, they merged smaller “child” models into a larger “main” model, and did so with a layer-wise algorithm that does not support residual connections or normalization layers. Raffel (2021); Matena & Raffel (2021); Sung et al. (2021) conceptualized the study of “model patching,” i.e., the idea that models should be easy to modify and submit changes to. Ilharco et al. (2022) investigated model patching for the fine-tuning of open-vocabulary vision models. Ashmore & Gashler (2015) first explored the use of matching algorithms for the alignment of network units. Singh & Jaggi (2020) proposed merging models by soft-aligning associations weights, inspired by optimal transport. Liu et al. (2022a); Uriot & Izzo (2020) further explored merging models taking possible permutations into account. Wortsman et al. (2022a) demonstrated state-of-the-art ImageNet performance by averaging the weights of many fine-tuned models. ", + "bbox": [ + 173, + 467, + 825, + 647 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "7 DISCUSSION AND FUTURE WORK ", + "text_level": 1, + "bbox": [ + 176, + 667, + 485, + 684 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "We explore the role of permutation symmetries in the linear mode connectivity of SGD solutions. We present three algorithms to canonicalize independent neural network weights in order to make the loss landscape between them as flat as possible. In contrast to prior work, we linearly mode connect large ResNet models with no barrier in seconds to minutes. Despite presenting successes across multiple architectures and datasets, linear mode connectivity between thin models remains elusive. Therefore, we conjecture that permutation symmetries are a necessary piece, though not a complete picture, of the fundamental invariances at play in neural network training dynamics. In particular, we hypothesize that linear, possibly non-permutation, relationships connect the layerwise activations between models trained by SGD. In the infinite width limit, there exist satisfactory linear relationships that are also permutations. ", + "bbox": [ + 174, + 699, + 825, + 838 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "An expanded theory and empirical exploration of other invariances – such as cross-layer scaling or general linear relationships between activations – presents an intriguing avenue for future work. Ultimately, we anticipate that a lucid understanding of loss landscape geometry will not only advance the theory of deep learning but will also promote the development of better optimization, federated learning, and ensembling techniques. ", + "bbox": [ + 176, + 844, + 823, + 915 + ], + "page_idx": 8 + }, + { + "type": "text", + "text": "ETHICS STATEMENT ", + "text_level": 1, + "bbox": [ + 174, + 103, + 316, + 117 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Merging models raises interesting ethical and technical questions about the resulting models. Do they inherit the same biases as their input models? Are rare examples forgotten when merging? Is it possible to gerrymander a subset of the dataset by splitting its elements across many shards? ", + "bbox": [ + 176, + 127, + 823, + 170 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Deployment of any form of model merging ought to be paired with thorough auditing of the resulting model, investigating in particular whether the merged model is representative of the entirety of the data distribution. ", + "bbox": [ + 176, + 176, + 823, + 218 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "REPRODUCIBILITY STATEMENT ", + "text_level": 1, + "bbox": [ + 176, + 234, + 393, + 248 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "Our code is open sourced at https://github.com/samuela/git-re-basin. Our experimental logs and downloadable model checkpoints are fully open source at https://wandb.ai/ skainswo/git-re-basin. ", + "bbox": [ + 176, + 258, + 825, + 300 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "ACKNOWLEDGMENTS ", + "text_level": 1, + "bbox": [ + 176, + 318, + 326, + 330 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "We are grateful to Vivek Ramanujan, Mitchell Wortsman, Aditya Kusupati, Rahim Entezari, Jason Yosinski, Krishna Pillutla, Ofir Press, Matt Wallingford, Tim Dettmers, Raghav Somani, Gabriel Ilharco, Ludwig Schmidt, Sewoong Oh, and Kevin Jamieson for enlightening discussions. Thank you to John Thickstun and Sandy Kaplan for their thoughtful review of an earlier draft of this work and to Ofir Press and Tim Dettmers for their potent advice on framing and communicating this work. This work was (partially) funded by the National Science Foundation NRI (#2132848) & CHS (#2007011), DARPA RACER, the Office of Naval Research, Honda Research Institute, and Amazon. This work is supported in part by Microsoft and NSF grants DMS-2134012 and CCF2019844 as a part of NSF Institute for Foundations of Machine Learning (IFML). ", + "bbox": [ + 174, + 340, + 825, + 465 + ], + "page_idx": 9 + }, + { + "type": "text", + "text": "REFERENCES ", + "text_level": 1, + "bbox": [ + 176, + 103, + 285, + 117 + ], + "page_idx": 10 + }, + { + "type": "text", + "text": "Samuel K. Ainsworth, Nicholas J. Foti, Adrian K. C. Lee, and Emily B. Fox. oi-vae: Output interpretable vaes for nonlinear group factor analysis. In Jennifer G. 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", + "bbox": [ + 176, + 444, + 823, + 473 + ], + "page_idx": 17 + }, + { + "type": "text", + "text": "A APPENDIX ", + "text_level": 1, + "bbox": [ + 176, + 102, + 299, + 117 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "A.1 KNOWN FAILURE MODES ", + "text_level": 1, + "bbox": [ + 176, + 133, + 397, + 148 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "We emphasize that none of the techniques presented in this paper are silver bullets. Here we list the failure cases that the authors are presently aware of, ", + "bbox": [ + 174, + 160, + 825, + 188 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "1. Models of insufficient width \n2. Models in the initial stages of training \n3. VGGs on MNIST \n4. MNIST MLPs trained with SGD and too low of a learning rate, or Adam and too high of a learning rate \n5. ConvNeXt architectures (Liu et al., 2022b), which have surprisingly few permutation symmetries due to extensive use of depth-wise convolutions ", + "bbox": [ + 210, + 200, + 825, + 320 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "Furthermore, we believe other failure modes certainly exist but have yet to be discovered. ", + "bbox": [ + 173, + 332, + 758, + 347 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "We are excited by the prospect of future work investigating these failure modes and improving our understanding of when and why model merging modulo permutation symmetries is feasible. ", + "bbox": [ + 174, + 353, + 823, + 382 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "A.2 EXTENDED RELATED WORK ", + "text_level": 1, + "bbox": [ + 176, + 398, + 415, + 412 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "Non-linear mode connectivity. A flourishing set of literature exists studying non-linear mode connectivity, including but not limited to Garipov et al. (2018); Draxler et al. (2018); Kuditipudi et al. (2019). This insightful line of work is inspirational to our own, however we take a strictly linear approach to mode connectivity as in Frankle et al. (2020); Juneja et al. (2022). Restricting ourselves to linear trajectories comes with the advantage of having direct implications for a single-basin theory. However, it comes at the cost of a more challenging, discrete optimization problem. In particular, we found that – in contrast to non-linear mode connectivity – linear mode connectivity becomes drastically harder with smaller width models. Note additionally that most pre-existing mode connectivity work does not account for permutation symmetries of weight space, a linchpin element of our work. A notable exception to this trend can be found in Tatro et al. (2020). ", + "bbox": [ + 174, + 425, + 825, + 564 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "To summarize: Freeman & Bruna (2017) introduced the notion of mode connectivity and proved that loss landscapes for single-hidden layer ReLU models contain only a single basin in the infinite width limit. Garipov et al. (2018) and Draxler et al. (2018) concurrently demonstrated that simple zero-barrier curves can be learned to connect the optima in weight space, thus reshaping our understanding of practical loss landscape geometries. Kuditipudi et al. (2019) proposes a theoretical explanation for the mode connectivity phenomenon. Benton et al. (2021) extends mode connectivity from one-dimensional paths to entire manifolds of low-loss, and show that these manifolds can be leveraged for state-of-the-art Bayesian ensembling of models. ", + "bbox": [ + 174, + 570, + 825, + 683 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "Relationship with Tatro et al. (2020). The impact of permutation symmetries on the non-linear mode connectivity of models is considered in Tatro et al. (2020). In particular, they independently propose an algorithm more-or-less equivalent to Section 3.1 but use it in conjunction with learned non-linear mode connecting curves. In contrast, we show that linear mode connectivity can be achieved without the need for learning non-linear paths between the aligned weights. Our derivation of Section 3.1 from the principle of least-squares regression is novel, to the best of our knowledge. ", + "bbox": [ + 174, + 689, + 825, + 773 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "Relationship with Singh & Jaggi (2020). Singh & Jaggi (2020) studies model merging with “soft matchings” between units from the perspective of optimal transport. We emphasize the following commonalities/differences with their work: ", + "bbox": [ + 176, + 780, + 823, + 821 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "• We focus on linear mode connectivity modulo permutation symmetries and its implications for a single-basin theory. On the other hand, Singh & Jaggi (2020) emphasizes “soft” (ie., non-permutation) matching of units via optimal transport. \n• The activation matching method of Singh & Jaggi (2020) reduces to that of Section 3.1 when the optimal transport regularization term is set to zero and the unit “importance” values are set to uniform across all units on all layers. \n• Our weight matching and straight-through estimator methods solve for an alignment across all layers jointly. In contrast, Singh & Jaggi (2020) executes greedy, single-pass matching looking only at weight information from the immediately previous layer when selecting permutations. Singh & Jaggi (2020) suggests jointly solving for alignments as an avenue for future work. \n• The “wts” method of Singh & Jaggi (2020) is not run on models including bias terms, skip connections, or normalization layers. In contrast, our Algorithm 1 works with models of nearly arbitrary architecture. \n• Our weight matching method (Algorithm 1) outperforms the “wts” method of Singh & Jaggi (2020). See Appendix A.7 for more information. \n• Singh & Jaggi (2020) introduces a method for merging multiple models simultaneously, but only demonstrates results on at most 8 models at a time and performs continued training after merging. In contrast, our Algorithm 3 has been shown to work with as many as 32 models at a time and does not require continued training after merging. Our analysis of the calibration of the resulting merged models has no parallel in Singh & Jaggi (2020). ", + "bbox": [ + 217, + 834, + 825, + 924 + ], + "page_idx": 18 + }, + { + "type": "text", + "text": "", + "bbox": [ + 215, + 103, + 825, + 332 + ], + "page_idx": 19 + }, + { + "type": "text", + "text": "Relationship with Entezari et al. (2021). Entezari et al. (2021) introduces the single-basin conjecture and provides the following evidence towards it: ", + "bbox": [ + 173, + 343, + 820, + 372 + ], + "page_idx": 19 + }, + { + "type": "text", + "text": "• Entezari et al. (2021) provides a statistical test which fails to detect a difference in barrier statistics between independently trained models and random permutations of the same model (Fig. 5 of Entezari et al. (2021)). Our work provides stronger support for the conjecture in that we give methods that can directly “unscramble” these permutations, proving that LMC can be found (Figures 4 and 5). Entezari et al. (2021)’s experimental protocol does not provide evidence for linear mode connectivity. Rather, their experimental results suggest that barriers resulting from independent training look like the barriers resulting from random permutations. But this result is consistent with a world in which all solutions have barriers between them – both between members of the same permutation equivalence class and between solutions in separate equivalence classes! In other words, there may still exist multiple equivalence classes of solutions. In contrast, we provide concrete evidence for a single-basin theory by developing algorithms that directly place independent solutions into the same basin (Figure 1). \n• Although Entezari et al. (2021)’s conjecture is an important intellectual ancestor to our work, their demonstration of linear mode connectivity is limited to a single hidden-layer MLP on MNIST (Fig. 2 of Entezari et al. (2021)). However, this result for single hiddenlayer MLP models is preceded by Freeman & Bruna (2017); Uriot & Izzo (2020). On the other hand, we focus on larger models and datasets that are more closely aligned with models used in practice at the time of writing. \n• Entezari et al. (2021) proposes a simulated annealing algorithm that yields modest reductions in barrier between independently trained models, yet requires multiple days to run. On the other hand, our weight matching algorithm (Algorithm 1) completely removes barriers between models for more challenging models and datasets (Figures 2 and 5), and runs in seconds (Appendix A.5). Moreover, our weight matching method does not require access to the training data, enabling its potential application in domains like federated learning and distributed training. ", + "bbox": [ + 215, + 383, + 825, + 765 + ], + "page_idx": 19 + }, + { + "type": "text", + "text": "In short, the work of Entezari et al. (2021) first proposed the “single-basin” conjecture. Our work is the first (to the best of our knowledge) to demonstrate that linear mode connectivity can be achieved between large models independently trained on challenging datasets. ", + "bbox": [ + 176, + 777, + 821, + 819 + ], + "page_idx": 19 + }, + { + "type": "text", + "text": "Differentiating through permutations. Akin to differentiable permutation learning, many prior works have studied differentiable sorting (Grover et al., 2019; Prillo & Eisenschlos, 2020; Cuturi et al., 2019; Petersen et al., 2022; 2021; Mena et al., 2018). Blondel et al. (2020) studied differentiable sorting and ranking with asymptotics that correspond to their non-differentiable versions. Fogel et al. (2015) explored recovering the linear orderings of items based on pairwise information, another form of permutation optimization. Bengio et al. (2013) introduced the straight-through estimator for differentiating through discrete projections that we utilize in Section 3.3. ", + "bbox": [ + 174, + 827, + 825, + 924 + ], + "page_idx": 19 + }, + { + "type": "text", + "text": "A.3 EXPERIMENTAL DETAILS ", + "text_level": 1, + "bbox": [ + 176, + 103, + 395, + 118 + ], + "page_idx": 20 + }, + { + "type": "text", + "text": "A.3.1 MULTI-LAYER PERCEPTRON MODELS ", + "text_level": 1, + "bbox": [ + 174, + 128, + 491, + 143 + ], + "page_idx": 20 + }, + { + "type": "text", + "text": "In these experiments we utilized networks with 3 hidden layers of 512 units each. ReLU activations were used between layers and no normalization was performed. Optimization was done with Adam and a learning rate of $1 e - 3$ . ", + "bbox": [ + 176, + 154, + 823, + 195 + ], + "page_idx": 20 + }, + { + "type": "text", + "text": "A.3.2 VGG-16 AND RESNET MODELS ON CIFAR DATASETS ", + "text_level": 1, + "bbox": [ + 174, + 209, + 606, + 224 + ], + "page_idx": 20 + }, + { + "type": "text", + "text": "We utilized the VGG-16 architecture of Simonyan & Zisserman (2015) with the exception that we used LayerNorm normalization in place of BatchNorm. Similarly we used the ResNet20 architecture of He et al. (2016) but with LayerNorms in place of BatchNorms. ", + "bbox": [ + 174, + 234, + 825, + 276 + ], + "page_idx": 20 + }, + { + "type": "text", + "text": "The following data augmentation was performed during training ", + "bbox": [ + 174, + 284, + 596, + 297 + ], + "page_idx": 20 + }, + { + "type": "text", + "text": "• Random resizes of the image between $0 . 8 \\times - 1 . 2 \\times$ \n• Random $3 2 \\times 3 2$ pixel crops \n• Random horizontal flips \n• Random rotations between $\\pm 3 0 ^ { \\circ }$ ", + "bbox": [ + 217, + 308, + 553, + 376 + ], + "page_idx": 20 + }, + { + "type": "text", + "text": "Optimization was done with SGD with momentum (momentum set to 0.9). A weight decay regularization term of $5 e - 4$ was applied. A single cosine decay schedule with linear warm-up was used. Learning rates were initialized at $1 e - 6$ and linearly increased to $1 e - 1$ over the span of an epoch. After that point a single cosine decay schedule (Loshchilov & Hutter, 2017) was used for the remainder of training. ", + "bbox": [ + 174, + 387, + 825, + 457 + ], + "page_idx": 20 + }, + { + "type": "text", + "text": "A.3.3 RESNET50 MODELS ON IMAGENET-1K ", + "text_level": 1, + "bbox": [ + 174, + 472, + 503, + 486 + ], + "page_idx": 20 + }, + { + "type": "text", + "text": "In this experiment we utilized pre-trained ResNet50 model available for download online, and one trained ourselves. These were standard ResNet50 models, including the use of BatchNorm. In line with prior work (Izmailov et al., 2018; Wortsman et al., 2021; Maddox et al., 2019; Wang et al., 2021), we recalculate BatchNorm statistics after performing weight interpolation. After our initial publication, the recalculation of BatchNorm statistics was suggested to us by the authors of Jordan et al. (2022). ", + "bbox": [ + 173, + 496, + 825, + 579 + ], + "page_idx": 20 + }, + { + "type": "text", + "text": "A.4 THE RELATIONSHIP BETWEEN PERMUTATION MATCHING AND NORMALIZATION LAYERS ", + "bbox": [ + 174, + 595, + 772, + 623 + ], + "page_idx": 20 + }, + { + "type": "text", + "text": "In this section we discuss the impact that different types of common normalization layers can have on the feasibility of model merging. ", + "bbox": [ + 173, + 635, + 825, + 665 + ], + "page_idx": 20 + }, + { + "type": "text", + "text": "• BatchNorm (Ioffe & Szegedy, 2015) generally breaks after interpolating between weights due to the so-called “variance collapse” problem (Jordan et al., 2022). Therefore, we recommend the recalculation of batch statistics after merging models (Izmailov et al., 2018; Wortsman et al., 2021; Maddox et al., 2019; Wang et al., 2021). \n• LayerNorm (Ba et al., 2016) is invariant to permutations of units and we found that architectures with LayerNorm can be merged without issue. \n• InstanceNorm (Ulyanov et al., 2016) also places no restrictions on unit order, and in principle does not present any issues, although we have not run any experiments with it. \n• GroupNorm (Wu & He, 2020) relies on unit indexes to organize units into groups, and therefore is not invariant to permutations of units. In principle, permutation alignment methods would not work on architectures with GroupNorm, though we have not tested this. ", + "bbox": [ + 217, + 674, + 825, + 853 + ], + "page_idx": 20 + }, + { + "type": "text", + "text": "A.5 ADDITIONAL INFORMATION ON ALGORITHM 1 ", + "text_level": 1, + "bbox": [ + 174, + 869, + 542, + 883 + ], + "page_idx": 20 + }, + { + "type": "text", + "text": "On currently available hardware (p3.2xlarge AWS instance with an NVIDIA V100 GPU), we observed the following timing results with Algorithm 1, ", + "bbox": [ + 176, + 895, + 823, + 924 + ], + "page_idx": 20 + }, + { + "type": "image", + "img_path": "images/7474fc86a4fbae61576200d8c26d718ff3e25733e6249c884ee1b940a23fa88d.jpg", + "image_caption": [ + "Figure 6: A counterexample to universal LMC. There exist models such that no possible permutation of weights allows for linear mode connectivity. Left: performance of all possible linear interpolations between the two models. Right: A visualization of the prediction functions $f ( { \\pmb x } )$ through each linear sweep. Each row corresponds to one of the four possible permutations, and each column corresponds to a value of $\\lambda$ , the linear interpolant. The existence of such cases suggests that linear mode connectivity is an artifact of SGD. " + ], + "image_footnote": [], + "bbox": [ + 187, + 103, + 815, + 233 + ], + "page_idx": 21 + }, + { + "type": "image", + "img_path": "images/d73dcc4fd3766fed56337c441e5c222fb4aefcf416bd1863b89bdb0e3b81d36e.jpg", + "image_caption": [ + "Figure 7: The counterexample classification problem data. " + ], + "image_footnote": [], + "bbox": [ + 349, + 349, + 648, + 520 + ], + "page_idx": 21 + }, + { + "type": "text", + "text": "1. MLP (3 layers, 512 units each): 3 seconds \n2. ResNet50 $1 \\times$ width): 33 seconds \n3. ResNet20 $3 2 \\times$ width): 194 seconds ", + "bbox": [ + 210, + 592, + 509, + 647 + ], + "page_idx": 21 + }, + { + "type": "text", + "text": "In addition, we tested the ability of Algorithm 1 to recover a known, randomly selected permutation. In a handful of experiments we found that Algorithm 1 was able to exactly recover the known, random permutation in just 3-4 of passes over the layers. ", + "bbox": [ + 174, + 659, + 825, + 702 + ], + "page_idx": 21 + }, + { + "type": "text", + "text": "A.6 COUNTEREXAMPLE DETAILS ", + "text_level": 1, + "bbox": [ + 176, + 719, + 419, + 734 + ], + "page_idx": 21 + }, + { + "type": "text", + "text": "Consider a simple 2-dimensional classification task. Our data points are drawn $\\textbf { \\textit { x } } \\sim$ Uniform $( [ - 1 , 1 ] ^ { 2 } )$ and $y = \\mathbf { 1 } _ { x _ { 1 } < 0 }$ and $x _ { 2 } > 0$ . Figure 7 provides a visualization of a sample of such data. ", + "bbox": [ + 174, + 746, + 825, + 789 + ], + "page_idx": 21 + }, + { + "type": "text", + "text": "We utilize an MLP architecture consisting of two hidden layers, with two units each, and ReLU nonlinearities. Consider two weight assignments that both achieve a perfect fit to the data: ", + "bbox": [ + 173, + 795, + 823, + 824 + ], + "page_idx": 21 + }, + { + "type": "equation", + "img_path": "images/0d3efdd8759e2871f999285c7f19bc03db4adae13acc2d21e5eb3e7608e95e1c.jpg", + "text": "$$\n\\begin{array}{c} \\begin{array} { r l } { f _ { A } ( \\pmb { x } ) = [ - 1 } & { - 1 ] \\sigma ( [ \\begin{array} { l l } { - 1 } & { 0 } \\\\ { 0 } & { 1 } \\end{array} ] \\sigma ( [ \\begin{array} { l l } { - 1 } & { 0 } \\\\ { 0 } & { - 1 } \\end{array} ] \\pmb { x } + [ 1 ] ) + [ \\begin{array} { l } { 1 } \\\\ { 0 } \\end{array} ] ) } \\\\ { f _ { B } ( \\pmb { x } ) = [ - 1 } & { - 1 ] \\sigma ( [ 1 } \\\\ { 0 } & { - 1 } \\end{array} ] \\sigma ( [ \\begin{array} { l l } { 1 } & { 0 } \\\\ { 0 } & { 1 } \\end{array} ] \\pmb { x } + [ \\begin{array} { l } { 0 } \\\\ { 1 } \\end{array} ] ) + [ \\begin{array} { l } { 0 } \\\\ { 1 } \\end{array} ] ) . \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 269, + 830, + 727, + 905 + ], + "page_idx": 21 + }, + { + "type": "text", + "text": "We predict a positive label when $f ( { \\pmb x } ) \\geq 0$ and a negative label otherwise. ", + "bbox": [ + 173, + 909, + 661, + 924 + ], + "page_idx": 21 + }, + { + "type": "text", + "text": "Intuitively, these networks are organized such that each layer makes a classification whether $\\mathbf { x } _ { 1 } < 0$ or $x _ { 2 } > 0$ . In model $A$ , the first layer tests whether $x _ { 2 } > 0$ , and the second layer tests whether $x _ { 1 } < 0$ , whereas in model $B$ the order is reversed. With a bit of algebra, it is possible to see that both $f _ { A }$ and $f _ { B }$ achieve perfect performance. However, no possible permutation of units results in linear mode connectivity between $f _ { A }$ and $f _ { B }$ . We visualize all possible permutations in Figure 6. ", + "bbox": [ + 174, + 103, + 825, + 174 + ], + "page_idx": 22 + }, + { + "type": "text", + "text": "We claim that this example, and the underlying trick, are simple enough to be embedded into larger models. For example, this could trivially be extended to ResNets where different subsets of layers could be set to identity functions. ", + "bbox": [ + 176, + 180, + 820, + 222 + ], + "page_idx": 22 + }, + { + "type": "text", + "text": "As discussed in Section 4, the existence of adversarial basins in the loss landscape has interesting consequences for our understanding of loss landscape geometry. In particular, we argue that this implies that common optimization algorithms are conveniently biased towards solutions that admit LMC. However, the precise connection between optimization algorithms and linear mode connectivity remains unclear. ", + "bbox": [ + 174, + 229, + 825, + 299 + ], + "page_idx": 22 + }, + { + "type": "text", + "text": "This counterexample does not constitute a contradiction of the conjecture in Entezari et al. (2021). To be more precise, Conjecture 1 of Entezari et al. (2021) proposes that there exists some subset, $s$ , of parameter space such that every pair of elements in $s$ can be linearly mode connected (after some permutation of units), and that with high probability SGD solutions are contained in $s$ . The example presented in this section does not contradict Entezari et al. (2021)’s conjecture, but instead illustrates that the restriction to SGD solutions is a “load-bearing” element of the conjecture. ", + "bbox": [ + 174, + 306, + 825, + 390 + ], + "page_idx": 22 + }, + { + "type": "text", + "text": "A.7 ON THE FAILURES OF GREEDY UNI-DIRECTIONAL MATCHING ", + "text_level": 1, + "bbox": [ + 176, + 414, + 648, + 429 + ], + "page_idx": 22 + }, + { + "type": "text", + "text": "In contrast to prior work (Pittorino et al., 2022; Singh & Jaggi, 2020; Wang et al., 2020), we eschew greedy uni-directional, single-pass matching between models. Instead we derive a weight matching algorithm from a principled, yet computationally infeasible optimization problem. In contrast to prior work, our method can be viewed as “bi-directional”: it selects unit associations based on weights in all relevant layers, not just in the immediately previous layer. In this section, we describe benefits of our holistic approach, including an example problem showing the failure modes of greedy uni-directional matching. We find that matching across all layers simultaneously allows our weight matching algorithm (Algorithm 1) to exploit units’ relationships with downstream weights in a way that greedy uni-directional matching cannot. ", + "bbox": [ + 174, + 443, + 825, + 569 + ], + "page_idx": 22 + }, + { + "type": "text", + "text": "Concretely, greedy uni-directional matching begins at the first layer and computes a matching, $P _ { 1 }$ , considering only ${ \\bf \\dot { W } } _ { 1 } ^ { ( A ) } , { \\bf W } _ { 1 } ^ { ( B ) }$ . After matching, $P _ { 1 }$ is applied throughout the remainder of the network. Then, we proceed through the layers in order repeating this process. ", + "bbox": [ + 174, + 575, + 825, + 622 + ], + "page_idx": 22 + }, + { + "type": "text", + "text": "We compare our Algorithm 1 to greedy uni-directional matching experimentally in Appendix A.7.1 and present a theoretical counterexample that illustrates the advantages of our method in Appendix A.7.2. ", + "bbox": [ + 176, + 627, + 820, + 670 + ], + "page_idx": 22 + }, + { + "type": "text", + "text": "A.7.1 EXPERIMENTAL COMPARISON ", + "text_level": 1, + "bbox": [ + 176, + 693, + 439, + 707 + ], + "page_idx": 22 + }, + { + "type": "text", + "text": "In order to further evaluate our performance relative to prior work, and Pittorino et al. (2022); Singh & Jaggi (2020) in particular, we explored experimental comparisons with VGG11 models trained on CIFAR-10 and on ResNet50 models trained on ImageNet. ", + "bbox": [ + 176, + 720, + 825, + 762 + ], + "page_idx": 22 + }, + { + "type": "text", + "text": "VGG11 models trained on CIFAR-10. Following an exact reproduction of experiment from Table 1 of Singh & Jaggi (2020), we merged the model weights released along with their paper. We present results in Table 2. We found that our weight matching method outperforms the “wts” method of Singh & Jaggi (2020) in both implementation speed and model performance when reproducing their experiment with their trained model weights. ", + "bbox": [ + 174, + 768, + 823, + 839 + ], + "page_idx": 22 + }, + { + "type": "text", + "text": "ResNet50 models trained on ImageNet. We applied OT-Fusion (“wts”) to the ImageNet experiment that we consider in Section 5.1. We present results in Figure 8. We found the OT-Fusion method resulted in models with $1 . 3 8 \\%$ top-1 accuracy on ImageNet, only marginally improving over na¨ıve averaging. On the other hand, we achieve $5 1 . 0 1 \\%$ . ", + "bbox": [ + 174, + 847, + 823, + 902 + ], + "page_idx": 22 + }, + { + "type": "text", + "text": "BatchNorm statistics were recalculated after interpolation for all methods shown. ", + "bbox": [ + 173, + 909, + 704, + 922 + ], + "page_idx": 22 + }, + { + "type": "table", + "img_path": "images/9cee49a07f8b5d95d48e8da119b6a4798a09bec1fd73a6eb25feea13d56c4c6a.jpg", + "table_caption": [ + "Table 2: VGG11/CIFAR-10 performance relative to Singh & Jaggi (2020). We found that our weight matching method outperforms the “wts” method of Singh & Jaggi (2020) in both implementation speed and model performance when reproducing one of their experiments with their published model weights. Our implementation is $4 . 5 \\times$ faster, and produces a solution with better model performance. " + ], + "table_footnote": [], + "table_body": "
MethodTest accuracy (个)Run-time (↓)
OT-Fusion (Singh & Jaggi, 2020)85.98%2.86s
Weight matching (ours)86.57 %0.64s
", + "bbox": [ + 263, + 101, + 733, + 159 + ], + "page_idx": 23 + }, + { + "type": "image", + "img_path": "images/7d040064349a8c780e2a2137ffec0c52df8ab0f6cb815bd347b925660871158a.jpg", + "image_caption": [ + "Figure 8: ResNet50/ImageNet performance relative to Singh $\\pmb { \\& }$ Jaggi (2020). We found the OT-Fusion method resulted in models with $1 . 3 8 \\%$ top-1 accuracy on ImageNet, only marginally improving over na¨ıve averaging. On the other hand, we achieve $5 1 . 0 1 \\%$ . " + ], + "image_footnote": [], + "bbox": [ + 214, + 262, + 781, + 417 + ], + "page_idx": 23 + }, + { + "type": "text", + "text": "Although a number of factors may be responsible for the difference in performance between weight matching and OT-Fusion, we found the number of alignment passes made over the network layers to have a substantial impact. OT-Fusion is inherently limited to a single pass over the layers. On the other hand, we are not limited to any specific number of optimization passes and instead continue until convergence (convergence is guaranteed by Lemma 2). For comparison, if our weight matching algorithm is artificially handicapped to a single pass over the layers, we achieve a similarly low $\\sim 7 \\%$ top-1 accuracy. ", + "bbox": [ + 173, + 515, + 825, + 613 + ], + "page_idx": 23 + }, + { + "type": "text", + "text": "A.7.2 AN EXAMPLE FAILURE CASE ", + "text_level": 1, + "bbox": [ + 176, + 627, + 436, + 642 + ], + "page_idx": 23 + }, + { + "type": "text", + "text": "Consider two networks, $A$ and $B$ , with the objective that they capture the identity function $f ( x ) = x$ ", + "bbox": [ + 176, + 651, + 823, + 667 + ], + "page_idx": 23 + }, + { + "type": "equation", + "img_path": "images/73c65bb1c8716518b1d7831eb5e8a63625dfc111673187365611760a4feed994.jpg", + "text": "$$\n\\begin{array} { r l } { f _ { \\Theta _ { A } } ( x ) = [ 1 } & { 0 ] \\left[ \\begin{array} { l l } { 1 } & { 0 } \\\\ { 0 } & { \\epsilon } \\end{array} \\right] \\left[ \\begin{array} { l } { 1 } \\\\ { 1 + \\epsilon } \\end{array} \\right] x } \\\\ { f _ { \\Theta _ { B } } ( x ) = [ 0 } & { 1 ] \\left[ \\begin{array} { l l } { 0 } & { 0 } \\\\ { 0 } & { 1 } \\end{array} \\right] \\left[ \\begin{array} { l } { 1 } \\\\ { 1 + \\epsilon } \\end{array} \\right] x } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 379, + 672, + 617, + 746 + ], + "page_idx": 23 + }, + { + "type": "text", + "text": "where $\\epsilon > 0$ is some negligible constant. It can be seen that these reduce to $f _ { \\Theta _ { A } } ( x ) = x$ and $f _ { \\Theta _ { B } } ( x ) = ( 1 + \\epsilon ) x$ . ", + "bbox": [ + 174, + 748, + 826, + 779 + ], + "page_idx": 23 + }, + { + "type": "text", + "text": "When aligning these models there are two possible opportunities for permutation, $\\pi = \\{ P _ { 1 } , P _ { 2 } \\}$ The permuted model $B$ then has the form ", + "bbox": [ + 174, + 784, + 821, + 813 + ], + "page_idx": 23 + }, + { + "type": "equation", + "img_path": "images/754c87fa936b6fdeac5999f11a61ef909cd13a77689fe0971192f074d860ada1.jpg", + "text": "$$\nf _ { \\pi ( \\Theta _ { B } ) } ( x ) = \\left( \\left[ 0 \\quad 1 \\right] P _ { 2 } ^ { \\top } \\right) \\left( P _ { 2 } \\left[ 0 \\quad 1 \\right] P _ { 1 } ^ { \\top } \\right) \\left( P _ { 1 } \\left[ 1 + \\epsilon \\right] \\right) x\n$$", + "text_format": "latex", + "bbox": [ + 289, + 818, + 709, + 854 + ], + "page_idx": 23 + }, + { + "type": "text", + "text": "Now, aligning with greedy uni-directional matching will result in the alignment $\\pi _ { g u d } = \\{ P _ { 1 } =$ $I , P _ { 2 } = I \\}$ . On the other hand, our weight matching method (Algorithm 1) results in $\\pi _ { w m } =$ $\\left\\{ P _ { 1 } = { \\left[ \\begin{array} { l l } { 0 } & { 1 } \\\\ { 1 } & { 0 } \\end{array} \\right] } , P _ { 2 } = { \\left[ \\begin{array} { l l } { 0 } & { 1 } \\\\ { 1 } & { 0 } \\end{array} \\right] } \\right\\}$ , regardless of the algorithm’s execution order. ", + "bbox": [ + 173, + 866, + 825, + 929 + ], + "page_idx": 23 + }, + { + "type": "image", + "img_path": "images/eb18a76b62f58b2fd38376d589eefbb880fcd31b6f90836ee8b0a234fbc2f71a.jpg", + "image_caption": [ + "Figure 9: Top-1 accuracy results for the MNIST and CIFAR-10 models of Figure 2. " + ], + "image_footnote": [], + "bbox": [ + 209, + 102, + 789, + 210 + ], + "page_idx": 24 + }, + { + "type": "image", + "img_path": "images/b0d0655148ed913cf96a1339fad177b2df353b8cf4ccff993d21e89acadb5e92.jpg", + "image_caption": [ + "Figure 10: Accuracy results for the CIFAR-100 split data experiment. " + ], + "image_footnote": [], + "bbox": [ + 214, + 271, + 784, + 428 + ], + "page_idx": 24 + }, + { + "type": "text", + "text": "Interpolating these matched models at $\\lambda = 0 . 5$ , we have ", + "bbox": [ + 173, + 496, + 544, + 511 + ], + "page_idx": 24 + }, + { + "type": "equation", + "img_path": "images/279bb7be2a15d42367353f8801d91fc42dc9865a65b01564e6ec49f80c605fd4.jpg", + "text": "$$\n\\begin{array} { r l r l } & { f _ { \\frac { 1 } { 2 } ( \\Theta _ { A } + \\pi _ { g u d } ( \\Theta _ { B } ) ) } ( x ) = [ 0 . 5 } & { 0 . 5 ] [ 0 . 5 \\qquad 0 } \\\\ & { f _ { \\frac { 1 } { 2 } ( \\Theta _ { A } + \\pi _ { w m } ( \\Theta _ { B } ) ) } ( x ) = [ 1 } & { 0 ] [ 0 \\qquad \\epsilon / 2 ] [ 1 + \\epsilon / 2 ] x \\qquad } & { = ( 0 . 5 + O ( \\epsilon ) ) x } \\\\ & { f _ { \\frac { 1 } { 2 } ( \\Theta _ { A } + \\pi _ { w m } ( \\Theta _ { B } ) ) } ( x ) = [ 1 } & { 0 ] [ 0 \\qquad \\epsilon / 2 ] [ 1 + \\epsilon / 2 ] x } & & { = ( 1 + \\epsilon / 2 ) x } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 212, + 517, + 785, + 590 + ], + "page_idx": 24 + }, + { + "type": "text", + "text": "Here we can see that the greedy uni-directional matching (Equation (9)) results in a merged model that fails to represent the input, identity-function models. On the other hand, our weight matching algorithm (Algorithm 1, Equation (10)) produces a merged model that accurately reflects both of the input models, and even improves performance over the $B$ model. 5 ", + "bbox": [ + 173, + 594, + 825, + 651 + ], + "page_idx": 24 + }, + { + "type": "text", + "text": "A.8 AUXILIARY PLOTS ", + "bbox": [ + 176, + 667, + 349, + 683 + ], + "page_idx": 24 + }, + { + "type": "text", + "text": "A.9 STRAIGHT-THROUGH ESTIMATOR DETAILS", + "text_level": 1, + "bbox": [ + 174, + 694, + 517, + 708 + ], + "page_idx": 24 + }, + { + "type": "text", + "text": "See Algorithm 2 for a complete description of the straight-through estimator algorithm. ", + "bbox": [ + 176, + 719, + 743, + 736 + ], + "page_idx": 24 + }, + { + "type": "text", + "text": "A.10 MERGING MANY MODELS ", + "bbox": [ + 176, + 751, + 413, + 767 + ], + "page_idx": 24 + }, + { + "type": "text", + "text": "We propose Algorithm 3 to merge the weights of more than two models at a time. ", + "bbox": [ + 173, + 777, + 709, + 792 + ], + "page_idx": 24 + }, + { + "type": "text", + "text": "Following an argument similar to Lemma 2, it can be seen that Algorithm 3 terminates. ", + "bbox": [ + 173, + 799, + 743, + 814 + ], + "page_idx": 24 + }, + { + "type": "text", + "text": "In our limited testing, we found that this algorithm converges quickly to solutions that extrapolate better than individual models and results in a merged model with better probability estimate calibra", + "bbox": [ + 176, + 820, + 826, + 849 + ], + "page_idx": 24 + }, + { + "type": "image", + "img_path": "images/f6f448ec9e78fac0fa4db3b8310a5ad096bbd940ab4553c98ec331efdb11f1d9.jpg", + "image_caption": [ + "Figure 11: Merging CIFAR-100 split data models results in superior probability calibration. Although our merged model is not competitive in terms of top-1 accuracy in the CIFAR-100 split data experiment, we find that it has far better calibrated probability estimates than either of the input models. In addition, we achieve calibration results on par with model ensembling while requiring $2 \\times$ less memory and compute. " + ], + "image_footnote": [], + "bbox": [ + 199, + 145, + 785, + 345 + ], + "page_idx": 25 + }, + { + "type": "image", + "img_path": "images/eb946f43847ac0e8805093a9388e1a3823856bda647d54fba047b6b50c06be3d.jpg", + "image_caption": [ + "Figure 12: Accuracy results for merged ResNet50 $1 \\times$ width) models on ImageNet. " + ], + "image_footnote": [], + "bbox": [ + 214, + 486, + 782, + 642 + ], + "page_idx": 25 + }, + { + "type": "text", + "text": "Algorithm 2: Straight-through estimator training ", + "text_level": 1, + "bbox": [ + 174, + 728, + 498, + 742 + ], + "page_idx": 25 + }, + { + "type": "text", + "text": "Given: Model weights $\\Theta _ { A }$ , $\\Theta _ { B }$ , and a learning rate $\\eta$ ", + "bbox": [ + 174, + 748, + 527, + 763 + ], + "page_idx": 25 + }, + { + "type": "text", + "text": "Result: A permutation $\\pi$ of $\\Theta _ { B }$ such that $\\begin{array} { r } { \\mathcal { L } ( \\frac { 1 } { 2 } ( \\Theta _ { A } + \\pi ( \\Theta _ { B } ) ) ) } \\end{array}$ is approximately minimized. ", + "bbox": [ + 171, + 765, + 776, + 784 + ], + "page_idx": 25 + }, + { + "type": "text", + "text": "Initialize: $\\tilde { \\Theta } _ { B } \\Theta _ { A }$ ", + "bbox": [ + 174, + 792, + 320, + 809 + ], + "page_idx": 25 + }, + { + "type": "text", + "text": "repeat ", + "text_level": 1, + "bbox": [ + 173, + 809, + 220, + 821 + ], + "page_idx": 25 + }, + { + "type": "text", + "text": "$\\pi ( \\Theta _ { B } ) \\mathrm { p r o j } ( \\tilde { \\Theta } _ { B } )$ using Algorithm 1. \nEvaluate the loss of the midpoint, $\\begin{array} { r } { \\mathcal { L } ( \\frac { 1 } { 2 } ( \\Theta _ { A } + \\pi ( \\Theta _ { B } ) ) ) } \\end{array}$ . \nEvaluate the gradient, $\\nabla \\mathcal { L }$ , using $\\tilde { \\Theta } _ { B }$ in place of $\\pi ( \\Theta _ { B } )$ in the backwards pass. \nUpdate parameters, $\\tilde { \\Theta } _ { B } \\gets \\tilde { \\Theta } _ { B } - \\eta \\nabla \\mathcal { L }$ . ", + "bbox": [ + 196, + 824, + 718, + 886 + ], + "page_idx": 25 + }, + { + "type": "text", + "text": "until convergence ", + "bbox": [ + 174, + 886, + 294, + 898 + ], + "page_idx": 25 + }, + { + "type": "text", + "text": "Algorithm 3: MERGEMANY ", + "text_level": 1, + "bbox": [ + 176, + 107, + 367, + 122 + ], + "page_idx": 26 + }, + { + "type": "text", + "text": "Given: Model weights $\\Theta _ { 1 } , \\dots , \\Theta _ { N }$ ", + "bbox": [ + 174, + 127, + 411, + 142 + ], + "page_idx": 26 + }, + { + "type": "text", + "text": "Result: A merged set of parameters $\\tilde { \\Theta }$ . ", + "bbox": [ + 174, + 147, + 431, + 161 + ], + "page_idx": 26 + }, + { + "type": "text", + "text": "repeat ", + "text_level": 1, + "bbox": [ + 173, + 176, + 220, + 189 + ], + "page_idx": 26 + }, + { + "type": "equation", + "img_path": "images/1da5344c249cac0a029eeb1883673b76997decbc2161890cff9970cc75c1bc53.jpg", + "text": "$$\n\\Theta _ { i } \\gets \\pi ( \\Theta _ { i } )\n$$", + "text_format": "latex", + "bbox": [ + 223, + 242, + 310, + 258 + ], + "page_idx": 26 + }, + { + "type": "table", + "img_path": "images/1b9e3d40df93f66fcd575945141d4a664e94dfc03f8137d9d980c5fb80da732c.jpg", + "table_caption": [ + "Table 3: Merging multiple models decreases test loss by $43 \\%$ . We train five separate MLPs on MNIST. Using Algorithm 3 we merge all these models together simultaneously. This produces a model that appears to have better out-of-distribution performance than any of the input models, with superior test loss performance. We are excited by potential applications of this methodology in federated learning and ensembling, esp. along the lines of “model soups” (Wortsman et al., 2022a). " + ], + "table_footnote": [], + "table_body": "
Train LossTrain Acc.Test LossTest Acc.
Seed 10.00001.00000.11530.9856
Seed 20.00001.00000.15310.9854
Seed 30.00001.00000.12290.9855
Seed 40.00001.00000.11080.9865
Seed 50.00001.00000.14430.9871
MERGEMANY0.01410.99520.07270.9831
", + "bbox": [ + 267, + 330, + 730, + 431 + ], + "page_idx": 26 + }, + { + "type": "text", + "text": "tion than any of the input models. For example, we present the results of this algorithm on MLPs trained on MNIST in Table A.10. ", + "bbox": [ + 174, + 549, + 821, + 577 + ], + "page_idx": 26 + }, + { + "type": "text", + "text": "In addition, we found that merging multiple models helps to calibrate the resulting model predictions. We present this effect in Figure 13. ", + "bbox": [ + 173, + 583, + 823, + 613 + ], + "page_idx": 26 + }, + { + "type": "text", + "text": "A.11 FAILED IDEA: A METHOD FOR STEEPEST DESCENT ", + "text_level": 1, + "bbox": [ + 173, + 633, + 584, + 648 + ], + "page_idx": 26 + }, + { + "type": "text", + "text": "Imagine standing in weight space at $\\Theta _ { A }$ and trying to decide in which immediate direction to move in order to approach a $\\Theta _ { B }$ -equivalent point. There are many, many possible permutations of $\\Theta _ { B } -$ call them $\\pi ^ { ( \\bar { 1 } ) } ( \\Theta _ { B } ) , \\pi ^ { ( 2 ) } ( \\Theta _ { B } ) , \\dots - \\mathrm { t }$ o aim for in the distance. Assuming that the loss landscape is in fact convex modulo these permutation symmetries, a natural choice would be to pick the $\\pi ^ { ( i ) } ( \\Theta _ { B } )$ that corresponds to the direction of steepest descent starting from $\\Theta _ { A }$ since we expect $\\pi ^ { ( i ) } ( \\Theta _ { B } )$ to lie in the same basin as $\\Theta _ { A }$ . In other words, ", + "bbox": [ + 173, + 661, + 825, + 751 + ], + "page_idx": 26 + }, + { + "type": "equation", + "img_path": "images/6a700b54fda0f4ec3152f09e19774c6c7246554269dff5becb43333914e8e06a.jpg", + "text": "$$\n\\begin{array} { r l } { \\operatorname* { m i n } _ { \\pi } \\left. \\frac { d \\mathcal { L } ( \\Theta _ { A } + \\lambda ( \\pi ( \\Theta _ { B } ) - \\Theta _ { A } ) ) } { d \\lambda } \\right| _ { \\lambda = 0 } } & { = \\underset { \\pi } { \\operatorname* { m i n } } ~ \\nabla \\mathcal { L } ( \\Theta _ { A } ) ^ { \\top } ( \\pi ( \\Theta _ { B } ) - \\Theta _ { A } ) } \\\\ & { = - \\nabla \\mathcal { L } ( \\Theta _ { A } ) ^ { \\top } \\Theta _ { A } + \\underset { \\pi } { \\operatorname* { m i n } } ~ \\nabla \\mathcal { L } ( \\Theta _ { A } ) ^ { \\top } \\pi ( \\Theta _ { B } ) } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 192, + 758, + 777, + 821 + ], + "page_idx": 26 + }, + { + "type": "text", + "text": "Now, we are tenuously in a favorable situation: $\\nabla { \\mathcal { L } } ( \\Theta _ { A } )$ is straightforward to compute, and picking the best $\\pi$ reduces to a matching problem. In particular it is a SOBLAP matching problem of the same form as in Section 3.2. In addition, there is a fast, exact solution for the single intermediate layer case $\\left( L = 2 \\right.$ ). ", + "bbox": [ + 176, + 832, + 823, + 888 + ], + "page_idx": 26 + }, + { + "type": "text", + "text": "In practice, we found that this method can certainly find directions of steepest descent, but that they are accompanied by high barriers in between the initial dip and $\\pi ( \\Theta _ { B } )$ . ", + "bbox": [ + 174, + 895, + 823, + 924 + ], + "page_idx": 26 + }, + { + "type": "image", + "img_path": "images/20266c9cfdd50d6e3474dcffd5e8e32c8ed48138717b4cb24febf27fae82893d.jpg", + "image_caption": [ + "Figure 13: Merging multiple models results in superior calibration. Here we show the results of running Algorithm 3 on 32 MLP models trained on MNIST, with each model given access to a random $50 \\%$ of the training dataset. The resulting merged model demonstrates substantively improved calibration of probability estimates on both the training and test datasets. MergeMany calibration results are competitive with model ensembling, despite requiring $3 2 \\times$ less memory and compute. " + ], + "image_footnote": [], + "bbox": [ + 215, + 128, + 769, + 320 + ], + "page_idx": 27 + }, + { + "type": "text", + "text": "A.12 PROOF OF LEMMA 1 ", + "text_level": 1, + "bbox": [ + 176, + 441, + 367, + 457 + ], + "page_idx": 27 + }, + { + "type": "text", + "text": "To lighten notation we use $\\langle \\cdot , \\cdot \\rangle = \\langle \\cdot , \\cdot \\rangle _ { F }$ in this section. ", + "bbox": [ + 173, + 468, + 542, + 484 + ], + "page_idx": 27 + }, + { + "type": "text", + "text": "Lemma. Given $\\pmb { A } , \\pmb { B } \\in \\mathbb { R } ^ { d \\times d }$ , ", + "bbox": [ + 174, + 486, + 380, + 501 + ], + "page_idx": 27 + }, + { + "type": "equation", + "img_path": "images/db77495cad43bd50a5f0cc012f916a36d548bff38b26a5dcd3361de637e3206a.jpg", + "text": "$$\n\\operatorname* { m i n } _ { P , Q p e r m . m a t r i c e s } \\left. P A Q ^ { \\top } , B \\right.\n$$", + "text_format": "latex", + "bbox": [ + 400, + 502, + 598, + 529 + ], + "page_idx": 27 + }, + { + "type": "text", + "text": "is strongly NP-hard and has no PTAS. ", + "bbox": [ + 174, + 532, + 423, + 547 + ], + "page_idx": 27 + }, + { + "type": "text", + "text": "Proof. We proceed by reduction from the quadratic assignment problem (QAP) (Koopmans & Beckmann, 1957; Cela, 2013). Consider a QAP, ", + "bbox": [ + 174, + 561, + 823, + 590 + ], + "page_idx": 27 + }, + { + "type": "equation", + "img_path": "images/3db3d5d4bb5623d9a4925b9f8df09662bab2df2017ed236c63b04a2c662cf49e.jpg", + "text": "$$\n\\operatorname* { m i n } _ { P \\mathrm { \\ p e r m . \\ m a t r i x } } \\left. P C P ^ { \\top } , D \\right.\n$$", + "text_format": "latex", + "bbox": [ + 411, + 593, + 584, + 618 + ], + "page_idx": 27 + }, + { + "type": "text", + "text": "for $C , D \\in \\mathbb { R } ^ { d \\times d }$ . ", + "bbox": [ + 173, + 623, + 297, + 640 + ], + "page_idx": 27 + }, + { + "type": "text", + "text": "Now, pick $A = C + \\lambda I$ , $B = D - \\lambda I$ . The we have, ", + "bbox": [ + 173, + 645, + 534, + 661 + ], + "page_idx": 27 + }, + { + "type": "equation", + "img_path": "images/cb918f610812778c50d9967d9fd7673225e7a9068a47accc9f3a3ea30d121dd7.jpg", + "text": "$$\n\\begin{array} { r l } & { \\underset { \\boldsymbol { \\sigma } , \\boldsymbol { Q } } { \\mathrm { n i n } } \\left. P ( \\boldsymbol { C } + \\lambda \\boldsymbol { I } ) \\boldsymbol { Q } ^ { \\top } , \\boldsymbol { D } - \\lambda \\boldsymbol { I } \\right. = \\left. P C \\boldsymbol { Q } ^ { \\top } + \\lambda P \\boldsymbol { Q } ^ { \\top } , \\boldsymbol { D } - \\lambda \\boldsymbol { I } \\right. } \\\\ & { \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad ( 1 3 ) } \\\\ & { \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad = \\left. P C \\boldsymbol { Q } ^ { \\top } , \\boldsymbol { D } \\right. - \\lambda \\langle P C \\boldsymbol { Q } ^ { \\top } , \\boldsymbol { I } \\rangle + \\lambda \\langle P \\boldsymbol { Q } ^ { \\top } , \\boldsymbol { D } \\rangle - \\lambda ^ { 2 } \\langle P \\boldsymbol { Q } ^ { \\top } , \\boldsymbol { I } \\rangle } \\\\ & { \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad ( 1 4 ) } \\\\ & { \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad = \\left. P C \\boldsymbol { Q } ^ { \\top } , \\boldsymbol { D } \\right. - \\lambda \\langle P ^ { \\top } \\boldsymbol { Q } , \\boldsymbol { C } \\rangle + \\lambda \\langle P \\boldsymbol { Q } ^ { \\top } , \\boldsymbol { D } \\rangle - \\lambda ^ { 2 } \\mathrm { t r } ( P \\boldsymbol { Q } ^ { \\top } ) _ { - \\lambda } \\mathrm { t r } ( P \\boldsymbol { Q } ^ { \\top } ) _ { - \\lambda } \\mathrm { t r } ( P \\boldsymbol { Q } ^ { \\top } ) _ { - \\lambda } , } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 181, + 664, + 825, + 747 + ], + "page_idx": 27 + }, + { + "type": "text", + "text": "For sufficiently large $\\lambda$ , the $\\operatorname { t r } ( P Q ^ { \\top } )$ term will dominate. Letting $\\alpha \\quad =$ max $\\begin{array} { r } { ( \\operatorname* { m a x } _ { i , j } | C _ { i , j } | , \\operatorname* { m a x } _ { i , j } | D _ { i , j } | ) } \\end{array}$ , we can bound the other terms, ", + "bbox": [ + 171, + 763, + 820, + 794 + ], + "page_idx": 27 + }, + { + "type": "equation", + "img_path": "images/6dae88405cba2dc837701db52817cdc0f70cfa11a9455c2d642e9db06ef95f07.jpg", + "text": "$$\n\\begin{array} { r l r } { - d ^ { 2 } \\alpha ^ { 2 } \\le } & { \\langle P C Q ^ { \\top } , D \\rangle \\le d ^ { 2 } \\alpha ^ { 2 } } & \\\\ { - \\lambda d \\alpha \\le - \\lambda \\langle P ^ { \\top } Q , C \\rangle } & { \\le \\lambda d \\alpha } & \\\\ { - \\lambda d \\alpha \\le } & { \\lambda \\langle P Q ^ { \\top } , D \\rangle } & { \\le \\lambda d \\alpha } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 382, + 796, + 614, + 859 + ], + "page_idx": 27 + }, + { + "type": "text", + "text": "Now there are two classes of solutions: those where $P = Q$ and those where $P \\neq Q$ . We seek to make the best (lowest) possible $P \\neq Q$ solution to have worse (higher) objective value than the worst (highest) $P = Q$ solution. When $P = Q$ , the highest possible objective value is ", + "bbox": [ + 173, + 862, + 825, + 905 + ], + "page_idx": 27 + }, + { + "type": "equation", + "img_path": "images/fa82c612e567daeb96af8b60003f67d092ef4b0a69c29b2ad42dc08d3c171fcc.jpg", + "text": "$$\nd ^ { 2 } \\alpha ^ { 2 } + \\lambda d \\alpha + \\lambda d \\alpha - \\lambda ^ { 2 } d\n$$", + "text_format": "latex", + "bbox": [ + 408, + 906, + 589, + 924 + ], + "page_idx": 27 + }, + { + "type": "text", + "text": "and similarly, the lowest possible objective value when $P \\neq Q$ is ", + "bbox": [ + 173, + 103, + 604, + 118 + ], + "page_idx": 28 + }, + { + "type": "equation", + "img_path": "images/4c87069b1a24d4655252b59984b51abbdbc32504375c6863148234ee7efefc88.jpg", + "text": "$$\n- d ^ { 2 } \\alpha ^ { 2 } - \\lambda d \\alpha - \\lambda d \\alpha - \\lambda ^ { 2 } d + \\lambda ^ { 2 }\n$$", + "text_format": "latex", + "bbox": [ + 380, + 123, + 612, + 141 + ], + "page_idx": 28 + }, + { + "type": "text", + "text": "where the final term is due to the fact that at least one entry of $P Q ^ { \\top }$ must be 0. With some algebra, it can be seen that $\\lambda > 5 d \\alpha$ is sufficient to guarantee that all $P = Q$ solutions are superior to all $P \\neq Q$ solutions. ", + "bbox": [ + 173, + 148, + 826, + 191 + ], + "page_idx": 28 + }, + { + "type": "text", + "text": "Now when $P = Q$ , all frivolous terms reduce to constants and we are left with the QAP objective: ", + "bbox": [ + 173, + 198, + 818, + 213 + ], + "page_idx": 28 + }, + { + "type": "equation", + "img_path": "images/4741fb4e5cb8698a8c61ce7081906598c57d379814bc82130b681a434ae25eab.jpg", + "text": "$$\n\\begin{array} { r l r } & { } & { \\underset { \\pmb { P } } { \\mathrm { m i n } } \\ \\langle \\pmb { P } \\pmb { C } \\pmb { P } ^ { \\top } , \\pmb { D } \\rangle - \\lambda \\langle \\pmb { P } ^ { \\top } \\pmb { P } , \\pmb { C } \\rangle + \\lambda \\langle \\pmb { P } \\pmb { P } ^ { \\top } , \\pmb { D } \\rangle - \\lambda ^ { 2 } \\mathrm { t r } ( \\pmb { P } \\pmb { P } ^ { \\top } ) } \\\\ & { } & \\\\ & { } & { = - \\lambda \\mathrm { t r } ( \\pmb { C } ) + \\lambda \\mathrm { t r } ( \\pmb { D } ) - \\lambda ^ { 2 } d + \\underset { \\pmb { P } } { \\mathrm { m i n } } \\ \\langle \\pmb { P } \\pmb { C } \\pmb { P } ^ { \\top } , \\pmb { D } \\rangle } \\end{array}\n$$", + "text_format": "latex", + "bbox": [ + 277, + 217, + 720, + 270 + ], + "page_idx": 28 + }, + { + "type": "text", + "text": "completing the reduction. QAP is known to be strongly NP-hard (Koopmans & Beckmann, 1957; Sahni & Gonzalez, 1976) and MaxQAP is known to not admit any PTAS (Makarychev et al., 2014), thus completing the proof. □ ", + "bbox": [ + 176, + 275, + 825, + 319 + ], + "page_idx": 28 + }, + { + "type": "text", + "text": "A.13 PROOF OF LEMMA 2 ", + "text_level": 1, + "bbox": [ + 176, + 334, + 369, + 349 + ], + "page_idx": 28 + }, + { + "type": "text", + "text": "Lemma. Algorithm 1 terminates. ", + "bbox": [ + 174, + 361, + 397, + 376 + ], + "page_idx": 28 + }, + { + "type": "text", + "text": "Proof. We proceed by contradiction. ", + "bbox": [ + 174, + 391, + 416, + 406 + ], + "page_idx": 28 + }, + { + "type": "text", + "text": "Consider a graph with each possible permutation $\\pi _ { i } = \\left\\{ P _ { 1 } , \\ldots , P _ { L - 1 } \\right\\}$ as a vertex and directed edges $\\pi _ { i } \\pi _ { j }$ if $\\pi _ { j }$ can be reached from $\\pi _ { i }$ with a single $P _ { \\ell }$ update, as in Algorithm 1. (Ignore those updates that result in no change to $P _ { \\ell }$ in order to avoid $\\pi _ { i } \\pi _ { i }$ cycles.) Let $\\rho ( \\pi ) = \\operatorname { v e c } ( \\Theta _ { A } )$ · $\\mathrm { v e c } ( \\pi ( { \\bar { \\Theta } } _ { B } ) )$ denote the utility of a particular $\\pi$ . Note that $\\pi _ { i } \\pi _ { j }$ implies $\\rho ( \\pi _ { i } ) < \\rho ( \\pi _ { j } )$ . There exist finitely many possible permutations $\\pi _ { i }$ , meaning that a failure to terminate must involve a cycle in the graph $\\pi _ { 1 } \\to \\cdot \\cdot \\cdot \\to \\pi _ { n } \\to \\pi _ { 1 }$ . However $\\rho$ forms a total order on the vertices and therefore we have a contradiction. □ ", + "bbox": [ + 173, + 411, + 825, + 510 + ], + "page_idx": 28 + } +] \ No newline at end of file diff --git a/parse/dev/CQsmMYmlP5T/CQsmMYmlP5T_middle.json b/parse/dev/CQsmMYmlP5T/CQsmMYmlP5T_middle.json new file mode 100644 index 0000000000000000000000000000000000000000..a5cb21d401d8cce4f1b9d5fb514e91b15e72f535 --- /dev/null +++ b/parse/dev/CQsmMYmlP5T/CQsmMYmlP5T_middle.json @@ -0,0 +1,75907 @@ +{ + "pdf_info": [ + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 107, + 78, + 502, + 116 + ], + "lines": [ + { + "bbox": [ + 106, + 78, + 504, + 97 + ], + "spans": [ + { + "bbox": [ + 106, + 78, + 504, + 97 + ], + "score": 1.0, + "content": "GIT RE-BASIN: MERGING MODELS MODULO PERMU-", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 99, + 266, + 118 + ], + "spans": [ + { + "bbox": [ + 106, + 99, + 266, + 118 + ], + "score": 1.0, + "content": "TATION SYMMETRIES", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "text", + "bbox": [ + 112, + 135, + 379, + 147 + ], + "lines": [ + { + "bbox": [ + 112, + 135, + 380, + 149 + ], + "spans": [ + { + "bbox": [ + 112, + 135, + 380, + 149 + ], + "score": 1.0, + "content": "Samuel K. 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Finally, we discuss shortcomings of the linear mode connectivity hypothesis,", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 141, + 407, + 360, + 421 + ], + "spans": [ + { + "bbox": [ + 141, + 407, + 360, + 421 + ], + "score": 1.0, + "content": "including a counterexample to the single basin theory.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 15 + }, + { + "type": "title", + "bbox": [ + 108, + 438, + 206, + 451 + ], + "lines": [ + { + "bbox": [ + 105, + 437, + 208, + 454 + ], + "spans": [ + { + "bbox": [ + 105, + 437, + 208, + 454 + ], + "score": 1.0, + "content": "1 INTRODUCTION", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 24 + }, + { + "type": "text", + "bbox": [ + 107, + 462, + 504, + 485 + ], + "lines": [ + { + "bbox": [ + 106, + 461, + 505, + 475 + ], + "spans": [ + { + "bbox": [ + 106, + 461, + 505, + 475 + ], + "score": 1.0, + "content": "We investigate the unreasonable effectiveness of stochastic gradient descent (SGD) algorithms on", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 474, + 458, + 487 + ], + "spans": [ + { + "bbox": [ + 106, + 474, + 458, + 487 + ], + "score": 1.0, + "content": "the high-dimensional non-convex optimization problems of deep learning. 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Why does SGD thrive in optimizing high-dimensional non-convex deep learning loss land-", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 135, + 505, + 505, + 517 + ], + "spans": [ + { + "bbox": [ + 135, + 505, + 505, + 517 + ], + "score": 1.0, + "content": "scapes despite being noticeably less robust in other non-convex optimization settings, like", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 134, + 515, + 505, + 529 + ], + "spans": [ + { + "bbox": [ + 134, + 515, + 505, + 529 + ], + "score": 1.0, + "content": "policy learning (Ainsworth et al., 2021), trajectory optimization (Kelly, 2017), and recom-", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 135, + 527, + 284, + 539 + ], + "spans": [ + { + "bbox": [ + 135, + 527, + 284, + 539 + ], + "score": 1.0, + "content": "mender systems (Kang et al., 2016)?", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 123, + 540, + 505, + 552 + ], + "spans": [ + { + "bbox": [ + 123, + 542, + 132, + 551 + ], + "score": 1.0, + "content": "2.", + "type": "text" + }, + { + "bbox": [ + 133, + 540, + 505, + 552 + ], + "score": 1.0, + "content": "What are all the local minima? 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How can two independently trained models with different random initializations and data", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 135, + 588, + 505, + 600 + ], + "spans": [ + { + "bbox": [ + 135, + 588, + 505, + 600 + ], + "score": 1.0, + "content": "batch orders inevitably achieve nearly identical performance? 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Hecht-", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 640, + 505, + 654 + ], + "spans": [ + { + "bbox": [ + 105, + 640, + 505, + 654 + ], + "score": 1.0, + "content": "Nielsen (1990) noted the permutation symmetries of hidden units in neural networks; briefly, one can", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 651, + 505, + 666 + ], + "spans": [ + { + "bbox": [ + 105, + 651, + 505, + 666 + ], + "score": 1.0, + "content": "swap any two units of a hidden layer in a network and – assuming weights are adjusted accordingly", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 663, + 505, + 675 + ], + "spans": [ + { + "bbox": [ + 105, + 663, + 505, + 675 + ], + "score": 1.0, + "content": "– network functionality will not change. Recently, Benton et al. (2021) demonstrated that SGD", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 674, + 505, + 686 + ], + "spans": [ + { + "bbox": [ + 105, + 674, + 505, + 686 + ], + "score": 1.0, + "content": "solutions form a connected volume of low loss and Entezari et al. (2021) conjectured that this volume", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 686, + 280, + 697 + ], + "spans": [ + { + "bbox": [ + 105, + 686, + 280, + 697 + ], + "score": 1.0, + "content": "is convex modulo permutation symmetries.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 40 + }, + { + "type": "text", + "bbox": [ + 108, + 699, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "score": 1.0, + "content": "Conjecture 1 (Permutation invariance, informal (Entezari et al., 2021)). Most SGD solutions belong", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 709, + 506, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 506, + 722 + ], + "score": 1.0, + "content": "to a set whose elements can be permuted so that no barrier (as in Definition 2.2) exists on the linear", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 720, + 311, + 734 + ], + "spans": [ + { + "bbox": [ + 106, + 720, + 311, + 734 + ], + "score": 1.0, + "content": "interpolation between any two permuted elements.", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 45 + } + ], + "page_idx": 0, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 25, + 293, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 25, + 293, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2023", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 303, + 751, + 308, + 760 + ], + "lines": [ + { + "bbox": [ + 302, + 751, + 308, + 761 + ], + "spans": [ + { + "bbox": [ + 302, + 751, + 308, + 761 + ], + "score": 1.0, + "content": "1", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 107, + 78, + 502, + 116 + ], + "lines": [ + { + "bbox": [ + 106, + 78, + 504, + 97 + ], + "spans": [ + { + "bbox": [ + 106, + 78, + 504, + 97 + ], + "score": 1.0, + "content": "GIT RE-BASIN: MERGING MODELS MODULO PERMU-", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 99, + 266, + 118 + ], + "spans": [ + { + "bbox": [ + 106, + 99, + 266, + 118 + ], + "score": 1.0, + "content": "TATION SYMMETRIES", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "text", + "bbox": [ + 112, + 135, + 379, + 147 + ], + "lines": [ + { + "bbox": [ + 112, + 135, + 380, + 149 + ], + "spans": [ + { + "bbox": [ + 112, + 135, + 380, + 149 + ], + "score": 1.0, + "content": "Samuel K. Ainsworth, Jonathan Hayase, Siddhartha Srinivasa", + "type": "text" + } + ], + "index": 2 + } + ], + "index": 2, + "bbox_fs": [ + 112, + 135, + 380, + 149 + ] + }, + { + "type": "text", + "bbox": [ + 113, + 147, + 362, + 180 + ], + "lines": [ + { + "bbox": [ + 111, + 144, + 354, + 160 + ], + "spans": [ + { + "bbox": [ + 111, + 144, + 354, + 160 + ], + "score": 1.0, + "content": "Paul G. Allen School of Computer Science and Engineering", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 112, + 156, + 218, + 169 + ], + "spans": [ + { + "bbox": [ + 112, + 156, + 218, + 169 + ], + "score": 1.0, + "content": "University of Washington", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 112, + 168, + 363, + 181 + ], + "spans": [ + { + "bbox": [ + 112, + 168, + 363, + 181 + ], + "score": 1.0, + "content": "{skainswo,jhayase,siddh}@cs.washington.edu", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4, + "bbox_fs": [ + 111, + 144, + 363, + 181 + ] + }, + { + "type": "title", + "bbox": [ + 278, + 208, + 333, + 220 + ], + "lines": [ + { + "bbox": [ + 276, + 208, + 335, + 221 + ], + "spans": [ + { + "bbox": [ + 276, + 208, + 335, + 221 + ], + "score": 1.0, + "content": "ABSTRACT", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 6 + }, + { + "type": "text", + "bbox": [ + 143, + 232, + 468, + 418 + ], + "lines": [ + { + "bbox": [ + 142, + 233, + 469, + 245 + ], + "spans": [ + { + "bbox": [ + 142, + 233, + 469, + 245 + ], + "score": 1.0, + "content": "The success of deep learning is due in large part to our ability to solve certain mas-", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 142, + 244, + 469, + 255 + ], + "spans": [ + { + "bbox": [ + 142, + 244, + 469, + 255 + ], + "score": 1.0, + "content": "sive non-convex optimization problems with relative ease. Though non-convex", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 142, + 255, + 470, + 267 + ], + "spans": [ + { + "bbox": [ + 142, + 255, + 470, + 267 + ], + "score": 1.0, + "content": "optimization is NP-hard, simple algorithms – often variants of stochastic gradient", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 141, + 266, + 469, + 277 + ], + "spans": [ + { + "bbox": [ + 141, + 266, + 469, + 277 + ], + "score": 1.0, + "content": "descent – exhibit surprising effectiveness in fitting large neural networks in prac-", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 141, + 276, + 469, + 288 + ], + "spans": [ + { + "bbox": [ + 141, + 276, + 469, + 288 + ], + "score": 1.0, + "content": "tice. We argue that neural network loss landscapes often contain (nearly) a single", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 141, + 287, + 469, + 299 + ], + "spans": [ + { + "bbox": [ + 141, + 287, + 469, + 299 + ], + "score": 1.0, + "content": "basin after accounting for all possible permutation symmetries of hidden units", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 141, + 298, + 469, + 310 + ], + "spans": [ + { + "bbox": [ + 141, + 298, + 469, + 310 + ], + "score": 1.0, + "content": "a la Entezari et al. (2021). We introduce three algorithms to permute the units", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 142, + 309, + 469, + 321 + ], + "spans": [ + { + "bbox": [ + 142, + 309, + 469, + 321 + ], + "score": 1.0, + "content": "of one model to bring them into alignment with a reference model in order to", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 141, + 320, + 469, + 332 + ], + "spans": [ + { + "bbox": [ + 141, + 320, + 469, + 332 + ], + "score": 1.0, + "content": "merge the two models in weight space. This transformation produces a function-", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 141, + 331, + 469, + 344 + ], + "spans": [ + { + "bbox": [ + 141, + 331, + 469, + 344 + ], + "score": 1.0, + "content": "ally equivalent set of weights that lie in an approximately convex basin near the", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 141, + 342, + 469, + 355 + ], + "spans": [ + { + "bbox": [ + 141, + 342, + 469, + 355 + ], + "score": 1.0, + "content": "reference model. Experimentally, we demonstrate the single basin phenomenon", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 141, + 353, + 469, + 365 + ], + "spans": [ + { + "bbox": [ + 141, + 353, + 469, + 365 + ], + "score": 1.0, + "content": "across a variety of model architectures and datasets, including the first (to our", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 141, + 363, + 469, + 376 + ], + "spans": [ + { + "bbox": [ + 141, + 363, + 469, + 376 + ], + "score": 1.0, + "content": "knowledge) demonstration of zero-barrier linear mode connectivity between in-", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 141, + 375, + 470, + 387 + ], + "spans": [ + { + "bbox": [ + 141, + 375, + 470, + 387 + ], + "score": 1.0, + "content": "dependently trained ResNet models on CIFAR-10. Additionally, we investigate", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 141, + 385, + 470, + 399 + ], + "spans": [ + { + "bbox": [ + 141, + 385, + 470, + 399 + ], + "score": 1.0, + "content": "intriguing phenomena relating model width and training time to mode connectiv-", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 141, + 397, + 469, + 410 + ], + "spans": [ + { + "bbox": [ + 141, + 397, + 469, + 410 + ], + "score": 1.0, + "content": "ity. Finally, we discuss shortcomings of the linear mode connectivity hypothesis,", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 141, + 407, + 360, + 421 + ], + "spans": [ + { + "bbox": [ + 141, + 407, + 360, + 421 + ], + "score": 1.0, + "content": "including a counterexample to the single basin theory.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 15, + "bbox_fs": [ + 141, + 233, + 470, + 421 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 438, + 206, + 451 + ], + "lines": [ + { + "bbox": [ + 105, + 437, + 208, + 454 + ], + "spans": [ + { + "bbox": [ + 105, + 437, + 208, + 454 + ], + "score": 1.0, + "content": "1 INTRODUCTION", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 24 + }, + { + "type": "text", + "bbox": [ + 107, + 462, + 504, + 485 + ], + "lines": [ + { + "bbox": [ + 106, + 461, + 505, + 475 + ], + "spans": [ + { + "bbox": [ + 106, + 461, + 505, + 475 + ], + "score": 1.0, + "content": "We investigate the unreasonable effectiveness of stochastic gradient descent (SGD) algorithms on", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 474, + 458, + 487 + ], + "spans": [ + { + "bbox": [ + 106, + 474, + 458, + 487 + ], + "score": 1.0, + "content": "the high-dimensional non-convex optimization problems of deep learning. 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Why does SGD thrive in optimizing high-dimensional non-convex deep learning loss land-", + "type": "text" + } + ], + "index": 27, + "is_list_start_line": true + }, + { + "bbox": [ + 135, + 505, + 505, + 517 + ], + "spans": [ + { + "bbox": [ + 135, + 505, + 505, + 517 + ], + "score": 1.0, + "content": "scapes despite being noticeably less robust in other non-convex optimization settings, like", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 134, + 515, + 505, + 529 + ], + "spans": [ + { + "bbox": [ + 134, + 515, + 505, + 529 + ], + "score": 1.0, + "content": "policy learning (Ainsworth et al., 2021), trajectory optimization (Kelly, 2017), and recom-", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 135, + 527, + 284, + 539 + ], + "spans": [ + { + "bbox": [ + 135, + 527, + 284, + 539 + ], + "score": 1.0, + "content": "mender systems (Kang et al., 2016)?", + "type": "text" + } + ], + "index": 30, + "is_list_end_line": true + }, + { + "bbox": [ + 123, + 540, + 505, + 552 + ], + "spans": [ + { + "bbox": [ + 123, + 542, + 132, + 551 + ], + "score": 1.0, + "content": "2.", + "type": "text" + }, + { + "bbox": [ + 133, + 540, + 505, + 552 + ], + "score": 1.0, + "content": "What are all the local minima? 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Hecht-", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 640, + 505, + 654 + ], + "spans": [ + { + "bbox": [ + 105, + 640, + 505, + 654 + ], + "score": 1.0, + "content": "Nielsen (1990) noted the permutation symmetries of hidden units in neural networks; briefly, one can", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 651, + 505, + 666 + ], + "spans": [ + { + "bbox": [ + 105, + 651, + 505, + 666 + ], + "score": 1.0, + "content": "swap any two units of a hidden layer in a network and – assuming weights are adjusted accordingly", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 663, + 505, + 675 + ], + "spans": [ + { + "bbox": [ + 105, + 663, + 505, + 675 + ], + "score": 1.0, + "content": "– network functionality will not change. Recently, Benton et al. (2021) demonstrated that SGD", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 674, + 505, + 686 + ], + "spans": [ + { + "bbox": [ + 105, + 674, + 505, + 686 + ], + "score": 1.0, + "content": "solutions form a connected volume of low loss and Entezari et al. (2021) conjectured that this volume", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 686, + 280, + 697 + ], + "spans": [ + { + "bbox": [ + 105, + 686, + 280, + 697 + ], + "score": 1.0, + "content": "is convex modulo permutation symmetries.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 40, + "bbox_fs": [ + 105, + 618, + 505, + 697 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 699, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "score": 1.0, + "content": "Conjecture 1 (Permutation invariance, informal (Entezari et al., 2021)). Most SGD solutions belong", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 709, + 506, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 506, + 722 + ], + "score": 1.0, + "content": "to a set whose elements can be permuted so that no barrier (as in Definition 2.2) exists on the linear", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 720, + 311, + 734 + ], + "spans": [ + { + "bbox": [ + 106, + 720, + 311, + 734 + ], + "score": 1.0, + "content": "interpolation between any two permuted elements.", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 45, + "bbox_fs": [ + 105, + 698, + 506, + 734 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 139, + 79, + 471, + 135 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 139, + 79, + 471, + 135 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 139, + 79, + 471, + 135 + ], + "spans": [ + { + "bbox": [ + 139, + 79, + 471, + 135 + ], + "score": 0.945, + "html": "
ARCHITECTURENUM.PERMUTATIONSYMMETRIES
MLP (3 layers, 512 width)10 ^ 3498
VGG1610 ^ 35160
ResNet5010 ^ 55109
", + "type": "table", + "image_path": "0bcd52f84cd857546638a85629ba832c80c4c331b2b27f2cf5493d4ff463ea44.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 139, + 79, + 471, + 97.66666666666667 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 139, + 97.66666666666667, + 471, + 116.33333333333334 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 139, + 116.33333333333334, + 471, + 135.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "table_footnote", + "bbox": [ + 145, + 135, + 324, + 146 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 145, + 134, + 324, + 148 + ], + "spans": [ + { + "bbox": [ + 145, + 134, + 324, + 148 + ], + "score": 1.0, + "content": "Atoms in the observable universe 10 ∧ 82", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 3 + }, + { + "type": "table_caption", + "bbox": [ + 107, + 154, + 505, + 188 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 154, + 505, + 167 + ], + "spans": [ + { + "bbox": [ + 105, + 154, + 505, + 167 + ], + "score": 1.0, + "content": "Table 1: Permutation symmetries of deep learning models vs. an upper estimate on the number", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 164, + 505, + 178 + ], + "spans": [ + { + "bbox": [ + 105, + 164, + 505, + 178 + ], + "score": 1.0, + "content": "of atoms in the known, observable universe. Deep learning loss landscapes contain incomprehen-", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 176, + 260, + 189 + ], + "spans": [ + { + "bbox": [ + 106, + 176, + 260, + 189 + ], + "score": 1.0, + "content": "sible amounts of geometric repetition.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 5 + } + ], + "index": 3 + }, + { + "type": "text", + "bbox": [ + 107, + 206, + 505, + 250 + ], + "lines": [ + { + "bbox": [ + 106, + 207, + 505, + 218 + ], + "spans": [ + { + "bbox": [ + 106, + 207, + 505, + 218 + ], + "score": 1.0, + "content": "We refer to such solutions as being linearly mode connected (LMC) (Frankle et al., 2020), an exten-", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 218, + 505, + 230 + ], + "spans": [ + { + "bbox": [ + 106, + 218, + 505, + 230 + ], + "score": 1.0, + "content": "sion of mode connectivity (Garipov et al., 2018; Draxler et al., 2018). If true, Conjecture 1 will both", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 228, + 506, + 241 + ], + "spans": [ + { + "bbox": [ + 105, + 228, + 506, + 241 + ], + "score": 1.0, + "content": "materially expand our understanding of how SGD works in the context of deep learning and offer a", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 240, + 364, + 252 + ], + "spans": [ + { + "bbox": [ + 106, + 240, + 364, + 252 + ], + "score": 1.0, + "content": "credible explanation for the preceding phenomena, in particular.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 8.5 + }, + { + "type": "text", + "bbox": [ + 108, + 262, + 505, + 296 + ], + "lines": [ + { + "bbox": [ + 106, + 261, + 505, + 275 + ], + "spans": [ + { + "bbox": [ + 106, + 261, + 505, + 275 + ], + "score": 1.0, + "content": "Contributions. In this paper, we attempt to uncover what invariances may be responsible for the", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 273, + 505, + 286 + ], + "spans": [ + { + "bbox": [ + 106, + 273, + 505, + 286 + ], + "score": 1.0, + "content": "phenomena cited above and the unreasonable effectiveness of SGD in deep learning. We make the", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 284, + 205, + 297 + ], + "spans": [ + { + "bbox": [ + 105, + 284, + 205, + 297 + ], + "score": 1.0, + "content": "following contributions:", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 12 + }, + { + "type": "text", + "bbox": [ + 122, + 304, + 505, + 476 + ], + "lines": [ + { + "bbox": [ + 122, + 303, + 506, + 318 + ], + "spans": [ + { + "bbox": [ + 122, + 303, + 506, + 318 + ], + "score": 1.0, + "content": "1. Matching methods. We propose three algorithms, grounded in concepts and techniques", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 134, + 316, + 505, + 328 + ], + "spans": [ + { + "bbox": [ + 134, + 316, + 505, + 328 + ], + "score": 1.0, + "content": "from combinatorial optimization, to align the weights of two independently trained models.", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 134, + 325, + 506, + 340 + ], + "spans": [ + { + "bbox": [ + 134, + 325, + 506, + 340 + ], + "score": 1.0, + "content": "Where appropriate, we prove hardness results for these problems and propose approximation", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 135, + 338, + 505, + 350 + ], + "spans": [ + { + "bbox": [ + 135, + 338, + 505, + 350 + ], + "score": 1.0, + "content": "algorithms. Our fastest method identifies permutations in mere seconds on current hardware.", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 123, + 351, + 505, + 364 + ], + "spans": [ + { + "bbox": [ + 123, + 351, + 505, + 364 + ], + "score": 1.0, + "content": "2. Relationship to optimization algorithms. We demonstrate by means of counterexample", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 133, + 362, + 506, + 376 + ], + "spans": [ + { + "bbox": [ + 133, + 362, + 506, + 376 + ], + "score": 1.0, + "content": "that linear mode connectivity is an emergent property of training procedures, not of model", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 134, + 374, + 460, + 387 + ], + "spans": [ + { + "bbox": [ + 134, + 374, + 460, + 387 + ], + "score": 1.0, + "content": "architectures. We connect this result to prior work on the implicit biases of SGD.", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 122, + 388, + 505, + 401 + ], + "spans": [ + { + "bbox": [ + 122, + 388, + 505, + 401 + ], + "score": 1.0, + "content": "3. Experiments, including zero-barrier LMC for ResNets. Empirically, we explore the exis-", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 133, + 399, + 506, + 412 + ], + "spans": [ + { + "bbox": [ + 133, + 399, + 506, + 412 + ], + "score": 1.0, + "content": "tence of linear mode connectivity modulo permutation symmetries in experiments across", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 134, + 409, + 505, + 422 + ], + "spans": [ + { + "bbox": [ + 134, + 409, + 505, + 422 + ], + "score": 1.0, + "content": "MLPs, CNNs, and ResNets trained on MNIST, CIFAR-10, and CIFAR-100. We con-", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 133, + 421, + 505, + 433 + ], + "spans": [ + { + "bbox": [ + 133, + 421, + 505, + 433 + ], + "score": 1.0, + "content": "tribute the first-ever demonstration of zero-barrier LMC between two independently trained", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 133, + 430, + 506, + 446 + ], + "spans": [ + { + "bbox": [ + 133, + 430, + 506, + 446 + ], + "score": 1.0, + "content": "ResNets. We explore the relationship between LMC and model width as well as training", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 134, + 443, + 505, + 455 + ], + "spans": [ + { + "bbox": [ + 134, + 443, + 505, + 455 + ], + "score": 1.0, + "content": "time. Finally, we show evidence of our methods’ ability to combine models trained on inde-", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 133, + 455, + 505, + 466 + ], + "spans": [ + { + "bbox": [ + 133, + 455, + 505, + 466 + ], + "score": 1.0, + "content": "pendent datasets into a merged model that outperforms both input models in terms of test loss", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 134, + 465, + 504, + 477 + ], + "spans": [ + { + "bbox": [ + 134, + 465, + 504, + 477 + ], + "score": 1.0, + "content": "(but not accuracy) and is no more expensive in compute or memory than either input model.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 21 + }, + { + "type": "title", + "bbox": [ + 107, + 492, + 200, + 504 + ], + "lines": [ + { + "bbox": [ + 104, + 490, + 201, + 507 + ], + "spans": [ + { + "bbox": [ + 104, + 490, + 201, + 507 + ], + "score": 1.0, + "content": "2 BACKGROUND", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 29 + }, + { + "type": "text", + "bbox": [ + 107, + 516, + 504, + 539 + ], + "lines": [ + { + "bbox": [ + 106, + 516, + 505, + 529 + ], + "spans": [ + { + "bbox": [ + 106, + 516, + 505, + 529 + ], + "score": 1.0, + "content": "Although our methods can be applied to arbitrary model architectures, we proceed with the multi-", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 528, + 484, + 540 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 427, + 540 + ], + "score": 1.0, + "content": "layer perceptron (MLP) for its ease of presentation (Bishop, 2007). Consider an", + "type": "text" + }, + { + "bbox": [ + 427, + 528, + 435, + 537 + ], + "score": 0.82, + "content": "L", + "type": "inline_equation" + }, + { + "bbox": [ + 435, + 528, + 484, + 540 + ], + "score": 1.0, + "content": "-layer MLP,", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 30.5 + }, + { + "type": "interline_equation", + "bbox": [ + 194, + 542, + 416, + 556 + ], + "lines": [ + { + "bbox": [ + 194, + 542, + 416, + 556 + ], + "spans": [ + { + "bbox": [ + 194, + 542, + 416, + 556 + ], + "score": 0.86, + "content": "f ( \\pmb { x } ; \\Theta ) = \\pmb { z } _ { L + 1 } , \\quad \\pmb { z } _ { \\ell + 1 } = \\sigma ( \\pmb { W } _ { \\ell } \\pmb { z } _ { \\ell } + \\pmb { b } _ { \\ell } ) , \\quad \\pmb { z } _ { 1 } = \\pmb { x } ,", + "type": "interline_equation", + "image_path": "ea4a7bb0234af057a08957fdba69bda86b0847be0c1cd6ffac165c6b11e5158f.jpg" + } + ] + } + ], + "index": 32, + "virtual_lines": [ + { + "bbox": [ + 194, + 542, + 416, + 556 + ], + "spans": [], + "index": 32 + } + ] + }, + { + "type": "text", + "bbox": [ + 108, + 559, + 505, + 592 + ], + "lines": [ + { + "bbox": [ + 106, + 559, + 505, + 572 + ], + "spans": [ + { + "bbox": [ + 106, + 559, + 133, + 572 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 133, + 561, + 140, + 569 + ], + "score": 0.74, + "content": "\\sigma", + "type": "inline_equation" + }, + { + "bbox": [ + 141, + 559, + 478, + 572 + ], + "score": 1.0, + "content": "denotes an element-wise nonlinear activation function. Furthermore, consider a loss,", + "type": "text" + }, + { + "bbox": [ + 478, + 559, + 501, + 571 + ], + "score": 0.91, + "content": "\\mathcal { L } ( \\Theta )", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 559, + 505, + 572 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 569, + 506, + 582 + ], + "spans": [ + { + "bbox": [ + 105, + 569, + 346, + 582 + ], + "score": 1.0, + "content": "that measures the suitability of a particular set of weights", + "type": "text" + }, + { + "bbox": [ + 346, + 570, + 355, + 580 + ], + "score": 0.83, + "content": "\\Theta", + "type": "inline_equation" + }, + { + "bbox": [ + 355, + 569, + 506, + 582 + ], + "score": 1.0, + "content": "towards some goal, e.g., fitting to a", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 581, + 172, + 594 + ], + "spans": [ + { + "bbox": [ + 106, + 581, + 172, + 594 + ], + "score": 1.0, + "content": "training dataset.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 34 + }, + { + "type": "text", + "bbox": [ + 108, + 597, + 504, + 631 + ], + "lines": [ + { + "bbox": [ + 106, + 598, + 505, + 610 + ], + "spans": [ + { + "bbox": [ + 106, + 598, + 505, + 610 + ], + "score": 1.0, + "content": "Central to our investigation is the phenomenon of permutation symmetries of weight space. Given", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 107, + 608, + 506, + 622 + ], + "spans": [ + { + "bbox": [ + 107, + 609, + 115, + 619 + ], + "score": 0.77, + "content": "\\Theta", + "type": "inline_equation" + }, + { + "bbox": [ + 116, + 608, + 440, + 622 + ], + "score": 1.0, + "content": ", we can apply some permutation to the output features of any intermediate layer,", + "type": "text" + }, + { + "bbox": [ + 441, + 610, + 446, + 619 + ], + "score": 0.67, + "content": "\\ell", + "type": "inline_equation" + }, + { + "bbox": [ + 446, + 608, + 506, + 622 + ], + "score": 1.0, + "content": ", of the model,", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 620, + 278, + 632 + ], + "spans": [ + { + "bbox": [ + 106, + 620, + 239, + 632 + ], + "score": 1.0, + "content": "denoted by a permutation matrix", + "type": "text" + }, + { + "bbox": [ + 239, + 620, + 272, + 631 + ], + "score": 0.91, + "content": "\\pmb { P } \\in S _ { d }", + "type": "inline_equation" + }, + { + "bbox": [ + 272, + 620, + 278, + 632 + ], + "score": 1.0, + "content": ",1", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 37 + }, + { + "type": "interline_equation", + "bbox": [ + 164, + 634, + 446, + 649 + ], + "lines": [ + { + "bbox": [ + 164, + 634, + 446, + 649 + ], + "spans": [ + { + "bbox": [ + 164, + 634, + 446, + 649 + ], + "score": 0.9, + "content": "z _ { \\ell + 1 } = P ^ { \\top } P z _ { \\ell + 1 } = P ^ { \\top } P \\sigma ( W _ { \\ell } z _ { \\ell } + b _ { \\ell } ) = P ^ { \\top } \\sigma ( P W _ { \\ell } z _ { \\ell } + P b _ { \\ell } )", + "type": "interline_equation", + "image_path": "b923a70720a5d86225af5c2cb203679e7ba8d3becb1e46ef362c972d5c6abc43.jpg" + } + ] + } + ], + "index": 39, + "virtual_lines": [ + { + "bbox": [ + 164, + 634, + 446, + 649 + ], + "spans": [], + "index": 39 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 652, + 506, + 686 + ], + "lines": [ + { + "bbox": [ + 106, + 653, + 504, + 664 + ], + "spans": [ + { + "bbox": [ + 106, + 653, + 120, + 664 + ], + "score": 1.0, + "content": "for", + "type": "text" + }, + { + "bbox": [ + 120, + 655, + 128, + 662 + ], + "score": 0.77, + "content": "\\sigma", + "type": "inline_equation" + }, + { + "bbox": [ + 128, + 653, + 483, + 664 + ], + "score": 1.0, + "content": ", an element-wise operator. It follows that as long as we reorder the input weights of layer", + "type": "text" + }, + { + "bbox": [ + 483, + 653, + 504, + 663 + ], + "score": 0.89, + "content": "\\ell + 1", + "type": "inline_equation" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 662, + 506, + 676 + ], + "spans": [ + { + "bbox": [ + 105, + 662, + 158, + 676 + ], + "score": 1.0, + "content": "according to", + "type": "text" + }, + { + "bbox": [ + 159, + 663, + 174, + 674 + ], + "score": 0.9, + "content": "P ^ { \\top }", + "type": "inline_equation" + }, + { + "bbox": [ + 175, + 662, + 470, + 676 + ], + "score": 1.0, + "content": ", we will have a functionally equivalent model. To be precise, if we define", + "type": "text" + }, + { + "bbox": [ + 470, + 664, + 482, + 673 + ], + "score": 0.88, + "content": "\\Theta ^ { \\prime }", + "type": "inline_equation" + }, + { + "bbox": [ + 482, + 662, + 506, + 676 + ], + "score": 1.0, + "content": "to be", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 674, + 251, + 686 + ], + "spans": [ + { + "bbox": [ + 106, + 674, + 154, + 686 + ], + "score": 1.0, + "content": "identical to", + "type": "text" + }, + { + "bbox": [ + 154, + 675, + 163, + 684 + ], + "score": 0.84, + "content": "\\Theta", + "type": "inline_equation" + }, + { + "bbox": [ + 163, + 674, + 251, + 686 + ], + "score": 1.0, + "content": "with the exception of", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 41 + }, + { + "type": "interline_equation", + "bbox": [ + 203, + 689, + 407, + 704 + ], + "lines": [ + { + "bbox": [ + 203, + 689, + 407, + 704 + ], + "spans": [ + { + "bbox": [ + 203, + 689, + 407, + 704 + ], + "score": 0.9, + "content": "\\begin{array} { r } { { W } _ { \\ell } ^ { \\prime } = P { W } _ { \\ell } , \\quad { b } _ { \\ell } ^ { \\prime } = P { b } _ { \\ell } , \\quad { W } _ { \\ell + 1 } ^ { \\prime } = { W } _ { \\ell + 1 } P ^ { \\top } , } \\end{array}", + "type": "interline_equation", + "image_path": "e6abd509c19d40e82533d1963bad757e97d3f5257da51fabd0250389599fa654.jpg" + } + ] + } + ], + "index": 43, + "virtual_lines": [ + { + "bbox": [ + 203, + 689, + 407, + 704 + ], + "spans": [], + "index": 43 + } + ] + } + ], + "page_idx": 1, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2023", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 106, + 711, + 506, + 732 + ], + "lines": [ + { + "bbox": [ + 118, + 709, + 505, + 724 + ], + "spans": [ + { + "bbox": [ + 118, + 709, + 211, + 724 + ], + "score": 1.0, + "content": "1We denote the set of all", + "type": "text" + }, + { + "bbox": [ + 211, + 713, + 233, + 721 + ], + "score": 0.84, + "content": "d \\times d", + "type": "inline_equation" + }, + { + "bbox": [ + 234, + 709, + 467, + 724 + ], + "score": 1.0, + "content": "permutation matrices – isomorphic to the symmetric group – as", + "type": "text" + }, + { + "bbox": [ + 468, + 712, + 478, + 721 + ], + "score": 0.87, + "content": "S _ { d }", + "type": "inline_equation" + }, + { + "bbox": [ + 478, + 709, + 505, + 724 + ], + "score": 1.0, + "content": ", to the", + "type": "text" + } + ] + }, + { + "bbox": [ + 105, + 721, + 256, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 721, + 256, + 733 + ], + "score": 1.0, + "content": "possible chagrin of pure mathematicians.", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 309, + 760 + ], + "lines": [ + { + "bbox": [ + 301, + 750, + 310, + 763 + ], + "spans": [ + { + "bbox": [ + 301, + 750, + 310, + 763 + ], + "score": 1.0, + "content": "2", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "table", + "bbox": [ + 139, + 79, + 471, + 135 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 139, + 79, + 471, + 135 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 139, + 79, + 471, + 135 + ], + "spans": [ + { + "bbox": [ + 139, + 79, + 471, + 135 + ], + "score": 0.945, + "html": "
ARCHITECTURENUM.PERMUTATIONSYMMETRIES
MLP (3 layers, 512 width)10 ^ 3498
VGG1610 ^ 35160
ResNet5010 ^ 55109
", + "type": "table", + "image_path": "0bcd52f84cd857546638a85629ba832c80c4c331b2b27f2cf5493d4ff463ea44.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 139, + 79, + 471, + 97.66666666666667 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 139, + 97.66666666666667, + 471, + 116.33333333333334 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 139, + 116.33333333333334, + 471, + 135.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "table_footnote", + "bbox": [ + 145, + 135, + 324, + 146 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 145, + 134, + 324, + 148 + ], + "spans": [ + { + "bbox": [ + 145, + 134, + 324, + 148 + ], + "score": 1.0, + "content": "Atoms in the observable universe 10 ∧ 82", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 3 + }, + { + "type": "table_caption", + "bbox": [ + 107, + 154, + 505, + 188 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 154, + 505, + 167 + ], + "spans": [ + { + "bbox": [ + 105, + 154, + 505, + 167 + ], + "score": 1.0, + "content": "Table 1: Permutation symmetries of deep learning models vs. an upper estimate on the number", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 164, + 505, + 178 + ], + "spans": [ + { + "bbox": [ + 105, + 164, + 505, + 178 + ], + "score": 1.0, + "content": "of atoms in the known, observable universe. Deep learning loss landscapes contain incomprehen-", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 176, + 260, + 189 + ], + "spans": [ + { + "bbox": [ + 106, + 176, + 260, + 189 + ], + "score": 1.0, + "content": "sible amounts of geometric repetition.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 5 + } + ], + "index": 3 + }, + { + "type": "text", + "bbox": [ + 107, + 206, + 505, + 250 + ], + "lines": [ + { + "bbox": [ + 106, + 207, + 505, + 218 + ], + "spans": [ + { + "bbox": [ + 106, + 207, + 505, + 218 + ], + "score": 1.0, + "content": "We refer to such solutions as being linearly mode connected (LMC) (Frankle et al., 2020), an exten-", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 218, + 505, + 230 + ], + "spans": [ + { + "bbox": [ + 106, + 218, + 505, + 230 + ], + "score": 1.0, + "content": "sion of mode connectivity (Garipov et al., 2018; Draxler et al., 2018). If true, Conjecture 1 will both", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 228, + 506, + 241 + ], + "spans": [ + { + "bbox": [ + 105, + 228, + 506, + 241 + ], + "score": 1.0, + "content": "materially expand our understanding of how SGD works in the context of deep learning and offer a", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 240, + 364, + 252 + ], + "spans": [ + { + "bbox": [ + 106, + 240, + 364, + 252 + ], + "score": 1.0, + "content": "credible explanation for the preceding phenomena, in particular.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 8.5, + "bbox_fs": [ + 105, + 207, + 506, + 252 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 262, + 505, + 296 + ], + "lines": [ + { + "bbox": [ + 106, + 261, + 505, + 275 + ], + "spans": [ + { + "bbox": [ + 106, + 261, + 505, + 275 + ], + "score": 1.0, + "content": "Contributions. In this paper, we attempt to uncover what invariances may be responsible for the", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 273, + 505, + 286 + ], + "spans": [ + { + "bbox": [ + 106, + 273, + 505, + 286 + ], + "score": 1.0, + "content": "phenomena cited above and the unreasonable effectiveness of SGD in deep learning. We make the", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 284, + 205, + 297 + ], + "spans": [ + { + "bbox": [ + 105, + 284, + 205, + 297 + ], + "score": 1.0, + "content": "following contributions:", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 12, + "bbox_fs": [ + 105, + 261, + 505, + 297 + ] + }, + { + "type": "text", + "bbox": [ + 122, + 304, + 505, + 476 + ], + "lines": [ + { + "bbox": [ + 122, + 303, + 506, + 318 + ], + "spans": [ + { + "bbox": [ + 122, + 303, + 506, + 318 + ], + "score": 1.0, + "content": "1. Matching methods. We propose three algorithms, grounded in concepts and techniques", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 134, + 316, + 505, + 328 + ], + "spans": [ + { + "bbox": [ + 134, + 316, + 505, + 328 + ], + "score": 1.0, + "content": "from combinatorial optimization, to align the weights of two independently trained models.", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 134, + 325, + 506, + 340 + ], + "spans": [ + { + "bbox": [ + 134, + 325, + 506, + 340 + ], + "score": 1.0, + "content": "Where appropriate, we prove hardness results for these problems and propose approximation", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 135, + 338, + 505, + 350 + ], + "spans": [ + { + "bbox": [ + 135, + 338, + 505, + 350 + ], + "score": 1.0, + "content": "algorithms. Our fastest method identifies permutations in mere seconds on current hardware.", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 123, + 351, + 505, + 364 + ], + "spans": [ + { + "bbox": [ + 123, + 351, + 505, + 364 + ], + "score": 1.0, + "content": "2. Relationship to optimization algorithms. We demonstrate by means of counterexample", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 133, + 362, + 506, + 376 + ], + "spans": [ + { + "bbox": [ + 133, + 362, + 506, + 376 + ], + "score": 1.0, + "content": "that linear mode connectivity is an emergent property of training procedures, not of model", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 134, + 374, + 460, + 387 + ], + "spans": [ + { + "bbox": [ + 134, + 374, + 460, + 387 + ], + "score": 1.0, + "content": "architectures. We connect this result to prior work on the implicit biases of SGD.", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 122, + 388, + 505, + 401 + ], + "spans": [ + { + "bbox": [ + 122, + 388, + 505, + 401 + ], + "score": 1.0, + "content": "3. Experiments, including zero-barrier LMC for ResNets. Empirically, we explore the exis-", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 133, + 399, + 506, + 412 + ], + "spans": [ + { + "bbox": [ + 133, + 399, + 506, + 412 + ], + "score": 1.0, + "content": "tence of linear mode connectivity modulo permutation symmetries in experiments across", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 134, + 409, + 505, + 422 + ], + "spans": [ + { + "bbox": [ + 134, + 409, + 505, + 422 + ], + "score": 1.0, + "content": "MLPs, CNNs, and ResNets trained on MNIST, CIFAR-10, and CIFAR-100. We con-", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 133, + 421, + 505, + 433 + ], + "spans": [ + { + "bbox": [ + 133, + 421, + 505, + 433 + ], + "score": 1.0, + "content": "tribute the first-ever demonstration of zero-barrier LMC between two independently trained", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 133, + 430, + 506, + 446 + ], + "spans": [ + { + "bbox": [ + 133, + 430, + 506, + 446 + ], + "score": 1.0, + "content": "ResNets. We explore the relationship between LMC and model width as well as training", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 134, + 443, + 505, + 455 + ], + "spans": [ + { + "bbox": [ + 134, + 443, + 505, + 455 + ], + "score": 1.0, + "content": "time. Finally, we show evidence of our methods’ ability to combine models trained on inde-", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 133, + 455, + 505, + 466 + ], + "spans": [ + { + "bbox": [ + 133, + 455, + 505, + 466 + ], + "score": 1.0, + "content": "pendent datasets into a merged model that outperforms both input models in terms of test loss", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 134, + 465, + 504, + 477 + ], + "spans": [ + { + "bbox": [ + 134, + 465, + 504, + 477 + ], + "score": 1.0, + "content": "(but not accuracy) and is no more expensive in compute or memory than either input model.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 21, + "bbox_fs": [ + 122, + 303, + 506, + 477 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 492, + 200, + 504 + ], + "lines": [ + { + "bbox": [ + 104, + 490, + 201, + 507 + ], + "spans": [ + { + "bbox": [ + 104, + 490, + 201, + 507 + ], + "score": 1.0, + "content": "2 BACKGROUND", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 29 + }, + { + "type": "text", + "bbox": [ + 107, + 516, + 504, + 539 + ], + "lines": [ + { + "bbox": [ + 106, + 516, + 505, + 529 + ], + "spans": [ + { + "bbox": [ + 106, + 516, + 505, + 529 + ], + "score": 1.0, + "content": "Although our methods can be applied to arbitrary model architectures, we proceed with the multi-", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 528, + 484, + 540 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 427, + 540 + ], + "score": 1.0, + "content": "layer perceptron (MLP) for its ease of presentation (Bishop, 2007). 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A function", + "type": "text" + }, + { + "bbox": [ + 270, + 339, + 327, + 351 + ], + "score": 0.9, + "content": "f : \\mathbb { R } ^ { D } \\mathbb { R }", + "type": "inline_equation" + }, + { + "bbox": [ + 328, + 338, + 506, + 353 + ], + "score": 1.0, + "content": "is convex if every one-dimensional slice is", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 348, + 450, + 365 + ], + "spans": [ + { + "bbox": [ + 105, + 348, + 183, + 365 + ], + "score": 1.0, + "content": "convex, i.e., for all", + "type": "text" + }, + { + "bbox": [ + 183, + 351, + 226, + 363 + ], + "score": 0.92, + "content": "x , y \\in \\mathbb { R } ^ { D }", + "type": "inline_equation" + }, + { + "bbox": [ + 226, + 348, + 281, + 365 + ], + "score": 1.0, + "content": ", the function", + "type": "text" + }, + { + "bbox": [ + 281, + 351, + 387, + 363 + ], + "score": 0.92, + "content": "g ( \\lambda ) = f ( ( 1 - \\lambda ) x + \\lambda y )", + "type": "inline_equation" + }, + { + "bbox": [ + 387, + 348, + 438, + 365 + ], + "score": 1.0, + "content": "is convex in", + "type": "text" + }, + { + "bbox": [ + 438, + 352, + 446, + 361 + ], + "score": 0.77, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 446, + 348, + 450, + 365 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 36.5 + }, + { + "type": "text", + "bbox": [ + 107, + 372, + 505, + 428 + ], + "lines": [ + { + "bbox": [ + 106, + 373, + 505, + 385 + ], + "spans": [ + { + "bbox": [ + 106, + 373, + 505, + 385 + ], + "score": 1.0, + "content": "Due to Definition 2.1, it suffices to show that arbitrary one-dimensional slices of a function are con-", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 384, + 505, + 398 + ], + "spans": [ + { + "bbox": [ + 105, + 384, + 505, + 398 + ], + "score": 1.0, + "content": "vex in order to reason about the convexity of complex, high-dimensional functions. In practice, we", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 104, + 394, + 506, + 410 + ], + "spans": [ + { + "bbox": [ + 104, + 394, + 506, + 410 + ], + "score": 1.0, + "content": "rarely observe perfect convexity but instead hope to approximate it as closely as possible. Following", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 404, + 506, + 420 + ], + "spans": [ + { + "bbox": [ + 105, + 404, + 506, + 420 + ], + "score": 1.0, + "content": "Frankle et al. (2020); Entezari et al. (2021); Draxler et al. (2018); Garipov et al. (2018) and others,", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 417, + 329, + 430 + ], + "spans": [ + { + "bbox": [ + 105, + 417, + 329, + 430 + ], + "score": 1.0, + "content": "we measure approximations to convexity via “barriers.”", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 40 + }, + { + "type": "text", + "bbox": [ + 106, + 432, + 502, + 456 + ], + "lines": [ + { + "bbox": [ + 105, + 432, + 505, + 445 + ], + "spans": [ + { + "bbox": [ + 105, + 432, + 388, + 445 + ], + "score": 1.0, + "content": "Definition 2.2 (Loss barrier (Frankle et al., 2020)). Given two points", + "type": "text" + }, + { + "bbox": [ + 388, + 433, + 422, + 444 + ], + "score": 0.89, + "content": "\\Theta _ { A } , \\Theta _ { B }", + "type": "inline_equation" + }, + { + "bbox": [ + 423, + 432, + 462, + 445 + ], + "score": 1.0, + "content": "such that", + "type": "text" + }, + { + "bbox": [ + 463, + 433, + 505, + 444 + ], + "score": 0.91, + "content": "\\mathcal { L } ( \\Theta _ { A } ) \\approx", + "type": "inline_equation" + } + ], + "index": 43 + }, + { + "bbox": [ + 107, + 443, + 497, + 457 + ], + "spans": [ + { + "bbox": [ + 107, + 443, + 137, + 456 + ], + "score": 0.91, + "content": "\\mathcal { L } ( \\Theta _ { B } )", + "type": "inline_equation" + }, + { + "bbox": [ + 137, + 443, + 256, + 457 + ], + "score": 1.0, + "content": ", the loss barrier is defined as", + "type": "text" + }, + { + "bbox": [ + 257, + 443, + 492, + 457 + ], + "score": 0.83, + "content": "\\begin{array} { r } { \\operatorname* { m a x } _ { \\lambda \\in [ 0 , 1 ] } \\mathcal { L } ( ( 1 - \\lambda ) \\Theta _ { A } + \\lambda \\Theta _ { B } ) - \\frac { 1 } { 2 } ( \\mathcal { L } ( \\Theta _ { A } ) + \\mathcal { L } ( \\dot { \\Theta } _ { B } ) \\dot { ) } } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 492, + 443, + 497, + 457 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 43.5 + }, + { + "type": "text", + "bbox": [ + 105, + 465, + 491, + 477 + ], + "lines": [ + { + "bbox": [ + 105, + 464, + 492, + 479 + ], + "spans": [ + { + "bbox": [ + 105, + 464, + 492, + 479 + ], + "score": 1.0, + "content": "Loss barriers are non-negative, with zero indicating an interpolation of flat or positive curvature.", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 45 + }, + { + "type": "title", + "bbox": [ + 108, + 494, + 318, + 507 + ], + "lines": [ + { + "bbox": [ + 104, + 493, + 319, + 510 + ], + "spans": [ + { + "bbox": [ + 104, + 493, + 319, + 510 + ], + "score": 1.0, + "content": "3 PERMUTATION SELECTION METHODS", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 46 + }, + { + "type": "text", + "bbox": [ + 107, + 520, + 505, + 554 + ], + "lines": [ + { + "bbox": [ + 105, + 520, + 505, + 533 + ], + "spans": [ + { + "bbox": [ + 105, + 520, + 357, + 533 + ], + "score": 1.0, + "content": "We introduce three methods of matching units between model", + "type": "text" + }, + { + "bbox": [ + 357, + 522, + 366, + 531 + ], + "score": 0.77, + "content": "A", + "type": "inline_equation" + }, + { + "bbox": [ + 366, + 520, + 411, + 533 + ], + "score": 1.0, + "content": "and model", + "type": "text" + }, + { + "bbox": [ + 412, + 522, + 421, + 531 + ], + "score": 0.77, + "content": "B", + "type": "inline_equation" + }, + { + "bbox": [ + 421, + 520, + 505, + 533 + ], + "score": 1.0, + "content": ". 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A function", + "type": "text" + }, + { + "bbox": [ + 270, + 339, + 327, + 351 + ], + "score": 0.9, + "content": "f : \\mathbb { R } ^ { D } \\mathbb { R }", + "type": "inline_equation" + }, + { + "bbox": [ + 328, + 338, + 506, + 353 + ], + "score": 1.0, + "content": "is convex if every one-dimensional slice is", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 348, + 450, + 365 + ], + "spans": [ + { + "bbox": [ + 105, + 348, + 183, + 365 + ], + "score": 1.0, + "content": "convex, i.e., for all", + "type": "text" + }, + { + "bbox": [ + 183, + 351, + 226, + 363 + ], + "score": 0.92, + "content": "x , y \\in \\mathbb { R } ^ { D }", + "type": "inline_equation" + }, + { + "bbox": [ + 226, + 348, + 281, + 365 + ], + "score": 1.0, + "content": ", the function", + "type": "text" + }, + { + "bbox": [ + 281, + 351, + 387, + 363 + ], + "score": 0.92, + "content": "g ( \\lambda ) = f ( ( 1 - \\lambda ) x + \\lambda y )", + "type": "inline_equation" + }, + { + "bbox": [ + 387, + 348, + 438, + 365 + ], + "score": 1.0, + "content": "is convex in", + "type": "text" + }, + { + "bbox": [ + 438, + 352, + 446, + 361 + ], + "score": 0.77, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 446, + 348, + 450, + 365 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 36.5, + "bbox_fs": [ + 105, + 338, + 506, + 365 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 372, + 505, + 428 + ], + "lines": [ + { + "bbox": [ + 106, + 373, + 505, + 385 + ], + "spans": [ + { + "bbox": [ + 106, + 373, + 505, + 385 + ], + "score": 1.0, + "content": "Due to Definition 2.1, it suffices to show that arbitrary one-dimensional slices of a function are con-", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 384, + 505, + 398 + ], + "spans": [ + { + "bbox": [ + 105, + 384, + 505, + 398 + ], + "score": 1.0, + "content": "vex in order to reason about the convexity of complex, high-dimensional functions. 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Given two points", + "type": "text" + }, + { + "bbox": [ + 388, + 433, + 422, + 444 + ], + "score": 0.89, + "content": "\\Theta _ { A } , \\Theta _ { B }", + "type": "inline_equation" + }, + { + "bbox": [ + 423, + 432, + 462, + 445 + ], + "score": 1.0, + "content": "such that", + "type": "text" + }, + { + "bbox": [ + 463, + 433, + 505, + 444 + ], + "score": 0.91, + "content": "\\mathcal { L } ( \\Theta _ { A } ) \\approx", + "type": "inline_equation" + } + ], + "index": 43 + }, + { + "bbox": [ + 107, + 443, + 497, + 457 + ], + "spans": [ + { + "bbox": [ + 107, + 443, + 137, + 456 + ], + "score": 0.91, + "content": "\\mathcal { L } ( \\Theta _ { B } )", + "type": "inline_equation" + }, + { + "bbox": [ + 137, + 443, + 256, + 457 + ], + "score": 1.0, + "content": ", the loss barrier is defined as", + "type": "text" + }, + { + "bbox": [ + 257, + 443, + 492, + 457 + ], + "score": 0.83, + "content": "\\begin{array} { r } { \\operatorname* { m a x } _ { \\lambda \\in [ 0 , 1 ] } \\mathcal { L } ( ( 1 - \\lambda ) \\Theta _ { A } + \\lambda \\Theta _ { B } ) - \\frac { 1 } { 2 } ( \\mathcal { L } ( \\Theta _ { A } ) + \\mathcal { L } ( \\dot { \\Theta } _ { B } ) \\dot { ) } } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 492, + 443, + 497, + 457 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 43.5, + "bbox_fs": [ + 105, + 432, + 505, + 457 + ] + }, + { + "type": "text", + "bbox": [ + 105, + 465, + 491, + 477 + ], + "lines": [ + { + "bbox": [ + 105, + 464, + 492, + 479 + ], + "spans": [ + { + "bbox": [ + 105, + 464, + 492, + 479 + ], + "score": 1.0, + "content": "Loss barriers are non-negative, with zero indicating an interpolation of flat or positive curvature.", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 45, + "bbox_fs": [ + 105, + 464, + 492, + 479 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 494, + 318, + 507 + ], + "lines": [ + { + "bbox": [ + 104, + 493, + 319, + 510 + ], + "spans": [ + { + "bbox": [ + 104, + 493, + 319, + 510 + ], + "score": 1.0, + "content": "3 PERMUTATION SELECTION METHODS", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 46 + }, + { + "type": "text", + "bbox": [ + 107, + 520, + 505, + 554 + ], + "lines": [ + { + "bbox": [ + 105, + 520, + 505, + 533 + ], + "spans": [ + { + "bbox": [ + 105, + 520, + 357, + 533 + ], + "score": 1.0, + "content": "We introduce three methods of matching units between model", + "type": "text" + }, + { + "bbox": [ + 357, + 522, + 366, + 531 + ], + "score": 0.77, + "content": "A", + "type": "inline_equation" + }, + { + "bbox": [ + 366, + 520, + 411, + 533 + ], + "score": 1.0, + "content": "and model", + "type": "text" + }, + { + "bbox": [ + 412, + 522, + 421, + 531 + ], + "score": 0.77, + "content": "B", + "type": "inline_equation" + }, + { + "bbox": [ + 421, + 520, + 505, + 533 + ], + "score": 1.0, + "content": ". 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We", + "type": "text" + } + ], + "index": 56 + }, + { + "bbox": [ + 106, + 657, + 505, + 669 + ], + "spans": [ + { + "bbox": [ + 106, + 657, + 505, + 669 + ], + "score": 1.0, + "content": "fit this into the regression framework by constraining ordinary least squares (OLS) to solutions in", + "type": "text" + } + ], + "index": 57 + }, + { + "bbox": [ + 104, + 665, + 507, + 683 + ], + "spans": [ + { + "bbox": [ + 104, + 665, + 235, + 683 + ], + "score": 1.0, + "content": "the set of permutation matrices,", + "type": "text" + }, + { + "bbox": [ + 235, + 669, + 246, + 680 + ], + "score": 0.87, + "content": "S _ { d }", + "type": "inline_equation" + }, + { + "bbox": [ + 246, + 665, + 337, + 683 + ], + "score": 1.0, + "content": ". 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Conveniently, eq. (1) constitutes a “linear assignment problem” (LAP) (Bertsekas, 1998)", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 106, + 505, + 118 + ], + "spans": [ + { + "bbox": [ + 106, + 106, + 505, + 118 + ], + "score": 1.0, + "content": "for which efficient, practical algorithms are known. Having solved this assignment problem on each", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 117, + 475, + 129 + ], + "spans": [ + { + "bbox": [ + 106, + 117, + 302, + 129 + ], + "score": 1.0, + "content": "layer, we can then permute the weights of model", + "type": "text" + }, + { + "bbox": [ + 303, + 117, + 312, + 127 + ], + "score": 0.83, + "content": "B", + "type": "inline_equation" + }, + { + "bbox": [ + 312, + 117, + 378, + 129 + ], + "score": 1.0, + "content": "to match model", + "type": "text" + }, + { + "bbox": [ + 378, + 117, + 386, + 127 + ], + "score": 0.77, + "content": "A", + "type": "inline_equation" + }, + { + "bbox": [ + 387, + 117, + 475, + 129 + ], + "score": 1.0, + "content": "as closely as possible", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 1.5 + }, + { + "type": "interline_equation", + "bbox": [ + 228, + 131, + 383, + 148 + ], + "lines": [ + { + "bbox": [ + 228, + 131, + 383, + 148 + ], + "spans": [ + { + "bbox": [ + 228, + 131, + 383, + 148 + ], + "score": 0.93, + "content": "\\pmb { W } _ { \\ell } ^ { \\prime } = \\pmb { P } _ { \\ell } \\pmb { W } _ { \\ell } ^ { ( B ) } \\pmb { P } _ { \\ell - 1 } ^ { \\top } , \\quad \\pmb { b } _ { \\ell } ^ { \\prime } = \\pmb { P } _ { \\ell } \\pmb { b } _ { \\ell } ^ { ( B ) }", + "type": "interline_equation", + "image_path": "90dcbc589365f08bb72d967fdc8bec98acc4a2843edbc4b9db87e394e6ff63c6.jpg" + } + ] + } + ], + "index": 4, + "virtual_lines": [ + { + "bbox": [ + 228, + 131, + 383, + 148 + ], + "spans": [], + "index": 4 + } + ] + }, + { + "type": "text", + "bbox": [ + 110, + 150, + 482, + 163 + ], + "lines": [ + { + "bbox": [ + 107, + 149, + 479, + 165 + ], + "spans": [ + { + "bbox": [ + 107, + 149, + 164, + 165 + ], + "score": 1.0, + "content": "for each layer", + "type": "text" + }, + { + "bbox": [ + 164, + 151, + 169, + 161 + ], + "score": 0.55, + "content": "\\ell", + "type": "inline_equation" + }, + { + "bbox": [ + 169, + 149, + 249, + 165 + ], + "score": 1.0, + "content": ", producing weights", + "type": "text" + }, + { + "bbox": [ + 249, + 151, + 261, + 161 + ], + "score": 0.88, + "content": "\\Theta ^ { \\prime }", + "type": "inline_equation" + }, + { + "bbox": [ + 261, + 149, + 464, + 165 + ], + "score": 1.0, + "content": "with activations that align as closely possible with", + "type": "text" + }, + { + "bbox": [ + 465, + 151, + 479, + 162 + ], + "score": 0.9, + "content": "\\Theta _ { A }", + "type": "inline_equation" + } + ], + "index": 5 + } + ], + "index": 5 + }, + { + "type": "text", + "bbox": [ + 106, + 168, + 505, + 246 + ], + "lines": [ + { + "bbox": [ + 105, + 167, + 506, + 182 + ], + "spans": [ + { + "bbox": [ + 105, + 167, + 373, + 182 + ], + "score": 1.0, + "content": "Computationally, this entire process is relatively lightweight: the", + "type": "text" + }, + { + "bbox": [ + 373, + 168, + 395, + 179 + ], + "score": 0.9, + "content": "\\pmb { Z } ^ { ( A ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 395, + 167, + 415, + 182 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 415, + 167, + 437, + 179 + ], + "score": 0.89, + "content": "{ \\pmb Z } ^ { ( B ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 437, + 167, + 506, + 182 + ], + "score": 1.0, + "content": "matrices can be", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 178, + 506, + 194 + ], + "spans": [ + { + "bbox": [ + 105, + 178, + 506, + 194 + ], + "score": 1.0, + "content": "computed in a single pass over the training dataset, and, in practice, a full run through the training", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 191, + 505, + 203 + ], + "spans": [ + { + "bbox": [ + 106, + 191, + 505, + 203 + ], + "score": 1.0, + "content": "dataset may be unnecessary. Solving eq. (1) is possible due to well-established, polynomial-time al-", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 201, + 505, + 215 + ], + "spans": [ + { + "bbox": [ + 105, + 201, + 505, + 215 + ], + "score": 1.0, + "content": "gorithms for solving the linear assignment problem (Kuhn, 2010; Jonker & Volgenant, 1987; Crouse,", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 213, + 505, + 225 + ], + "spans": [ + { + "bbox": [ + 106, + 213, + 505, + 225 + ], + "score": 1.0, + "content": "2016). Also, conveniently, the activation matching at each layer is independent of the matching at", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 224, + 505, + 236 + ], + "spans": [ + { + "bbox": [ + 106, + 224, + 505, + 236 + ], + "score": 1.0, + "content": "every other layer, resulting in a separable and straightforward optimization problem; this advantage", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 235, + 292, + 246 + ], + "spans": [ + { + "bbox": [ + 106, + 235, + 292, + 246 + ], + "score": 1.0, + "content": "will not be enjoyed by the following methods.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 9 + }, + { + "type": "text", + "bbox": [ + 107, + 251, + 505, + 286 + ], + "lines": [ + { + "bbox": [ + 105, + 251, + 506, + 265 + ], + "spans": [ + { + "bbox": [ + 105, + 251, + 506, + 265 + ], + "score": 1.0, + "content": "Dispensing with regression, one could similarly associate units by matching against a matrix of", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 262, + 506, + 277 + ], + "spans": [ + { + "bbox": [ + 105, + 262, + 270, + 277 + ], + "score": 1.0, + "content": "cross-correlation coefficients in place of", + "type": "text" + }, + { + "bbox": [ + 270, + 262, + 327, + 276 + ], + "score": 0.94, + "content": "Z ^ { ( A ) } ( \\dot { Z } ^ { ( B ) } ) ^ { \\top }", + "type": "inline_equation" + }, + { + "bbox": [ + 327, + 262, + 506, + 277 + ], + "score": 1.0, + "content": ". We observed correlation matching to work", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 274, + 491, + 288 + ], + "spans": [ + { + "bbox": [ + 105, + 274, + 491, + 288 + ], + "score": 1.0, + "content": "equally well but found OLS regression matching to be more principled and easier to implement.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 14 + }, + { + "type": "text", + "bbox": [ + 105, + 291, + 504, + 314 + ], + "lines": [ + { + "bbox": [ + 106, + 291, + 505, + 304 + ], + "spans": [ + { + "bbox": [ + 106, + 291, + 505, + 304 + ], + "score": 1.0, + "content": "Activation matching has previously been studied for model merging in Tatro et al. (2020); Singh &", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 302, + 426, + 316 + ], + "spans": [ + { + "bbox": [ + 105, + 302, + 426, + 316 + ], + "score": 1.0, + "content": "Jaggi (2020); Li et al. (2016) albeit not from the perspective of OLS regression.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 16.5 + }, + { + "type": "title", + "bbox": [ + 108, + 326, + 223, + 338 + ], + "lines": [ + { + "bbox": [ + 106, + 326, + 224, + 339 + ], + "spans": [ + { + "bbox": [ + 106, + 326, + 224, + 339 + ], + "score": 1.0, + "content": "3.2 MATCHING WEIGHTS", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 18 + }, + { + "type": "text", + "bbox": [ + 106, + 347, + 505, + 406 + ], + "lines": [ + { + "bbox": [ + 105, + 347, + 505, + 360 + ], + "spans": [ + { + "bbox": [ + 105, + 347, + 505, + 360 + ], + "score": 1.0, + "content": "Instead of associating units by their activations, we could alternatively inspect the weights of the", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 359, + 505, + 371 + ], + "spans": [ + { + "bbox": [ + 106, + 359, + 290, + 371 + ], + "score": 1.0, + "content": "model itself. Consider the first layer weights,", + "type": "text" + }, + { + "bbox": [ + 290, + 359, + 306, + 370 + ], + "score": 0.89, + "content": "W _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 306, + 359, + 360, + 371 + ], + "score": 1.0, + "content": "; each row of", + "type": "text" + }, + { + "bbox": [ + 360, + 359, + 376, + 370 + ], + "score": 0.9, + "content": "W _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 377, + 359, + 505, + 371 + ], + "score": 1.0, + "content": "corresponds to a single feature.", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 369, + 505, + 382 + ], + "spans": [ + { + "bbox": [ + 105, + 369, + 505, + 382 + ], + "score": 1.0, + "content": "If two such rows were equal, they would compute exactly the same feature (ignoring bias terms for", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 101, + 380, + 507, + 400 + ], + "spans": [ + { + "bbox": [ + 101, + 380, + 210, + 400 + ], + "score": 1.0, + "content": "the time being). And, if", + "type": "text" + }, + { + "bbox": [ + 210, + 380, + 306, + 395 + ], + "score": 0.92, + "content": "[ \\pmb { W } _ { 1 } ^ { ( A ) } ] _ { i , : } \\approx [ \\pmb { W } _ { 1 } ^ { ( B ) } ] _ { j , : }", + "type": "inline_equation" + }, + { + "bbox": [ + 307, + 381, + 430, + 398 + ], + "score": 1.0, + "content": ", it stands to reason that units", + "type": "text" + }, + { + "bbox": [ + 430, + 384, + 435, + 393 + ], + "score": 0.73, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 436, + 381, + 454, + 398 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 455, + 384, + 461, + 395 + ], + "score": 0.81, + "content": "j", + "type": "inline_equation" + }, + { + "bbox": [ + 461, + 381, + 507, + 398 + ], + "score": 1.0, + "content": "should be", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 394, + 462, + 407 + ], + "spans": [ + { + "bbox": [ + 105, + 394, + 462, + 407 + ], + "score": 1.0, + "content": "associated. Extending this idea to every layer, we are inspired to pursue the optimization", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 21 + }, + { + "type": "interline_equation", + "bbox": [ + 153, + 407, + 456, + 429 + ], + "lines": [ + { + "bbox": [ + 153, + 407, + 456, + 429 + ], + "spans": [ + { + "bbox": [ + 153, + 407, + 456, + 429 + ], + "score": 0.89, + "content": "\\underset { \\pi } { \\arg \\operatorname* { m i n } } \\ \\| \\mathrm { v e c } ( \\Theta _ { A } ) - \\mathrm { v e c } ( \\pi ( \\Theta _ { B } ) ) \\| ^ { 2 } = \\underset { \\pi } { \\arg \\operatorname* { m a x } } \\ \\mathrm { v e c } ( \\Theta _ { A } ) \\cdot \\mathrm { v e c } ( \\pi ( \\Theta _ { B } ) ) .", + "type": "interline_equation", + "image_path": "ccac0ad022d9b4a00fd7b103057d8e82de0d6151108ae319b214b4f742acf009.jpg" + } + ] + } + ], + "index": 24, + "virtual_lines": [ + { + "bbox": [ + 153, + 407, + 456, + 429 + ], + "spans": [], + "index": 24 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 431, + 311, + 443 + ], + "lines": [ + { + "bbox": [ + 106, + 429, + 312, + 445 + ], + "spans": [ + { + "bbox": [ + 106, + 429, + 312, + 445 + ], + "score": 1.0, + "content": "We can re-express this in terms of the full weights,", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 25 + }, + { + "type": "interline_equation", + "bbox": [ + 116, + 445, + 482, + 472 + ], + "lines": [ + { + "bbox": [ + 116, + 445, + 482, + 472 + ], + "spans": [ + { + "bbox": [ + 116, + 445, + 482, + 472 + ], + "score": 0.88, + "content": "\\operatorname * { a r g m a x } _ { \\pi = \\{ P _ { i } \\} } \\langle { \\pmb W } _ { 1 } ^ { ( A ) } , { \\pmb P } _ { 1 } { \\pmb W } _ { 1 } ^ { ( B ) } \\rangle _ { F } + \\langle { \\pmb W } _ { 2 } ^ { ( A ) } , { \\pmb P } _ { 2 } { \\pmb W } _ { 2 } ^ { ( B ) } { \\pmb P } _ { 1 } ^ { \\top } \\rangle _ { F } + \\cdot \\cdot + \\langle { \\pmb W } _ { L } ^ { ( A ) } , { \\pmb W } _ { L } ^ { ( B ) } { \\pmb P } _ { L - 1 } ^ { \\top } \\rangle _ { F } ,", + "type": "interline_equation", + "image_path": "58b834d3484224836a28b0db421ea6bad78e819bdbb2b79252c52a58a4367cd2.jpg" + } + ] + } + ], + "index": 27, + "virtual_lines": [ + { + "bbox": [ + 116, + 445, + 482, + 454.0 + ], + "spans": [], + "index": 26 + }, + { + "bbox": [ + 116, + 454.0, + 482, + 463.0 + ], + "spans": [], + "index": 27 + }, + { + "bbox": [ + 116, + 463.0, + 482, + 472.0 + ], + "spans": [], + "index": 28 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 473, + 505, + 532 + ], + "lines": [ + { + "bbox": [ + 106, + 474, + 505, + 486 + ], + "spans": [ + { + "bbox": [ + 106, + 474, + 505, + 486 + ], + "score": 1.0, + "content": "resulting in another matching problem. We term this formulation the “sum of bilinear assignments", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 484, + 505, + 498 + ], + "spans": [ + { + "bbox": [ + 106, + 484, + 505, + 498 + ], + "score": 1.0, + "content": "problem” (SOBLAP). Unfortunately, this matching problem is thornier than the classic linear as-", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 496, + 505, + 509 + ], + "spans": [ + { + "bbox": [ + 105, + 496, + 505, + 509 + ], + "score": 1.0, + "content": "signment matching problem presented in eq. (1). Unlike LAP, we are interested in permuting both", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 104, + 507, + 505, + 523 + ], + "spans": [ + { + "bbox": [ + 104, + 507, + 208, + 523 + ], + "score": 1.0, + "content": "the rows and columns of", + "type": "text" + }, + { + "bbox": [ + 208, + 507, + 234, + 522 + ], + "score": 0.93, + "content": "W _ { \\ell } ^ { ( B ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 232, + 507, + 303, + 523 + ], + "score": 1.0, + "content": ") to match W (A)ℓ ,", + "type": "text" + }, + { + "bbox": [ + 300, + 508, + 505, + 523 + ], + "score": 1.0, + "content": "which fundamentally differs from permuting only", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 520, + 356, + 533 + ], + "spans": [ + { + "bbox": [ + 106, + 520, + 356, + 533 + ], + "score": 1.0, + "content": "rows or only columns. We formalize this difficulty as follows.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 31 + }, + { + "type": "text", + "bbox": [ + 106, + 534, + 501, + 557 + ], + "lines": [ + { + "bbox": [ + 106, + 534, + 504, + 547 + ], + "spans": [ + { + "bbox": [ + 106, + 534, + 504, + 547 + ], + "score": 1.0, + "content": "Lemma 1. The sum of a bilinear assignments problem (SOBLAP) is NP-hard and admits no", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 546, + 374, + 558 + ], + "spans": [ + { + "bbox": [ + 105, + 546, + 344, + 558 + ], + "score": 1.0, + "content": "polynomial-time constant-factor approximation scheme for", + "type": "text" + }, + { + "bbox": [ + 344, + 546, + 370, + 556 + ], + "score": 0.88, + "content": "L > 2", + "type": "inline_equation" + }, + { + "bbox": [ + 371, + 546, + 374, + 558 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 34.5 + }, + { + "type": "text", + "bbox": [ + 106, + 565, + 493, + 577 + ], + "lines": [ + { + "bbox": [ + 105, + 564, + 495, + 579 + ], + "spans": [ + { + "bbox": [ + 105, + 564, + 495, + 579 + ], + "score": 1.0, + "content": "Lemma 1 contrasts starkly with classical LAP, for which polynomial-time algorithms are known.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 36 + }, + { + "type": "text", + "bbox": [ + 106, + 582, + 504, + 605 + ], + "lines": [ + { + "bbox": [ + 106, + 582, + 506, + 595 + ], + "spans": [ + { + "bbox": [ + 106, + 582, + 465, + 595 + ], + "score": 1.0, + "content": "Undeterred, we propose a approximation algorithm for SOBLAP. Looking at a single", + "type": "text" + }, + { + "bbox": [ + 466, + 583, + 478, + 594 + ], + "score": 0.86, + "content": "P _ { \\ell }", + "type": "inline_equation" + }, + { + "bbox": [ + 478, + 582, + 506, + 595 + ], + "score": 1.0, + "content": "while", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 593, + 453, + 606 + ], + "spans": [ + { + "bbox": [ + 105, + 593, + 453, + 606 + ], + "score": 1.0, + "content": "holding the others fixed, we observe that the problem can be reduced to a classic LAP,", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 37.5 + }, + { + "type": "interline_equation", + "bbox": [ + 149, + 607, + 463, + 657 + ], + "lines": [ + { + "bbox": [ + 149, + 607, + 463, + 657 + ], + "spans": [ + { + "bbox": [ + 149, + 607, + 463, + 657 + ], + "score": 0.9, + "content": "\\begin{array} { r l } & { \\underset { P _ { \\ell } } { \\arg \\operatorname* { m a x } } \\ \\langle { \\boldsymbol W } _ { \\ell } ^ { ( A ) } , P _ { \\ell } { \\boldsymbol W } _ { \\ell } ^ { ( B ) } { \\boldsymbol P } _ { \\ell - 1 } ^ { \\top } \\rangle _ { F } + \\langle { \\boldsymbol W } _ { \\ell + 1 } ^ { ( A ) } , P _ { \\ell + 1 } { \\boldsymbol W } _ { \\ell + 1 } ^ { ( B ) } { \\boldsymbol P } _ { \\ell } ^ { \\top } \\rangle _ { F } } \\\\ & { \\qquad = \\underset { P _ { \\ell } } { \\arg \\operatorname* { m a x } } \\ \\langle P _ { \\ell } , { \\boldsymbol W } _ { \\ell } ^ { ( A ) } { \\boldsymbol P } _ { \\ell - 1 } ( { \\boldsymbol W } _ { \\ell } ^ { ( B ) } ) ^ { \\top } + ( { \\boldsymbol W } _ { \\ell + 1 } ^ { ( A ) } ) ^ { \\top } P _ { \\ell + 1 } { \\boldsymbol W } _ { \\ell + 1 } ^ { ( B ) } \\rangle _ { F } . } \\end{array}", + "type": "interline_equation", + "image_path": "4447cd1d6a13725ed51f953c610d4b3e8d0f89dee4f989f069596808c91fb38e.jpg" + } + ] + } + ], + "index": 40, + "virtual_lines": [ + { + "bbox": [ + 149, + 607, + 463, + 623.6666666666666 + ], + "spans": [], + "index": 39 + }, + { + "bbox": [ + 149, + 623.6666666666666, + 463, + 640.3333333333333 + ], + "spans": [], + "index": 40 + }, + { + "bbox": [ + 149, + 640.3333333333333, + 463, + 656.9999999999999 + ], + "spans": [], + "index": 41 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 659, + 502, + 682 + ], + "lines": [ + { + "bbox": [ + 105, + 658, + 504, + 673 + ], + "spans": [ + { + "bbox": [ + 105, + 658, + 504, + 673 + ], + "score": 1.0, + "content": "This leads to a convenient coordinate descent algorithm: go through each layer and greedily select", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 671, + 388, + 684 + ], + "spans": [ + { + "bbox": [ + 106, + 671, + 137, + 684 + ], + "score": 1.0, + "content": "its best", + "type": "text" + }, + { + "bbox": [ + 137, + 671, + 149, + 682 + ], + "score": 0.86, + "content": "P _ { \\ell }", + "type": "inline_equation" + }, + { + "bbox": [ + 149, + 671, + 388, + 684 + ], + "score": 1.0, + "content": ". Repeat until convergence. We present this in Algorithm 1.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 42.5 + }, + { + "type": "text", + "bbox": [ + 107, + 687, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 688, + 504, + 700 + ], + "spans": [ + { + "bbox": [ + 106, + 688, + 504, + 700 + ], + "score": 1.0, + "content": "Although we present Algorithm 1 in terms of an MLP without bias terms, in practice our imple-", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "score": 1.0, + "content": "mentation can handle the weights of models of nearly arbitrary architectures, including bias terms,", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 709, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 505, + 723 + ], + "score": 1.0, + "content": "residual connections, convolutional layers, attention mechanisms, and so forth. We propose an ex-", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 720, + 450, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 450, + 734 + ], + "score": 1.0, + "content": "tension of Algorithm 1 to merging more than two models at a time in Appendix A.10.", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 45.5 + } + ], + "page_idx": 3, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 26, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 25, + 293, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 25, + 293, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2023", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 308, + 759 + ], + "lines": [ + { + "bbox": [ + 302, + 750, + 310, + 762 + ], + "spans": [ + { + "bbox": [ + 302, + 750, + 310, + 762 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 12, + "width": 8 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 81, + 505, + 128 + ], + "lines": [ + { + "bbox": [ + 105, + 81, + 506, + 97 + ], + "spans": [ + { + "bbox": [ + 105, + 81, + 133, + 97 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 134, + 82, + 239, + 96 + ], + "score": 0.93, + "content": "\\begin{array} { r } { \\langle { \\boldsymbol A } , { \\boldsymbol B } \\rangle _ { F } = \\sum _ { i , j } A _ { i , j } B _ { i , j } } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 240, + 81, + 506, + 97 + ], + "score": 1.0, + "content": "denotes the Frobenius inner product between real-valued matrices", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 107, + 93, + 505, + 108 + ], + "spans": [ + { + "bbox": [ + 107, + 95, + 117, + 105 + ], + "score": 0.73, + "content": "\\pmb { A }", + "type": "inline_equation" + }, + { + "bbox": [ + 117, + 93, + 135, + 108 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 135, + 96, + 145, + 105 + ], + "score": 0.73, + "content": "\\textbf { { B } }", + "type": "inline_equation" + }, + { + "bbox": [ + 145, + 93, + 505, + 108 + ], + "score": 1.0, + "content": ". Conveniently, eq. (1) constitutes a “linear assignment problem” (LAP) (Bertsekas, 1998)", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 106, + 505, + 118 + ], + "spans": [ + { + "bbox": [ + 106, + 106, + 505, + 118 + ], + "score": 1.0, + "content": "for which efficient, practical algorithms are known. Having solved this assignment problem on each", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 117, + 475, + 129 + ], + "spans": [ + { + "bbox": [ + 106, + 117, + 302, + 129 + ], + "score": 1.0, + "content": "layer, we can then permute the weights of model", + "type": "text" + }, + { + "bbox": [ + 303, + 117, + 312, + 127 + ], + "score": 0.83, + "content": "B", + "type": "inline_equation" + }, + { + "bbox": [ + 312, + 117, + 378, + 129 + ], + "score": 1.0, + "content": "to match model", + "type": "text" + }, + { + "bbox": [ + 378, + 117, + 386, + 127 + ], + "score": 0.77, + "content": "A", + "type": "inline_equation" + }, + { + "bbox": [ + 387, + 117, + 475, + 129 + ], + "score": 1.0, + "content": "as closely as possible", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 1.5, + "bbox_fs": [ + 105, + 81, + 506, + 129 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 228, + 131, + 383, + 148 + ], + "lines": [ + { + "bbox": [ + 228, + 131, + 383, + 148 + ], + "spans": [ + { + "bbox": [ + 228, + 131, + 383, + 148 + ], + "score": 0.93, + "content": "\\pmb { W } _ { \\ell } ^ { \\prime } = \\pmb { P } _ { \\ell } \\pmb { W } _ { \\ell } ^ { ( B ) } \\pmb { P } _ { \\ell - 1 } ^ { \\top } , \\quad \\pmb { b } _ { \\ell } ^ { \\prime } = \\pmb { P } _ { \\ell } \\pmb { b } _ { \\ell } ^ { ( B ) }", + "type": "interline_equation", + "image_path": "90dcbc589365f08bb72d967fdc8bec98acc4a2843edbc4b9db87e394e6ff63c6.jpg" + } + ] + } + ], + "index": 4, + "virtual_lines": [ + { + "bbox": [ + 228, + 131, + 383, + 148 + ], + "spans": [], + "index": 4 + } + ] + }, + { + "type": "text", + "bbox": [ + 110, + 150, + 482, + 163 + ], + "lines": [ + { + "bbox": [ + 107, + 149, + 479, + 165 + ], + "spans": [ + { + "bbox": [ + 107, + 149, + 164, + 165 + ], + "score": 1.0, + "content": "for each layer", + "type": "text" + }, + { + "bbox": [ + 164, + 151, + 169, + 161 + ], + "score": 0.55, + "content": "\\ell", + "type": "inline_equation" + }, + { + "bbox": [ + 169, + 149, + 249, + 165 + ], + "score": 1.0, + "content": ", producing weights", + "type": "text" + }, + { + "bbox": [ + 249, + 151, + 261, + 161 + ], + "score": 0.88, + "content": "\\Theta ^ { \\prime }", + "type": "inline_equation" + }, + { + "bbox": [ + 261, + 149, + 464, + 165 + ], + "score": 1.0, + "content": "with activations that align as closely possible with", + "type": "text" + }, + { + "bbox": [ + 465, + 151, + 479, + 162 + ], + "score": 0.9, + "content": "\\Theta _ { A }", + "type": "inline_equation" + } + ], + "index": 5 + } + ], + "index": 5, + "bbox_fs": [ + 107, + 149, + 479, + 165 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 168, + 505, + 246 + ], + "lines": [ + { + "bbox": [ + 105, + 167, + 506, + 182 + ], + "spans": [ + { + "bbox": [ + 105, + 167, + 373, + 182 + ], + "score": 1.0, + "content": "Computationally, this entire process is relatively lightweight: the", + "type": "text" + }, + { + "bbox": [ + 373, + 168, + 395, + 179 + ], + "score": 0.9, + "content": "\\pmb { Z } ^ { ( A ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 395, + 167, + 415, + 182 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 415, + 167, + 437, + 179 + ], + "score": 0.89, + "content": "{ \\pmb Z } ^ { ( B ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 437, + 167, + 506, + 182 + ], + "score": 1.0, + "content": "matrices can be", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 178, + 506, + 194 + ], + "spans": [ + { + "bbox": [ + 105, + 178, + 506, + 194 + ], + "score": 1.0, + "content": "computed in a single pass over the training dataset, and, in practice, a full run through the training", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 191, + 505, + 203 + ], + "spans": [ + { + "bbox": [ + 106, + 191, + 505, + 203 + ], + "score": 1.0, + "content": "dataset may be unnecessary. Solving eq. (1) is possible due to well-established, polynomial-time al-", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 201, + 505, + 215 + ], + "spans": [ + { + "bbox": [ + 105, + 201, + 505, + 215 + ], + "score": 1.0, + "content": "gorithms for solving the linear assignment problem (Kuhn, 2010; Jonker & Volgenant, 1987; Crouse,", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 213, + 505, + 225 + ], + "spans": [ + { + "bbox": [ + 106, + 213, + 505, + 225 + ], + "score": 1.0, + "content": "2016). Also, conveniently, the activation matching at each layer is independent of the matching at", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 224, + 505, + 236 + ], + "spans": [ + { + "bbox": [ + 106, + 224, + 505, + 236 + ], + "score": 1.0, + "content": "every other layer, resulting in a separable and straightforward optimization problem; this advantage", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 235, + 292, + 246 + ], + "spans": [ + { + "bbox": [ + 106, + 235, + 292, + 246 + ], + "score": 1.0, + "content": "will not be enjoyed by the following methods.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 9, + "bbox_fs": [ + 105, + 167, + 506, + 246 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 251, + 505, + 286 + ], + "lines": [ + { + "bbox": [ + 105, + 251, + 506, + 265 + ], + "spans": [ + { + "bbox": [ + 105, + 251, + 506, + 265 + ], + "score": 1.0, + "content": "Dispensing with regression, one could similarly associate units by matching against a matrix of", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 262, + 506, + 277 + ], + "spans": [ + { + "bbox": [ + 105, + 262, + 270, + 277 + ], + "score": 1.0, + "content": "cross-correlation coefficients in place of", + "type": "text" + }, + { + "bbox": [ + 270, + 262, + 327, + 276 + ], + "score": 0.94, + "content": "Z ^ { ( A ) } ( \\dot { Z } ^ { ( B ) } ) ^ { \\top }", + "type": "inline_equation" + }, + { + "bbox": [ + 327, + 262, + 506, + 277 + ], + "score": 1.0, + "content": ". We observed correlation matching to work", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 274, + 491, + 288 + ], + "spans": [ + { + "bbox": [ + 105, + 274, + 491, + 288 + ], + "score": 1.0, + "content": "equally well but found OLS regression matching to be more principled and easier to implement.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 14, + "bbox_fs": [ + 105, + 251, + 506, + 288 + ] + }, + { + "type": "text", + "bbox": [ + 105, + 291, + 504, + 314 + ], + "lines": [ + { + "bbox": [ + 106, + 291, + 505, + 304 + ], + "spans": [ + { + "bbox": [ + 106, + 291, + 505, + 304 + ], + "score": 1.0, + "content": "Activation matching has previously been studied for model merging in Tatro et al. (2020); Singh &", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 302, + 426, + 316 + ], + "spans": [ + { + "bbox": [ + 105, + 302, + 426, + 316 + ], + "score": 1.0, + "content": "Jaggi (2020); Li et al. (2016) albeit not from the perspective of OLS regression.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 16.5, + "bbox_fs": [ + 105, + 291, + 505, + 316 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 326, + 223, + 338 + ], + "lines": [ + { + "bbox": [ + 106, + 326, + 224, + 339 + ], + "spans": [ + { + "bbox": [ + 106, + 326, + 224, + 339 + ], + "score": 1.0, + "content": "3.2 MATCHING WEIGHTS", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 18 + }, + { + "type": "text", + "bbox": [ + 106, + 347, + 505, + 406 + ], + "lines": [ + { + "bbox": [ + 105, + 347, + 505, + 360 + ], + "spans": [ + { + "bbox": [ + 105, + 347, + 505, + 360 + ], + "score": 1.0, + "content": "Instead of associating units by their activations, we could alternatively inspect the weights of the", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 359, + 505, + 371 + ], + "spans": [ + { + "bbox": [ + 106, + 359, + 290, + 371 + ], + "score": 1.0, + "content": "model itself. Consider the first layer weights,", + "type": "text" + }, + { + "bbox": [ + 290, + 359, + 306, + 370 + ], + "score": 0.89, + "content": "W _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 306, + 359, + 360, + 371 + ], + "score": 1.0, + "content": "; each row of", + "type": "text" + }, + { + "bbox": [ + 360, + 359, + 376, + 370 + ], + "score": 0.9, + "content": "W _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 377, + 359, + 505, + 371 + ], + "score": 1.0, + "content": "corresponds to a single feature.", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 369, + 505, + 382 + ], + "spans": [ + { + "bbox": [ + 105, + 369, + 505, + 382 + ], + "score": 1.0, + "content": "If two such rows were equal, they would compute exactly the same feature (ignoring bias terms for", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 101, + 380, + 507, + 400 + ], + "spans": [ + { + "bbox": [ + 101, + 380, + 210, + 400 + ], + "score": 1.0, + "content": "the time being). And, if", + "type": "text" + }, + { + "bbox": [ + 210, + 380, + 306, + 395 + ], + "score": 0.92, + "content": "[ \\pmb { W } _ { 1 } ^ { ( A ) } ] _ { i , : } \\approx [ \\pmb { W } _ { 1 } ^ { ( B ) } ] _ { j , : }", + "type": "inline_equation" + }, + { + "bbox": [ + 307, + 381, + 430, + 398 + ], + "score": 1.0, + "content": ", it stands to reason that units", + "type": "text" + }, + { + "bbox": [ + 430, + 384, + 435, + 393 + ], + "score": 0.73, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 436, + 381, + 454, + 398 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 455, + 384, + 461, + 395 + ], + "score": 0.81, + "content": "j", + "type": "inline_equation" + }, + { + "bbox": [ + 461, + 381, + 507, + 398 + ], + "score": 1.0, + "content": "should be", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 394, + 462, + 407 + ], + "spans": [ + { + "bbox": [ + 105, + 394, + 462, + 407 + ], + "score": 1.0, + "content": "associated. Extending this idea to every layer, we are inspired to pursue the optimization", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 21, + "bbox_fs": [ + 101, + 347, + 507, + 407 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 153, + 407, + 456, + 429 + ], + "lines": [ + { + "bbox": [ + 153, + 407, + 456, + 429 + ], + "spans": [ + { + "bbox": [ + 153, + 407, + 456, + 429 + ], + "score": 0.89, + "content": "\\underset { \\pi } { \\arg \\operatorname* { m i n } } \\ \\| \\mathrm { v e c } ( \\Theta _ { A } ) - \\mathrm { v e c } ( \\pi ( \\Theta _ { B } ) ) \\| ^ { 2 } = \\underset { \\pi } { \\arg \\operatorname* { m a x } } \\ \\mathrm { v e c } ( \\Theta _ { A } ) \\cdot \\mathrm { v e c } ( \\pi ( \\Theta _ { B } ) ) .", + "type": "interline_equation", + "image_path": "ccac0ad022d9b4a00fd7b103057d8e82de0d6151108ae319b214b4f742acf009.jpg" + } + ] + } + ], + "index": 24, + "virtual_lines": [ + { + "bbox": [ + 153, + 407, + 456, + 429 + ], + "spans": [], + "index": 24 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 431, + 311, + 443 + ], + "lines": [ + { + "bbox": [ + 106, + 429, + 312, + 445 + ], + "spans": [ + { + "bbox": [ + 106, + 429, + 312, + 445 + ], + "score": 1.0, + "content": "We can re-express this in terms of the full weights,", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 25, + "bbox_fs": [ + 106, + 429, + 312, + 445 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 116, + 445, + 482, + 472 + ], + "lines": [ + { + "bbox": [ + 116, + 445, + 482, + 472 + ], + "spans": [ + { + "bbox": [ + 116, + 445, + 482, + 472 + ], + "score": 0.88, + "content": "\\operatorname * { a r g m a x } _ { \\pi = \\{ P _ { i } \\} } \\langle { \\pmb W } _ { 1 } ^ { ( A ) } , { \\pmb P } _ { 1 } { \\pmb W } _ { 1 } ^ { ( B ) } \\rangle _ { F } + \\langle { \\pmb W } _ { 2 } ^ { ( A ) } , { \\pmb P } _ { 2 } { \\pmb W } _ { 2 } ^ { ( B ) } { \\pmb P } _ { 1 } ^ { \\top } \\rangle _ { F } + \\cdot \\cdot + \\langle { \\pmb W } _ { L } ^ { ( A ) } , { \\pmb W } _ { L } ^ { ( B ) } { \\pmb P } _ { L - 1 } ^ { \\top } \\rangle _ { F } ,", + "type": "interline_equation", + "image_path": "58b834d3484224836a28b0db421ea6bad78e819bdbb2b79252c52a58a4367cd2.jpg" + } + ] + } + ], + "index": 27, + "virtual_lines": [ + { + "bbox": [ + 116, + 445, + 482, + 454.0 + ], + "spans": [], + "index": 26 + }, + { + "bbox": [ + 116, + 454.0, + 482, + 463.0 + ], + "spans": [], + "index": 27 + }, + { + "bbox": [ + 116, + 463.0, + 482, + 472.0 + ], + "spans": [], + "index": 28 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 473, + 505, + 532 + ], + "lines": [ + { + "bbox": [ + 106, + 474, + 505, + 486 + ], + "spans": [ + { + "bbox": [ + 106, + 474, + 505, + 486 + ], + "score": 1.0, + "content": "resulting in another matching problem. We term this formulation the “sum of bilinear assignments", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 484, + 505, + 498 + ], + "spans": [ + { + "bbox": [ + 106, + 484, + 505, + 498 + ], + "score": 1.0, + "content": "problem” (SOBLAP). Unfortunately, this matching problem is thornier than the classic linear as-", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 496, + 505, + 509 + ], + "spans": [ + { + "bbox": [ + 105, + 496, + 505, + 509 + ], + "score": 1.0, + "content": "signment matching problem presented in eq. (1). Unlike LAP, we are interested in permuting both", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 104, + 507, + 505, + 523 + ], + "spans": [ + { + "bbox": [ + 104, + 507, + 208, + 523 + ], + "score": 1.0, + "content": "the rows and columns of", + "type": "text" + }, + { + "bbox": [ + 208, + 507, + 234, + 522 + ], + "score": 0.93, + "content": "W _ { \\ell } ^ { ( B ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 232, + 507, + 303, + 523 + ], + "score": 1.0, + "content": ") to match W (A)ℓ ,", + "type": "text" + }, + { + "bbox": [ + 300, + 508, + 505, + 523 + ], + "score": 1.0, + "content": "which fundamentally differs from permuting only", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 520, + 356, + 533 + ], + "spans": [ + { + "bbox": [ + 106, + 520, + 356, + 533 + ], + "score": 1.0, + "content": "rows or only columns. We formalize this difficulty as follows.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 31, + "bbox_fs": [ + 104, + 474, + 505, + 533 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 534, + 501, + 557 + ], + "lines": [ + { + "bbox": [ + 106, + 534, + 504, + 547 + ], + "spans": [ + { + "bbox": [ + 106, + 534, + 504, + 547 + ], + "score": 1.0, + "content": "Lemma 1. The sum of a bilinear assignments problem (SOBLAP) is NP-hard and admits no", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 546, + 374, + 558 + ], + "spans": [ + { + "bbox": [ + 105, + 546, + 344, + 558 + ], + "score": 1.0, + "content": "polynomial-time constant-factor approximation scheme for", + "type": "text" + }, + { + "bbox": [ + 344, + 546, + 370, + 556 + ], + "score": 0.88, + "content": "L > 2", + "type": "inline_equation" + }, + { + "bbox": [ + 371, + 546, + 374, + 558 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 34.5, + "bbox_fs": [ + 105, + 534, + 504, + 558 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 565, + 493, + 577 + ], + "lines": [ + { + "bbox": [ + 105, + 564, + 495, + 579 + ], + "spans": [ + { + "bbox": [ + 105, + 564, + 495, + 579 + ], + "score": 1.0, + "content": "Lemma 1 contrasts starkly with classical LAP, for which polynomial-time algorithms are known.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 36, + "bbox_fs": [ + 105, + 564, + 495, + 579 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 582, + 504, + 605 + ], + "lines": [ + { + "bbox": [ + 106, + 582, + 506, + 595 + ], + "spans": [ + { + "bbox": [ + 106, + 582, + 465, + 595 + ], + "score": 1.0, + "content": "Undeterred, we propose a approximation algorithm for SOBLAP. Looking at a single", + "type": "text" + }, + { + "bbox": [ + 466, + 583, + 478, + 594 + ], + "score": 0.86, + "content": "P _ { \\ell }", + "type": "inline_equation" + }, + { + "bbox": [ + 478, + 582, + 506, + 595 + ], + "score": 1.0, + "content": "while", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 593, + 453, + 606 + ], + "spans": [ + { + "bbox": [ + 105, + 593, + 453, + 606 + ], + "score": 1.0, + "content": "holding the others fixed, we observe that the problem can be reduced to a classic LAP,", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 37.5, + "bbox_fs": [ + 105, + 582, + 506, + 606 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 149, + 607, + 463, + 657 + ], + "lines": [ + { + "bbox": [ + 149, + 607, + 463, + 657 + ], + "spans": [ + { + "bbox": [ + 149, + 607, + 463, + 657 + ], + "score": 0.9, + "content": "\\begin{array} { r l } & { \\underset { P _ { \\ell } } { \\arg \\operatorname* { m a x } } \\ \\langle { \\boldsymbol W } _ { \\ell } ^ { ( A ) } , P _ { \\ell } { \\boldsymbol W } _ { \\ell } ^ { ( B ) } { \\boldsymbol P } _ { \\ell - 1 } ^ { \\top } \\rangle _ { F } + \\langle { \\boldsymbol W } _ { \\ell + 1 } ^ { ( A ) } , P _ { \\ell + 1 } { \\boldsymbol W } _ { \\ell + 1 } ^ { ( B ) } { \\boldsymbol P } _ { \\ell } ^ { \\top } \\rangle _ { F } } \\\\ & { \\qquad = \\underset { P _ { \\ell } } { \\arg \\operatorname* { m a x } } \\ \\langle P _ { \\ell } , { \\boldsymbol W } _ { \\ell } ^ { ( A ) } { \\boldsymbol P } _ { \\ell - 1 } ( { \\boldsymbol W } _ { \\ell } ^ { ( B ) } ) ^ { \\top } + ( { \\boldsymbol W } _ { \\ell + 1 } ^ { ( A ) } ) ^ { \\top } P _ { \\ell + 1 } { \\boldsymbol W } _ { \\ell + 1 } ^ { ( B ) } \\rangle _ { F } . } \\end{array}", + "type": "interline_equation", + "image_path": "4447cd1d6a13725ed51f953c610d4b3e8d0f89dee4f989f069596808c91fb38e.jpg" + } + ] + } + ], + "index": 40, + "virtual_lines": [ + { + "bbox": [ + 149, + 607, + 463, + 623.6666666666666 + ], + "spans": [], + "index": 39 + }, + { + "bbox": [ + 149, + 623.6666666666666, + 463, + 640.3333333333333 + ], + "spans": [], + "index": 40 + }, + { + "bbox": [ + 149, + 640.3333333333333, + 463, + 656.9999999999999 + ], + "spans": [], + "index": 41 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 659, + 502, + 682 + ], + "lines": [ + { + "bbox": [ + 105, + 658, + 504, + 673 + ], + "spans": [ + { + "bbox": [ + 105, + 658, + 504, + 673 + ], + "score": 1.0, + "content": "This leads to a convenient coordinate descent algorithm: go through each layer and greedily select", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 671, + 388, + 684 + ], + "spans": [ + { + "bbox": [ + 106, + 671, + 137, + 684 + ], + "score": 1.0, + "content": "its best", + "type": "text" + }, + { + "bbox": [ + 137, + 671, + 149, + 682 + ], + "score": 0.86, + "content": "P _ { \\ell }", + "type": "inline_equation" + }, + { + "bbox": [ + 149, + 671, + 388, + 684 + ], + "score": 1.0, + "content": ". Repeat until convergence. We present this in Algorithm 1.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 42.5, + "bbox_fs": [ + 105, + 658, + 504, + 684 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 687, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 688, + 504, + 700 + ], + "spans": [ + { + "bbox": [ + 106, + 688, + 504, + 700 + ], + "score": 1.0, + "content": "Although we present Algorithm 1 in terms of an MLP without bias terms, in practice our imple-", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 506, + 712 + ], + "score": 1.0, + "content": "mentation can handle the weights of models of nearly arbitrary architectures, including bias terms,", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 709, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 505, + 723 + ], + "score": 1.0, + "content": "residual connections, convolutional layers, attention mechanisms, and so forth. We propose an ex-", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 720, + 450, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 450, + 734 + ], + "score": 1.0, + "content": "tension of Algorithm 1 to merging more than two models at a time in Appendix A.10.", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 45.5, + "bbox_fs": [ + 105, + 688, + 506, + 734 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 113, + 81, + 497, + 149 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 113, + 81, + 497, + 149 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 113, + 81, + 497, + 149 + ], + "spans": [ + { + "bbox": [ + 113, + 81, + 497, + 149 + ], + "score": 0.958, + "type": "image", + "image_path": "6728305d713c85f40792a9007e2fd199d0797f18b8248371f77b8af3c0dced39.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 113, + 81, + 497, + 103.66666666666667 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 113, + 103.66666666666667, + 497, + 126.33333333333334 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 113, + 126.33333333333334, + 497, + 149.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 155, + 505, + 222 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 155, + 505, + 168 + ], + "spans": [ + { + "bbox": [ + 105, + 155, + 505, + 168 + ], + "score": 1.0, + "content": "Figure 2: Linear mode connectivity is possible after permuting. Loss landscapes when interpo-", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 165, + 505, + 180 + ], + "spans": [ + { + "bbox": [ + 105, + 165, + 505, + 180 + ], + "score": 1.0, + "content": "lating between models trained on MNIST, CIFAR-10, and ImageNet. In all cases we can signifi-", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 177, + 506, + 190 + ], + "spans": [ + { + "bbox": [ + 106, + 177, + 506, + 190 + ], + "score": 1.0, + "content": "cantly improve over na¨ıve interpolation. Straight-through estimator matching performs best but is", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 188, + 506, + 201 + ], + "spans": [ + { + "bbox": [ + 105, + 188, + 506, + 201 + ], + "score": 1.0, + "content": "very computationally expensive. Weight and activation matching perform similarly, although weight", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 199, + 505, + 212 + ], + "spans": [ + { + "bbox": [ + 105, + 199, + 505, + 212 + ], + "score": 1.0, + "content": "matching is orders of magnitude faster and does not rely on the input data distribution. We hypoth-", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 210, + 497, + 223 + ], + "spans": [ + { + "bbox": [ + 105, + 210, + 497, + 223 + ], + "score": 1.0, + "content": "esize that the ImageNet barrier could be reduced by increasing the model width as in Section 5.3.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 5.5 + } + ], + "index": 3.25 + }, + { + "type": "table", + "bbox": [ + 105, + 244, + 503, + 391 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 106, + 239, + 325, + 252 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 239, + 326, + 253 + ], + "spans": [ + { + "bbox": [ + 106, + 239, + 326, + 253 + ], + "score": 1.0, + "content": "Algorithm 1: PERMUTATIONCOORDINATEDESCENT", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 9 + }, + { + "type": "table_body", + "bbox": [ + 105, + 244, + 503, + 391 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 244, + 503, + 391 + ], + "spans": [ + { + "bbox": [ + 105, + 244, + 503, + 391 + ], + "score": 0.753, + "html": "
AIgorIthmI:PERMUTATIONCOORDINATEDESCENT Given:Mode weigts A = {w(4),., [4)} and θB ={~w(B),.. W}
Result: A permutation π = {P1,...,PL-1} of OB such that vec(ΘA) · vec(π(OB)) is approximately maximized.
Initialize:Pl←I,...,PL-1 ←I
repeat
for l∈RANDOMPERMUTATION(1,...,L-1) do
P←SOLvELAP（W()P-1(W(B）+(W(）1W)）
end until convergence
", + "type": "table", + "image_path": "3433ccab35bbbe356ec4ce2ae88f1f5b8c19fdd9f37263c6f1964bb9d1e4e9bf.jpg" + } + ] + } + ], + "index": 11, + "virtual_lines": [ + { + "bbox": [ + 105, + 244, + 503, + 293.0 + ], + "spans": [], + "index": 10 + }, + { + "bbox": [ + 105, + 293.0, + 503, + 342.0 + ], + "spans": [], + "index": 11 + }, + { + "bbox": [ + 105, + 342.0, + 503, + 391.0 + ], + "spans": [], + "index": 12 + } + ] + }, + { + "type": "table_caption", + "bbox": [ + 106, + 417, + 249, + 429 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 416, + 251, + 430 + ], + "spans": [ + { + "bbox": [ + 106, + 416, + 251, + 430 + ], + "score": 1.0, + "content": "Lemma 2. Algorithm 1 terminates.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 13 + } + ], + "index": 11 + }, + { + "type": "text", + "bbox": [ + 106, + 439, + 503, + 462 + ], + "lines": [ + { + "bbox": [ + 106, + 439, + 504, + 452 + ], + "spans": [ + { + "bbox": [ + 106, + 439, + 504, + 452 + ], + "score": 1.0, + "content": "Our experiments showed this algorithm to be fast in terms of both iterations necessary for conver-", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 451, + 423, + 463 + ], + "spans": [ + { + "bbox": [ + 105, + 451, + 423, + 463 + ], + "score": 1.0, + "content": "gence and wall-clock time, generally on the order of seconds to a few minutes.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 14.5 + }, + { + "type": "text", + "bbox": [ + 106, + 467, + 505, + 545 + ], + "lines": [ + { + "bbox": [ + 105, + 466, + 505, + 480 + ], + "spans": [ + { + "bbox": [ + 105, + 466, + 505, + 480 + ], + "score": 1.0, + "content": "Unlike the activation matching method presented in Section 3.1, weight matching ignores the data", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 478, + 505, + 492 + ], + "spans": [ + { + "bbox": [ + 105, + 478, + 505, + 492 + ], + "score": 1.0, + "content": "distribution entirely. Ignoring the input data distribution and therefore the loss landscape handicaps", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 489, + 505, + 502 + ], + "spans": [ + { + "bbox": [ + 106, + 489, + 505, + 502 + ], + "score": 1.0, + "content": "weight matching but allows it to be much faster. We therefore anticipate its potential application in", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 500, + 504, + 513 + ], + "spans": [ + { + "bbox": [ + 105, + 500, + 504, + 513 + ], + "score": 1.0, + "content": "fields such as finetuning (Devlin et al., 2019; Wortsman et al., 2022b;a), federated learning (McMa-", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 512, + 504, + 523 + ], + "spans": [ + { + "bbox": [ + 106, + 512, + 504, + 523 + ], + "score": 1.0, + "content": "han et al., 2017; Konecnˇ y et al., 2016a;b), and model patching (Matena & Raffel, 2021; Sung et al.,´", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 521, + 505, + 536 + ], + "spans": [ + { + "bbox": [ + 105, + 521, + 505, + 536 + ], + "score": 1.0, + "content": "2021; Raffel, 2021). 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Loss landscapes when interpo-", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 165, + 505, + 180 + ], + "spans": [ + { + "bbox": [ + 105, + 165, + 505, + 180 + ], + "score": 1.0, + "content": "lating between models trained on MNIST, CIFAR-10, and ImageNet. In all cases we can signifi-", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 177, + 506, + 190 + ], + "spans": [ + { + "bbox": [ + 106, + 177, + 506, + 190 + ], + "score": 1.0, + "content": "cantly improve over na¨ıve interpolation. Straight-through estimator matching performs best but is", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 188, + 506, + 201 + ], + "spans": [ + { + "bbox": [ + 105, + 188, + 506, + 201 + ], + "score": 1.0, + "content": "very computationally expensive. Weight and activation matching perform similarly, although weight", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 199, + 505, + 212 + ], + "spans": [ + { + "bbox": [ + 105, + 199, + 505, + 212 + ], + "score": 1.0, + "content": "matching is orders of magnitude faster and does not rely on the input data distribution. We hypoth-", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 210, + 497, + 223 + ], + "spans": [ + { + "bbox": [ + 105, + 210, + 497, + 223 + ], + "score": 1.0, + "content": "esize that the ImageNet barrier could be reduced by increasing the model width as in Section 5.3.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 5.5 + } + ], + "index": 3.25 + }, + { + "type": "table", + "bbox": [ + 105, + 244, + 503, + 391 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 106, + 239, + 325, + 252 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 239, + 326, + 253 + ], + "spans": [ + { + "bbox": [ + 106, + 239, + 326, + 253 + ], + "score": 1.0, + "content": "Algorithm 1: PERMUTATIONCOORDINATEDESCENT", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 9 + }, + { + "type": "table_body", + "bbox": [ + 105, + 244, + 503, + 391 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 244, + 503, + 391 + ], + "spans": [ + { + "bbox": [ + 105, + 244, + 503, + 391 + ], + "score": 0.753, + "html": "
AIgorIthmI:PERMUTATIONCOORDINATEDESCENT Given:Mode weigts A = {w(4),., [4)} and θB ={~w(B),.. W}
Result: A permutation π = {P1,...,PL-1} of OB such that vec(ΘA) · vec(π(OB)) is approximately maximized.
Initialize:Pl←I,...,PL-1 ←I
repeat
for l∈RANDOMPERMUTATION(1,...,L-1) do
P←SOLvELAP（W()P-1(W(B）+(W(）1W)）
end until convergence
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Algorithm 1 terminates.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 13 + } + ], + "index": 11 + }, + { + "type": "text", + "bbox": [ + 106, + 439, + 503, + 462 + ], + "lines": [ + { + "bbox": [ + 106, + 439, + 504, + 452 + ], + "spans": [ + { + "bbox": [ + 106, + 439, + 504, + 452 + ], + "score": 1.0, + "content": "Our experiments showed this algorithm to be fast in terms of both iterations necessary for conver-", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 451, + 423, + 463 + ], + "spans": [ + { + "bbox": [ + 105, + 451, + 423, + 463 + ], + "score": 1.0, + "content": "gence and wall-clock time, generally on the order of seconds to a few minutes.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 14.5, + "bbox_fs": [ + 105, + 439, + 504, + 463 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 467, + 505, + 545 + ], + "lines": [ + { + "bbox": [ + 105, + 466, + 505, + 480 + ], + "spans": [ + { + "bbox": [ + 105, + 466, + 505, + 480 + ], + "score": 1.0, + "content": "Unlike the activation matching method presented in Section 3.1, weight matching ignores the data", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 478, + 505, + 492 + ], + "spans": [ + { + "bbox": [ + 105, + 478, + 505, + 492 + ], + "score": 1.0, + "content": "distribution entirely. 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In the forward pass, we project", + "type": "text" + }, + { + "bbox": [ + 393, + 706, + 408, + 719 + ], + "score": 0.91, + "content": "\\tilde { \\Theta } _ { B }", + "type": "inline_equation" + }, + { + "bbox": [ + 409, + 707, + 505, + 721 + ], + "score": 1.0, + "content": "to the closest realizable", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 719, + 505, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 720, + 136, + 732 + ], + "score": 0.92, + "content": "\\pi ( \\Theta _ { B } )", + "type": "inline_equation" + }, + { + "bbox": [ + 136, + 720, + 423, + 733 + ], + "score": 1.0, + "content": ". In the backwards pass, we then switch back to the unrestricted weights", + "type": "text" + }, + { + "bbox": [ + 423, + 719, + 438, + 732 + ], + "score": 0.91, + "content": "\\tilde { \\Theta } _ { B }", + "type": "inline_equation" + }, + { + "bbox": [ + 439, + 720, + 505, + 733 + ], + "score": 1.0, + "content": ". In this way, we", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 266, + 505, + 279 + ], + "spans": [ + { + "bbox": [ + 106, + 266, + 505, + 279 + ], + "score": 1.0, + "content": "are guaranteed to stay true to the projection constraints in evaluating the loss but can still compute", + "type": "text", + "cross_page": true + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 277, + 303, + 291 + ], + "spans": [ + { + "bbox": [ + 105, + 277, + 278, + 291 + ], + "score": 1.0, + "content": "usable gradients at our current parameters,", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 279, + 277, + 294, + 290 + ], + "score": 0.9, + "content": "\\tilde { \\Theta } _ { B }", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 294, + 277, + 303, + 291 + ], + "score": 1.0, + "content": ".2", + "type": "text", + "cross_page": true + } + ], + "index": 9 + } + ], + "index": 31, + "bbox_fs": [ + 105, + 672, + 505, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 146, + 70, + 465, + 183 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 146, + 70, + 465, + 183 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 146, + 70, + 465, + 183 + ], + "spans": [ + { + "bbox": [ + 146, + 70, + 465, + 183 + ], + "score": 0.973, + "type": "image", + "image_path": "66fdb92d5345a394d0ef2d04adc18349df134e93a47aae13eddad25cda8fb2bb.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 146, + 70, + 465, + 107.66666666666666 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 146, + 107.66666666666666, + 465, + 145.33333333333331 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 146, + 145.33333333333331, + 465, + 182.99999999999997 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 192, + 506, + 247 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 192, + 505, + 204 + ], + "spans": [ + { + "bbox": [ + 105, + 192, + 505, + 204 + ], + "score": 1.0, + "content": "Figure 3: Linear mode connectivity is challenging at initialization. We show loss barriers per", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 202, + 506, + 216 + ], + "spans": [ + { + "bbox": [ + 105, + 202, + 506, + 216 + ], + "score": 1.0, + "content": "training time for MLPs trained on MNIST (left) and CIFAR-10 (right). Loss interpolation plots are", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 212, + 505, + 228 + ], + "spans": [ + { + "bbox": [ + 105, + 212, + 505, + 228 + ], + "score": 1.0, + "content": "inlaid to highlight results in initial and later epochs. LMC manifests gradually throughout training.", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 222, + 506, + 239 + ], + "spans": [ + { + "bbox": [ + 105, + 222, + 506, + 239 + ], + "score": 1.0, + "content": "We hypothesize that the variance in CIFAR-10 training is higher due to our MLP architecture being", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 236, + 421, + 249 + ], + "spans": [ + { + "bbox": [ + 106, + 236, + 421, + 249 + ], + "score": 1.0, + "content": "under-powered relative to the dataset. (Y-axis scales differ in each inlaid plot.)", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 5 + } + ], + "index": 3.0 + }, + { + "type": "text", + "bbox": [ + 107, + 266, + 503, + 290 + ], + "lines": [ + { + "bbox": [ + 106, + 266, + 505, + 279 + ], + "spans": [ + { + "bbox": [ + 106, + 266, + 505, + 279 + ], + "score": 1.0, + "content": "are guaranteed to stay true to the projection constraints in evaluating the loss but can still compute", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 277, + 303, + 291 + ], + "spans": [ + { + "bbox": [ + 105, + 277, + 278, + 291 + ], + "score": 1.0, + "content": "usable gradients at our current parameters,", + "type": "text" + }, + { + "bbox": [ + 279, + 277, + 294, + 290 + ], + "score": 0.9, + "content": "\\tilde { \\Theta } _ { B }", + "type": "inline_equation" + }, + { + "bbox": [ + 294, + 277, + 303, + 291 + ], + "score": 1.0, + "content": ".2", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 8.5 + }, + { + "type": "text", + "bbox": [ + 106, + 296, + 504, + 354 + ], + "lines": [ + { + "bbox": [ + 106, + 295, + 505, + 309 + ], + "spans": [ + { + "bbox": [ + 106, + 295, + 346, + 309 + ], + "score": 1.0, + "content": "Conveniently, we can re-purpose Algorithm 1 to solve proj", + "type": "text" + }, + { + "bbox": [ + 347, + 295, + 368, + 309 + ], + "score": 0.81, + "content": "( { \\tilde { \\Theta } } _ { B } )", + "type": "inline_equation" + }, + { + "bbox": [ + 369, + 295, + 505, + 309 + ], + "score": 1.0, + "content": ". Furthermore, we found that ini-", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 308, + 505, + 323 + ], + "spans": [ + { + "bbox": [ + 105, + 308, + 141, + 323 + ], + "score": 1.0, + "content": "tializing", + "type": "text" + }, + { + "bbox": [ + 142, + 308, + 185, + 321 + ], + "score": 0.93, + "content": "\\tilde { \\Theta } _ { B } = \\Theta _ { A }", + "type": "inline_equation" + }, + { + "bbox": [ + 185, + 308, + 505, + 323 + ], + "score": 1.0, + "content": "performed better than random initialization. This is to be expected immediately", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 320, + 506, + 334 + ], + "spans": [ + { + "bbox": [ + 105, + 320, + 506, + 334 + ], + "score": 1.0, + "content": "at initialization since the initial matching will be equivalent to the weight matching method of Sec-", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 331, + 505, + 343 + ], + "spans": [ + { + "bbox": [ + 106, + 331, + 505, + 343 + ], + "score": 1.0, + "content": "tion 3.1. However, it is not immediately clear why these solutions continue to outperform a random", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 342, + 222, + 355 + ], + "spans": [ + { + "bbox": [ + 105, + 342, + 222, + 355 + ], + "score": 1.0, + "content": "initialization asymptotically.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 12 + }, + { + "type": "text", + "bbox": [ + 107, + 359, + 505, + 403 + ], + "lines": [ + { + "bbox": [ + 105, + 359, + 505, + 371 + ], + "spans": [ + { + "bbox": [ + 105, + 359, + 505, + 371 + ], + "score": 1.0, + "content": "Unlike the aforementioned methods, Algorithm 2 attempts to explicitly “learn” the best permutation", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 370, + 506, + 382 + ], + "spans": [ + { + "bbox": [ + 106, + 372, + 114, + 380 + ], + "score": 0.69, + "content": "\\pi", + "type": "inline_equation" + }, + { + "bbox": [ + 114, + 370, + 506, + 382 + ], + "score": 1.0, + "content": "using a conventional training loop. By initializing to the weight matching solution of Section 3.2", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 382, + 505, + 393 + ], + "spans": [ + { + "bbox": [ + 106, + 382, + 505, + 393 + ], + "score": 1.0, + "content": "and leveraging the data distribution as in Section 3.1, it seeks to offer a best-of-both-worlds solution.", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 392, + 466, + 405 + ], + "spans": [ + { + "bbox": [ + 105, + 392, + 466, + 405 + ], + "score": 1.0, + "content": "However, this comes at a very steep computational cost relative to the other two methods.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 16.5 + }, + { + "type": "title", + "bbox": [ + 107, + 419, + 482, + 432 + ], + "lines": [ + { + "bbox": [ + 105, + 418, + 483, + 433 + ], + "spans": [ + { + "bbox": [ + 105, + 418, + 483, + 433 + ], + "score": 1.0, + "content": "4 A COUNTEREXAMPLE TO UNIVERSAL LINEAR MODE CONNECTIVITY", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 19 + }, + { + "type": "text", + "bbox": [ + 107, + 443, + 505, + 499 + ], + "lines": [ + { + "bbox": [ + 105, + 443, + 505, + 456 + ], + "spans": [ + { + "bbox": [ + 105, + 443, + 505, + 456 + ], + "score": 1.0, + "content": "In this section we argue that common optimization algorithms, especially SGD and its relatives, are", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 455, + 504, + 467 + ], + "spans": [ + { + "bbox": [ + 106, + 455, + 504, + 467 + ], + "score": 1.0, + "content": "implicitly biased towards solutions admitting linear mode connectivity. In particular, we demon-", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 466, + 505, + 479 + ], + "spans": [ + { + "bbox": [ + 105, + 466, + 505, + 479 + ], + "score": 1.0, + "content": "strate – by way of a counterexample – that adversarial, non-SGD solutions exist in loss landscapes", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 478, + 505, + 489 + ], + "spans": [ + { + "bbox": [ + 106, + 478, + 505, + 489 + ], + "score": 1.0, + "content": "such that no permutation of units results in linear mode connectivity. We present this counterexam-", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 488, + 267, + 500 + ], + "spans": [ + { + "bbox": [ + 105, + 488, + 267, + 500 + ], + "score": 1.0, + "content": "ple in complete detail in Appendix A.6.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 22 + }, + { + "type": "text", + "bbox": [ + 107, + 505, + 504, + 560 + ], + "lines": [ + { + "bbox": [ + 106, + 504, + 505, + 517 + ], + "spans": [ + { + "bbox": [ + 106, + 504, + 505, + 517 + ], + "score": 1.0, + "content": "The existence of adversarial basins suggests that our ability to find LMC between independently", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 516, + 505, + 528 + ], + "spans": [ + { + "bbox": [ + 106, + 516, + 505, + 528 + ], + "score": 1.0, + "content": "trained models is thanks to inherent biases in optimization methods. We emphasize that this coun-", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 527, + 505, + 539 + ], + "spans": [ + { + "bbox": [ + 106, + 527, + 505, + 539 + ], + "score": 1.0, + "content": "terexample does not contradict Conjecture 1; rather, it illustrates the importance of the conjecture’s", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 538, + 505, + 550 + ], + "spans": [ + { + "bbox": [ + 106, + 538, + 505, + 550 + ], + "score": 1.0, + "content": "restriction to SGD solutions (Entezari et al., 2021). Characterizing the precise mechanism by which", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 549, + 446, + 560 + ], + "spans": [ + { + "bbox": [ + 106, + 549, + 446, + 560 + ], + "score": 1.0, + "content": "these solutions are biased towards LMC could be an exciting avenue for future work.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 27 + }, + { + "type": "text", + "bbox": [ + 107, + 565, + 505, + 610 + ], + "lines": [ + { + "bbox": [ + 105, + 565, + 505, + 579 + ], + "spans": [ + { + "bbox": [ + 105, + 565, + 505, + 579 + ], + "score": 1.0, + "content": "We also note that there are invariances beyond permutation symmetries: It is possible to move", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 577, + 505, + 588 + ], + "spans": [ + { + "bbox": [ + 106, + 577, + 505, + 588 + ], + "score": 1.0, + "content": "features between layers, re-scale layers, and so forth. Prior works noted the feature/layer associa-", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 588, + 505, + 600 + ], + "spans": [ + { + "bbox": [ + 106, + 588, + 505, + 600 + ], + "score": 1.0, + "content": "tion (Nguyen et al., 2021) and re-scaling invariances (Ainsworth et al., 2018). The importance of", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 599, + 462, + 612 + ], + "spans": [ + { + "bbox": [ + 105, + 599, + 462, + 612 + ], + "score": 1.0, + "content": "these other symmetries and their interplay with optimization algorithms remains unclear.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 31.5 + }, + { + "type": "title", + "bbox": [ + 108, + 626, + 200, + 638 + ], + "lines": [ + { + "bbox": [ + 104, + 624, + 202, + 640 + ], + "spans": [ + { + "bbox": [ + 104, + 624, + 202, + 640 + ], + "score": 1.0, + "content": "5 EXPERIMENTS", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 34 + }, + { + "type": "text", + "bbox": [ + 108, + 650, + 504, + 673 + ], + "lines": [ + { + "bbox": [ + 106, + 650, + 505, + 663 + ], + "spans": [ + { + "bbox": [ + 106, + 650, + 338, + 663 + ], + "score": 1.0, + "content": "Our base methodology is to separately train two models,", + "type": "text" + }, + { + "bbox": [ + 339, + 651, + 347, + 660 + ], + "score": 0.78, + "content": "A", + "type": "inline_equation" + }, + { + "bbox": [ + 348, + 650, + 366, + 663 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 366, + 651, + 375, + 660 + ], + "score": 0.81, + "content": "B", + "type": "inline_equation" + }, + { + "bbox": [ + 376, + 650, + 505, + 663 + ], + "score": 1.0, + "content": ", starting from different random", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 660, + 505, + 675 + ], + "spans": [ + { + "bbox": [ + 106, + 660, + 449, + 675 + ], + "score": 1.0, + "content": "initializations and with different random batch orders, resulting in trained weights", + "type": "text" + }, + { + "bbox": [ + 449, + 662, + 465, + 672 + ], + "score": 0.89, + "content": "\\Theta _ { A }", + "type": "inline_equation" + }, + { + "bbox": [ + 465, + 660, + 485, + 675 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 486, + 662, + 501, + 672 + ], + "score": 0.89, + "content": "\\Theta _ { B }", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 660, + 505, + 675 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 35.5 + } + ], + "page_idx": 5, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 680, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 118, + 678, + 506, + 693 + ], + "spans": [ + { + "bbox": [ + 118, + 678, + 506, + 693 + ], + "score": 1.0, + "content": "2Note again that projecting according to inner product distance is equivalent to projecting according to the", + "type": "text" + } + ] + }, + { + "bbox": [ + 106, + 689, + 506, + 703 + ], + "spans": [ + { + "bbox": [ + 106, + 691, + 118, + 700 + ], + "score": 0.84, + "content": "L _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 118, + 689, + 326, + 703 + ], + "score": 1.0, + "content": "distance when parameterizing the estimator based on the", + "type": "text" + }, + { + "bbox": [ + 326, + 691, + 335, + 699 + ], + "score": 0.82, + "content": "B", + "type": "inline_equation" + }, + { + "bbox": [ + 335, + 689, + 506, + 703 + ], + "score": 1.0, + "content": "endpoint. We also experimented with learning", + "type": "text" + } + ] + }, + { + "bbox": [ + 105, + 700, + 506, + 713 + ], + "spans": [ + { + "bbox": [ + 105, + 700, + 187, + 713 + ], + "score": 1.0, + "content": "the midpoint directly,", + "type": "text" + }, + { + "bbox": [ + 187, + 700, + 272, + 713 + ], + "score": 0.92, + "content": "\\begin{array} { r } { \\tilde { \\Theta } \\approx \\frac { 1 } { 2 } ( \\Theta _ { A } + \\pi ( \\Theta _ { B } ) ) } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 272, + 700, + 341, + 713 + ], + "score": 1.0, + "content": ", in which case the", + "type": "text" + }, + { + "bbox": [ + 342, + 702, + 353, + 711 + ], + "score": 0.85, + "content": "L _ { 2 }", + "type": "inline_equation" + }, + { + "bbox": [ + 353, + 700, + 506, + 713 + ], + "score": 1.0, + "content": "and inner product projections diverge. In", + "type": "text" + } + ] + }, + { + "bbox": [ + 106, + 712, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 106, + 712, + 321, + 723 + ], + "score": 1.0, + "content": "testing all possible variations, we found that optimizing the", + "type": "text" + }, + { + "bbox": [ + 321, + 712, + 329, + 721 + ], + "score": 0.82, + "content": "B", + "type": "inline_equation" + }, + { + "bbox": [ + 330, + 712, + 505, + 723 + ], + "score": 1.0, + "content": "endpoint had a slight advantage, but all possible", + "type": "text" + } + ] + }, + { + "bbox": [ + 106, + 721, + 223, + 733 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 223, + 733 + ], + "score": 1.0, + "content": "variations performed admirably.", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 107, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2023", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 752, + 309, + 760 + ], + "lines": [ + { + "bbox": [ + 302, + 751, + 310, + 762 + ], + "spans": [ + { + "bbox": [ + 302, + 751, + 310, + 762 + ], + "score": 1.0, + "content": "6", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "image", + "bbox": [ + 146, + 70, + 465, + 183 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 146, + 70, + 465, + 183 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 146, + 70, + 465, + 183 + ], + "spans": [ + { + "bbox": [ + 146, + 70, + 465, + 183 + ], + "score": 0.973, + "type": "image", + "image_path": "66fdb92d5345a394d0ef2d04adc18349df134e93a47aae13eddad25cda8fb2bb.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 146, + 70, + 465, + 107.66666666666666 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 146, + 107.66666666666666, + 465, + 145.33333333333331 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 146, + 145.33333333333331, + 465, + 182.99999999999997 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 192, + 506, + 247 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 192, + 505, + 204 + ], + "spans": [ + { + "bbox": [ + 105, + 192, + 505, + 204 + ], + "score": 1.0, + "content": "Figure 3: Linear mode connectivity is challenging at initialization. We show loss barriers per", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 202, + 506, + 216 + ], + "spans": [ + { + "bbox": [ + 105, + 202, + 506, + 216 + ], + "score": 1.0, + "content": "training time for MLPs trained on MNIST (left) and CIFAR-10 (right). Loss interpolation plots are", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 212, + 505, + 228 + ], + "spans": [ + { + "bbox": [ + 105, + 212, + 505, + 228 + ], + "score": 1.0, + "content": "inlaid to highlight results in initial and later epochs. LMC manifests gradually throughout training.", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 222, + 506, + 239 + ], + "spans": [ + { + "bbox": [ + 105, + 222, + 506, + 239 + ], + "score": 1.0, + "content": "We hypothesize that the variance in CIFAR-10 training is higher due to our MLP architecture being", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 236, + 421, + 249 + ], + "spans": [ + { + "bbox": [ + 106, + 236, + 421, + 249 + ], + "score": 1.0, + "content": "under-powered relative to the dataset. (Y-axis scales differ in each inlaid plot.)", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 5 + } + ], + "index": 3.0 + }, + { + "type": "text", + "bbox": [ + 107, + 266, + 503, + 290 + ], + "lines": [], + "index": 8.5, + "bbox_fs": [ + 105, + 266, + 505, + 291 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 106, + 296, + 504, + 354 + ], + "lines": [ + { + "bbox": [ + 106, + 295, + 505, + 309 + ], + "spans": [ + { + "bbox": [ + 106, + 295, + 346, + 309 + ], + "score": 1.0, + "content": "Conveniently, we can re-purpose Algorithm 1 to solve proj", + "type": "text" + }, + { + "bbox": [ + 347, + 295, + 368, + 309 + ], + "score": 0.81, + "content": "( { \\tilde { \\Theta } } _ { B } )", + "type": "inline_equation" + }, + { + "bbox": [ + 369, + 295, + 505, + 309 + ], + "score": 1.0, + "content": ". Furthermore, we found that ini-", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 308, + 505, + 323 + ], + "spans": [ + { + "bbox": [ + 105, + 308, + 141, + 323 + ], + "score": 1.0, + "content": "tializing", + "type": "text" + }, + { + "bbox": [ + 142, + 308, + 185, + 321 + ], + "score": 0.93, + "content": "\\tilde { \\Theta } _ { B } = \\Theta _ { A }", + "type": "inline_equation" + }, + { + "bbox": [ + 185, + 308, + 505, + 323 + ], + "score": 1.0, + "content": "performed better than random initialization. This is to be expected immediately", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 320, + 506, + 334 + ], + "spans": [ + { + "bbox": [ + 105, + 320, + 506, + 334 + ], + "score": 1.0, + "content": "at initialization since the initial matching will be equivalent to the weight matching method of Sec-", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 331, + 505, + 343 + ], + "spans": [ + { + "bbox": [ + 106, + 331, + 505, + 343 + ], + "score": 1.0, + "content": "tion 3.1. However, it is not immediately clear why these solutions continue to outperform a random", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 342, + 222, + 355 + ], + "spans": [ + { + "bbox": [ + 105, + 342, + 222, + 355 + ], + "score": 1.0, + "content": "initialization asymptotically.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 12, + "bbox_fs": [ + 105, + 295, + 506, + 355 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 359, + 505, + 403 + ], + "lines": [ + { + "bbox": [ + 105, + 359, + 505, + 371 + ], + "spans": [ + { + "bbox": [ + 105, + 359, + 505, + 371 + ], + "score": 1.0, + "content": "Unlike the aforementioned methods, Algorithm 2 attempts to explicitly “learn” the best permutation", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 370, + 506, + 382 + ], + "spans": [ + { + "bbox": [ + 106, + 372, + 114, + 380 + ], + "score": 0.69, + "content": "\\pi", + "type": "inline_equation" + }, + { + "bbox": [ + 114, + 370, + 506, + 382 + ], + "score": 1.0, + "content": "using a conventional training loop. By initializing to the weight matching solution of Section 3.2", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 382, + 505, + 393 + ], + "spans": [ + { + "bbox": [ + 106, + 382, + 505, + 393 + ], + "score": 1.0, + "content": "and leveraging the data distribution as in Section 3.1, it seeks to offer a best-of-both-worlds solution.", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 392, + 466, + 405 + ], + "spans": [ + { + "bbox": [ + 105, + 392, + 466, + 405 + ], + "score": 1.0, + "content": "However, this comes at a very steep computational cost relative to the other two methods.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 16.5, + "bbox_fs": [ + 105, + 359, + 506, + 405 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 419, + 482, + 432 + ], + "lines": [ + { + "bbox": [ + 105, + 418, + 483, + 433 + ], + "spans": [ + { + "bbox": [ + 105, + 418, + 483, + 433 + ], + "score": 1.0, + "content": "4 A COUNTEREXAMPLE TO UNIVERSAL LINEAR MODE CONNECTIVITY", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 19 + }, + { + "type": "text", + "bbox": [ + 107, + 443, + 505, + 499 + ], + "lines": [ + { + "bbox": [ + 105, + 443, + 505, + 456 + ], + "spans": [ + { + "bbox": [ + 105, + 443, + 505, + 456 + ], + "score": 1.0, + "content": "In this section we argue that common optimization algorithms, especially SGD and its relatives, are", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 455, + 504, + 467 + ], + "spans": [ + { + "bbox": [ + 106, + 455, + 504, + 467 + ], + "score": 1.0, + "content": "implicitly biased towards solutions admitting linear mode connectivity. In particular, we demon-", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 466, + 505, + 479 + ], + "spans": [ + { + "bbox": [ + 105, + 466, + 505, + 479 + ], + "score": 1.0, + "content": "strate – by way of a counterexample – that adversarial, non-SGD solutions exist in loss landscapes", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 478, + 505, + 489 + ], + "spans": [ + { + "bbox": [ + 106, + 478, + 505, + 489 + ], + "score": 1.0, + "content": "such that no permutation of units results in linear mode connectivity. We present this counterexam-", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 488, + 267, + 500 + ], + "spans": [ + { + "bbox": [ + 105, + 488, + 267, + 500 + ], + "score": 1.0, + "content": "ple in complete detail in Appendix A.6.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 22, + "bbox_fs": [ + 105, + 443, + 505, + 500 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 505, + 504, + 560 + ], + "lines": [ + { + "bbox": [ + 106, + 504, + 505, + 517 + ], + "spans": [ + { + "bbox": [ + 106, + 504, + 505, + 517 + ], + "score": 1.0, + "content": "The existence of adversarial basins suggests that our ability to find LMC between independently", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 516, + 505, + 528 + ], + "spans": [ + { + "bbox": [ + 106, + 516, + 505, + 528 + ], + "score": 1.0, + "content": "trained models is thanks to inherent biases in optimization methods. We emphasize that this coun-", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 527, + 505, + 539 + ], + "spans": [ + { + "bbox": [ + 106, + 527, + 505, + 539 + ], + "score": 1.0, + "content": "terexample does not contradict Conjecture 1; rather, it illustrates the importance of the conjecture’s", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 538, + 505, + 550 + ], + "spans": [ + { + "bbox": [ + 106, + 538, + 505, + 550 + ], + "score": 1.0, + "content": "restriction to SGD solutions (Entezari et al., 2021). Characterizing the precise mechanism by which", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 549, + 446, + 560 + ], + "spans": [ + { + "bbox": [ + 106, + 549, + 446, + 560 + ], + "score": 1.0, + "content": "these solutions are biased towards LMC could be an exciting avenue for future work.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 27, + "bbox_fs": [ + 106, + 504, + 505, + 560 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 565, + 505, + 610 + ], + "lines": [ + { + "bbox": [ + 105, + 565, + 505, + 579 + ], + "spans": [ + { + "bbox": [ + 105, + 565, + 505, + 579 + ], + "score": 1.0, + "content": "We also note that there are invariances beyond permutation symmetries: It is possible to move", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 577, + 505, + 588 + ], + "spans": [ + { + "bbox": [ + 106, + 577, + 505, + 588 + ], + "score": 1.0, + "content": "features between layers, re-scale layers, and so forth. Prior works noted the feature/layer associa-", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 588, + 505, + 600 + ], + "spans": [ + { + "bbox": [ + 106, + 588, + 505, + 600 + ], + "score": 1.0, + "content": "tion (Nguyen et al., 2021) and re-scaling invariances (Ainsworth et al., 2018). 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As discussed in Section 2, the ability to", + "type": "text", + "cross_page": true + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 287, + 505, + 301 + ], + "spans": [ + { + "bbox": [ + 105, + 287, + 248, + 301 + ], + "score": 1.0, + "content": "exhibit this behavior for arbitrary", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 248, + 288, + 282, + 299 + ], + "score": 0.92, + "content": "\\Theta _ { A } , \\Theta _ { B }", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 283, + 287, + 505, + 301 + ], + "score": 1.0, + "content": "empirically suggests that the loss landscape contains", + "type": "text", + "cross_page": true + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 299, + 317, + 311 + ], + "spans": [ + { + "bbox": [ + 106, + 299, + 317, + 311 + ], + "score": 1.0, + "content": "only a single basin modulo permutation symmetries.", + "type": "text", + "cross_page": true + } + ], + "index": 11 + } + ], + "index": 35.5, + "bbox_fs": [ + 106, + 650, + 505, + 675 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 146, + 70, + 465, + 183 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 146, + 70, + 465, + 183 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 146, + 70, + 465, + 183 + ], + "spans": [ + { + "bbox": [ + 146, + 70, + 465, + 183 + ], + "score": 0.971, + "type": "image", + "image_path": "3e2b1e1ca8930ad7cb63f4865ef94b31090d2207fcd8a0648f4d185bd101dc14.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 146, + 70, + 465, + 107.66666666666666 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 146, + 107.66666666666666, + 465, + 145.33333333333331 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 146, + 145.33333333333331, + 465, + 182.99999999999997 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 192, + 505, + 235 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 192, + 505, + 204 + ], + "spans": [ + { + "bbox": [ + 106, + 192, + 505, + 204 + ], + "score": 1.0, + "content": "Figure 4: Wider models exhibit better linear mode connectivity. Training convolutional and", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 202, + 505, + 215 + ], + "spans": [ + { + "bbox": [ + 105, + 202, + 505, + 215 + ], + "score": 1.0, + "content": "ResNet architectures on CIFAR-10, we ablate their width and visualize loss barriers after weight", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 214, + 505, + 226 + ], + "spans": [ + { + "bbox": [ + 106, + 214, + 505, + 226 + ], + "score": 1.0, + "content": "matching. Notably, we achieve zero-barrier linear mode connectivity between ResNet models, the", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 224, + 207, + 237 + ], + "spans": [ + { + "bbox": [ + 105, + 224, + 207, + 237 + ], + "score": 1.0, + "content": "first such demonstration.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 4.5 + } + ], + "index": 2.75 + }, + { + "type": "text", + "bbox": [ + 107, + 255, + 505, + 309 + ], + "lines": [ + { + "bbox": [ + 105, + 254, + 505, + 267 + ], + "spans": [ + { + "bbox": [ + 105, + 254, + 378, + 267 + ], + "score": 1.0, + "content": "respectively. We then evaluate slices through the loss landscape,", + "type": "text" + }, + { + "bbox": [ + 378, + 254, + 488, + 267 + ], + "score": 0.89, + "content": "\\mathcal { L } ( ( 1 - \\lambda ) \\Theta _ { A } + \\lambda \\pi ( \\Theta _ { B } ) )", + "type": "inline_equation" + }, + { + "bbox": [ + 488, + 254, + 505, + 267 + ], + "score": 1.0, + "content": "for", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 107, + 264, + 505, + 278 + ], + "spans": [ + { + "bbox": [ + 107, + 266, + 147, + 278 + ], + "score": 0.91, + "content": "\\lambda \\in [ 0 , 1 ]", + "type": "inline_equation" + }, + { + "bbox": [ + 147, + 264, + 178, + 278 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 179, + 267, + 186, + 276 + ], + "score": 0.74, + "content": "\\pi", + "type": "inline_equation" + }, + { + "bbox": [ + 187, + 264, + 505, + 278 + ], + "score": 1.0, + "content": "is selected according to the methods presented in Section 3.3 Ideally, we seek", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 276, + 505, + 289 + ], + "spans": [ + { + "bbox": [ + 105, + 276, + 505, + 289 + ], + "score": 1.0, + "content": "a completely flat or even convex one-dimensional slice. As discussed in Section 2, the ability to", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 287, + 505, + 301 + ], + "spans": [ + { + "bbox": [ + 105, + 287, + 248, + 301 + ], + "score": 1.0, + "content": "exhibit this behavior for arbitrary", + "type": "text" + }, + { + "bbox": [ + 248, + 288, + 282, + 299 + ], + "score": 0.92, + "content": "\\Theta _ { A } , \\Theta _ { B }", + "type": "inline_equation" + }, + { + "bbox": [ + 283, + 287, + 505, + 301 + ], + "score": 1.0, + "content": "empirically suggests that the loss landscape contains", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 299, + 317, + 311 + ], + "spans": [ + { + "bbox": [ + 106, + 299, + 317, + 311 + ], + "score": 1.0, + "content": "only a single basin modulo permutation symmetries.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 9 + }, + { + "type": "text", + "bbox": [ + 107, + 315, + 505, + 348 + ], + "lines": [ + { + "bbox": [ + 106, + 315, + 505, + 327 + ], + "spans": [ + { + "bbox": [ + 106, + 315, + 247, + 327 + ], + "score": 1.0, + "content": "We remark that a failure to find a", + "type": "text" + }, + { + "bbox": [ + 248, + 318, + 255, + 325 + ], + "score": 0.71, + "content": "\\pi", + "type": "inline_equation" + }, + { + "bbox": [ + 255, + 315, + 505, + 327 + ], + "score": 1.0, + "content": "such that linear mode connectivity holds cannot rule out the", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 326, + 505, + 339 + ], + "spans": [ + { + "bbox": [ + 105, + 326, + 505, + 339 + ], + "score": 1.0, + "content": "existence of a satisfactory permutation. Given the astronomical number of permutation symmetries,", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 337, + 488, + 351 + ], + "spans": [ + { + "bbox": [ + 106, + 337, + 488, + 351 + ], + "score": 1.0, + "content": "Conjecture 1 is essentially impossible to disprove for any realistically wide model architecture.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 13 + }, + { + "type": "title", + "bbox": [ + 107, + 362, + 355, + 373 + ], + "lines": [ + { + "bbox": [ + 105, + 362, + 356, + 375 + ], + "spans": [ + { + "bbox": [ + 105, + 362, + 356, + 375 + ], + "score": 1.0, + "content": "5.1 LOSS LANDSCAPES BEFORE AND AFTER MATCHING", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 15 + }, + { + "type": "text", + "bbox": [ + 107, + 383, + 505, + 482 + ], + "lines": [ + { + "bbox": [ + 105, + 383, + 505, + 396 + ], + "spans": [ + { + "bbox": [ + 105, + 383, + 505, + 396 + ], + "score": 1.0, + "content": "We present results for models trained on MNIST (LeCun et al., 1998), CIFAR-10 (Krizhevsky,", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 394, + 505, + 407 + ], + "spans": [ + { + "bbox": [ + 106, + 394, + 419, + 407 + ], + "score": 1.0, + "content": "2009), and ImageNet (Deng et al., 2009) in Figure 2. Na¨ıve interpolation", + "type": "text" + }, + { + "bbox": [ + 419, + 394, + 480, + 406 + ], + "score": 0.93, + "content": "( \\pi ( \\Theta _ { B } ) = \\Theta _ { B } )", + "type": "inline_equation" + }, + { + "bbox": [ + 480, + 394, + 505, + 407 + ], + "score": 1.0, + "content": ") sub-", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 405, + 505, + 418 + ], + "spans": [ + { + "bbox": [ + 105, + 405, + 505, + 418 + ], + "score": 1.0, + "content": "stantially degrades performance when interpolating. On the other hand, the methods introduced in", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 415, + 505, + 429 + ], + "spans": [ + { + "bbox": [ + 105, + 415, + 505, + 429 + ], + "score": 1.0, + "content": "Section 3 can achieve much better barriers. We achieve zero-barrier linear mode connectivity on", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 426, + 505, + 440 + ], + "spans": [ + { + "bbox": [ + 105, + 426, + 505, + 440 + ], + "score": 1.0, + "content": "MNIST with all three methods, although activation matching performs just slightly less favorably", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 438, + 505, + 451 + ], + "spans": [ + { + "bbox": [ + 105, + 438, + 505, + 451 + ], + "score": 1.0, + "content": "than weight matching and straight-through estimator (STE) matching. We especially note that the", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 448, + 505, + 461 + ], + "spans": [ + { + "bbox": [ + 105, + 448, + 505, + 461 + ], + "score": 1.0, + "content": "test loss landscape becomes convex after applying our weight matching and STE permutations! In", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 460, + 505, + 472 + ], + "spans": [ + { + "bbox": [ + 105, + 460, + 478, + 472 + ], + "score": 1.0, + "content": "other words, our interpolation actually yields a merged model that outperforms both models", + "type": "text" + }, + { + "bbox": [ + 478, + 460, + 487, + 470 + ], + "score": 0.72, + "content": "A", + "type": "inline_equation" + }, + { + "bbox": [ + 487, + 460, + 505, + 472 + ], + "score": 1.0, + "content": "and", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 107, + 469, + 399, + 483 + ], + "spans": [ + { + "bbox": [ + 107, + 471, + 116, + 480 + ], + "score": 0.54, + "content": "B", + "type": "inline_equation" + }, + { + "bbox": [ + 116, + 469, + 399, + 483 + ], + "score": 1.0, + "content": ". We elaborate on this phenomenon in Section 5.4 and Appendix A.10.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 20 + }, + { + "type": "text", + "bbox": [ + 107, + 488, + 505, + 543 + ], + "lines": [ + { + "bbox": [ + 106, + 488, + 505, + 500 + ], + "spans": [ + { + "bbox": [ + 106, + 488, + 409, + 500 + ], + "score": 1.0, + "content": "On ImageNet we fall short of zero-barrier connections, although we do see a", + "type": "text" + }, + { + "bbox": [ + 409, + 488, + 429, + 498 + ], + "score": 0.86, + "content": "67 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 429, + 488, + 505, + 500 + ], + "score": 1.0, + "content": "decrease in barrier", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 498, + 505, + 510 + ], + "spans": [ + { + "bbox": [ + 106, + 498, + 505, + 510 + ], + "score": 1.0, + "content": "relative to na¨ıve interpolation. As we demonstrate in Section 5.3, we can achieve zero-barrier LMC", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 509, + 505, + 522 + ], + "spans": [ + { + "bbox": [ + 105, + 509, + 505, + 522 + ], + "score": 1.0, + "content": "on CIFAR-10 with large ResNet models. Therefore, we hypothesize that the presence of LMC", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 520, + 505, + 534 + ], + "spans": [ + { + "bbox": [ + 105, + 520, + 505, + 534 + ], + "score": 1.0, + "content": "depends on the model having sufficient capacity (esp. width) to capture the complexity of the input", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 531, + 468, + 545 + ], + "spans": [ + { + "bbox": [ + 105, + 531, + 468, + 545 + ], + "score": 1.0, + "content": "data distribution, and that ImageNet results could be improved by expanding model width.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 27 + }, + { + "type": "text", + "bbox": [ + 107, + 548, + 505, + 604 + ], + "lines": [ + { + "bbox": [ + 106, + 549, + 505, + 561 + ], + "spans": [ + { + "bbox": [ + 106, + 549, + 505, + 561 + ], + "score": 1.0, + "content": "STE matching, the most expensive method, produces the best solutions. Somewhat surprising, how-", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 559, + 506, + 572 + ], + "spans": [ + { + "bbox": [ + 105, + 559, + 506, + 572 + ], + "score": 1.0, + "content": "ever, is that the gap between STE and the other two methods is relatively small. In particular, it is", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 570, + 505, + 583 + ], + "spans": [ + { + "bbox": [ + 105, + 570, + 505, + 583 + ], + "score": 1.0, + "content": "remarkable how well Algorithm 1 performs without access to the input data at all. We found that", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 581, + 505, + 594 + ], + "spans": [ + { + "bbox": [ + 106, + 581, + 505, + 594 + ], + "score": 1.0, + "content": "weight matching offered a compelling balance between computational cost and performance: It runs", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 592, + 409, + 604 + ], + "spans": [ + { + "bbox": [ + 106, + 592, + 409, + 604 + ], + "score": 1.0, + "content": "in mere seconds (on current hardware) and produces high-quality solutions.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 32 + }, + { + "type": "title", + "bbox": [ + 108, + 617, + 272, + 628 + ], + "lines": [ + { + "bbox": [ + 105, + 615, + 275, + 630 + ], + "spans": [ + { + "bbox": [ + 105, + 615, + 275, + 630 + ], + "score": 1.0, + "content": "5.2 ONSET OF MODE CONNECTIVITY", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 35 + }, + { + "type": "text", + "bbox": [ + 107, + 637, + 505, + 693 + ], + "lines": [ + { + "bbox": [ + 106, + 637, + 505, + 651 + ], + "spans": [ + { + "bbox": [ + 106, + 637, + 505, + 651 + ], + "score": 1.0, + "content": "Given the results of Section 5.1, it may be tempting to conclude that the entirety of weight space", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 649, + 505, + 661 + ], + "spans": [ + { + "bbox": [ + 106, + 649, + 505, + 661 + ], + "score": 1.0, + "content": "contains only a single basin modulo permutation symmetries. However, we found that linear mode", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 659, + 506, + 674 + ], + "spans": [ + { + "bbox": [ + 105, + 659, + 506, + 674 + ], + "score": 1.0, + "content": "connectivity is an emergent property of training, and we were unable to uncover it early in training.", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 669, + 505, + 684 + ], + "spans": [ + { + "bbox": [ + 105, + 669, + 505, + 684 + ], + "score": 1.0, + "content": "We explore the emergence of LMC in Figure 3. Concurrent to our work, Benzing et al. (2022)", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 681, + 482, + 695 + ], + "spans": [ + { + "bbox": [ + 105, + 681, + 482, + 695 + ], + "score": 1.0, + "content": "showed that LMC at initialization is possible using a permutation found at the end of training.", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 38 + } + ], + "page_idx": 6, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 106, + 701, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 118, + 699, + 506, + 714 + ], + "spans": [ + { + "bbox": [ + 118, + 699, + 506, + 714 + ], + "score": 1.0, + "content": "3We also experimented with spherical linear interpolation (“slerp”) and found it to perform slightly better", + "type": "text" + } + ] + }, + { + "bbox": [ + 106, + 712, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 712, + 505, + 722 + ], + "score": 1.0, + "content": "than linear interpolation in some cases; however, the difference was not sufficiently significant to warrant", + "type": "text" + } + ] + }, + { + "bbox": [ + 105, + 721, + 258, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 721, + 258, + 733 + ], + "score": 1.0, + "content": "diverging from the pre-existing literature.", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 107, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2023", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 309, + 759 + ], + "lines": [ + { + "bbox": [ + 302, + 750, + 309, + 762 + ], + "spans": [ + { + "bbox": [ + 302, + 750, + 309, + 762 + ], + "score": 1.0, + "content": "7", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "image", + "bbox": [ + 146, + 70, + 465, + 183 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 146, + 70, + 465, + 183 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 146, + 70, + 465, + 183 + ], + "spans": [ + { + "bbox": [ + 146, + 70, + 465, + 183 + ], + "score": 0.971, + "type": "image", + "image_path": "3e2b1e1ca8930ad7cb63f4865ef94b31090d2207fcd8a0648f4d185bd101dc14.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 146, + 70, + 465, + 107.66666666666666 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 146, + 107.66666666666666, + 465, + 145.33333333333331 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 146, + 145.33333333333331, + 465, + 182.99999999999997 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 192, + 505, + 235 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 192, + 505, + 204 + ], + "spans": [ + { + "bbox": [ + 106, + 192, + 505, + 204 + ], + "score": 1.0, + "content": "Figure 4: Wider models exhibit better linear mode connectivity. Training convolutional and", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 202, + 505, + 215 + ], + "spans": [ + { + "bbox": [ + 105, + 202, + 505, + 215 + ], + "score": 1.0, + "content": "ResNet architectures on CIFAR-10, we ablate their width and visualize loss barriers after weight", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 214, + 505, + 226 + ], + "spans": [ + { + "bbox": [ + 106, + 214, + 505, + 226 + ], + "score": 1.0, + "content": "matching. 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Given the astronomical number of permutation symmetries,", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 337, + 488, + 351 + ], + "spans": [ + { + "bbox": [ + 106, + 337, + 488, + 351 + ], + "score": 1.0, + "content": "Conjecture 1 is essentially impossible to disprove for any realistically wide model architecture.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 13, + "bbox_fs": [ + 105, + 315, + 505, + 351 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 362, + 355, + 373 + ], + "lines": [ + { + "bbox": [ + 105, + 362, + 356, + 375 + ], + "spans": [ + { + "bbox": [ + 105, + 362, + 356, + 375 + ], + "score": 1.0, + "content": "5.1 LOSS LANDSCAPES BEFORE AND AFTER MATCHING", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 15 + }, + { + "type": "text", + "bbox": [ + 107, + 383, + 505, + 482 + ], + "lines": [ + { + "bbox": [ + 105, + 383, + 505, + 396 + ], + "spans": [ + { + "bbox": [ + 105, + 383, + 505, + 396 + ], + "score": 1.0, + "content": "We present results for models trained on MNIST (LeCun et al., 1998), CIFAR-10 (Krizhevsky,", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 394, + 505, + 407 + ], + "spans": [ + { + "bbox": [ + 106, + 394, + 419, + 407 + ], + "score": 1.0, + "content": "2009), and ImageNet (Deng et al., 2009) in Figure 2. Na¨ıve interpolation", + "type": "text" + }, + { + "bbox": [ + 419, + 394, + 480, + 406 + ], + "score": 0.93, + "content": "( \\pi ( \\Theta _ { B } ) = \\Theta _ { B } )", + "type": "inline_equation" + }, + { + "bbox": [ + 480, + 394, + 505, + 407 + ], + "score": 1.0, + "content": ") sub-", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 405, + 505, + 418 + ], + "spans": [ + { + "bbox": [ + 105, + 405, + 505, + 418 + ], + "score": 1.0, + "content": "stantially degrades performance when interpolating. On the other hand, the methods introduced in", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 415, + 505, + 429 + ], + "spans": [ + { + "bbox": [ + 105, + 415, + 505, + 429 + ], + "score": 1.0, + "content": "Section 3 can achieve much better barriers. We achieve zero-barrier linear mode connectivity on", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 426, + 505, + 440 + ], + "spans": [ + { + "bbox": [ + 105, + 426, + 505, + 440 + ], + "score": 1.0, + "content": "MNIST with all three methods, although activation matching performs just slightly less favorably", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 438, + 505, + 451 + ], + "spans": [ + { + "bbox": [ + 105, + 438, + 505, + 451 + ], + "score": 1.0, + "content": "than weight matching and straight-through estimator (STE) matching. We especially note that the", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 448, + 505, + 461 + ], + "spans": [ + { + "bbox": [ + 105, + 448, + 505, + 461 + ], + "score": 1.0, + "content": "test loss landscape becomes convex after applying our weight matching and STE permutations! In", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 460, + 505, + 472 + ], + "spans": [ + { + "bbox": [ + 105, + 460, + 478, + 472 + ], + "score": 1.0, + "content": "other words, our interpolation actually yields a merged model that outperforms both models", + "type": "text" + }, + { + "bbox": [ + 478, + 460, + 487, + 470 + ], + "score": 0.72, + "content": "A", + "type": "inline_equation" + }, + { + "bbox": [ + 487, + 460, + 505, + 472 + ], + "score": 1.0, + "content": "and", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 107, + 469, + 399, + 483 + ], + "spans": [ + { + "bbox": [ + 107, + 471, + 116, + 480 + ], + "score": 0.54, + "content": "B", + "type": "inline_equation" + }, + { + "bbox": [ + 116, + 469, + 399, + 483 + ], + "score": 1.0, + "content": ". We elaborate on this phenomenon in Section 5.4 and Appendix A.10.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 20, + "bbox_fs": [ + 105, + 383, + 505, + 483 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 488, + 505, + 543 + ], + "lines": [ + { + "bbox": [ + 106, + 488, + 505, + 500 + ], + "spans": [ + { + "bbox": [ + 106, + 488, + 409, + 500 + ], + "score": 1.0, + "content": "On ImageNet we fall short of zero-barrier connections, although we do see a", + "type": "text" + }, + { + "bbox": [ + 409, + 488, + 429, + 498 + ], + "score": 0.86, + "content": "67 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 429, + 488, + 505, + 500 + ], + "score": 1.0, + "content": "decrease in barrier", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 498, + 505, + 510 + ], + "spans": [ + { + "bbox": [ + 106, + 498, + 505, + 510 + ], + "score": 1.0, + "content": "relative to na¨ıve interpolation. As we demonstrate in Section 5.3, we can achieve zero-barrier LMC", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 509, + 505, + 522 + ], + "spans": [ + { + "bbox": [ + 105, + 509, + 505, + 522 + ], + "score": 1.0, + "content": "on CIFAR-10 with large ResNet models. Therefore, we hypothesize that the presence of LMC", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 520, + 505, + 534 + ], + "spans": [ + { + "bbox": [ + 105, + 520, + 505, + 534 + ], + "score": 1.0, + "content": "depends on the model having sufficient capacity (esp. width) to capture the complexity of the input", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 531, + 468, + 545 + ], + "spans": [ + { + "bbox": [ + 105, + 531, + 468, + 545 + ], + "score": 1.0, + "content": "data distribution, and that ImageNet results could be improved by expanding model width.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 27, + "bbox_fs": [ + 105, + 488, + 505, + 545 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 548, + 505, + 604 + ], + "lines": [ + { + "bbox": [ + 106, + 549, + 505, + 561 + ], + "spans": [ + { + "bbox": [ + 106, + 549, + 505, + 561 + ], + "score": 1.0, + "content": "STE matching, the most expensive method, produces the best solutions. Somewhat surprising, how-", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 559, + 506, + 572 + ], + "spans": [ + { + "bbox": [ + 105, + 559, + 506, + 572 + ], + "score": 1.0, + "content": "ever, is that the gap between STE and the other two methods is relatively small. In particular, it is", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 570, + 505, + 583 + ], + "spans": [ + { + "bbox": [ + 105, + 570, + 505, + 583 + ], + "score": 1.0, + "content": "remarkable how well Algorithm 1 performs without access to the input data at all. We found that", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 581, + 505, + 594 + ], + "spans": [ + { + "bbox": [ + 106, + 581, + 505, + 594 + ], + "score": 1.0, + "content": "weight matching offered a compelling balance between computational cost and performance: It runs", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 592, + 409, + 604 + ], + "spans": [ + { + "bbox": [ + 106, + 592, + 409, + 604 + ], + "score": 1.0, + "content": "in mere seconds (on current hardware) and produces high-quality solutions.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 32, + "bbox_fs": [ + 105, + 549, + 506, + 604 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 617, + 272, + 628 + ], + "lines": [ + { + "bbox": [ + 105, + 615, + 275, + 630 + ], + "spans": [ + { + "bbox": [ + 105, + 615, + 275, + 630 + ], + "score": 1.0, + "content": "5.2 ONSET OF MODE CONNECTIVITY", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 35 + }, + { + "type": "text", + "bbox": [ + 107, + 637, + 505, + 693 + ], + "lines": [ + { + "bbox": [ + 106, + 637, + 505, + 651 + ], + "spans": [ + { + "bbox": [ + 106, + 637, + 505, + 651 + ], + "score": 1.0, + "content": "Given the results of Section 5.1, it may be tempting to conclude that the entirety of weight space", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 649, + 505, + 661 + ], + "spans": [ + { + "bbox": [ + 106, + 649, + 505, + 661 + ], + "score": 1.0, + "content": "contains only a single basin modulo permutation symmetries. However, we found that linear mode", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 659, + 506, + 674 + ], + "spans": [ + { + "bbox": [ + 105, + 659, + 506, + 674 + ], + "score": 1.0, + "content": "connectivity is an emergent property of training, and we were unable to uncover it early in training.", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 669, + 505, + 684 + ], + "spans": [ + { + "bbox": [ + 105, + 669, + 505, + 684 + ], + "score": 1.0, + "content": "We explore the emergence of LMC in Figure 3. Concurrent to our work, Benzing et al. (2022)", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 681, + 482, + 695 + ], + "spans": [ + { + "bbox": [ + 105, + 681, + 482, + 695 + ], + "score": 1.0, + "content": "showed that LMC at initialization is possible using a permutation found at the end of training.", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 38, + "bbox_fs": [ + 105, + 637, + 506, + 695 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 108, + 82, + 504, + 116 + ], + "lines": [ + { + "bbox": [ + 105, + 81, + 506, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 81, + 506, + 96 + ], + "score": 1.0, + "content": "Note that the final inlaid interpolation plot in Figure 3(right) demonstrates an important shortcoming", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 93, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 106, + 93, + 505, + 106 + ], + "score": 1.0, + "content": "of the loss barrier metric, i.e., the interpolation includes points with lower loss than either of the two", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 105, + 501, + 117 + ], + "spans": [ + { + "bbox": [ + 106, + 105, + 501, + 117 + ], + "score": 1.0, + "content": "models. However, the loss barrier is still positive due to non-negativity, as mentioned in Section 2.", + "type": "text" + } + ], + "index": 2 + } + ], + "index": 1 + }, + { + "type": "title", + "bbox": [ + 108, + 129, + 246, + 141 + ], + "lines": [ + { + "bbox": [ + 105, + 128, + 248, + 142 + ], + "spans": [ + { + "bbox": [ + 105, + 128, + 248, + 142 + ], + "score": 1.0, + "content": "5.3 EFFECT OF MODEL WIDTH", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 3 + }, + { + "type": "text", + "bbox": [ + 107, + 150, + 505, + 194 + ], + "lines": [ + { + "bbox": [ + 105, + 150, + 505, + 162 + ], + "spans": [ + { + "bbox": [ + 105, + 150, + 505, + 162 + ], + "score": 1.0, + "content": "Conventional wisdom maintains that wider architectures are easier to optimize (Jacot et al., 2018;", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 161, + 505, + 173 + ], + "spans": [ + { + "bbox": [ + 105, + 161, + 505, + 173 + ], + "score": 1.0, + "content": "Lee et al., 2019). We now investigate whether they are also easier to linearly mode connect. We train", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 171, + 505, + 186 + ], + "spans": [ + { + "bbox": [ + 105, + 171, + 505, + 186 + ], + "score": 1.0, + "content": "VGG-16 (Simonyan & Zisserman, 2015) and ResNet20 (He et al., 2016) architectures of varying", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 183, + 380, + 195 + ], + "spans": [ + { + "bbox": [ + 105, + 183, + 380, + 195 + ], + "score": 1.0, + "content": "widths on the CIFAR-10 dataset. Results are presented in Figure 4.4", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 5.5 + }, + { + "type": "text", + "bbox": [ + 107, + 200, + 504, + 255 + ], + "lines": [ + { + "bbox": [ + 105, + 200, + 505, + 212 + ], + "spans": [ + { + "bbox": [ + 105, + 200, + 505, + 212 + ], + "score": 1.0, + "content": "A clear relationship emerges between model width and linear mode connectivity, as measured by", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 211, + 505, + 223 + ], + "spans": [ + { + "bbox": [ + 106, + 211, + 288, + 223 + ], + "score": 1.0, + "content": "the loss barrier between solutions. Although", + "type": "text" + }, + { + "bbox": [ + 288, + 212, + 302, + 222 + ], + "score": 0.85, + "content": "1 \\times", + "type": "inline_equation" + }, + { + "bbox": [ + 303, + 211, + 505, + 223 + ], + "score": 1.0, + "content": "-sized models did not seem to exhibit linear mode", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 222, + 505, + 234 + ], + "spans": [ + { + "bbox": [ + 105, + 222, + 505, + 234 + ], + "score": 1.0, + "content": "connectivity, we found that larger width models decreased loss barriers all the way to zero. In", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 232, + 506, + 245 + ], + "spans": [ + { + "bbox": [ + 105, + 232, + 506, + 245 + ], + "score": 1.0, + "content": "Figure 4(right), we show what is to our knowledge the premiere demonstration of zero-barrier linear", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 244, + 447, + 256 + ], + "spans": [ + { + "bbox": [ + 106, + 244, + 447, + 256 + ], + "score": 1.0, + "content": "mode connectivity between two large ResNet models trained on a non-trivial dataset.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 10 + }, + { + "type": "text", + "bbox": [ + 107, + 261, + 505, + 305 + ], + "lines": [ + { + "bbox": [ + 106, + 260, + 505, + 273 + ], + "spans": [ + { + "bbox": [ + 106, + 260, + 505, + 273 + ], + "score": 1.0, + "content": "We highlight that relatively thin models do not seem to obey linear mode connectivity yet still exhibit", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 271, + 506, + 285 + ], + "spans": [ + { + "bbox": [ + 105, + 271, + 506, + 285 + ], + "score": 1.0, + "content": "similarities in training dynamics. This suggests that either our permutation selection methods are", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 282, + 506, + 295 + ], + "spans": [ + { + "bbox": [ + 105, + 282, + 506, + 295 + ], + "score": 1.0, + "content": "failing to find satisfactory permutations on thinner models or that some form of invariance other than", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 294, + 372, + 307 + ], + "spans": [ + { + "bbox": [ + 105, + 294, + 372, + 307 + ], + "score": 1.0, + "content": "permutation symmetries must be at play in the thin model regime.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 14.5 + }, + { + "type": "title", + "bbox": [ + 108, + 318, + 446, + 330 + ], + "lines": [ + { + "bbox": [ + 106, + 318, + 449, + 331 + ], + "spans": [ + { + "bbox": [ + 106, + 318, + 449, + 331 + ], + "score": 1.0, + "content": "5.4 MODEL PATCHING, SPLIT DATA TRAINING, AND IMPROVED CALIBRATION", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 17 + }, + { + "type": "text", + "bbox": [ + 107, + 340, + 296, + 504 + ], + "lines": [ + { + "bbox": [ + 106, + 339, + 297, + 352 + ], + "spans": [ + { + "bbox": [ + 106, + 339, + 297, + 352 + ], + "score": 1.0, + "content": "Inspired by work on finetuning (Wortsman", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 349, + 297, + 363 + ], + "spans": [ + { + "bbox": [ + 105, + 349, + 297, + 363 + ], + "score": 1.0, + "content": "et al., 2022a), model patching (Singh &", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 361, + 297, + 373 + ], + "spans": [ + { + "bbox": [ + 105, + 361, + 297, + 373 + ], + "score": 1.0, + "content": "Jaggi, 2020; Raffel, 2021), and federated learn-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 372, + 297, + 385 + ], + "spans": [ + { + "bbox": [ + 106, + 372, + 297, + 385 + ], + "score": 1.0, + "content": "ing (McMahan et al., 2017; Konecnˇ y et al., ´", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 383, + 297, + 396 + ], + "spans": [ + { + "bbox": [ + 105, + 383, + 297, + 396 + ], + "score": 1.0, + "content": "2016a;b), we study whether it is possible to", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 394, + 297, + 406 + ], + "spans": [ + { + "bbox": [ + 105, + 394, + 297, + 406 + ], + "score": 1.0, + "content": "synergistically merge the weights of two mod-", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 405, + 297, + 417 + ], + "spans": [ + { + "bbox": [ + 106, + 405, + 297, + 417 + ], + "score": 1.0, + "content": "els trained on disjoint datasets. Consider, for", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 416, + 297, + 429 + ], + "spans": [ + { + "bbox": [ + 106, + 416, + 297, + 429 + ], + "score": 1.0, + "content": "example, an organization with multiple (pos-", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 426, + 297, + 440 + ], + "spans": [ + { + "bbox": [ + 105, + 426, + 297, + 440 + ], + "score": 1.0, + "content": "sibly biased) datasets separated for regulatory", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 438, + 297, + 450 + ], + "spans": [ + { + "bbox": [ + 105, + 438, + 297, + 450 + ], + "score": 1.0, + "content": "(e.g., GDPR) or privacy (e.g., on-device data)", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 449, + 297, + 460 + ], + "spans": [ + { + "bbox": [ + 106, + 449, + 297, + 460 + ], + "score": 1.0, + "content": "considerations. Models can be trained on each", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 459, + 297, + 473 + ], + "spans": [ + { + "bbox": [ + 106, + 459, + 297, + 473 + ], + "score": 1.0, + "content": "dataset individually, but training in aggregate", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 470, + 297, + 484 + ], + "spans": [ + { + "bbox": [ + 105, + 470, + 297, + 484 + ], + "score": 1.0, + "content": "is not feasible. Can we combine separately", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 482, + 297, + 494 + ], + "spans": [ + { + "bbox": [ + 106, + 482, + 297, + 494 + ], + "score": 1.0, + "content": "trained models so that the merged model per-", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 492, + 261, + 505 + ], + "spans": [ + { + "bbox": [ + 106, + 492, + 261, + 505 + ], + "score": 1.0, + "content": "forms well on the entirety of the data?", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 25 + }, + { + "type": "text", + "bbox": [ + 107, + 510, + 296, + 564 + ], + "lines": [ + { + "bbox": [ + 106, + 509, + 296, + 521 + ], + "spans": [ + { + "bbox": [ + 106, + 509, + 296, + 521 + ], + "score": 1.0, + "content": "To address this question, we split the CIFAR-", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 520, + 296, + 532 + ], + "spans": [ + { + "bbox": [ + 106, + 520, + 296, + 532 + ], + "score": 1.0, + "content": "100 dataset (Krizhevsky, 2009) into two dis-", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 532, + 297, + 543 + ], + "spans": [ + { + "bbox": [ + 105, + 532, + 192, + 543 + ], + "score": 1.0, + "content": "joint subsets: dataset", + "type": "text" + }, + { + "bbox": [ + 192, + 532, + 200, + 542 + ], + "score": 0.66, + "content": "A", + "type": "inline_equation" + }, + { + "bbox": [ + 201, + 532, + 249, + 543 + ], + "score": 1.0, + "content": ", containing", + "type": "text" + }, + { + "bbox": [ + 249, + 532, + 268, + 542 + ], + "score": 0.86, + "content": "20 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 269, + 532, + 297, + 543 + ], + "score": 1.0, + "content": "exam-", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 542, + 297, + 554 + ], + "spans": [ + { + "bbox": [ + 105, + 542, + 197, + 554 + ], + "score": 1.0, + "content": "ples labelled 0-49 and", + "type": "text" + }, + { + "bbox": [ + 197, + 543, + 217, + 554 + ], + "score": 0.86, + "content": "80 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 217, + 542, + 297, + 554 + ], + "score": 1.0, + "content": "labelled 50-99, and", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 554, + 297, + 565 + ], + "spans": [ + { + "bbox": [ + 106, + 554, + 137, + 565 + ], + "score": 1.0, + "content": "dataset", + "type": "text" + }, + { + "bbox": [ + 137, + 554, + 146, + 564 + ], + "score": 0.73, + "content": "B", + "type": "inline_equation" + }, + { + "bbox": [ + 146, + 554, + 270, + 565 + ], + "score": 1.0, + "content": ", vice versa. 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Algorithm 1", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 304, + 496, + 505, + 507 + ], + "spans": [ + { + "bbox": [ + 304, + 496, + 505, + 507 + ], + "score": 1.0, + "content": "makes it possible for two ResNet models trained", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 303, + 507, + 505, + 519 + ], + "spans": [ + { + "bbox": [ + 303, + 507, + 505, + 519 + ], + "score": 1.0, + "content": "on disjoint, biased subsets of CIFAR-100 to be", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 303, + 518, + 505, + 529 + ], + "spans": [ + { + "bbox": [ + 303, + 518, + 505, + 529 + ], + "score": 1.0, + "content": "merged in weight space such that their combina-", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 303, + 529, + 506, + 540 + ], + "spans": [ + { + "bbox": [ + 303, + 529, + 506, + 540 + ], + "score": 1.0, + "content": "tion outperforms both input models in terms of", + "type": "text" + } + ], + "index": 53 + }, + { + "bbox": [ + 304, + 540, + 440, + 551 + ], + "spans": [ + { + "bbox": [ + 304, + 540, + 440, + 551 + ], + "score": 1.0, + "content": "test loss on the combined dataset.", + "type": "text" + } + ], + "index": 54 + } + ], + "index": 51 + } + ], + "index": 46.75 + }, + { + "type": "text", + "bbox": [ + 107, + 565, + 506, + 609 + ], + "lines": [ + { + "bbox": [ + 106, + 565, + 506, + 576 + ], + "spans": [ + { + "bbox": [ + 106, + 565, + 116, + 574 + ], + "score": 0.76, + "content": "B", + "type": "inline_equation" + }, + { + "bbox": [ + 116, + 565, + 506, + 576 + ], + "score": 1.0, + "content": "were trained on their corresponding datasets. Privacy requirements mandate that we utilize a", + "type": "text" + } + ], + "index": 55 + }, + { + "bbox": [ + 106, + 576, + 505, + 588 + ], + "spans": [ + { + "bbox": [ + 106, + 576, + 505, + 588 + ], + "score": 1.0, + "content": "data-agnostic algorithm like Algorithm 1. Figure 5 shows the result of merging the two models with", + "type": "text" + } + ], + "index": 56 + }, + { + "bbox": [ + 105, + 586, + 505, + 599 + ], + "spans": [ + { + "bbox": [ + 105, + 586, + 505, + 599 + ], + "score": 1.0, + "content": "weight matching. For comparison, we benchmark na¨ıve weight interpolation, ensembling of the", + "type": "text" + } + ], + "index": 57 + }, + { + "bbox": [ + 105, + 596, + 250, + 611 + ], + "spans": [ + { + "bbox": [ + 105, + 596, + 250, + 611 + ], + "score": 1.0, + "content": "model logits, and full-data training.", + "type": "text" + } + ], + "index": 58 + } + ], + "index": 56.5 + }, + { + "type": "text", + "bbox": [ + 106, + 614, + 505, + 703 + ], + "lines": [ + { + "bbox": [ + 105, + 614, + 506, + 627 + ], + "spans": [ + { + "bbox": [ + 105, + 614, + 506, + 627 + ], + "score": 1.0, + "content": "As expected, merging separately trained models did not match the performance of an omniscient", + "type": "text" + } + ], + "index": 59 + }, + { + "bbox": [ + 106, + 626, + 505, + 637 + ], + "spans": [ + { + "bbox": [ + 106, + 626, + 505, + 637 + ], + "score": 1.0, + "content": "model trained on the full dataset or an ensemble of the two models with twice the number of effec-", + "type": "text" + } + ], + "index": 60 + }, + { + "bbox": [ + 105, + 635, + 505, + 650 + ], + "spans": [ + { + "bbox": [ + 105, + 635, + 505, + 650 + ], + "score": 1.0, + "content": "tive weights. On the other hand, we did manage to merge the two models in weight space, achieving", + "type": "text" + } + ], + "index": 61 + }, + { + "bbox": [ + 106, + 648, + 505, + 660 + ], + "spans": [ + { + "bbox": [ + 106, + 648, + 505, + 660 + ], + "score": 1.0, + "content": "an interpolated model that outperforms both input models in terms of test loss while using half the", + "type": "text" + } + ], + "index": 62 + }, + { + "bbox": [ + 104, + 659, + 505, + 671 + ], + "spans": [ + { + "bbox": [ + 104, + 659, + 505, + 671 + ], + "score": 1.0, + "content": "memory and compute required for ensembling. Furthermore, the merged model’s probability esti-", + "type": "text" + } + ], + "index": 63 + }, + { + "bbox": [ + 104, + 668, + 505, + 683 + ], + "spans": [ + { + "bbox": [ + 104, + 668, + 505, + 683 + ], + "score": 1.0, + "content": "mates are better calibrated than either of the input models as demonstrated in Figure 11. Accuracy", + "type": "text" + } + ], + "index": 64 + }, + { + "bbox": [ + 105, + 681, + 505, + 693 + ], + "spans": [ + { + "bbox": [ + 105, + 681, + 505, + 693 + ], + "score": 1.0, + "content": "results are presented in Figure 10. Algorithm 1 also vastly outperformed na¨ıve interpolation, the", + "type": "text" + } + ], + "index": 65 + }, + { + "bbox": [ + 105, + 690, + 426, + 705 + ], + "spans": [ + { + "bbox": [ + 105, + 690, + 426, + 705 + ], + "score": 1.0, + "content": "status quo for model combination in federated learning and distributed training.", + "type": "text" + } + ], + "index": 66 + } + ], + "index": 62.5 + } + ], + "page_idx": 7, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 711, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 117, + 709, + 506, + 724 + ], + "spans": [ + { + "bbox": [ + 117, + 709, + 177, + 724 + ], + "score": 1.0, + "content": "4Unfortunately,", + "type": "text" + }, + { + "bbox": [ + 177, + 712, + 190, + 721 + ], + "score": 0.81, + "content": "8 \\times", + "type": "inline_equation" + }, + { + "bbox": [ + 191, + 709, + 506, + 724 + ], + "score": 1.0, + "content": "width VGG-16 training was unattainable since it exhausted GPU memory on available", + "type": "text" + } + ] + }, + { + "bbox": [ + 105, + 719, + 223, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 719, + 223, + 734 + ], + "score": 1.0, + "content": "hardware at the time of writing.", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2023", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 752, + 308, + 760 + ], + "lines": [ + { + "bbox": [ + 301, + 750, + 310, + 762 + ], + "spans": [ + { + "bbox": [ + 301, + 750, + 310, + 762 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 12, + "width": 9 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 108, + 82, + 504, + 116 + ], + "lines": [ + { + "bbox": [ + 105, + 81, + 506, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 81, + 506, + 96 + ], + "score": 1.0, + "content": "Note that the final inlaid interpolation plot in Figure 3(right) demonstrates an important shortcoming", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 93, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 106, + 93, + 505, + 106 + ], + "score": 1.0, + "content": "of the loss barrier metric, i.e., the interpolation includes points with lower loss than either of the two", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 105, + 501, + 117 + ], + "spans": [ + { + "bbox": [ + 106, + 105, + 501, + 117 + ], + "score": 1.0, + "content": "models. However, the loss barrier is still positive due to non-negativity, as mentioned in Section 2.", + "type": "text" + } + ], + "index": 2 + } + ], + "index": 1, + "bbox_fs": [ + 105, + 81, + 506, + 117 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 129, + 246, + 141 + ], + "lines": [ + { + "bbox": [ + 105, + 128, + 248, + 142 + ], + "spans": [ + { + "bbox": [ + 105, + 128, + 248, + 142 + ], + "score": 1.0, + "content": "5.3 EFFECT OF MODEL WIDTH", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 3 + }, + { + "type": "text", + "bbox": [ + 107, + 150, + 505, + 194 + ], + "lines": [ + { + "bbox": [ + 105, + 150, + 505, + 162 + ], + "spans": [ + { + "bbox": [ + 105, + 150, + 505, + 162 + ], + "score": 1.0, + "content": "Conventional wisdom maintains that wider architectures are easier to optimize (Jacot et al., 2018;", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 161, + 505, + 173 + ], + "spans": [ + { + "bbox": [ + 105, + 161, + 505, + 173 + ], + "score": 1.0, + "content": "Lee et al., 2019). We now investigate whether they are also easier to linearly mode connect. We train", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 171, + 505, + 186 + ], + "spans": [ + { + "bbox": [ + 105, + 171, + 505, + 186 + ], + "score": 1.0, + "content": "VGG-16 (Simonyan & Zisserman, 2015) and ResNet20 (He et al., 2016) architectures of varying", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 183, + 380, + 195 + ], + "spans": [ + { + "bbox": [ + 105, + 183, + 380, + 195 + ], + "score": 1.0, + "content": "widths on the CIFAR-10 dataset. Results are presented in Figure 4.4", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 5.5, + "bbox_fs": [ + 105, + 150, + 505, + 195 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 200, + 504, + 255 + ], + "lines": [ + { + "bbox": [ + 105, + 200, + 505, + 212 + ], + "spans": [ + { + "bbox": [ + 105, + 200, + 505, + 212 + ], + "score": 1.0, + "content": "A clear relationship emerges between model width and linear mode connectivity, as measured by", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 211, + 505, + 223 + ], + "spans": [ + { + "bbox": [ + 106, + 211, + 288, + 223 + ], + "score": 1.0, + "content": "the loss barrier between solutions. Although", + "type": "text" + }, + { + "bbox": [ + 288, + 212, + 302, + 222 + ], + "score": 0.85, + "content": "1 \\times", + "type": "inline_equation" + }, + { + "bbox": [ + 303, + 211, + 505, + 223 + ], + "score": 1.0, + "content": "-sized models did not seem to exhibit linear mode", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 222, + 505, + 234 + ], + "spans": [ + { + "bbox": [ + 105, + 222, + 505, + 234 + ], + "score": 1.0, + "content": "connectivity, we found that larger width models decreased loss barriers all the way to zero. In", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 232, + 506, + 245 + ], + "spans": [ + { + "bbox": [ + 105, + 232, + 506, + 245 + ], + "score": 1.0, + "content": "Figure 4(right), we show what is to our knowledge the premiere demonstration of zero-barrier linear", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 244, + 447, + 256 + ], + "spans": [ + { + "bbox": [ + 106, + 244, + 447, + 256 + ], + "score": 1.0, + "content": "mode connectivity between two large ResNet models trained on a non-trivial dataset.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 10, + "bbox_fs": [ + 105, + 200, + 506, + 256 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 261, + 505, + 305 + ], + "lines": [ + { + "bbox": [ + 106, + 260, + 505, + 273 + ], + "spans": [ + { + "bbox": [ + 106, + 260, + 505, + 273 + ], + "score": 1.0, + "content": "We highlight that relatively thin models do not seem to obey linear mode connectivity yet still exhibit", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 271, + 506, + 285 + ], + "spans": [ + { + "bbox": [ + 105, + 271, + 506, + 285 + ], + "score": 1.0, + "content": "similarities in training dynamics. This suggests that either our permutation selection methods are", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 282, + 506, + 295 + ], + "spans": [ + { + "bbox": [ + 105, + 282, + 506, + 295 + ], + "score": 1.0, + "content": "failing to find satisfactory permutations on thinner models or that some form of invariance other than", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 294, + 372, + 307 + ], + "spans": [ + { + "bbox": [ + 105, + 294, + 372, + 307 + ], + "score": 1.0, + "content": "permutation symmetries must be at play in the thin model regime.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 14.5, + "bbox_fs": [ + 105, + 260, + 506, + 307 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 318, + 446, + 330 + ], + "lines": [ + { + "bbox": [ + 106, + 318, + 449, + 331 + ], + "spans": [ + { + "bbox": [ + 106, + 318, + 449, + 331 + ], + "score": 1.0, + "content": "5.4 MODEL PATCHING, SPLIT DATA TRAINING, AND IMPROVED CALIBRATION", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 17 + }, + { + "type": "text", + "bbox": [ + 107, + 340, + 296, + 504 + ], + "lines": [ + { + "bbox": [ + 106, + 339, + 297, + 352 + ], + "spans": [ + { + "bbox": [ + 106, + 339, + 297, + 352 + ], + "score": 1.0, + "content": "Inspired by work on finetuning (Wortsman", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 349, + 297, + 363 + ], + "spans": [ + { + "bbox": [ + 105, + 349, + 297, + 363 + ], + "score": 1.0, + "content": "et al., 2022a), model patching (Singh &", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 361, + 297, + 373 + ], + "spans": [ + { + "bbox": [ + 105, + 361, + 297, + 373 + ], + "score": 1.0, + "content": "Jaggi, 2020; Raffel, 2021), and federated learn-", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 372, + 297, + 385 + ], + "spans": [ + { + "bbox": [ + 106, + 372, + 297, + 385 + ], + "score": 1.0, + "content": "ing (McMahan et al., 2017; Konecnˇ y et al., ´", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 383, + 297, + 396 + ], + "spans": [ + { + "bbox": [ + 105, + 383, + 297, + 396 + ], + "score": 1.0, + "content": "2016a;b), we study whether it is possible to", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 394, + 297, + 406 + ], + "spans": [ + { + "bbox": [ + 105, + 394, + 297, + 406 + ], + "score": 1.0, + "content": "synergistically merge the weights of two mod-", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 405, + 297, + 417 + ], + "spans": [ + { + "bbox": [ + 106, + 405, + 297, + 417 + ], + "score": 1.0, + "content": "els trained on disjoint datasets. Consider, for", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 416, + 297, + 429 + ], + "spans": [ + { + "bbox": [ + 106, + 416, + 297, + 429 + ], + "score": 1.0, + "content": "example, an organization with multiple (pos-", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 426, + 297, + 440 + ], + "spans": [ + { + "bbox": [ + 105, + 426, + 297, + 440 + ], + "score": 1.0, + "content": "sibly biased) datasets separated for regulatory", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 438, + 297, + 450 + ], + "spans": [ + { + "bbox": [ + 105, + 438, + 297, + 450 + ], + "score": 1.0, + "content": "(e.g., GDPR) or privacy (e.g., on-device data)", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 449, + 297, + 460 + ], + "spans": [ + { + "bbox": [ + 106, + 449, + 297, + 460 + ], + "score": 1.0, + "content": "considerations. Models can be trained on each", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 459, + 297, + 473 + ], + "spans": [ + { + "bbox": [ + 106, + 459, + 297, + 473 + ], + "score": 1.0, + "content": "dataset individually, but training in aggregate", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 470, + 297, + 484 + ], + "spans": [ + { + "bbox": [ + 105, + 470, + 297, + 484 + ], + "score": 1.0, + "content": "is not feasible. Can we combine separately", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 482, + 297, + 494 + ], + "spans": [ + { + "bbox": [ + 106, + 482, + 297, + 494 + ], + "score": 1.0, + "content": "trained models so that the merged model per-", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 492, + 261, + 505 + ], + "spans": [ + { + "bbox": [ + 106, + 492, + 261, + 505 + ], + "score": 1.0, + "content": "forms well on the entirety of the data?", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 25, + "bbox_fs": [ + 105, + 339, + 297, + 505 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 510, + 296, + 564 + ], + "lines": [ + { + "bbox": [ + 106, + 509, + 296, + 521 + ], + "spans": [ + { + "bbox": [ + 106, + 509, + 296, + 521 + ], + "score": 1.0, + "content": "To address this question, we split the CIFAR-", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 520, + 296, + 532 + ], + "spans": [ + { + "bbox": [ + 106, + 520, + 296, + 532 + ], + "score": 1.0, + "content": "100 dataset (Krizhevsky, 2009) into two dis-", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 532, + 297, + 543 + ], + "spans": [ + { + "bbox": [ + 105, + 532, + 192, + 543 + ], + "score": 1.0, + "content": "joint subsets: dataset", + "type": "text" + }, + { + "bbox": [ + 192, + 532, + 200, + 542 + ], + "score": 0.66, + "content": "A", + "type": "inline_equation" + }, + { + "bbox": [ + 201, + 532, + 249, + 543 + ], + "score": 1.0, + "content": ", containing", + "type": "text" + }, + { + "bbox": [ + 249, + 532, + 268, + 542 + ], + "score": 0.86, + "content": "20 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 269, + 532, + 297, + 543 + ], + "score": 1.0, + "content": "exam-", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 542, + 297, + 554 + ], + "spans": [ + { + "bbox": [ + 105, + 542, + 197, + 554 + ], + "score": 1.0, + "content": "ples labelled 0-49 and", + "type": "text" + }, + { + "bbox": [ + 197, + 543, + 217, + 554 + ], + "score": 0.86, + "content": "80 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 217, + 542, + 297, + 554 + ], + "score": 1.0, + "content": "labelled 50-99, and", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 554, + 297, + 565 + ], + "spans": [ + { + "bbox": [ + 106, + 554, + 137, + 565 + ], + "score": 1.0, + "content": "dataset", + "type": "text" + }, + { + "bbox": [ + 137, + 554, + 146, + 564 + ], + "score": 0.73, + "content": "B", + "type": "inline_equation" + }, + { + "bbox": [ + 146, + 554, + 270, + 565 + ], + "score": 1.0, + "content": ", vice versa. 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Algorithm 1", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 304, + 496, + 505, + 507 + ], + "spans": [ + { + "bbox": [ + 304, + 496, + 505, + 507 + ], + "score": 1.0, + "content": "makes it possible for two ResNet models trained", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 303, + 507, + 505, + 519 + ], + "spans": [ + { + "bbox": [ + 303, + 507, + 505, + 519 + ], + "score": 1.0, + "content": "on disjoint, biased subsets of CIFAR-100 to be", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 303, + 518, + 505, + 529 + ], + "spans": [ + { + "bbox": [ + 303, + 518, + 505, + 529 + ], + "score": 1.0, + "content": "merged in weight space such that their combina-", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 303, + 529, + 506, + 540 + ], + "spans": [ + { + "bbox": [ + 303, + 529, + 506, + 540 + ], + "score": 1.0, + "content": "tion outperforms both input models in terms of", + "type": "text" + } + ], + "index": 53 + }, + { + "bbox": [ + 304, + 540, + 440, + 551 + ], + "spans": [ + { + "bbox": [ + 304, + 540, + 440, + 551 + ], + "score": 1.0, + "content": "test loss on the combined dataset.", + "type": "text" + } + ], + "index": 54 + } + ], + "index": 51 + } + ], + "index": 46.75 + }, + { + "type": "text", + "bbox": [ + 107, + 565, + 506, + 609 + ], + "lines": [ + { + "bbox": [ + 106, + 565, + 506, + 576 + ], + "spans": [ + { + "bbox": [ + 106, + 565, + 116, + 574 + ], + "score": 0.76, + "content": "B", + "type": "inline_equation" + }, + { + "bbox": [ + 116, + 565, + 506, + 576 + ], + "score": 1.0, + "content": "were trained on their corresponding datasets. Privacy requirements mandate that we utilize a", + "type": "text" + } + ], + "index": 55 + }, + { + "bbox": [ + 106, + 576, + 505, + 588 + ], + "spans": [ + { + "bbox": [ + 106, + 576, + 505, + 588 + ], + "score": 1.0, + "content": "data-agnostic algorithm like Algorithm 1. Figure 5 shows the result of merging the two models with", + "type": "text" + } + ], + "index": 56 + }, + { + "bbox": [ + 105, + 586, + 505, + 599 + ], + "spans": [ + { + "bbox": [ + 105, + 586, + 505, + 599 + ], + "score": 1.0, + "content": "weight matching. For comparison, we benchmark na¨ıve weight interpolation, ensembling of the", + "type": "text" + } + ], + "index": 57 + }, + { + "bbox": [ + 105, + 596, + 250, + 611 + ], + "spans": [ + { + "bbox": [ + 105, + 596, + 250, + 611 + ], + "score": 1.0, + "content": "model logits, and full-data training.", + "type": "text" + } + ], + "index": 58 + } + ], + "index": 56.5, + "bbox_fs": [ + 105, + 565, + 506, + 611 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 614, + 505, + 703 + ], + "lines": [ + { + "bbox": [ + 105, + 614, + 506, + 627 + ], + "spans": [ + { + "bbox": [ + 105, + 614, + 506, + 627 + ], + "score": 1.0, + "content": "As expected, merging separately trained models did not match the performance of an omniscient", + "type": "text" + } + ], + "index": 59 + }, + { + "bbox": [ + 106, + 626, + 505, + 637 + ], + "spans": [ + { + "bbox": [ + 106, + 626, + 505, + 637 + ], + "score": 1.0, + "content": "model trained on the full dataset or an ensemble of the two models with twice the number of effec-", + "type": "text" + } + ], + "index": 60 + }, + { + "bbox": [ + 105, + 635, + 505, + 650 + ], + "spans": [ + { + "bbox": [ + 105, + 635, + 505, + 650 + ], + "score": 1.0, + "content": "tive weights. On the other hand, we did manage to merge the two models in weight space, achieving", + "type": "text" + } + ], + "index": 61 + }, + { + "bbox": [ + 106, + 648, + 505, + 660 + ], + "spans": [ + { + "bbox": [ + 106, + 648, + 505, + 660 + ], + "score": 1.0, + "content": "an interpolated model that outperforms both input models in terms of test loss while using half the", + "type": "text" + } + ], + "index": 62 + }, + { + "bbox": [ + 104, + 659, + 505, + 671 + ], + "spans": [ + { + "bbox": [ + 104, + 659, + 505, + 671 + ], + "score": 1.0, + "content": "memory and compute required for ensembling. Furthermore, the merged model’s probability esti-", + "type": "text" + } + ], + "index": 63 + }, + { + "bbox": [ + 104, + 668, + 505, + 683 + ], + "spans": [ + { + "bbox": [ + 104, + 668, + 505, + 683 + ], + "score": 1.0, + "content": "mates are better calibrated than either of the input models as demonstrated in Figure 11. Accuracy", + "type": "text" + } + ], + "index": 64 + }, + { + "bbox": [ + 105, + 681, + 505, + 693 + ], + "spans": [ + { + "bbox": [ + 105, + 681, + 505, + 693 + ], + "score": 1.0, + "content": "results are presented in Figure 10. Algorithm 1 also vastly outperformed na¨ıve interpolation, the", + "type": "text" + } + ], + "index": 65 + }, + { + "bbox": [ + 105, + 690, + 426, + 705 + ], + "spans": [ + { + "bbox": [ + 105, + 690, + 426, + 705 + ], + "score": 1.0, + "content": "status quo for model combination in federated learning and distributed training.", + "type": "text" + } + ], + "index": 66 + } + ], + "index": 62.5, + "bbox_fs": [ + 104, + 614, + 506, + 705 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 108, + 81, + 211, + 93 + ], + "lines": [ + { + "bbox": [ + 105, + 80, + 213, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 80, + 213, + 95 + ], + "score": 1.0, + "content": "6 RELATED WORK", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 107, + 106, + 505, + 238 + ], + "lines": [ + { + "bbox": [ + 106, + 106, + 505, + 119 + ], + "spans": [ + { + "bbox": [ + 106, + 106, + 505, + 119 + ], + "score": 1.0, + "content": "(Linear) mode connectivity. Garipov et al. (2018); Draxler et al. (2018); Freeman & Bruna (2017)", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 117, + 506, + 129 + ], + "spans": [ + { + "bbox": [ + 105, + 117, + 506, + 129 + ], + "score": 1.0, + "content": "showed that different solutions in the neural network loss landscape could be connected by paths of", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 104, + 127, + 505, + 141 + ], + "spans": [ + { + "bbox": [ + 104, + 127, + 505, + 141 + ], + "score": 1.0, + "content": "near-constant loss, which Garipov et al. (2018) coined “mode connectivity.” Tatro et al. (2020) ex-", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 139, + 504, + 151 + ], + "spans": [ + { + "bbox": [ + 105, + 139, + 504, + 151 + ], + "score": 1.0, + "content": "plored non-linear mode connectivity modulo permutation symmetries. Frankle et al. (2020) demon-", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 151, + 505, + 163 + ], + "spans": [ + { + "bbox": [ + 105, + 151, + 505, + 163 + ], + "score": 1.0, + "content": "strated a connection between linear mode connectivity and the lottery ticket hypothesis. Juneja et al.", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 161, + 505, + 173 + ], + "spans": [ + { + "bbox": [ + 105, + 161, + 505, + 173 + ], + "score": 1.0, + "content": "(2022) demonstrated that LMC does not always hold, even when fine-tuning. Hecht-Nielsen (1990);", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 172, + 505, + 184 + ], + "spans": [ + { + "bbox": [ + 105, + 172, + 505, + 184 + ], + "score": 1.0, + "content": "Chen et al. (1993) noted the existence of permutation symmetries, and Brea et al. (2019) implicated", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 183, + 505, + 195 + ], + "spans": [ + { + "bbox": [ + 105, + 183, + 505, + 195 + ], + "score": 1.0, + "content": "them as a source of saddle points in the loss landscape. Recently, the prescient work of Entezari", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 194, + 505, + 206 + ], + "spans": [ + { + "bbox": [ + 105, + 194, + 505, + 206 + ], + "score": 1.0, + "content": "et al. (2021) conjectured that SGD solutions could be linear mode connected modulo permutation", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 205, + 505, + 218 + ], + "spans": [ + { + "bbox": [ + 105, + 205, + 505, + 218 + ], + "score": 1.0, + "content": "symmetries and offered experiments buttressing this claim. Unlike previous works on LMC we ac-", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 216, + 505, + 228 + ], + "spans": [ + { + "bbox": [ + 105, + 216, + 505, + 228 + ], + "score": 1.0, + "content": "complish zero-barrier paths between two independently-trained models with an algorithm that runs", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 227, + 204, + 238 + ], + "spans": [ + { + "bbox": [ + 106, + 227, + 204, + 238 + ], + "score": 1.0, + "content": "on the order of seconds.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 6.5 + }, + { + "type": "text", + "bbox": [ + 107, + 244, + 505, + 365 + ], + "lines": [ + { + "bbox": [ + 105, + 244, + 505, + 256 + ], + "spans": [ + { + "bbox": [ + 105, + 244, + 505, + 256 + ], + "score": 1.0, + "content": "Loss landscapes and training dynamics. Li et al. (2016); Yosinski et al. (2014) investigated", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 255, + 505, + 267 + ], + "spans": [ + { + "bbox": [ + 105, + 255, + 505, + 267 + ], + "score": 1.0, + "content": "whether independently trained networks learn similar features, and to what extent they transfer.", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 265, + 505, + 279 + ], + "spans": [ + { + "bbox": [ + 105, + 265, + 505, + 279 + ], + "score": 1.0, + "content": "Jiang et al. (2021) argued that independently trained networks meaningfully differ in the features", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 277, + 505, + 289 + ], + "spans": [ + { + "bbox": [ + 105, + 277, + 505, + 289 + ], + "score": 1.0, + "content": "they learn in certain scenarios. Zhang et al. (2019) studied the relative importance of layers. Ben-", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 287, + 505, + 300 + ], + "spans": [ + { + "bbox": [ + 105, + 287, + 505, + 300 + ], + "score": 1.0, + "content": "ton et al. (2021) argued that SGD solutions form a connected volume of low loss. Pittorino et al.", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 298, + 505, + 311 + ], + "spans": [ + { + "bbox": [ + 106, + 298, + 505, + 311 + ], + "score": 1.0, + "content": "(2022) proposed a toroidal topology of solutions and a set of algorithms for symmetry removal. On", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 309, + 505, + 322 + ], + "spans": [ + { + "bbox": [ + 105, + 309, + 505, + 322 + ], + "score": 1.0, + "content": "the theoretical front, Kawaguchi (2016) proved that deep linear networks contain no local minima.", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 321, + 505, + 333 + ], + "spans": [ + { + "bbox": [ + 105, + 321, + 505, + 333 + ], + "score": 1.0, + "content": "Boursier et al. (2022); Chizat & Bach (2018); Mei et al. (2018) characterized the training dynamics", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 331, + 505, + 344 + ], + "spans": [ + { + "bbox": [ + 105, + 331, + 505, + 344 + ], + "score": 1.0, + "content": "of one-hidden layer networks, proving that they converge to zero loss. Godfrey et al. (2022); Sim-", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 343, + 505, + 355 + ], + "spans": [ + { + "bbox": [ + 105, + 343, + 505, + 355 + ], + "score": 1.0, + "content": "sek et al. (2021) investigated the algebraic structure of symmetries in neural networks and how this", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 353, + 297, + 366 + ], + "spans": [ + { + "bbox": [ + 105, + 353, + 297, + 366 + ], + "score": 1.0, + "content": "structure manifests in loss landscape geometry.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 18 + }, + { + "type": "text", + "bbox": [ + 106, + 370, + 505, + 513 + ], + "lines": [ + { + "bbox": [ + 105, + 369, + 505, + 383 + ], + "spans": [ + { + "bbox": [ + 105, + 369, + 505, + 383 + ], + "score": 1.0, + "content": "Federated learning and model merging. McMahan et al. (2017); Konecnˇ y et al. (2016a;b) in- ´", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 381, + 506, + 394 + ], + "spans": [ + { + "bbox": [ + 106, + 381, + 506, + 394 + ], + "score": 1.0, + "content": "troduced the concept of “federated learning,” i.e., learning split across across multiple devices and", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 390, + 505, + 406 + ], + "spans": [ + { + "bbox": [ + 105, + 390, + 505, + 406 + ], + "score": 1.0, + "content": "datasets. Wang et al. (2020) proposed an exciting federated learning method in which model averag-", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 402, + 505, + 416 + ], + "spans": [ + { + "bbox": [ + 105, + 402, + 505, + 416 + ], + "score": 1.0, + "content": "ing is done after permuting units. Unlike this work, they merged smaller “child” models into a larger", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 414, + 506, + 427 + ], + "spans": [ + { + "bbox": [ + 106, + 414, + 506, + 427 + ], + "score": 1.0, + "content": "“main” model, and did so with a layer-wise algorithm that does not support residual connections or", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 425, + 505, + 438 + ], + "spans": [ + { + "bbox": [ + 105, + 425, + 505, + 438 + ], + "score": 1.0, + "content": "normalization layers. Raffel (2021); Matena & Raffel (2021); Sung et al. (2021) conceptualized the", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 435, + 505, + 450 + ], + "spans": [ + { + "bbox": [ + 105, + 435, + 505, + 450 + ], + "score": 1.0, + "content": "study of “model patching,” i.e., the idea that models should be easy to modify and submit changes", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 447, + 505, + 460 + ], + "spans": [ + { + "bbox": [ + 105, + 447, + 505, + 460 + ], + "score": 1.0, + "content": "to. Ilharco et al. (2022) investigated model patching for the fine-tuning of open-vocabulary vision", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 457, + 505, + 471 + ], + "spans": [ + { + "bbox": [ + 105, + 457, + 505, + 471 + ], + "score": 1.0, + "content": "models. Ashmore & Gashler (2015) first explored the use of matching algorithms for the alignment", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 469, + 505, + 482 + ], + "spans": [ + { + "bbox": [ + 106, + 469, + 505, + 482 + ], + "score": 1.0, + "content": "of network units. Singh & Jaggi (2020) proposed merging models by soft-aligning associations", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 480, + 505, + 493 + ], + "spans": [ + { + "bbox": [ + 106, + 480, + 505, + 493 + ], + "score": 1.0, + "content": "weights, inspired by optimal transport. Liu et al. (2022a); Uriot & Izzo (2020) further explored", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 490, + 506, + 504 + ], + "spans": [ + { + "bbox": [ + 105, + 490, + 506, + 504 + ], + "score": 1.0, + "content": "merging models taking possible permutations into account. Wortsman et al. (2022a) demonstrated", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 501, + 477, + 515 + ], + "spans": [ + { + "bbox": [ + 106, + 501, + 477, + 515 + ], + "score": 1.0, + "content": "state-of-the-art ImageNet performance by averaging the weights of many fine-tuned models.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 30 + }, + { + "type": "title", + "bbox": [ + 108, + 529, + 297, + 542 + ], + "lines": [ + { + "bbox": [ + 105, + 528, + 299, + 544 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 299, + 544 + ], + "score": 1.0, + "content": "7 DISCUSSION AND FUTURE WORK", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 37 + }, + { + "type": "text", + "bbox": [ + 107, + 554, + 505, + 664 + ], + "lines": [ + { + "bbox": [ + 106, + 554, + 505, + 567 + ], + "spans": [ + { + "bbox": [ + 106, + 554, + 505, + 567 + ], + "score": 1.0, + "content": "We explore the role of permutation symmetries in the linear mode connectivity of SGD solutions.", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 566, + 505, + 577 + ], + "spans": [ + { + "bbox": [ + 106, + 566, + 505, + 577 + ], + "score": 1.0, + "content": "We present three algorithms to canonicalize independent neural network weights in order to make", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 576, + 505, + 589 + ], + "spans": [ + { + "bbox": [ + 105, + 576, + 505, + 589 + ], + "score": 1.0, + "content": "the loss landscape between them as flat as possible. In contrast to prior work, we linearly mode", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 587, + 505, + 600 + ], + "spans": [ + { + "bbox": [ + 105, + 587, + 505, + 600 + ], + "score": 1.0, + "content": "connect large ResNet models with no barrier in seconds to minutes. Despite presenting successes", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 599, + 505, + 610 + ], + "spans": [ + { + "bbox": [ + 105, + 599, + 505, + 610 + ], + "score": 1.0, + "content": "across multiple architectures and datasets, linear mode connectivity between thin models remains", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 609, + 506, + 622 + ], + "spans": [ + { + "bbox": [ + 105, + 609, + 506, + 622 + ], + "score": 1.0, + "content": "elusive. Therefore, we conjecture that permutation symmetries are a necessary piece, though not a", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 620, + 505, + 633 + ], + "spans": [ + { + "bbox": [ + 105, + 620, + 505, + 633 + ], + "score": 1.0, + "content": "complete picture, of the fundamental invariances at play in neural network training dynamics. In", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 632, + 505, + 644 + ], + "spans": [ + { + "bbox": [ + 105, + 632, + 505, + 644 + ], + "score": 1.0, + "content": "particular, we hypothesize that linear, possibly non-permutation, relationships connect the layer-", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 641, + 505, + 655 + ], + "spans": [ + { + "bbox": [ + 105, + 641, + 505, + 655 + ], + "score": 1.0, + "content": "wise activations between models trained by SGD. In the infinite width limit, there exist satisfactory", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 653, + 292, + 665 + ], + "spans": [ + { + "bbox": [ + 105, + 653, + 292, + 665 + ], + "score": 1.0, + "content": "linear relationships that are also permutations.", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 42.5 + }, + { + "type": "text", + "bbox": [ + 108, + 669, + 504, + 725 + ], + "lines": [ + { + "bbox": [ + 107, + 670, + 505, + 682 + ], + "spans": [ + { + "bbox": [ + 107, + 670, + 505, + 682 + ], + "score": 1.0, + "content": "An expanded theory and empirical exploration of other invariances – such as cross-layer scaling or", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 681, + 505, + 693 + ], + "spans": [ + { + "bbox": [ + 105, + 681, + 505, + 693 + ], + "score": 1.0, + "content": "general linear relationships between activations – presents an intriguing avenue for future work. Ul-", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 106, + 691, + 506, + 705 + ], + "spans": [ + { + "bbox": [ + 106, + 691, + 506, + 705 + ], + "score": 1.0, + "content": "timately, we anticipate that a lucid understanding of loss landscape geometry will not only advance", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 106, + 703, + 506, + 716 + ], + "spans": [ + { + "bbox": [ + 106, + 703, + 506, + 716 + ], + "score": 1.0, + "content": "the theory of deep learning but will also promote the development of better optimization, federated", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 106, + 713, + 257, + 727 + ], + "spans": [ + { + "bbox": [ + 106, + 713, + 257, + 727 + ], + "score": 1.0, + "content": "learning, and ensembling techniques.", + "type": "text" + } + ], + "index": 52 + } + ], + "index": 50 + } + ], + "page_idx": 8, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2023", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 308, + 759 + ], + "lines": [ + { + "bbox": [ + 302, + 751, + 309, + 762 + ], + "spans": [ + { + "bbox": [ + 302, + 751, + 309, + 762 + ], + "score": 1.0, + "content": "9", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 108, + 81, + 211, + 93 + ], + "lines": [ + { + "bbox": [ + 105, + 80, + 213, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 80, + 213, + 95 + ], + "score": 1.0, + "content": "6 RELATED WORK", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 107, + 106, + 505, + 238 + ], + "lines": [ + { + "bbox": [ + 106, + 106, + 505, + 119 + ], + "spans": [ + { + "bbox": [ + 106, + 106, + 505, + 119 + ], + "score": 1.0, + "content": "(Linear) mode connectivity. Garipov et al. (2018); Draxler et al. (2018); Freeman & Bruna (2017)", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 117, + 506, + 129 + ], + "spans": [ + { + "bbox": [ + 105, + 117, + 506, + 129 + ], + "score": 1.0, + "content": "showed that different solutions in the neural network loss landscape could be connected by paths of", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 104, + 127, + 505, + 141 + ], + "spans": [ + { + "bbox": [ + 104, + 127, + 505, + 141 + ], + "score": 1.0, + "content": "near-constant loss, which Garipov et al. (2018) coined “mode connectivity.” Tatro et al. (2020) ex-", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 139, + 504, + 151 + ], + "spans": [ + { + "bbox": [ + 105, + 139, + 504, + 151 + ], + "score": 1.0, + "content": "plored non-linear mode connectivity modulo permutation symmetries. Frankle et al. (2020) demon-", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 151, + 505, + 163 + ], + "spans": [ + { + "bbox": [ + 105, + 151, + 505, + 163 + ], + "score": 1.0, + "content": "strated a connection between linear mode connectivity and the lottery ticket hypothesis. Juneja et al.", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 161, + 505, + 173 + ], + "spans": [ + { + "bbox": [ + 105, + 161, + 505, + 173 + ], + "score": 1.0, + "content": "(2022) demonstrated that LMC does not always hold, even when fine-tuning. Hecht-Nielsen (1990);", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 172, + 505, + 184 + ], + "spans": [ + { + "bbox": [ + 105, + 172, + 505, + 184 + ], + "score": 1.0, + "content": "Chen et al. (1993) noted the existence of permutation symmetries, and Brea et al. (2019) implicated", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 183, + 505, + 195 + ], + "spans": [ + { + "bbox": [ + 105, + 183, + 505, + 195 + ], + "score": 1.0, + "content": "them as a source of saddle points in the loss landscape. Recently, the prescient work of Entezari", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 194, + 505, + 206 + ], + "spans": [ + { + "bbox": [ + 105, + 194, + 505, + 206 + ], + "score": 1.0, + "content": "et al. (2021) conjectured that SGD solutions could be linear mode connected modulo permutation", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 205, + 505, + 218 + ], + "spans": [ + { + "bbox": [ + 105, + 205, + 505, + 218 + ], + "score": 1.0, + "content": "symmetries and offered experiments buttressing this claim. Unlike previous works on LMC we ac-", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 216, + 505, + 228 + ], + "spans": [ + { + "bbox": [ + 105, + 216, + 505, + 228 + ], + "score": 1.0, + "content": "complish zero-barrier paths between two independently-trained models with an algorithm that runs", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 227, + 204, + 238 + ], + "spans": [ + { + "bbox": [ + 106, + 227, + 204, + 238 + ], + "score": 1.0, + "content": "on the order of seconds.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 6.5, + "bbox_fs": [ + 104, + 106, + 506, + 238 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 244, + 505, + 365 + ], + "lines": [ + { + "bbox": [ + 105, + 244, + 505, + 256 + ], + "spans": [ + { + "bbox": [ + 105, + 244, + 505, + 256 + ], + "score": 1.0, + "content": "Loss landscapes and training dynamics. Li et al. (2016); Yosinski et al. (2014) investigated", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 255, + 505, + 267 + ], + "spans": [ + { + "bbox": [ + 105, + 255, + 505, + 267 + ], + "score": 1.0, + "content": "whether independently trained networks learn similar features, and to what extent they transfer.", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 265, + 505, + 279 + ], + "spans": [ + { + "bbox": [ + 105, + 265, + 505, + 279 + ], + "score": 1.0, + "content": "Jiang et al. (2021) argued that independently trained networks meaningfully differ in the features", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 277, + 505, + 289 + ], + "spans": [ + { + "bbox": [ + 105, + 277, + 505, + 289 + ], + "score": 1.0, + "content": "they learn in certain scenarios. Zhang et al. (2019) studied the relative importance of layers. Ben-", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 287, + 505, + 300 + ], + "spans": [ + { + "bbox": [ + 105, + 287, + 505, + 300 + ], + "score": 1.0, + "content": "ton et al. (2021) argued that SGD solutions form a connected volume of low loss. Pittorino et al.", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 298, + 505, + 311 + ], + "spans": [ + { + "bbox": [ + 106, + 298, + 505, + 311 + ], + "score": 1.0, + "content": "(2022) proposed a toroidal topology of solutions and a set of algorithms for symmetry removal. On", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 309, + 505, + 322 + ], + "spans": [ + { + "bbox": [ + 105, + 309, + 505, + 322 + ], + "score": 1.0, + "content": "the theoretical front, Kawaguchi (2016) proved that deep linear networks contain no local minima.", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 321, + 505, + 333 + ], + "spans": [ + { + "bbox": [ + 105, + 321, + 505, + 333 + ], + "score": 1.0, + "content": "Boursier et al. (2022); Chizat & Bach (2018); Mei et al. (2018) characterized the training dynamics", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 331, + 505, + 344 + ], + "spans": [ + { + "bbox": [ + 105, + 331, + 505, + 344 + ], + "score": 1.0, + "content": "of one-hidden layer networks, proving that they converge to zero loss. Godfrey et al. (2022); Sim-", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 343, + 505, + 355 + ], + "spans": [ + { + "bbox": [ + 105, + 343, + 505, + 355 + ], + "score": 1.0, + "content": "sek et al. (2021) investigated the algebraic structure of symmetries in neural networks and how this", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 353, + 297, + 366 + ], + "spans": [ + { + "bbox": [ + 105, + 353, + 297, + 366 + ], + "score": 1.0, + "content": "structure manifests in loss landscape geometry.", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 18, + "bbox_fs": [ + 105, + 244, + 505, + 366 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 370, + 505, + 513 + ], + "lines": [ + { + "bbox": [ + 105, + 369, + 505, + 383 + ], + "spans": [ + { + "bbox": [ + 105, + 369, + 505, + 383 + ], + "score": 1.0, + "content": "Federated learning and model merging. McMahan et al. (2017); Konecnˇ y et al. (2016a;b) in- ´", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 381, + 506, + 394 + ], + "spans": [ + { + "bbox": [ + 106, + 381, + 506, + 394 + ], + "score": 1.0, + "content": "troduced the concept of “federated learning,” i.e., learning split across across multiple devices and", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 390, + 505, + 406 + ], + "spans": [ + { + "bbox": [ + 105, + 390, + 505, + 406 + ], + "score": 1.0, + "content": "datasets. Wang et al. (2020) proposed an exciting federated learning method in which model averag-", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 402, + 505, + 416 + ], + "spans": [ + { + "bbox": [ + 105, + 402, + 505, + 416 + ], + "score": 1.0, + "content": "ing is done after permuting units. Unlike this work, they merged smaller “child” models into a larger", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 414, + 506, + 427 + ], + "spans": [ + { + "bbox": [ + 106, + 414, + 506, + 427 + ], + "score": 1.0, + "content": "“main” model, and did so with a layer-wise algorithm that does not support residual connections or", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 425, + 505, + 438 + ], + "spans": [ + { + "bbox": [ + 105, + 425, + 505, + 438 + ], + "score": 1.0, + "content": "normalization layers. Raffel (2021); Matena & Raffel (2021); Sung et al. (2021) conceptualized the", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 435, + 505, + 450 + ], + "spans": [ + { + "bbox": [ + 105, + 435, + 505, + 450 + ], + "score": 1.0, + "content": "study of “model patching,” i.e., the idea that models should be easy to modify and submit changes", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 447, + 505, + 460 + ], + "spans": [ + { + "bbox": [ + 105, + 447, + 505, + 460 + ], + "score": 1.0, + "content": "to. Ilharco et al. (2022) investigated model patching for the fine-tuning of open-vocabulary vision", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 457, + 505, + 471 + ], + "spans": [ + { + "bbox": [ + 105, + 457, + 505, + 471 + ], + "score": 1.0, + "content": "models. Ashmore & Gashler (2015) first explored the use of matching algorithms for the alignment", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 469, + 505, + 482 + ], + "spans": [ + { + "bbox": [ + 106, + 469, + 505, + 482 + ], + "score": 1.0, + "content": "of network units. Singh & Jaggi (2020) proposed merging models by soft-aligning associations", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 480, + 505, + 493 + ], + "spans": [ + { + "bbox": [ + 106, + 480, + 505, + 493 + ], + "score": 1.0, + "content": "weights, inspired by optimal transport. Liu et al. (2022a); Uriot & Izzo (2020) further explored", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 490, + 506, + 504 + ], + "spans": [ + { + "bbox": [ + 105, + 490, + 506, + 504 + ], + "score": 1.0, + "content": "merging models taking possible permutations into account. Wortsman et al. (2022a) demonstrated", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 501, + 477, + 515 + ], + "spans": [ + { + "bbox": [ + 106, + 501, + 477, + 515 + ], + "score": 1.0, + "content": "state-of-the-art ImageNet performance by averaging the weights of many fine-tuned models.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 30, + "bbox_fs": [ + 105, + 369, + 506, + 515 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 529, + 297, + 542 + ], + "lines": [ + { + "bbox": [ + 105, + 528, + 299, + 544 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 299, + 544 + ], + "score": 1.0, + "content": "7 DISCUSSION AND FUTURE WORK", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 37 + }, + { + "type": "text", + "bbox": [ + 107, + 554, + 505, + 664 + ], + "lines": [ + { + "bbox": [ + 106, + 554, + 505, + 567 + ], + "spans": [ + { + "bbox": [ + 106, + 554, + 505, + 567 + ], + "score": 1.0, + "content": "We explore the role of permutation symmetries in the linear mode connectivity of SGD solutions.", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 566, + 505, + 577 + ], + "spans": [ + { + "bbox": [ + 106, + 566, + 505, + 577 + ], + "score": 1.0, + "content": "We present three algorithms to canonicalize independent neural network weights in order to make", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 576, + 505, + 589 + ], + "spans": [ + { + "bbox": [ + 105, + 576, + 505, + 589 + ], + "score": 1.0, + "content": "the loss landscape between them as flat as possible. 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Are all layers created equal?", + "type": "text" + }, + { + "bbox": [ + 474, + 352, + 506, + 365 + ], + "score": 1.0, + "content": "CoRR,", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 115, + 362, + 424, + 375 + ], + "spans": [ + { + "bbox": [ + 115, + 362, + 424, + 375 + ], + "score": 1.0, + "content": "abs/1902.01996, 2019. 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Here we list the", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 138, + 315, + 150 + ], + "spans": [ + { + "bbox": [ + 106, + 138, + 315, + 150 + ], + "score": 1.0, + "content": "failure cases that the authors are presently aware of,", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 2.5 + }, + { + "type": "text", + "bbox": [ + 129, + 159, + 505, + 254 + ], + "lines": [ + { + "bbox": [ + 130, + 159, + 257, + 171 + ], + "spans": [ + { + "bbox": [ + 130, + 159, + 257, + 171 + ], + "score": 1.0, + "content": "1. Models of insufficient width", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 128, + 173, + 297, + 188 + ], + "spans": [ + { + "bbox": [ + 128, + 173, + 297, + 188 + ], + "score": 1.0, + "content": "2. Models in the initial stages of training", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 129, + 190, + 217, + 201 + ], + "spans": [ + { + "bbox": [ + 129, + 190, + 217, + 201 + ], + "score": 1.0, + "content": "3. 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ConvNeXt architectures (Liu et al., 2022b), which have surprisingly few permutation sym-", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 142, + 243, + 367, + 254 + ], + "spans": [ + { + "bbox": [ + 142, + 243, + 367, + 254 + ], + "score": 1.0, + "content": "metries due to extensive use of depth-wise convolutions", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 7 + }, + { + "type": "text", + "bbox": [ + 106, + 263, + 464, + 275 + ], + "lines": [ + { + "bbox": [ + 105, + 262, + 465, + 276 + ], + "spans": [ + { + "bbox": [ + 105, + 262, + 465, + 276 + ], + "score": 1.0, + "content": "Furthermore, we believe other failure modes certainly exist but have yet to be discovered.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 11 + }, + { + "type": "text", + "bbox": [ + 107, + 280, + 504, + 303 + ], + "lines": [ + { + "bbox": [ + 106, + 279, + 505, + 294 + ], + "spans": [ + { + "bbox": [ + 106, + 279, + 505, + 294 + ], + "score": 1.0, + "content": "We are excited by the prospect of future work investigating these failure modes and improving our", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 291, + 477, + 304 + ], + "spans": [ + { + "bbox": [ + 106, + 291, + 477, + 304 + ], + "score": 1.0, + "content": "understanding of when and why model merging modulo permutation symmetries is feasible.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 12.5 + }, + { + "type": "title", + "bbox": [ + 108, + 316, + 254, + 327 + ], + "lines": [ + { + "bbox": [ + 106, + 315, + 257, + 330 + ], + "spans": [ + { + "bbox": [ + 106, + 315, + 257, + 330 + ], + "score": 1.0, + "content": "A.2 EXTENDED RELATED WORK", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 14 + }, + { + "type": "text", + "bbox": [ + 107, + 337, + 505, + 447 + ], + "lines": [ + { + "bbox": [ + 105, + 337, + 505, + 350 + ], + "spans": [ + { + "bbox": [ + 105, + 337, + 505, + 350 + ], + "score": 1.0, + "content": "Non-linear mode connectivity. A flourishing set of literature exists studying non-linear mode con-", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 349, + 505, + 361 + ], + "spans": [ + { + "bbox": [ + 105, + 349, + 505, + 361 + ], + "score": 1.0, + "content": "nectivity, including but not limited to Garipov et al. (2018); Draxler et al. (2018); Kuditipudi et al.", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 358, + 505, + 374 + ], + "spans": [ + { + "bbox": [ + 105, + 358, + 505, + 374 + ], + "score": 1.0, + "content": "(2019). This insightful line of work is inspirational to our own, however we take a strictly linear ap-", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 371, + 506, + 383 + ], + "spans": [ + { + "bbox": [ + 105, + 371, + 506, + 383 + ], + "score": 1.0, + "content": "proach to mode connectivity as in Frankle et al. (2020); Juneja et al. (2022). Restricting ourselves to", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 380, + 505, + 395 + ], + "spans": [ + { + "bbox": [ + 105, + 380, + 505, + 395 + ], + "score": 1.0, + "content": "linear trajectories comes with the advantage of having direct implications for a single-basin theory.", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 392, + 505, + 405 + ], + "spans": [ + { + "bbox": [ + 105, + 392, + 505, + 405 + ], + "score": 1.0, + "content": "However, it comes at the cost of a more challenging, discrete optimization problem. In particular,", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 403, + 506, + 416 + ], + "spans": [ + { + "bbox": [ + 105, + 403, + 506, + 416 + ], + "score": 1.0, + "content": "we found that – in contrast to non-linear mode connectivity – linear mode connectivity becomes", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 415, + 505, + 426 + ], + "spans": [ + { + "bbox": [ + 106, + 415, + 505, + 426 + ], + "score": 1.0, + "content": "drastically harder with smaller width models. Note additionally that most pre-existing mode con-", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 425, + 506, + 437 + ], + "spans": [ + { + "bbox": [ + 105, + 425, + 506, + 437 + ], + "score": 1.0, + "content": "nectivity work does not account for permutation symmetries of weight space, a linchpin element of", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 436, + 422, + 448 + ], + "spans": [ + { + "bbox": [ + 105, + 436, + 422, + 448 + ], + "score": 1.0, + "content": "our work. A notable exception to this trend can be found in Tatro et al. (2020).", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 19.5 + }, + { + "type": "text", + "bbox": [ + 107, + 452, + 505, + 541 + ], + "lines": [ + { + "bbox": [ + 106, + 453, + 505, + 465 + ], + "spans": [ + { + "bbox": [ + 106, + 453, + 505, + 465 + ], + "score": 1.0, + "content": "To summarize: Freeman & Bruna (2017) introduced the notion of mode connectivity and proved", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 465, + 505, + 475 + ], + "spans": [ + { + "bbox": [ + 106, + 465, + 505, + 475 + ], + "score": 1.0, + "content": "that loss landscapes for single-hidden layer ReLU models contain only a single basin in the infinite", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 475, + 505, + 487 + ], + "spans": [ + { + "bbox": [ + 106, + 475, + 505, + 487 + ], + "score": 1.0, + "content": "width limit. Garipov et al. (2018) and Draxler et al. (2018) concurrently demonstrated that simple", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 486, + 505, + 499 + ], + "spans": [ + { + "bbox": [ + 105, + 486, + 505, + 499 + ], + "score": 1.0, + "content": "zero-barrier curves can be learned to connect the optima in weight space, thus reshaping our un-", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 497, + 506, + 510 + ], + "spans": [ + { + "bbox": [ + 105, + 497, + 506, + 510 + ], + "score": 1.0, + "content": "derstanding of practical loss landscape geometries. Kuditipudi et al. (2019) proposes a theoretical", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 507, + 505, + 521 + ], + "spans": [ + { + "bbox": [ + 105, + 507, + 505, + 521 + ], + "score": 1.0, + "content": "explanation for the mode connectivity phenomenon. Benton et al. 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The impact of permutation symmetries on the non-linear", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 558, + 505, + 570 + ], + "spans": [ + { + "bbox": [ + 105, + 558, + 505, + 570 + ], + "score": 1.0, + "content": "mode connectivity of models is considered in Tatro et al. (2020). In particular, they independently", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 569, + 505, + 581 + ], + "spans": [ + { + "bbox": [ + 105, + 569, + 505, + 581 + ], + "score": 1.0, + "content": "propose an algorithm more-or-less equivalent to Section 3.1 but use it in conjunction with learned", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 579, + 505, + 592 + ], + "spans": [ + { + "bbox": [ + 105, + 579, + 505, + 592 + ], + "score": 1.0, + "content": "non-linear mode connecting curves. In contrast, we show that linear mode connectivity can be", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 591, + 505, + 603 + ], + "spans": [ + { + "bbox": [ + 106, + 591, + 505, + 603 + ], + "score": 1.0, + "content": "achieved without the need for learning non-linear paths between the aligned weights. Our derivation", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 601, + 501, + 614 + ], + "spans": [ + { + "bbox": [ + 105, + 601, + 501, + 614 + ], + "score": 1.0, + "content": "of Section 3.1 from the principle of least-squares regression is novel, to the best of our knowledge.", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 35.5 + }, + { + "type": "text", + "bbox": [ + 108, + 618, + 504, + 651 + ], + "lines": [ + { + "bbox": [ + 106, + 618, + 506, + 631 + ], + "spans": [ + { + "bbox": [ + 106, + 618, + 506, + 631 + ], + "score": 1.0, + "content": "Relationship with Singh & Jaggi (2020). 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We emphasize the following", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 640, + 281, + 651 + ], + "spans": [ + { + "bbox": [ + 106, + 640, + 281, + 651 + ], + "score": 1.0, + "content": "commonalities/differences with their work:", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 40 + }, + { + "type": "text", + "bbox": [ + 133, + 661, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 132, + 660, + 505, + 675 + ], + "spans": [ + { + "bbox": [ + 132, + 660, + 505, + 675 + ], + "score": 1.0, + "content": "• We focus on linear mode connectivity modulo permutation symmetries and its implications", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 141, + 672, + 506, + 685 + ], + "spans": [ + { + "bbox": [ + 141, + 672, + 506, + 685 + ], + "score": 1.0, + "content": "for a single-basin theory. 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Here we list the", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 138, + 315, + 150 + ], + "spans": [ + { + "bbox": [ + 106, + 138, + 315, + 150 + ], + "score": 1.0, + "content": "failure cases that the authors are presently aware of,", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 2.5, + "bbox_fs": [ + 106, + 126, + 505, + 150 + ] + }, + { + "type": "list", + "bbox": [ + 129, + 159, + 505, + 254 + ], + "lines": [ + { + "bbox": [ + 130, + 159, + 257, + 171 + ], + "spans": [ + { + "bbox": [ + 130, + 159, + 257, + 171 + ], + "score": 1.0, + "content": "1. Models of insufficient width", + "type": "text" + } + ], + "index": 4, + "is_list_start_line": true, + "is_list_end_line": true + }, + { + "bbox": [ + 128, + 173, + 297, + 188 + ], + "spans": [ + { + "bbox": [ + 128, + 173, + 297, + 188 + ], + "score": 1.0, + "content": "2. Models in the initial stages of training", + "type": "text" + } + ], + "index": 5, + "is_list_start_line": true, + "is_list_end_line": true + }, + { + "bbox": [ + 129, + 190, + 217, + 201 + ], + "spans": [ + { + "bbox": [ + 129, + 190, + 217, + 201 + ], + "score": 1.0, + "content": "3. VGGs on MNIST", + "type": "text" + } + ], + "index": 6, + "is_list_start_line": true, + "is_list_end_line": true + }, + { + "bbox": [ + 128, + 204, + 506, + 218 + ], + "spans": [ + { + "bbox": [ + 128, + 204, + 506, + 218 + ], + "score": 1.0, + "content": "4. MNIST MLPs trained with SGD and too low of a learning rate, or Adam and too high of a", + "type": "text" + } + ], + "index": 7, + "is_list_start_line": true + }, + { + "bbox": [ + 141, + 216, + 195, + 229 + ], + "spans": [ + { + "bbox": [ + 141, + 216, + 195, + 229 + ], + "score": 1.0, + "content": "learning rate", + "type": "text" + } + ], + "index": 8, + "is_list_end_line": true + }, + { + "bbox": [ + 128, + 230, + 505, + 245 + ], + "spans": [ + { + "bbox": [ + 128, + 230, + 505, + 245 + ], + "score": 1.0, + "content": "5. ConvNeXt architectures (Liu et al., 2022b), which have surprisingly few permutation sym-", + "type": "text" + } + ], + "index": 9, + "is_list_start_line": true + }, + { + "bbox": [ + 142, + 243, + 367, + 254 + ], + "spans": [ + { + "bbox": [ + 142, + 243, + 367, + 254 + ], + "score": 1.0, + "content": "metries due to extensive use of depth-wise convolutions", + "type": "text" + } + ], + "index": 10, + "is_list_end_line": true + } + ], + "index": 7, + "bbox_fs": [ + 128, + 159, + 506, + 254 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 263, + 464, + 275 + ], + "lines": [ + { + "bbox": [ + 105, + 262, + 465, + 276 + ], + "spans": [ + { + "bbox": [ + 105, + 262, + 465, + 276 + ], + "score": 1.0, + "content": "Furthermore, we believe other failure modes certainly exist but have yet to be discovered.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 11, + "bbox_fs": [ + 105, + 262, + 465, + 276 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 280, + 504, + 303 + ], + "lines": [ + { + "bbox": [ + 106, + 279, + 505, + 294 + ], + "spans": [ + { + "bbox": [ + 106, + 279, + 505, + 294 + ], + "score": 1.0, + "content": "We are excited by the prospect of future work investigating these failure modes and improving our", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 291, + 477, + 304 + ], + "spans": [ + { + "bbox": [ + 106, + 291, + 477, + 304 + ], + "score": 1.0, + "content": "understanding of when and why model merging modulo permutation symmetries is feasible.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 12.5, + "bbox_fs": [ + 106, + 279, + 505, + 304 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 316, + 254, + 327 + ], + "lines": [ + { + "bbox": [ + 106, + 315, + 257, + 330 + ], + "spans": [ + { + "bbox": [ + 106, + 315, + 257, + 330 + ], + "score": 1.0, + "content": "A.2 EXTENDED RELATED WORK", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 14 + }, + { + "type": "text", + "bbox": [ + 107, + 337, + 505, + 447 + ], + "lines": [ + { + "bbox": [ + 105, + 337, + 505, + 350 + ], + "spans": [ + { + "bbox": [ + 105, + 337, + 505, + 350 + ], + "score": 1.0, + "content": "Non-linear mode connectivity. A flourishing set of literature exists studying non-linear mode con-", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 349, + 505, + 361 + ], + "spans": [ + { + "bbox": [ + 105, + 349, + 505, + 361 + ], + "score": 1.0, + "content": "nectivity, including but not limited to Garipov et al. (2018); Draxler et al. (2018); Kuditipudi et al.", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 358, + 505, + 374 + ], + "spans": [ + { + "bbox": [ + 105, + 358, + 505, + 374 + ], + "score": 1.0, + "content": "(2019). This insightful line of work is inspirational to our own, however we take a strictly linear ap-", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 371, + 506, + 383 + ], + "spans": [ + { + "bbox": [ + 105, + 371, + 506, + 383 + ], + "score": 1.0, + "content": "proach to mode connectivity as in Frankle et al. (2020); Juneja et al. (2022). Restricting ourselves to", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 380, + 505, + 395 + ], + "spans": [ + { + "bbox": [ + 105, + 380, + 505, + 395 + ], + "score": 1.0, + "content": "linear trajectories comes with the advantage of having direct implications for a single-basin theory.", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 392, + 505, + 405 + ], + "spans": [ + { + "bbox": [ + 105, + 392, + 505, + 405 + ], + "score": 1.0, + "content": "However, it comes at the cost of a more challenging, discrete optimization problem. In particular,", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 403, + 506, + 416 + ], + "spans": [ + { + "bbox": [ + 105, + 403, + 506, + 416 + ], + "score": 1.0, + "content": "we found that – in contrast to non-linear mode connectivity – linear mode connectivity becomes", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 415, + 505, + 426 + ], + "spans": [ + { + "bbox": [ + 106, + 415, + 505, + 426 + ], + "score": 1.0, + "content": "drastically harder with smaller width models. Note additionally that most pre-existing mode con-", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 425, + 506, + 437 + ], + "spans": [ + { + "bbox": [ + 105, + 425, + 506, + 437 + ], + "score": 1.0, + "content": "nectivity work does not account for permutation symmetries of weight space, a linchpin element of", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 436, + 422, + 448 + ], + "spans": [ + { + "bbox": [ + 105, + 436, + 422, + 448 + ], + "score": 1.0, + "content": "our work. A notable exception to this trend can be found in Tatro et al. (2020).", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 19.5, + "bbox_fs": [ + 105, + 337, + 506, + 448 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 452, + 505, + 541 + ], + "lines": [ + { + "bbox": [ + 106, + 453, + 505, + 465 + ], + "spans": [ + { + "bbox": [ + 106, + 453, + 505, + 465 + ], + "score": 1.0, + "content": "To summarize: Freeman & Bruna (2017) introduced the notion of mode connectivity and proved", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 465, + 505, + 475 + ], + "spans": [ + { + "bbox": [ + 106, + 465, + 505, + 475 + ], + "score": 1.0, + "content": "that loss landscapes for single-hidden layer ReLU models contain only a single basin in the infinite", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 475, + 505, + 487 + ], + "spans": [ + { + "bbox": [ + 106, + 475, + 505, + 487 + ], + "score": 1.0, + "content": "width limit. Garipov et al. (2018) and Draxler et al. (2018) concurrently demonstrated that simple", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 486, + 505, + 499 + ], + "spans": [ + { + "bbox": [ + 105, + 486, + 505, + 499 + ], + "score": 1.0, + "content": "zero-barrier curves can be learned to connect the optima in weight space, thus reshaping our un-", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 497, + 506, + 510 + ], + "spans": [ + { + "bbox": [ + 105, + 497, + 506, + 510 + ], + "score": 1.0, + "content": "derstanding of practical loss landscape geometries. Kuditipudi et al. (2019) proposes a theoretical", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 507, + 505, + 521 + ], + "spans": [ + { + "bbox": [ + 105, + 507, + 505, + 521 + ], + "score": 1.0, + "content": "explanation for the mode connectivity phenomenon. Benton et al. (2021) extends mode connectivity", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 520, + 505, + 531 + ], + "spans": [ + { + "bbox": [ + 106, + 520, + 505, + 531 + ], + "score": 1.0, + "content": "from one-dimensional paths to entire manifolds of low-loss, and show that these manifolds can be", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 529, + 356, + 542 + ], + "spans": [ + { + "bbox": [ + 105, + 529, + 356, + 542 + ], + "score": 1.0, + "content": "leveraged for state-of-the-art Bayesian ensembling of models.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 28.5, + "bbox_fs": [ + 105, + 453, + 506, + 542 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 546, + 505, + 613 + ], + "lines": [ + { + "bbox": [ + 105, + 546, + 506, + 559 + ], + "spans": [ + { + "bbox": [ + 105, + 546, + 506, + 559 + ], + "score": 1.0, + "content": "Relationship with Tatro et al. (2020). The impact of permutation symmetries on the non-linear", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 558, + 505, + 570 + ], + "spans": [ + { + "bbox": [ + 105, + 558, + 505, + 570 + ], + "score": 1.0, + "content": "mode connectivity of models is considered in Tatro et al. (2020). In particular, they independently", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 569, + 505, + 581 + ], + "spans": [ + { + "bbox": [ + 105, + 569, + 505, + 581 + ], + "score": 1.0, + "content": "propose an algorithm more-or-less equivalent to Section 3.1 but use it in conjunction with learned", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 579, + 505, + 592 + ], + "spans": [ + { + "bbox": [ + 105, + 579, + 505, + 592 + ], + "score": 1.0, + "content": "non-linear mode connecting curves. In contrast, we show that linear mode connectivity can be", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 591, + 505, + 603 + ], + "spans": [ + { + "bbox": [ + 106, + 591, + 505, + 603 + ], + "score": 1.0, + "content": "achieved without the need for learning non-linear paths between the aligned weights. Our derivation", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 601, + 501, + 614 + ], + "spans": [ + { + "bbox": [ + 105, + 601, + 501, + 614 + ], + "score": 1.0, + "content": "of Section 3.1 from the principle of least-squares regression is novel, to the best of our knowledge.", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 35.5, + "bbox_fs": [ + 105, + 546, + 506, + 614 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 618, + 504, + 651 + ], + "lines": [ + { + "bbox": [ + 106, + 618, + 506, + 631 + ], + "spans": [ + { + "bbox": [ + 106, + 618, + 506, + 631 + ], + "score": 1.0, + "content": "Relationship with Singh & Jaggi (2020). Singh & Jaggi (2020) studies model merging with “soft", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 628, + 505, + 643 + ], + "spans": [ + { + "bbox": [ + 105, + 628, + 505, + 643 + ], + "score": 1.0, + "content": "matchings” between units from the perspective of optimal transport. We emphasize the following", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 640, + 281, + 651 + ], + "spans": [ + { + "bbox": [ + 106, + 640, + 281, + 651 + ], + "score": 1.0, + "content": "commonalities/differences with their work:", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 40, + "bbox_fs": [ + 105, + 618, + 506, + 651 + ] + }, + { + "type": "list", + "bbox": [ + 133, + 661, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 132, + 660, + 505, + 675 + ], + "spans": [ + { + "bbox": [ + 132, + 660, + 505, + 675 + ], + "score": 1.0, + "content": "• We focus on linear mode connectivity modulo permutation symmetries and its implications", + "type": "text" + } + ], + "index": 42, + "is_list_start_line": true + }, + { + "bbox": [ + 141, + 672, + 506, + 685 + ], + "spans": [ + { + "bbox": [ + 141, + 672, + 506, + 685 + ], + "score": 1.0, + "content": "for a single-basin theory. 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Singh & Jaggi (2020) suggests jointly solving for alignments as an avenue", + "type": "text", + "cross_page": true + } + ], + "index": 3 + }, + { + "bbox": [ + 142, + 127, + 208, + 138 + ], + "spans": [ + { + "bbox": [ + 142, + 127, + 208, + 138 + ], + "score": 1.0, + "content": "for future work.", + "type": "text", + "cross_page": true + } + ], + "index": 4, + "is_list_end_line": true + }, + { + "bbox": [ + 132, + 141, + 505, + 155 + ], + "spans": [ + { + "bbox": [ + 132, + 141, + 505, + 155 + ], + "score": 1.0, + "content": "• The “wts” method of Singh & Jaggi (2020) is not run on models including bias terms, skip", + "type": "text", + "cross_page": true + } + ], + "index": 5, + "is_list_start_line": true + }, + { + "bbox": [ + 141, + 154, + 506, + 165 + ], + "spans": [ + { + "bbox": [ + 141, + 154, + 506, + 165 + ], + "score": 1.0, + "content": "connections, or normalization layers. In contrast, our Algorithm 1 works with models of", + "type": "text", + "cross_page": true + } + ], + "index": 6 + }, + { + "bbox": [ + 141, + 164, + 259, + 177 + ], + "spans": [ + { + "bbox": [ + 141, + 164, + 259, + 177 + ], + "score": 1.0, + "content": "nearly arbitrary architecture.", + "type": "text", + "cross_page": true + } + ], + "index": 7, + "is_list_end_line": true + }, + { + "bbox": [ + 133, + 179, + 506, + 194 + ], + "spans": [ + { + "bbox": [ + 133, + 179, + 506, + 194 + ], + "score": 1.0, + "content": "• Our weight matching method (Algorithm 1) outperforms the “wts” method of Singh &", + "type": "text", + "cross_page": true + } + ], + "index": 8, + "is_list_start_line": true + }, + { + "bbox": [ + 140, + 191, + 363, + 204 + ], + "spans": [ + { + "bbox": [ + 140, + 191, + 363, + 204 + ], + "score": 1.0, + "content": "Jaggi (2020). See Appendix A.7 for more information.", + "type": "text", + "cross_page": true + } + ], + "index": 9, + "is_list_end_line": true + }, + { + "bbox": [ + 135, + 207, + 506, + 220 + ], + "spans": [ + { + "bbox": [ + 135, + 207, + 506, + 220 + ], + "score": 1.0, + "content": "• Singh & Jaggi (2020) introduces a method for merging multiple models simultaneously, but", + "type": "text", + "cross_page": true + } + ], + "index": 10, + "is_list_start_line": true + }, + { + "bbox": [ + 141, + 218, + 506, + 231 + ], + "spans": [ + { + "bbox": [ + 141, + 218, + 506, + 231 + ], + "score": 1.0, + "content": "only demonstrates results on at most 8 models at a time and performs continued training", + "type": "text", + "cross_page": true + } + ], + "index": 11 + }, + { + "bbox": [ + 142, + 230, + 505, + 241 + ], + "spans": [ + { + "bbox": [ + 142, + 230, + 505, + 241 + ], + "score": 1.0, + "content": "after merging. 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Our analysis of the", + "type": "text", + "cross_page": true + } + ], + "index": 13 + }, + { + "bbox": [ + 142, + 252, + 475, + 264 + ], + "spans": [ + { + "bbox": [ + 142, + 252, + 475, + 264 + ], + "score": 1.0, + "content": "calibration of the resulting merged models has no parallel in Singh & Jaggi (2020).", + "type": "text", + "cross_page": true + } + ], + "index": 14, + "is_list_end_line": true + } + ], + "index": 44.5, + "bbox_fs": [ + 132, + 660, + 506, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 132, + 82, + 505, + 263 + ], + "lines": [ + { + "bbox": [ + 135, + 82, + 506, + 96 + ], + "spans": [ + { + "bbox": [ + 135, + 82, + 506, + 96 + ], + "score": 1.0, + "content": "• Our weight matching and straight-through estimator methods solve for an alignment across", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 142, + 93, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 142, + 93, + 505, + 106 + ], + "score": 1.0, + "content": "all layers jointly. 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(2021) introduces the single-basin conjec-", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 284, + 316, + 296 + ], + "spans": [ + { + "bbox": [ + 106, + 284, + 316, + 296 + ], + "score": 1.0, + "content": "ture and provides the following evidence towards it:", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 15.5 + }, + { + "type": "text", + "bbox": [ + 132, + 304, + 505, + 606 + ], + "lines": [ + { + "bbox": [ + 134, + 306, + 505, + 317 + ], + "spans": [ + { + "bbox": [ + 134, + 306, + 505, + 317 + ], + "score": 1.0, + "content": "• Entezari et al. (2021) provides a statistical test which fails to detect a difference in bar-", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 141, + 316, + 506, + 329 + ], + "spans": [ + { + "bbox": [ + 141, + 316, + 506, + 329 + ], + "score": 1.0, + "content": "rier statistics between independently trained models and random permutations of the same", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 141, + 327, + 505, + 340 + ], + "spans": [ + { + "bbox": [ + 141, + 327, + 505, + 340 + ], + "score": 1.0, + "content": "model (Fig. 5 of Entezari et al. (2021)). Our work provides stronger support for the con-", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 140, + 338, + 505, + 351 + ], + "spans": [ + { + "bbox": [ + 140, + 338, + 505, + 351 + ], + "score": 1.0, + "content": "jecture in that we give methods that can directly “unscramble” these permutations, proving", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 142, + 349, + 311, + 361 + ], + "spans": [ + { + "bbox": [ + 142, + 349, + 311, + 361 + ], + "score": 1.0, + "content": "that LMC can be found (Figures 4 and 5).", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 141, + 363, + 505, + 374 + ], + "spans": [ + { + "bbox": [ + 141, + 363, + 505, + 374 + ], + "score": 1.0, + "content": "Entezari et al. (2021)’s experimental protocol does not provide evidence for linear mode", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 141, + 374, + 505, + 385 + ], + "spans": [ + { + "bbox": [ + 141, + 374, + 505, + 385 + ], + "score": 1.0, + "content": "connectivity. Rather, their experimental results suggest that barriers resulting from inde-", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 141, + 385, + 506, + 397 + ], + "spans": [ + { + "bbox": [ + 141, + 385, + 506, + 397 + ], + "score": 1.0, + "content": "pendent training look like the barriers resulting from random permutations. But this result", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 142, + 396, + 505, + 407 + ], + "spans": [ + { + "bbox": [ + 142, + 396, + 505, + 407 + ], + "score": 1.0, + "content": "is consistent with a world in which all solutions have barriers between them – both be-", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 140, + 406, + 506, + 420 + ], + "spans": [ + { + "bbox": [ + 140, + 406, + 506, + 420 + ], + "score": 1.0, + "content": "tween members of the same permutation equivalence class and between solutions in sepa-", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 141, + 417, + 505, + 429 + ], + "spans": [ + { + "bbox": [ + 141, + 417, + 505, + 429 + ], + "score": 1.0, + "content": "rate equivalence classes! 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(2021)’s conjecture is an important intellectual ancestor to our", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 141, + 466, + 505, + 479 + ], + "spans": [ + { + "bbox": [ + 141, + 466, + 505, + 479 + ], + "score": 1.0, + "content": "work, their demonstration of linear mode connectivity is limited to a single hidden-layer", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 141, + 477, + 505, + 489 + ], + "spans": [ + { + "bbox": [ + 141, + 477, + 505, + 489 + ], + "score": 1.0, + "content": "MLP on MNIST (Fig. 2 of Entezari et al. (2021)). However, this result for single hidden-", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 142, + 488, + 505, + 500 + ], + "spans": [ + { + "bbox": [ + 142, + 488, + 505, + 500 + ], + "score": 1.0, + "content": "layer MLP models is preceded by Freeman & Bruna (2017); Uriot & Izzo (2020). On", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 142, + 499, + 505, + 511 + ], + "spans": [ + { + "bbox": [ + 142, + 499, + 505, + 511 + ], + "score": 1.0, + "content": "the other hand, we focus on larger models and datasets that are more closely aligned with", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 141, + 510, + 327, + 523 + ], + "spans": [ + { + "bbox": [ + 141, + 510, + 327, + 523 + ], + "score": 1.0, + "content": "models used in practice at the time of writing.", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 136, + 525, + 506, + 538 + ], + "spans": [ + { + "bbox": [ + 136, + 525, + 506, + 538 + ], + "score": 1.0, + "content": "• Entezari et al. (2021) proposes a simulated annealing algorithm that yields modest reduc-", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 141, + 537, + 496, + 550 + ], + "spans": [ + { + "bbox": [ + 141, + 537, + 496, + 550 + ], + "score": 1.0, + "content": "tions in barrier between independently trained models, yet requires multiple days to run.", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 142, + 551, + 505, + 563 + ], + "spans": [ + { + "bbox": [ + 142, + 551, + 505, + 563 + ], + "score": 1.0, + "content": "On the other hand, our weight matching algorithm (Algorithm 1) completely removes barri-", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 141, + 561, + 506, + 574 + ], + "spans": [ + { + "bbox": [ + 141, + 561, + 506, + 574 + ], + "score": 1.0, + "content": "ers between models for more challenging models and datasets (Figures 2 and 5), and runs in", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 141, + 573, + 505, + 585 + ], + "spans": [ + { + "bbox": [ + 141, + 573, + 505, + 585 + ], + "score": 1.0, + "content": "seconds (Appendix A.5). Moreover, our weight matching method does not require access", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 140, + 583, + 505, + 597 + ], + "spans": [ + { + "bbox": [ + 140, + 583, + 505, + 597 + ], + "score": 1.0, + "content": "to the training data, enabling its potential application in domains like federated learning", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 141, + 594, + 240, + 607 + ], + "spans": [ + { + "bbox": [ + 141, + 594, + 240, + 607 + ], + "score": 1.0, + "content": "and distributed training.", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 29.5 + }, + { + "type": "text", + "bbox": [ + 108, + 616, + 503, + 649 + ], + "lines": [ + { + "bbox": [ + 105, + 615, + 505, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 615, + 505, + 628 + ], + "score": 1.0, + "content": "In short, the work of Entezari et al. (2021) first proposed the “single-basin” conjecture. Our work is", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 627, + 505, + 639 + ], + "spans": [ + { + "bbox": [ + 106, + 627, + 505, + 639 + ], + "score": 1.0, + "content": "the first (to the best of our knowledge) to demonstrate that linear mode connectivity can be achieved", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 638, + 383, + 650 + ], + "spans": [ + { + "bbox": [ + 106, + 638, + 383, + 650 + ], + "score": 1.0, + "content": "between large models independently trained on challenging datasets.", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 44 + }, + { + "type": "text", + "bbox": [ + 107, + 655, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "score": 1.0, + "content": "Differentiating through permutations. Akin to differentiable permutation learning, many prior", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "score": 1.0, + "content": "works have studied differentiable sorting (Grover et al., 2019; Prillo & Eisenschlos, 2020; Cuturi", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 676, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 676, + 505, + 689 + ], + "score": 1.0, + "content": "et al., 2019; Petersen et al., 2022; 2021; Mena et al., 2018). Blondel et al. 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(2021). Entezari et al. (2021) introduces the single-basin conjec-", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 284, + 316, + 296 + ], + "spans": [ + { + "bbox": [ + 106, + 284, + 316, + 296 + ], + "score": 1.0, + "content": "ture and provides the following evidence towards it:", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 15.5, + "bbox_fs": [ + 105, + 271, + 504, + 296 + ] + }, + { + "type": "list", + "bbox": [ + 132, + 304, + 505, + 606 + ], + "lines": [ + { + "bbox": [ + 134, + 306, + 505, + 317 + ], + "spans": [ + { + "bbox": [ + 134, + 306, + 505, + 317 + ], + "score": 1.0, + "content": "• Entezari et al. 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Our work provides stronger support for the con-", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 140, + 338, + 505, + 351 + ], + "spans": [ + { + "bbox": [ + 140, + 338, + 505, + 351 + ], + "score": 1.0, + "content": "jecture in that we give methods that can directly “unscramble” these permutations, proving", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 142, + 349, + 311, + 361 + ], + "spans": [ + { + "bbox": [ + 142, + 349, + 311, + 361 + ], + "score": 1.0, + "content": "that LMC can be found (Figures 4 and 5).", + "type": "text" + } + ], + "index": 21, + "is_list_end_line": true + }, + { + "bbox": [ + 141, + 363, + 505, + 374 + ], + "spans": [ + { + "bbox": [ + 141, + 363, + 505, + 374 + ], + "score": 1.0, + "content": "Entezari et al. 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But this result", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 142, + 396, + 505, + 407 + ], + "spans": [ + { + "bbox": [ + 142, + 396, + 505, + 407 + ], + "score": 1.0, + "content": "is consistent with a world in which all solutions have barriers between them – both be-", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 140, + 406, + 506, + 420 + ], + "spans": [ + { + "bbox": [ + 140, + 406, + 506, + 420 + ], + "score": 1.0, + "content": "tween members of the same permutation equivalence class and between solutions in sepa-", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 141, + 417, + 505, + 429 + ], + "spans": [ + { + "bbox": [ + 141, + 417, + 505, + 429 + ], + "score": 1.0, + "content": "rate equivalence classes! 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On", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 142, + 499, + 505, + 511 + ], + "spans": [ + { + "bbox": [ + 142, + 499, + 505, + 511 + ], + "score": 1.0, + "content": "the other hand, we focus on larger models and datasets that are more closely aligned with", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 141, + 510, + 327, + 523 + ], + "spans": [ + { + "bbox": [ + 141, + 510, + 327, + 523 + ], + "score": 1.0, + "content": "models used in practice at the time of writing.", + "type": "text" + } + ], + "index": 35, + "is_list_end_line": true + }, + { + "bbox": [ + 136, + 525, + 506, + 538 + ], + "spans": [ + { + "bbox": [ + 136, + 525, + 506, + 538 + ], + "score": 1.0, + "content": "• Entezari et al. 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After our initial", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 437, + 505, + 450 + ], + "spans": [ + { + "bbox": [ + 105, + 437, + 505, + 450 + ], + "score": 1.0, + "content": "publication, the recalculation of BatchNorm statistics was suggested to us by the authors of Jordan", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 448, + 160, + 460 + ], + "spans": [ + { + "bbox": [ + 105, + 448, + 160, + 460 + ], + "score": 1.0, + "content": "et al. 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Therefore, we rec-", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 141, + 556, + 505, + 568 + ], + "spans": [ + { + "bbox": [ + 141, + 556, + 505, + 568 + ], + "score": 1.0, + "content": "ommend the recalculation of batch statistics after merging models (Izmailov et al., 2018;", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 142, + 567, + 398, + 579 + ], + "spans": [ + { + "bbox": [ + 142, + 567, + 398, + 579 + ], + "score": 1.0, + "content": "Wortsman et al., 2021; Maddox et al., 2019; Wang et al., 2021).", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 134, + 582, + 505, + 594 + ], + "spans": [ + { + "bbox": [ + 134, + 582, + 505, + 594 + ], + "score": 1.0, + "content": "• LayerNorm (Ba et al., 2016) is invariant to permutations of units and we found that archi-", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 141, + 593, + 363, + 605 + ], + "spans": [ + { + "bbox": [ + 141, + 593, + 363, + 605 + ], + "score": 1.0, + "content": "tectures with LayerNorm can be merged without issue.", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 132, + 605, + 504, + 620 + ], + "spans": [ + { + "bbox": [ + 132, + 605, + 504, + 620 + ], + "score": 1.0, + "content": "• InstanceNorm (Ulyanov et al., 2016) also places no restrictions on unit order, and in prin-", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 141, + 618, + 479, + 631 + ], + "spans": [ + { + "bbox": [ + 141, + 618, + 479, + 631 + ], + "score": 1.0, + "content": "ciple does not present any issues, although we have not run any experiments with it.", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 132, + 631, + 506, + 645 + ], + "spans": [ + { + "bbox": [ + 132, + 631, + 506, + 645 + ], + "score": 1.0, + "content": "• GroupNorm (Wu & He, 2020) relies on unit indexes to organize units into groups, and", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 141, + 642, + 505, + 655 + ], + "spans": [ + { + "bbox": [ + 141, + 642, + 505, + 655 + ], + "score": 1.0, + "content": "therefore is not invariant to permutations of units. In principle, permutation alignment", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 141, + 654, + 505, + 666 + ], + "spans": [ + { + "bbox": [ + 141, + 654, + 505, + 666 + ], + "score": 1.0, + "content": "methods would not work on architectures with GroupNorm, though we have not tested", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 141, + 664, + 162, + 676 + ], + "spans": [ + { + "bbox": [ + 141, + 664, + 162, + 676 + ], + "score": 1.0, + "content": "this.", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 35.5 + }, + { + "type": "title", + "bbox": [ + 107, + 689, + 332, + 700 + ], + "lines": [ + { + "bbox": [ + 106, + 689, + 333, + 701 + ], + "spans": [ + { + "bbox": [ + 106, + 689, + 333, + 701 + ], + "score": 1.0, + "content": "A.5 ADDITIONAL INFORMATION ON ALGORITHM 1", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 42 + }, + { + "type": "text", + "bbox": [ + 108, + 709, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "On currently available hardware (p3.2xlarge AWS instance with an NVIDIA V100 GPU), we ob-", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 721, + 322, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 721, + 322, + 733 + ], + "score": 1.0, + "content": "served the following timing results with Algorithm 1,", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 43.5 + } + ], + "page_idx": 20, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2023", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 751, + 310, + 760 + ], + "lines": [ + { + "bbox": [ + 298, + 750, + 312, + 765 + ], + "spans": [ + { + "bbox": [ + 298, + 750, + 312, + 765 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 15, + "width": 14 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "title", + "bbox": [ + 108, + 82, + 242, + 94 + ], + "lines": [ + { + "bbox": [ + 105, + 81, + 243, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 81, + 243, + 95 + ], + "score": 1.0, + "content": "A.3 EXPERIMENTAL DETAILS", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "title", + "bbox": [ + 107, + 102, + 301, + 114 + ], + "lines": [ + { + "bbox": [ + 106, + 102, + 302, + 115 + ], + "spans": [ + { + "bbox": [ + 106, + 102, + 302, + 115 + ], + "score": 1.0, + "content": "A.3.1 MULTI-LAYER PERCEPTRON MODELS", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 1 + }, + { + "type": "text", + "bbox": [ + 108, + 122, + 504, + 155 + ], + "lines": [ + { + "bbox": [ + 105, + 122, + 505, + 134 + ], + "spans": [ + { + "bbox": [ + 105, + 122, + 505, + 134 + ], + "score": 1.0, + "content": "In these experiments we utilized networks with 3 hidden layers of 512 units each. ReLU activations", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 133, + 506, + 145 + ], + "spans": [ + { + "bbox": [ + 106, + 133, + 506, + 145 + ], + "score": 1.0, + "content": "were used between layers and no normalization was performed. Optimization was done with Adam", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 107, + 144, + 225, + 155 + ], + "spans": [ + { + "bbox": [ + 107, + 145, + 194, + 155 + ], + "score": 1.0, + "content": "and a learning rate of", + "type": "text" + }, + { + "bbox": [ + 194, + 144, + 222, + 155 + ], + "score": 0.86, + "content": "1 e - 3", + "type": "inline_equation" + }, + { + "bbox": [ + 222, + 145, + 225, + 155 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 3, + "bbox_fs": [ + 105, + 122, + 506, + 155 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 166, + 371, + 178 + ], + "lines": [ + { + "bbox": [ + 106, + 166, + 373, + 179 + ], + "spans": [ + { + "bbox": [ + 106, + 166, + 373, + 179 + ], + "score": 1.0, + "content": "A.3.2 VGG-16 AND RESNET MODELS ON CIFAR DATASETS", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 5 + }, + { + "type": "text", + "bbox": [ + 107, + 186, + 505, + 219 + ], + "lines": [ + { + "bbox": [ + 106, + 185, + 505, + 199 + ], + "spans": [ + { + "bbox": [ + 106, + 185, + 505, + 199 + ], + "score": 1.0, + "content": "We utilized the VGG-16 architecture of Simonyan & Zisserman (2015) with the exception that we", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 198, + 505, + 209 + ], + "spans": [ + { + "bbox": [ + 106, + 198, + 505, + 209 + ], + "score": 1.0, + "content": "used LayerNorm normalization in place of BatchNorm. 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(2016) but with LayerNorms in place of BatchNorms.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 7, + "bbox_fs": [ + 106, + 185, + 505, + 221 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 225, + 365, + 236 + ], + "lines": [ + { + "bbox": [ + 105, + 222, + 366, + 240 + ], + "spans": [ + { + "bbox": [ + 105, + 222, + 366, + 240 + ], + "score": 1.0, + "content": "The following data augmentation was performed during training", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 9, + "bbox_fs": [ + 105, + 222, + 366, + 240 + ] + }, + { + "type": "list", + "bbox": [ + 133, + 244, + 339, + 298 + ], + "lines": [ + { + "bbox": [ + 133, + 244, + 341, + 257 + ], + "spans": [ + { + "bbox": [ + 133, + 244, + 296, + 257 + ], + "score": 1.0, + "content": "• Random resizes of the image between", + "type": "text" + }, + { + "bbox": [ + 296, + 245, + 341, + 256 + ], + "score": 0.85, + "content": "0 . 8 \\times - 1 . 2 \\times", + "type": "inline_equation" + } + ], + "index": 10, + "is_list_start_line": true + }, + { + "bbox": [ + 133, + 257, + 255, + 272 + ], + "spans": [ + { + "bbox": [ + 133, + 257, + 178, + 272 + ], + "score": 1.0, + "content": "• Random", + "type": "text" + }, + { + "bbox": [ + 178, + 259, + 208, + 270 + ], + "score": 0.85, + "content": "3 2 \\times 3 2", + "type": "inline_equation" + }, + { + "bbox": [ + 208, + 257, + 255, + 272 + ], + "score": 1.0, + "content": "pixel crops", + "type": "text" + } + ], + "index": 11, + "is_list_start_line": true + }, + { + "bbox": [ + 133, + 272, + 241, + 286 + ], + "spans": [ + { + "bbox": [ + 133, + 272, + 241, + 286 + ], + "score": 1.0, + "content": "• Random horizontal flips", + "type": "text" + } + ], + "index": 12, + "is_list_start_line": true + }, + { + "bbox": [ + 133, + 287, + 275, + 298 + ], + "spans": [ + { + "bbox": [ + 133, + 287, + 251, + 298 + ], + "score": 1.0, + "content": "• Random rotations between", + "type": "text" + }, + { + "bbox": [ + 252, + 288, + 275, + 298 + ], + "score": 0.84, + "content": "\\pm 3 0 ^ { \\circ }", + "type": "inline_equation" + } + ], + "index": 13, + "is_list_start_line": true + } + ], + "index": 11.5, + "bbox_fs": [ + 133, + 244, + 341, + 298 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 307, + 505, + 362 + ], + "lines": [ + { + "bbox": [ + 105, + 306, + 505, + 320 + ], + "spans": [ + { + "bbox": [ + 105, + 306, + 505, + 320 + ], + "score": 1.0, + "content": "Optimization was done with SGD with momentum (momentum set to 0.9). A weight decay reg-", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 318, + 505, + 330 + ], + "spans": [ + { + "bbox": [ + 105, + 318, + 185, + 330 + ], + "score": 1.0, + "content": "ularization term of", + "type": "text" + }, + { + "bbox": [ + 185, + 318, + 214, + 329 + ], + "score": 0.81, + "content": "5 e - 4", + "type": "inline_equation" + }, + { + "bbox": [ + 215, + 318, + 505, + 330 + ], + "score": 1.0, + "content": "was applied. A single cosine decay schedule with linear warm-up was", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 329, + 505, + 342 + ], + "spans": [ + { + "bbox": [ + 105, + 329, + 266, + 342 + ], + "score": 1.0, + "content": "used. Learning rates were initialized at", + "type": "text" + }, + { + "bbox": [ + 266, + 330, + 294, + 340 + ], + "score": 0.85, + "content": "1 e - 6", + "type": "inline_equation" + }, + { + "bbox": [ + 295, + 329, + 396, + 342 + ], + "score": 1.0, + "content": "and linearly increased to", + "type": "text" + }, + { + "bbox": [ + 397, + 329, + 425, + 340 + ], + "score": 0.88, + "content": "1 e - 1", + "type": "inline_equation" + }, + { + "bbox": [ + 425, + 329, + 505, + 342 + ], + "score": 1.0, + "content": "over the span of an", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 339, + 506, + 353 + ], + "spans": [ + { + "bbox": [ + 105, + 339, + 506, + 353 + ], + "score": 1.0, + "content": "epoch. After that point a single cosine decay schedule (Loshchilov & Hutter, 2017) was used for the", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 350, + 196, + 364 + ], + "spans": [ + { + "bbox": [ + 105, + 350, + 196, + 364 + ], + "score": 1.0, + "content": "remainder of training.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 16, + "bbox_fs": [ + 105, + 306, + 506, + 364 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 374, + 308, + 385 + ], + "lines": [ + { + "bbox": [ + 106, + 373, + 309, + 386 + ], + "spans": [ + { + "bbox": [ + 106, + 373, + 309, + 386 + ], + "score": 1.0, + "content": "A.3.3 RESNET50 MODELS ON IMAGENET-1K", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 19 + }, + { + "type": "text", + "bbox": [ + 106, + 393, + 505, + 459 + ], + "lines": [ + { + "bbox": [ + 106, + 393, + 505, + 405 + ], + "spans": [ + { + "bbox": [ + 106, + 393, + 505, + 405 + ], + "score": 1.0, + "content": "In this experiment we utilized pre-trained ResNet50 model available for download online, and one", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 403, + 505, + 416 + ], + "spans": [ + { + "bbox": [ + 105, + 403, + 505, + 416 + ], + "score": 1.0, + "content": "trained ourselves. These were standard ResNet50 models, including the use of BatchNorm. In line", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 415, + 504, + 427 + ], + "spans": [ + { + "bbox": [ + 106, + 415, + 504, + 427 + ], + "score": 1.0, + "content": "with prior work (Izmailov et al., 2018; Wortsman et al., 2021; Maddox et al., 2019; Wang et al.,", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 425, + 505, + 438 + ], + "spans": [ + { + "bbox": [ + 105, + 425, + 505, + 438 + ], + "score": 1.0, + "content": "2021), we recalculate BatchNorm statistics after performing weight interpolation. After our initial", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 437, + 505, + 450 + ], + "spans": [ + { + "bbox": [ + 105, + 437, + 505, + 450 + ], + "score": 1.0, + "content": "publication, the recalculation of BatchNorm statistics was suggested to us by the authors of Jordan", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 448, + 160, + 460 + ], + "spans": [ + { + "bbox": [ + 105, + 448, + 160, + 460 + ], + "score": 1.0, + "content": "et al. 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Therefore, we rec-", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 141, + 556, + 505, + 568 + ], + "spans": [ + { + "bbox": [ + 141, + 556, + 505, + 568 + ], + "score": 1.0, + "content": "ommend the recalculation of batch statistics after merging models (Izmailov et al., 2018;", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 142, + 567, + 398, + 579 + ], + "spans": [ + { + "bbox": [ + 142, + 567, + 398, + 579 + ], + "score": 1.0, + "content": "Wortsman et al., 2021; Maddox et al., 2019; Wang et al., 2021).", + "type": "text" + } + ], + "index": 33, + "is_list_end_line": true + }, + { + "bbox": [ + 134, + 582, + 505, + 594 + ], + "spans": [ + { + "bbox": [ + 134, + 582, + 505, + 594 + ], + "score": 1.0, + "content": "• LayerNorm (Ba et al., 2016) is invariant to permutations of units and we found that archi-", + "type": "text" + } + ], + "index": 34, + "is_list_start_line": true + }, + { + "bbox": [ + 141, + 593, + 363, + 605 + ], + "spans": [ + { + "bbox": [ + 141, + 593, + 363, + 605 + ], + "score": 1.0, + "content": "tectures with LayerNorm can be merged without issue.", + "type": "text" + } + ], + "index": 35, + "is_list_end_line": true + }, + { + "bbox": [ + 132, + 605, + 504, + 620 + ], + "spans": [ + { + "bbox": [ + 132, + 605, + 504, + 620 + ], + "score": 1.0, + "content": "• InstanceNorm (Ulyanov et al., 2016) also places no restrictions on unit order, and in prin-", + "type": "text" + } + ], + "index": 36, + "is_list_start_line": true + }, + { + "bbox": [ + 141, + 618, + 479, + 631 + ], + "spans": [ + { + "bbox": [ + 141, + 618, + 479, + 631 + ], + "score": 1.0, + "content": "ciple does not present any issues, although we have not run any experiments with it.", + "type": "text" + } + ], + "index": 37, + "is_list_end_line": true + }, + { + "bbox": [ + 132, + 631, + 506, + 645 + ], + "spans": [ + { + "bbox": [ + 132, + 631, + 506, + 645 + ], + "score": 1.0, + "content": "• GroupNorm (Wu & He, 2020) relies on unit indexes to organize units into groups, and", + "type": "text" + } + ], + "index": 38, + "is_list_start_line": true + }, + { + "bbox": [ + 141, + 642, + 505, + 655 + ], + "spans": [ + { + "bbox": [ + 141, + 642, + 505, + 655 + ], + "score": 1.0, + "content": "therefore is not invariant to permutations of units. In principle, permutation alignment", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 141, + 654, + 505, + 666 + ], + "spans": [ + { + "bbox": [ + 141, + 654, + 505, + 666 + ], + "score": 1.0, + "content": "methods would not work on architectures with GroupNorm, though we have not tested", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 141, + 664, + 162, + 676 + ], + "spans": [ + { + "bbox": [ + 141, + 664, + 162, + 676 + ], + "score": 1.0, + "content": "this.", + "type": "text" + } + ], + "index": 41, + "is_list_end_line": true + } + ], + "index": 35.5, + "bbox_fs": [ + 132, + 533, + 506, + 676 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 689, + 332, + 700 + ], + "lines": [ + { + "bbox": [ + 106, + 689, + 333, + 701 + ], + "spans": [ + { + "bbox": [ + 106, + 689, + 333, + 701 + ], + "score": 1.0, + "content": "A.5 ADDITIONAL INFORMATION ON ALGORITHM 1", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 42 + }, + { + "type": "text", + "bbox": [ + 108, + 709, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "On currently available hardware (p3.2xlarge AWS instance with an NVIDIA V100 GPU), we ob-", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 721, + 322, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 721, + 322, + 733 + ], + "score": 1.0, + "content": "served the following timing results with Algorithm 1,", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 43.5, + "bbox_fs": [ + 105, + 709, + 505, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 115, + 82, + 499, + 185 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 115, + 82, + 499, + 185 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 115, + 82, + 499, + 185 + ], + "spans": [ + { + "bbox": [ + 115, + 82, + 499, + 185 + ], + "score": 0.972, + "type": "image", + "image_path": "7474fc86a4fbae61576200d8c26d718ff3e25733e6249c884ee1b940a23fa88d.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 115, + 82, + 499, + 116.33333333333334 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 115, + 116.33333333333334, + 499, + 150.66666666666669 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 115, + 150.66666666666669, + 499, + 185.00000000000003 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 192, + 506, + 258 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 192, + 506, + 205 + ], + "spans": [ + { + "bbox": [ + 105, + 192, + 506, + 205 + ], + "score": 1.0, + "content": "Figure 6: A counterexample to universal LMC. There exist models such that no possible per-", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 203, + 505, + 214 + ], + "spans": [ + { + "bbox": [ + 105, + 203, + 505, + 214 + ], + "score": 1.0, + "content": "mutation of weights allows for linear mode connectivity. Left: performance of all possible linear", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 213, + 504, + 228 + ], + "spans": [ + { + "bbox": [ + 105, + 213, + 482, + 228 + ], + "score": 1.0, + "content": "interpolations between the two models. Right: A visualization of the prediction functions", + "type": "text" + }, + { + "bbox": [ + 482, + 214, + 504, + 226 + ], + "score": 0.91, + "content": "f ( { \\pmb x } )", + "type": "inline_equation" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 226, + 505, + 237 + ], + "spans": [ + { + "bbox": [ + 106, + 226, + 505, + 237 + ], + "score": 1.0, + "content": "through each linear sweep. 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There exist models such that no possible per-", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 203, + 505, + 214 + ], + "spans": [ + { + "bbox": [ + 105, + 203, + 505, + 214 + ], + "score": 1.0, + "content": "mutation of weights allows for linear mode connectivity. Left: performance of all possible linear", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 213, + 504, + 228 + ], + "spans": [ + { + "bbox": [ + 105, + 213, + 482, + 228 + ], + "score": 1.0, + "content": "interpolations between the two models. Right: A visualization of the prediction functions", + "type": "text" + }, + { + "bbox": [ + 482, + 214, + 504, + 226 + ], + "score": 0.91, + "content": "f ( { \\pmb x } )", + "type": "inline_equation" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 226, + 505, + 237 + ], + "spans": [ + { + "bbox": [ + 106, + 226, + 505, + 237 + ], + "score": 1.0, + "content": "through each linear sweep. 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However, no possible permutation of units results in", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 126, + 496, + 140 + ], + "spans": [ + { + "bbox": [ + 105, + 126, + 243, + 140 + ], + "score": 1.0, + "content": "linear mode connectivity between", + "type": "text" + }, + { + "bbox": [ + 244, + 127, + 256, + 138 + ], + "score": 0.88, + "content": "f _ { A }", + "type": "inline_equation" + }, + { + "bbox": [ + 257, + 126, + 274, + 140 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 274, + 127, + 287, + 138 + ], + "score": 0.87, + "content": "f _ { B }", + "type": "inline_equation" + }, + { + "bbox": [ + 287, + 126, + 496, + 140 + ], + "score": 1.0, + "content": ". We visualize all possible permutations in Figure 6.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 2 + }, + { + "type": "text", + "bbox": [ + 108, + 143, + 502, + 176 + ], + "lines": [ + { + "bbox": [ + 105, + 142, + 505, + 156 + ], + "spans": [ + { + "bbox": [ + 105, + 142, + 505, + 156 + ], + "score": 1.0, + "content": "We claim that this example, and the underlying trick, are simple enough to be embedded into larger", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 154, + 504, + 166 + ], + "spans": [ + { + "bbox": [ + 106, + 154, + 504, + 166 + ], + "score": 1.0, + "content": "models. For example, this could trivially be extended to ResNets where different subsets of layers", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 165, + 242, + 177 + ], + "spans": [ + { + "bbox": [ + 106, + 165, + 242, + 177 + ], + "score": 1.0, + "content": "could be set to identity functions.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 6 + }, + { + "type": "text", + "bbox": [ + 107, + 182, + 505, + 237 + ], + "lines": [ + { + "bbox": [ + 105, + 180, + 506, + 196 + ], + "spans": [ + { + "bbox": [ + 105, + 180, + 506, + 196 + ], + "score": 1.0, + "content": "As discussed in Section 4, the existence of adversarial basins in the loss landscape has interesting", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 193, + 505, + 206 + ], + "spans": [ + { + "bbox": [ + 105, + 193, + 505, + 206 + ], + "score": 1.0, + "content": "consequences for our understanding of loss landscape geometry. In particular, we argue that this", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 204, + 505, + 217 + ], + "spans": [ + { + "bbox": [ + 105, + 204, + 505, + 217 + ], + "score": 1.0, + "content": "implies that common optimization algorithms are conveniently biased towards solutions that admit", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 214, + 506, + 228 + ], + "spans": [ + { + "bbox": [ + 105, + 214, + 506, + 228 + ], + "score": 1.0, + "content": "LMC. However, the precise connection between optimization algorithms and linear mode connec-", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 226, + 198, + 239 + ], + "spans": [ + { + "bbox": [ + 105, + 226, + 198, + 239 + ], + "score": 1.0, + "content": "tivity remains unclear.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 10 + }, + { + "type": "text", + "bbox": [ + 107, + 243, + 505, + 309 + ], + "lines": [ + { + "bbox": [ + 105, + 243, + 505, + 255 + ], + "spans": [ + { + "bbox": [ + 105, + 243, + 505, + 255 + ], + "score": 1.0, + "content": "This counterexample does not constitute a contradiction of the conjecture in Entezari et al. (2021).", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 253, + 506, + 266 + ], + "spans": [ + { + "bbox": [ + 105, + 253, + 506, + 266 + ], + "score": 1.0, + "content": "To be more precise, Conjecture 1 of Entezari et al. (2021) proposes that there exists some subset,", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 263, + 506, + 278 + ], + "spans": [ + { + "bbox": [ + 106, + 265, + 114, + 275 + ], + "score": 0.72, + "content": "s", + "type": "inline_equation" + }, + { + "bbox": [ + 115, + 263, + 340, + 278 + ], + "score": 1.0, + "content": ", of parameter space such that every pair of elements in", + "type": "text" + }, + { + "bbox": [ + 340, + 266, + 348, + 275 + ], + "score": 0.79, + "content": "s", + "type": "inline_equation" + }, + { + "bbox": [ + 349, + 263, + 506, + 278 + ], + "score": 1.0, + "content": "can be linearly mode connected (after", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 276, + 506, + 288 + ], + "spans": [ + { + "bbox": [ + 105, + 276, + 473, + 288 + ], + "score": 1.0, + "content": "some permutation of units), and that with high probability SGD solutions are contained in", + "type": "text" + }, + { + "bbox": [ + 473, + 276, + 481, + 286 + ], + "score": 0.69, + "content": "s", + "type": "inline_equation" + }, + { + "bbox": [ + 482, + 276, + 506, + 288 + ], + "score": 1.0, + "content": ". The", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 286, + 506, + 299 + ], + "spans": [ + { + "bbox": [ + 105, + 286, + 506, + 299 + ], + "score": 1.0, + "content": "example presented in this section does not contradict Entezari et al. (2021)’s conjecture, but instead", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 298, + 477, + 310 + ], + "spans": [ + { + "bbox": [ + 106, + 298, + 477, + 310 + ], + "score": 1.0, + "content": "illustrates that the restriction to SGD solutions is a “load-bearing” element of the conjecture.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 15.5 + }, + { + "type": "title", + "bbox": [ + 108, + 328, + 397, + 340 + ], + "lines": [ + { + "bbox": [ + 105, + 327, + 399, + 342 + ], + "spans": [ + { + "bbox": [ + 105, + 327, + 399, + 342 + ], + "score": 1.0, + "content": "A.7 ON THE FAILURES OF GREEDY UNI-DIRECTIONAL MATCHING", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 19 + }, + { + "type": "text", + "bbox": [ + 107, + 351, + 505, + 451 + ], + "lines": [ + { + "bbox": [ + 105, + 351, + 504, + 364 + ], + "spans": [ + { + "bbox": [ + 105, + 351, + 504, + 364 + ], + "score": 1.0, + "content": "In contrast to prior work (Pittorino et al., 2022; Singh & Jaggi, 2020; Wang et al., 2020), we eschew", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 362, + 506, + 376 + ], + "spans": [ + { + "bbox": [ + 105, + 362, + 506, + 376 + ], + "score": 1.0, + "content": "greedy uni-directional, single-pass matching between models. Instead we derive a weight matching", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 374, + 505, + 386 + ], + "spans": [ + { + "bbox": [ + 106, + 374, + 505, + 386 + ], + "score": 1.0, + "content": "algorithm from a principled, yet computationally infeasible optimization problem. In contrast to", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 384, + 505, + 397 + ], + "spans": [ + { + "bbox": [ + 105, + 384, + 505, + 397 + ], + "score": 1.0, + "content": "prior work, our method can be viewed as “bi-directional”: it selects unit associations based on", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 396, + 506, + 409 + ], + "spans": [ + { + "bbox": [ + 106, + 396, + 506, + 409 + ], + "score": 1.0, + "content": "weights in all relevant layers, not just in the immediately previous layer. In this section, we describe", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 407, + 504, + 419 + ], + "spans": [ + { + "bbox": [ + 106, + 407, + 504, + 419 + ], + "score": 1.0, + "content": "benefits of our holistic approach, including an example problem showing the failure modes of greedy", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 417, + 505, + 431 + ], + "spans": [ + { + "bbox": [ + 106, + 417, + 505, + 431 + ], + "score": 1.0, + "content": "uni-directional matching. We find that matching across all layers simultaneously allows our weight", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 427, + 505, + 443 + ], + "spans": [ + { + "bbox": [ + 105, + 427, + 505, + 443 + ], + "score": 1.0, + "content": "matching algorithm (Algorithm 1) to exploit units’ relationships with downstream weights in a way", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 440, + 285, + 453 + ], + "spans": [ + { + "bbox": [ + 105, + 440, + 285, + 453 + ], + "score": 1.0, + "content": "that greedy uni-directional matching cannot.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 24 + }, + { + "type": "text", + "bbox": [ + 107, + 456, + 505, + 493 + ], + "lines": [ + { + "bbox": [ + 106, + 455, + 505, + 470 + ], + "spans": [ + { + "bbox": [ + 106, + 455, + 488, + 470 + ], + "score": 1.0, + "content": "Concretely, greedy uni-directional matching begins at the first layer and computes a matching,", + "type": "text" + }, + { + "bbox": [ + 488, + 457, + 501, + 468 + ], + "score": 0.85, + "content": "P _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 455, + 505, + 470 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 104, + 465, + 507, + 484 + ], + "spans": [ + { + "bbox": [ + 104, + 465, + 178, + 484 + ], + "score": 1.0, + "content": "considering only", + "type": "text" + }, + { + "bbox": [ + 179, + 467, + 234, + 482 + ], + "score": 0.92, + "content": "{ \\bf \\dot { W } } _ { 1 } ^ { ( A ) } , { \\bf W } _ { 1 } ^ { ( B ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 235, + 465, + 311, + 484 + ], + "score": 1.0, + "content": ". After matching,", + "type": "text" + }, + { + "bbox": [ + 312, + 470, + 325, + 481 + ], + "score": 0.86, + "content": "P _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 325, + 465, + 507, + 484 + ], + "score": 1.0, + "content": "is applied throughout the remainder of the", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 480, + 418, + 495 + ], + "spans": [ + { + "bbox": [ + 105, + 480, + 418, + 495 + ], + "score": 1.0, + "content": "network. Then, we proceed through the layers in order repeating this process.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 30 + }, + { + "type": "text", + "bbox": [ + 108, + 497, + 502, + 531 + ], + "lines": [ + { + "bbox": [ + 106, + 497, + 504, + 511 + ], + "spans": [ + { + "bbox": [ + 106, + 497, + 504, + 511 + ], + "score": 1.0, + "content": "We compare our Algorithm 1 to greedy uni-directional matching experimentally in Appendix A.7.1", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 507, + 505, + 523 + ], + "spans": [ + { + "bbox": [ + 105, + 507, + 505, + 523 + ], + "score": 1.0, + "content": "and present a theoretical counterexample that illustrates the advantages of our method in Ap-", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 520, + 164, + 531 + ], + "spans": [ + { + "bbox": [ + 105, + 520, + 164, + 531 + ], + "score": 1.0, + "content": "pendix A.7.2.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 33 + }, + { + "type": "title", + "bbox": [ + 108, + 549, + 269, + 560 + ], + "lines": [ + { + "bbox": [ + 106, + 548, + 271, + 562 + ], + "spans": [ + { + "bbox": [ + 106, + 548, + 271, + 562 + ], + "score": 1.0, + "content": "A.7.1 EXPERIMENTAL COMPARISON", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 35 + }, + { + "type": "text", + "bbox": [ + 108, + 571, + 505, + 604 + ], + "lines": [ + { + "bbox": [ + 105, + 570, + 505, + 584 + ], + "spans": [ + { + "bbox": [ + 105, + 570, + 505, + 584 + ], + "score": 1.0, + "content": "In order to further evaluate our performance relative to prior work, and Pittorino et al. (2022); Singh", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 582, + 505, + 594 + ], + "spans": [ + { + "bbox": [ + 106, + 582, + 505, + 594 + ], + "score": 1.0, + "content": "& Jaggi (2020) in particular, we explored experimental comparisons with VGG11 models trained", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 592, + 353, + 605 + ], + "spans": [ + { + "bbox": [ + 105, + 592, + 353, + 605 + ], + "score": 1.0, + "content": "on CIFAR-10 and on ResNet50 models trained on ImageNet.", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 37 + }, + { + "type": "text", + "bbox": [ + 107, + 609, + 504, + 665 + ], + "lines": [ + { + "bbox": [ + 106, + 609, + 506, + 623 + ], + "spans": [ + { + "bbox": [ + 106, + 609, + 506, + 623 + ], + "score": 1.0, + "content": "VGG11 models trained on CIFAR-10. Following an exact reproduction of experiment from Table", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 621, + 505, + 633 + ], + "spans": [ + { + "bbox": [ + 106, + 621, + 505, + 633 + ], + "score": 1.0, + "content": "1 of Singh & Jaggi (2020), we merged the model weights released along with their paper. We present", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 631, + 506, + 645 + ], + "spans": [ + { + "bbox": [ + 105, + 631, + 506, + 645 + ], + "score": 1.0, + "content": "results in Table 2. We found that our weight matching method outperforms the “wts” method of", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 643, + 506, + 656 + ], + "spans": [ + { + "bbox": [ + 106, + 643, + 506, + 656 + ], + "score": 1.0, + "content": "Singh & Jaggi (2020) in both implementation speed and model performance when reproducing their", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 654, + 288, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 288, + 667 + ], + "score": 1.0, + "content": "experiment with their trained model weights.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 41 + }, + { + "type": "text", + "bbox": [ + 107, + 671, + 504, + 715 + ], + "lines": [ + { + "bbox": [ + 105, + 669, + 505, + 684 + ], + "spans": [ + { + "bbox": [ + 105, + 669, + 505, + 684 + ], + "score": 1.0, + "content": "ResNet50 models trained on ImageNet. We applied OT-Fusion (“wts”) to the ImageNet exper-", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 682, + 505, + 694 + ], + "spans": [ + { + "bbox": [ + 106, + 682, + 505, + 694 + ], + "score": 1.0, + "content": "iment that we consider in Section 5.1. We present results in Figure 8. We found the OT-Fusion", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 692, + 506, + 706 + ], + "spans": [ + { + "bbox": [ + 105, + 692, + 241, + 706 + ], + "score": 1.0, + "content": "method resulted in models with", + "type": "text" + }, + { + "bbox": [ + 241, + 693, + 268, + 703 + ], + "score": 0.87, + "content": "1 . 3 8 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 268, + 692, + 506, + 706 + ], + "score": 1.0, + "content": "top-1 accuracy on ImageNet, only marginally improving", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 704, + 354, + 715 + ], + "spans": [ + { + "bbox": [ + 105, + 704, + 318, + 715 + ], + "score": 1.0, + "content": "over na¨ıve averaging. On the other hand, we achieve", + "type": "text" + }, + { + "bbox": [ + 318, + 704, + 350, + 714 + ], + "score": 0.87, + "content": "5 1 . 0 1 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 350, + 704, + 354, + 715 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 45.5 + }, + { + "type": "text", + "bbox": [ + 106, + 720, + 431, + 731 + ], + "lines": [ + { + "bbox": [ + 105, + 720, + 433, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 433, + 733 + ], + "score": 1.0, + "content": "BatchNorm statistics were recalculated after interpolation for all methods shown.", + "type": "text" + } + ], + "index": 48 + } + ], + "index": 48 + } + ], + "page_idx": 22, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2023", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 751, + 311, + 760 + ], + "lines": [ + { + "bbox": [ + 298, + 750, + 313, + 764 + ], + "spans": [ + { + "bbox": [ + 298, + 750, + 313, + 764 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 14, + "width": 15 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 505, + 138 + ], + "lines": [ + { + "bbox": [ + 105, + 82, + 504, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 473, + 95 + ], + "score": 1.0, + "content": "Intuitively, these networks are organized such that each layer makes a classification whether", + "type": "text" + }, + { + "bbox": [ + 473, + 83, + 504, + 93 + ], + "score": 0.9, + "content": "\\mathbf { x } _ { 1 } < 0", + "type": "inline_equation" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 94, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 94, + 118, + 106 + ], + "score": 1.0, + "content": "or", + "type": "text" + }, + { + "bbox": [ + 118, + 94, + 151, + 105 + ], + "score": 0.9, + "content": "x _ { 2 } > 0", + "type": "inline_equation" + }, + { + "bbox": [ + 151, + 94, + 197, + 106 + ], + "score": 1.0, + "content": ". In model", + "type": "text" + }, + { + "bbox": [ + 198, + 94, + 206, + 104 + ], + "score": 0.7, + "content": "A", + "type": "inline_equation" + }, + { + "bbox": [ + 207, + 94, + 324, + 106 + ], + "score": 1.0, + "content": ", the first layer tests whether", + "type": "text" + }, + { + "bbox": [ + 324, + 94, + 358, + 105 + ], + "score": 0.91, + "content": "x _ { 2 } > 0", + "type": "inline_equation" + }, + { + "bbox": [ + 358, + 94, + 505, + 106 + ], + "score": 1.0, + "content": ", and the second layer tests whether", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 104, + 505, + 117 + ], + "spans": [ + { + "bbox": [ + 106, + 105, + 139, + 115 + ], + "score": 0.91, + "content": "x _ { 1 } < 0", + "type": "inline_equation" + }, + { + "bbox": [ + 139, + 104, + 217, + 117 + ], + "score": 1.0, + "content": ", whereas in model", + "type": "text" + }, + { + "bbox": [ + 217, + 105, + 227, + 114 + ], + "score": 0.78, + "content": "B", + "type": "inline_equation" + }, + { + "bbox": [ + 227, + 104, + 505, + 117 + ], + "score": 1.0, + "content": "the order is reversed. With a bit of algebra, it is possible to see that", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 505, + 128 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 127, + 128 + ], + "score": 1.0, + "content": "both", + "type": "text" + }, + { + "bbox": [ + 127, + 116, + 140, + 127 + ], + "score": 0.88, + "content": "f _ { A }", + "type": "inline_equation" + }, + { + "bbox": [ + 140, + 115, + 158, + 128 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 158, + 115, + 171, + 127 + ], + "score": 0.9, + "content": "f _ { B }", + "type": "inline_equation" + }, + { + "bbox": [ + 172, + 115, + 505, + 128 + ], + "score": 1.0, + "content": "achieve perfect performance. However, no possible permutation of units results in", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 126, + 496, + 140 + ], + "spans": [ + { + "bbox": [ + 105, + 126, + 243, + 140 + ], + "score": 1.0, + "content": "linear mode connectivity between", + "type": "text" + }, + { + "bbox": [ + 244, + 127, + 256, + 138 + ], + "score": 0.88, + "content": "f _ { A }", + "type": "inline_equation" + }, + { + "bbox": [ + 257, + 126, + 274, + 140 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 274, + 127, + 287, + 138 + ], + "score": 0.87, + "content": "f _ { B }", + "type": "inline_equation" + }, + { + "bbox": [ + 287, + 126, + 496, + 140 + ], + "score": 1.0, + "content": ". We visualize all possible permutations in Figure 6.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 2, + "bbox_fs": [ + 105, + 82, + 505, + 140 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 143, + 502, + 176 + ], + "lines": [ + { + "bbox": [ + 105, + 142, + 505, + 156 + ], + "spans": [ + { + "bbox": [ + 105, + 142, + 505, + 156 + ], + "score": 1.0, + "content": "We claim that this example, and the underlying trick, are simple enough to be embedded into larger", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 154, + 504, + 166 + ], + "spans": [ + { + "bbox": [ + 106, + 154, + 504, + 166 + ], + "score": 1.0, + "content": "models. For example, this could trivially be extended to ResNets where different subsets of layers", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 165, + 242, + 177 + ], + "spans": [ + { + "bbox": [ + 106, + 165, + 242, + 177 + ], + "score": 1.0, + "content": "could be set to identity functions.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 6, + "bbox_fs": [ + 105, + 142, + 505, + 177 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 182, + 505, + 237 + ], + "lines": [ + { + "bbox": [ + 105, + 180, + 506, + 196 + ], + "spans": [ + { + "bbox": [ + 105, + 180, + 506, + 196 + ], + "score": 1.0, + "content": "As discussed in Section 4, the existence of adversarial basins in the loss landscape has interesting", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 193, + 505, + 206 + ], + "spans": [ + { + "bbox": [ + 105, + 193, + 505, + 206 + ], + "score": 1.0, + "content": "consequences for our understanding of loss landscape geometry. In particular, we argue that this", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 204, + 505, + 217 + ], + "spans": [ + { + "bbox": [ + 105, + 204, + 505, + 217 + ], + "score": 1.0, + "content": "implies that common optimization algorithms are conveniently biased towards solutions that admit", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 214, + 506, + 228 + ], + "spans": [ + { + "bbox": [ + 105, + 214, + 506, + 228 + ], + "score": 1.0, + "content": "LMC. However, the precise connection between optimization algorithms and linear mode connec-", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 226, + 198, + 239 + ], + "spans": [ + { + "bbox": [ + 105, + 226, + 198, + 239 + ], + "score": 1.0, + "content": "tivity remains unclear.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 10, + "bbox_fs": [ + 105, + 180, + 506, + 239 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 243, + 505, + 309 + ], + "lines": [ + { + "bbox": [ + 105, + 243, + 505, + 255 + ], + "spans": [ + { + "bbox": [ + 105, + 243, + 505, + 255 + ], + "score": 1.0, + "content": "This counterexample does not constitute a contradiction of the conjecture in Entezari et al. (2021).", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 253, + 506, + 266 + ], + "spans": [ + { + "bbox": [ + 105, + 253, + 506, + 266 + ], + "score": 1.0, + "content": "To be more precise, Conjecture 1 of Entezari et al. (2021) proposes that there exists some subset,", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 263, + 506, + 278 + ], + "spans": [ + { + "bbox": [ + 106, + 265, + 114, + 275 + ], + "score": 0.72, + "content": "s", + "type": "inline_equation" + }, + { + "bbox": [ + 115, + 263, + 340, + 278 + ], + "score": 1.0, + "content": ", of parameter space such that every pair of elements in", + "type": "text" + }, + { + "bbox": [ + 340, + 266, + 348, + 275 + ], + "score": 0.79, + "content": "s", + "type": "inline_equation" + }, + { + "bbox": [ + 349, + 263, + 506, + 278 + ], + "score": 1.0, + "content": "can be linearly mode connected (after", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 276, + 506, + 288 + ], + "spans": [ + { + "bbox": [ + 105, + 276, + 473, + 288 + ], + "score": 1.0, + "content": "some permutation of units), and that with high probability SGD solutions are contained in", + "type": "text" + }, + { + "bbox": [ + 473, + 276, + 481, + 286 + ], + "score": 0.69, + "content": "s", + "type": "inline_equation" + }, + { + "bbox": [ + 482, + 276, + 506, + 288 + ], + "score": 1.0, + "content": ". The", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 286, + 506, + 299 + ], + "spans": [ + { + "bbox": [ + 105, + 286, + 506, + 299 + ], + "score": 1.0, + "content": "example presented in this section does not contradict Entezari et al. (2021)’s conjecture, but instead", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 298, + 477, + 310 + ], + "spans": [ + { + "bbox": [ + 106, + 298, + 477, + 310 + ], + "score": 1.0, + "content": "illustrates that the restriction to SGD solutions is a “load-bearing” element of the conjecture.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 15.5, + "bbox_fs": [ + 105, + 243, + 506, + 310 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 328, + 397, + 340 + ], + "lines": [ + { + "bbox": [ + 105, + 327, + 399, + 342 + ], + "spans": [ + { + "bbox": [ + 105, + 327, + 399, + 342 + ], + "score": 1.0, + "content": "A.7 ON THE FAILURES OF GREEDY UNI-DIRECTIONAL MATCHING", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 19 + }, + { + "type": "text", + "bbox": [ + 107, + 351, + 505, + 451 + ], + "lines": [ + { + "bbox": [ + 105, + 351, + 504, + 364 + ], + "spans": [ + { + "bbox": [ + 105, + 351, + 504, + 364 + ], + "score": 1.0, + "content": "In contrast to prior work (Pittorino et al., 2022; Singh & Jaggi, 2020; Wang et al., 2020), we eschew", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 362, + 506, + 376 + ], + "spans": [ + { + "bbox": [ + 105, + 362, + 506, + 376 + ], + "score": 1.0, + "content": "greedy uni-directional, single-pass matching between models. Instead we derive a weight matching", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 374, + 505, + 386 + ], + "spans": [ + { + "bbox": [ + 106, + 374, + 505, + 386 + ], + "score": 1.0, + "content": "algorithm from a principled, yet computationally infeasible optimization problem. In contrast to", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 384, + 505, + 397 + ], + "spans": [ + { + "bbox": [ + 105, + 384, + 505, + 397 + ], + "score": 1.0, + "content": "prior work, our method can be viewed as “bi-directional”: it selects unit associations based on", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 396, + 506, + 409 + ], + "spans": [ + { + "bbox": [ + 106, + 396, + 506, + 409 + ], + "score": 1.0, + "content": "weights in all relevant layers, not just in the immediately previous layer. In this section, we describe", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 407, + 504, + 419 + ], + "spans": [ + { + "bbox": [ + 106, + 407, + 504, + 419 + ], + "score": 1.0, + "content": "benefits of our holistic approach, including an example problem showing the failure modes of greedy", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 417, + 505, + 431 + ], + "spans": [ + { + "bbox": [ + 106, + 417, + 505, + 431 + ], + "score": 1.0, + "content": "uni-directional matching. We find that matching across all layers simultaneously allows our weight", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 427, + 505, + 443 + ], + "spans": [ + { + "bbox": [ + 105, + 427, + 505, + 443 + ], + "score": 1.0, + "content": "matching algorithm (Algorithm 1) to exploit units’ relationships with downstream weights in a way", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 440, + 285, + 453 + ], + "spans": [ + { + "bbox": [ + 105, + 440, + 285, + 453 + ], + "score": 1.0, + "content": "that greedy uni-directional matching cannot.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 24, + "bbox_fs": [ + 105, + 351, + 506, + 453 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 456, + 505, + 493 + ], + "lines": [ + { + "bbox": [ + 106, + 455, + 505, + 470 + ], + "spans": [ + { + "bbox": [ + 106, + 455, + 488, + 470 + ], + "score": 1.0, + "content": "Concretely, greedy uni-directional matching begins at the first layer and computes a matching,", + "type": "text" + }, + { + "bbox": [ + 488, + 457, + 501, + 468 + ], + "score": 0.85, + "content": "P _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 455, + 505, + 470 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 104, + 465, + 507, + 484 + ], + "spans": [ + { + "bbox": [ + 104, + 465, + 178, + 484 + ], + "score": 1.0, + "content": "considering only", + "type": "text" + }, + { + "bbox": [ + 179, + 467, + 234, + 482 + ], + "score": 0.92, + "content": "{ \\bf \\dot { W } } _ { 1 } ^ { ( A ) } , { \\bf W } _ { 1 } ^ { ( B ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 235, + 465, + 311, + 484 + ], + "score": 1.0, + "content": ". After matching,", + "type": "text" + }, + { + "bbox": [ + 312, + 470, + 325, + 481 + ], + "score": 0.86, + "content": "P _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 325, + 465, + 507, + 484 + ], + "score": 1.0, + "content": "is applied throughout the remainder of the", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 480, + 418, + 495 + ], + "spans": [ + { + "bbox": [ + 105, + 480, + 418, + 495 + ], + "score": 1.0, + "content": "network. Then, we proceed through the layers in order repeating this process.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 30, + "bbox_fs": [ + 104, + 455, + 507, + 495 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 497, + 502, + 531 + ], + "lines": [ + { + "bbox": [ + 106, + 497, + 504, + 511 + ], + "spans": [ + { + "bbox": [ + 106, + 497, + 504, + 511 + ], + "score": 1.0, + "content": "We compare our Algorithm 1 to greedy uni-directional matching experimentally in Appendix A.7.1", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 507, + 505, + 523 + ], + "spans": [ + { + "bbox": [ + 105, + 507, + 505, + 523 + ], + "score": 1.0, + "content": "and present a theoretical counterexample that illustrates the advantages of our method in Ap-", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 520, + 164, + 531 + ], + "spans": [ + { + "bbox": [ + 105, + 520, + 164, + 531 + ], + "score": 1.0, + "content": "pendix A.7.2.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 33, + "bbox_fs": [ + 105, + 497, + 505, + 531 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 549, + 269, + 560 + ], + "lines": [ + { + "bbox": [ + 106, + 548, + 271, + 562 + ], + "spans": [ + { + "bbox": [ + 106, + 548, + 271, + 562 + ], + "score": 1.0, + "content": "A.7.1 EXPERIMENTAL COMPARISON", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 35 + }, + { + "type": "text", + "bbox": [ + 108, + 571, + 505, + 604 + ], + "lines": [ + { + "bbox": [ + 105, + 570, + 505, + 584 + ], + "spans": [ + { + "bbox": [ + 105, + 570, + 505, + 584 + ], + "score": 1.0, + "content": "In order to further evaluate our performance relative to prior work, and Pittorino et al. (2022); Singh", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 582, + 505, + 594 + ], + "spans": [ + { + "bbox": [ + 106, + 582, + 505, + 594 + ], + "score": 1.0, + "content": "& Jaggi (2020) in particular, we explored experimental comparisons with VGG11 models trained", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 592, + 353, + 605 + ], + "spans": [ + { + "bbox": [ + 105, + 592, + 353, + 605 + ], + "score": 1.0, + "content": "on CIFAR-10 and on ResNet50 models trained on ImageNet.", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 37, + "bbox_fs": [ + 105, + 570, + 505, + 605 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 609, + 504, + 665 + ], + "lines": [ + { + "bbox": [ + 106, + 609, + 506, + 623 + ], + "spans": [ + { + "bbox": [ + 106, + 609, + 506, + 623 + ], + "score": 1.0, + "content": "VGG11 models trained on CIFAR-10. Following an exact reproduction of experiment from Table", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 621, + 505, + 633 + ], + "spans": [ + { + "bbox": [ + 106, + 621, + 505, + 633 + ], + "score": 1.0, + "content": "1 of Singh & Jaggi (2020), we merged the model weights released along with their paper. We present", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 631, + 506, + 645 + ], + "spans": [ + { + "bbox": [ + 105, + 631, + 506, + 645 + ], + "score": 1.0, + "content": "results in Table 2. We found that our weight matching method outperforms the “wts” method of", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 643, + 506, + 656 + ], + "spans": [ + { + "bbox": [ + 106, + 643, + 506, + 656 + ], + "score": 1.0, + "content": "Singh & Jaggi (2020) in both implementation speed and model performance when reproducing their", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 654, + 288, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 288, + 667 + ], + "score": 1.0, + "content": "experiment with their trained model weights.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 41, + "bbox_fs": [ + 105, + 609, + 506, + 667 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 671, + 504, + 715 + ], + "lines": [ + { + "bbox": [ + 105, + 669, + 505, + 684 + ], + "spans": [ + { + "bbox": [ + 105, + 669, + 505, + 684 + ], + "score": 1.0, + "content": "ResNet50 models trained on ImageNet. We applied OT-Fusion (“wts”) to the ImageNet exper-", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 682, + 505, + 694 + ], + "spans": [ + { + "bbox": [ + 106, + 682, + 505, + 694 + ], + "score": 1.0, + "content": "iment that we consider in Section 5.1. We present results in Figure 8. We found the OT-Fusion", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 692, + 506, + 706 + ], + "spans": [ + { + "bbox": [ + 105, + 692, + 241, + 706 + ], + "score": 1.0, + "content": "method resulted in models with", + "type": "text" + }, + { + "bbox": [ + 241, + 693, + 268, + 703 + ], + "score": 0.87, + "content": "1 . 3 8 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 268, + 692, + 506, + 706 + ], + "score": 1.0, + "content": "top-1 accuracy on ImageNet, only marginally improving", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 704, + 354, + 715 + ], + "spans": [ + { + "bbox": [ + 105, + 704, + 318, + 715 + ], + "score": 1.0, + "content": "over na¨ıve averaging. 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MethodTest accuracy (个)Run-time (↓)
OT-Fusion (Singh & Jaggi, 2020)85.98%2.86s
Weight matching (ours)86.57 %0.64s
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We found that our", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 150, + 504, + 163 + ], + "spans": [ + { + "bbox": [ + 106, + 150, + 504, + 163 + ], + "score": 1.0, + "content": "weight matching method outperforms the “wts” method of Singh & Jaggi (2020) in both implemen-", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 161, + 505, + 174 + ], + "spans": [ + { + "bbox": [ + 105, + 161, + 505, + 174 + ], + "score": 1.0, + "content": "tation speed and model performance when reproducing one of their experiments with their published", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 171, + 506, + 186 + ], + "spans": [ + { + "bbox": [ + 104, + 171, + 264, + 186 + ], + "score": 1.0, + "content": "model weights. 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MethodTest accuracy (个)Run-time (↓)
OT-Fusion (Singh & Jaggi, 2020)85.98%2.86s
Weight matching (ours)86.57 %0.64s
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On the other hand, we achieve", + "type": "text" + }, + { + "bbox": [ + 362, + 377, + 393, + 387 + ], + "score": 0.87, + "content": "5 1 . 0 1 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 394, + 376, + 398, + 389 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 12 + } + ], + "index": 10.5 + }, + { + "type": "text", + "bbox": [ + 106, + 408, + 505, + 486 + ], + "lines": [ + { + "bbox": [ + 105, + 408, + 506, + 421 + ], + "spans": [ + { + "bbox": [ + 105, + 408, + 506, + 421 + ], + "score": 1.0, + "content": "Although a number of factors may be responsible for the difference in performance between weight", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 419, + 505, + 432 + ], + "spans": [ + { + "bbox": [ + 105, + 419, + 505, + 432 + ], + "score": 1.0, + "content": "matching and OT-Fusion, we found the number of alignment passes made over the network layers", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 430, + 505, + 443 + ], + "spans": [ + { + "bbox": [ + 105, + 430, + 505, + 443 + ], + "score": 1.0, + "content": "to have a substantial impact. OT-Fusion is inherently limited to a single pass over the layers. On the", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 441, + 505, + 453 + ], + "spans": [ + { + "bbox": [ + 105, + 441, + 505, + 453 + ], + "score": 1.0, + "content": "other hand, we are not limited to any specific number of optimization passes and instead continue", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 452, + 505, + 466 + ], + "spans": [ + { + "bbox": [ + 105, + 452, + 505, + 466 + ], + "score": 1.0, + "content": "until convergence (convergence is guaranteed by Lemma 2). For comparison, if our weight matching", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 462, + 506, + 478 + ], + "spans": [ + { + "bbox": [ + 105, + 462, + 506, + 478 + ], + "score": 1.0, + "content": "algorithm is artificially handicapped to a single pass over the layers, we achieve a similarly low", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 472, + 196, + 488 + ], + "spans": [ + { + "bbox": [ + 106, + 474, + 132, + 485 + ], + "score": 0.87, + "content": "\\sim 7 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 132, + 472, + 196, + 488 + ], + "score": 1.0, + "content": "top-1 accuracy.", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 17, + "bbox_fs": [ + 105, + 408, + 506, + 488 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 497, + 267, + 509 + ], + "lines": [ + { + "bbox": [ + 106, + 496, + 269, + 510 + ], + "spans": [ + { + "bbox": [ + 106, + 496, + 269, + 510 + ], + "score": 1.0, + "content": "A.7.2 AN EXAMPLE FAILURE CASE", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 21 + }, + { + "type": "text", + "bbox": [ + 108, + 516, + 504, + 529 + ], + "lines": [ + { + "bbox": [ + 106, + 513, + 501, + 531 + ], + "spans": [ + { + "bbox": [ + 106, + 513, + 202, + 531 + ], + "score": 1.0, + "content": "Consider two networks,", + "type": "text" + }, + { + "bbox": [ + 203, + 517, + 211, + 527 + ], + "score": 0.79, + "content": "A", + "type": "inline_equation" + }, + { + "bbox": [ + 211, + 513, + 228, + 531 + ], + "score": 1.0, + "content": "and", + "type": "text" + }, + { + "bbox": [ + 228, + 517, + 237, + 527 + ], + "score": 0.82, + "content": "B", + "type": "inline_equation" + }, + { + "bbox": [ + 237, + 513, + 462, + 531 + ], + "score": 1.0, + "content": ", with the objective that they capture the identity function", + "type": "text" + }, + { + "bbox": [ + 462, + 516, + 501, + 529 + ], + "score": 0.92, + "content": "f ( x ) = x", + "type": "inline_equation" + } + ], + "index": 22 + } + ], + "index": 22, + "bbox_fs": [ + 106, + 513, + 501, + 531 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 232, + 533, + 378, + 591 + ], + "lines": [ + { + "bbox": [ + 232, + 533, + 378, + 591 + ], + "spans": [ + { + "bbox": [ + 232, + 533, + 378, + 591 + ], + "score": 0.93, + "content": "\\begin{array} { r l } { f _ { \\Theta _ { A } } ( x ) = [ 1 } & { 0 ] \\left[ \\begin{array} { l l } { 1 } & { 0 } \\\\ { 0 } & { \\epsilon } \\end{array} \\right] \\left[ \\begin{array} { l } { 1 } \\\\ { 1 + \\epsilon } \\end{array} \\right] x } \\\\ { f _ { \\Theta _ { B } } ( x ) = [ 0 } & { 1 ] \\left[ \\begin{array} { l l } { 0 } & { 0 } \\\\ { 0 } & { 1 } \\end{array} \\right] \\left[ \\begin{array} { l } { 1 } \\\\ { 1 + \\epsilon } \\end{array} \\right] x } \\end{array}", + "type": "interline_equation", + "image_path": "73c65bb1c8716518b1d7831eb5e8a63625dfc111673187365611760a4feed994.jpg" + } + ] + } + ], + "index": 23.5, + "virtual_lines": [ + { + "bbox": [ + 232, + 533, + 378, + 562.0 + ], + "spans": [], + "index": 23 + }, + { + "bbox": [ + 232, + 562.0, + 378, + 591.0 + ], + "spans": [], + "index": 24 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 593, + 506, + 617 + ], + "lines": [ + { + "bbox": [ + 105, + 591, + 506, + 607 + ], + "spans": [ + { + "bbox": [ + 105, + 591, + 134, + 607 + ], + "score": 1.0, + "content": "where", + "type": "text" + }, + { + "bbox": [ + 134, + 594, + 162, + 604 + ], + "score": 0.88, + "content": "\\epsilon > 0", + "type": "inline_equation" + }, + { + "bbox": [ + 163, + 591, + 430, + 607 + ], + "score": 1.0, + "content": "is some negligible constant. It can be seen that these reduce to", + "type": "text" + }, + { + "bbox": [ + 431, + 594, + 486, + 606 + ], + "score": 0.93, + "content": "f _ { \\Theta _ { A } } ( x ) = x", + "type": "inline_equation" + }, + { + "bbox": [ + 486, + 591, + 506, + 607 + ], + "score": 1.0, + "content": "and", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 604, + 191, + 618 + ], + "spans": [ + { + "bbox": [ + 106, + 604, + 187, + 617 + ], + "score": 0.9, + "content": "f _ { \\Theta _ { B } } ( x ) = ( 1 + \\epsilon ) x", + "type": "inline_equation" + }, + { + "bbox": [ + 187, + 604, + 191, + 618 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 25.5, + "bbox_fs": [ + 105, + 591, + 506, + 618 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 621, + 503, + 644 + ], + "lines": [ + { + "bbox": [ + 105, + 621, + 501, + 635 + ], + "spans": [ + { + "bbox": [ + 105, + 621, + 441, + 635 + ], + "score": 1.0, + "content": "When aligning these models there are two possible opportunities for permutation,", + "type": "text" + }, + { + "bbox": [ + 441, + 621, + 501, + 634 + ], + "score": 0.93, + "content": "\\pi = \\{ P _ { 1 } , P _ { 2 } \\}", + "type": "inline_equation" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 632, + 274, + 645 + ], + "spans": [ + { + "bbox": [ + 106, + 632, + 192, + 645 + ], + "score": 1.0, + "content": "The permuted model", + "type": "text" + }, + { + "bbox": [ + 192, + 633, + 201, + 642 + ], + "score": 0.81, + "content": "B", + "type": "inline_equation" + }, + { + "bbox": [ + 202, + 632, + 274, + 645 + ], + "score": 1.0, + "content": "then has the form", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 27.5, + "bbox_fs": [ + 105, + 621, + 501, + 645 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 177, + 648, + 434, + 677 + ], + "lines": [ + { + "bbox": [ + 177, + 648, + 434, + 677 + ], + "spans": [ + { + "bbox": [ + 177, + 648, + 434, + 677 + ], + "score": 0.93, + "content": "f _ { \\pi ( \\Theta _ { B } ) } ( x ) = \\left( \\left[ 0 \\quad 1 \\right] P _ { 2 } ^ { \\top } \\right) \\left( P _ { 2 } \\left[ 0 \\quad 1 \\right] P _ { 1 } ^ { \\top } \\right) \\left( P _ { 1 } \\left[ 1 + \\epsilon \\right] \\right) x", + "type": "interline_equation", + "image_path": "754c87fa936b6fdeac5999f11a61ef909cd13a77689fe0971192f074d860ada1.jpg" + } + ] + } + ], + "index": 30, + "virtual_lines": [ + { + "bbox": [ + 177, + 648, + 434, + 657.6666666666666 + ], + "spans": [], + "index": 29 + }, + { + "bbox": [ + 177, + 657.6666666666666, + 434, + 667.3333333333333 + ], + "spans": [], + "index": 30 + }, + { + "bbox": [ + 177, + 667.3333333333333, + 434, + 676.9999999999999 + ], + "spans": [], + "index": 31 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 686, + 505, + 736 + ], + "lines": [ + { + "bbox": [ + 105, + 685, + 504, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 685, + 437, + 700 + ], + "score": 1.0, + "content": "Now, aligning with greedy uni-directional matching will result in the alignment", + "type": "text" + }, + { + "bbox": [ + 437, + 687, + 504, + 699 + ], + "score": 0.9, + "content": "\\pi _ { g u d } = \\{ P _ { 1 } =", + "type": "inline_equation" + } + ], + "index": 32 + }, + { + "bbox": [ + 107, + 696, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 107, + 698, + 158, + 710 + ], + "score": 0.88, + "content": "I , P _ { 2 } = I \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 158, + 696, + 470, + 712 + ], + "score": 1.0, + "content": ". 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On the other hand, our weight matching", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 494, + 505, + 506 + ], + "spans": [ + { + "bbox": [ + 106, + 494, + 505, + 506 + ], + "score": 1.0, + "content": "algorithm (Algorithm 1, Equation (10)) produces a merged model that accurately reflects both of the", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 104, + 504, + 376, + 516 + ], + "spans": [ + { + "bbox": [ + 104, + 504, + 327, + 516 + ], + "score": 1.0, + "content": "input models, and even improves performance over the", + "type": "text" + }, + { + "bbox": [ + 328, + 505, + 337, + 514 + ], + "score": 0.81, + "content": "B", + "type": "inline_equation" + }, + { + "bbox": [ + 338, + 504, + 376, + 516 + ], + "score": 1.0, + "content": "model. 5", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 13.5 + }, + { + "type": "text", + "bbox": [ + 108, + 529, + 214, + 541 + ], + "lines": [ + { + "bbox": [ + 105, + 527, + 215, + 542 + ], + "spans": [ + { + "bbox": [ + 105, + 527, + 215, + 542 + ], + "score": 1.0, + "content": "A.8 AUXILIARY PLOTS", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 16 + }, + { + "type": "title", + "bbox": [ + 107, + 550, + 317, + 561 + ], + "lines": [ + { + "bbox": [ + 106, + 549, + 317, + 563 + ], + "spans": [ + { + "bbox": [ + 106, + 549, + 317, + 563 + ], + "score": 1.0, + "content": "A.9 STRAIGHT-THROUGH ESTIMATOR DETAILS", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 17 + }, + { + "type": "text", + "bbox": [ + 108, + 570, + 455, + 583 + ], + "lines": [ + { + "bbox": [ + 106, + 570, + 456, + 584 + ], + "spans": [ + { + "bbox": [ + 106, + 570, + 456, + 584 + ], + "score": 1.0, + "content": "See Algorithm 2 for a complete description of the straight-through estimator algorithm.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 18 + }, + { + "type": "text", + "bbox": [ + 108, + 595, + 253, + 608 + ], + "lines": [ + { + "bbox": [ + 105, + 594, + 254, + 609 + ], + "spans": [ + { + "bbox": [ + 105, + 594, + 254, + 609 + ], + "score": 1.0, + "content": "A.10 MERGING MANY MODELS", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 19 + }, + { + "type": "text", + "bbox": [ + 106, + 616, + 434, + 628 + ], + "lines": [ + { + "bbox": [ + 105, + 616, + 435, + 630 + ], + "spans": [ + { + "bbox": [ + 105, + 616, + 435, + 630 + ], + "score": 1.0, + "content": "We propose Algorithm 3 to merge the weights of more than two models at a time.", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 20 + }, + { + "type": "text", + "bbox": [ + 106, + 633, + 455, + 645 + ], + "lines": [ + { + "bbox": [ + 104, + 632, + 457, + 648 + ], + "spans": [ + { + "bbox": [ + 104, + 632, + 457, + 648 + ], + "score": 1.0, + "content": "Following an argument similar to Lemma 2, it can be seen that Algorithm 3 terminates.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 21 + }, + { + "type": "text", + "bbox": [ + 108, + 650, + 506, + 673 + ], + 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Assuming that the loss landscape is", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 104, + 557, + 504, + 574 + ], + "spans": [ + { + "bbox": [ + 104, + 557, + 464, + 574 + ], + "score": 1.0, + "content": "in fact convex modulo these permutation symmetries, a natural choice would be to pick the", + "type": "text" + }, + { + "bbox": [ + 465, + 559, + 504, + 572 + ], + "score": 0.91, + "content": "\\pi ^ { ( i ) } ( \\Theta _ { B } )", + "type": "inline_equation" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 571, + 506, + 586 + ], + "spans": [ + { + "bbox": [ + 105, + 571, + 371, + 586 + ], + "score": 1.0, + "content": "that corresponds to the direction of steepest descent starting from", + "type": "text" + }, + { + "bbox": [ + 371, + 573, + 387, + 584 + ], + "score": 0.88, + "content": "\\Theta _ { A }", + "type": "inline_equation" + }, + { + "bbox": [ + 387, + 571, + 454, + 586 + ], + "score": 1.0, + "content": "since we expect", + "type": "text" + }, + { + "bbox": [ + 454, + 572, + 493, + 585 + ], + "score": 0.93, + "content": "\\pi ^ { ( i ) } ( \\Theta _ { B } )", + "type": "inline_equation" + }, + { + "bbox": [ + 493, + 571, + 506, + 586 + ], + "score": 1.0, + "content": "to", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 583, + 284, + 596 + ], + "spans": [ + { + "bbox": [ + 105, + 583, + 201, + 596 + ], + "score": 1.0, + "content": "lie in the same basin as", + "type": "text" + }, + { + "bbox": [ + 201, + 584, + 216, + 595 + ], + "score": 0.88, + "content": "\\Theta _ { A }", + "type": "inline_equation" + }, + { + "bbox": [ + 217, + 583, + 284, + 596 + ], + "score": 1.0, + "content": ". In other words,", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 20.5, + "bbox_fs": [ + 104, + 524, + 506, + 596 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 118, + 601, + 476, + 651 + ], + "lines": [ + { + "bbox": [ + 118, + 601, + 476, + 651 + ], + "spans": [ + { + "bbox": [ + 118, + 601, + 476, + 651 + ], + "score": 0.93, + "content": "\\begin{array} { r l } { \\operatorname* { m i n } _ { \\pi } \\left. \\frac { d \\mathcal { L } ( \\Theta _ { A } + \\lambda ( \\pi ( \\Theta _ { B } ) - \\Theta _ { A } ) ) } { d \\lambda } \\right| _ { \\lambda = 0 } } & { = \\underset { \\pi } { \\operatorname* { m i n } } ~ \\nabla \\mathcal { L } ( \\Theta _ { A } ) ^ { \\top } ( \\pi ( \\Theta _ { B } ) - \\Theta _ { A } ) } \\\\ & { = - \\nabla \\mathcal { L } ( \\Theta _ { A } ) ^ { \\top } \\Theta _ { A } + \\underset { \\pi } { \\operatorname* { m i n } } ~ \\nabla \\mathcal { L } ( \\Theta _ { A } ) ^ { \\top } \\pi ( \\Theta _ { B } ) } \\end{array}", + "type": "interline_equation", + "image_path": "6a700b54fda0f4ec3152f09e19774c6c7246554269dff5becb43333914e8e06a.jpg" + } + ] + } + ], + "index": 25, + "virtual_lines": [ + { + "bbox": [ + 118, + 601, + 476, + 617.6666666666666 + ], + "spans": [], + "index": 24 + }, + { + "bbox": [ + 118, + 617.6666666666666, + 476, + 634.3333333333333 + ], + "spans": [], + "index": 25 + }, + { + "bbox": [ + 118, + 634.3333333333333, + 476, + 650.9999999999999 + ], + "spans": [], + "index": 26 + } + ] + }, + { + "type": "text", + "bbox": [ + 108, + 659, + 504, + 704 + ], + "lines": [ + { + "bbox": [ + 104, + 658, + 506, + 674 + ], + "spans": [ + { + "bbox": [ + 104, + 658, + 295, + 674 + ], + "score": 1.0, + "content": "Now, we are tenuously in a favorable situation:", + "type": "text" + }, + { + "bbox": [ + 295, + 660, + 333, + 672 + ], + "score": 0.93, + "content": "\\nabla { \\mathcal { L } } ( \\Theta _ { A } )", + "type": "inline_equation" + }, + { + "bbox": [ + 334, + 658, + 506, + 674 + ], + "score": 1.0, + "content": "is straightforward to compute, and picking", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 671, + 505, + 683 + ], + "spans": [ + { + "bbox": [ + 106, + 671, + 140, + 683 + ], + "score": 1.0, + "content": "the best", + "type": "text" + }, + { + "bbox": [ + 141, + 673, + 149, + 681 + ], + "score": 0.73, + "content": "\\pi", + "type": "inline_equation" + }, + { + "bbox": [ + 149, + 671, + 505, + 683 + ], + "score": 1.0, + "content": "reduces to a matching problem. In particular it is a SOBLAP matching problem of the", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 681, + 505, + 693 + ], + "spans": [ + { + "bbox": [ + 105, + 681, + 505, + 693 + ], + "score": 1.0, + "content": "same form as in Section 3.2. In addition, there is a fast, exact solution for the single intermediate", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 693, + 185, + 704 + ], + "spans": [ + { + "bbox": [ + 106, + 693, + 151, + 704 + ], + "score": 1.0, + "content": "layer case", + "type": "text" + }, + { + "bbox": [ + 151, + 693, + 179, + 703 + ], + "score": 0.84, + "content": "\\left( L = 2 \\right.", + "type": "inline_equation" + }, + { + "bbox": [ + 179, + 693, + 185, + 704 + ], + "score": 1.0, + "content": ").", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 28.5, + "bbox_fs": [ + 104, + 658, + 506, + 704 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 709, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 708, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 708, + 505, + 723 + ], + "score": 1.0, + "content": "In practice, we found that this method can certainly find directions of steepest descent, but that they", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 720, + 394, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 360, + 734 + ], + "score": 1.0, + "content": "are accompanied by high barriers in between the initial dip and", + "type": "text" + }, + { + "bbox": [ + 361, + 721, + 389, + 732 + ], + "score": 0.93, + "content": "\\pi ( \\Theta _ { B } )", + "type": "inline_equation" + }, + { + "bbox": [ + 390, + 720, + 394, + 734 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 31.5, + "bbox_fs": [ + 105, + 708, + 505, + 734 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 132, + 102, + 471, + 254 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 132, + 102, + 471, + 254 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 132, + 102, + 471, + 254 + ], + "spans": [ + { + "bbox": [ + 132, + 102, + 471, + 254 + ], + "score": 0.963, + "type": "image", + "image_path": "20266c9cfdd50d6e3474dcffd5e8e32c8ed48138717b4cb24febf27fae82893d.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 132, + 102, + 471, + 152.66666666666666 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 132, + 152.66666666666666, + 471, + 203.33333333333331 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 132, + 203.33333333333331, + 471, + 253.99999999999997 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 276, + 506, + 332 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 276, + 505, + 288 + ], + "spans": [ + { + "bbox": [ + 106, + 276, + 505, + 288 + ], + "score": 1.0, + "content": "Figure 13: Merging multiple models results in superior calibration. Here we show the results of", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 287, + 505, + 300 + ], + "spans": [ + { + "bbox": [ + 105, + 287, + 505, + 300 + ], + "score": 1.0, + "content": "running Algorithm 3 on 32 MLP models trained on MNIST, with each model given access to a ran-", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 297, + 505, + 312 + ], + "spans": [ + { + "bbox": [ + 105, + 297, + 126, + 312 + ], + "score": 1.0, + "content": "dom", + "type": "text" + }, + { + "bbox": [ + 127, + 299, + 146, + 309 + ], + "score": 0.87, + "content": "50 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 147, + 297, + 505, + 312 + ], + "score": 1.0, + "content": "of the training dataset. The resulting merged model demonstrates substantively improved", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 309, + 505, + 323 + ], + "spans": [ + { + "bbox": [ + 105, + 309, + 505, + 323 + ], + "score": 1.0, + "content": "calibration of probability estimates on both the training and test datasets. MergeMany calibration", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 320, + 497, + 334 + ], + "spans": [ + { + "bbox": [ + 105, + 320, + 367, + 334 + ], + "score": 1.0, + "content": "results are competitive with model ensembling, despite requiring", + "type": "text" + }, + { + "bbox": [ + 367, + 321, + 387, + 331 + ], + "score": 0.87, + "content": "3 2 \\times", + "type": "inline_equation" + }, + { + "bbox": [ + 387, + 320, + 497, + 334 + ], + "score": 1.0, + "content": "less memory and compute.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 5 + } + ], + "index": 3.0 + }, + { + "type": "title", + "bbox": [ + 108, + 350, + 225, + 362 + ], + "lines": [ + { + "bbox": [ + 106, + 350, + 226, + 363 + ], + "spans": [ + { + "bbox": [ + 106, + 350, + 226, + 363 + ], + "score": 1.0, + "content": "A.12 PROOF OF LEMMA 1", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 8 + }, + { + "type": "text", + "bbox": [ + 106, + 371, + 332, + 384 + ], + "lines": [ + { + "bbox": [ + 106, + 370, + 333, + 384 + ], + "spans": [ + { + "bbox": [ + 106, + 370, + 214, + 384 + ], + "score": 1.0, + "content": "To lighten notation we use", + "type": "text" + }, + { + "bbox": [ + 215, + 371, + 271, + 383 + ], + "score": 0.93, + "content": "\\langle \\cdot , \\cdot \\rangle = \\langle \\cdot , \\cdot \\rangle _ { F }", + "type": "inline_equation" + }, + { + "bbox": [ + 271, + 370, + 333, + 384 + ], + "score": 1.0, + "content": "in this section.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 9 + }, + { + "type": "text", + "bbox": [ + 107, + 385, + 233, + 397 + ], + "lines": [ + { + "bbox": [ + 105, + 384, + 233, + 397 + ], + "spans": [ + { + "bbox": [ + 105, + 384, + 173, + 397 + ], + "score": 1.0, + "content": "Lemma. Given", + "type": "text" + }, + { + "bbox": [ + 173, + 384, + 230, + 397 + ], + "score": 0.91, + "content": "\\pmb { A } , \\pmb { B } \\in \\mathbb { R } ^ { d \\times d }", + "type": "inline_equation" + }, + { + "bbox": [ + 231, + 384, + 233, + 397 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 10 + }, + { + "type": "interline_equation", + "bbox": [ + 245, + 398, + 366, + 419 + ], + "lines": [ + { + "bbox": [ + 245, + 398, + 366, + 419 + ], + "spans": [ + { + "bbox": [ + 245, + 398, + 366, + 419 + ], + "score": 0.88, + "content": "\\operatorname* { m i n } _ { P , Q p e r m . m a t r i c e s } \\left. P A Q ^ { \\top } , B \\right.", + "type": "interline_equation", + "image_path": "db77495cad43bd50a5f0cc012f916a36d548bff38b26a5dcd3361de637e3206a.jpg" + } + ] + } + ], + "index": 11, + "virtual_lines": [ + { + "bbox": [ + 245, + 398, + 366, + 419 + ], + "spans": [], + "index": 11 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 422, + 259, + 434 + ], + "lines": [ + { + "bbox": [ + 105, + 421, + 260, + 434 + ], + "spans": [ + { + "bbox": [ + 105, + 421, + 260, + 434 + ], + "score": 1.0, + "content": "is strongly NP-hard and has no PTAS.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 12 + }, + { + "type": "text", + "bbox": [ + 107, + 445, + 504, + 468 + ], + "lines": [ + { + "bbox": [ + 105, + 445, + 505, + 459 + ], + "spans": [ + { + "bbox": [ + 105, + 445, + 505, + 459 + ], + "score": 1.0, + "content": "Proof. We proceed by reduction from the quadratic assignment problem (QAP) (Koopmans & Beck-", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 457, + 280, + 470 + ], + "spans": [ + { + "bbox": [ + 105, + 457, + 280, + 470 + ], + "score": 1.0, + "content": "mann, 1957; Cela, 2013). Consider a QAP,", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 13.5 + }, + { + "type": "interline_equation", + "bbox": [ + 252, + 470, + 358, + 490 + ], + "lines": [ + { + "bbox": [ + 252, + 470, + 358, + 490 + ], + "spans": [ + { + "bbox": [ + 252, + 470, + 358, + 490 + ], + "score": 0.9, + "content": "\\operatorname* { m i n } _ { P \\mathrm { \\ p e r m . \\ m a t r i x } } \\left. P C P ^ { \\top } , D \\right.", + "type": "interline_equation", + "image_path": "3db3d5d4bb5623d9a4925b9f8df09662bab2df2017ed236c63b04a2c662cf49e.jpg" + } + ] + } + ], + "index": 15, + "virtual_lines": [ + { + "bbox": [ + 252, + 470, + 358, + 490 + ], + "spans": [], + "index": 15 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 494, + 182, + 507 + ], + "lines": [ + { + "bbox": [ + 105, + 494, + 182, + 507 + ], + "spans": [ + { + "bbox": [ + 105, + 494, + 120, + 507 + ], + "score": 1.0, + "content": "for", + "type": "text" + }, + { + "bbox": [ + 121, + 494, + 179, + 507 + ], + "score": 0.92, + "content": "C , D \\in \\mathbb { R } ^ { d \\times d }", + "type": "inline_equation" + }, + { + "bbox": [ + 180, + 494, + 182, + 507 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 16 + }, + { + "type": "text", + "bbox": [ + 106, + 511, + 327, + 524 + ], + "lines": [ + { + "bbox": [ + 105, + 509, + 327, + 527 + ], + "spans": [ + { + "bbox": [ + 105, + 509, + 150, + 527 + ], + "score": 1.0, + "content": "Now, pick", + "type": "text" + }, + { + "bbox": [ + 150, + 512, + 205, + 523 + ], + "score": 0.85, + "content": "A = C + \\lambda I", + "type": "inline_equation" + }, + { + "bbox": [ + 206, + 509, + 209, + 527 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 209, + 512, + 267, + 523 + ], + "score": 0.84, + "content": "B = D - \\lambda I", + "type": "inline_equation" + }, + { + "bbox": [ + 267, + 509, + 327, + 527 + ], + "score": 1.0, + "content": ". The we have,", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 17 + }, + { + "type": "interline_equation", + "bbox": [ + 111, + 526, + 505, + 592 + ], + "lines": [ + { + "bbox": [ + 111, + 526, + 505, + 592 + ], + "spans": [ + { + "bbox": [ + 111, + 526, + 505, + 592 + ], + "score": 0.9, + "content": "\\begin{array} { r l } & { \\underset { \\boldsymbol { \\sigma } , \\boldsymbol { Q } } { \\mathrm { n i n } } \\left. P ( \\boldsymbol { C } + \\lambda \\boldsymbol { I } ) \\boldsymbol { Q } ^ { \\top } , \\boldsymbol { D } - \\lambda \\boldsymbol { I } \\right. = \\left. P C \\boldsymbol { Q } ^ { \\top } + \\lambda P \\boldsymbol { Q } ^ { \\top } , \\boldsymbol { D } - \\lambda \\boldsymbol { I } \\right. } \\\\ & { \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad ( 1 3 ) } \\\\ & { \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad = \\left. P C \\boldsymbol { Q } ^ { \\top } , \\boldsymbol { D } \\right. - \\lambda \\langle P C \\boldsymbol { Q } ^ { \\top } , \\boldsymbol { I } \\rangle + \\lambda \\langle P \\boldsymbol { Q } ^ { \\top } , \\boldsymbol { D } \\rangle - \\lambda ^ { 2 } \\langle P \\boldsymbol { Q } ^ { \\top } , \\boldsymbol { I } \\rangle } \\\\ & { \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad ( 1 4 ) } \\\\ & { \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\quad = \\left. P C \\boldsymbol { Q } ^ { \\top } , \\boldsymbol { D } \\right. - \\lambda \\langle P ^ { \\top } \\boldsymbol { Q } , \\boldsymbol { C } \\rangle + \\lambda \\langle P \\boldsymbol { Q } ^ { \\top } , \\boldsymbol { D } \\rangle - \\lambda ^ { 2 } \\mathrm { t r } ( P \\boldsymbol { Q } ^ { \\top } ) _ { - \\lambda } \\mathrm { t r } ( P \\boldsymbol { Q } ^ { \\top } ) _ { - \\lambda } \\mathrm { t r } ( P \\boldsymbol { Q } ^ { \\top } ) _ { - \\lambda } , } \\end{array}", + "type": "interline_equation", + "image_path": "cb918f610812778c50d9967d9fd7673225e7a9068a47accc9f3a3ea30d121dd7.jpg" + } + ] + } + ], + "index": 19, + "virtual_lines": [ + { + "bbox": [ + 111, + 526, + 505, + 548.0 + ], + "spans": [], + "index": 18 + }, + { + "bbox": [ + 111, + 548.0, + 505, + 570.0 + ], + "spans": [], + "index": 19 + }, + { + "bbox": [ + 111, + 570.0, + 505, + 592.0 + ], + "spans": [], + "index": 20 + } + ] + }, + { + "type": "text", + "bbox": [ + 105, + 605, + 502, + 629 + ], + "lines": [ + { + "bbox": [ + 105, + 604, + 505, + 620 + ], + "spans": [ + { + "bbox": [ + 105, + 604, + 216, + 619 + ], + "score": 1.0, + "content": "For sufficiently large", + "type": "text" + }, + { + "bbox": [ + 216, + 607, + 223, + 617 + ], + "score": 0.69, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 223, + 604, + 259, + 619 + ], + "score": 1.0, + "content": ", the", + "type": "text" + }, + { + "bbox": [ + 259, + 606, + 300, + 619 + ], + "score": 0.91, + "content": "\\operatorname { t r } ( P Q ^ { \\top } )", + "type": "inline_equation" + }, + { + "bbox": [ + 301, + 604, + 408, + 619 + ], + "score": 1.0, + "content": "term will dominate.", + "type": "text" + }, + { + "bbox": [ + 429, + 605, + 470, + 620 + ], + "score": 1.0, + "content": "Letting", + "type": "text" + }, + { + "bbox": [ + 470, + 607, + 505, + 619 + ], + "score": 0.81, + "content": "\\alpha \\quad =", + "type": "inline_equation" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 617, + 371, + 631 + ], + "spans": [ + { + "bbox": [ + 105, + 617, + 127, + 631 + ], + "score": 1.0, + "content": "max", + "type": "text" + }, + { + "bbox": [ + 128, + 618, + 244, + 630 + ], + "score": 0.85, + "content": "\\begin{array} { r } { ( \\operatorname* { m a x } _ { i , j } | C _ { i , j } | , \\operatorname* { m a x } _ { i , j } | D _ { i , j } | ) } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 244, + 617, + 371, + 631 + ], + "score": 1.0, + "content": ", we can bound the other terms,", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 21.5 + }, + { + "type": "interline_equation", + "bbox": [ + 234, + 631, + 376, + 681 + ], + "lines": [ + { + "bbox": [ + 234, + 631, + 376, + 681 + ], + "spans": [ + { + "bbox": [ + 234, + 631, + 376, + 681 + ], + "score": 0.93, + "content": "\\begin{array} { r l r } { - d ^ { 2 } \\alpha ^ { 2 } \\le } & { \\langle P C Q ^ { \\top } , D \\rangle \\le d ^ { 2 } \\alpha ^ { 2 } } & \\\\ { - \\lambda d \\alpha \\le - \\lambda \\langle P ^ { \\top } Q , C \\rangle } & { \\le \\lambda d \\alpha } & \\\\ { - \\lambda d \\alpha \\le } & { \\lambda \\langle P Q ^ { \\top } , D \\rangle } & { \\le \\lambda d \\alpha } \\end{array}", + "type": "interline_equation", + "image_path": "6dae88405cba2dc837701db52817cdc0f70cfa11a9455c2d642e9db06ef95f07.jpg" + } + ] + } + ], + "index": 23.5, + "virtual_lines": [ + { + "bbox": [ + 234, + 631, + 376, + 656.0 + ], + "spans": [], + "index": 23 + }, + { + "bbox": [ + 234, + 656.0, + 376, + 681.0 + ], + "spans": [], + "index": 24 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 683, + 505, + 717 + ], + "lines": [ + { + "bbox": [ + 105, + 682, + 506, + 696 + ], + "spans": [ + { + "bbox": [ + 105, + 682, + 322, + 696 + ], + "score": 1.0, + "content": "Now there are two classes of solutions: those where", + "type": "text" + }, + { + "bbox": [ + 322, + 683, + 357, + 695 + ], + "score": 0.91, + "content": "P = Q", + "type": "inline_equation" + }, + { + "bbox": [ + 357, + 682, + 428, + 696 + ], + "score": 1.0, + "content": "and those where", + "type": "text" + }, + { + "bbox": [ + 428, + 683, + 462, + 695 + ], + "score": 0.92, + "content": "P \\neq Q", + "type": "inline_equation" + }, + { + "bbox": [ + 462, + 682, + 506, + 696 + ], + "score": 1.0, + "content": ". 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Given", + "type": "text" + }, + { + "bbox": [ + 173, + 384, + 230, + 397 + ], + "score": 0.91, + "content": "\\pmb { A } , \\pmb { B } \\in \\mathbb { R } ^ { d \\times d }", + "type": "inline_equation" + }, + { + "bbox": [ + 231, + 384, + 233, + 397 + ], + "score": 1.0, + "content": ",", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 10, + "bbox_fs": [ + 105, + 384, + 233, + 397 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 245, + 398, + 366, + 419 + ], + "lines": [ + { + "bbox": [ + 245, + 398, + 366, + 419 + ], + "spans": [ + { + "bbox": [ + 245, + 398, + 366, + 419 + ], + "score": 0.88, + "content": "\\operatorname* { m i n } _ { P , Q p e r m . m a t r i c e s } \\left. P A Q ^ { \\top } , B \\right.", + "type": "interline_equation", + "image_path": "db77495cad43bd50a5f0cc012f916a36d548bff38b26a5dcd3361de637e3206a.jpg" + } + ] + } + ], + "index": 11, + "virtual_lines": [ + { + "bbox": [ + 245, + 398, + 366, + 419 + ], + "spans": [], + "index": 11 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 422, + 259, + 434 + ], + "lines": [ + { + "bbox": [ + 105, + 421, + 260, + 434 + ], + "spans": [ + { + "bbox": [ + 105, + 421, + 260, + 434 + ], + "score": 1.0, + "content": "is strongly NP-hard and has no PTAS.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 12, + "bbox_fs": [ + 105, + 421, + 260, + 434 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 445, + 504, + 468 + ], + "lines": [ + { + "bbox": [ + 105, + 445, + 505, + 459 + ], + "spans": [ + { + "bbox": [ + 105, + 445, + 505, + 459 + ], + "score": 1.0, + "content": "Proof. We proceed by reduction from the quadratic assignment problem (QAP) (Koopmans & Beck-", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 457, + 280, + 470 + ], + "spans": [ + { + "bbox": [ + 105, + 457, + 280, + 470 + ], + "score": 1.0, + "content": "mann, 1957; Cela, 2013). Consider a QAP,", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 13.5, + "bbox_fs": [ + 105, + 445, + 505, + 470 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 252, + 470, + 358, + 490 + ], + "lines": [ + { + "bbox": [ + 252, + 470, + 358, + 490 + ], + "spans": [ + { + "bbox": [ + 252, + 470, + 358, + 490 + ], + "score": 0.9, + "content": "\\operatorname* { m i n } _ { P \\mathrm { \\ p e r m . \\ m a t r i x } } \\left. P C P ^ { \\top } , D \\right.", + "type": "interline_equation", + "image_path": "3db3d5d4bb5623d9a4925b9f8df09662bab2df2017ed236c63b04a2c662cf49e.jpg" + } + ] + } + ], + "index": 15, + "virtual_lines": [ + { + "bbox": [ + 252, + 470, + 358, + 490 + ], + "spans": [], + "index": 15 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 494, + 182, + 507 + ], + "lines": [ + { + "bbox": [ + 105, + 494, + 182, + 507 + ], + "spans": [ + { + "bbox": [ + 105, + 494, + 120, + 507 + ], + "score": 1.0, + "content": "for", + "type": "text" + }, + { + "bbox": [ + 121, + 494, + 179, + 507 + ], + "score": 0.92, + "content": "C , D \\in \\mathbb { R } ^ { d \\times d }", + "type": "inline_equation" + }, + { + "bbox": [ + 180, + 494, + 182, + 507 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 16, + "bbox_fs": [ + 105, + 494, + 182, + 507 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 511, + 327, + 524 + ], + "lines": [ + { + "bbox": [ + 105, + 509, + 327, + 527 + ], + "spans": [ + { + "bbox": [ + 105, + 509, + 150, + 527 + ], + "score": 1.0, + "content": "Now, pick", + "type": "text" + }, + { + "bbox": [ + 150, + 512, + 205, + 523 + ], + "score": 0.85, + "content": "A = C + \\lambda I", + "type": "inline_equation" + }, + { + "bbox": [ + 206, + 509, + 209, + 527 + ], + "score": 1.0, + "content": ",", + "type": "text" + }, + { + "bbox": [ + 209, + 512, + 267, + 523 + ], + "score": 0.84, + "content": "B = D - \\lambda I", + "type": "inline_equation" + }, + { + "bbox": [ + 267, + 509, + 327, + 527 + ], + "score": 1.0, + "content": ". 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P C \\boldsymbol { Q } ^ { \\top } , \\boldsymbol { D } \\right. - \\lambda \\langle P ^ { \\top } \\boldsymbol { Q } , \\boldsymbol { C } \\rangle + \\lambda \\langle P \\boldsymbol { Q } ^ { \\top } , \\boldsymbol { D } \\rangle - \\lambda ^ { 2 } \\mathrm { t r } ( P \\boldsymbol { Q } ^ { \\top } ) _ { - \\lambda } \\mathrm { t r } ( P \\boldsymbol { Q } ^ { \\top } ) _ { - \\lambda } \\mathrm { t r } ( P \\boldsymbol { Q } ^ { \\top } ) _ { - \\lambda } , } \\end{array}", + "type": "interline_equation", + "image_path": "cb918f610812778c50d9967d9fd7673225e7a9068a47accc9f3a3ea30d121dd7.jpg" + } + ] + } + ], + "index": 19, + "virtual_lines": [ + { + "bbox": [ + 111, + 526, + 505, + 548.0 + ], + "spans": [], + "index": 18 + }, + { + "bbox": [ + 111, + 548.0, + 505, + 570.0 + ], + "spans": [], + "index": 19 + }, + { + "bbox": [ + 111, + 570.0, + 505, + 592.0 + ], + "spans": [], + "index": 20 + } + ] + }, + { + "type": "text", + "bbox": [ + 105, + 605, + 502, + 629 + ], + "lines": [ + { + "bbox": [ + 105, + 604, + 505, + 620 + ], + "spans": [ + { + "bbox": [ + 105, + 604, + 216, + 619 + ], + "score": 1.0, + "content": "For sufficiently large", + "type": "text" + }, + { + "bbox": [ + 216, + 607, + 223, + 617 + ], + "score": 0.69, + "content": "\\lambda", + "type": "inline_equation" + }, + { + "bbox": [ + 223, + 604, + 259, + 619 + ], + "score": 1.0, + "content": ", the", + "type": "text" + }, + { + "bbox": [ + 259, + 606, + 300, + 619 + ], + "score": 0.91, + "content": "\\operatorname { t r } ( P Q ^ { \\top } )", + "type": "inline_equation" + }, + { + "bbox": [ + 301, + 604, + 408, + 619 + ], + "score": 1.0, + "content": "term will dominate.", + "type": "text" + }, + { + "bbox": [ + 429, + 605, + 470, + 620 + ], + "score": 1.0, + "content": "Letting", + "type": "text" + }, + { + "bbox": [ + 470, + 607, + 505, + 619 + ], + "score": 0.81, + "content": "\\alpha \\quad =", + "type": "inline_equation" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 617, + 371, + 631 + ], + "spans": [ + { + "bbox": [ + 105, + 617, + 127, + 631 + ], + "score": 1.0, + "content": "max", + "type": "text" + }, + { + "bbox": [ + 128, + 618, + 244, + 630 + ], + "score": 0.85, + "content": "\\begin{array} { r } { ( \\operatorname* { m a x } _ { i , j } | C _ { i , j } | , \\operatorname* { m a x } _ { i , j } | D _ { i , j } | ) } \\end{array}", + "type": "inline_equation" + }, + { + "bbox": [ + 244, + 617, + 371, + 631 + ], + "score": 1.0, + "content": ", we can bound the other terms,", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 21.5, + "bbox_fs": [ + 105, + 604, + 505, + 631 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 234, + 631, + 376, + 681 + ], + "lines": [ + { + "bbox": [ + 234, + 631, + 376, + 681 + ], + "spans": [ + { + "bbox": [ + 234, + 631, + 376, + 681 + ], + "score": 0.93, + "content": "\\begin{array} { r l r } { - d ^ { 2 } \\alpha ^ { 2 } \\le } & { \\langle P C Q ^ { \\top } , D \\rangle \\le d ^ { 2 } \\alpha ^ { 2 } } & \\\\ { - \\lambda d \\alpha \\le - \\lambda \\langle P ^ { \\top } Q , C \\rangle } & { \\le \\lambda d \\alpha } & \\\\ { - \\lambda d \\alpha \\le } & { \\lambda \\langle P Q ^ { \\top } , D \\rangle } & { \\le \\lambda d \\alpha } \\end{array}", + "type": "interline_equation", + "image_path": "6dae88405cba2dc837701db52817cdc0f70cfa11a9455c2d642e9db06ef95f07.jpg" + } + ] + } + ], + "index": 23.5, + "virtual_lines": [ + { + "bbox": [ + 234, + 631, + 376, + 656.0 + ], + "spans": [], + "index": 23 + }, + { + "bbox": [ + 234, + 656.0, + 376, + 681.0 + ], + "spans": [], + "index": 24 + } + ] + }, + { + "type": "text", + "bbox": [ + 106, + 683, + 505, + 717 + ], + "lines": [ + { + "bbox": [ + 105, + 682, + 506, + 696 + ], + "spans": [ + { + "bbox": [ + 105, + 682, + 322, + 696 + ], + "score": 1.0, + "content": "Now there are two classes of solutions: those where", + "type": "text" + }, + { + "bbox": [ + 322, + 683, + 357, + 695 + ], + "score": 0.91, + "content": "P = Q", + "type": "inline_equation" + }, + { + "bbox": [ + 357, + 682, + 428, + 696 + ], + "score": 1.0, + "content": "and those where", + "type": "text" + }, + { + "bbox": [ + 428, + 683, + 462, + 695 + ], + "score": 0.92, + "content": "P \\neq Q", + "type": "inline_equation" + }, + { + "bbox": [ + 462, + 682, + 506, + 696 + ], + "score": 1.0, + "content": ". 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QAP is known to be strongly NP-hard (Koopmans & Beckmann, 1957;", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 228, + 505, + 243 + ], + "spans": [ + { + "bbox": [ + 105, + 228, + 505, + 243 + ], + "score": 1.0, + "content": "Sahni & Gonzalez, 1976) and MaxQAP is known to not admit any PTAS (Makarychev et al., 2014),", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 241, + 505, + 253 + ], + "spans": [ + { + "bbox": [ + 106, + 241, + 214, + 253 + ], + "score": 1.0, + "content": "thus completing the proof.", + "type": "text" + }, + { + "bbox": [ + 494, + 241, + 505, + 252 + ], + "score": 0.999, + "content": "□", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 10 + }, + { + "type": "title", + "bbox": [ + 108, + 265, + 226, + 277 + ], + "lines": [ + { + "bbox": [ + 106, + 264, + 227, + 279 + ], + "spans": [ + { + "bbox": [ + 106, + 264, + 227, + 279 + ], + "score": 1.0, + "content": "A.13 PROOF OF LEMMA 2", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 12 + }, + { + "type": "text", + "bbox": [ + 107, + 286, + 243, + 298 + ], + "lines": [ + { + "bbox": [ + 106, + 285, + 244, + 299 + ], + "spans": [ + { + "bbox": [ + 106, + 285, + 244, + 299 + ], + "score": 1.0, + "content": "Lemma. Algorithm 1 terminates.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 13 + }, + { + "type": "text", + "bbox": [ + 107, + 310, + 255, + 322 + ], + "lines": [ + { + "bbox": [ + 106, + 308, + 255, + 324 + ], + "spans": [ + { + "bbox": [ + 106, + 308, + 255, + 324 + ], + "score": 1.0, + "content": "Proof. We proceed by contradiction.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 14 + }, + { + "type": "text", + "bbox": [ + 106, + 326, + 505, + 404 + ], + "lines": [ + { + "bbox": [ + 105, + 326, + 506, + 340 + ], + "spans": [ + { + "bbox": [ + 105, + 326, + 309, + 340 + ], + "score": 1.0, + "content": "Consider a graph with each possible permutation", + "type": "text" + }, + { + "bbox": [ + 309, + 327, + 403, + 339 + ], + "score": 0.91, + "content": "\\pi _ { i } = \\left\\{ P _ { 1 } , \\ldots , P _ { L - 1 } \\right\\}", + "type": "inline_equation" + }, + { + "bbox": [ + 404, + 326, + 506, + 340 + ], + "score": 1.0, + "content": "as a vertex and directed", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 338, + 506, + 351 + ], + "spans": [ + { + "bbox": [ + 106, + 338, + 132, + 351 + ], + "score": 1.0, + "content": "edges", + "type": "text" + }, + { + "bbox": [ + 132, + 340, + 170, + 350 + ], + "score": 0.9, + "content": "\\pi _ { i } \\pi _ { j }", + "type": "inline_equation" + }, + { + "bbox": [ + 171, + 338, + 181, + 351 + ], + "score": 1.0, + "content": "if", + "type": "text" + }, + { + "bbox": [ + 181, + 340, + 192, + 350 + ], + "score": 0.86, + "content": "\\pi _ { j }", + "type": "inline_equation" + }, + { + "bbox": [ + 193, + 338, + 280, + 351 + ], + "score": 1.0, + "content": "can be reached from", + "type": "text" + }, + { + "bbox": [ + 280, + 340, + 290, + 349 + ], + "score": 0.86, + "content": "\\pi _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 291, + 338, + 347, + 351 + ], + "score": 1.0, + "content": "with a single", + "type": "text" + }, + { + "bbox": [ + 348, + 339, + 360, + 349 + ], + "score": 0.86, + "content": "P _ { \\ell }", + "type": "inline_equation" + }, + { + "bbox": [ + 360, + 338, + 506, + 351 + ], + "score": 1.0, + "content": "update, as in Algorithm 1. (Ignore", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 349, + 505, + 362 + ], + "spans": [ + { + "bbox": [ + 106, + 349, + 266, + 362 + ], + "score": 1.0, + "content": "those updates that result in no change to", + "type": "text" + }, + { + "bbox": [ + 266, + 350, + 278, + 360 + ], + "score": 0.88, + "content": "P _ { \\ell }", + "type": "inline_equation" + }, + { + "bbox": [ + 279, + 349, + 346, + 362 + ], + "score": 1.0, + "content": "in order to avoid", + "type": "text" + }, + { + "bbox": [ + 346, + 351, + 381, + 360 + ], + "score": 0.9, + "content": "\\pi _ { i } \\pi _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 381, + 349, + 431, + 362 + ], + "score": 1.0, + "content": "cycles.) Let", + "type": "text" + }, + { + "bbox": [ + 431, + 349, + 501, + 361 + ], + "score": 0.9, + "content": "\\rho ( \\pi ) = \\operatorname { v e c } ( \\Theta _ { A } )", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 349, + 505, + 362 + ], + "score": 1.0, + "content": "·", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 360, + 506, + 373 + ], + "spans": [ + { + "bbox": [ + 106, + 360, + 157, + 372 + ], + "score": 0.91, + "content": "\\mathrm { v e c } ( \\pi ( { \\bar { \\Theta } } _ { B } ) )", + "type": "inline_equation" + }, + { + "bbox": [ + 158, + 360, + 289, + 373 + ], + "score": 1.0, + "content": "denote the utility of a particular", + "type": "text" + }, + { + "bbox": [ + 290, + 362, + 297, + 370 + ], + "score": 0.73, + "content": "\\pi", + "type": "inline_equation" + }, + { + "bbox": [ + 297, + 360, + 342, + 373 + ], + "score": 1.0, + "content": ". 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QAP is known to be strongly NP-hard (Koopmans & Beckmann, 1957;", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 228, + 505, + 243 + ], + "spans": [ + { + "bbox": [ + 105, + 228, + 505, + 243 + ], + "score": 1.0, + "content": "Sahni & Gonzalez, 1976) and MaxQAP is known to not admit any PTAS (Makarychev et al., 2014),", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 241, + 505, + 253 + ], + "spans": [ + { + "bbox": [ + 106, + 241, + 214, + 253 + ], + "score": 1.0, + "content": "thus completing the proof.", + "type": "text" + }, + { + "bbox": [ + 494, + 241, + 505, + 252 + ], + "score": 0.999, + "content": "□", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 10, + "bbox_fs": [ + 105, + 218, + 506, + 253 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 265, + 226, + 277 + ], + "lines": [ + { + "bbox": [ + 106, + 264, + 227, + 279 + ], + "spans": [ + { + "bbox": [ + 106, + 264, + 227, + 279 + ], + "score": 1.0, + "content": "A.13 PROOF OF LEMMA 2", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 12 + }, + { + "type": "text", + "bbox": [ + 107, + 286, + 243, + 298 + ], + "lines": [ + { + "bbox": [ + 106, + 285, + 244, + 299 + ], + "spans": [ + { + "bbox": [ + 106, + 285, + 244, + 299 + ], + "score": 1.0, + "content": "Lemma. Algorithm 1 terminates.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 13, + "bbox_fs": [ + 106, + 285, + 244, + 299 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 310, + 255, + 322 + ], + "lines": [ + { + "bbox": [ + 106, + 308, + 255, + 324 + ], + "spans": [ + { + "bbox": [ + 106, + 308, + 255, + 324 + ], + "score": 1.0, + "content": "Proof. We proceed by contradiction.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 14, + "bbox_fs": [ + 106, + 308, + 255, + 324 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 326, + 505, + 404 + ], + "lines": [ + { + "bbox": [ + 105, + 326, + 506, + 340 + ], + "spans": [ + { + "bbox": [ + 105, + 326, + 309, + 340 + ], + "score": 1.0, + "content": "Consider a graph with each possible permutation", + "type": "text" + }, + { + "bbox": [ + 309, + 327, + 403, + 339 + ], + "score": 0.91, + "content": "\\pi _ { i } = \\left\\{ P _ { 1 } , \\ldots , P _ { L - 1 } \\right\\}", + "type": "inline_equation" + }, + { + "bbox": [ + 404, + 326, + 506, + 340 + ], + "score": 1.0, + "content": "as a vertex and directed", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 338, + 506, + 351 + ], + "spans": [ + { + "bbox": [ + 106, + 338, + 132, + 351 + ], + "score": 1.0, + "content": "edges", + "type": "text" + }, + { + "bbox": [ + 132, + 340, + 170, + 350 + ], + "score": 0.9, + "content": "\\pi _ { i } \\pi _ { j }", + "type": "inline_equation" + }, + { + "bbox": [ + 171, + 338, + 181, + 351 + ], + "score": 1.0, + "content": "if", + "type": "text" + }, + { + "bbox": [ + 181, + 340, + 192, + 350 + ], + "score": 0.86, + "content": "\\pi _ { j }", + "type": "inline_equation" + }, + { + "bbox": [ + 193, + 338, + 280, + 351 + ], + "score": 1.0, + "content": "can be reached from", + "type": "text" + }, + { + "bbox": [ + 280, + 340, + 290, + 349 + ], + "score": 0.86, + "content": "\\pi _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 291, + 338, + 347, + 351 + ], + "score": 1.0, + "content": "with a single", + "type": "text" + }, + { + "bbox": [ + 348, + 339, + 360, + 349 + ], + "score": 0.86, + "content": "P _ { \\ell }", + "type": "inline_equation" + }, + { + "bbox": [ + 360, + 338, + 506, + 351 + ], + "score": 1.0, + "content": "update, as in Algorithm 1. (Ignore", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 349, + 505, + 362 + ], + "spans": [ + { + "bbox": [ + 106, + 349, + 266, + 362 + ], + "score": 1.0, + "content": "those updates that result in no change to", + "type": "text" + }, + { + "bbox": [ + 266, + 350, + 278, + 360 + ], + "score": 0.88, + "content": "P _ { \\ell }", + "type": "inline_equation" + }, + { + "bbox": [ + 279, + 349, + 346, + 362 + ], + "score": 1.0, + "content": "in order to avoid", + "type": "text" + }, + { + "bbox": [ + 346, + 351, + 381, + 360 + ], + "score": 0.9, + "content": "\\pi _ { i } \\pi _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 381, + 349, + 431, + 362 + ], + "score": 1.0, + "content": "cycles.) Let", + "type": "text" + }, + { + "bbox": [ + 431, + 349, + 501, + 361 + ], + "score": 0.9, + "content": "\\rho ( \\pi ) = \\operatorname { v e c } ( \\Theta _ { A } )", + "type": "inline_equation" + }, + { + "bbox": [ + 501, + 349, + 505, + 362 + ], + "score": 1.0, + "content": "·", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 360, + 506, + 373 + ], + "spans": [ + { + "bbox": [ + 106, + 360, + 157, + 372 + ], + "score": 0.91, + "content": "\\mathrm { v e c } ( \\pi ( { \\bar { \\Theta } } _ { B } ) )", + "type": "inline_equation" + }, + { + "bbox": [ + 158, + 360, + 289, + 373 + ], + "score": 1.0, + "content": "denote the utility of a particular", + "type": "text" + }, + { + "bbox": [ + 290, + 362, + 297, + 370 + ], + "score": 0.73, + "content": "\\pi", + "type": "inline_equation" + }, + { + "bbox": [ + 297, + 360, + 342, + 373 + ], + "score": 1.0, + "content": ". Note that", + "type": "text" + }, + { + "bbox": [ + 343, + 362, + 379, + 372 + ], + "score": 0.9, + "content": "\\pi _ { i } \\pi _ { j }", + "type": "inline_equation" + }, + { + "bbox": [ + 380, + 360, + 413, + 373 + ], + "score": 1.0, + "content": "implies", + "type": "text" + }, + { + "bbox": [ + 414, + 361, + 474, + 372 + ], + "score": 0.92, + "content": "\\rho ( \\pi _ { i } ) < \\rho ( \\pi _ { j } )", + "type": "inline_equation" + }, + { + "bbox": [ + 474, + 360, + 506, + 373 + ], + "score": 1.0, + "content": ". There", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 371, + 505, + 384 + ], + "spans": [ + { + "bbox": [ + 105, + 371, + 270, + 384 + ], + "score": 1.0, + "content": "exist finitely many possible permutations", + "type": "text" + }, + { + "bbox": [ + 271, + 373, + 281, + 382 + ], + "score": 0.86, + "content": "\\pi _ { i }", + "type": "inline_equation" + }, + { + "bbox": [ + 281, + 371, + 505, + 384 + ], + "score": 1.0, + "content": ", meaning that a failure to terminate must involve a cycle", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 382, + 506, + 394 + ], + "spans": [ + { + "bbox": [ + 105, + 382, + 156, + 394 + ], + "score": 1.0, + "content": "in the graph", + "type": "text" + }, + { + "bbox": [ + 157, + 383, + 248, + 393 + ], + "score": 0.89, + "content": "\\pi _ { 1 } \\to \\cdot \\cdot \\cdot \\to \\pi _ { n } \\to \\pi _ { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 248, + 382, + 290, + 394 + ], + "score": 1.0, + "content": ". 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ARCHITECTURENUM.PERMUTATIONSYMMETRIES
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AIgorIthmI:PERMUTATIONCOORDINATEDESCENT Given:Mode weigts A = {w(4),., [4)} and θB ={~w(B),.. W}
Result: A permutation π = {P1,...,PL-1} of OB such that vec(ΘA) · vec(π(OB)) is approximately maximized.
Initialize:Pl←I,...,PL-1 ←I
repeat
for l∈RANDOMPERMUTATION(1,...,L-1) do
P←SOLvELAP（W()P-1(W(B）+(W(）1W)）
end until convergence
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MethodTest accuracy (个)Run-time (↓)
OT-Fusion (Singh & Jaggi, 2020)85.98%2.86s
Weight matching (ours)86.57 %0.64s
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Train LossTrain Acc.Test LossTest Acc.
Seed 10.00001.00000.11530.9856
Seed 20.00001.00000.15310.9854
Seed 30.00001.00000.12290.9855
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Seed 50.00001.00000.14430.9871
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Failure", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 397, + 506, + 409 + ], + "spans": [ + { + "bbox": [ + 106, + 397, + 506, + 409 + ], + "score": 1.0, + "content": "cases rarely happen: for example in (f) the model manages to generate many pipes and some blocks,", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 407, + 418, + 420 + ], + "spans": [ + { + "bbox": [ + 105, + 407, + 418, + 420 + ], + "score": 1.0, + "content": "but it still generates enemies even though it was prompted with \"no enemies\".", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 10 + } + ], + "index": 8.5 + }, + { + "type": "title", + "bbox": [ + 283, + 431, + 328, + 443 + ], + "lines": [ + { + "bbox": [ + 281, + 429, + 331, + 445 + ], + "spans": [ + { + "bbox": [ + 281, + 429, + 331, + 445 + ], + "score": 1.0, + "content": "Abstract", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 12 + }, + { + "type": "text", + "bbox": [ + 143, + 447, + 469, + 622 + ], + "lines": [ + { + "bbox": [ + 141, + 446, + 469, + 460 + ], + "spans": [ + { + "bbox": [ + 141, + 446, + 469, + 460 + ], + "score": 1.0, + "content": "Procedural Content Generation (PCG) is a technique to generate complex and", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 141, + 457, + 469, + 470 + ], + "spans": [ + { + "bbox": [ + 141, + 457, + 469, + 470 + ], + "score": 1.0, + "content": "diverse environments in an automated way. 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Failure", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 397, + 506, + 409 + ], + "spans": [ + { + "bbox": [ + 106, + 397, + 506, + 409 + ], + "score": 1.0, + "content": "cases rarely happen: for example in (f) the model manages to generate many pipes and some blocks,", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 407, + 418, + 420 + ], + "spans": [ + { + "bbox": [ + 105, + 407, + 418, + 420 + ], + "score": 1.0, + "content": "but it still generates enemies even though it was prompted with \"no enemies\".", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 10 + } + ], + "index": 8.5 + }, + { + "type": "title", + "bbox": [ + 283, + 431, + 328, + 443 + ], + "lines": [ + { + "bbox": [ + 281, + 429, + 331, + 445 + ], + "spans": [ + { + "bbox": [ + 281, + 429, + 331, + 445 + ], + "score": 1.0, + "content": "Abstract", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 12 + }, + { + "type": "text", + "bbox": [ + 143, + 447, + 469, + 622 + ], + "lines": [ + { + "bbox": [ + 141, + 446, + 469, + 460 + ], + "spans": [ + { + "bbox": [ + 141, + 446, + 469, + 460 + ], + "score": 1.0, + "content": "Procedural Content Generation (PCG) is a technique to generate complex and", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 141, + 457, + 469, + 470 + ], + "spans": [ + { + "bbox": [ + 141, + 457, + 469, + 470 + ], + "score": 1.0, + "content": "diverse environments in an automated way. However, while generating content", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 141, + 468, + 470, + 482 + ], + "spans": [ + { + "bbox": [ + 141, + 468, + 470, + 482 + ], + "score": 1.0, + "content": "with PCG methods is often straightforward, generating meaningful content that", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 141, + 480, + 469, + 493 + ], + "spans": [ + { + "bbox": [ + 141, + 480, + 469, + 493 + ], + "score": 1.0, + "content": "reflects specific intentions and constraints remains challenging. Furthermore, many", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 141, + 490, + 471, + 504 + ], + "spans": [ + { + "bbox": [ + 141, + 490, + 471, + 504 + ], + "score": 1.0, + "content": "PCG algorithms lack the ability to generate content in an open-ended manner.", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 141, + 501, + 470, + 515 + ], + "spans": [ + { + "bbox": [ + 141, + 501, + 470, + 515 + ], + "score": 1.0, + "content": "Recently, Large Language Models (LLMs) have shown to be incredibly effective", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 141, + 513, + 470, + 525 + ], + "spans": [ + { + "bbox": [ + 141, + 513, + 470, + 525 + ], + "score": 1.0, + "content": "in many diverse domains. These trained LLMs can be fine-tuned, re-using infor-", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 141, + 523, + 470, + 536 + ], + "spans": [ + { + "bbox": [ + 141, + 523, + 470, + 536 + ], + "score": 1.0, + "content": "mation and accelerating training for new tasks. Here, we introduce MarioGPT,", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 141, + 534, + 470, + 547 + ], + "spans": [ + { + "bbox": [ + 141, + 534, + 470, + 547 + ], + "score": 1.0, + "content": "a fine-tuned GPT2 model trained to generate tile-based game levels, in our case", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 142, + 545, + 469, + 557 + ], + "spans": [ + { + "bbox": [ + 142, + 545, + 469, + 557 + ], + "score": 1.0, + "content": "Super Mario Bros levels. MarioGPT can not only generate diverse levels, but", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 141, + 556, + 470, + 569 + ], + "spans": [ + { + "bbox": [ + 141, + 556, + 470, + 569 + ], + "score": 1.0, + "content": "can be text-prompted for controllable level generation, addressing one of the key", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 141, + 567, + 470, + 579 + ], + "spans": [ + { + "bbox": [ + 141, + 567, + 470, + 579 + ], + "score": 1.0, + "content": "challenges of current PCG techniques. 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Our MarioGPT model is a finetuned version of the distilled GPT2", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 180, + 506, + 192 + ], + "spans": [ + { + "bbox": [ + 106, + 180, + 506, + 192 + ], + "score": 1.0, + "content": "language model. Like GPT2, MarioGPT is trained to predict next token sequences. Levels are represented as", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 190, + 505, + 202 + ], + "spans": [ + { + "bbox": [ + 106, + 190, + 505, + 202 + ], + "score": 1.0, + "content": "strings, which are tokenized by a Byte-Pair Encoding, similar to the original GPT2 model. The level is split", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 200, + 505, + 212 + ], + "spans": [ + { + "bbox": [ + 106, + 200, + 505, + 212 + ], + "score": 1.0, + "content": "by columns and flattened into a single vector (or batch of vectors for multiple levels). To incorporate prompt", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 209, + 506, + 222 + ], + "spans": [ + { + "bbox": [ + 105, + 209, + 506, + 222 + ], + "score": 1.0, + "content": "information, we utilize a frozen text encoder in the form of a pretrained bidirectional LLM (BART), and output", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 220, + 505, + 232 + ], + "spans": [ + { + "bbox": [ + 106, + 220, + 505, + 232 + ], + "score": 1.0, + "content": "the average hidden states of the model’s forward pass. This average hidden state is then used in the cross attention", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 230, + 492, + 242 + ], + "spans": [ + { + "bbox": [ + 106, + 230, + 492, + 242 + ], + "score": 1.0, + "content": "layers of the GPT2 architecture in combination with the actual level sequence being passed into the model.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 6 + } + ], + "index": 3.5 + }, + { + "type": "text", + "bbox": [ + 107, + 261, + 505, + 349 + ], + "lines": [ + { + "bbox": [ + 105, + 262, + 506, + 273 + ], + "spans": [ + { + "bbox": [ + 105, + 262, + 506, + 273 + ], + "score": 1.0, + "content": "Recently, developments in PCG and machine learning have started to influence each other in different", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 271, + 506, + 285 + ], + "spans": [ + { + "bbox": [ + 105, + 271, + 506, + 285 + ], + "score": 1.0, + "content": "ways [30]. PCG researchers are now incorporating machine learning-based approaches into their", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 283, + 505, + 296 + ], + "spans": [ + { + "bbox": [ + 105, + 283, + 505, + 296 + ], + "score": 1.0, + "content": "systems and models such as Generative Adversarial Networks (GANs) [13] can be trained to generate", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 294, + 505, + 306 + ], + "spans": [ + { + "bbox": [ + 105, + 294, + 505, + 306 + ], + "score": 1.0, + "content": "levels for games as diverse as Doom [10] or Super Mario Bros, training on levels from the Video", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 304, + 505, + 318 + ], + "spans": [ + { + "bbox": [ + 105, + 304, + 505, + 318 + ], + "score": 1.0, + "content": "Game Level Corpus [45]. However, current approaches in this field of Procedural Content Generation", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 315, + 505, + 328 + ], + "spans": [ + { + "bbox": [ + 105, + 315, + 505, + 328 + ], + "score": 1.0, + "content": "via Machine Learning (PCGML) [39] often rely on costly searching inside of the latent space of the", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 327, + 505, + 339 + ], + "spans": [ + { + "bbox": [ + 106, + 327, + 505, + 339 + ], + "score": 1.0, + "content": "underlying neural networks. It would be more desirable to being able to directly condition a generator", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 337, + 374, + 351 + ], + "spans": [ + { + "bbox": [ + 105, + 337, + 374, + 351 + ], + "score": 1.0, + "content": "to create levels with certain properties, ideally in natural language.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 13.5 + }, + { + "type": "text", + "bbox": [ + 106, + 353, + 506, + 453 + ], + "lines": [ + { + "bbox": [ + 105, + 353, + 506, + 366 + ], + "spans": [ + { + "bbox": [ + 105, + 353, + 506, + 366 + ], + "score": 1.0, + "content": "To address these challenges, we propose MarioGPT (Figure 2), a fine-tuned GPT-2 model trained to", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 364, + 507, + 378 + ], + "spans": [ + { + "bbox": [ + 105, + 364, + 507, + 378 + ], + "score": 1.0, + "content": "generate Mario levels. Our model demonstrates how LLMs can be combined with PCG techniques,", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 376, + 507, + 389 + ], + "spans": [ + { + "bbox": [ + 106, + 376, + 507, + 389 + ], + "score": 1.0, + "content": "enabling the effective creation of new and diverse levels through natural language prompts (Figure 1).", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 386, + 506, + 399 + ], + "spans": [ + { + "bbox": [ + 105, + 386, + 506, + 399 + ], + "score": 1.0, + "content": "Large language models (LLMs) trained on a diverse corpus such as the GPT-n family model [29],", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 398, + 506, + 410 + ], + "spans": [ + { + "bbox": [ + 106, + 398, + 506, + 410 + ], + "score": 1.0, + "content": "capture the statistical correlations of the human experience in the form of language correlations.", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 408, + 507, + 422 + ], + "spans": [ + { + "bbox": [ + 105, + 408, + 507, + 422 + ], + "score": 1.0, + "content": "Through this process, GPT acquires knowledge of how to represent and predict intricate sequences.", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 419, + 506, + 432 + ], + "spans": [ + { + "bbox": [ + 105, + 419, + 506, + 432 + ], + "score": 1.0, + "content": "We utilize this knowledge to provide our model with the ability to generate levels that incorporate", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 430, + 504, + 443 + ], + "spans": [ + { + "bbox": [ + 106, + 431, + 479, + 443 + ], + "score": 1.0, + "content": "simple artefacts as well as more complex relational properties. Surprisingly, a high percentage", + "type": "text" + }, + { + "bbox": [ + 479, + 430, + 504, + 442 + ], + "score": 0.84, + "content": "( 8 8 \\% )", + "type": "inline_equation" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 441, + 311, + 454 + ], + "spans": [ + { + "bbox": [ + 106, + 441, + 311, + 454 + ], + "score": 1.0, + "content": "of MarioGPT generated levels are in fact playable.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 22 + }, + { + "type": "text", + "bbox": [ + 107, + 457, + 505, + 524 + ], + "lines": [ + { + "bbox": [ + 106, + 457, + 505, + 469 + ], + "spans": [ + { + "bbox": [ + 106, + 457, + 505, + 469 + ], + "score": 1.0, + "content": "Furthermore, we combine MarioGPT with novelty search [22], a diversity-seeking algorithm, to", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 469, + 505, + 480 + ], + "spans": [ + { + "bbox": [ + 105, + 469, + 505, + 480 + ], + "score": 1.0, + "content": "continually generate diverse levels in an open-ended manner. The combination of LLMs with", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 479, + 505, + 492 + ], + "spans": [ + { + "bbox": [ + 105, + 479, + 505, + 492 + ], + "score": 1.0, + "content": "algorithms such as novelty search opens up many interesting new directions for future research. We", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 491, + 504, + 502 + ], + "spans": [ + { + "bbox": [ + 106, + 491, + 504, + 502 + ], + "score": 1.0, + "content": "hope our work opens the door to more flexible and controllable PCG methods that can generate infinite", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 501, + 505, + 513 + ], + "spans": [ + { + "bbox": [ + 106, + 501, + 505, + 513 + ], + "score": 1.0, + "content": "content that is complex, diverse, and functional. To facilitate this, the code to run the experiments in", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 511, + 447, + 526 + ], + "spans": [ + { + "bbox": [ + 105, + 511, + 447, + 526 + ], + "score": 1.0, + "content": "this paper is publicly available at: https://github.com/shyamsn97/mario-gpt.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 29.5 + }, + { + "type": "title", + "bbox": [ + 108, + 538, + 285, + 552 + ], + "lines": [ + { + "bbox": [ + 104, + 538, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 104, + 538, + 287, + 555 + ], + "score": 1.0, + "content": "2 Background and Related Work", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 33 + }, + { + "type": "text", + "bbox": [ + 107, + 563, + 505, + 673 + ], + "lines": [ + { + "bbox": [ + 106, + 564, + 505, + 575 + ], + "spans": [ + { + "bbox": [ + 106, + 564, + 505, + 575 + ], + "score": 1.0, + "content": "Procedural Content Generation. Procedural Content Generation (PCG) algorithms [36] deal with", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 573, + 506, + 587 + ], + "spans": [ + { + "bbox": [ + 105, + 573, + 506, + 587 + ], + "score": 1.0, + "content": "the automatic creation of game content (e.g. for level design, character generation, environment", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 584, + 507, + 599 + ], + "spans": [ + { + "bbox": [ + 105, + 584, + 507, + 599 + ], + "score": 1.0, + "content": "modeling, etc.). As reviewed in [36, 46], earlier works often focused on evolutionary computation [4],", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 595, + 507, + 609 + ], + "spans": [ + { + "bbox": [ + 105, + 595, + 507, + 609 + ], + "score": 1.0, + "content": "solver-based methods [37] or constructive generation methods (such as cellular automata, grammar-", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 606, + 505, + 621 + ], + "spans": [ + { + "bbox": [ + 105, + 606, + 505, + 621 + ], + "score": 1.0, + "content": "based methods, etc). More recently, deep learning for PCG [27, 39] has emerged as a promising", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 618, + 506, + 631 + ], + "spans": [ + { + "bbox": [ + 105, + 618, + 506, + 631 + ], + "score": 1.0, + "content": "approach to learning to generate high-quality game content in a data-driven manner, which is not", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 628, + 505, + 642 + ], + "spans": [ + { + "bbox": [ + 105, + 628, + 505, + 642 + ], + "score": 1.0, + "content": "only aesthetically pleasing but also functional and challenging. However, the diversity, originality", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 640, + 505, + 653 + ], + "spans": [ + { + "bbox": [ + 106, + 640, + 505, + 653 + ], + "score": 1.0, + "content": "and playability of the generated content in addition to the controllability of its generation, remain", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 651, + 505, + 663 + ], + "spans": [ + { + "bbox": [ + 106, + 651, + 505, + 663 + ], + "score": 1.0, + "content": "major challenges [39]. Our work aims to show how conditioned language models, paired with", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 661, + 484, + 675 + ], + "spans": [ + { + "bbox": [ + 105, + 661, + 484, + 675 + ], + "score": 1.0, + "content": "novelty-driven approaches to content generation [26, 2], could help tackle these shortcomings.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 38.5 + }, + { + "type": "text", + "bbox": [ + 107, + 678, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 105, + 677, + 506, + 691 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 506, + 691 + ], + "score": 1.0, + "content": "Neural Network-based Level Generation. Recent works in the space of video game level generation,", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 689, + 506, + 701 + ], + "spans": [ + { + "bbox": [ + 105, + 689, + 506, + 701 + ], + "score": 1.0, + "content": "particularly for Super Mario [2, 8, 45, 33, 35, 34], also leveraged neural network architectures to", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 700, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 700, + 505, + 712 + ], + "score": 1.0, + "content": "create levels. Beukman et al. [2] evolved neural networks in order to generate levels, while others", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 710, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 505, + 723 + ], + "score": 1.0, + "content": "[8, 45, 12, 34] performed evolution / search in the latent space of a trained generative model. These", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 45.5 + } + ], + "page_idx": 1, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 302, + 741, + 309, + 750 + ], + "lines": [ + { + "bbox": [ + 301, + 740, + 310, + 753 + ], + "spans": [ + { + "bbox": [ + 301, + 740, + 310, + 753 + ], + "score": 1.0, + "content": "2", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "image", + "bbox": [ + 151, + 70, + 465, + 163 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 151, + 70, + 465, + 163 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 151, + 70, + 465, + 163 + ], + "spans": [ + { + "bbox": [ + 151, + 70, + 465, + 163 + ], + "score": 0.961, + "type": "image", + "image_path": "9f449b787212abc4b1bc31e2af92c5b21e9247026302321260eaaf567f1ac8ce.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 151, + 70, + 465, + 101.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 151, + 101.0, + 465, + 132.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 151, + 132.0, + 465, + 163.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 170, + 506, + 240 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 170, + 505, + 182 + ], + "spans": [ + { + "bbox": [ + 106, + 170, + 505, + 182 + ], + "score": 1.0, + "content": "Figure 2: MarioGPT prediction pipeline. Our MarioGPT model is a finetuned version of the distilled GPT2", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 180, + 506, + 192 + ], + "spans": [ + { + "bbox": [ + 106, + 180, + 506, + 192 + ], + "score": 1.0, + "content": "language model. Like GPT2, MarioGPT is trained to predict next token sequences. Levels are represented as", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 190, + 505, + 202 + ], + "spans": [ + { + "bbox": [ + 106, + 190, + 505, + 202 + ], + "score": 1.0, + "content": "strings, which are tokenized by a Byte-Pair Encoding, similar to the original GPT2 model. The level is split", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 200, + 505, + 212 + ], + "spans": [ + { + "bbox": [ + 106, + 200, + 505, + 212 + ], + "score": 1.0, + "content": "by columns and flattened into a single vector (or batch of vectors for multiple levels). To incorporate prompt", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 209, + 506, + 222 + ], + "spans": [ + { + "bbox": [ + 105, + 209, + 506, + 222 + ], + "score": 1.0, + "content": "information, we utilize a frozen text encoder in the form of a pretrained bidirectional LLM (BART), and output", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 220, + 505, + 232 + ], + "spans": [ + { + "bbox": [ + 106, + 220, + 505, + 232 + ], + "score": 1.0, + "content": "the average hidden states of the model’s forward pass. This average hidden state is then used in the cross attention", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 230, + 492, + 242 + ], + "spans": [ + { + "bbox": [ + 106, + 230, + 492, + 242 + ], + "score": 1.0, + "content": "layers of the GPT2 architecture in combination with the actual level sequence being passed into the model.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 6 + } + ], + "index": 3.5 + }, + { + "type": "text", + "bbox": [ + 107, + 261, + 505, + 349 + ], + "lines": [ + { + "bbox": [ + 105, + 262, + 506, + 273 + ], + "spans": [ + { + "bbox": [ + 105, + 262, + 506, + 273 + ], + "score": 1.0, + "content": "Recently, developments in PCG and machine learning have started to influence each other in different", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 271, + 506, + 285 + ], + "spans": [ + { + "bbox": [ + 105, + 271, + 506, + 285 + ], + "score": 1.0, + "content": "ways [30]. PCG researchers are now incorporating machine learning-based approaches into their", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 283, + 505, + 296 + ], + "spans": [ + { + "bbox": [ + 105, + 283, + 505, + 296 + ], + "score": 1.0, + "content": "systems and models such as Generative Adversarial Networks (GANs) [13] can be trained to generate", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 294, + 505, + 306 + ], + "spans": [ + { + "bbox": [ + 105, + 294, + 505, + 306 + ], + "score": 1.0, + "content": "levels for games as diverse as Doom [10] or Super Mario Bros, training on levels from the Video", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 304, + 505, + 318 + ], + "spans": [ + { + "bbox": [ + 105, + 304, + 505, + 318 + ], + "score": 1.0, + "content": "Game Level Corpus [45]. However, current approaches in this field of Procedural Content Generation", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 315, + 505, + 328 + ], + "spans": [ + { + "bbox": [ + 105, + 315, + 505, + 328 + ], + "score": 1.0, + "content": "via Machine Learning (PCGML) [39] often rely on costly searching inside of the latent space of the", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 327, + 505, + 339 + ], + "spans": [ + { + "bbox": [ + 106, + 327, + 505, + 339 + ], + "score": 1.0, + "content": "underlying neural networks. It would be more desirable to being able to directly condition a generator", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 337, + 374, + 351 + ], + "spans": [ + { + "bbox": [ + 105, + 337, + 374, + 351 + ], + "score": 1.0, + "content": "to create levels with certain properties, ideally in natural language.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 13.5, + "bbox_fs": [ + 105, + 262, + 506, + 351 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 353, + 506, + 453 + ], + "lines": [ + { + "bbox": [ + 105, + 353, + 506, + 366 + ], + "spans": [ + { + "bbox": [ + 105, + 353, + 506, + 366 + ], + "score": 1.0, + "content": "To address these challenges, we propose MarioGPT (Figure 2), a fine-tuned GPT-2 model trained to", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 364, + 507, + 378 + ], + "spans": [ + { + "bbox": [ + 105, + 364, + 507, + 378 + ], + "score": 1.0, + "content": "generate Mario levels. Our model demonstrates how LLMs can be combined with PCG techniques,", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 376, + 507, + 389 + ], + "spans": [ + { + "bbox": [ + 106, + 376, + 507, + 389 + ], + "score": 1.0, + "content": "enabling the effective creation of new and diverse levels through natural language prompts (Figure 1).", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 386, + 506, + 399 + ], + "spans": [ + { + "bbox": [ + 105, + 386, + 506, + 399 + ], + "score": 1.0, + "content": "Large language models (LLMs) trained on a diverse corpus such as the GPT-n family model [29],", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 398, + 506, + 410 + ], + "spans": [ + { + "bbox": [ + 106, + 398, + 506, + 410 + ], + "score": 1.0, + "content": "capture the statistical correlations of the human experience in the form of language correlations.", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 408, + 507, + 422 + ], + "spans": [ + { + "bbox": [ + 105, + 408, + 507, + 422 + ], + "score": 1.0, + "content": "Through this process, GPT acquires knowledge of how to represent and predict intricate sequences.", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 419, + 506, + 432 + ], + "spans": [ + { + "bbox": [ + 105, + 419, + 506, + 432 + ], + "score": 1.0, + "content": "We utilize this knowledge to provide our model with the ability to generate levels that incorporate", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 430, + 504, + 443 + ], + "spans": [ + { + "bbox": [ + 106, + 431, + 479, + 443 + ], + "score": 1.0, + "content": "simple artefacts as well as more complex relational properties. Surprisingly, a high percentage", + "type": "text" + }, + { + "bbox": [ + 479, + 430, + 504, + 442 + ], + "score": 0.84, + "content": "( 8 8 \\% )", + "type": "inline_equation" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 441, + 311, + 454 + ], + "spans": [ + { + "bbox": [ + 106, + 441, + 311, + 454 + ], + "score": 1.0, + "content": "of MarioGPT generated levels are in fact playable.", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 22, + "bbox_fs": [ + 105, + 353, + 507, + 454 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 457, + 505, + 524 + ], + "lines": [ + { + "bbox": [ + 106, + 457, + 505, + 469 + ], + "spans": [ + { + "bbox": [ + 106, + 457, + 505, + 469 + ], + "score": 1.0, + "content": "Furthermore, we combine MarioGPT with novelty search [22], a diversity-seeking algorithm, to", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 469, + 505, + 480 + ], + "spans": [ + { + "bbox": [ + 105, + 469, + 505, + 480 + ], + "score": 1.0, + "content": "continually generate diverse levels in an open-ended manner. The combination of LLMs with", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 479, + 505, + 492 + ], + "spans": [ + { + "bbox": [ + 105, + 479, + 505, + 492 + ], + "score": 1.0, + "content": "algorithms such as novelty search opens up many interesting new directions for future research. We", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 491, + 504, + 502 + ], + "spans": [ + { + "bbox": [ + 106, + 491, + 504, + 502 + ], + "score": 1.0, + "content": "hope our work opens the door to more flexible and controllable PCG methods that can generate infinite", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 501, + 505, + 513 + ], + "spans": [ + { + "bbox": [ + 106, + 501, + 505, + 513 + ], + "score": 1.0, + "content": "content that is complex, diverse, and functional. To facilitate this, the code to run the experiments in", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 511, + 447, + 526 + ], + "spans": [ + { + "bbox": [ + 105, + 511, + 447, + 526 + ], + "score": 1.0, + "content": "this paper is publicly available at: https://github.com/shyamsn97/mario-gpt.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 29.5, + "bbox_fs": [ + 105, + 457, + 505, + 526 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 538, + 285, + 552 + ], + "lines": [ + { + "bbox": [ + 104, + 538, + 287, + 555 + ], + "spans": [ + { + "bbox": [ + 104, + 538, + 287, + 555 + ], + "score": 1.0, + "content": "2 Background and Related Work", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 33 + }, + { + "type": "text", + "bbox": [ + 107, + 563, + 505, + 673 + ], + "lines": [ + { + "bbox": [ + 106, + 564, + 505, + 575 + ], + "spans": [ + { + "bbox": [ + 106, + 564, + 505, + 575 + ], + "score": 1.0, + "content": "Procedural Content Generation. Procedural Content Generation (PCG) algorithms [36] deal with", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 573, + 506, + 587 + ], + "spans": [ + { + "bbox": [ + 105, + 573, + 506, + 587 + ], + "score": 1.0, + "content": "the automatic creation of game content (e.g. for level design, character generation, environment", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 584, + 507, + 599 + ], + "spans": [ + { + "bbox": [ + 105, + 584, + 507, + 599 + ], + "score": 1.0, + "content": "modeling, etc.). 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More recently, deep learning for PCG [27, 39] has emerged as a promising", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 618, + 506, + 631 + ], + "spans": [ + { + "bbox": [ + 105, + 618, + 506, + 631 + ], + "score": 1.0, + "content": "approach to learning to generate high-quality game content in a data-driven manner, which is not", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 628, + 505, + 642 + ], + "spans": [ + { + "bbox": [ + 105, + 628, + 505, + 642 + ], + "score": 1.0, + "content": "only aesthetically pleasing but also functional and challenging. However, the diversity, originality", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 640, + 505, + 653 + ], + "spans": [ + { + "bbox": [ + 106, + 640, + 505, + 653 + ], + "score": 1.0, + "content": "and playability of the generated content in addition to the controllability of its generation, remain", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 651, + 505, + 663 + ], + "spans": [ + { + "bbox": [ + 106, + 651, + 505, + 663 + ], + "score": 1.0, + "content": "major challenges [39]. Our work aims to show how conditioned language models, paired with", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 661, + 484, + 675 + ], + "spans": [ + { + "bbox": [ + 105, + 661, + 484, + 675 + ], + "score": 1.0, + "content": "novelty-driven approaches to content generation [26, 2], could help tackle these shortcomings.", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 38.5, + "bbox_fs": [ + 105, + 564, + 507, + 675 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 678, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 105, + 677, + 506, + 691 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 506, + 691 + ], + "score": 1.0, + "content": "Neural Network-based Level Generation. Recent works in the space of video game level generation,", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 689, + 506, + 701 + ], + "spans": [ + { + "bbox": [ + 105, + 689, + 506, + 701 + ], + "score": 1.0, + "content": "particularly for Super Mario [2, 8, 45, 33, 35, 34], also leveraged neural network architectures to", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 700, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 700, + 505, + 712 + ], + "score": 1.0, + "content": "create levels. Beukman et al. [2] evolved neural networks in order to generate levels, while others", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 710, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 710, + 505, + 723 + ], + "score": 1.0, + "content": "[8, 45, 12, 34] performed evolution / search in the latent space of a trained generative model. These", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 72, + 505, + 85 + ], + "spans": [ + { + "bbox": [ + 105, + 72, + 505, + 85 + ], + "score": 1.0, + "content": "works showed that guided sampling of the latent space of the learned generative model could result", + "type": "text", + "cross_page": true + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 83, + 207, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 83, + 207, + 96 + ], + "score": 1.0, + "content": "in a diverse set of levels.", + "type": "text", + "cross_page": true + } + ], + "index": 1 + } + ], + "index": 45.5, + "bbox_fs": [ + 105, + 677, + 506, + 723 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 73, + 504, + 95 + ], + "lines": [ + { + "bbox": [ + 105, + 72, + 505, + 85 + ], + "spans": [ + { + "bbox": [ + 105, + 72, + 505, + 85 + ], + "score": 1.0, + "content": "works showed that guided sampling of the latent space of the learned generative model could result", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 83, + 207, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 83, + 207, + 96 + ], + "score": 1.0, + "content": "in a diverse set of levels.", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "text", + "bbox": [ + 107, + 100, + 505, + 220 + ], + "lines": [ + { + "bbox": [ + 106, + 100, + 505, + 112 + ], + "spans": [ + { + "bbox": [ + 106, + 100, + 505, + 112 + ], + "score": 1.0, + "content": "Previous works that utilize a trained generative model [8, 45, 34, 12] also explored the abilities to", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 110, + 506, + 124 + ], + "spans": [ + { + "bbox": [ + 105, + 110, + 506, + 124 + ], + "score": 1.0, + "content": "control characteristics in generated levels. However, to do so these methods relied on searching", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 122, + 505, + 135 + ], + "spans": [ + { + "bbox": [ + 106, + 122, + 505, + 135 + ], + "score": 1.0, + "content": "the latent space (e.g. through quality diversity algorithms [28, 9] or evolutionary strategies [14])", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 132, + 506, + 146 + ], + "spans": [ + { + "bbox": [ + 105, + 132, + 506, + 146 + ], + "score": 1.0, + "content": "for levels with specific target characteristics (e.g. a level with many pipes). This is a significant", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 144, + 505, + 156 + ], + "spans": [ + { + "bbox": [ + 106, + 144, + 505, + 156 + ], + "score": 1.0, + "content": "limitation because even though the generative models may represent a rich set of content, one has to", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 155, + 507, + 168 + ], + "spans": [ + { + "bbox": [ + 105, + 155, + 507, + 168 + ], + "score": 1.0, + "content": "search through its latent space to try to find the content that actually satisfies specific characteristics.", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 165, + 506, + 178 + ], + "spans": [ + { + "bbox": [ + 105, + 165, + 506, + 178 + ], + "score": 1.0, + "content": "MarioGPT is able to improve upon this limitation by incorporating text prompts into the actual", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 176, + 506, + 189 + ], + "spans": [ + { + "bbox": [ + 105, + 176, + 506, + 189 + ], + "score": 1.0, + "content": "generative process, allowing for easily controllable level generation. In other words, instead of", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 188, + 505, + 199 + ], + "spans": [ + { + "bbox": [ + 106, + 188, + 505, + 199 + ], + "score": 1.0, + "content": "searching for a level with specific characteristics, MarioGPT allows us to just ask for it. Concurrently", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 198, + 505, + 211 + ], + "spans": [ + { + "bbox": [ + 105, + 198, + 505, + 211 + ], + "score": 1.0, + "content": "to our work, Todd et al. [42] showed that LLMs can also be used to generate levels for other games", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 208, + 388, + 223 + ], + "spans": [ + { + "bbox": [ + 105, + 208, + 388, + 223 + ], + "score": 1.0, + "content": "such as Sokoban but their model did not allow for any text-prompting.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 7 + }, + { + "type": "text", + "bbox": [ + 107, + 225, + 505, + 313 + ], + "lines": [ + { + "bbox": [ + 106, + 225, + 505, + 238 + ], + "spans": [ + { + "bbox": [ + 106, + 225, + 505, + 238 + ], + "score": 1.0, + "content": "Open-Endedness and Genetic Algorithms. The open-endedness paradigm focuses on algorithms", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 236, + 506, + 249 + ], + "spans": [ + { + "bbox": [ + 106, + 236, + 506, + 249 + ], + "score": 1.0, + "content": "that can produce infinite innovation [24]. These open-ended algorithms are popular in the field of", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 247, + 506, + 260 + ], + "spans": [ + { + "bbox": [ + 105, + 247, + 506, + 260 + ], + "score": 1.0, + "content": "PCG, where designers and players both can benefit from diverse and never-ending content. However,", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 258, + 505, + 271 + ], + "spans": [ + { + "bbox": [ + 105, + 258, + 505, + 271 + ], + "score": 1.0, + "content": "PCG must balance the hard task of generating content with diversity as well as playability. Genetic", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 269, + 505, + 281 + ], + "spans": [ + { + "bbox": [ + 106, + 269, + 505, + 281 + ], + "score": 1.0, + "content": "algorithms (GA), a family of optimization algorithms that are inspired by the principles of natural", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 280, + 505, + 292 + ], + "spans": [ + { + "bbox": [ + 106, + 280, + 505, + 292 + ], + "score": 1.0, + "content": "selection, are commonly used as the backbone for more open-ended search methods. Because GAs", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 291, + 506, + 304 + ], + "spans": [ + { + "bbox": [ + 105, + 291, + 506, + 304 + ], + "score": 1.0, + "content": "allow the integration of multiple objectives, they are particularly suitable for achieving a balance", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 301, + 226, + 315 + ], + "spans": [ + { + "bbox": [ + 105, + 301, + 226, + 315 + ], + "score": 1.0, + "content": "between fitness and diversity.", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 16.5 + }, + { + "type": "text", + "bbox": [ + 107, + 318, + 505, + 395 + ], + "lines": [ + { + "bbox": [ + 105, + 318, + 505, + 331 + ], + "spans": [ + { + "bbox": [ + 105, + 318, + 505, + 331 + ], + "score": 1.0, + "content": "In that regard, novelty search approaches [23] aim at finding the most novel solutions at each", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 329, + 506, + 342 + ], + "spans": [ + { + "bbox": [ + 105, + 329, + 506, + 342 + ], + "score": 1.0, + "content": "generation, in comparison to what has been seen (i.e. an archive of previously discovered highly-", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 340, + 506, + 352 + ], + "spans": [ + { + "bbox": [ + 105, + 340, + 506, + 352 + ], + "score": 1.0, + "content": "novel individuals). What makes novelty-search powerful, and motivated its use in this paper, is that", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 351, + 505, + 363 + ], + "spans": [ + { + "bbox": [ + 105, + 351, + 505, + 363 + ], + "score": 1.0, + "content": "it guides the generation towards increasingly diverse solutions in an open-ended fashion. Novelty", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 362, + 506, + 374 + ], + "spans": [ + { + "bbox": [ + 105, + 362, + 506, + 374 + ], + "score": 1.0, + "content": "search keeps track of solutions in an archive and measures diversity by the distance between their", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 373, + 505, + 385 + ], + "spans": [ + { + "bbox": [ + 105, + 373, + 337, + 385 + ], + "score": 1.0, + "content": "behavior characteristics (BCs) compared to that of their", + "type": "text" + }, + { + "bbox": [ + 337, + 373, + 344, + 383 + ], + "score": 0.78, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 345, + 373, + 505, + 385 + ], + "score": 1.0, + "content": "closest neighbors. This makes novelty", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 384, + 461, + 397 + ], + "spans": [ + { + "bbox": [ + 105, + 384, + 461, + 397 + ], + "score": 1.0, + "content": "search very flexible, allowing for the use of many different behavior characteristic types.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 24 + }, + { + "type": "text", + "bbox": [ + 107, + 400, + 505, + 498 + ], + "lines": [ + { + "bbox": [ + 106, + 401, + 505, + 412 + ], + "spans": [ + { + "bbox": [ + 106, + 401, + 505, + 412 + ], + "score": 1.0, + "content": "Sequence Modelling and Transformers. Classic approaches to sequence modelling using recurrent", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 411, + 505, + 423 + ], + "spans": [ + { + "bbox": [ + 105, + 411, + 505, + 423 + ], + "score": 1.0, + "content": "neural networks (RNNs) [31] and Long Short Term Memory (LSTM) networks [15] have traditionally", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 421, + 505, + 434 + ], + "spans": [ + { + "bbox": [ + 105, + 421, + 505, + 434 + ], + "score": 1.0, + "content": "been constrained by the fading memory of the network’s state vector, as well as limited scalability", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 432, + 505, + 446 + ], + "spans": [ + { + "bbox": [ + 105, + 432, + 505, + 446 + ], + "score": 1.0, + "content": "due to the temporal interdependency of the operations. Transformers [44] address both challenges by", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 443, + 506, + 456 + ], + "spans": [ + { + "bbox": [ + 105, + 443, + 506, + 456 + ], + "score": 1.0, + "content": "applying associative attention [1] to learned reprojections of the windowed input sequence, which is", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 453, + 506, + 469 + ], + "spans": [ + { + "bbox": [ + 105, + 453, + 506, + 469 + ], + "score": 1.0, + "content": "commonly referred to as self-attention. These architectural innovations have enabled Large Language", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 465, + 505, + 478 + ], + "spans": [ + { + "bbox": [ + 106, + 465, + 505, + 478 + ], + "score": 1.0, + "content": "Models (LLMs) to learn from massive datasets. Additionally, such models have also shown to", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 474, + 505, + 491 + ], + "spans": [ + { + "bbox": [ + 105, + 474, + 505, + 491 + ], + "score": 1.0, + "content": "be effective in accelerated learning of down-stream tasks. Fine-tuning LLMs [7] involves using", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 487, + 372, + 500 + ], + "spans": [ + { + "bbox": [ + 105, + 487, + 372, + 500 + ], + "score": 1.0, + "content": "pre-trained model weights as a weight initialization for new tasks.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 32 + }, + { + "type": "text", + "bbox": [ + 107, + 504, + 505, + 570 + ], + "lines": [ + { + "bbox": [ + 106, + 504, + 505, + 515 + ], + "spans": [ + { + "bbox": [ + 106, + 504, + 505, + 515 + ], + "score": 1.0, + "content": "One particularly relevant use of pretrained / fine-tuned LLMs comes from the method Evolution", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 514, + 506, + 527 + ], + "spans": [ + { + "bbox": [ + 105, + 514, + 506, + 527 + ], + "score": 1.0, + "content": "through Large Models (ELM), proposed in Lehman et al. [21]. ELM utilizes an LLM diff model [3],", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 525, + 505, + 538 + ], + "spans": [ + { + "bbox": [ + 105, + 525, + 505, + 538 + ], + "score": 1.0, + "content": "which is trained on code diffs obtained by Github data, giving the model the ability to modify a code", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 536, + 506, + 549 + ], + "spans": [ + { + "bbox": [ + 105, + 536, + 506, + 549 + ], + "score": 1.0, + "content": "snippet based on a particular commit message. This diff model is used as a \"mutation operator\", for a", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 547, + 506, + 560 + ], + "spans": [ + { + "bbox": [ + 105, + 547, + 506, + 560 + ], + "score": 1.0, + "content": "GA that evolves a population of programs. The wide generative capabilities of the LLM produce", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 558, + 497, + 571 + ], + "spans": [ + { + "bbox": [ + 105, + 558, + 497, + 571 + ], + "score": 1.0, + "content": "diverse mutations, resulting in novel individuals that vary increasingly over the course of the GA.", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 39.5 + }, + { + "type": "title", + "bbox": [ + 106, + 590, + 362, + 604 + ], + "lines": [ + { + "bbox": [ + 103, + 588, + 363, + 607 + ], + "spans": [ + { + "bbox": [ + 103, + 588, + 363, + 607 + ], + "score": 1.0, + "content": "3 Open-Ended Level Generation through LLMs", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 43 + }, + { + "type": "text", + "bbox": [ + 107, + 617, + 505, + 673 + ], + "lines": [ + { + "bbox": [ + 106, + 617, + 506, + 631 + ], + "spans": [ + { + "bbox": [ + 106, + 617, + 506, + 631 + ], + "score": 1.0, + "content": "Here we present our complete approach to open-ended level generation through LLMs, which is", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 628, + 506, + 642 + ], + "spans": [ + { + "bbox": [ + 106, + 628, + 506, + 642 + ], + "score": 1.0, + "content": "composed of two parts. First, we introduce our prompt-conditioned model MarioGPT (Figure 2) in", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 640, + 506, + 653 + ], + "spans": [ + { + "bbox": [ + 106, + 640, + 506, + 653 + ], + "score": 1.0, + "content": "Section 3.1, which generates levels –encoded as text– given a natural-language prompt. Second, we", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 649, + 507, + 664 + ], + "spans": [ + { + "bbox": [ + 105, + 649, + 507, + 664 + ], + "score": 1.0, + "content": "detail how MarioGPT can be used in a novelty-search evolutionary loop (Figure 3) in Section 3.2,", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 662, + 387, + 674 + ], + "spans": [ + { + "bbox": [ + 105, + 662, + 387, + 674 + ], + "score": 1.0, + "content": "allowing the approach to produce a continual stream of diverse levels.", + "type": "text" + } + ], + "index": 48 + } + ], + "index": 46 + }, + { + "type": "text", + "bbox": [ + 107, + 678, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 105, + 677, + 506, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 506, + 690 + ], + "score": 1.0, + "content": "Level Representation. Mario levels are represented similarly to previous works [45, 8, 35, 33, 34, 12],", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 106, + 689, + 505, + 701 + ], + "spans": [ + { + "bbox": [ + 106, + 689, + 505, + 701 + ], + "score": 1.0, + "content": "using the levels provided in the Video Game Level Corpus (VGLC) [40]. We utilize a relatively small", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 105, + 699, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 505, + 712 + ], + "score": 1.0, + "content": "set of path-annotated levels, taken from Super Mario Bros. and Super Mario Bros.: The Lost Levels", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 105, + 711, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 711, + 505, + 723 + ], + "score": 1.0, + "content": "(in total 37 levels). For more details on specific tiles present, see Section 6.1 in the Appendix. These", + "type": "text" + } + ], + "index": 52 + } + ], + "index": 50.5 + } + ], + "page_idx": 2, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 302, + 741, + 309, + 750 + ], + "lines": [ + { + "bbox": [ + 301, + 740, + 309, + 752 + ], + "spans": [ + { + "bbox": [ + 301, + 740, + 309, + 752 + ], + "score": 1.0, + "content": "3", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 73, + 504, + 95 + ], + "lines": [], + "index": 0.5, + "bbox_fs": [ + 105, + 72, + 505, + 96 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 107, + 100, + 505, + 220 + ], + "lines": [ + { + "bbox": [ + 106, + 100, + 505, + 112 + ], + "spans": [ + { + "bbox": [ + 106, + 100, + 505, + 112 + ], + "score": 1.0, + "content": "Previous works that utilize a trained generative model [8, 45, 34, 12] also explored the abilities to", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 110, + 506, + 124 + ], + "spans": [ + { + "bbox": [ + 105, + 110, + 506, + 124 + ], + "score": 1.0, + "content": "control characteristics in generated levels. However, to do so these methods relied on searching", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 122, + 505, + 135 + ], + "spans": [ + { + "bbox": [ + 106, + 122, + 505, + 135 + ], + "score": 1.0, + "content": "the latent space (e.g. through quality diversity algorithms [28, 9] or evolutionary strategies [14])", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 132, + 506, + 146 + ], + "spans": [ + { + "bbox": [ + 105, + 132, + 506, + 146 + ], + "score": 1.0, + "content": "for levels with specific target characteristics (e.g. a level with many pipes). This is a significant", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 144, + 505, + 156 + ], + "spans": [ + { + "bbox": [ + 106, + 144, + 505, + 156 + ], + "score": 1.0, + "content": "limitation because even though the generative models may represent a rich set of content, one has to", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 155, + 507, + 168 + ], + "spans": [ + { + "bbox": [ + 105, + 155, + 507, + 168 + ], + "score": 1.0, + "content": "search through its latent space to try to find the content that actually satisfies specific characteristics.", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 165, + 506, + 178 + ], + "spans": [ + { + "bbox": [ + 105, + 165, + 506, + 178 + ], + "score": 1.0, + "content": "MarioGPT is able to improve upon this limitation by incorporating text prompts into the actual", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 176, + 506, + 189 + ], + "spans": [ + { + "bbox": [ + 105, + 176, + 506, + 189 + ], + "score": 1.0, + "content": "generative process, allowing for easily controllable level generation. In other words, instead of", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 188, + 505, + 199 + ], + "spans": [ + { + "bbox": [ + 106, + 188, + 505, + 199 + ], + "score": 1.0, + "content": "searching for a level with specific characteristics, MarioGPT allows us to just ask for it. Concurrently", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 198, + 505, + 211 + ], + "spans": [ + { + "bbox": [ + 105, + 198, + 505, + 211 + ], + "score": 1.0, + "content": "to our work, Todd et al. [42] showed that LLMs can also be used to generate levels for other games", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 208, + 388, + 223 + ], + "spans": [ + { + "bbox": [ + 105, + 208, + 388, + 223 + ], + "score": 1.0, + "content": "such as Sokoban but their model did not allow for any text-prompting.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 7, + "bbox_fs": [ + 105, + 100, + 507, + 223 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 225, + 505, + 313 + ], + "lines": [ + { + "bbox": [ + 106, + 225, + 505, + 238 + ], + "spans": [ + { + "bbox": [ + 106, + 225, + 505, + 238 + ], + "score": 1.0, + "content": "Open-Endedness and Genetic Algorithms. The open-endedness paradigm focuses on algorithms", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 236, + 506, + 249 + ], + "spans": [ + { + "bbox": [ + 106, + 236, + 506, + 249 + ], + "score": 1.0, + "content": "that can produce infinite innovation [24]. These open-ended algorithms are popular in the field of", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 247, + 506, + 260 + ], + "spans": [ + { + "bbox": [ + 105, + 247, + 506, + 260 + ], + "score": 1.0, + "content": "PCG, where designers and players both can benefit from diverse and never-ending content. However,", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 258, + 505, + 271 + ], + "spans": [ + { + "bbox": [ + 105, + 258, + 505, + 271 + ], + "score": 1.0, + "content": "PCG must balance the hard task of generating content with diversity as well as playability. Genetic", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 269, + 505, + 281 + ], + "spans": [ + { + "bbox": [ + 106, + 269, + 505, + 281 + ], + "score": 1.0, + "content": "algorithms (GA), a family of optimization algorithms that are inspired by the principles of natural", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 280, + 505, + 292 + ], + "spans": [ + { + "bbox": [ + 106, + 280, + 505, + 292 + ], + "score": 1.0, + "content": "selection, are commonly used as the backbone for more open-ended search methods. Because GAs", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 291, + 506, + 304 + ], + "spans": [ + { + "bbox": [ + 105, + 291, + 506, + 304 + ], + "score": 1.0, + "content": "allow the integration of multiple objectives, they are particularly suitable for achieving a balance", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 301, + 226, + 315 + ], + "spans": [ + { + "bbox": [ + 105, + 301, + 226, + 315 + ], + "score": 1.0, + "content": "between fitness and diversity.", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 16.5, + "bbox_fs": [ + 105, + 225, + 506, + 315 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 318, + 505, + 395 + ], + "lines": [ + { + "bbox": [ + 105, + 318, + 505, + 331 + ], + "spans": [ + { + "bbox": [ + 105, + 318, + 505, + 331 + ], + "score": 1.0, + "content": "In that regard, novelty search approaches [23] aim at finding the most novel solutions at each", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 329, + 506, + 342 + ], + "spans": [ + { + "bbox": [ + 105, + 329, + 506, + 342 + ], + "score": 1.0, + "content": "generation, in comparison to what has been seen (i.e. an archive of previously discovered highly-", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 340, + 506, + 352 + ], + "spans": [ + { + "bbox": [ + 105, + 340, + 506, + 352 + ], + "score": 1.0, + "content": "novel individuals). What makes novelty-search powerful, and motivated its use in this paper, is that", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 351, + 505, + 363 + ], + "spans": [ + { + "bbox": [ + 105, + 351, + 505, + 363 + ], + "score": 1.0, + "content": "it guides the generation towards increasingly diverse solutions in an open-ended fashion. Novelty", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 362, + 506, + 374 + ], + "spans": [ + { + "bbox": [ + 105, + 362, + 506, + 374 + ], + "score": 1.0, + "content": "search keeps track of solutions in an archive and measures diversity by the distance between their", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 373, + 505, + 385 + ], + "spans": [ + { + "bbox": [ + 105, + 373, + 337, + 385 + ], + "score": 1.0, + "content": "behavior characteristics (BCs) compared to that of their", + "type": "text" + }, + { + "bbox": [ + 337, + 373, + 344, + 383 + ], + "score": 0.78, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 345, + 373, + 505, + 385 + ], + "score": 1.0, + "content": "closest neighbors. This makes novelty", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 384, + 461, + 397 + ], + "spans": [ + { + "bbox": [ + 105, + 384, + 461, + 397 + ], + "score": 1.0, + "content": "search very flexible, allowing for the use of many different behavior characteristic types.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 24, + "bbox_fs": [ + 105, + 318, + 506, + 397 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 400, + 505, + 498 + ], + "lines": [ + { + "bbox": [ + 106, + 401, + 505, + 412 + ], + "spans": [ + { + "bbox": [ + 106, + 401, + 505, + 412 + ], + "score": 1.0, + "content": "Sequence Modelling and Transformers. Classic approaches to sequence modelling using recurrent", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 411, + 505, + 423 + ], + "spans": [ + { + "bbox": [ + 105, + 411, + 505, + 423 + ], + "score": 1.0, + "content": "neural networks (RNNs) [31] and Long Short Term Memory (LSTM) networks [15] have traditionally", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 421, + 505, + 434 + ], + "spans": [ + { + "bbox": [ + 105, + 421, + 505, + 434 + ], + "score": 1.0, + "content": "been constrained by the fading memory of the network’s state vector, as well as limited scalability", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 432, + 505, + 446 + ], + "spans": [ + { + "bbox": [ + 105, + 432, + 505, + 446 + ], + "score": 1.0, + "content": "due to the temporal interdependency of the operations. Transformers [44] address both challenges by", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 443, + 506, + 456 + ], + "spans": [ + { + "bbox": [ + 105, + 443, + 506, + 456 + ], + "score": 1.0, + "content": "applying associative attention [1] to learned reprojections of the windowed input sequence, which is", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 453, + 506, + 469 + ], + "spans": [ + { + "bbox": [ + 105, + 453, + 506, + 469 + ], + "score": 1.0, + "content": "commonly referred to as self-attention. These architectural innovations have enabled Large Language", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 465, + 505, + 478 + ], + "spans": [ + { + "bbox": [ + 106, + 465, + 505, + 478 + ], + "score": 1.0, + "content": "Models (LLMs) to learn from massive datasets. Additionally, such models have also shown to", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 474, + 505, + 491 + ], + "spans": [ + { + "bbox": [ + 105, + 474, + 505, + 491 + ], + "score": 1.0, + "content": "be effective in accelerated learning of down-stream tasks. Fine-tuning LLMs [7] involves using", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 487, + 372, + 500 + ], + "spans": [ + { + "bbox": [ + 105, + 487, + 372, + 500 + ], + "score": 1.0, + "content": "pre-trained model weights as a weight initialization for new tasks.", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 32, + "bbox_fs": [ + 105, + 401, + 506, + 500 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 504, + 505, + 570 + ], + "lines": [ + { + "bbox": [ + 106, + 504, + 505, + 515 + ], + "spans": [ + { + "bbox": [ + 106, + 504, + 505, + 515 + ], + "score": 1.0, + "content": "One particularly relevant use of pretrained / fine-tuned LLMs comes from the method Evolution", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 514, + 506, + 527 + ], + "spans": [ + { + "bbox": [ + 105, + 514, + 506, + 527 + ], + "score": 1.0, + "content": "through Large Models (ELM), proposed in Lehman et al. [21]. ELM utilizes an LLM diff model [3],", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 525, + 505, + 538 + ], + "spans": [ + { + "bbox": [ + 105, + 525, + 505, + 538 + ], + "score": 1.0, + "content": "which is trained on code diffs obtained by Github data, giving the model the ability to modify a code", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 536, + 506, + 549 + ], + "spans": [ + { + "bbox": [ + 105, + 536, + 506, + 549 + ], + "score": 1.0, + "content": "snippet based on a particular commit message. This diff model is used as a \"mutation operator\", for a", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 547, + 506, + 560 + ], + "spans": [ + { + "bbox": [ + 105, + 547, + 506, + 560 + ], + "score": 1.0, + "content": "GA that evolves a population of programs. The wide generative capabilities of the LLM produce", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 558, + 497, + 571 + ], + "spans": [ + { + "bbox": [ + 105, + 558, + 497, + 571 + ], + "score": 1.0, + "content": "diverse mutations, resulting in novel individuals that vary increasingly over the course of the GA.", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 39.5, + "bbox_fs": [ + 105, + 504, + 506, + 571 + ] + }, + { + "type": "title", + "bbox": [ + 106, + 590, + 362, + 604 + ], + "lines": [ + { + "bbox": [ + 103, + 588, + 363, + 607 + ], + "spans": [ + { + "bbox": [ + 103, + 588, + 363, + 607 + ], + "score": 1.0, + "content": "3 Open-Ended Level Generation through LLMs", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 43 + }, + { + "type": "text", + "bbox": [ + 107, + 617, + 505, + 673 + ], + "lines": [ + { + "bbox": [ + 106, + 617, + 506, + 631 + ], + "spans": [ + { + "bbox": [ + 106, + 617, + 506, + 631 + ], + "score": 1.0, + "content": "Here we present our complete approach to open-ended level generation through LLMs, which is", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 628, + 506, + 642 + ], + "spans": [ + { + "bbox": [ + 106, + 628, + 506, + 642 + ], + "score": 1.0, + "content": "composed of two parts. First, we introduce our prompt-conditioned model MarioGPT (Figure 2) in", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 640, + 506, + 653 + ], + "spans": [ + { + "bbox": [ + 106, + 640, + 506, + 653 + ], + "score": 1.0, + "content": "Section 3.1, which generates levels –encoded as text– given a natural-language prompt. Second, we", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 649, + 507, + 664 + ], + "spans": [ + { + "bbox": [ + 105, + 649, + 507, + 664 + ], + "score": 1.0, + "content": "detail how MarioGPT can be used in a novelty-search evolutionary loop (Figure 3) in Section 3.2,", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 662, + 387, + 674 + ], + "spans": [ + { + "bbox": [ + 105, + 662, + 387, + 674 + ], + "score": 1.0, + "content": "allowing the approach to produce a continual stream of diverse levels.", + "type": "text" + } + ], + "index": 48 + } + ], + "index": 46, + "bbox_fs": [ + 105, + 617, + 507, + 674 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 678, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 105, + 677, + 506, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 506, + 690 + ], + "score": 1.0, + "content": "Level Representation. Mario levels are represented similarly to previous works [45, 8, 35, 33, 34, 12],", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 106, + 689, + 505, + 701 + ], + "spans": [ + { + "bbox": [ + 106, + 689, + 505, + 701 + ], + "score": 1.0, + "content": "using the levels provided in the Video Game Level Corpus (VGLC) [40]. We utilize a relatively small", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 105, + 699, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 505, + 712 + ], + "score": 1.0, + "content": "set of path-annotated levels, taken from Super Mario Bros. and Super Mario Bros.: The Lost Levels", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 105, + 711, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 711, + 505, + 723 + ], + "score": 1.0, + "content": "(in total 37 levels). For more details on specific tiles present, see Section 6.1 in the Appendix. These", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 105, + 312, + 505, + 325 + ], + "spans": [ + { + "bbox": [ + 105, + 312, + 505, + 325 + ], + "score": 1.0, + "content": "levels are stitched together, to essentially make one giant level, allowing us to sample freely without", + "type": "text", + "cross_page": true + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 324, + 505, + 336 + ], + "spans": [ + { + "bbox": [ + 105, + 324, + 505, + 336 + ], + "score": 1.0, + "content": "worrying about the ends of the levels. Each tile is represented as a string. The string representation", + "type": "text", + "cross_page": true + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 334, + 505, + 347 + ], + "spans": [ + { + "bbox": [ + 105, + 334, + 505, + 347 + ], + "score": 1.0, + "content": "and characters are tokenized into discrete values using a Byte Pair Encoding tokenizer used in the", + "type": "text", + "cross_page": true + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 345, + 505, + 358 + ], + "spans": [ + { + "bbox": [ + 105, + 345, + 505, + 358 + ], + "score": 1.0, + "content": "original GPT2 model [29]. The tokenizer learns a mapping that maps each tile to its own unique", + "type": "text", + "cross_page": true + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 356, + 505, + 368 + ], + "spans": [ + { + "bbox": [ + 105, + 356, + 505, + 368 + ], + "score": 1.0, + "content": "token. One limitation from the dataset is the simplified representation of enemies. Even though levels", + "type": "text", + "cross_page": true + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 367, + 505, + 380 + ], + "spans": [ + { + "bbox": [ + 105, + 367, + 505, + 380 + ], + "score": 1.0, + "content": "contain many different enemies, each with different behaviors and features, the dataset represents", + "type": "text", + "cross_page": true + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 379, + 216, + 389 + ], + "spans": [ + { + "bbox": [ + 106, + 379, + 216, + 389 + ], + "score": 1.0, + "content": "them all as the same token.", + "type": "text", + "cross_page": true + } + ], + "index": 13 + } + ], + "index": 50.5, + "bbox_fs": [ + 105, + 677, + 506, + 723 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 155, + 69, + 455, + 239 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 155, + 69, + 455, + 239 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 155, + 69, + 455, + 239 + ], + "spans": [ + { + "bbox": [ + 155, + 69, + 455, + 239 + ], + "score": 0.846, + "type": "image", + "image_path": "c7dc2c6fdb7821d852c4b6296feaf5113a60c91d29ae427824319eec7c7b20b7.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 155, + 69, + 455, + 125.66666666666666 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 155, + 125.66666666666666, + 455, + 182.33333333333331 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 155, + 182.33333333333331, + 455, + 238.99999999999997 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 107, + 245, + 505, + 286 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 245, + 505, + 257 + ], + "spans": [ + { + "bbox": [ + 106, + 245, + 505, + 257 + ], + "score": 1.0, + "content": "Figure 3: Novelty search setup and MarioGPT mutation operators. A level is sampled from a set of top elites in", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 255, + 506, + 267 + ], + "spans": [ + { + "bbox": [ + 105, + 255, + 506, + 267 + ], + "score": 1.0, + "content": "the archive, mutated, and, if novel enough, added to the archive. The mutation process involves two main steps:", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 264, + 506, + 278 + ], + "spans": [ + { + "bbox": [ + 105, + 264, + 506, + 278 + ], + "score": 1.0, + "content": "(1) Pick a random slice from the level and replace it with a new MarioGPT sample, using a random prompt. (2)", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 275, + 360, + 288 + ], + "spans": [ + { + "bbox": [ + 105, + 275, + 360, + 288 + ], + "score": 1.0, + "content": "Inpaint the border region with MarioBert to preserve path consistency.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 4.5 + } + ], + "index": 2.75 + }, + { + "type": "text", + "bbox": [ + 107, + 312, + 505, + 389 + ], + "lines": [ + { + "bbox": [ + 105, + 312, + 505, + 325 + ], + "spans": [ + { + "bbox": [ + 105, + 312, + 505, + 325 + ], + "score": 1.0, + "content": "levels are stitched together, to essentially make one giant level, allowing us to sample freely without", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 324, + 505, + 336 + ], + "spans": [ + { + "bbox": [ + 105, + 324, + 505, + 336 + ], + "score": 1.0, + "content": "worrying about the ends of the levels. Each tile is represented as a string. The string representation", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 334, + 505, + 347 + ], + "spans": [ + { + "bbox": [ + 105, + 334, + 505, + 347 + ], + "score": 1.0, + "content": "and characters are tokenized into discrete values using a Byte Pair Encoding tokenizer used in the", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 345, + 505, + 358 + ], + "spans": [ + { + "bbox": [ + 105, + 345, + 505, + 358 + ], + "score": 1.0, + "content": "original GPT2 model [29]. The tokenizer learns a mapping that maps each tile to its own unique", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 356, + 505, + 368 + ], + "spans": [ + { + "bbox": [ + 105, + 356, + 505, + 368 + ], + "score": 1.0, + "content": "token. One limitation from the dataset is the simplified representation of enemies. 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Because the model is relatively small, it can", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 578, + 352, + 590 + ], + "spans": [ + { + "bbox": [ + 105, + 578, + 352, + 590 + ], + "score": 1.0, + "content": "be trained using a single Nvidia GeForce RTX 2080 Ti GPU.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 24.5 + }, + { + "type": "text", + "bbox": [ + 107, + 594, + 505, + 693 + ], + "lines": [ + { + "bbox": [ + 105, + 594, + 505, + 606 + ], + "spans": [ + { + "bbox": [ + 105, + 594, + 505, + 606 + ], + "score": 1.0, + "content": "Prompting details: In order to incorporate prompt information, we fine-tune the attention layers’", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 605, + 505, + 618 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 505, + 618 + ], + "score": 1.0, + "content": "cross attention weights, as illustrated in Figure 2. 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This allows us to easily", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 104, + 669, + 507, + 685 + ], + "spans": [ + { + "bbox": [ + 104, + 669, + 507, + 685 + ], + "score": 1.0, + "content": "generate level/prompt pairs by counting corresponding tile values. 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When it comes to creating Mario levels, the focus", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 149, + 505, + 163 + ], + "spans": [ + { + "bbox": [ + 105, + 149, + 505, + 163 + ], + "score": 1.0, + "content": "is on the different paths a player can take to complete the level. This is often a challenge for many", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 161, + 505, + 173 + ], + "spans": [ + { + "bbox": [ + 105, + 161, + 505, + 173 + ], + "score": 1.0, + "content": "algorithms (such as [45, 8]) and requires the use of an external agent for evaluation. However, with", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 171, + 506, + 185 + ], + "spans": [ + { + "bbox": [ + 105, + 171, + 506, + 185 + ], + "score": 1.0, + "content": "MarioGPT, it is possible to generate diverse and controllable levels that approximate a realistic player", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 183, + 506, + 196 + ], + "spans": [ + { + "bbox": [ + 106, + 183, + 506, + 196 + ], + "score": 1.0, + "content": "path, reducing the need for an external agent and producing levels that are directly playable. To", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 194, + 506, + 206 + ], + "spans": [ + { + "bbox": [ + 106, + 194, + 506, + 206 + ], + "score": 1.0, + "content": "encourage diversity in generated levels, we integrate MarioGPT within a novelty search augmented", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 204, + 506, + 217 + ], + "spans": [ + { + "bbox": [ + 105, + 204, + 506, + 217 + ], + "score": 1.0, + "content": "genetic algorithm (NS-MarioGPT), where language-models play the role of mutation operators. As", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 216, + 506, + 228 + ], + "spans": [ + { + "bbox": [ + 106, + 216, + 506, + 228 + ], + "score": 1.0, + "content": "illustrated in Figure 3, NS-MarioGPT iteratively samples and mutates elite levels from an archive of", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 227, + 176, + 237 + ], + "spans": [ + { + "bbox": [ + 106, + 227, + 176, + 237 + ], + "score": 1.0, + "content": "generated levels.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 7.5 + }, + { + "type": "text", + "bbox": [ + 107, + 243, + 505, + 417 + ], + "lines": [ + { + "bbox": [ + 105, + 241, + 505, + 255 + ], + "spans": [ + { + "bbox": [ + 105, + 241, + 505, + 255 + ], + "score": 1.0, + "content": "Novelty Search: Mutated levels are only stored in the archive if they achieve a higher novelty", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 254, + 506, + 266 + ], + "spans": [ + { + "bbox": [ + 105, + 254, + 506, + 266 + ], + "score": 1.0, + "content": "score compared to the previous elites. The novelty score is measured as the mean distance between", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 264, + 504, + 277 + ], + "spans": [ + { + "bbox": [ + 105, + 264, + 493, + 277 + ], + "score": 1.0, + "content": "the behavioral characteristic vector of the levels and the behavioral characteristic vector of the", + "type": "text" + }, + { + "bbox": [ + 493, + 265, + 504, + 275 + ], + "score": 0.74, + "content": "K", + "type": "inline_equation" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 276, + 506, + 288 + ], + "spans": [ + { + "bbox": [ + 106, + 276, + 249, + 288 + ], + "score": 1.0, + "content": "closest elements from the archive", + "type": "text" + }, + { + "bbox": [ + 250, + 276, + 260, + 286 + ], + "score": 0.75, + "content": "K", + "type": "inline_equation" + }, + { + "bbox": [ + 260, + 276, + 506, + 288 + ], + "score": 1.0, + "content": "-means). Our goal in level generation is to create paths that", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 287, + 505, + 299 + ], + "spans": [ + { + "bbox": [ + 106, + 287, + 505, + 299 + ], + "score": 1.0, + "content": "result in diverse player behavior, so we use predicted player paths as our basis for these behavior", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 298, + 506, + 310 + ], + "spans": [ + { + "bbox": [ + 106, + 298, + 506, + 310 + ], + "score": 1.0, + "content": "characteristics. More specifically, we are interested in the relative patterns of predicted paths. For", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 309, + 505, + 320 + ], + "spans": [ + { + "bbox": [ + 106, + 309, + 505, + 320 + ], + "score": 1.0, + "content": "instance, if a player character moves in a straight line on high elevated blocks, we want the path’s", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 104, + 319, + 506, + 332 + ], + "spans": [ + { + "bbox": [ + 104, + 319, + 506, + 332 + ], + "score": 1.0, + "content": "representation to be close in behavior space to a path that moves straight in lower elevation. To", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 330, + 506, + 343 + ], + "spans": [ + { + "bbox": [ + 106, + 330, + 506, + 343 + ], + "score": 1.0, + "content": "achieve this, we represent the behavior characteristic as the normalized average of the predicted", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 341, + 506, + 353 + ], + "spans": [ + { + "bbox": [ + 105, + 341, + 506, + 353 + ], + "score": 1.0, + "content": "path’s coordinates, allowing a smooth representation of paths (Figure 4). Thus the significance of", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 352, + 506, + 363 + ], + "spans": [ + { + "bbox": [ + 106, + 352, + 506, + 363 + ], + "score": 1.0, + "content": "a single block difference is reduced, making it harder for mutated levels to be added to the archive.", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 362, + 505, + 375 + ], + "spans": [ + { + "bbox": [ + 105, + 362, + 505, + 375 + ], + "score": 1.0, + "content": "This is desired because we don’t want the archive to fill up with levels that only vary slightly from the", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 374, + 506, + 386 + ], + "spans": [ + { + "bbox": [ + 106, + 374, + 506, + 386 + ], + "score": 1.0, + "content": "existing levels in the archive. For all our novelty search experiments, we use a small neighborhood of", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 384, + 506, + 397 + ], + "spans": [ + { + "bbox": [ + 105, + 384, + 506, + 397 + ], + "score": 1.0, + "content": "size 4, which results in a behavioral characteristic of dimension 100. We initialize our archive with a", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 396, + 506, + 408 + ], + "spans": [ + { + "bbox": [ + 106, + 396, + 506, + 408 + ], + "score": 1.0, + "content": "small number of levels (30), as we found mutations are significant enough to generate a diverse set of", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 407, + 266, + 418 + ], + "spans": [ + { + "bbox": [ + 106, + 407, + 266, + 418 + ], + "score": 1.0, + "content": "levels without a big starting population.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 20.5 + }, + { + "type": "image", + "bbox": [ + 124, + 429, + 486, + 457 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 124, + 429, + 486, + 457 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 124, + 429, + 486, + 457 + ], + "spans": [ + { + "bbox": [ + 124, + 429, + 486, + 457 + ], + "score": 0.944, + "type": "image", + "image_path": "042a059868c0553a7a60e438afd451a3c9c6cc9b670ad7daaf595ec5078a860b.jpg" + } + ] + } + ], + "index": 30, + "virtual_lines": [ + { + "bbox": [ + 124, + 429, + 486, + 438.3333333333333 + ], + "spans": [], + "index": 29 + }, + { + "bbox": [ + 124, + 438.3333333333333, + 486, + 447.66666666666663 + ], + "spans": [], + "index": 30 + }, + { + "bbox": [ + 124, + 447.66666666666663, + 486, + 456.99999999999994 + ], + "spans": [], + "index": 31 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 107, + 473, + 505, + 495 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 471, + 506, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 471, + 506, + 486 + ], + "score": 1.0, + "content": "Figure 4: Novelty search behavior characteristic. Left: level, Right: smoothed moving average of", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 484, + 170, + 497 + ], + "spans": [ + { + "bbox": [ + 105, + 484, + 170, + 497 + ], + "score": 1.0, + "content": "generated path.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 32.5 + } + ], + "index": 31.25 + }, + { + "type": "text", + "bbox": [ + 106, + 507, + 505, + 628 + ], + "lines": [ + { + "bbox": [ + 105, + 507, + 506, + 521 + ], + "spans": [ + { + "bbox": [ + 105, + 507, + 506, + 521 + ], + "score": 1.0, + "content": "Mutations: The LLM-based mutation operation introduced in this paper (Figure 3) transforms a", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 519, + 506, + 531 + ], + "spans": [ + { + "bbox": [ + 105, + 519, + 298, + 531 + ], + "score": 1.0, + "content": "randomly picked slice of a level (a slice between", + "type": "text" + }, + { + "bbox": [ + 299, + 519, + 332, + 529 + ], + "score": 0.69, + "content": "4 0 - 8 0", + "type": "inline_equation" + }, + { + "bbox": [ + 333, + 519, + 506, + 531 + ], + "score": 1.0, + "content": "columns) with a new MarioGPT prediction,", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 529, + 506, + 542 + ], + "spans": [ + { + "bbox": [ + 105, + 529, + 506, + 542 + ], + "score": 1.0, + "content": "guided by a random prompt. By itself, MarioGPT is able, through mutations, to produce a variety of", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 540, + 506, + 554 + ], + "spans": [ + { + "bbox": [ + 105, + 540, + 506, + 554 + ], + "score": 1.0, + "content": "levels with varying agent paths. However, because MarioGPT is a unidirectional model, we cannot", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 551, + 506, + 564 + ], + "spans": [ + { + "bbox": [ + 105, + 551, + 506, + 564 + ], + "score": 1.0, + "content": "guarantee that the new generated path is consistent with the rest of the level. To further improve path", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 563, + 505, + 575 + ], + "spans": [ + { + "bbox": [ + 105, + 563, + 505, + 575 + ], + "score": 1.0, + "content": "consistency, we incorporate a fine-tuned mask prediction model (which we call MarioBert), based on", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 573, + 505, + 586 + ], + "spans": [ + { + "bbox": [ + 105, + 573, + 505, + 586 + ], + "score": 1.0, + "content": "the Bert architecture. The BERT language model [7] is a bidirectional LLM that shows impressive", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 585, + 505, + 597 + ], + "spans": [ + { + "bbox": [ + 105, + 585, + 505, + 597 + ], + "score": 1.0, + "content": "performance in the task of mask prediction, which is analogous to image in-painting. This ability is", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 594, + 505, + 608 + ], + "spans": [ + { + "bbox": [ + 105, + 594, + 505, + 608 + ], + "score": 1.0, + "content": "ideal for our use case, where MarioBert is used to inpaint its border region after the newly sampled", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 606, + 506, + 618 + ], + "spans": [ + { + "bbox": [ + 106, + 606, + 506, + 618 + ], + "score": 1.0, + "content": "slice, smoothly joining the mutated slice and the rest of level. This can be observed in the second", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 617, + 297, + 630 + ], + "spans": [ + { + "bbox": [ + 106, + 617, + 297, + 630 + ], + "score": 1.0, + "content": "step of the \"Mutation process\" part of Figure 3.", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 39 + }, + { + "type": "title", + "bbox": [ + 108, + 644, + 253, + 657 + ], + "lines": [ + { + "bbox": [ + 104, + 642, + 255, + 660 + ], + "spans": [ + { + "bbox": [ + 104, + 642, + 255, + 660 + ], + "score": 1.0, + "content": "4 Experiments and Results", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 45 + }, + { + "type": "title", + "bbox": [ + 107, + 668, + 236, + 680 + ], + "lines": [ + { + "bbox": [ + 105, + 666, + 237, + 684 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 237, + 684 + ], + "score": 1.0, + "content": "4.1 Tile Prediction Accuracy", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 46 + }, + { + "type": "text", + "bbox": [ + 107, + 689, + 504, + 722 + ], + "lines": [ + { + "bbox": [ + 105, + 688, + 506, + 702 + ], + "spans": [ + { + "bbox": [ + 105, + 688, + 506, + 702 + ], + "score": 1.0, + "content": "To measure how proficient MarioGPT is in generating levels and because the majority of tiles in", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 700, + 506, + 713 + ], + "spans": [ + { + "bbox": [ + 105, + 700, + 506, + 713 + ], + "score": 1.0, + "content": "these levels are air tiles, we focus on comparing non-air tile prediction accuracy. We compare", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 711, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 711, + 506, + 723 + ], + "score": 1.0, + "content": "to baselines: LSTM, as proposed in Summerville and Mateas [38] and MarioGPT that is trained", + "type": "text" + } + ], + "index": 49 + } + ], + "index": 48 + } + ], + "page_idx": 4, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 302, + 741, + 309, + 750 + ], + "lines": [ + { + "bbox": [ + 301, + 740, + 310, + 753 + ], + "spans": [ + { + "bbox": [ + 301, + 740, + 310, + 753 + ], + "score": 1.0, + "content": "5", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 73, + 504, + 95 + ], + "lines": [ + { + "bbox": [ + 105, + 72, + 506, + 86 + ], + "spans": [ + { + "bbox": [ + 105, + 72, + 506, + 86 + ], + "score": 1.0, + "content": "In addition, it is possible to use synonyms for words. For example, changing “many” to “a lot” or “a", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 83, + 419, + 96 + ], + "spans": [ + { + "bbox": [ + 106, + 83, + 419, + 96 + ], + "score": 1.0, + "content": "ton”, produces similar results because the BART encoder can generalize well.", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5, + "bbox_fs": [ + 105, + 72, + 506, + 96 + ] + }, + { + "type": "title", + "bbox": [ + 106, + 108, + 378, + 119 + ], + "lines": [ + { + "bbox": [ + 105, + 107, + 379, + 122 + ], + "spans": [ + { + "bbox": [ + 105, + 107, + 379, + 122 + ], + "score": 1.0, + "content": "3.2 Open-Ended Mario Level Generation with Novelty Search", + "type": "text" + } + ], + "index": 2 + } + ], + "index": 2 + }, + { + "type": "text", + "bbox": [ + 106, + 128, + 505, + 237 + ], + "lines": [ + { + "bbox": [ + 105, + 128, + 506, + 141 + ], + "spans": [ + { + "bbox": [ + 105, + 128, + 506, + 141 + ], + "score": 1.0, + "content": "In the realm of PCG, it is important to not only generate levels with diverse physical features, but also", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 138, + 505, + 151 + ], + "spans": [ + { + "bbox": [ + 105, + 138, + 505, + 151 + ], + "score": 1.0, + "content": "levels that elicit a wide range of player behavior. When it comes to creating Mario levels, the focus", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 149, + 505, + 163 + ], + "spans": [ + { + "bbox": [ + 105, + 149, + 505, + 163 + ], + "score": 1.0, + "content": "is on the different paths a player can take to complete the level. This is often a challenge for many", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 161, + 505, + 173 + ], + "spans": [ + { + "bbox": [ + 105, + 161, + 505, + 173 + ], + "score": 1.0, + "content": "algorithms (such as [45, 8]) and requires the use of an external agent for evaluation. However, with", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 171, + 506, + 185 + ], + "spans": [ + { + "bbox": [ + 105, + 171, + 506, + 185 + ], + "score": 1.0, + "content": "MarioGPT, it is possible to generate diverse and controllable levels that approximate a realistic player", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 183, + 506, + 196 + ], + "spans": [ + { + "bbox": [ + 106, + 183, + 506, + 196 + ], + "score": 1.0, + "content": "path, reducing the need for an external agent and producing levels that are directly playable. To", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 194, + 506, + 206 + ], + "spans": [ + { + "bbox": [ + 106, + 194, + 506, + 206 + ], + "score": 1.0, + "content": "encourage diversity in generated levels, we integrate MarioGPT within a novelty search augmented", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 204, + 506, + 217 + ], + "spans": [ + { + "bbox": [ + 105, + 204, + 506, + 217 + ], + "score": 1.0, + "content": "genetic algorithm (NS-MarioGPT), where language-models play the role of mutation operators. As", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 106, + 216, + 506, + 228 + ], + "spans": [ + { + "bbox": [ + 106, + 216, + 506, + 228 + ], + "score": 1.0, + "content": "illustrated in Figure 3, NS-MarioGPT iteratively samples and mutates elite levels from an archive of", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 227, + 176, + 237 + ], + "spans": [ + { + "bbox": [ + 106, + 227, + 176, + 237 + ], + "score": 1.0, + "content": "generated levels.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 7.5, + "bbox_fs": [ + 105, + 128, + 506, + 237 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 243, + 505, + 417 + ], + "lines": [ + { + "bbox": [ + 105, + 241, + 505, + 255 + ], + "spans": [ + { + "bbox": [ + 105, + 241, + 505, + 255 + ], + "score": 1.0, + "content": "Novelty Search: Mutated levels are only stored in the archive if they achieve a higher novelty", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 254, + 506, + 266 + ], + "spans": [ + { + "bbox": [ + 105, + 254, + 506, + 266 + ], + "score": 1.0, + "content": "score compared to the previous elites. The novelty score is measured as the mean distance between", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 264, + 504, + 277 + ], + "spans": [ + { + "bbox": [ + 105, + 264, + 493, + 277 + ], + "score": 1.0, + "content": "the behavioral characteristic vector of the levels and the behavioral characteristic vector of the", + "type": "text" + }, + { + "bbox": [ + 493, + 265, + 504, + 275 + ], + "score": 0.74, + "content": "K", + "type": "inline_equation" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 276, + 506, + 288 + ], + "spans": [ + { + "bbox": [ + 106, + 276, + 249, + 288 + ], + "score": 1.0, + "content": "closest elements from the archive", + "type": "text" + }, + { + "bbox": [ + 250, + 276, + 260, + 286 + ], + "score": 0.75, + "content": "K", + "type": "inline_equation" + }, + { + "bbox": [ + 260, + 276, + 506, + 288 + ], + "score": 1.0, + "content": "-means). Our goal in level generation is to create paths that", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 287, + 505, + 299 + ], + "spans": [ + { + "bbox": [ + 106, + 287, + 505, + 299 + ], + "score": 1.0, + "content": "result in diverse player behavior, so we use predicted player paths as our basis for these behavior", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 298, + 506, + 310 + ], + "spans": [ + { + "bbox": [ + 106, + 298, + 506, + 310 + ], + "score": 1.0, + "content": "characteristics. More specifically, we are interested in the relative patterns of predicted paths. For", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 309, + 505, + 320 + ], + "spans": [ + { + "bbox": [ + 106, + 309, + 505, + 320 + ], + "score": 1.0, + "content": "instance, if a player character moves in a straight line on high elevated blocks, we want the path’s", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 104, + 319, + 506, + 332 + ], + "spans": [ + { + "bbox": [ + 104, + 319, + 506, + 332 + ], + "score": 1.0, + "content": "representation to be close in behavior space to a path that moves straight in lower elevation. To", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 330, + 506, + 343 + ], + "spans": [ + { + "bbox": [ + 106, + 330, + 506, + 343 + ], + "score": 1.0, + "content": "achieve this, we represent the behavior characteristic as the normalized average of the predicted", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 341, + 506, + 353 + ], + "spans": [ + { + "bbox": [ + 105, + 341, + 506, + 353 + ], + "score": 1.0, + "content": "path’s coordinates, allowing a smooth representation of paths (Figure 4). Thus the significance of", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 352, + 506, + 363 + ], + "spans": [ + { + "bbox": [ + 106, + 352, + 506, + 363 + ], + "score": 1.0, + "content": "a single block difference is reduced, making it harder for mutated levels to be added to the archive.", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 362, + 505, + 375 + ], + "spans": [ + { + "bbox": [ + 105, + 362, + 505, + 375 + ], + "score": 1.0, + "content": "This is desired because we don’t want the archive to fill up with levels that only vary slightly from the", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 374, + 506, + 386 + ], + "spans": [ + { + "bbox": [ + 106, + 374, + 506, + 386 + ], + "score": 1.0, + "content": "existing levels in the archive. For all our novelty search experiments, we use a small neighborhood of", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 384, + 506, + 397 + ], + "spans": [ + { + "bbox": [ + 105, + 384, + 506, + 397 + ], + "score": 1.0, + "content": "size 4, which results in a behavioral characteristic of dimension 100. We initialize our archive with a", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 396, + 506, + 408 + ], + "spans": [ + { + "bbox": [ + 106, + 396, + 506, + 408 + ], + "score": 1.0, + "content": "small number of levels (30), as we found mutations are significant enough to generate a diverse set of", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 407, + 266, + 418 + ], + "spans": [ + { + "bbox": [ + 106, + 407, + 266, + 418 + ], + "score": 1.0, + "content": "levels without a big starting population.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 20.5, + "bbox_fs": [ + 104, + 241, + 506, + 418 + ] + }, + { + "type": "image", + "bbox": [ + 124, + 429, + 486, + 457 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 124, + 429, + 486, + 457 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 124, + 429, + 486, + 457 + ], + "spans": [ + { + "bbox": [ + 124, + 429, + 486, + 457 + ], + "score": 0.944, + "type": "image", + "image_path": "042a059868c0553a7a60e438afd451a3c9c6cc9b670ad7daaf595ec5078a860b.jpg" + } + ] + } + ], + "index": 30, + "virtual_lines": [ + { + "bbox": [ + 124, + 429, + 486, + 438.3333333333333 + ], + "spans": [], + "index": 29 + }, + { + "bbox": [ + 124, + 438.3333333333333, + 486, + 447.66666666666663 + ], + "spans": [], + "index": 30 + }, + { + "bbox": [ + 124, + 447.66666666666663, + 486, + 456.99999999999994 + ], + "spans": [], + "index": 31 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 107, + 473, + 505, + 495 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 471, + 506, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 471, + 506, + 486 + ], + "score": 1.0, + "content": "Figure 4: Novelty search behavior characteristic. Left: level, Right: smoothed moving average of", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 484, + 170, + 497 + ], + "spans": [ + { + "bbox": [ + 105, + 484, + 170, + 497 + ], + "score": 1.0, + "content": "generated path.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 32.5 + } + ], + "index": 31.25 + }, + { + "type": "text", + "bbox": [ + 106, + 507, + 505, + 628 + ], + "lines": [ + { + "bbox": [ + 105, + 507, + 506, + 521 + ], + "spans": [ + { + "bbox": [ + 105, + 507, + 506, + 521 + ], + "score": 1.0, + "content": "Mutations: The LLM-based mutation operation introduced in this paper (Figure 3) transforms a", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 519, + 506, + 531 + ], + "spans": [ + { + "bbox": [ + 105, + 519, + 298, + 531 + ], + "score": 1.0, + "content": "randomly picked slice of a level (a slice between", + "type": "text" + }, + { + "bbox": [ + 299, + 519, + 332, + 529 + ], + "score": 0.69, + "content": "4 0 - 8 0", + "type": "inline_equation" + }, + { + "bbox": [ + 333, + 519, + 506, + 531 + ], + "score": 1.0, + "content": "columns) with a new MarioGPT prediction,", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 529, + 506, + 542 + ], + "spans": [ + { + "bbox": [ + 105, + 529, + 506, + 542 + ], + "score": 1.0, + "content": "guided by a random prompt. By itself, MarioGPT is able, through mutations, to produce a variety of", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 540, + 506, + 554 + ], + "spans": [ + { + "bbox": [ + 105, + 540, + 506, + 554 + ], + "score": 1.0, + "content": "levels with varying agent paths. However, because MarioGPT is a unidirectional model, we cannot", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 551, + 506, + 564 + ], + "spans": [ + { + "bbox": [ + 105, + 551, + 506, + 564 + ], + "score": 1.0, + "content": "guarantee that the new generated path is consistent with the rest of the level. To further improve path", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 563, + 505, + 575 + ], + "spans": [ + { + "bbox": [ + 105, + 563, + 505, + 575 + ], + "score": 1.0, + "content": "consistency, we incorporate a fine-tuned mask prediction model (which we call MarioBert), based on", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 573, + 505, + 586 + ], + "spans": [ + { + "bbox": [ + 105, + 573, + 505, + 586 + ], + "score": 1.0, + "content": "the Bert architecture. The BERT language model [7] is a bidirectional LLM that shows impressive", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 585, + 505, + 597 + ], + "spans": [ + { + "bbox": [ + 105, + 585, + 505, + 597 + ], + "score": 1.0, + "content": "performance in the task of mask prediction, which is analogous to image in-painting. This ability is", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 594, + 505, + 608 + ], + "spans": [ + { + "bbox": [ + 105, + 594, + 505, + 608 + ], + "score": 1.0, + "content": "ideal for our use case, where MarioBert is used to inpaint its border region after the newly sampled", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 606, + 506, + 618 + ], + "spans": [ + { + "bbox": [ + 106, + 606, + 506, + 618 + ], + "score": 1.0, + "content": "slice, smoothly joining the mutated slice and the rest of level. This can be observed in the second", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 617, + 297, + 630 + ], + "spans": [ + { + "bbox": [ + 106, + 617, + 297, + 630 + ], + "score": 1.0, + "content": "step of the \"Mutation process\" part of Figure 3.", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 39, + "bbox_fs": [ + 105, + 507, + 506, + 630 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 644, + 253, + 657 + ], + "lines": [ + { + "bbox": [ + 104, + 642, + 255, + 660 + ], + "spans": [ + { + "bbox": [ + 104, + 642, + 255, + 660 + ], + "score": 1.0, + "content": "4 Experiments and Results", + "type": "text" + } + ], + "index": 45 + } + ], + "index": 45 + }, + { + "type": "title", + "bbox": [ + 107, + 668, + 236, + 680 + ], + "lines": [ + { + "bbox": [ + 105, + 666, + 237, + 684 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 237, + 684 + ], + "score": 1.0, + "content": "4.1 Tile Prediction Accuracy", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 46 + }, + { + "type": "text", + "bbox": [ + 107, + 689, + 504, + 722 + ], + "lines": [ + { + "bbox": [ + 105, + 688, + 506, + 702 + ], + "spans": [ + { + "bbox": [ + 105, + 688, + 506, + 702 + ], + "score": 1.0, + "content": "To measure how proficient MarioGPT is in generating levels and because the majority of tiles in", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 700, + 506, + 713 + ], + "spans": [ + { + "bbox": [ + 105, + 700, + 506, + 713 + ], + "score": 1.0, + "content": "these levels are air tiles, we focus on comparing non-air tile prediction accuracy. We compare", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 711, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 711, + 506, + 723 + ], + "score": 1.0, + "content": "to baselines: LSTM, as proposed in Summerville and Mateas [38] and MarioGPT that is trained", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 106, + 180, + 505, + 192 + ], + "spans": [ + { + "bbox": [ + 106, + 180, + 505, + 192 + ], + "score": 1.0, + "content": "from scratch (without using pretrained GPT2 weights), with results reported in Table 1. For all our", + "type": "text", + "cross_page": true + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 190, + 506, + 204 + ], + "spans": [ + { + "bbox": [ + 105, + 190, + 506, + 204 + ], + "score": 1.0, + "content": "baselines, we train for the same amount (200,000 samples). The results show that MarioGPT (using a", + "type": "text", + "cross_page": true + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 201, + 507, + 214 + ], + "spans": [ + { + "bbox": [ + 104, + 201, + 507, + 214 + ], + "score": 1.0, + "content": "pretrained GPT2 model) outperforms all other baselines with regards to tile prediction. In addition,", + "type": "text", + "cross_page": true + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 212, + 506, + 225 + ], + "spans": [ + { + "bbox": [ + 105, + 212, + 506, + 225 + ], + "score": 1.0, + "content": "training MarioGPT from scratch and training an adapter layer (a small multi layer network on top of", + "type": "text", + "cross_page": true + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 222, + 506, + 237 + ], + "spans": [ + { + "bbox": [ + 105, + 222, + 506, + 237 + ], + "score": 1.0, + "content": "the original prediction layer) results in models that performs worse than even the LSTM baseline", + "type": "text", + "cross_page": true + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 234, + 505, + 247 + ], + "spans": [ + { + "bbox": [ + 106, + 234, + 505, + 247 + ], + "score": 1.0, + "content": "(given the 200,000 training samples). These models were trained with minimal hyperparameter", + "type": "text", + "cross_page": true + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 245, + 506, + 258 + ], + "spans": [ + { + "bbox": [ + 105, + 245, + 506, + 258 + ], + "score": 1.0, + "content": "search, so their performance can likely be improved. However, as a tangential point, this shows a", + "type": "text", + "cross_page": true + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 255, + 506, + 269 + ], + "spans": [ + { + "bbox": [ + 105, + 255, + 506, + 269 + ], + "score": 1.0, + "content": "major benefit of fine-tuning pretrained models, which seem to require much less effort in regards to", + "type": "text", + "cross_page": true + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 268, + 178, + 280 + ], + "spans": [ + { + "bbox": [ + 106, + 268, + 178, + 280 + ], + "score": 1.0, + "content": "hyperparameters.", + "type": "text", + "cross_page": true + } + ], + "index": 12 + } + ], + "index": 48, + "bbox_fs": [ + 105, + 688, + 506, + 723 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 168, + 89, + 443, + 157 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 185, + 78, + 426, + 88 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 184, + 77, + 427, + 90 + ], + "spans": [ + { + "bbox": [ + 184, + 77, + 427, + 90 + ], + "score": 1.0, + "content": "Table 1: Training Reconstruction Accuracy – Validation Set", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "table_body", + "bbox": [ + 168, + 89, + 443, + 157 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 168, + 89, + 443, + 157 + ], + "spans": [ + { + "bbox": [ + 168, + 89, + 443, + 157 + ], + "score": 0.981, + "html": "
ModelTile Acc.Path Acc.Promptable?
LSTM46%39%NO
from-scratch-MarioGPT31%23%YES
adapter-MarioGPT21%11%YES
MarioGPT93%91%YES
", + "type": "table", + "image_path": "fd7503bc856b6f5020a8e0441e611cb5211e64a2ebdb6a26f4d6e684a18df2bb.jpg" + } + ] + } + ], + "index": 2, + "virtual_lines": [ + { + "bbox": [ + 168, + 89, + 443, + 111.66666666666667 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 168, + 111.66666666666667, + 443, + 134.33333333333334 + ], + "spans": [], + "index": 2 + }, + { + "bbox": [ + 168, + 134.33333333333334, + 443, + 157.0 + ], + "spans": [], + "index": 3 + } + ] + } + ], + "index": 1.0 + }, + { + "type": "text", + "bbox": [ + 106, + 179, + 505, + 279 + ], + "lines": [ + { + "bbox": [ + 106, + 180, + 505, + 192 + ], + "spans": [ + { + "bbox": [ + 106, + 180, + 505, + 192 + ], + "score": 1.0, + "content": "from scratch (without using pretrained GPT2 weights), with results reported in Table 1. For all our", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 190, + 506, + 204 + ], + "spans": [ + { + "bbox": [ + 105, + 190, + 506, + 204 + ], + "score": 1.0, + "content": "baselines, we train for the same amount (200,000 samples). The results show that MarioGPT (using a", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 104, + 201, + 507, + 214 + ], + "spans": [ + { + "bbox": [ + 104, + 201, + 507, + 214 + ], + "score": 1.0, + "content": "pretrained GPT2 model) outperforms all other baselines with regards to tile prediction. In addition,", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 212, + 506, + 225 + ], + "spans": [ + { + "bbox": [ + 105, + 212, + 506, + 225 + ], + "score": 1.0, + "content": "training MarioGPT from scratch and training an adapter layer (a small multi layer network on top of", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 222, + 506, + 237 + ], + "spans": [ + { + "bbox": [ + 105, + 222, + 506, + 237 + ], + "score": 1.0, + "content": "the original prediction layer) results in models that performs worse than even the LSTM baseline", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 234, + 505, + 247 + ], + "spans": [ + { + "bbox": [ + 106, + 234, + 505, + 247 + ], + "score": 1.0, + "content": "(given the 200,000 training samples). These models were trained with minimal hyperparameter", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 245, + 506, + 258 + ], + "spans": [ + { + "bbox": [ + 105, + 245, + 506, + 258 + ], + "score": 1.0, + "content": "search, so their performance can likely be improved. However, as a tangential point, this shows a", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 255, + 506, + 269 + ], + "spans": [ + { + "bbox": [ + 105, + 255, + 506, + 269 + ], + "score": 1.0, + "content": "major benefit of fine-tuning pretrained models, which seem to require much less effort in regards to", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 268, + 178, + 280 + ], + "spans": [ + { + "bbox": [ + 106, + 268, + 178, + 280 + ], + "score": 1.0, + "content": "hyperparameters.", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 8 + }, + { + "type": "title", + "bbox": [ + 108, + 293, + 265, + 306 + ], + "lines": [ + { + "bbox": [ + 105, + 292, + 267, + 308 + ], + "spans": [ + { + "bbox": [ + 105, + 292, + 267, + 308 + ], + "score": 1.0, + "content": "4.2 Measuring Playability of Levels", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 13 + }, + { + "type": "text", + "bbox": [ + 106, + 314, + 505, + 490 + ], + "lines": [ + { + "bbox": [ + 104, + 313, + 506, + 328 + ], + "spans": [ + { + "bbox": [ + 104, + 313, + 329, + 328 + ], + "score": 1.0, + "content": "To test for playability, we deploy Robin Baumgarten’s", + "type": "text" + }, + { + "bbox": [ + 330, + 315, + 344, + 325 + ], + "score": 0.76, + "content": "\\mathbf { A } ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 344, + 313, + 506, + 328 + ], + "score": 1.0, + "content": "agent [43, 19] in 250 generated levels*.", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 326, + 505, + 338 + ], + "spans": [ + { + "bbox": [ + 106, + 326, + 295, + 338 + ], + "score": 1.0, + "content": "The reason for choosing Robin Baumgarten’s", + "type": "text" + }, + { + "bbox": [ + 295, + 326, + 309, + 336 + ], + "score": 0.82, + "content": "\\mathbf { A } ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 309, + 326, + 505, + 338 + ], + "score": 1.0, + "content": "agent for measuring playability comes from its", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 337, + 505, + 349 + ], + "spans": [ + { + "bbox": [ + 105, + 337, + 505, + 349 + ], + "score": 1.0, + "content": "performance on the 2009 Mario AI competition, where it beat handcrafted controllers and even simple", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 347, + 505, + 360 + ], + "spans": [ + { + "bbox": [ + 105, + 347, + 505, + 360 + ], + "score": 1.0, + "content": "evolved neural networks on getting the furthest in an infinite-level setting, as well as solving a corpus", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 357, + 506, + 371 + ], + "spans": [ + { + "bbox": [ + 105, + 357, + 216, + 371 + ], + "score": 1.0, + "content": "of levels [43]. We find that", + "type": "text" + }, + { + "bbox": [ + 216, + 358, + 243, + 369 + ], + "score": 0.87, + "content": "8 8 . 4 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 244, + 357, + 506, + 371 + ], + "score": 1.0, + "content": "of all MarioGPT-generated levels can be completed by the agent,", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 370, + 506, + 382 + ], + "spans": [ + { + "bbox": [ + 106, + 370, + 506, + 382 + ], + "score": 1.0, + "content": "and are therefore considered playable (compared to the best baseline, the LSTM, which achieves", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 380, + 505, + 393 + ], + "spans": [ + { + "bbox": [ + 105, + 380, + 138, + 393 + ], + "score": 1.0, + "content": "around", + "type": "text" + }, + { + "bbox": [ + 138, + 380, + 158, + 391 + ], + "score": 0.87, + "content": "31 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 159, + 380, + 505, + 393 + ], + "score": 1.0, + "content": "solvable levels). Moreover, we find that only one of the successful levels needed a retry", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 391, + 505, + 403 + ], + "spans": [ + { + "bbox": [ + 105, + 391, + 141, + 403 + ], + "score": 1.0, + "content": "with the", + "type": "text" + }, + { + "bbox": [ + 141, + 392, + 155, + 402 + ], + "score": 0.77, + "content": "\\mathbf { A } ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 155, + 391, + 491, + 403 + ], + "score": 1.0, + "content": "agent. We further test whether the path generated by the model matches that of the", + "type": "text" + }, + { + "bbox": [ + 491, + 392, + 505, + 401 + ], + "score": 0.77, + "content": "\\mathbf { A } ^ { * }", + "type": "inline_equation" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 401, + 506, + 415 + ], + "spans": [ + { + "bbox": [ + 105, + 401, + 506, + 415 + ], + "score": 1.0, + "content": "agent to assess their feasibility. Table 2 shows the mean absolute error (MAE) between suggested and", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 413, + 505, + 426 + ], + "spans": [ + { + "bbox": [ + 105, + 413, + 505, + 426 + ], + "score": 1.0, + "content": "actual agent path for playable and not playable levels respectively. We see that for playable levels, the", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 424, + 506, + 436 + ], + "spans": [ + { + "bbox": [ + 105, + 424, + 506, + 436 + ], + "score": 1.0, + "content": "MAE between the path generated by the model and the actually taken path by the agent is 1.15 tiles,", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 434, + 506, + 447 + ], + "spans": [ + { + "bbox": [ + 106, + 434, + 506, + 447 + ], + "score": 1.0, + "content": "i.e. paths are on average about 1 tile apart. For the non-playable levels, this average difference of", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 445, + 506, + 458 + ], + "spans": [ + { + "bbox": [ + 105, + 445, + 506, + 458 + ], + "score": 1.0, + "content": "taken paths is significantly higher with 4.56 tiles. Thus, we can conclude that in playable levels, the", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 456, + 506, + 469 + ], + "spans": [ + { + "bbox": [ + 105, + 456, + 506, + 469 + ], + "score": 1.0, + "content": "agent mostly takes a similar path as the one generated by the model. The significantly higher MAE", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 468, + 506, + 480 + ], + "spans": [ + { + "bbox": [ + 106, + 468, + 506, + 480 + ], + "score": 1.0, + "content": "of 4.56 in non-playable levels on the other hand indicates that the path generated by the models in", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 478, + 288, + 491 + ], + "spans": [ + { + "bbox": [ + 105, + 478, + 288, + 491 + ], + "score": 1.0, + "content": "these cases may not be feasible for the agent.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 21.5 + }, + { + "type": "table", + "bbox": [ + 234, + 553, + 376, + 588 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 106, + 509, + 507, + 552 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 105, + 509, + 507, + 523 + ], + "spans": [ + { + "bbox": [ + 105, + 509, + 465, + 523 + ], + "score": 1.0, + "content": "Table 2: Mean average error (MAE) between paths suggested by model and Baumgarten’s", + "type": "text" + }, + { + "bbox": [ + 466, + 510, + 479, + 520 + ], + "score": 0.83, + "content": "\\mathbf { A } ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 480, + 509, + 507, + 523 + ], + "score": 1.0, + "content": "agent.", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 520, + 506, + 533 + ], + "spans": [ + { + "bbox": [ + 106, + 520, + 506, + 533 + ], + "score": 1.0, + "content": "Results are averaged over 5 runs per level to account for minor stochastic variation in agent simulation.", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 531, + 505, + 543 + ], + "spans": [ + { + "bbox": [ + 106, + 531, + 226, + 543 + ], + "score": 1.0, + "content": "MAEs are computed between", + "type": "text" + }, + { + "bbox": [ + 227, + 533, + 234, + 542 + ], + "score": 0.56, + "content": "y", + "type": "inline_equation" + }, + { + "bbox": [ + 234, + 531, + 448, + 543 + ], + "score": 1.0, + "content": "coordinates of path trajectories for every point on the", + "type": "text" + }, + { + "bbox": [ + 448, + 533, + 455, + 541 + ], + "score": 0.78, + "content": "x", + "type": "inline_equation" + }, + { + "bbox": [ + 456, + 531, + 505, + 543 + ], + "score": 1.0, + "content": "axis (which", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 542, + 313, + 555 + ], + "spans": [ + { + "bbox": [ + 105, + 542, + 313, + 555 + ], + "score": 1.0, + "content": "goes across the level) both trajectories have visited.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 31.5 + }, + { + "type": "table_body", + "bbox": [ + 234, + 553, + 376, + 588 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 234, + 553, + 376, + 588 + ], + "spans": [ + { + "bbox": [ + 234, + 553, + 376, + 588 + ], + "score": 0.967, + "html": "
PlayableNot PlayableAll
1.154.561.56
", + "type": "table", + "image_path": "d9701067ac77f16799d9a12493db1efca3e920680e9c02df606d1ea65a192347.jpg" + } + ] + } + ], + "index": 34.5, + "virtual_lines": [ + { + "bbox": [ + 234, + 553, + 376, + 570.5 + ], + "spans": [], + "index": 34 + }, + { + "bbox": [ + 234, + 570.5, + 376, + 588.0 + ], + "spans": [], + "index": 35 + } + ] + } + ], + "index": 33.0 + }, + { + "type": "text", + "bbox": [ + 106, + 606, + 505, + 651 + ], + "lines": [ + { + "bbox": [ + 106, + 607, + 505, + 618 + ], + "spans": [ + { + "bbox": [ + 106, + 607, + 505, + 618 + ], + "score": 1.0, + "content": "Considering the MAE of 1.56 tiles for paths in all levels, we can conclude that in the majority of the", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 616, + 505, + 632 + ], + "spans": [ + { + "bbox": [ + 105, + 616, + 505, + 632 + ], + "score": 1.0, + "content": "cases, the path generated by the model is similar to the path taken by an actual agent, and having", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 629, + 505, + 641 + ], + "spans": [ + { + "bbox": [ + 106, + 629, + 505, + 641 + ], + "score": 1.0, + "content": "the model generate a path through the level jointly with the level is an effective approach to obtain", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 640, + 275, + 652 + ], + "spans": [ + { + "bbox": [ + 106, + 640, + 275, + 652 + ], + "score": 1.0, + "content": "high-quality levels in terms of playability.", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 37.5 + }, + { + "type": "text", + "bbox": [ + 108, + 656, + 503, + 689 + ], + "lines": [ + { + "bbox": [ + 106, + 656, + 505, + 668 + ], + "spans": [ + { + "bbox": [ + 106, + 656, + 505, + 668 + ], + "score": 1.0, + "content": "To investigate the quality of the generated paths further, we visualize the paths with the most, least", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 667, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 106, + 667, + 505, + 678 + ], + "score": 1.0, + "content": "and median overlap (i.e. the levels corresponding to the maximum, minimum and median values for", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 678, + 483, + 690 + ], + "spans": [ + { + "bbox": [ + 106, + 678, + 483, + 690 + ], + "score": 1.0, + "content": "the mean absolute error in height) as well as two interesting handpicked examples in Figure 5.", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 41 + } + ], + "page_idx": 5, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 106, + 701, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 119, + 699, + 505, + 714 + ], + "spans": [ + { + "bbox": [ + 119, + 699, + 505, + 714 + ], + "score": 1.0, + "content": "*Since the agent’s performance depends on the available compute, we test for playability by running each", + "type": "text" + } + ] + }, + { + "bbox": [ + 105, + 709, + 158, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 158, + 723 + ], + "score": 1.0, + "content": "level 5 times.", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 742, + 309, + 750 + ], + "lines": [ + { + "bbox": [ + 302, + 741, + 310, + 752 + ], + "spans": [ + { + "bbox": [ + 302, + 741, + 310, + 752 + ], + "score": 1.0, + "content": "6", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "table", + "bbox": [ + 168, + 89, + 443, + 157 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 185, + 78, + 426, + 88 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 184, + 77, + 427, + 90 + ], + "spans": [ + { + "bbox": [ + 184, + 77, + 427, + 90 + ], + "score": 1.0, + "content": "Table 1: Training Reconstruction Accuracy – Validation Set", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "table_body", + "bbox": [ + 168, + 89, + 443, + 157 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 168, + 89, + 443, + 157 + ], + "spans": [ + { + "bbox": [ + 168, + 89, + 443, + 157 + ], + "score": 0.981, + "html": "
ModelTile Acc.Path Acc.Promptable?
LSTM46%39%NO
from-scratch-MarioGPT31%23%YES
adapter-MarioGPT21%11%YES
MarioGPT93%91%YES
", + "type": "table", + "image_path": "fd7503bc856b6f5020a8e0441e611cb5211e64a2ebdb6a26f4d6e684a18df2bb.jpg" + } + ] + } + ], + "index": 2, + "virtual_lines": [ + { + "bbox": [ + 168, + 89, + 443, + 111.66666666666667 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 168, + 111.66666666666667, + 443, + 134.33333333333334 + ], + "spans": [], + "index": 2 + }, + { + "bbox": [ + 168, + 134.33333333333334, + 443, + 157.0 + ], + "spans": [], + "index": 3 + } + ] + } + ], + "index": 1.0 + }, + { + "type": "text", + "bbox": [ + 106, + 179, + 505, + 279 + ], + "lines": [], + "index": 8, + "bbox_fs": [ + 104, + 180, + 507, + 280 + ], + "lines_deleted": true + }, + { + "type": "title", + "bbox": [ + 108, + 293, + 265, + 306 + ], + "lines": [ + { + "bbox": [ + 105, + 292, + 267, + 308 + ], + "spans": [ + { + "bbox": [ + 105, + 292, + 267, + 308 + ], + "score": 1.0, + "content": "4.2 Measuring Playability of Levels", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 13 + }, + { + "type": "text", + "bbox": [ + 106, + 314, + 505, + 490 + ], + "lines": [ + { + "bbox": [ + 104, + 313, + 506, + 328 + ], + "spans": [ + { + "bbox": [ + 104, + 313, + 329, + 328 + ], + "score": 1.0, + "content": "To test for playability, we deploy Robin Baumgarten’s", + "type": "text" + }, + { + "bbox": [ + 330, + 315, + 344, + 325 + ], + "score": 0.76, + "content": "\\mathbf { A } ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 344, + 313, + 506, + 328 + ], + "score": 1.0, + "content": "agent [43, 19] in 250 generated levels*.", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 326, + 505, + 338 + ], + "spans": [ + { + "bbox": [ + 106, + 326, + 295, + 338 + ], + "score": 1.0, + "content": "The reason for choosing Robin Baumgarten’s", + "type": "text" + }, + { + "bbox": [ + 295, + 326, + 309, + 336 + ], + "score": 0.82, + "content": "\\mathbf { A } ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 309, + 326, + 505, + 338 + ], + "score": 1.0, + "content": "agent for measuring playability comes from its", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 337, + 505, + 349 + ], + "spans": [ + { + "bbox": [ + 105, + 337, + 505, + 349 + ], + "score": 1.0, + "content": "performance on the 2009 Mario AI competition, where it beat handcrafted controllers and even simple", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 347, + 505, + 360 + ], + "spans": [ + { + "bbox": [ + 105, + 347, + 505, + 360 + ], + "score": 1.0, + "content": "evolved neural networks on getting the furthest in an infinite-level setting, as well as solving a corpus", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 357, + 506, + 371 + ], + "spans": [ + { + "bbox": [ + 105, + 357, + 216, + 371 + ], + "score": 1.0, + "content": "of levels [43]. We find that", + "type": "text" + }, + { + "bbox": [ + 216, + 358, + 243, + 369 + ], + "score": 0.87, + "content": "8 8 . 4 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 244, + 357, + 506, + 371 + ], + "score": 1.0, + "content": "of all MarioGPT-generated levels can be completed by the agent,", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 370, + 506, + 382 + ], + "spans": [ + { + "bbox": [ + 106, + 370, + 506, + 382 + ], + "score": 1.0, + "content": "and are therefore considered playable (compared to the best baseline, the LSTM, which achieves", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 380, + 505, + 393 + ], + "spans": [ + { + "bbox": [ + 105, + 380, + 138, + 393 + ], + "score": 1.0, + "content": "around", + "type": "text" + }, + { + "bbox": [ + 138, + 380, + 158, + 391 + ], + "score": 0.87, + "content": "31 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 159, + 380, + 505, + 393 + ], + "score": 1.0, + "content": "solvable levels). Moreover, we find that only one of the successful levels needed a retry", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 391, + 505, + 403 + ], + "spans": [ + { + "bbox": [ + 105, + 391, + 141, + 403 + ], + "score": 1.0, + "content": "with the", + "type": "text" + }, + { + "bbox": [ + 141, + 392, + 155, + 402 + ], + "score": 0.77, + "content": "\\mathbf { A } ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 155, + 391, + 491, + 403 + ], + "score": 1.0, + "content": "agent. We further test whether the path generated by the model matches that of the", + "type": "text" + }, + { + "bbox": [ + 491, + 392, + 505, + 401 + ], + "score": 0.77, + "content": "\\mathbf { A } ^ { * }", + "type": "inline_equation" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 401, + 506, + 415 + ], + "spans": [ + { + "bbox": [ + 105, + 401, + 506, + 415 + ], + "score": 1.0, + "content": "agent to assess their feasibility. Table 2 shows the mean absolute error (MAE) between suggested and", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 413, + 505, + 426 + ], + "spans": [ + { + "bbox": [ + 105, + 413, + 505, + 426 + ], + "score": 1.0, + "content": "actual agent path for playable and not playable levels respectively. We see that for playable levels, the", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 424, + 506, + 436 + ], + "spans": [ + { + "bbox": [ + 105, + 424, + 506, + 436 + ], + "score": 1.0, + "content": "MAE between the path generated by the model and the actually taken path by the agent is 1.15 tiles,", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 434, + 506, + 447 + ], + "spans": [ + { + "bbox": [ + 106, + 434, + 506, + 447 + ], + "score": 1.0, + "content": "i.e. paths are on average about 1 tile apart. For the non-playable levels, this average difference of", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 445, + 506, + 458 + ], + "spans": [ + { + "bbox": [ + 105, + 445, + 506, + 458 + ], + "score": 1.0, + "content": "taken paths is significantly higher with 4.56 tiles. Thus, we can conclude that in playable levels, the", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 456, + 506, + 469 + ], + "spans": [ + { + "bbox": [ + 105, + 456, + 506, + 469 + ], + "score": 1.0, + "content": "agent mostly takes a similar path as the one generated by the model. The significantly higher MAE", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 468, + 506, + 480 + ], + "spans": [ + { + "bbox": [ + 106, + 468, + 506, + 480 + ], + "score": 1.0, + "content": "of 4.56 in non-playable levels on the other hand indicates that the path generated by the models in", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 478, + 288, + 491 + ], + "spans": [ + { + "bbox": [ + 105, + 478, + 288, + 491 + ], + "score": 1.0, + "content": "these cases may not be feasible for the agent.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 21.5, + "bbox_fs": [ + 104, + 313, + 506, + 491 + ] + }, + { + "type": "table", + "bbox": [ + 234, + 553, + 376, + 588 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 106, + 509, + 507, + 552 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 105, + 509, + 507, + 523 + ], + "spans": [ + { + "bbox": [ + 105, + 509, + 465, + 523 + ], + "score": 1.0, + "content": "Table 2: Mean average error (MAE) between paths suggested by model and Baumgarten’s", + "type": "text" + }, + { + "bbox": [ + 466, + 510, + 479, + 520 + ], + "score": 0.83, + "content": "\\mathbf { A } ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 480, + 509, + 507, + 523 + ], + "score": 1.0, + "content": "agent.", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 520, + 506, + 533 + ], + "spans": [ + { + "bbox": [ + 106, + 520, + 506, + 533 + ], + "score": 1.0, + "content": "Results are averaged over 5 runs per level to account for minor stochastic variation in agent simulation.", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 531, + 505, + 543 + ], + "spans": [ + { + "bbox": [ + 106, + 531, + 226, + 543 + ], + "score": 1.0, + "content": "MAEs are computed between", + "type": "text" + }, + { + "bbox": [ + 227, + 533, + 234, + 542 + ], + "score": 0.56, + "content": "y", + "type": "inline_equation" + }, + { + "bbox": [ + 234, + 531, + 448, + 543 + ], + "score": 1.0, + "content": "coordinates of path trajectories for every point on the", + "type": "text" + }, + { + "bbox": [ + 448, + 533, + 455, + 541 + ], + "score": 0.78, + "content": "x", + "type": "inline_equation" + }, + { + "bbox": [ + 456, + 531, + 505, + 543 + ], + "score": 1.0, + "content": "axis (which", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 542, + 313, + 555 + ], + "spans": [ + { + "bbox": [ + 105, + 542, + 313, + 555 + ], + "score": 1.0, + "content": "goes across the level) both trajectories have visited.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 31.5 + }, + { + "type": "table_body", + "bbox": [ + 234, + 553, + 376, + 588 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 234, + 553, + 376, + 588 + ], + "spans": [ + { + "bbox": [ + 234, + 553, + 376, + 588 + ], + "score": 0.967, + "html": "
PlayableNot PlayableAll
1.154.561.56
", + "type": "table", + "image_path": "d9701067ac77f16799d9a12493db1efca3e920680e9c02df606d1ea65a192347.jpg" + } + ] + } + ], + "index": 34.5, + "virtual_lines": [ + { + "bbox": [ + 234, + 553, + 376, + 570.5 + ], + "spans": [], + "index": 34 + }, + { + "bbox": [ + 234, + 570.5, + 376, + 588.0 + ], + "spans": [], + "index": 35 + } + ] + } + ], + "index": 33.0 + }, + { + "type": "text", + "bbox": [ + 106, + 606, + 505, + 651 + ], + "lines": [ + { + "bbox": [ + 106, + 607, + 505, + 618 + ], + "spans": [ + { + "bbox": [ + 106, + 607, + 505, + 618 + ], + "score": 1.0, + "content": "Considering the MAE of 1.56 tiles for paths in all levels, we can conclude that in the majority of the", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 616, + 505, + 632 + ], + "spans": [ + { + "bbox": [ + 105, + 616, + 505, + 632 + ], + "score": 1.0, + "content": "cases, the path generated by the model is similar to the path taken by an actual agent, and having", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 629, + 505, + 641 + ], + "spans": [ + { + "bbox": [ + 106, + 629, + 505, + 641 + ], + "score": 1.0, + "content": "the model generate a path through the level jointly with the level is an effective approach to obtain", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 640, + 275, + 652 + ], + "spans": [ + { + "bbox": [ + 106, + 640, + 275, + 652 + ], + "score": 1.0, + "content": "high-quality levels in terms of playability.", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 37.5, + "bbox_fs": [ + 105, + 607, + 505, + 652 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 656, + 503, + 689 + ], + "lines": [ + { + "bbox": [ + 106, + 656, + 505, + 668 + ], + "spans": [ + { + "bbox": [ + 106, + 656, + 505, + 668 + ], + "score": 1.0, + "content": "To investigate the quality of the generated paths further, we visualize the paths with the most, least", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 667, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 106, + 667, + 505, + 678 + ], + "score": 1.0, + "content": "and median overlap (i.e. the levels corresponding to the maximum, minimum and median values for", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 678, + 483, + 690 + ], + "spans": [ + { + "bbox": [ + 106, + 678, + 483, + 690 + ], + "score": 1.0, + "content": "the mean absolute error in height) as well as two interesting handpicked examples in Figure 5.", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 41, + "bbox_fs": [ + 106, + 656, + 505, + 690 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 72, + 506, + 193 + ], + "lines": [ + { + "bbox": [ + 106, + 73, + 506, + 85 + ], + "spans": [ + { + "bbox": [ + 106, + 73, + 506, + 85 + ], + "score": 1.0, + "content": "Figures 5d and 5e show that paths generated by MarioGPT tend to have more airtime than Baum-", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 83, + 506, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 83, + 506, + 96 + ], + "score": 1.0, + "content": "garten’s agent in the sense that they only weakly take into account \"gravity\". This result may be", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 104, + 93, + 506, + 108 + ], + "spans": [ + { + "bbox": [ + 104, + 93, + 506, + 108 + ], + "score": 1.0, + "content": "attributed to the nature of the path annotations in the models training set. In Summerville et al. [40],", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 107, + 106, + 505, + 117 + ], + "spans": [ + { + "bbox": [ + 107, + 106, + 180, + 117 + ], + "score": 1.0, + "content": "the authors use an", + "type": "text" + }, + { + "bbox": [ + 181, + 106, + 195, + 116 + ], + "score": 0.81, + "content": "\\mathbf { A } ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 195, + 106, + 505, + 117 + ], + "score": 1.0, + "content": "path solver to find a path through the level, while an actual agent, such as the", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 116, + 505, + 128 + ], + "spans": [ + { + "bbox": [ + 105, + 116, + 505, + 128 + ], + "score": 1.0, + "content": "one we used for comparison here, is more strongly bound by game physics (especially \"gravity\") and", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 127, + 506, + 140 + ], + "spans": [ + { + "bbox": [ + 105, + 127, + 506, + 140 + ], + "score": 1.0, + "content": "has to avoid enemies in the level. A second reason for non-playable levels can be seen in Figure 5c:", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 138, + 505, + 150 + ], + "spans": [ + { + "bbox": [ + 106, + 138, + 505, + 150 + ], + "score": 1.0, + "content": "Baumgarten’s agent is spawned in a tight space from which it can not escape, while the model has", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 148, + 506, + 163 + ], + "spans": [ + { + "bbox": [ + 104, + 148, + 506, + 163 + ], + "score": 1.0, + "content": "generated a path that traverses beyond the actual level, again a path that would likely be suggested by", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 104, + 158, + 506, + 174 + ], + "spans": [ + { + "bbox": [ + 104, + 158, + 506, + 174 + ], + "score": 1.0, + "content": "a solver. We argue that these issues can in part be attributed to the paths in the training data stemming", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 170, + 505, + 183 + ], + "spans": [ + { + "bbox": [ + 105, + 170, + 505, + 183 + ], + "score": 1.0, + "content": "from a solver rather than an actual agent, and could be alleviated in future work by annotating the", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 183, + 308, + 194 + ], + "spans": [ + { + "bbox": [ + 106, + 183, + 308, + 194 + ], + "score": 1.0, + "content": "training data with the trajectories of actual agents.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 5 + }, + { + "type": "image", + "bbox": [ + 164, + 203, + 447, + 392 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 164, + 203, + 447, + 392 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 164, + 203, + 447, + 392 + ], + "spans": [ + { + "bbox": [ + 164, + 203, + 447, + 392 + ], + "score": 0.976, + "type": "image", + "image_path": "b78426ce06283b9732abb3b14fa1a167f5be8825be0c2fcd2139ac575dcb3141.jpg" + } + ] + } + ], + "index": 12, + "virtual_lines": [ + { + "bbox": [ + 164, + 203, + 447, + 266.0 + ], + "spans": [], + "index": 11 + }, + { + "bbox": [ + 164, + 266.0, + 447, + 329.0 + ], + "spans": [], + "index": 12 + }, + { + "bbox": [ + 164, + 329.0, + 447, + 392.0 + ], + "spans": [], + "index": 13 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 398, + 505, + 465 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 398, + 506, + 411 + ], + "spans": [ + { + "bbox": [ + 106, + 398, + 147, + 411 + ], + "score": 1.0, + "content": "Figure 5:", + "type": "text" + }, + { + "bbox": [ + 147, + 399, + 161, + 410 + ], + "score": 0.59, + "content": "\\mathbf { A } ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 162, + 398, + 506, + 411 + ], + "score": 1.0, + "content": "vs. MarioGPT generated paths. Levels with (a) minimum (0.02), (a) median (0.89)", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 409, + 506, + 422 + ], + "spans": [ + { + "bbox": [ + 105, + 409, + 429, + 422 + ], + "score": 1.0, + "content": "and (a) maximum (11.0) mean absolute error (MAE) between trajectory of actual", + "type": "text" + }, + { + "bbox": [ + 430, + 410, + 443, + 420 + ], + "score": 0.81, + "content": "\\mathbf { A } ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 444, + 409, + 506, + 422 + ], + "score": 1.0, + "content": "agent (denoted", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 421, + 505, + 434 + ], + "spans": [ + { + "bbox": [ + 105, + 421, + 505, + 434 + ], + "score": 1.0, + "content": "as A), and model suggestion (denoted as P), as well as interesting hand-picked examples. Positions", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 432, + 505, + 444 + ], + "spans": [ + { + "bbox": [ + 105, + 432, + 505, + 444 + ], + "score": 1.0, + "content": "where both trajectories overlap are marked with *. Paths suggested by the model generally tend to", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 442, + 506, + 456 + ], + "spans": [ + { + "bbox": [ + 105, + 442, + 213, + 456 + ], + "score": 1.0, + "content": "have more airtime than the", + "type": "text" + }, + { + "bbox": [ + 214, + 443, + 227, + 453 + ], + "score": 0.7, + "content": "\\mathbf { A } ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 228, + 442, + 506, + 456 + ], + "score": 1.0, + "content": "agent (d, e), likely due to game physics not being accounted for in the", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 453, + 289, + 466 + ], + "spans": [ + { + "bbox": [ + 106, + 453, + 289, + 466 + ], + "score": 1.0, + "content": "original path annotations of the training data.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 16.5 + } + ], + "index": 14.25 + }, + { + "type": "title", + "bbox": [ + 107, + 484, + 246, + 496 + ], + "lines": [ + { + "bbox": [ + 105, + 482, + 247, + 499 + ], + "spans": [ + { + "bbox": [ + 105, + 482, + 247, + 499 + ], + "score": 1.0, + "content": "4.3 Is MarioGPT memorizing?", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 144, + 509, + 467, + 627 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 144, + 509, + 467, + 627 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 144, + 509, + 467, + 627 + ], + "spans": [ + { + "bbox": [ + 144, + 509, + 467, + 627 + ], + "score": 0.973, + "type": "image", + "image_path": "03847a0c8d25f6319ea8e373ca069b827d2df759372e6d48ae6240ba803a9e47.jpg" + } + ] + } + ], + "index": 22, + "virtual_lines": [ + { + "bbox": [ + 144, + 509, + 467, + 548.3333333333334 + ], + "spans": [], + "index": 21 + }, + { + "bbox": [ + 144, + 548.3333333333334, + 467, + 587.6666666666667 + ], + "spans": [], + "index": 22 + }, + { + "bbox": [ + 144, + 587.6666666666667, + 467, + 627.0000000000001 + ], + "spans": [], + "index": 23 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 632, + 504, + 655 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 106, + 632, + 505, + 645 + ], + "spans": [ + { + "bbox": [ + 106, + 632, + 505, + 645 + ], + "score": 1.0, + "content": "Figure 6: Generated levels vs closest in dataset. Temperature of 1.0 ends up spitting out almost", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 643, + 453, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 643, + 453, + 657 + ], + "score": 1.0, + "content": "exactly what is in the dataset, while increasing temperature improves sample diversity.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 24.5 + } + ], + "index": 23.25 + }, + { + "type": "text", + "bbox": [ + 107, + 667, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 106, + 667, + 505, + 679 + ], + "spans": [ + { + "bbox": [ + 106, + 667, + 505, + 679 + ], + "score": 1.0, + "content": "Memorization dynamics in LLMs remain an open problem when training transformer architectures", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 677, + 505, + 691 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 505, + 691 + ], + "score": 1.0, + "content": "[41, 5, 16]. While LLMs are incredibly powerful, they can sometimes overfit extremely and end up", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 104, + 689, + 506, + 701 + ], + "spans": [ + { + "bbox": [ + 104, + 689, + 506, + 701 + ], + "score": 1.0, + "content": "regurgitating training data. One popular way to alleviate this issue is to add some randomness in", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 699, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 506, + 712 + ], + "score": 1.0, + "content": "predictions in the form a tunable \"temperature\" parameter [17]. To evaluate whether MarioGPT is", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 711, + 506, + 724 + ], + "spans": [ + { + "bbox": [ + 105, + 711, + 506, + 724 + ], + "score": 1.0, + "content": "generating levels that are identical to the training set, we sample with different temperature parameters", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 28 + } + ], + "page_idx": 6, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 302, + 741, + 308, + 750 + ], + "lines": [ + { + "bbox": [ + 302, + 741, + 309, + 752 + ], + "spans": [ + { + "bbox": [ + 302, + 741, + 309, + 752 + ], + "score": 1.0, + "content": "7", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 72, + 506, + 193 + ], + "lines": [ + { + "bbox": [ + 106, + 73, + 506, + 85 + ], + "spans": [ + { + "bbox": [ + 106, + 73, + 506, + 85 + ], + "score": 1.0, + "content": "Figures 5d and 5e show that paths generated by MarioGPT tend to have more airtime than Baum-", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 83, + 506, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 83, + 506, + 96 + ], + "score": 1.0, + "content": "garten’s agent in the sense that they only weakly take into account \"gravity\". This result may be", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 104, + 93, + 506, + 108 + ], + "spans": [ + { + "bbox": [ + 104, + 93, + 506, + 108 + ], + "score": 1.0, + "content": "attributed to the nature of the path annotations in the models training set. In Summerville et al. [40],", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 107, + 106, + 505, + 117 + ], + "spans": [ + { + "bbox": [ + 107, + 106, + 180, + 117 + ], + "score": 1.0, + "content": "the authors use an", + "type": "text" + }, + { + "bbox": [ + 181, + 106, + 195, + 116 + ], + "score": 0.81, + "content": "\\mathbf { A } ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 195, + 106, + 505, + 117 + ], + "score": 1.0, + "content": "path solver to find a path through the level, while an actual agent, such as the", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 116, + 505, + 128 + ], + "spans": [ + { + "bbox": [ + 105, + 116, + 505, + 128 + ], + "score": 1.0, + "content": "one we used for comparison here, is more strongly bound by game physics (especially \"gravity\") and", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 127, + 506, + 140 + ], + "spans": [ + { + "bbox": [ + 105, + 127, + 506, + 140 + ], + "score": 1.0, + "content": "has to avoid enemies in the level. A second reason for non-playable levels can be seen in Figure 5c:", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 138, + 505, + 150 + ], + "spans": [ + { + "bbox": [ + 106, + 138, + 505, + 150 + ], + "score": 1.0, + "content": "Baumgarten’s agent is spawned in a tight space from which it can not escape, while the model has", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 148, + 506, + 163 + ], + "spans": [ + { + "bbox": [ + 104, + 148, + 506, + 163 + ], + "score": 1.0, + "content": "generated a path that traverses beyond the actual level, again a path that would likely be suggested by", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 104, + 158, + 506, + 174 + ], + "spans": [ + { + "bbox": [ + 104, + 158, + 506, + 174 + ], + "score": 1.0, + "content": "a solver. We argue that these issues can in part be attributed to the paths in the training data stemming", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 170, + 505, + 183 + ], + "spans": [ + { + "bbox": [ + 105, + 170, + 505, + 183 + ], + "score": 1.0, + "content": "from a solver rather than an actual agent, and could be alleviated in future work by annotating the", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 183, + 308, + 194 + ], + "spans": [ + { + "bbox": [ + 106, + 183, + 308, + 194 + ], + "score": 1.0, + "content": "training data with the trajectories of actual agents.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 5, + "bbox_fs": [ + 104, + 73, + 506, + 194 + ] + }, + { + "type": "image", + "bbox": [ + 164, + 203, + 447, + 392 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 164, + 203, + 447, + 392 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 164, + 203, + 447, + 392 + ], + "spans": [ + { + "bbox": [ + 164, + 203, + 447, + 392 + ], + "score": 0.976, + "type": "image", + "image_path": "b78426ce06283b9732abb3b14fa1a167f5be8825be0c2fcd2139ac575dcb3141.jpg" + } + ] + } + ], + "index": 12, + "virtual_lines": [ + { + "bbox": [ + 164, + 203, + 447, + 266.0 + ], + "spans": [], + "index": 11 + }, + { + "bbox": [ + 164, + 266.0, + 447, + 329.0 + ], + "spans": [], + "index": 12 + }, + { + "bbox": [ + 164, + 329.0, + 447, + 392.0 + ], + "spans": [], + "index": 13 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 398, + 505, + 465 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 398, + 506, + 411 + ], + "spans": [ + { + "bbox": [ + 106, + 398, + 147, + 411 + ], + "score": 1.0, + "content": "Figure 5:", + "type": "text" + }, + { + "bbox": [ + 147, + 399, + 161, + 410 + ], + "score": 0.59, + "content": "\\mathbf { A } ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 162, + 398, + 506, + 411 + ], + "score": 1.0, + "content": "vs. MarioGPT generated paths. Levels with (a) minimum (0.02), (a) median (0.89)", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 409, + 506, + 422 + ], + "spans": [ + { + "bbox": [ + 105, + 409, + 429, + 422 + ], + "score": 1.0, + "content": "and (a) maximum (11.0) mean absolute error (MAE) between trajectory of actual", + "type": "text" + }, + { + "bbox": [ + 430, + 410, + 443, + 420 + ], + "score": 0.81, + "content": "\\mathbf { A } ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 444, + 409, + 506, + 422 + ], + "score": 1.0, + "content": "agent (denoted", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 421, + 505, + 434 + ], + "spans": [ + { + "bbox": [ + 105, + 421, + 505, + 434 + ], + "score": 1.0, + "content": "as A), and model suggestion (denoted as P), as well as interesting hand-picked examples. Positions", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 432, + 505, + 444 + ], + "spans": [ + { + "bbox": [ + 105, + 432, + 505, + 444 + ], + "score": 1.0, + "content": "where both trajectories overlap are marked with *. Paths suggested by the model generally tend to", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 442, + 506, + 456 + ], + "spans": [ + { + "bbox": [ + 105, + 442, + 213, + 456 + ], + "score": 1.0, + "content": "have more airtime than the", + "type": "text" + }, + { + "bbox": [ + 214, + 443, + 227, + 453 + ], + "score": 0.7, + "content": "\\mathbf { A } ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 228, + 442, + 506, + 456 + ], + "score": 1.0, + "content": "agent (d, e), likely due to game physics not being accounted for in the", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 453, + 289, + 466 + ], + "spans": [ + { + "bbox": [ + 106, + 453, + 289, + 466 + ], + "score": 1.0, + "content": "original path annotations of the training data.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 16.5 + } + ], + "index": 14.25 + }, + { + "type": "title", + "bbox": [ + 107, + 484, + 246, + 496 + ], + "lines": [ + { + "bbox": [ + 105, + 482, + 247, + 499 + ], + "spans": [ + { + "bbox": [ + 105, + 482, + 247, + 499 + ], + "score": 1.0, + "content": "4.3 Is MarioGPT memorizing?", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 20 + }, + { + "type": "image", + "bbox": [ + 144, + 509, + 467, + 627 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 144, + 509, + 467, + 627 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 144, + 509, + 467, + 627 + ], + "spans": [ + { + "bbox": [ + 144, + 509, + 467, + 627 + ], + "score": 0.973, + "type": "image", + "image_path": "03847a0c8d25f6319ea8e373ca069b827d2df759372e6d48ae6240ba803a9e47.jpg" + } + ] + } + ], + "index": 22, + "virtual_lines": [ + { + "bbox": [ + 144, + 509, + 467, + 548.3333333333334 + ], + "spans": [], + "index": 21 + }, + { + "bbox": [ + 144, + 548.3333333333334, + 467, + 587.6666666666667 + ], + "spans": [], + "index": 22 + }, + { + "bbox": [ + 144, + 587.6666666666667, + 467, + 627.0000000000001 + ], + "spans": [], + "index": 23 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 632, + 504, + 655 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 106, + 632, + 505, + 645 + ], + "spans": [ + { + "bbox": [ + 106, + 632, + 505, + 645 + ], + "score": 1.0, + "content": "Figure 6: Generated levels vs closest in dataset. Temperature of 1.0 ends up spitting out almost", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 643, + 453, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 643, + 453, + 657 + ], + "score": 1.0, + "content": "exactly what is in the dataset, while increasing temperature improves sample diversity.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 24.5 + } + ], + "index": 23.25 + }, + { + "type": "text", + "bbox": [ + 107, + 667, + 505, + 722 + ], + "lines": [ + { + "bbox": [ + 106, + 667, + 505, + 679 + ], + "spans": [ + { + "bbox": [ + 106, + 667, + 505, + 679 + ], + "score": 1.0, + "content": "Memorization dynamics in LLMs remain an open problem when training transformer architectures", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 677, + 505, + 691 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 505, + 691 + ], + "score": 1.0, + "content": "[41, 5, 16]. While LLMs are incredibly powerful, they can sometimes overfit extremely and end up", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 104, + 689, + 506, + 701 + ], + "spans": [ + { + "bbox": [ + 104, + 689, + 506, + 701 + ], + "score": 1.0, + "content": "regurgitating training data. One popular way to alleviate this issue is to add some randomness in", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 699, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 506, + 712 + ], + "score": 1.0, + "content": "predictions in the form a tunable \"temperature\" parameter [17]. To evaluate whether MarioGPT is", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 711, + 506, + 724 + ], + "spans": [ + { + "bbox": [ + 105, + 711, + 506, + 724 + ], + "score": 1.0, + "content": "generating levels that are identical to the training set, we sample with different temperature parameters", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 72, + 505, + 86 + ], + "spans": [ + { + "bbox": [ + 106, + 72, + 505, + 86 + ], + "score": 1.0, + "content": "and compare them the closest level in the training dataset. From Figure 6, we can see that increasing", + "type": "text", + "cross_page": true + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 82, + 505, + 97 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 505, + 97 + ], + "score": 1.0, + "content": "temperature results in samples that are more diverse, but lack quality. In our case, when generating", + "type": "text", + "cross_page": true + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 94, + 505, + 107 + ], + "spans": [ + { + "bbox": [ + 105, + 94, + 505, + 107 + ], + "score": 1.0, + "content": "levels we use a temperature of 2.4-2.7, as it can generate diverse samples while still retaining some", + "type": "text", + "cross_page": true + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 105, + 506, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 105, + 506, + 118 + ], + "score": 1.0, + "content": "quality. There are many possible improvements to explore in the future. One common way is to", + "type": "text", + "cross_page": true + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 117, + 505, + 129 + ], + "spans": [ + { + "bbox": [ + 105, + 117, + 505, + 129 + ], + "score": 1.0, + "content": "simply increase the richness of the dataset. The more samples the model has access to, the less likely", + "type": "text", + "cross_page": true + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 127, + 505, + 140 + ], + "spans": [ + { + "bbox": [ + 105, + 127, + 505, + 140 + ], + "score": 1.0, + "content": "it is to overfit. We could also improve MarioGPT’s sampling abilities by introducing different search", + "type": "text", + "cross_page": true + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 138, + 506, + 150 + ], + "spans": [ + { + "bbox": [ + 105, + 138, + 506, + 150 + ], + "score": 1.0, + "content": "methods other than sampling with temperature, such as constrained beam search [6] and dataset", + "type": "text", + "cross_page": true + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 150, + 408, + 162 + ], + "spans": [ + { + "bbox": [ + 106, + 150, + 408, + 162 + ], + "score": 1.0, + "content": "augmented search [16], to increase diversity while preserving more quality.", + "type": "text", + "cross_page": true + } + ], + "index": 7 + } + ], + "index": 28, + "bbox_fs": [ + 104, + 667, + 506, + 724 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 72, + 505, + 161 + ], + "lines": [ + { + "bbox": [ + 106, + 72, + 505, + 86 + ], + "spans": [ + { + "bbox": [ + 106, + 72, + 505, + 86 + ], + "score": 1.0, + "content": "and compare them the closest level in the training dataset. From Figure 6, we can see that increasing", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 82, + 505, + 97 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 505, + 97 + ], + "score": 1.0, + "content": "temperature results in samples that are more diverse, but lack quality. In our case, when generating", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 94, + 505, + 107 + ], + "spans": [ + { + "bbox": [ + 105, + 94, + 505, + 107 + ], + "score": 1.0, + "content": "levels we use a temperature of 2.4-2.7, as it can generate diverse samples while still retaining some", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 105, + 506, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 105, + 506, + 118 + ], + "score": 1.0, + "content": "quality. There are many possible improvements to explore in the future. One common way is to", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 117, + 505, + 129 + ], + "spans": [ + { + "bbox": [ + 105, + 117, + 505, + 129 + ], + "score": 1.0, + "content": "simply increase the richness of the dataset. The more samples the model has access to, the less likely", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 127, + 505, + 140 + ], + "spans": [ + { + "bbox": [ + 105, + 127, + 505, + 140 + ], + "score": 1.0, + "content": "it is to overfit. We could also improve MarioGPT’s sampling abilities by introducing different search", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 138, + 506, + 150 + ], + "spans": [ + { + "bbox": [ + 105, + 138, + 506, + 150 + ], + "score": 1.0, + "content": "methods other than sampling with temperature, such as constrained beam search [6] and dataset", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 150, + 408, + 162 + ], + "spans": [ + { + "bbox": [ + 106, + 150, + 408, + 162 + ], + "score": 1.0, + "content": "augmented search [16], to increase diversity while preserving more quality.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 3.5 + }, + { + "type": "title", + "bbox": [ + 107, + 174, + 302, + 186 + ], + "lines": [ + { + "bbox": [ + 105, + 172, + 303, + 189 + ], + "spans": [ + { + "bbox": [ + 105, + 172, + 303, + 189 + ], + "score": 1.0, + "content": "4.4 Guided Level Generation via Prompting", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 8 + }, + { + "type": "text", + "bbox": [ + 107, + 194, + 505, + 272 + ], + "lines": [ + { + "bbox": [ + 105, + 195, + 505, + 207 + ], + "spans": [ + { + "bbox": [ + 105, + 195, + 505, + 207 + ], + "score": 1.0, + "content": "Through simple prompting, we are able to guide MarioGPT towards controllable and diverse level", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 206, + 505, + 219 + ], + "spans": [ + { + "bbox": [ + 105, + 206, + 505, + 219 + ], + "score": 1.0, + "content": "generation. We empirically evaluate the prompting ability of MarioGPT by generating 1,000 samples", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 216, + 505, + 230 + ], + "spans": [ + { + "bbox": [ + 105, + 216, + 505, + 230 + ], + "score": 1.0, + "content": "with various combinations of prompts, and check how accurate the generated levels are to the prompt", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 227, + 505, + 240 + ], + "spans": [ + { + "bbox": [ + 105, + 227, + 505, + 240 + ], + "score": 1.0, + "content": "descriptions. The results suggest that MarioGPT can generate levels that match their given prompts", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 238, + 505, + 252 + ], + "spans": [ + { + "bbox": [ + 105, + 238, + 505, + 252 + ], + "score": 1.0, + "content": "most of the time (Table 3). MarioGPT is the most accurate with blocks and the least accurate with", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 249, + 504, + 262 + ], + "spans": [ + { + "bbox": [ + 105, + 249, + 504, + 262 + ], + "score": 1.0, + "content": "enemies. This is expected because there are fewer total tiles of enemies, while there are many more", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 259, + 253, + 273 + ], + "spans": [ + { + "bbox": [ + 105, + 259, + 253, + 273 + ], + "score": 1.0, + "content": "block tiles observed during training.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 12 + }, + { + "type": "table", + "bbox": [ + 223, + 302, + 388, + 336 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 212, + 290, + 399, + 302 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 209, + 288, + 401, + 305 + ], + "spans": [ + { + "bbox": [ + 209, + 288, + 401, + 305 + ], + "score": 1.0, + "content": "Table 3: Prompt vs actual description accuracy", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 16 + }, + { + "type": "table_body", + "bbox": [ + 223, + 302, + 388, + 336 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 223, + 302, + 388, + 336 + ], + "spans": [ + { + "bbox": [ + 223, + 302, + 388, + 336 + ], + "score": 0.969, + "html": "
pipesenemiesblockselevation
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", + "type": "table", + "image_path": "dba01289c61600c3718a12ea7c44df8bc369c526e93c0f51b80b6a96e0c0e73a.jpg" + } + ] + } + ], + "index": 17.5, + "virtual_lines": [ + { + "bbox": [ + 223, + 302, + 388, + 319.0 + ], + "spans": [], + "index": 17 + }, + { + "bbox": [ + 223, + 319.0, + 388, + 336.0 + ], + "spans": [], + "index": 18 + } + ] + } + ], + "index": 16.75 + }, + { + "type": "text", + "bbox": [ + 106, + 348, + 505, + 436 + ], + "lines": [ + { + "bbox": [ + 105, + 348, + 506, + 361 + ], + "spans": [ + { + "bbox": [ + 105, + 348, + 506, + 361 + ], + "score": 1.0, + "content": "We visually evaluated the system, displaying selected prompt-conditioned generations in Figure 1. In", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 360, + 506, + 372 + ], + "spans": [ + { + "bbox": [ + 106, + 360, + 506, + 372 + ], + "score": 1.0, + "content": "addition, we evaluate the importance of the keywords in the prompt by comparing the distribution of", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 370, + 506, + 383 + ], + "spans": [ + { + "bbox": [ + 105, + 370, + 506, + 383 + ], + "score": 1.0, + "content": "the number of pipes between levels generated with random prompts without pipes-related commands", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 381, + 505, + 393 + ], + "spans": [ + { + "bbox": [ + 105, + 381, + 505, + 393 + ], + "score": 1.0, + "content": "(e.g. \"some enemies, some blocks, high elevation\") versus random prompts with pipes-related", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 392, + 505, + 405 + ], + "spans": [ + { + "bbox": [ + 105, + 392, + 505, + 405 + ], + "score": 1.0, + "content": "commands (e.g. \"little pipes, some enemies, some blocks, high elevation\"). The distribution without", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 403, + 506, + 416 + ], + "spans": [ + { + "bbox": [ + 105, + 403, + 506, + 416 + ], + "score": 1.0, + "content": "pipe prompts is scattered, while the ones with pipe prompts result in distributions with peaks,", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 414, + 505, + 426 + ], + "spans": [ + { + "bbox": [ + 105, + 414, + 505, + 426 + ], + "score": 1.0, + "content": "indicating that the keywords actually have an effect on the level generated (see Figure 11 in the", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 424, + 154, + 438 + ], + "spans": [ + { + "bbox": [ + 105, + 424, + 154, + 438 + ], + "score": 1.0, + "content": "Appendix).", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 22.5 + }, + { + "type": "text", + "bbox": [ + 106, + 441, + 505, + 529 + ], + "lines": [ + { + "bbox": [ + 105, + 440, + 507, + 454 + ], + "spans": [ + { + "bbox": [ + 105, + 440, + 507, + 454 + ], + "score": 1.0, + "content": "MarioGPT is also able to generate levels from text descriptions that are not represented in the dataset.", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 451, + 506, + 465 + ], + "spans": [ + { + "bbox": [ + 105, + 451, + 506, + 465 + ], + "score": 1.0, + "content": "For instance, Figure 1e shows a successful approximation of the prompt, \"many pipes, no enemies,", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 463, + 505, + 475 + ], + "spans": [ + { + "bbox": [ + 106, + 463, + 505, + 475 + ], + "score": 1.0, + "content": "many blocks\", with a slight inaccuracy in that it has 1 less pipe (5 pipes is considered \"many\", while", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 474, + 506, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 474, + 506, + 486 + ], + "score": 1.0, + "content": "4 are present). However, this is not always the case, as can be seen in Figure 1f, where the model,", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 485, + 506, + 497 + ], + "spans": [ + { + "bbox": [ + 105, + 485, + 506, + 497 + ], + "score": 1.0, + "content": "prompted by \"many pipes, no enemies, some blocks\", generates a level with the correct number of", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 495, + 506, + 509 + ], + "spans": [ + { + "bbox": [ + 105, + 495, + 506, + 509 + ], + "score": 1.0, + "content": "pipes and blocks but generates too many enemies. In future work, we hope to explore more ways to", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 506, + 506, + 520 + ], + "spans": [ + { + "bbox": [ + 105, + 506, + 506, + 520 + ], + "score": 1.0, + "content": "incorporate prompt importance, such as editing levels with tiles to create more samples or prompt", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 517, + 157, + 531 + ], + "spans": [ + { + "bbox": [ + 105, + 517, + 157, + 531 + ], + "score": 1.0, + "content": "tuning [18].", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 30.5 + }, + { + "type": "title", + "bbox": [ + 107, + 542, + 330, + 555 + ], + "lines": [ + { + "bbox": [ + 105, + 541, + 331, + 556 + ], + "spans": [ + { + "bbox": [ + 105, + 541, + 331, + 556 + ], + "score": 1.0, + "content": "4.5 Generating Diverse Levels with Novelty Search", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 35 + }, + { + "type": "text", + "bbox": [ + 107, + 563, + 505, + 695 + ], + "lines": [ + { + "bbox": [ + 106, + 563, + 505, + 576 + ], + "spans": [ + { + "bbox": [ + 106, + 563, + 505, + 576 + ], + "score": 1.0, + "content": "Through the combination of an LLM (Section 3.1) and novelty search (Section 3.2), we are able to", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 574, + 506, + 586 + ], + "spans": [ + { + "bbox": [ + 105, + 574, + 506, + 586 + ], + "score": 1.0, + "content": "continuously generate diverse levels in an open-ended fashion. Specifically, NS-MarioGPT is able to", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 585, + 506, + 598 + ], + "spans": [ + { + "bbox": [ + 105, + 585, + 506, + 598 + ], + "score": 1.0, + "content": "generate a collection of levels with a diverse set of predicted agent paths. We project the archive as a", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 595, + 507, + 610 + ], + "spans": [ + { + "bbox": [ + 105, + 595, + 507, + 610 + ], + "score": 1.0, + "content": "set of 2D embeddings in Figure 7 and darken the embedding points that are added later in the process.", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 606, + 505, + 620 + ], + "spans": [ + { + "bbox": [ + 105, + 606, + 505, + 620 + ], + "score": 1.0, + "content": "We can see that the levels are increasingly filling up empty spots in the embedding space. We also", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 618, + 505, + 631 + ], + "spans": [ + { + "bbox": [ + 106, + 618, + 505, + 631 + ], + "score": 1.0, + "content": "compare the distribution of levels generated by novelty search to levels generated by random prompts", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 629, + 506, + 641 + ], + "spans": [ + { + "bbox": [ + 106, + 629, + 506, + 641 + ], + "score": 1.0, + "content": "in Figure 8a. Visually, we can see that the levels generated by novelty search are more spread out", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 640, + 505, + 652 + ], + "spans": [ + { + "bbox": [ + 106, + 640, + 505, + 652 + ], + "score": 1.0, + "content": "in t-SNE space and the sampled ones, indicating that they are more diverse. Finally, we have also", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 651, + 505, + 663 + ], + "spans": [ + { + "bbox": [ + 106, + 651, + 505, + 663 + ], + "score": 1.0, + "content": "evaluated the playability of levels generated by novelty search, and find that the majority are solvable", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 662, + 505, + 673 + ], + "spans": [ + { + "bbox": [ + 106, + 662, + 505, + 673 + ], + "score": 1.0, + "content": "and non-playable levels are not clustered but rather scattered across t-SNE space. This indicates that", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 672, + 505, + 685 + ], + "spans": [ + { + "bbox": [ + 105, + 672, + 505, + 685 + ], + "score": 1.0, + "content": "there is no trade-off between path diversity and the ability to generate solvable levels. Figure 8b", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 684, + 238, + 696 + ], + "spans": [ + { + "bbox": [ + 106, + 684, + 238, + 696 + ], + "score": 1.0, + "content": "shows the corresponding results.", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 41.5 + }, + { + "type": "text", + "bbox": [ + 106, + 700, + 503, + 722 + ], + "lines": [ + { + "bbox": [ + 106, + 700, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 106, + 700, + 505, + 712 + ], + "score": 1.0, + "content": "Figure 9 displays all the overlayed predicted paths (in a level grid) as more and more levels get added", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 106, + 711, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 106, + 711, + 505, + 723 + ], + "score": 1.0, + "content": "to the archive during novelty search. Similar as in Figure 7, we can see that over time, the space", + "type": "text" + } + ], + "index": 49 + } + ], + "index": 48.5 + } + ], + "page_idx": 7, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 302, + 742, + 308, + 750 + ], + "lines": [ + { + "bbox": [ + 302, + 741, + 309, + 752 + ], + "spans": [ + { + "bbox": [ + 302, + 741, + 309, + 752 + ], + "score": 1.0, + "content": "8", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 72, + 505, + 161 + ], + "lines": [], + "index": 3.5, + "bbox_fs": [ + 105, + 72, + 506, + 162 + ], + "lines_deleted": true + }, + { + "type": "title", + "bbox": [ + 107, + 174, + 302, + 186 + ], + "lines": [ + { + "bbox": [ + 105, + 172, + 303, + 189 + ], + "spans": [ + { + "bbox": [ + 105, + 172, + 303, + 189 + ], + "score": 1.0, + "content": "4.4 Guided Level Generation via Prompting", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 8 + }, + { + "type": "text", + "bbox": [ + 107, + 194, + 505, + 272 + ], + "lines": [ + { + "bbox": [ + 105, + 195, + 505, + 207 + ], + "spans": [ + { + "bbox": [ + 105, + 195, + 505, + 207 + ], + "score": 1.0, + "content": "Through simple prompting, we are able to guide MarioGPT towards controllable and diverse level", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 206, + 505, + 219 + ], + "spans": [ + { + "bbox": [ + 105, + 206, + 505, + 219 + ], + "score": 1.0, + "content": "generation. We empirically evaluate the prompting ability of MarioGPT by generating 1,000 samples", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 216, + 505, + 230 + ], + "spans": [ + { + "bbox": [ + 105, + 216, + 505, + 230 + ], + "score": 1.0, + "content": "with various combinations of prompts, and check how accurate the generated levels are to the prompt", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 227, + 505, + 240 + ], + "spans": [ + { + "bbox": [ + 105, + 227, + 505, + 240 + ], + "score": 1.0, + "content": "descriptions. The results suggest that MarioGPT can generate levels that match their given prompts", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 238, + 505, + 252 + ], + "spans": [ + { + "bbox": [ + 105, + 238, + 505, + 252 + ], + "score": 1.0, + "content": "most of the time (Table 3). MarioGPT is the most accurate with blocks and the least accurate with", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 249, + 504, + 262 + ], + "spans": [ + { + "bbox": [ + 105, + 249, + 504, + 262 + ], + "score": 1.0, + "content": "enemies. This is expected because there are fewer total tiles of enemies, while there are many more", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 259, + 253, + 273 + ], + "spans": [ + { + "bbox": [ + 105, + 259, + 253, + 273 + ], + "score": 1.0, + "content": "block tiles observed during training.", + "type": "text" + } + ], + "index": 15 + } + ], + "index": 12, + "bbox_fs": [ + 105, + 195, + 505, + 273 + ] + }, + { + "type": "table", + "bbox": [ + 223, + 302, + 388, + 336 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 212, + 290, + 399, + 302 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 209, + 288, + 401, + 305 + ], + "spans": [ + { + "bbox": [ + 209, + 288, + 401, + 305 + ], + "score": 1.0, + "content": "Table 3: Prompt vs actual description accuracy", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 16 + }, + { + "type": "table_body", + "bbox": [ + 223, + 302, + 388, + 336 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 223, + 302, + 388, + 336 + ], + "spans": [ + { + "bbox": [ + 223, + 302, + 388, + 336 + ], + "score": 0.969, + "html": "
pipesenemiesblockselevation
81%68%92%76%
", + "type": "table", + "image_path": "dba01289c61600c3718a12ea7c44df8bc369c526e93c0f51b80b6a96e0c0e73a.jpg" + } + ] + } + ], + "index": 17.5, + "virtual_lines": [ + { + "bbox": [ + 223, + 302, + 388, + 319.0 + ], + "spans": [], + "index": 17 + }, + { + "bbox": [ + 223, + 319.0, + 388, + 336.0 + ], + "spans": [], + "index": 18 + } + ] + } + ], + "index": 16.75 + }, + { + "type": "text", + "bbox": [ + 106, + 348, + 505, + 436 + ], + "lines": [ + { + "bbox": [ + 105, + 348, + 506, + 361 + ], + "spans": [ + { + "bbox": [ + 105, + 348, + 506, + 361 + ], + "score": 1.0, + "content": "We visually evaluated the system, displaying selected prompt-conditioned generations in Figure 1. In", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 360, + 506, + 372 + ], + "spans": [ + { + "bbox": [ + 106, + 360, + 506, + 372 + ], + "score": 1.0, + "content": "addition, we evaluate the importance of the keywords in the prompt by comparing the distribution of", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 370, + 506, + 383 + ], + "spans": [ + { + "bbox": [ + 105, + 370, + 506, + 383 + ], + "score": 1.0, + "content": "the number of pipes between levels generated with random prompts without pipes-related commands", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 381, + 505, + 393 + ], + "spans": [ + { + "bbox": [ + 105, + 381, + 505, + 393 + ], + "score": 1.0, + "content": "(e.g. \"some enemies, some blocks, high elevation\") versus random prompts with pipes-related", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 392, + 505, + 405 + ], + "spans": [ + { + "bbox": [ + 105, + 392, + 505, + 405 + ], + "score": 1.0, + "content": "commands (e.g. \"little pipes, some enemies, some blocks, high elevation\"). The distribution without", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 403, + 506, + 416 + ], + "spans": [ + { + "bbox": [ + 105, + 403, + 506, + 416 + ], + "score": 1.0, + "content": "pipe prompts is scattered, while the ones with pipe prompts result in distributions with peaks,", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 414, + 505, + 426 + ], + "spans": [ + { + "bbox": [ + 105, + 414, + 505, + 426 + ], + "score": 1.0, + "content": "indicating that the keywords actually have an effect on the level generated (see Figure 11 in the", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 424, + 154, + 438 + ], + "spans": [ + { + "bbox": [ + 105, + 424, + 154, + 438 + ], + "score": 1.0, + "content": "Appendix).", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 22.5, + "bbox_fs": [ + 105, + 348, + 506, + 438 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 441, + 505, + 529 + ], + "lines": [ + { + "bbox": [ + 105, + 440, + 507, + 454 + ], + "spans": [ + { + "bbox": [ + 105, + 440, + 507, + 454 + ], + "score": 1.0, + "content": "MarioGPT is also able to generate levels from text descriptions that are not represented in the dataset.", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 451, + 506, + 465 + ], + "spans": [ + { + "bbox": [ + 105, + 451, + 506, + 465 + ], + "score": 1.0, + "content": "For instance, Figure 1e shows a successful approximation of the prompt, \"many pipes, no enemies,", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 463, + 505, + 475 + ], + "spans": [ + { + "bbox": [ + 106, + 463, + 505, + 475 + ], + "score": 1.0, + "content": "many blocks\", with a slight inaccuracy in that it has 1 less pipe (5 pipes is considered \"many\", while", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 474, + 506, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 474, + 506, + 486 + ], + "score": 1.0, + "content": "4 are present). However, this is not always the case, as can be seen in Figure 1f, where the model,", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 485, + 506, + 497 + ], + "spans": [ + { + "bbox": [ + 105, + 485, + 506, + 497 + ], + "score": 1.0, + "content": "prompted by \"many pipes, no enemies, some blocks\", generates a level with the correct number of", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 495, + 506, + 509 + ], + "spans": [ + { + "bbox": [ + 105, + 495, + 506, + 509 + ], + "score": 1.0, + "content": "pipes and blocks but generates too many enemies. In future work, we hope to explore more ways to", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 506, + 506, + 520 + ], + "spans": [ + { + "bbox": [ + 105, + 506, + 506, + 520 + ], + "score": 1.0, + "content": "incorporate prompt importance, such as editing levels with tiles to create more samples or prompt", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 517, + 157, + 531 + ], + "spans": [ + { + "bbox": [ + 105, + 517, + 157, + 531 + ], + "score": 1.0, + "content": "tuning [18].", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 30.5, + "bbox_fs": [ + 105, + 440, + 507, + 531 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 542, + 330, + 555 + ], + "lines": [ + { + "bbox": [ + 105, + 541, + 331, + 556 + ], + "spans": [ + { + "bbox": [ + 105, + 541, + 331, + 556 + ], + "score": 1.0, + "content": "4.5 Generating Diverse Levels with Novelty Search", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 35 + }, + { + "type": "text", + "bbox": [ + 107, + 563, + 505, + 695 + ], + "lines": [ + { + "bbox": [ + 106, + 563, + 505, + 576 + ], + "spans": [ + { + "bbox": [ + 106, + 563, + 505, + 576 + ], + "score": 1.0, + "content": "Through the combination of an LLM (Section 3.1) and novelty search (Section 3.2), we are able to", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 574, + 506, + 586 + ], + "spans": [ + { + "bbox": [ + 105, + 574, + 506, + 586 + ], + "score": 1.0, + "content": "continuously generate diverse levels in an open-ended fashion. Specifically, NS-MarioGPT is able to", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 585, + 506, + 598 + ], + "spans": [ + { + "bbox": [ + 105, + 585, + 506, + 598 + ], + "score": 1.0, + "content": "generate a collection of levels with a diverse set of predicted agent paths. We project the archive as a", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 595, + 507, + 610 + ], + "spans": [ + { + "bbox": [ + 105, + 595, + 507, + 610 + ], + "score": 1.0, + "content": "set of 2D embeddings in Figure 7 and darken the embedding points that are added later in the process.", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 606, + 505, + 620 + ], + "spans": [ + { + "bbox": [ + 105, + 606, + 505, + 620 + ], + "score": 1.0, + "content": "We can see that the levels are increasingly filling up empty spots in the embedding space. We also", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 618, + 505, + 631 + ], + "spans": [ + { + "bbox": [ + 106, + 618, + 505, + 631 + ], + "score": 1.0, + "content": "compare the distribution of levels generated by novelty search to levels generated by random prompts", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 629, + 506, + 641 + ], + "spans": [ + { + "bbox": [ + 106, + 629, + 506, + 641 + ], + "score": 1.0, + "content": "in Figure 8a. Visually, we can see that the levels generated by novelty search are more spread out", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 640, + 505, + 652 + ], + "spans": [ + { + "bbox": [ + 106, + 640, + 505, + 652 + ], + "score": 1.0, + "content": "in t-SNE space and the sampled ones, indicating that they are more diverse. Finally, we have also", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 651, + 505, + 663 + ], + "spans": [ + { + "bbox": [ + 106, + 651, + 505, + 663 + ], + "score": 1.0, + "content": "evaluated the playability of levels generated by novelty search, and find that the majority are solvable", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 662, + 505, + 673 + ], + "spans": [ + { + "bbox": [ + 106, + 662, + 505, + 673 + ], + "score": 1.0, + "content": "and non-playable levels are not clustered but rather scattered across t-SNE space. This indicates that", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 672, + 505, + 685 + ], + "spans": [ + { + "bbox": [ + 105, + 672, + 505, + 685 + ], + "score": 1.0, + "content": "there is no trade-off between path diversity and the ability to generate solvable levels. Figure 8b", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 684, + 238, + 696 + ], + "spans": [ + { + "bbox": [ + 106, + 684, + 238, + 696 + ], + "score": 1.0, + "content": "shows the corresponding results.", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 41.5, + "bbox_fs": [ + 105, + 563, + 507, + 696 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 700, + 503, + 722 + ], + "lines": [ + { + "bbox": [ + 106, + 700, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 106, + 700, + 505, + 712 + ], + "score": 1.0, + "content": "Figure 9 displays all the overlayed predicted paths (in a level grid) as more and more levels get added", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 106, + 711, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 106, + 711, + 505, + 723 + ], + "score": 1.0, + "content": "to the archive during novelty search. Similar as in Figure 7, we can see that over time, the space", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 106, + 596, + 505, + 609 + ], + "spans": [ + { + "bbox": [ + 106, + 596, + 505, + 609 + ], + "score": 1.0, + "content": "of possible predicted agent paths gets filled, as increasingly diverse levels are mutated and added", + "type": "text", + "cross_page": true + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 606, + 506, + 620 + ], + "spans": [ + { + "bbox": [ + 105, + 606, + 506, + 620 + ], + "score": 1.0, + "content": "to the archive. As more levels are added to the archive, more and more of the tiles / empty space", + "type": "text", + "cross_page": true + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 618, + 506, + 630 + ], + "spans": [ + { + "bbox": [ + 105, + 618, + 506, + 630 + ], + "score": 1.0, + "content": "in the grid are being filled up, indicating that NS-MarioGPT is discovering a variety of levels that", + "type": "text", + "cross_page": true + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 629, + 506, + 642 + ], + "spans": [ + { + "bbox": [ + 105, + 629, + 506, + 642 + ], + "score": 1.0, + "content": "produce diverse paths. Concretely, we found that after 300 levels are added to the archive, around", + "type": "text", + "cross_page": true + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 640, + 505, + 652 + ], + "spans": [ + { + "bbox": [ + 106, + 640, + 126, + 650 + ], + "score": 0.87, + "content": "78 \\%", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 126, + 640, + 505, + 652 + ], + "score": 1.0, + "content": "of the possible coordinates are filled up. However, there are still many overlapping paths in the", + "type": "text", + "cross_page": true + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 651, + 505, + 663 + ], + "spans": [ + { + "bbox": [ + 106, + 651, + 505, + 663 + ], + "score": 1.0, + "content": "archive, meaning that similar paths are still being added to the archive. This is an issue that could be", + "type": "text", + "cross_page": true + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 662, + 506, + 674 + ], + "spans": [ + { + "bbox": [ + 105, + 662, + 506, + 674 + ], + "score": 1.0, + "content": "improved by using more related time series distance metrics that account for patterns in a path [11].", + "type": "text", + "cross_page": true + } + ], + "index": 21 + } + ], + "index": 48.5, + "bbox_fs": [ + 106, + 700, + 505, + 723 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 147, + 73, + 464, + 266 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 147, + 73, + 464, + 266 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 147, + 73, + 464, + 266 + ], + "spans": [ + { + "bbox": [ + 147, + 73, + 464, + 266 + ], + "score": 0.97, + "type": "image", + "image_path": "208fe07045a41ef1c234698159461b3e3cd2f821cf7f5a044a07747c1839e0f7.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 147, + 73, + 464, + 137.33333333333331 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 147, + 137.33333333333331, + 464, + 201.66666666666663 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 147, + 201.66666666666663, + 464, + 265.99999999999994 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 275, + 505, + 309 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 276, + 505, + 288 + ], + "spans": [ + { + "bbox": [ + 106, + 276, + 505, + 288 + ], + "score": 1.0, + "content": "Figure 7: t-SNE of the levels in the archive. t-SNE embeddings are computed from the behavioral", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 285, + 506, + 300 + ], + "spans": [ + { + "bbox": [ + 105, + 285, + 506, + 300 + ], + "score": 1.0, + "content": "characteristic. Darker points indicate more recently added elements. Although novelty search is using", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 297, + 473, + 310 + ], + "spans": [ + { + "bbox": [ + 105, + 297, + 473, + 310 + ], + "score": 1.0, + "content": "the behavioral characteristics of the player paths, the levels also demonstrate visual novelty.", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4 + } + ], + "index": 2.5 + }, + { + "type": "image", + "bbox": [ + 149, + 342, + 450, + 499 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 149, + 342, + 450, + 499 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 149, + 342, + 450, + 499 + ], + "spans": [ + { + "bbox": [ + 149, + 342, + 450, + 499 + ], + "score": 0.963, + "type": "image", + "image_path": "28891b163aea4c875fc0f487d07616dc91f2294ba644197603eac33c1243be2c.jpg" + } + ] + } + ], + "index": 7, + "virtual_lines": [ + { + "bbox": [ + 149, + 342, + 450, + 394.3333333333333 + ], + "spans": [], + "index": 6 + }, + { + "bbox": [ + 149, + 394.3333333333333, + 450, + 446.66666666666663 + ], + "spans": [], + "index": 7 + }, + { + "bbox": [ + 149, + 446.66666666666663, + 450, + 498.99999999999994 + ], + "spans": [], + "index": 8 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 505, + 506, + 570 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 106, + 506, + 506, + 517 + ], + "spans": [ + { + "bbox": [ + 106, + 506, + 506, + 517 + ], + "score": 1.0, + "content": "Figure 8: Comparing exploration for novelty search vs. random sampling and playable vs. non-", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 516, + 505, + 528 + ], + "spans": [ + { + "bbox": [ + 105, + 516, + 505, + 528 + ], + "score": 1.0, + "content": "playable levels. (a) t-SNE of both the embeddings of novelty-search levels and levels generated with", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 527, + 506, + 540 + ], + "spans": [ + { + "bbox": [ + 105, + 527, + 506, + 540 + ], + "score": 1.0, + "content": "random prompts. The visualization suggests that novelty search enables a much wider exploration of", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 538, + 505, + 550 + ], + "spans": [ + { + "bbox": [ + 106, + 538, + 505, + 550 + ], + "score": 1.0, + "content": "the space of levels. (b) Unsolvable levels are not clustered together but instead scattered across the", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 549, + 505, + 560 + ], + "spans": [ + { + "bbox": [ + 106, + 549, + 505, + 560 + ], + "score": 1.0, + "content": "t-SNE space. This distribution indicates that there is no correlation between the diversity of levels", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 558, + 190, + 572 + ], + "spans": [ + { + "bbox": [ + 105, + 558, + 190, + 572 + ], + "score": 1.0, + "content": "and their solvability.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 11.5 + } + ], + "index": 9.25 + }, + { + "type": "text", + "bbox": [ + 106, + 596, + 505, + 673 + ], + "lines": [ + { + "bbox": [ + 106, + 596, + 505, + 609 + ], + "spans": [ + { + "bbox": [ + 106, + 596, + 505, + 609 + ], + "score": 1.0, + "content": "of possible predicted agent paths gets filled, as increasingly diverse levels are mutated and added", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 606, + 506, + 620 + ], + "spans": [ + { + "bbox": [ + 105, + 606, + 506, + 620 + ], + "score": 1.0, + "content": "to the archive. As more levels are added to the archive, more and more of the tiles / empty space", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 618, + 506, + 630 + ], + "spans": [ + { + "bbox": [ + 105, + 618, + 506, + 630 + ], + "score": 1.0, + "content": "in the grid are being filled up, indicating that NS-MarioGPT is discovering a variety of levels that", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 629, + 506, + 642 + ], + "spans": [ + { + "bbox": [ + 105, + 629, + 506, + 642 + ], + "score": 1.0, + "content": "produce diverse paths. 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This is an issue that could be", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 662, + 506, + 674 + ], + "spans": [ + { + "bbox": [ + 105, + 662, + 506, + 674 + ], + "score": 1.0, + "content": "improved by using more related time series distance metrics that account for patterns in a path [11].", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 18 + }, + { + "type": "text", + "bbox": [ + 107, + 678, + 504, + 722 + ], + "lines": [ + { + "bbox": [ + 105, + 677, + 505, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 505, + 690 + ], + "score": 1.0, + "content": "Levels with the highest and lowest novelty score from the archive are also shown in Figure 10. The", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 689, + 506, + 701 + ], + "spans": [ + { + "bbox": [ + 106, + 689, + 506, + 701 + ], + "score": 1.0, + "content": "level with the lowest novelty, shown in Figure 10a, has a path that is much more common in the", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 699, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 506, + 712 + ], + "score": 1.0, + "content": "archive, which can be seen by its almost identical look compared to the 2nd lowest in Figure 10c. 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The two least novel levels are", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 272, + 455, + 285 + ], + "spans": [ + { + "bbox": [ + 106, + 272, + 455, + 285 + ], + "score": 1.0, + "content": "very similar to each other, while the most novel levels have more distinct path patterns.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 8.5 + } + ], + "index": 7.25 + }, + { + "type": "text", + "bbox": [ + 107, + 314, + 505, + 358 + ], + "lines": [ + { + "bbox": [ + 105, + 314, + 506, + 326 + ], + "spans": [ + { + "bbox": [ + 105, + 314, + 506, + 326 + ], + "score": 1.0, + "content": "pattern towards the end. This indicates that one was created by mutating the other. We also found", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 325, + 505, + 337 + ], + "spans": [ + { + "bbox": [ + 105, + 325, + 505, + 337 + ], + "score": 1.0, + "content": "that the diversity starts to plateau after around 350-400 generations. However, this is very sensitive to", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 335, + 505, + 348 + ], + "spans": [ + { + "bbox": [ + 105, + 335, + 505, + 348 + ], + "score": 1.0, + "content": "the behavior characteristic (the smoothed predicted path of the level), so it may be different for other", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 347, + 206, + 358 + ], + "spans": [ + { + "bbox": [ + 105, + 347, + 206, + 358 + ], + "score": 1.0, + "content": "behavior characteristics.", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 11.5 + }, + { + "type": "text", + "bbox": [ + 108, + 363, + 505, + 396 + ], + "lines": [ + { + "bbox": [ + 105, + 362, + 507, + 376 + ], + "spans": [ + { + "bbox": [ + 105, + 362, + 507, + 376 + ], + "score": 1.0, + "content": "While NS-MarioGPT is still able to discover many diverse levels through its simple mutation process,", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 374, + 505, + 386 + ], + "spans": [ + { + "bbox": [ + 106, + 374, + 505, + 386 + ], + "score": 1.0, + "content": "more complex functions could also be explored. For instance, crossover, a common mutation utilized", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 385, + 506, + 397 + ], + "spans": [ + { + "bbox": [ + 106, + 385, + 506, + 397 + ], + "score": 1.0, + "content": "in many genetic algorithms, would increase mutation diversity which can lead to more diverse levels.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 15 + }, + { + "type": "title", + "bbox": [ + 107, + 421, + 182, + 435 + ], + "lines": [ + { + "bbox": [ + 104, + 419, + 185, + 438 + ], + "spans": [ + { + "bbox": [ + 104, + 419, + 185, + 438 + ], + "score": 1.0, + "content": "5 Conclusion", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 17 + }, + { + "type": "text", + "bbox": [ + 107, + 452, + 505, + 561 + ], + "lines": [ + { + "bbox": [ + 105, + 451, + 506, + 465 + ], + "spans": [ + { + "bbox": [ + 105, + 451, + 506, + 465 + ], + "score": 1.0, + "content": "Here we introduced MarioGPT, a fine-tuned GPT2 LLM that can not only generate diverse levels, but", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 462, + 506, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 462, + 506, + 475 + ], + "score": 1.0, + "content": "can guide its generation via a language prompt. 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The ability to fine-tune these models on human feedback allows", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 621, + 505, + 634 + ], + "spans": [ + { + "bbox": [ + 105, + 621, + 505, + 634 + ], + "score": 1.0, + "content": "users to continually tune their generated levels towards desired characteristics. 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The keywords \"no\", \"little\", \"some\", \"many\" are calculated from quantiles", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 463, + 505, + 475 + ], + "spans": [ + { + "bbox": [ + 106, + 463, + 505, + 475 + ], + "score": 1.0, + "content": "of the corresponding count within a 50 column window (Table 5). The \"low\" and \"high\" elevation are", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 473, + 456, + 486 + ], + "spans": [ + { + "bbox": [ + 105, + 473, + 456, + 486 + ], + "score": 1.0, + "content": "determined from the height of the highest unbreakable blocks in a segment of the level.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 22.5, + "bbox_fs": [ + 105, + 440, + 505, + 486 + ] + }, + { + "type": "table", + "bbox": [ + 144, + 514, + 466, + 570 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 142, + 502, + 468, + 514 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 141, + 501, + 469, + 515 + ], + "spans": [ + { + "bbox": [ + 141, + 501, + 469, + 515 + ], + "score": 1.0, + "content": "Table 5: Prompt Quantiles and corresponding counts within a 50 column window", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 25 + }, + { + "type": "table_body", + "bbox": [ + 144, + 514, + 466, + 570 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 144, + 514, + 466, + 570 + ], + "spans": [ + { + "bbox": [ + 144, + 514, + 466, + 570 + ], + "score": 0.978, + "html": "
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Comparison of the distribution of the number of pipes", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 427, + 506, + 439 + ], + "spans": [ + { + "bbox": [ + 106, + 427, + 506, + 439 + ], + "score": 1.0, + "content": "between levels generated with random prompts without pipes-related commands (e.g. \"some enemies,", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 437, + 507, + 451 + ], + "spans": [ + { + "bbox": [ + 105, + 437, + 507, + 451 + ], + "score": 1.0, + "content": "some blocks, high elevation\") versus random prompts with pipes-related commands (e.g. \"little pipes,", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 447, + 507, + 463 + ], + "spans": [ + { + "bbox": [ + 105, + 447, + 507, + 463 + ], + "score": 1.0, + "content": "some enemies, some blocks, high elevation\"). The distribution without pipe prompts is scattered,", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 459, + 376, + 473 + ], + "spans": [ + { + "bbox": [ + 105, + 459, + 376, + 473 + ], + "score": 1.0, + "content": "while the ones with pipe prompts result in distributions with peaks.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 5 + } + ], + "index": 3.0 + } + ], + "page_idx": 14, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 300, + 741, + 311, + 750 + ], + "lines": [ + { + "bbox": [ + 299, + 740, + 313, + 754 + ], + "spans": [ + { + "bbox": [ + 299, + 740, + 313, + 754 + ], + "score": 1.0, + "content": "15", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "image", + "bbox": [ + 130, + 324, + 477, + 411 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 130, + 324, + 477, + 411 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 130, + 324, + 477, + 411 + ], + "spans": [ + { + "bbox": [ + 130, + 324, + 477, + 411 + ], + "score": 0.772, + "type": "image", + "image_path": "10df4768e1712dda7107c01bf02b54c8ef44c75d1b29eca59eaa5effe083c825.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 130, + 324, + 477, + 353.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 130, + 353.0, + 477, + 382.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 130, + 382.0, + 477, + 411.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 105, + 416, + 507, + 471 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 416, + 505, + 428 + ], + "spans": [ + { + "bbox": [ + 106, + 416, + 505, + 428 + ], + "score": 1.0, + "content": "Figure 11: Effect of prompt conditioning. Comparison of the distribution of the number of pipes", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 427, + 506, + 439 + ], + "spans": [ + { + "bbox": [ + 106, + 427, + 506, + 439 + ], + "score": 1.0, + "content": "between levels generated with random prompts without pipes-related commands (e.g. \"some enemies,", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 437, + 507, + 451 + ], + "spans": [ + { + "bbox": [ + 105, + 437, + 507, + 451 + ], + "score": 1.0, + "content": "some blocks, high elevation\") versus random prompts with pipes-related commands (e.g. \"little pipes,", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 447, + 507, + 463 + ], + "spans": [ + { + "bbox": [ + 105, + 447, + 507, + 463 + ], + "score": 1.0, + "content": "some enemies, some blocks, high elevation\"). The distribution without pipe prompts is scattered,", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 459, + 376, + 473 + ], + "spans": [ + { + "bbox": [ + 105, + 459, + 376, + 473 + ], + "score": 1.0, + "content": "while the ones with pipe prompts result in distributions with peaks.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 5 + } + ], + "index": 3.0 + } + ] + } + ], + "_backend": "pipeline", + "_version_name": "2.2.2" +} \ No newline at end of file diff --git a/parse/dev/aa8KsqfTPa/aa8KsqfTPa_model.json b/parse/dev/aa8KsqfTPa/aa8KsqfTPa_model.json new file mode 100644 index 0000000000000000000000000000000000000000..8399d16646a3d7ab56aa61ff269f73a7f0d9c50b --- /dev/null +++ b/parse/dev/aa8KsqfTPa/aa8KsqfTPa_model.json @@ -0,0 +1,16647 @@ +[ + { + "layout_dets": [ + { + "category_id": 1, + "poly": [ + 398, + 1244, + 1304, + 1244, + 1304, + 1729, + 398, + 1729 + ], + "score": 0.982 + }, + { + "category_id": 3, + "poly": [ + 347, + 655, + 1352, + 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ModelTile Acc.Path Acc.Promptable?
LSTM46%39%NO
from-scratch-MarioGPT31%23%YES
adapter-MarioGPT21%11%YES
MarioGPT93%91%YES
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However, such models generate code left-", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 470, + 506, + 483 + ], + "spans": [ + { + "bbox": [ + 105, + 470, + 506, + 483 + ], + "score": 1.0, + "content": "to-right, which makes them less directly applicable to many ubiquitous code editing tasks, such as", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 482, + 506, + 493 + ], + "spans": [ + { + "bbox": [ + 105, + 482, + 506, + 493 + ], + "score": 1.0, + "content": "fixing bugs, adding comments, or re-naming variables. We introduce INCODER, a unified model for", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 492, + 506, + 504 + ], + "spans": [ + { + "bbox": [ + 105, + 492, + 506, + 504 + ], + "score": 1.0, + "content": "program synthesis and editing. 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On the other hand,", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 620, + 505, + 633 + ], + "spans": [ + { + "bbox": [ + 105, + 620, + 505, + 633 + ], + "score": 1.0, + "content": "masked language models can condition on both the left and right contexts to infill a masked region,", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 631, + 506, + 644 + ], + "spans": [ + { + "bbox": [ + 105, + 631, + 420, + 644 + ], + "score": 1.0, + "content": "however, their training objective is typically limited to generating only about", + "type": "text" + }, + { + "bbox": [ + 421, + 631, + 441, + 642 + ], + "score": 0.86, + "content": "15 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 441, + 631, + 506, + 644 + ], + "score": 1.0, + "content": "of a document.", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 642, + 506, + 655 + ], + "spans": [ + { + "bbox": [ + 105, + 642, + 506, + 655 + ], + "score": 1.0, + "content": "In this paper, we adopt the recently proposed causal masking objective (Aghajanyan et al., 2022a),", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 653, + 435, + 666 + ], + "spans": [ + { + "bbox": [ + 105, + 653, + 435, + 666 + ], + "score": 1.0, + "content": "which aims to combine the strengths of both causal and masked language models.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 26, + "bbox_fs": [ + 104, + 566, + 506, + 666 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 678, + 175, + 689 + ], + "lines": [ + { + "bbox": [ + 105, + 677, + 177, + 691 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 177, + 691 + ], + "score": 1.0, + "content": "2.1 TRAINING", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 31 + }, + { + "type": "text", + "bbox": [ + 108, + 699, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 699, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 505, + 711 + ], + "score": 1.0, + "content": "At training time, the causal masking procedure samples a number of spans of contiguous tokens", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 708, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 105, + 708, + 506, + 723 + ], + "score": 1.0, + "content": "in each document to mask (Figure 1, top left). We sample the number of spans from a Poisson", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 719, + 505, + 734 + ], + "spans": [ + { + "bbox": [ + 106, + 719, + 505, + 734 + ], + "score": 1.0, + "content": "distribution with a mean of one, truncated to the support [1, 256], so that there are typically a small", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 80, + 505, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 80, + 281, + 96 + ], + "score": 1.0, + "content": "number of spans (with a single span around", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 282, + 83, + 302, + 93 + ], + "score": 0.87, + "content": "50 \\%", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 302, + 80, + 505, + 96 + ], + "score": 1.0, + "content": "of the time), but the distribution has a long tail (up", + "type": "text", + "cross_page": true + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 94, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 94, + 505, + 106 + ], + "score": 1.0, + "content": "to 256 spans). Each span’s endpoints are sampled uniformly from the length of the document and", + "type": "text", + "cross_page": true + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 104, + 393, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 104, + 393, + 118 + ], + "score": 1.0, + "content": "the set of sampled spans is rejected and resampled if any spans overlap.", + "type": "text", + "cross_page": true + } + ], + "index": 2 + } + ], + "index": 33, + "bbox_fs": [ + 105, + 699, + 506, + 734 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 505, + 116 + ], + "lines": [ + { + "bbox": [ + 105, + 80, + 505, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 80, + 281, + 96 + ], + "score": 1.0, + "content": "number of spans (with a single span around", + "type": "text" + }, + { + "bbox": [ + 282, + 83, + 302, + 93 + ], + "score": 0.87, + "content": "50 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 302, + 80, + 505, + 96 + ], + "score": 1.0, + "content": "of the time), but the distribution has a long tail (up", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 94, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 94, + 505, + 106 + ], + "score": 1.0, + "content": "to 256 spans). Each span’s endpoints are sampled uniformly from the length of the document and", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 104, + 393, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 104, + 393, + 118 + ], + "score": 1.0, + "content": "the set of sampled spans is rejected and resampled if any spans overlap.", + "type": "text" + } + ], + "index": 2 + } + ], + "index": 1 + }, + { + "type": "text", + "bbox": [ + 106, + 121, + 505, + 209 + ], + "lines": [ + { + "bbox": [ + 106, + 122, + 505, + 133 + ], + "spans": [ + { + "bbox": [ + 106, + 122, + 248, + 133 + ], + "score": 1.0, + "content": "Once spans are sampled, each span", + "type": "text" + }, + { + "bbox": [ + 249, + 122, + 255, + 131 + ], + "score": 0.8, + "content": "k", + "type": "inline_equation" + }, + { + "bbox": [ + 256, + 122, + 505, + 133 + ], + "score": 1.0, + "content": "is replaced with a special mask sentinel token, . The", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 132, + 505, + 144 + ], + "spans": [ + { + "bbox": [ + 105, + 132, + 505, + 144 + ], + "score": 1.0, + "content": "sequence of tokens in the span is then moved to the end of the document (Figure 1, top right), with", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 144, + 505, + 156 + ], + "spans": [ + { + "bbox": [ + 106, + 144, + 375, + 156 + ], + "score": 1.0, + "content": "the mask sentinel token prepended and a special end-of-mask token", + "type": "text" + }, + { + "bbox": [ + 376, + 144, + 403, + 154 + ], + "score": 0.82, + "content": "\\mathsf { \\mathrm { \\tt { E O M } > } }", + "type": "inline_equation" + }, + { + "bbox": [ + 403, + 144, + 505, + 156 + ], + "score": 1.0, + "content": "token appended. In other", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 155, + 505, + 165 + ], + "spans": [ + { + "bbox": [ + 106, + 155, + 505, + 165 + ], + "score": 1.0, + "content": "words, when a mask token appears for the first time in the left-to-right ordering, it marks the location", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 165, + 505, + 177 + ], + "spans": [ + { + "bbox": [ + 106, + 165, + 505, + 177 + ], + "score": 1.0, + "content": "the span was removed from; when it appears for the second time, it marks the start of the moved", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 176, + 505, + 189 + ], + "spans": [ + { + "bbox": [ + 105, + 176, + 356, + 189 + ], + "score": 1.0, + "content": "span text. More formally, assume we have a document D with", + "type": "text" + }, + { + "bbox": [ + 357, + 177, + 367, + 186 + ], + "score": 0.79, + "content": "N", + "type": "inline_equation" + }, + { + "bbox": [ + 367, + 176, + 505, + 189 + ], + "score": 1.0, + "content": "tokens, and we have sampled one", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 187, + 505, + 201 + ], + "spans": [ + { + "bbox": [ + 105, + 187, + 127, + 201 + ], + "score": 1.0, + "content": "span", + "type": "text" + }, + { + "bbox": [ + 127, + 188, + 176, + 199 + ], + "score": 0.8, + "content": "\\mathsf { S p a n } = \\mathsf { D } _ { i : j }", + "type": "inline_equation" + }, + { + "bbox": [ + 177, + 187, + 295, + 201 + ], + "score": 1.0, + "content": ". Let Left be the left context", + "type": "text" + }, + { + "bbox": [ + 296, + 188, + 312, + 199 + ], + "score": 0.89, + "content": "\\mathsf { D } _ { 0 : i }", + "type": "inline_equation" + }, + { + "bbox": [ + 313, + 187, + 439, + 201 + ], + "score": 1.0, + "content": "and Right be the right context", + "type": "text" + }, + { + "bbox": [ + 439, + 188, + 459, + 200 + ], + "score": 0.91, + "content": "\\mathsf { D } _ { j : N }", + "type": "inline_equation" + }, + { + "bbox": [ + 460, + 187, + 505, + 201 + ], + "score": 1.0, + "content": ". Then, we", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 199, + 327, + 210 + ], + "spans": [ + { + "bbox": [ + 106, + 199, + 327, + 210 + ], + "score": 1.0, + "content": "maximize the log probability of the masked document:", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 6.5 + }, + { + "type": "interline_equation", + "bbox": [ + 182, + 211, + 428, + 224 + ], + "lines": [ + { + "bbox": [ + 183, + 211, + 428, + 224 + ], + "spans": [ + { + "bbox": [ + 183, + 211, + 428, + 224 + ], + "score": 0.63, + "content": "\\log P ( [ \\mathsf { L e f t } ; \\mathsf { \\texttt { < M a s k : } } 0 > ; \\mathsf { R i g h t } ; \\mathsf { \\texttt { < M a s k : } } 0 > ; \\mathsf { \\texttt { S p a n } } ; \\mathsf { \\texttt { < E O M > } } ] )", + "type": "interline_equation", + "image_path": "b1195563ac81d53a75786e68ccefd3a9c211d689c4ffe8e6b957f1fc9071cc74.jpg" + } + ] + } + ], + "index": 11, + "virtual_lines": [ + { + "bbox": [ + 182, + 211, + 428, + 224 + ], + "spans": [], + "index": 11 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 226, + 504, + 281 + ], + "lines": [ + { + "bbox": [ + 106, + 226, + 505, + 237 + ], + "spans": [ + { + "bbox": [ + 106, + 226, + 505, + 237 + ], + "score": 1.0, + "content": "where ; denotes sequence concatenation. If more than one span were sampled, each would be", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 236, + 506, + 249 + ], + "spans": [ + { + "bbox": [ + 105, + 236, + 506, + 249 + ], + "score": 1.0, + "content": "similarly appended at the end of the document in order. As in standard left-to-right generative", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 247, + 506, + 260 + ], + "spans": [ + { + "bbox": [ + 105, + 247, + 506, + 260 + ], + "score": 1.0, + "content": "language modeling, we compute the probability of the sequence auto-regressively and train the", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 258, + 506, + 270 + ], + "spans": [ + { + "bbox": [ + 105, + 258, + 506, + 270 + ], + "score": 1.0, + "content": "model using cross-entropy loss on all tokens except the mask sentinel tokens , so that", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 269, + 343, + 282 + ], + "spans": [ + { + "bbox": [ + 105, + 269, + 343, + 282 + ], + "score": 1.0, + "content": "the model does not generate these tokens during inference.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 14 + }, + { + "type": "title", + "bbox": [ + 107, + 293, + 181, + 304 + ], + "lines": [ + { + "bbox": [ + 105, + 291, + 183, + 307 + ], + "spans": [ + { + "bbox": [ + 105, + 291, + 183, + 307 + ], + "score": 1.0, + "content": "2.2 INFERENCE", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 17 + }, + { + "type": "text", + "bbox": [ + 107, + 313, + 505, + 380 + ], + "lines": [ + { + "bbox": [ + 105, + 312, + 505, + 327 + ], + "spans": [ + { + "bbox": [ + 105, + 312, + 505, + 327 + ], + "score": 1.0, + "content": "During inference, the model can either be used for left-to-right generation in the standard way (by", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 325, + 506, + 337 + ], + "spans": [ + { + "bbox": [ + 105, + 325, + 506, + 337 + ], + "score": 1.0, + "content": "sampling autoregressively from the model, without using any special tokens), or it can insert code at", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 336, + 505, + 349 + ], + "spans": [ + { + "bbox": [ + 105, + 336, + 505, + 349 + ], + "score": 1.0, + "content": "arbitrary locations in an existing document by inserting a tokens at the desired location(s)", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 347, + 506, + 360 + ], + "spans": [ + { + "bbox": [ + 105, + 347, + 506, + 360 + ], + "score": 1.0, + "content": "and continuing generation at the end of the document. Assuming for simplicity of notation that we", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 358, + 506, + 371 + ], + "spans": [ + { + "bbox": [ + 105, + 358, + 506, + 371 + ], + "score": 1.0, + "content": "want to insert text at only a single location, we can generate a span to insert between the location’s", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 369, + 480, + 381 + ], + "spans": [ + { + "bbox": [ + 105, + 369, + 480, + 381 + ], + "score": 1.0, + "content": "Left and Right context sequences by sampling tokens autoregressively from the distribution", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 20.5 + }, + { + "type": "interline_equation", + "bbox": [ + 213, + 381, + 398, + 395 + ], + "lines": [ + { + "bbox": [ + 213, + 381, + 398, + 395 + ], + "spans": [ + { + "bbox": [ + 213, + 381, + 398, + 395 + ], + "score": 0.62, + "content": "P ( \\cdot \\mid [ \\mathsf { L e f t } ; \\mathsf { < M a s k : } 0 > ; \\mathsf { R i g h t } ; \\mathsf { < M a s k : } 0 > ] )", + "type": "interline_equation", + "image_path": "b065f758048a38eab9e6d7570b28a10e0f7a7548f34733d7e880b354c6e57d59.jpg" + } + ] + } + ], + "index": 24, + "virtual_lines": [ + { + "bbox": [ + 213, + 381, + 398, + 395 + ], + "spans": [], + "index": 24 + } + ] + }, + { + "type": "text", + "bbox": [ + 107, + 398, + 505, + 465 + ], + "lines": [ + { + "bbox": [ + 105, + 398, + 505, + 410 + ], + "spans": [ + { + "bbox": [ + 105, + 398, + 165, + 410 + ], + "score": 1.0, + "content": "until either an", + "type": "text" + }, + { + "bbox": [ + 165, + 399, + 192, + 409 + ], + "score": 0.82, + "content": "{ \\tt { \\tt { \\tt { E 0 M } } } } >", + "type": "inline_equation" + }, + { + "bbox": [ + 192, + 398, + 505, + 410 + ], + "score": 1.0, + "content": "token is generated or a task-dependent stopping criterion is achieved.2 When", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 408, + 506, + 421 + ], + "spans": [ + { + "bbox": [ + 105, + 408, + 506, + 421 + ], + "score": 1.0, + "content": "applied to code, this allows us to perform tasks that benefit from the bidirectional context in a", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 419, + 506, + 434 + ], + "spans": [ + { + "bbox": [ + 105, + 419, + 506, + 434 + ], + "score": 1.0, + "content": "zero-shot fashion, as shown in Figure 1, bottom. For example, we can perform Python docstring", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 430, + 506, + 444 + ], + "spans": [ + { + "bbox": [ + 105, + 430, + 506, + 444 + ], + "score": 1.0, + "content": "generation conditioned on both the left context (function signature) and right context (function im-", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 441, + 506, + 456 + ], + "spans": [ + { + "bbox": [ + 105, + 441, + 506, + 456 + ], + "score": 1.0, + "content": "plementation). We can also infill multiple dependent regions, e.g., generate imports required by a", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 451, + 499, + 466 + ], + "spans": [ + { + "bbox": [ + 105, + 451, + 499, + 466 + ], + "score": 1.0, + "content": "function that the model is generating. See Section B.2 for details, including multi-region infilling.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 27.5 + }, + { + "type": "title", + "bbox": [ + 108, + 479, + 171, + 492 + ], + "lines": [ + { + "bbox": [ + 104, + 477, + 173, + 495 + ], + "spans": [ + { + "bbox": [ + 104, + 477, + 173, + 495 + ], + "score": 1.0, + "content": "3 MODELS", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 31 + }, + { + "type": "text", + "bbox": [ + 107, + 503, + 504, + 548 + ], + "lines": [ + { + "bbox": [ + 105, + 504, + 505, + 516 + ], + "spans": [ + { + "bbox": [ + 105, + 504, + 505, + 516 + ], + "score": 1.0, + "content": "Our primary model is INCODER-6.7B, a 6.7B Transformer (Vaswani et al., 2017) language model.", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 514, + 506, + 528 + ], + "spans": [ + { + "bbox": [ + 105, + 514, + 506, + 528 + ], + "score": 1.0, + "content": "We use the same architecture as the dense 6.7B models described in Artetxe et al. (2021); the Fairseq", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 526, + 506, + 539 + ], + "spans": [ + { + "bbox": [ + 105, + 526, + 506, + 539 + ], + "score": 1.0, + "content": "architecture description can be found in Table 6 in the appendix. All experiments use this model", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 537, + 421, + 549 + ], + "spans": [ + { + "bbox": [ + 106, + 537, + 421, + 549 + ], + "score": 1.0, + "content": "unless stated otherwise (we train smaller models for comparison in Section 5).", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 33.5 + }, + { + "type": "text", + "bbox": [ + 107, + 553, + 505, + 631 + ], + "lines": [ + { + "bbox": [ + 105, + 553, + 505, + 567 + ], + "spans": [ + { + "bbox": [ + 105, + 553, + 505, + 567 + ], + "score": 1.0, + "content": "To train our models, we collect a corpus of (1) public code with permissive, non-copyleft, open-", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 564, + 505, + 577 + ], + "spans": [ + { + "bbox": [ + 105, + 564, + 505, + 577 + ], + "score": 1.0, + "content": "source licenses from GitHub and GitLab and (2) StackOverflow questions, answers, and comments.", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 576, + 505, + 588 + ], + "spans": [ + { + "bbox": [ + 106, + 576, + 505, + 588 + ], + "score": 1.0, + "content": "Our primary focus in this paper is on the Python language, but we also include code files from", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 585, + 506, + 600 + ], + "spans": [ + { + "bbox": [ + 105, + 585, + 506, + 600 + ], + "score": 1.0, + "content": "28 total languages and StackOverflow content from all available languages. We decontaminate", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 598, + 506, + 610 + ], + "spans": [ + { + "bbox": [ + 105, + 598, + 506, + 610 + ], + "score": 1.0, + "content": "our pre-training corpus by removing all datasets which we use in our evaluation experiments. See", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 608, + 506, + 621 + ], + "spans": [ + { + "bbox": [ + 105, + 608, + 457, + 621 + ], + "score": 1.0, + "content": "Section A.1 for details. 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For example, we can perform Python docstring", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 430, + 506, + 444 + ], + "spans": [ + { + "bbox": [ + 105, + 430, + 506, + 444 + ], + "score": 1.0, + "content": "generation conditioned on both the left context (function signature) and right context (function im-", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 441, + 506, + 456 + ], + "spans": [ + { + "bbox": [ + 105, + 441, + 506, + 456 + ], + "score": 1.0, + "content": "plementation). We can also infill multiple dependent regions, e.g., generate imports required by a", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 451, + 499, + 466 + ], + "spans": [ + { + "bbox": [ + 105, + 451, + 499, + 466 + ], + "score": 1.0, + "content": "function that the model is generating. See Section B.2 for details, including multi-region infilling.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 27.5, + "bbox_fs": [ + 105, + 398, + 506, + 466 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 479, + 171, + 492 + ], + "lines": [ + { + "bbox": [ + 104, + 477, + 173, + 495 + ], + "spans": [ + { + "bbox": [ + 104, + 477, + 173, + 495 + ], + "score": 1.0, + "content": "3 MODELS", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 31 + }, + { + "type": "text", + "bbox": [ + 107, + 503, + 504, + 548 + ], + "lines": [ + { + "bbox": [ + 105, + 504, + 505, + 516 + ], + "spans": [ + { + "bbox": [ + 105, + 504, + 505, + 516 + ], + "score": 1.0, + "content": "Our primary model is INCODER-6.7B, a 6.7B Transformer (Vaswani et al., 2017) language model.", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 514, + 506, + 528 + ], + "spans": [ + { + "bbox": [ + 105, + 514, + 506, + 528 + ], + "score": 1.0, + "content": "We use the same architecture as the dense 6.7B models described in Artetxe et al. (2021); the Fairseq", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 526, + 506, + 539 + ], + "spans": [ + { + "bbox": [ + 105, + 526, + 506, + 539 + ], + "score": 1.0, + "content": "architecture description can be found in Table 6 in the appendix. All experiments use this model", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 537, + 421, + 549 + ], + "spans": [ + { + "bbox": [ + 106, + 537, + 421, + 549 + ], + "score": 1.0, + "content": "unless stated otherwise (we train smaller models for comparison in Section 5).", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 33.5, + "bbox_fs": [ + 105, + 504, + 506, + 549 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 553, + 505, + 631 + ], + "lines": [ + { + "bbox": [ + 105, + 553, + 505, + 567 + ], + "spans": [ + { + "bbox": [ + 105, + 553, + 505, + 567 + ], + "score": 1.0, + "content": "To train our models, we collect a corpus of (1) public code with permissive, non-copyleft, open-", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 564, + 505, + 577 + ], + "spans": [ + { + "bbox": [ + 105, + 564, + 505, + 577 + ], + "score": 1.0, + "content": "source licenses from GitHub and GitLab and (2) StackOverflow questions, answers, and comments.", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 106, + 576, + 505, + 588 + ], + "spans": [ + { + "bbox": [ + 106, + 576, + 505, + 588 + ], + "score": 1.0, + "content": "Our primary focus in this paper is on the Python language, but we also include code files from", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 585, + 506, + 600 + ], + "spans": [ + { + "bbox": [ + 105, + 585, + 506, + 600 + ], + "score": 1.0, + "content": "28 total languages and StackOverflow content from all available languages. We decontaminate", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 598, + 506, + 610 + ], + "spans": [ + { + "bbox": [ + 105, + 598, + 506, + 610 + ], + "score": 1.0, + "content": "our pre-training corpus by removing all datasets which we use in our evaluation experiments. See", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 608, + 506, + 621 + ], + "spans": [ + { + "bbox": [ + 105, + 608, + 457, + 621 + ], + "score": 1.0, + "content": "Section A.1 for details. Our final pre-training corpus contains a total of 159 GB of code,", + "type": "text" + }, + { + "bbox": [ + 458, + 608, + 486, + 619 + ], + "score": 0.28, + "content": "5 2 \\mathrm { G B }", + "type": "inline_equation" + }, + { + "bbox": [ + 486, + 608, + 506, + 621 + ], + "score": 1.0, + "content": "of it", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 618, + 501, + 633 + ], + "spans": [ + { + "bbox": [ + 105, + 618, + 501, + 633 + ], + "score": 1.0, + "content": "in Python, and a total of 57 GB of content from StackOverflow. See Figure 3 for size by language.", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 39, + "bbox_fs": [ + 105, + 553, + 506, + 633 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 646, + 256, + 659 + ], + "lines": [ + { + "bbox": [ + 105, + 645, + 257, + 661 + ], + "spans": [ + { + "bbox": [ + 105, + 645, + 257, + 661 + ], + "score": 1.0, + "content": "4 INFILLING EXPERIMENTS", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 43 + }, + { + "type": "text", + "bbox": [ + 107, + 670, + 505, + 703 + ], + "lines": [ + { + "bbox": [ + 105, + 670, + 505, + 684 + ], + "spans": [ + { + "bbox": [ + 105, + 670, + 505, + 684 + ], + "score": 1.0, + "content": "Our primary evaluation is performing zero-shot infilling for a diverse set of tasks: inserting lines", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 681, + 505, + 695 + ], + "spans": [ + { + "bbox": [ + 105, + 681, + 505, + 695 + ], + "score": 1.0, + "content": "of code, predicting function return types, generating docstrings, renaming variables, and inserting", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 693, + 502, + 705 + ], + "spans": [ + { + "bbox": [ + 106, + 693, + 502, + 705 + ], + "score": 1.0, + "content": "missing code tokens. We formulate each task as filling in one or more masked-out regions of code.", + "type": "text" + } + ], + "index": 46 + } + ], + "index": 45, + "bbox_fs": [ + 105, + 670, + 505, + 705 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 505, + 172 + ], + "lines": [ + { + "bbox": [ + 105, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "To evaluate how INCODER benefits from bidirectional context when generating infills, we compare", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "score": 1.0, + "content": "three different inference methods: the causal masking inference procedure described in Section 2,", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 105, + 505, + 117 + ], + "spans": [ + { + "bbox": [ + 105, + 105, + 505, + 117 + ], + "score": 1.0, + "content": "a standard left-to-right generation approach (left-to-right single), and a left-to-right generation and", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 116, + 505, + 127 + ], + "spans": [ + { + "bbox": [ + 105, + 116, + 505, + 127 + ], + "score": 1.0, + "content": "reranking approach (left-to-right reranking). Since our model is also able to generate left-to-right,", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 127, + 505, + 138 + ], + "spans": [ + { + "bbox": [ + 105, + 127, + 505, + 138 + ], + "score": 1.0, + "content": "we can compare all three inference methods using the same INCODER-6.7B model and thus avoid", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 137, + 505, + 150 + ], + "spans": [ + { + "bbox": [ + 105, + 137, + 505, + 150 + ], + "score": 1.0, + "content": "any confounding effects due to a change in the model. For all three inference methods, we obtain", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 149, + 504, + 161 + ], + "spans": [ + { + "bbox": [ + 105, + 149, + 261, + 161 + ], + "score": 1.0, + "content": "generations from the model using top-", + "type": "text" + }, + { + "bbox": [ + 261, + 150, + 268, + 160 + ], + "score": 0.78, + "content": "p", + "type": "inline_equation" + }, + { + "bbox": [ + 268, + 149, + 465, + 161 + ], + "score": 1.0, + "content": "(nucleus) sampling (Holtzman et al., 2020) with", + "type": "text" + }, + { + "bbox": [ + 466, + 149, + 504, + 160 + ], + "score": 0.85, + "content": "p = 0 . 9 5", + "type": "inline_equation" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 162, + 489, + 173 + ], + "spans": [ + { + "bbox": [ + 105, + 162, + 489, + 173 + ], + "score": 1.0, + "content": "and a temperature tuned for each task and inference method using the task’s development data.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 3.5 + }, + { + "type": "text", + "bbox": [ + 107, + 185, + 504, + 229 + ], + "lines": [ + { + "bbox": [ + 105, + 184, + 506, + 197 + ], + "spans": [ + { + "bbox": [ + 105, + 184, + 506, + 197 + ], + "score": 1.0, + "content": "Left-to-right single. This baseline does not use the context to the right of the masked location at", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 196, + 505, + 208 + ], + "spans": [ + { + "bbox": [ + 105, + 196, + 505, + 208 + ], + "score": 1.0, + "content": "all. It generates a single completion for the location by conditioning on the left context and sampling", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 207, + 506, + 220 + ], + "spans": [ + { + "bbox": [ + 105, + 207, + 267, + 220 + ], + "score": 1.0, + "content": "tokens autoregressively from the model", + "type": "text" + }, + { + "bbox": [ + 268, + 207, + 292, + 219 + ], + "score": 0.73, + "content": "P ( \\cdot \\mid", + "type": "inline_equation" + }, + { + "bbox": [ + 292, + 207, + 506, + 220 + ], + "score": 1.0, + "content": "Left) until a task-specific stop condition is reached", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 218, + 424, + 230 + ], + "spans": [ + { + "bbox": [ + 105, + 218, + 424, + 230 + ], + "score": 1.0, + "content": "(e.g., for comment generation, when a comment-ending delimiter is produced).", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 9.5 + }, + { + "type": "text", + "bbox": [ + 107, + 241, + 505, + 330 + ], + "lines": [ + { + "bbox": [ + 105, + 241, + 505, + 254 + ], + "spans": [ + { + "bbox": [ + 105, + 241, + 505, + 254 + ], + "score": 1.0, + "content": "Left-to-right reranking. This baseline uses only the left context to propose candidates to infill", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 253, + 505, + 264 + ], + "spans": [ + { + "bbox": [ + 106, + 253, + 505, + 264 + ], + "score": 1.0, + "content": "the blank, but uses both the left and right contexts to choose among these candidates. Concretely,", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 264, + 505, + 276 + ], + "spans": [ + { + "bbox": [ + 106, + 264, + 175, + 276 + ], + "score": 1.0, + "content": "we first generate", + "type": "text" + }, + { + "bbox": [ + 175, + 264, + 186, + 274 + ], + "score": 0.77, + "content": "K", + "type": "inline_equation" + }, + { + "bbox": [ + 186, + 264, + 357, + 276 + ], + "score": 1.0, + "content": "possible completions for the blank region,", + "type": "text" + }, + { + "bbox": [ + 357, + 264, + 425, + 275 + ], + "score": 0.83, + "content": "\\mathsf { S p a n } _ { 1 } \\ldots \\mathsf { S p a n } _ { K }", + "type": "inline_equation" + }, + { + "bbox": [ + 425, + 264, + 505, + 276 + ], + "score": 1.0, + "content": "following the same", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 274, + 506, + 287 + ], + "spans": [ + { + "bbox": [ + 105, + 274, + 264, + 287 + ], + "score": 1.0, + "content": "procedure as left-to-right single, using", + "type": "text" + }, + { + "bbox": [ + 264, + 275, + 299, + 285 + ], + "score": 0.9, + "content": "K = 1 0", + "type": "inline_equation" + }, + { + "bbox": [ + 299, + 274, + 506, + 287 + ], + "score": 1.0, + "content": "unless otherwise specified. We then evaluate each", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 286, + 505, + 298 + ], + "spans": [ + { + "bbox": [ + 105, + 286, + 505, + 298 + ], + "score": 1.0, + "content": "candidate by substituting it into the blank and scoring the completed document. We use either total", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 296, + 506, + 309 + ], + "spans": [ + { + "bbox": [ + 105, + 296, + 280, + 309 + ], + "score": 1.0, + "content": "log probability of the completed document", + "type": "text" + }, + { + "bbox": [ + 280, + 296, + 395, + 308 + ], + "score": 0.48, + "content": "\\log P ( [ \\mathsf { L e f t } ; \\mathsf { S p a n } _ { k } ; \\mathsf { R i g h t }", + "type": "inline_equation" + }, + { + "bbox": [ + 395, + 296, + 506, + 309 + ], + "score": 1.0, + "content": "]) or, following Chen et al.", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 307, + 506, + 320 + ], + "spans": [ + { + "bbox": [ + 106, + 307, + 506, + 320 + ], + "score": 1.0, + "content": "(2021a), log probability averaged across the number of tokens in the completed document. We select", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 319, + 505, + 331 + ], + "spans": [ + { + "bbox": [ + 105, + 319, + 505, + 331 + ], + "score": 1.0, + "content": "between these two scoring methods for each task using performance on the task’s development data.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 15.5 + }, + { + "type": "title", + "bbox": [ + 107, + 343, + 313, + 354 + ], + "lines": [ + { + "bbox": [ + 105, + 340, + 315, + 357 + ], + "spans": [ + { + "bbox": [ + 105, + 340, + 315, + 357 + ], + "score": 1.0, + "content": "4.1 INFILLING LINES OF CODE (HUMANEVAL)", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 20 + }, + { + "type": "text", + "bbox": [ + 107, + 363, + 505, + 462 + ], + "lines": [ + { + "bbox": [ + 106, + 364, + 505, + 376 + ], + "spans": [ + { + "bbox": [ + 106, + 364, + 505, + 376 + ], + "score": 1.0, + "content": "We create an infilling benchmark for complete lines of code from the HumanEval dataset (Chen", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 375, + 505, + 387 + ], + "spans": [ + { + "bbox": [ + 105, + 375, + 505, + 387 + ], + "score": 1.0, + "content": "et al., 2021a). This dataset provides comment descriptions of functions paired with a canonical", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 385, + 505, + 399 + ], + "spans": [ + { + "bbox": [ + 105, + 385, + 505, + 399 + ], + "score": 1.0, + "content": "implementation of each function and several input–output pairs that the function should pass. Hu-", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 396, + 505, + 410 + ], + "spans": [ + { + "bbox": [ + 105, + 396, + 505, + 410 + ], + "score": 1.0, + "content": "manEval was introduced as a benchmark for the synthesis of entire Python functions; we evaluate", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 408, + 505, + 420 + ], + "spans": [ + { + "bbox": [ + 105, + 408, + 505, + 420 + ], + "score": 1.0, + "content": "our models on this original synthesis setting in Section C.6. We use this dataset because it affords", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 419, + 505, + 432 + ], + "spans": [ + { + "bbox": [ + 105, + 419, + 505, + 432 + ], + "score": 1.0, + "content": "functional testing of completed code (as opposed to relying solely on an evaluation of the code sur-", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 429, + 505, + 442 + ], + "spans": [ + { + "bbox": [ + 105, + 429, + 505, + 442 + ], + "score": 1.0, + "content": "face form), which is particularly important when infilling longer regions that have more potential", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 440, + 506, + 454 + ], + "spans": [ + { + "bbox": [ + 105, + 440, + 506, + 454 + ], + "score": 1.0, + "content": "ways to be completed correctly. We construct two infilling tasks from the dataset, for single lines", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 452, + 183, + 464 + ], + "spans": [ + { + "bbox": [ + 106, + 452, + 183, + 464 + ], + "score": 1.0, + "content": "and multiple lines:", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 25 + }, + { + "type": "text", + "bbox": [ + 107, + 475, + 505, + 563 + ], + "lines": [ + { + "bbox": [ + 106, + 476, + 504, + 487 + ], + "spans": [ + { + "bbox": [ + 106, + 476, + 504, + 487 + ], + "score": 1.0, + "content": "Single-line infilling. In this task, we mask out each non-blank line of code in the canonical func-", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 487, + 505, + 497 + ], + "spans": [ + { + "bbox": [ + 106, + 487, + 257, + 497 + ], + "score": 1.0, + "content": "tion implementation in turn (creating", + "type": "text" + }, + { + "bbox": [ + 257, + 487, + 267, + 496 + ], + "score": 0.75, + "content": "N", + "type": "inline_equation" + }, + { + "bbox": [ + 267, + 487, + 385, + 497 + ], + "score": 1.0, + "content": "examples for a function with", + "type": "text" + }, + { + "bbox": [ + 386, + 487, + 396, + 496 + ], + "score": 0.77, + "content": "N", + "type": "inline_equation" + }, + { + "bbox": [ + 396, + 487, + 505, + 497 + ], + "score": 1.0, + "content": "non-blank lines). The task", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 497, + 505, + 510 + ], + "spans": [ + { + "bbox": [ + 105, + 497, + 505, + 510 + ], + "score": 1.0, + "content": "is to generate a single-line completion for the blank conditioned on the natural language description", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 508, + 505, + 520 + ], + "spans": [ + { + "bbox": [ + 105, + 508, + 505, + 520 + ], + "score": 1.0, + "content": "of the function and the code lines before and after the blank. We evaluate using (1) pass rate: the", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 104, + 518, + 506, + 532 + ], + "spans": [ + { + "bbox": [ + 104, + 518, + 506, + 532 + ], + "score": 1.0, + "content": "rate at which the completed function passes all of the function’s input–output pairs (i.e., analogous", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 529, + 506, + 543 + ], + "spans": [ + { + "bbox": [ + 105, + 529, + 151, + 543 + ], + "score": 1.0, + "content": "to the pass", + "type": "text" + }, + { + "bbox": [ + 151, + 530, + 165, + 541 + ], + "score": 0.8, + "content": "@ 1", + "type": "inline_equation" + }, + { + "bbox": [ + 166, + 529, + 506, + 543 + ], + "score": 1.0, + "content": "metric from Chen et al. (2021a) and (2) exact match: percentage of times that the", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 541, + 506, + 553 + ], + "spans": [ + { + "bbox": [ + 105, + 541, + 506, + 553 + ], + "score": 1.0, + "content": "completed lines exactly match the masked lines in the canonical implementation. Performance is", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 552, + 390, + 564 + ], + "spans": [ + { + "bbox": [ + 105, + 552, + 390, + 564 + ], + "score": 1.0, + "content": "averaged across all examples generated for all programs in the dataset.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 33.5 + }, + { + "type": "text", + "bbox": [ + 107, + 575, + 505, + 619 + ], + "lines": [ + { + "bbox": [ + 105, + 575, + 505, + 587 + ], + "spans": [ + { + "bbox": [ + 105, + 575, + 505, + 587 + ], + "score": 1.0, + "content": "Multi-line infilling. This task is constructed in the same way as single-line infilling above but", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 586, + 506, + 599 + ], + "spans": [ + { + "bbox": [ + 105, + 586, + 384, + 599 + ], + "score": 1.0, + "content": "allows each masked region to contain multiple lines of code, creating", + "type": "text" + }, + { + "bbox": [ + 384, + 586, + 450, + 598 + ], + "score": 0.93, + "content": "N \\times ( N + 1 ) / 2", + "type": "inline_equation" + }, + { + "bbox": [ + 450, + 586, + 506, + 599 + ], + "score": 1.0, + "content": "examples for", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 598, + 505, + 609 + ], + "spans": [ + { + "bbox": [ + 105, + 598, + 169, + 609 + ], + "score": 1.0, + "content": "a function with", + "type": "text" + }, + { + "bbox": [ + 169, + 598, + 180, + 607 + ], + "score": 0.76, + "content": "N", + "type": "inline_equation" + }, + { + "bbox": [ + 180, + 598, + 505, + 609 + ], + "score": 1.0, + "content": "non-blank lines. We again evaluate completions using pass rate and exact match,", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 609, + 261, + 621 + ], + "spans": [ + { + "bbox": [ + 106, + 609, + 261, + 621 + ], + "score": 1.0, + "content": "averaged across all infilling examples.", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 39.5 + }, + { + "type": "text", + "bbox": [ + 107, + 632, + 505, + 698 + ], + "lines": [ + { + "bbox": [ + 106, + 632, + 505, + 644 + ], + "spans": [ + { + "bbox": [ + 106, + 632, + 505, + 644 + ], + "score": 1.0, + "content": "Inference details. To choose when to end the infill produced by our inference methods, we trun-", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 643, + 505, + 655 + ], + "spans": [ + { + "bbox": [ + 106, + 643, + 505, + 655 + ], + "score": 1.0, + "content": "cate the candidates generated by the left-to-right (L-R) baselines to the actual number of lines in", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 653, + 506, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 653, + 506, + 667 + ], + "score": 1.0, + "content": "the blanked-out region. For our causal-masked (CM) infilling method, we end the infill when the", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 663, + 506, + 679 + ], + "spans": [ + { + "bbox": [ + 105, + 663, + 190, + 679 + ], + "score": 1.0, + "content": "model generates the", + "type": "text" + }, + { + "bbox": [ + 190, + 666, + 217, + 676 + ], + "score": 0.81, + "content": "\\mathsf { \\mathrm { \\tt { E O M } } } \\mathrm { \\mathrm { > } }", + "type": "inline_equation" + }, + { + "bbox": [ + 217, + 663, + 506, + 679 + ], + "score": 1.0, + "content": "token. For the L-R single and CM infilling methods, we sample using", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 676, + 504, + 687 + ], + "spans": [ + { + "bbox": [ + 105, + 676, + 469, + 687 + ], + "score": 1.0, + "content": "a temperature of 0.2. For the L-R rerank method, we use a temperature of 0.8 to sample", + "type": "text" + }, + { + "bbox": [ + 469, + 676, + 504, + 686 + ], + "score": 0.88, + "content": "K = 1 0", + "type": "inline_equation" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 686, + 423, + 699 + ], + "spans": [ + { + "bbox": [ + 105, + 686, + 423, + 699 + ], + "score": 1.0, + "content": "candidates and rescore with the total log probability of the completed function.", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 44.5 + } + ], + "page_idx": 3, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 106, + 712, + 504, + 731 + ], + "lines": [ + { + "bbox": [ + 120, + 710, + 506, + 723 + ], + "spans": [ + { + "bbox": [ + 120, + 710, + 506, + 723 + ], + "score": 1.0, + "content": "3For all generation experiments, we prefix prompts with meta-data indicating the code generated should be", + "type": "text" + } + ] + }, + { + "bbox": [ + 106, + 721, + 276, + 732 + ], + "spans": [ + { + "bbox": [ + 106, + 721, + 276, + 732 + ], + "score": 1.0, + "content": "Python; see Section A.3) for meta-data details.", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2023", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 752, + 308, + 759 + ], + "lines": [] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 505, + 172 + ], + "lines": [ + { + "bbox": [ + 105, + 82, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 82, + 505, + 95 + ], + "score": 1.0, + "content": "To evaluate how INCODER benefits from bidirectional context when generating infills, we compare", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 105, + 93, + 505, + 106 + ], + "score": 1.0, + "content": "three different inference methods: the causal masking inference procedure described in Section 2,", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 105, + 505, + 117 + ], + "spans": [ + { + "bbox": [ + 105, + 105, + 505, + 117 + ], + "score": 1.0, + "content": "a standard left-to-right generation approach (left-to-right single), and a left-to-right generation and", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 116, + 505, + 127 + ], + "spans": [ + { + "bbox": [ + 105, + 116, + 505, + 127 + ], + "score": 1.0, + "content": "reranking approach (left-to-right reranking). Since our model is also able to generate left-to-right,", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 127, + 505, + 138 + ], + "spans": [ + { + "bbox": [ + 105, + 127, + 505, + 138 + ], + "score": 1.0, + "content": "we can compare all three inference methods using the same INCODER-6.7B model and thus avoid", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 137, + 505, + 150 + ], + "spans": [ + { + "bbox": [ + 105, + 137, + 505, + 150 + ], + "score": 1.0, + "content": "any confounding effects due to a change in the model. For all three inference methods, we obtain", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 149, + 504, + 161 + ], + "spans": [ + { + "bbox": [ + 105, + 149, + 261, + 161 + ], + "score": 1.0, + "content": "generations from the model using top-", + "type": "text" + }, + { + "bbox": [ + 261, + 150, + 268, + 160 + ], + "score": 0.78, + "content": "p", + "type": "inline_equation" + }, + { + "bbox": [ + 268, + 149, + 465, + 161 + ], + "score": 1.0, + "content": "(nucleus) sampling (Holtzman et al., 2020) with", + "type": "text" + }, + { + "bbox": [ + 466, + 149, + 504, + 160 + ], + "score": 0.85, + "content": "p = 0 . 9 5", + "type": "inline_equation" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 162, + 489, + 173 + ], + "spans": [ + { + "bbox": [ + 105, + 162, + 489, + 173 + ], + "score": 1.0, + "content": "and a temperature tuned for each task and inference method using the task’s development data.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 3.5, + "bbox_fs": [ + 105, + 82, + 505, + 173 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 185, + 504, + 229 + ], + "lines": [ + { + "bbox": [ + 105, + 184, + 506, + 197 + ], + "spans": [ + { + "bbox": [ + 105, + 184, + 506, + 197 + ], + "score": 1.0, + "content": "Left-to-right single. This baseline does not use the context to the right of the masked location at", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 196, + 505, + 208 + ], + "spans": [ + { + "bbox": [ + 105, + 196, + 505, + 208 + ], + "score": 1.0, + "content": "all. It generates a single completion for the location by conditioning on the left context and sampling", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 207, + 506, + 220 + ], + "spans": [ + { + "bbox": [ + 105, + 207, + 267, + 220 + ], + "score": 1.0, + "content": "tokens autoregressively from the model", + "type": "text" + }, + { + "bbox": [ + 268, + 207, + 292, + 219 + ], + "score": 0.73, + "content": "P ( \\cdot \\mid", + "type": "inline_equation" + }, + { + "bbox": [ + 292, + 207, + 506, + 220 + ], + "score": 1.0, + "content": "Left) until a task-specific stop condition is reached", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 218, + 424, + 230 + ], + "spans": [ + { + "bbox": [ + 105, + 218, + 424, + 230 + ], + "score": 1.0, + "content": "(e.g., for comment generation, when a comment-ending delimiter is produced).", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 9.5, + "bbox_fs": [ + 105, + 184, + 506, + 230 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 241, + 505, + 330 + ], + "lines": [ + { + "bbox": [ + 105, + 241, + 505, + 254 + ], + "spans": [ + { + "bbox": [ + 105, + 241, + 505, + 254 + ], + "score": 1.0, + "content": "Left-to-right reranking. This baseline uses only the left context to propose candidates to infill", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 253, + 505, + 264 + ], + "spans": [ + { + "bbox": [ + 106, + 253, + 505, + 264 + ], + "score": 1.0, + "content": "the blank, but uses both the left and right contexts to choose among these candidates. Concretely,", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 264, + 505, + 276 + ], + "spans": [ + { + "bbox": [ + 106, + 264, + 175, + 276 + ], + "score": 1.0, + "content": "we first generate", + "type": "text" + }, + { + "bbox": [ + 175, + 264, + 186, + 274 + ], + "score": 0.77, + "content": "K", + "type": "inline_equation" + }, + { + "bbox": [ + 186, + 264, + 357, + 276 + ], + "score": 1.0, + "content": "possible completions for the blank region,", + "type": "text" + }, + { + "bbox": [ + 357, + 264, + 425, + 275 + ], + "score": 0.83, + "content": "\\mathsf { S p a n } _ { 1 } \\ldots \\mathsf { S p a n } _ { K }", + "type": "inline_equation" + }, + { + "bbox": [ + 425, + 264, + 505, + 276 + ], + "score": 1.0, + "content": "following the same", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 274, + 506, + 287 + ], + "spans": [ + { + "bbox": [ + 105, + 274, + 264, + 287 + ], + "score": 1.0, + "content": "procedure as left-to-right single, using", + "type": "text" + }, + { + "bbox": [ + 264, + 275, + 299, + 285 + ], + "score": 0.9, + "content": "K = 1 0", + "type": "inline_equation" + }, + { + "bbox": [ + 299, + 274, + 506, + 287 + ], + "score": 1.0, + "content": "unless otherwise specified. We then evaluate each", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 286, + 505, + 298 + ], + "spans": [ + { + "bbox": [ + 105, + 286, + 505, + 298 + ], + "score": 1.0, + "content": "candidate by substituting it into the blank and scoring the completed document. We use either total", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 296, + 506, + 309 + ], + "spans": [ + { + "bbox": [ + 105, + 296, + 280, + 309 + ], + "score": 1.0, + "content": "log probability of the completed document", + "type": "text" + }, + { + "bbox": [ + 280, + 296, + 395, + 308 + ], + "score": 0.48, + "content": "\\log P ( [ \\mathsf { L e f t } ; \\mathsf { S p a n } _ { k } ; \\mathsf { R i g h t }", + "type": "inline_equation" + }, + { + "bbox": [ + 395, + 296, + 506, + 309 + ], + "score": 1.0, + "content": "]) or, following Chen et al.", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 307, + 506, + 320 + ], + "spans": [ + { + "bbox": [ + 106, + 307, + 506, + 320 + ], + "score": 1.0, + "content": "(2021a), log probability averaged across the number of tokens in the completed document. We select", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 319, + 505, + 331 + ], + "spans": [ + { + "bbox": [ + 105, + 319, + 505, + 331 + ], + "score": 1.0, + "content": "between these two scoring methods for each task using performance on the task’s development data.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 15.5, + "bbox_fs": [ + 105, + 241, + 506, + 331 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 343, + 313, + 354 + ], + "lines": [ + { + "bbox": [ + 105, + 340, + 315, + 357 + ], + "spans": [ + { + "bbox": [ + 105, + 340, + 315, + 357 + ], + "score": 1.0, + "content": "4.1 INFILLING LINES OF CODE (HUMANEVAL)", + "type": "text" + } + ], + "index": 20 + } + ], + "index": 20 + }, + { + "type": "text", + "bbox": [ + 107, + 363, + 505, + 462 + ], + "lines": [ + { + "bbox": [ + 106, + 364, + 505, + 376 + ], + "spans": [ + { + "bbox": [ + 106, + 364, + 505, + 376 + ], + "score": 1.0, + "content": "We create an infilling benchmark for complete lines of code from the HumanEval dataset (Chen", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 375, + 505, + 387 + ], + "spans": [ + { + "bbox": [ + 105, + 375, + 505, + 387 + ], + "score": 1.0, + "content": "et al., 2021a). This dataset provides comment descriptions of functions paired with a canonical", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 385, + 505, + 399 + ], + "spans": [ + { + "bbox": [ + 105, + 385, + 505, + 399 + ], + "score": 1.0, + "content": "implementation of each function and several input–output pairs that the function should pass. Hu-", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 396, + 505, + 410 + ], + "spans": [ + { + "bbox": [ + 105, + 396, + 505, + 410 + ], + "score": 1.0, + "content": "manEval was introduced as a benchmark for the synthesis of entire Python functions; we evaluate", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 408, + 505, + 420 + ], + "spans": [ + { + "bbox": [ + 105, + 408, + 505, + 420 + ], + "score": 1.0, + "content": "our models on this original synthesis setting in Section C.6. We use this dataset because it affords", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 419, + 505, + 432 + ], + "spans": [ + { + "bbox": [ + 105, + 419, + 505, + 432 + ], + "score": 1.0, + "content": "functional testing of completed code (as opposed to relying solely on an evaluation of the code sur-", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 429, + 505, + 442 + ], + "spans": [ + { + "bbox": [ + 105, + 429, + 505, + 442 + ], + "score": 1.0, + "content": "face form), which is particularly important when infilling longer regions that have more potential", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 440, + 506, + 454 + ], + "spans": [ + { + "bbox": [ + 105, + 440, + 506, + 454 + ], + "score": 1.0, + "content": "ways to be completed correctly. We construct two infilling tasks from the dataset, for single lines", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 452, + 183, + 464 + ], + "spans": [ + { + "bbox": [ + 106, + 452, + 183, + 464 + ], + "score": 1.0, + "content": "and multiple lines:", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 25, + "bbox_fs": [ + 105, + 364, + 506, + 464 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 475, + 505, + 563 + ], + "lines": [ + { + "bbox": [ + 106, + 476, + 504, + 487 + ], + "spans": [ + { + "bbox": [ + 106, + 476, + 504, + 487 + ], + "score": 1.0, + "content": "Single-line infilling. In this task, we mask out each non-blank line of code in the canonical func-", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 487, + 505, + 497 + ], + "spans": [ + { + "bbox": [ + 106, + 487, + 257, + 497 + ], + "score": 1.0, + "content": "tion implementation in turn (creating", + "type": "text" + }, + { + "bbox": [ + 257, + 487, + 267, + 496 + ], + "score": 0.75, + "content": "N", + "type": "inline_equation" + }, + { + "bbox": [ + 267, + 487, + 385, + 497 + ], + "score": 1.0, + "content": "examples for a function with", + "type": "text" + }, + { + "bbox": [ + 386, + 487, + 396, + 496 + ], + "score": 0.77, + "content": "N", + "type": "inline_equation" + }, + { + "bbox": [ + 396, + 487, + 505, + 497 + ], + "score": 1.0, + "content": "non-blank lines). The task", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 497, + 505, + 510 + ], + "spans": [ + { + "bbox": [ + 105, + 497, + 505, + 510 + ], + "score": 1.0, + "content": "is to generate a single-line completion for the blank conditioned on the natural language description", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 508, + 505, + 520 + ], + "spans": [ + { + "bbox": [ + 105, + 508, + 505, + 520 + ], + "score": 1.0, + "content": "of the function and the code lines before and after the blank. We evaluate using (1) pass rate: the", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 104, + 518, + 506, + 532 + ], + "spans": [ + { + "bbox": [ + 104, + 518, + 506, + 532 + ], + "score": 1.0, + "content": "rate at which the completed function passes all of the function’s input–output pairs (i.e., analogous", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 529, + 506, + 543 + ], + "spans": [ + { + "bbox": [ + 105, + 529, + 151, + 543 + ], + "score": 1.0, + "content": "to the pass", + "type": "text" + }, + { + "bbox": [ + 151, + 530, + 165, + 541 + ], + "score": 0.8, + "content": "@ 1", + "type": "inline_equation" + }, + { + "bbox": [ + 166, + 529, + 506, + 543 + ], + "score": 1.0, + "content": "metric from Chen et al. (2021a) and (2) exact match: percentage of times that the", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 541, + 506, + 553 + ], + "spans": [ + { + "bbox": [ + 105, + 541, + 506, + 553 + ], + "score": 1.0, + "content": "completed lines exactly match the masked lines in the canonical implementation. Performance is", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 552, + 390, + 564 + ], + "spans": [ + { + "bbox": [ + 105, + 552, + 390, + 564 + ], + "score": 1.0, + "content": "averaged across all examples generated for all programs in the dataset.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 33.5, + "bbox_fs": [ + 104, + 476, + 506, + 564 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 575, + 505, + 619 + ], + "lines": [ + { + "bbox": [ + 105, + 575, + 505, + 587 + ], + "spans": [ + { + "bbox": [ + 105, + 575, + 505, + 587 + ], + "score": 1.0, + "content": "Multi-line infilling. This task is constructed in the same way as single-line infilling above but", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 586, + 506, + 599 + ], + "spans": [ + { + "bbox": [ + 105, + 586, + 384, + 599 + ], + "score": 1.0, + "content": "allows each masked region to contain multiple lines of code, creating", + "type": "text" + }, + { + "bbox": [ + 384, + 586, + 450, + 598 + ], + "score": 0.93, + "content": "N \\times ( N + 1 ) / 2", + "type": "inline_equation" + }, + { + "bbox": [ + 450, + 586, + 506, + 599 + ], + "score": 1.0, + "content": "examples for", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 598, + 505, + 609 + ], + "spans": [ + { + "bbox": [ + 105, + 598, + 169, + 609 + ], + "score": 1.0, + "content": "a function with", + "type": "text" + }, + { + "bbox": [ + 169, + 598, + 180, + 607 + ], + "score": 0.76, + "content": "N", + "type": "inline_equation" + }, + { + "bbox": [ + 180, + 598, + 505, + 609 + ], + "score": 1.0, + "content": "non-blank lines. We again evaluate completions using pass rate and exact match,", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 609, + 261, + 621 + ], + "spans": [ + { + "bbox": [ + 106, + 609, + 261, + 621 + ], + "score": 1.0, + "content": "averaged across all infilling examples.", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 39.5, + "bbox_fs": [ + 105, + 575, + 506, + 621 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 632, + 505, + 698 + ], + "lines": [ + { + "bbox": [ + 106, + 632, + 505, + 644 + ], + "spans": [ + { + "bbox": [ + 106, + 632, + 505, + 644 + ], + "score": 1.0, + "content": "Inference details. To choose when to end the infill produced by our inference methods, we trun-", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 643, + 505, + 655 + ], + "spans": [ + { + "bbox": [ + 106, + 643, + 505, + 655 + ], + "score": 1.0, + "content": "cate the candidates generated by the left-to-right (L-R) baselines to the actual number of lines in", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 653, + 506, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 653, + 506, + 667 + ], + "score": 1.0, + "content": "the blanked-out region. For our causal-masked (CM) infilling method, we end the infill when the", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 663, + 506, + 679 + ], + "spans": [ + { + "bbox": [ + 105, + 663, + 190, + 679 + ], + "score": 1.0, + "content": "model generates the", + "type": "text" + }, + { + "bbox": [ + 190, + 666, + 217, + 676 + ], + "score": 0.81, + "content": "\\mathsf { \\mathrm { \\tt { E O M } } } \\mathrm { \\mathrm { > } }", + "type": "inline_equation" + }, + { + "bbox": [ + 217, + 663, + 506, + 679 + ], + "score": 1.0, + "content": "token. For the L-R single and CM infilling methods, we sample using", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 676, + 504, + 687 + ], + "spans": [ + { + "bbox": [ + 105, + 676, + 469, + 687 + ], + "score": 1.0, + "content": "a temperature of 0.2. For the L-R rerank method, we use a temperature of 0.8 to sample", + "type": "text" + }, + { + "bbox": [ + 469, + 676, + 504, + 686 + ], + "score": 0.88, + "content": "K = 1 0", + "type": "inline_equation" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 686, + 423, + 699 + ], + "spans": [ + { + "bbox": [ + 105, + 686, + 423, + 699 + ], + "score": 1.0, + "content": "candidates and rescore with the total log probability of the completed function.", + "type": "text" + } + ], + "index": 47 + } + ], + "index": 44.5, + "bbox_fs": [ + 105, + 632, + 506, + 699 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 120, + 80, + 306, + 171 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 120, + 80, + 306, + 171 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 120, + 80, + 306, + 171 + ], + "spans": [ + { + "bbox": [ + 120, + 80, + 306, + 171 + ], + "score": 0.936, + "html": "
MethodPass RateExact Match
L-R single48.238.7
L-R reranking54.944.1
CM infilling69.056.3
PLBART41.6一
code-cushman-00153.142.0
code-davinci-00163.056.0
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MethodPass RateExact Match
L-R single24.915.8
L-R reranking28.217.6
CM infilling38.620.6
PLBART13.1一
code-cushman-00130.817.4
code-davinci-00137.819.8
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MethodPass RateExact Match
L-R single48.238.7
L-R reranking54.944.1
CM infilling69.056.3
PLBART41.6一
code-cushman-00153.142.0
code-davinci-00163.056.0
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MethodPass RateExact Match
L-R single24.915.8
L-R reranking28.217.6
CM infilling38.620.6
PLBART13.1一
code-cushman-00130.817.4
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Figure 2 shows a finer-grained comparison,", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 530, + 506, + 543 + ], + "spans": [ + { + "bbox": [ + 105, + 530, + 506, + 543 + ], + "score": 1.0, + "content": "where we group examples by the fraction of lines in the canonical function which are contained in", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 106, + 542, + 505, + 554 + ], + "spans": [ + { + "bbox": [ + 106, + 542, + 505, + 554 + ], + "score": 1.0, + "content": "the context to the right of the infill. The CM infilling method sees larger improvements over the", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 551, + 506, + 565 + ], + "spans": [ + { + "bbox": [ + 105, + 551, + 506, + 565 + ], + "score": 1.0, + "content": "L-R baselines as more right-sided context becomes available (i.e., when the blanked region occurs", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 565, + 201, + 577 + ], + "spans": [ + { + "bbox": [ + 106, + 565, + 201, + 577 + ], + "score": 1.0, + "content": "earlier in the function).", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 30, + "bbox_fs": [ + 105, + 476, + 506, + 577 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 582, + 505, + 662 + ], + "lines": [ + { + "bbox": [ + 106, + 582, + 505, + 595 + ], + "spans": [ + { + "bbox": [ + 106, + 582, + 505, + 595 + ], + "score": 1.0, + "content": "We also compare against two alternate zero-shot methods for incorporating right-sided context: (1)", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 593, + 505, + 606 + ], + "spans": [ + { + "bbox": [ + 105, + 593, + 505, + 606 + ], + "score": 1.0, + "content": "an encoder-decoder code model trained with a denoising infilling objective (PLBART, Ahmad et al.", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 106, + 605, + 505, + 617 + ], + "spans": [ + { + "bbox": [ + 106, + 605, + 505, + 617 + ], + "score": 1.0, + "content": "2021), and (2) templated prompting of large left-to-right generative code models (the cushman-001", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 614, + 505, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 614, + 505, + 628 + ], + "score": 1.0, + "content": "and davinci-001 Codex models available through OpenAI’s API). See Section C.1 for details on", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 627, + 505, + 641 + ], + "spans": [ + { + "bbox": [ + 105, + 627, + 505, + 641 + ], + "score": 1.0, + "content": "these experiments.5 InCoder outperforms all models in both single-line and multi-line infilling, de-", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 639, + 506, + 653 + ], + "spans": [ + { + "bbox": [ + 105, + 639, + 506, + 653 + ], + "score": 1.0, + "content": "spite having lower performance in left-to-right generation than Codex (see Table 11), demonstrating", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 650, + 291, + 664 + ], + "spans": [ + { + "bbox": [ + 105, + 650, + 291, + 664 + ], + "score": 1.0, + "content": "that causal masking training benefits infilling.", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 38, + "bbox_fs": [ + 105, + 582, + 506, + 664 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 226, + 80, + 384, + 181 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 226, + 80, + 384, + 181 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 226, + 80, + 384, + 181 + ], + "spans": [ + { + "bbox": [ + 226, + 80, + 384, + 181 + ], + "score": 0.975, + "html": "
MethodBLEU
Ours: L-R single16.05
Ours: : L-R reranking Ours: ：Causal-masked infilling17.14
18.27
RoBERTa (Finetuned) CodeBERT (Finetuned)18.14
PLBART (Finetuned)19.06 19.30
CodeT5 (Finetuned)20.36
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Our model is evaluated in a", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 201, + 506, + 213 + ], + "spans": [ + { + "bbox": [ + 105, + 201, + 506, + 213 + ], + "score": 1.0, + "content": "zero-shot setting, with no fine-tuning for docstring generation, but it approaches the performance of", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 211, + 458, + 223 + ], + "spans": [ + { + "bbox": [ + 105, + 211, + 458, + 223 + ], + "score": 1.0, + "content": "pretrained code models that are fine-tuned on the task’s 250K examples (bottom block).", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 8 + }, + { + "type": "title", + "bbox": [ + 107, + 234, + 313, + 245 + ], + "lines": [ + { + "bbox": [ + 105, + 233, + 313, + 248 + ], + "spans": [ + { + "bbox": [ + 105, + 233, + 313, + 248 + ], + "score": 1.0, + "content": "4.2 DOCSTRING GENERATION (CODEXGLUE)", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 10 + }, + { + "type": "text", + "bbox": [ + 107, + 254, + 505, + 321 + ], + "lines": [ + { + "bbox": [ + 106, + 254, + 505, + 267 + ], + "spans": [ + { + "bbox": [ + 106, + 254, + 505, + 267 + ], + "score": 1.0, + "content": "We next evaluate documentation string (docstring) generation, where models must generate a nat-", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 266, + 505, + 278 + ], + "spans": [ + { + "bbox": [ + 106, + 266, + 505, + 278 + ], + "score": 1.0, + "content": "ural language docstring that summarizes a Python code snippet. Right context may be particularly", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 277, + 505, + 289 + ], + "spans": [ + { + "bbox": [ + 106, + 277, + 505, + 289 + ], + "score": 1.0, + "content": "useful for docstring generation, as conditioning on the function body can allow models to generate", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 288, + 505, + 300 + ], + "spans": [ + { + "bbox": [ + 105, + 288, + 505, + 300 + ], + "score": 1.0, + "content": "more informative descriptions. Prior neural code generation models are fine-tuned on supervised", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 299, + 504, + 310 + ], + "spans": [ + { + "bbox": [ + 106, + 299, + 504, + 310 + ], + "score": 1.0, + "content": "docstring-code pairs to perform this task (e.g., Clement et al. 2020; Chen et al. 2021a; Lu et al.", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 308, + 500, + 322 + ], + "spans": [ + { + "bbox": [ + 105, + 308, + 500, + 322 + ], + "score": 1.0, + "content": "2021; Ahmad et al. 2021), however we evaluate our model zero-shot, with no explicit supervision.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 13.5 + }, + { + "type": "text", + "bbox": [ + 107, + 326, + 505, + 381 + ], + "lines": [ + { + "bbox": [ + 106, + 325, + 505, + 339 + ], + "spans": [ + { + "bbox": [ + 106, + 325, + 505, + 339 + ], + "score": 1.0, + "content": "We use the CodeXGLUE code-to-text docstring generation task (Lu et al., 2021), which is con-", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 337, + 505, + 350 + ], + "spans": [ + { + "bbox": [ + 105, + 337, + 505, + 350 + ], + "score": 1.0, + "content": "structed from CodeSearchNet (Husain et al., 2019), consisting of docstring-code pairs scraped from", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 348, + 506, + 362 + ], + "spans": [ + { + "bbox": [ + 105, + 348, + 506, + 362 + ], + "score": 1.0, + "content": "publicly available GitHub repositories. The L-R single candidate baseline is prompted with the", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 357, + 505, + 373 + ], + "spans": [ + { + "bbox": [ + 105, + 357, + 505, + 373 + ], + "score": 1.0, + "content": "function signature in the left context preceding the docstring. The CM infilling and L-R reranking", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 370, + 393, + 384 + ], + "spans": [ + { + "bbox": [ + 105, + 370, + 393, + 384 + ], + "score": 1.0, + "content": "methods also observe the right context, consisting of the function body.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 19 + }, + { + "type": "text", + "bbox": [ + 107, + 387, + 505, + 497 + ], + "lines": [ + { + "bbox": [ + 106, + 387, + 505, + 400 + ], + "spans": [ + { + "bbox": [ + 106, + 387, + 505, + 400 + ], + "score": 1.0, + "content": "We compare models following the original automatic evaluation setup for the task. In Table 2, we", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 104, + 397, + 506, + 411 + ], + "spans": [ + { + "bbox": [ + 104, + 397, + 506, + 411 + ], + "score": 1.0, + "content": "report smoothed 4-gram BLEU scores for all models, using the reference docstrings provided in", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 408, + 506, + 422 + ], + "spans": [ + { + "bbox": [ + 105, + 408, + 506, + 422 + ], + "score": 1.0, + "content": "the dataset. These references have been preprocessed to strip extraneous content (e.g., argument", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 419, + 506, + 433 + ], + "spans": [ + { + "bbox": [ + 105, + 419, + 506, + 433 + ], + "score": 1.0, + "content": "definitions) from the original scraped docstrings. We use greedy generation for the CM infilling and", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 430, + 505, + 443 + ], + "spans": [ + { + "bbox": [ + 105, + 430, + 325, + 443 + ], + "score": 1.0, + "content": "L-R single candidate generation methods and sample", + "type": "text" + }, + { + "bbox": [ + 325, + 431, + 361, + 442 + ], + "score": 0.9, + "content": "K = 1 0", + "type": "inline_equation" + }, + { + "bbox": [ + 361, + 430, + 505, + 443 + ], + "score": 1.0, + "content": "candidates at temperature 0.8 with", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 442, + 505, + 455 + ], + "spans": [ + { + "bbox": [ + 105, + 442, + 505, + 455 + ], + "score": 1.0, + "content": "average log probability scoring for the L-R reranking method (selected by tuning on the validation", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 452, + 506, + 466 + ], + "spans": [ + { + "bbox": [ + 105, + 452, + 506, + 466 + ], + "score": 1.0, + "content": "set of the task). For all inference methods, we stop generation if the model generates a newline. We", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 464, + 505, + 477 + ], + "spans": [ + { + "bbox": [ + 105, + 464, + 505, + 477 + ], + "score": 1.0, + "content": "also include the performance of the supervised baseline from the CodeXGLUE paper: an encoder-", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 474, + 505, + 487 + ], + "spans": [ + { + "bbox": [ + 106, + 474, + 330, + 487 + ], + "score": 1.0, + "content": "decoder model with a CodeBERT encoder fine-tuned on", + "type": "text" + }, + { + "bbox": [ + 330, + 475, + 363, + 486 + ], + "score": 0.54, + "content": "\\sim 2 5 0 \\mathrm { K }", + "type": "inline_equation" + }, + { + "bbox": [ + 363, + 474, + 505, + 487 + ], + "score": 1.0, + "content": "training examples from the dataset.", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 486, + 478, + 498 + ], + "spans": [ + { + "bbox": [ + 105, + 486, + 478, + 498 + ], + "score": 1.0, + "content": "Our zero-shot performance approaches the performance of the fine-tuned CodeBERT model.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 26.5 + }, + { + "type": "title", + "bbox": [ + 108, + 511, + 249, + 522 + ], + "lines": [ + { + "bbox": [ + 106, + 511, + 250, + 523 + ], + "spans": [ + { + "bbox": [ + 106, + 511, + 250, + 523 + ], + "score": 1.0, + "content": "4.3 RETURN TYPE PREDICTION", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 32 + }, + { + "type": "text", + "bbox": [ + 107, + 531, + 505, + 564 + ], + "lines": [ + { + "bbox": [ + 105, + 530, + 505, + 544 + ], + "spans": [ + { + "bbox": [ + 105, + 530, + 505, + 544 + ], + "score": 1.0, + "content": "Predicting return type hints for Python functions is a challenging structured generation task (see", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 542, + 505, + 555 + ], + "spans": [ + { + "bbox": [ + 105, + 542, + 505, + 555 + ], + "score": 1.0, + "content": "Figure 1, “type inference”). We evaluate on two datasets: one we construct from CodeXGLUE and", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 554, + 326, + 565 + ], + "spans": [ + { + "bbox": [ + 106, + 554, + 326, + 565 + ], + "score": 1.0, + "content": "the dataset from TypeWriter OSS (Pradel et al., 2020).", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 34 + }, + { + "type": "text", + "bbox": [ + 107, + 577, + 505, + 645 + ], + "lines": [ + { + "bbox": [ + 105, + 576, + 505, + 590 + ], + "spans": [ + { + "bbox": [ + 105, + 576, + 505, + 590 + ], + "score": 1.0, + "content": "CodeXGLUE. We develop a benchmark for return type prediction using the same Python", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 587, + 505, + 601 + ], + "spans": [ + { + "bbox": [ + 105, + 587, + 505, + 601 + ], + "score": 1.0, + "content": "CodeXGLUE dataset used in the code-to-text (docstring generation) task. 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This leaves 232", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 634, + 355, + 646 + ], + "spans": [ + { + "bbox": [ + 106, + 634, + 355, + 646 + ], + "score": 1.0, + "content": "functions in the development and 469 functions in the test set.", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 38.5 + }, + { + "type": "text", + "bbox": [ + 107, + 651, + 505, + 686 + ], + "lines": [ + { + "bbox": [ + 106, + 650, + 505, + 663 + ], + "spans": [ + { + "bbox": [ + 106, + 650, + 505, + 663 + ], + "score": 1.0, + "content": "The task is to condition on the function signature and body and predict the type hint. We compare", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 661, + 505, + 674 + ], + "spans": [ + { + "bbox": [ + 106, + 661, + 505, + 674 + ], + "score": 1.0, + "content": "the type hints predicted by our various methods to the annotated type hint in the original function,", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 674, + 336, + 687 + ], + "spans": [ + { + "bbox": [ + 105, + 674, + 336, + 687 + ], + "score": 1.0, + "content": "using exact match accuracy on the normalized type hint.7", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 43 + } + ], + "page_idx": 5, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 699, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 120, + 698, + 276, + 712 + ], + "spans": [ + { + "bbox": [ + 120, + 698, + 276, + 712 + ], + "score": 1.0, + "content": "6https://peps.python.org/pep-0484/", + "type": "text" + } + ] + }, + { + "bbox": [ + 120, + 708, + 506, + 725 + ], + "spans": [ + { + "bbox": [ + 120, + 708, + 506, + 725 + ], + "score": 1.0, + "content": "7We normalize each type hint by first parsing the type to an AST and then un-parsing the AST to a surface", + "type": "text" + } + ] + }, + { + "bbox": [ + 105, + 720, + 506, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 506, + 733 + ], + "score": 1.0, + "content": "form string, then compute exact match on these surface forms. We note that this metric is somewhat noisy, given", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 107, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2023", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 752, + 309, + 760 + ], + "lines": [ + { + "bbox": [ + 302, + 751, + 310, + 762 + ], + "spans": [ + { + "bbox": [ + 302, + 751, + 310, + 762 + ], + "score": 1.0, + "content": "6", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "table", + "bbox": [ + 226, + 80, + 384, + 181 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 226, + 80, + 384, + 181 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 226, + 80, + 384, + 181 + ], + "spans": [ + { + "bbox": [ + 226, + 80, + 384, + 181 + ], + "score": 0.975, + "html": "
MethodBLEU
Ours: L-R single16.05
Ours: : L-R reranking Ours: ：Causal-masked infilling17.14
18.27
RoBERTa (Finetuned) CodeBERT (Finetuned)18.14
PLBART (Finetuned)19.06 19.30
CodeT5 (Finetuned)20.36
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Our model is evaluated in a", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 201, + 506, + 213 + ], + "spans": [ + { + "bbox": [ + 105, + 201, + 506, + 213 + ], + "score": 1.0, + "content": "zero-shot setting, with no fine-tuning for docstring generation, but it approaches the performance of", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 211, + 458, + 223 + ], + "spans": [ + { + "bbox": [ + 105, + 211, + 458, + 223 + ], + "score": 1.0, + "content": "pretrained code models that are fine-tuned on the task’s 250K examples (bottom block).", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 8, + "bbox_fs": [ + 105, + 189, + 506, + 223 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 234, + 313, + 245 + ], + "lines": [ + { + "bbox": [ + 105, + 233, + 313, + 248 + ], + "spans": [ + { + "bbox": [ + 105, + 233, + 313, + 248 + ], + "score": 1.0, + "content": "4.2 DOCSTRING GENERATION (CODEXGLUE)", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 10 + }, + { + "type": "text", + "bbox": [ + 107, + 254, + 505, + 321 + ], + "lines": [ + { + "bbox": [ + 106, + 254, + 505, + 267 + ], + "spans": [ + { + "bbox": [ + 106, + 254, + 505, + 267 + ], + "score": 1.0, + "content": "We next evaluate documentation string (docstring) generation, where models must generate a nat-", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 266, + 505, + 278 + ], + "spans": [ + { + "bbox": [ + 106, + 266, + 505, + 278 + ], + "score": 1.0, + "content": "ural language docstring that summarizes a Python code snippet. Right context may be particularly", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 106, + 277, + 505, + 289 + ], + "spans": [ + { + "bbox": [ + 106, + 277, + 505, + 289 + ], + "score": 1.0, + "content": "useful for docstring generation, as conditioning on the function body can allow models to generate", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 288, + 505, + 300 + ], + "spans": [ + { + "bbox": [ + 105, + 288, + 505, + 300 + ], + "score": 1.0, + "content": "more informative descriptions. Prior neural code generation models are fine-tuned on supervised", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 106, + 299, + 504, + 310 + ], + "spans": [ + { + "bbox": [ + 106, + 299, + 504, + 310 + ], + "score": 1.0, + "content": "docstring-code pairs to perform this task (e.g., Clement et al. 2020; Chen et al. 2021a; Lu et al.", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 308, + 500, + 322 + ], + "spans": [ + { + "bbox": [ + 105, + 308, + 500, + 322 + ], + "score": 1.0, + "content": "2021; Ahmad et al. 2021), however we evaluate our model zero-shot, with no explicit supervision.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 13.5, + "bbox_fs": [ + 105, + 254, + 505, + 322 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 326, + 505, + 381 + ], + "lines": [ + { + "bbox": [ + 106, + 325, + 505, + 339 + ], + "spans": [ + { + "bbox": [ + 106, + 325, + 505, + 339 + ], + "score": 1.0, + "content": "We use the CodeXGLUE code-to-text docstring generation task (Lu et al., 2021), which is con-", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 337, + 505, + 350 + ], + "spans": [ + { + "bbox": [ + 105, + 337, + 505, + 350 + ], + "score": 1.0, + "content": "structed from CodeSearchNet (Husain et al., 2019), consisting of docstring-code pairs scraped from", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 348, + 506, + 362 + ], + "spans": [ + { + "bbox": [ + 105, + 348, + 506, + 362 + ], + "score": 1.0, + "content": "publicly available GitHub repositories. The L-R single candidate baseline is prompted with the", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 357, + 505, + 373 + ], + "spans": [ + { + "bbox": [ + 105, + 357, + 505, + 373 + ], + "score": 1.0, + "content": "function signature in the left context preceding the docstring. The CM infilling and L-R reranking", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 370, + 393, + 384 + ], + "spans": [ + { + "bbox": [ + 105, + 370, + 393, + 384 + ], + "score": 1.0, + "content": "methods also observe the right context, consisting of the function body.", + "type": "text" + } + ], + "index": 21 + } + ], + "index": 19, + "bbox_fs": [ + 105, + 325, + 506, + 384 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 387, + 505, + 497 + ], + "lines": [ + { + "bbox": [ + 106, + 387, + 505, + 400 + ], + "spans": [ + { + "bbox": [ + 106, + 387, + 505, + 400 + ], + "score": 1.0, + "content": "We compare models following the original automatic evaluation setup for the task. In Table 2, we", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 104, + 397, + 506, + 411 + ], + "spans": [ + { + "bbox": [ + 104, + 397, + 506, + 411 + ], + "score": 1.0, + "content": "report smoothed 4-gram BLEU scores for all models, using the reference docstrings provided in", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 408, + 506, + 422 + ], + "spans": [ + { + "bbox": [ + 105, + 408, + 506, + 422 + ], + "score": 1.0, + "content": "the dataset. These references have been preprocessed to strip extraneous content (e.g., argument", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 419, + 506, + 433 + ], + "spans": [ + { + "bbox": [ + 105, + 419, + 506, + 433 + ], + "score": 1.0, + "content": "definitions) from the original scraped docstrings. We use greedy generation for the CM infilling and", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 430, + 505, + 443 + ], + "spans": [ + { + "bbox": [ + 105, + 430, + 325, + 443 + ], + "score": 1.0, + "content": "L-R single candidate generation methods and sample", + "type": "text" + }, + { + "bbox": [ + 325, + 431, + 361, + 442 + ], + "score": 0.9, + "content": "K = 1 0", + "type": "inline_equation" + }, + { + "bbox": [ + 361, + 430, + 505, + 443 + ], + "score": 1.0, + "content": "candidates at temperature 0.8 with", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 442, + 505, + 455 + ], + "spans": [ + { + "bbox": [ + 105, + 442, + 505, + 455 + ], + "score": 1.0, + "content": "average log probability scoring for the L-R reranking method (selected by tuning on the validation", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 452, + 506, + 466 + ], + "spans": [ + { + "bbox": [ + 105, + 452, + 506, + 466 + ], + "score": 1.0, + "content": "set of the task). For all inference methods, we stop generation if the model generates a newline. We", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 464, + 505, + 477 + ], + "spans": [ + { + "bbox": [ + 105, + 464, + 505, + 477 + ], + "score": 1.0, + "content": "also include the performance of the supervised baseline from the CodeXGLUE paper: an encoder-", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 474, + 505, + 487 + ], + "spans": [ + { + "bbox": [ + 106, + 474, + 330, + 487 + ], + "score": 1.0, + "content": "decoder model with a CodeBERT encoder fine-tuned on", + "type": "text" + }, + { + "bbox": [ + 330, + 475, + 363, + 486 + ], + "score": 0.54, + "content": "\\sim 2 5 0 \\mathrm { K }", + "type": "inline_equation" + }, + { + "bbox": [ + 363, + 474, + 505, + 487 + ], + "score": 1.0, + "content": "training examples from the dataset.", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 486, + 478, + 498 + ], + "spans": [ + { + "bbox": [ + 105, + 486, + 478, + 498 + ], + "score": 1.0, + "content": "Our zero-shot performance approaches the performance of the fine-tuned CodeBERT model.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 26.5, + "bbox_fs": [ + 104, + 387, + 506, + 498 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 511, + 249, + 522 + ], + "lines": [ + { + "bbox": [ + 106, + 511, + 250, + 523 + ], + "spans": [ + { + "bbox": [ + 106, + 511, + 250, + 523 + ], + "score": 1.0, + "content": "4.3 RETURN TYPE PREDICTION", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 32 + }, + { + "type": "text", + "bbox": [ + 107, + 531, + 505, + 564 + ], + "lines": [ + { + "bbox": [ + 105, + 530, + 505, + 544 + ], + "spans": [ + { + "bbox": [ + 105, + 530, + 505, + 544 + ], + "score": 1.0, + "content": "Predicting return type hints for Python functions is a challenging structured generation task (see", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 542, + 505, + 555 + ], + "spans": [ + { + "bbox": [ + 105, + 542, + 505, + 555 + ], + "score": 1.0, + "content": "Figure 1, “type inference”). We evaluate on two datasets: one we construct from CodeXGLUE and", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 554, + 326, + 565 + ], + "spans": [ + { + "bbox": [ + 106, + 554, + 326, + 565 + ], + "score": 1.0, + "content": "the dataset from TypeWriter OSS (Pradel et al., 2020).", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 34, + "bbox_fs": [ + 105, + 530, + 505, + 565 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 577, + 505, + 645 + ], + "lines": [ + { + "bbox": [ + 105, + 576, + 505, + 590 + ], + "spans": [ + { + "bbox": [ + 105, + 576, + 505, + 590 + ], + "score": 1.0, + "content": "CodeXGLUE. We develop a benchmark for return type prediction using the same Python", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 587, + 505, + 601 + ], + "spans": [ + { + "bbox": [ + 105, + 587, + 505, + 601 + ], + "score": 1.0, + "content": "CodeXGLUE dataset used in the code-to-text (docstring generation) task. We run an abstract syntax", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 598, + 505, + 612 + ], + "spans": [ + { + "bbox": [ + 105, + 598, + 505, + 612 + ], + "score": 1.0, + "content": "tree (AST) processor on all functions in the development and test sets of this dataset to (1) identify", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 610, + 506, + 626 + ], + "spans": [ + { + "bbox": [ + 105, + 610, + 192, + 626 + ], + "score": 1.0, + "content": "functions with a PEP", + "type": "text" + }, + { + "bbox": [ + 192, + 610, + 213, + 622 + ], + "score": 0.89, + "content": "4 8 4 ^ { 6 }", + "type": "inline_equation" + }, + { + "bbox": [ + 213, + 610, + 506, + 626 + ], + "score": 1.0, + "content": "return type hint annotation that is not None and (2) remove all other type", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 622, + 505, + 635 + ], + "spans": [ + { + "bbox": [ + 105, + 622, + 505, + 635 + ], + "score": 1.0, + "content": "hints (e.g., for function arguments and variable declarations) from the function. This leaves 232", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 106, + 634, + 355, + 646 + ], + "spans": [ + { + "bbox": [ + 106, + 634, + 355, + 646 + ], + "score": 1.0, + "content": "functions in the development and 469 functions in the test set.", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 38.5, + "bbox_fs": [ + 105, + 576, + 506, + 646 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 651, + 505, + 686 + ], + "lines": [ + { + "bbox": [ + 106, + 650, + 505, + 663 + ], + "spans": [ + { + "bbox": [ + 106, + 650, + 505, + 663 + ], + "score": 1.0, + "content": "The task is to condition on the function signature and body and predict the type hint. We compare", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 661, + 505, + 674 + ], + "spans": [ + { + "bbox": [ + 106, + 661, + 505, + 674 + ], + "score": 1.0, + "content": "the type hints predicted by our various methods to the annotated type hint in the original function,", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 674, + 336, + 687 + ], + "spans": [ + { + "bbox": [ + 105, + 674, + 336, + 687 + ], + "score": 1.0, + "content": "using exact match accuracy on the normalized type hint.7", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 43, + "bbox_fs": [ + 105, + 650, + 505, + 687 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 113, + 80, + 258, + 133 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 113, + 80, + 258, + 133 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 113, + 80, + 258, + 133 + ], + "spans": [ + { + "bbox": [ + 113, + 80, + 258, + 133 + ], + "score": 0.966, + "html": "
MethodAccuracy
Left-to-right single12.0
Left-to-right reranking12.4
Causal-masked infilling58.1
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MethodPrecisionRecallF1
Ours: Left-to-right single30.830.830.8
Ours: ：Left-to-right reranking33.333.333.3
Ours: ：Causal-masked infilling59.259.259.2
TypeWriter (Supervised)54.943.248.3
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We include examples from", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 266, + 174, + 487, + 186 + ], + "spans": [ + { + "bbox": [ + 266, + 174, + 487, + 186 + ], + "score": 1.0, + "content": "which we were able to obtain source files, successfully ex-", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 265, + 184, + 487, + 197 + ], + "spans": [ + { + "bbox": [ + 265, + 184, + 487, + 197 + ], + "score": 1.0, + "content": "tract functions and types, that have non-None return type", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 265, + 194, + 487, + 206 + ], + "spans": [ + { + "bbox": [ + 265, + 194, + 487, + 206 + ], + "score": 1.0, + "content": "hints, and that were not included in our model’s training data.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 12 + } + ], + "index": 9.5 + }, + { + "type": "text", + "bbox": [ + 105, + 210, + 504, + 232 + ], + "lines": [ + { + "bbox": [ + 105, + 209, + 505, + 223 + ], + "spans": [ + { + "bbox": [ + 105, + 209, + 505, + 223 + ], + "score": 1.0, + "content": "Table 3: Results for predicting Python function return type hints on two datasets. We see substantial", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 220, + 488, + 235 + ], + "spans": [ + { + "bbox": [ + 105, + 220, + 488, + 235 + ], + "score": 1.0, + "content": "improvements from causal masked infilling over baseline methods using left-to-right inference.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 15.5 + }, + { + "type": "text", + "bbox": [ + 107, + 238, + 505, + 304 + ], + "lines": [ + { + "bbox": [ + 106, + 238, + 505, + 251 + ], + "spans": [ + { + "bbox": [ + 106, + 238, + 505, + 251 + ], + "score": 1.0, + "content": "To compare our three generation methods, we stop generation when a : is generated, which ends", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 249, + 506, + 262 + ], + "spans": [ + { + "bbox": [ + 105, + 249, + 506, + 262 + ], + "score": 1.0, + "content": "the type hint and signals the start of the function body. We tune inference hyperparameters on", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 260, + 505, + 273 + ], + "spans": [ + { + "bbox": [ + 105, + 260, + 505, + 273 + ], + "score": 1.0, + "content": "the development set, and we use a temperature of 0.2 for left-to-right-single, 0.8 for left-to-right", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 271, + 505, + 284 + ], + "spans": [ + { + "bbox": [ + 105, + 271, + 505, + 284 + ], + "score": 1.0, + "content": "reranking, and greedy generation for causal masked infilling. Results on the test set are given in", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 281, + 505, + 295 + ], + "spans": [ + { + "bbox": [ + 105, + 281, + 505, + 295 + ], + "score": 1.0, + "content": "Table 3a. Conditioning on the right context (i.e., the function body) gives some benefit in the left-", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 293, + 484, + 306 + ], + "spans": [ + { + "bbox": [ + 105, + 293, + 484, + 306 + ], + "score": 1.0, + "content": "to-right reranking setting, but gives a substantial improvement via our causal masked infilling.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 19.5 + }, + { + "type": "text", + "bbox": [ + 107, + 316, + 505, + 383 + ], + "lines": [ + { + "bbox": [ + 106, + 316, + 506, + 329 + ], + "spans": [ + { + "bbox": [ + 106, + 316, + 506, + 329 + ], + "score": 1.0, + "content": "TypeWriter OSS. Some recent work has developed supervised machine learning approaches for", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 327, + 505, + 340 + ], + "spans": [ + { + "bbox": [ + 105, + 327, + 505, + 340 + ], + "score": 1.0, + "content": "predicting type annotations for dynamically-typed languages including Python (Xu et al., 2016;", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 104, + 336, + 505, + 352 + ], + "spans": [ + { + "bbox": [ + 104, + 336, + 505, + 352 + ], + "score": 1.0, + "content": "Allamanis et al., 2020; Pradel et al., 2020) and TypeScript (Hellendoorn et al., 2018; Wei et al.,", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 104, + 348, + 505, + 363 + ], + "spans": [ + { + "bbox": [ + 104, + 348, + 505, + 363 + ], + "score": 1.0, + "content": "2020; Jesse et al., 2021). We compare our zero-shot model to one such approach for Python, Type-", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 360, + 506, + 373 + ], + "spans": [ + { + "bbox": [ + 105, + 360, + 506, + 373 + ], + "score": 1.0, + "content": "Writer (Pradel et al., 2020), which combines a neural architecture for type hint prediction with a", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 372, + 316, + 383 + ], + "spans": [ + { + "bbox": [ + 106, + 372, + 316, + 383 + ], + "score": 1.0, + "content": "search-based incremental type validation procedure.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 25.5 + }, + { + "type": "text", + "bbox": [ + 106, + 388, + 505, + 487 + ], + "lines": [ + { + "bbox": [ + 106, + 387, + 505, + 401 + ], + "spans": [ + { + "bbox": [ + 106, + 387, + 505, + 401 + ], + "score": 1.0, + "content": "To compare to the supervised TypeWriter approach, we obtain its predictions on the open-source", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 399, + 505, + 411 + ], + "spans": [ + { + "bbox": [ + 106, + 399, + 505, + 411 + ], + "score": 1.0, + "content": "software (OSS) dataset used in that work (Pradel et al., 2020), consisting of Python functions from", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 409, + 505, + 423 + ], + "spans": [ + { + "bbox": [ + 105, + 409, + 505, + 423 + ], + "score": 1.0, + "content": "GitHub. Unfortunately, we could not evaluate on their full evaluation set since much of it was in-", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 420, + 505, + 434 + ], + "spans": [ + { + "bbox": [ + 105, + 420, + 505, + 434 + ], + "score": 1.0, + "content": "cluded in our model’s training data. We filter to instances that were not included in our training data,", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 431, + 506, + 445 + ], + "spans": [ + { + "bbox": [ + 105, + 431, + 506, + 445 + ], + "score": 1.0, + "content": "for which we were able to obtain files and extract functions and types from via AST parsing, and", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 442, + 506, + 456 + ], + "spans": [ + { + "bbox": [ + 105, + 442, + 410, + 456 + ], + "score": 1.0, + "content": "which have non-NONE return type hints. This leaves 2,092 examples (about", + "type": "text" + }, + { + "bbox": [ + 410, + 443, + 429, + 453 + ], + "score": 0.89, + "content": "1 2 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 430, + 442, + 506, + 456 + ], + "score": 1.0, + "content": "of their evaluation", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 453, + 505, + 467 + ], + "spans": [ + { + "bbox": [ + 105, + 453, + 505, + 467 + ], + "score": 1.0, + "content": "set). We otherwise emulate their exact setup, which allows our model to condition on file imports,", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 464, + 505, + 478 + ], + "spans": [ + { + "bbox": [ + 105, + 464, + 505, + 478 + ], + "score": 1.0, + "content": "the function body, and the function signature to predict return type hints. We use the same inference", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 476, + 370, + 488 + ], + "spans": [ + { + "bbox": [ + 105, + 476, + 370, + 488 + ], + "score": 1.0, + "content": "hyperparameters as we did for CodeXGLUE type hint prediction.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 33 + }, + { + "type": "text", + "bbox": [ + 107, + 493, + 505, + 539 + ], + "lines": [ + { + "bbox": [ + 105, + 492, + 505, + 506 + ], + "spans": [ + { + "bbox": [ + 105, + 492, + 505, + 506 + ], + "score": 1.0, + "content": "We present our results in two tables: Table 3b containing metrics across non-None types, and Ta-", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 505, + 505, + 518 + ], + "spans": [ + { + "bbox": [ + 105, + 505, + 505, + 518 + ], + "score": 1.0, + "content": "ble 10 in the Appendix, which includes None types as well (following Pradel et al. 2020).8 We again", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 516, + 505, + 530 + ], + "spans": [ + { + "bbox": [ + 105, + 516, + 505, + 530 + ], + "score": 1.0, + "content": "see benefits from causal masked infilling’s ability to condition on the function body when generating", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 528, + 482, + 540 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 482, + 540 + ], + "score": 1.0, + "content": "return types, and find that our zero-shot model outperforms the supervised TypeWriter model.", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 39.5 + }, + { + "type": "title", + "bbox": [ + 108, + 552, + 261, + 563 + ], + "lines": [ + { + "bbox": [ + 106, + 552, + 263, + 565 + ], + "spans": [ + { + "bbox": [ + 106, + 552, + 263, + 565 + ], + "score": 1.0, + "content": "4.4 VARIABLE NAME PREDICTION", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 42 + }, + { + "type": "text", + "bbox": [ + 106, + 573, + 505, + 684 + ], + "lines": [ + { + "bbox": [ + 105, + 572, + 505, + 585 + ], + "spans": [ + { + "bbox": [ + 105, + 572, + 505, + 585 + ], + "score": 1.0, + "content": "Variable name prediction is a less-constrained code generation task that requires modeling bidirec-", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 583, + 505, + 597 + ], + "spans": [ + { + "bbox": [ + 105, + 583, + 505, + 597 + ], + "score": 1.0, + "content": "tional context. We again use the test set from the CodexGlue code-to-text task (docstring generation)", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 595, + 505, + 608 + ], + "spans": [ + { + "bbox": [ + 105, + 595, + 505, + 608 + ], + "score": 1.0, + "content": "and run an AST transform to isolate and either mask all the occurrences of the variable name (in-", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 606, + 505, + 619 + ], + "spans": [ + { + "bbox": [ + 105, + 606, + 505, + 619 + ], + "score": 1.0, + "content": "filling) or take the left-most context from the first variable name (left-to-right mode). In the infilling", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 617, + 505, + 630 + ], + "spans": [ + { + "bbox": [ + 105, + 617, + 505, + 630 + ], + "score": 1.0, + "content": "setting, given that we generate the number of masks equivalent to the number of times a variable", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 628, + 505, + 640 + ], + "spans": [ + { + "bbox": [ + 105, + 628, + 505, + 640 + ], + "score": 1.0, + "content": "is seen, we select the most common prediction as our singular prediction. Furthermore, we only", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 638, + 505, + 651 + ], + "spans": [ + { + "bbox": [ + 105, + 638, + 505, + 651 + ], + "score": 1.0, + "content": "evaluate the set of variable names containing four or more characters. For our re-ranking, we con-", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 106, + 650, + 505, + 662 + ], + "spans": [ + { + "bbox": [ + 106, + 650, + 505, + 662 + ], + "score": 1.0, + "content": "sider a candidate set of 25 variables. We present our results in Table 4. We again see substantial", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 104, + 659, + 506, + 675 + ], + "spans": [ + { + "bbox": [ + 104, + 659, + 506, + 675 + ], + "score": 1.0, + "content": "benefits from using both left and right context: left-to-right reranking and causal-masked infilling", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 105, + 672, + 505, + 685 + ], + "spans": [ + { + "bbox": [ + 105, + 672, + 505, + 685 + ], + "score": 1.0, + "content": "both outperform the left-to-right single baseline (which uses only the left context). Causal-masked", + "type": "text" + } + ], + "index": 52 + } + ], + "index": 47.5 + } + ], + "page_idx": 6, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2023", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 106, + 689, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 689, + 505, + 703 + ], + "spans": [ + { + "bbox": [ + 105, + 689, + 505, + 703 + ], + "score": 1.0, + "content": "that human-annotated type hints can be inaccurate, and that exact match does not reason about type unification", + "type": "text" + } + ] + }, + { + "bbox": [ + 105, + 699, + 505, + 714 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 505, + 714 + ], + "score": 1.0, + "content": "or equivalence (e.g., there is no partial credit given for predicting Optional[str] rather than Union[None,", + "type": "text" + } + ] + }, + { + "bbox": [ + 106, + 709, + 132, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 132, + 722 + ], + "score": 1.0, + "content": "str]).", + "type": "text" + } + ] + }, + { + "bbox": [ + 120, + 718, + 486, + 736 + ], + "spans": [ + { + "bbox": [ + 120, + 718, + 486, + 736 + ], + "score": 1.0, + "content": "8Our model makes a prediction for every example, so it has identical precision, recall, and F1 scores.", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 309, + 759 + ], + "lines": [ + { + "bbox": [ + 302, + 750, + 309, + 762 + ], + "spans": [ + { + "bbox": [ + 302, + 750, + 309, + 762 + ], + "score": 1.0, + "content": "7", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "table", + "bbox": [ + 113, + 80, + 258, + 133 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 113, + 80, + 258, + 133 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 113, + 80, + 258, + 133 + ], + "spans": [ + { + "bbox": [ + 113, + 80, + 258, + 133 + ], + "score": 0.966, + "html": "
MethodAccuracy
Left-to-right single12.0
Left-to-right reranking12.4
Causal-masked infilling58.1
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MethodPrecisionRecallF1
Ours: Left-to-right single30.830.830.8
Ours: ：Left-to-right reranking33.333.333.3
Ours: ：Causal-masked infilling59.259.259.2
TypeWriter (Supervised)54.943.248.3
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We include examples from", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 266, + 174, + 487, + 186 + ], + "spans": [ + { + "bbox": [ + 266, + 174, + 487, + 186 + ], + "score": 1.0, + "content": "which we were able to obtain source files, successfully ex-", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 265, + 184, + 487, + 197 + ], + "spans": [ + { + "bbox": [ + 265, + 184, + 487, + 197 + ], + "score": 1.0, + "content": "tract functions and types, that have non-None return type", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 265, + 194, + 487, + 206 + ], + "spans": [ + { + "bbox": [ + 265, + 194, + 487, + 206 + ], + "score": 1.0, + "content": "hints, and that were not included in our model’s training data.", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 12 + } + ], + "index": 9.5 + }, + { + "type": "text", + "bbox": [ + 105, + 210, + 504, + 232 + ], + "lines": [ + { + "bbox": [ + 105, + 209, + 505, + 223 + ], + "spans": [ + { + "bbox": [ + 105, + 209, + 505, + 223 + ], + "score": 1.0, + "content": "Table 3: Results for predicting Python function return type hints on two datasets. We see substantial", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 220, + 488, + 235 + ], + "spans": [ + { + "bbox": [ + 105, + 220, + 488, + 235 + ], + "score": 1.0, + "content": "improvements from causal masked infilling over baseline methods using left-to-right inference.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 15.5, + "bbox_fs": [ + 105, + 209, + 505, + 235 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 238, + 505, + 304 + ], + "lines": [ + { + "bbox": [ + 106, + 238, + 505, + 251 + ], + "spans": [ + { + "bbox": [ + 106, + 238, + 505, + 251 + ], + "score": 1.0, + "content": "To compare our three generation methods, we stop generation when a : is generated, which ends", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 249, + 506, + 262 + ], + "spans": [ + { + "bbox": [ + 105, + 249, + 506, + 262 + ], + "score": 1.0, + "content": "the type hint and signals the start of the function body. We tune inference hyperparameters on", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 260, + 505, + 273 + ], + "spans": [ + { + "bbox": [ + 105, + 260, + 505, + 273 + ], + "score": 1.0, + "content": "the development set, and we use a temperature of 0.2 for left-to-right-single, 0.8 for left-to-right", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 271, + 505, + 284 + ], + "spans": [ + { + "bbox": [ + 105, + 271, + 505, + 284 + ], + "score": 1.0, + "content": "reranking, and greedy generation for causal masked infilling. Results on the test set are given in", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 281, + 505, + 295 + ], + "spans": [ + { + "bbox": [ + 105, + 281, + 505, + 295 + ], + "score": 1.0, + "content": "Table 3a. Conditioning on the right context (i.e., the function body) gives some benefit in the left-", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 293, + 484, + 306 + ], + "spans": [ + { + "bbox": [ + 105, + 293, + 484, + 306 + ], + "score": 1.0, + "content": "to-right reranking setting, but gives a substantial improvement via our causal masked infilling.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 19.5, + "bbox_fs": [ + 105, + 238, + 506, + 306 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 316, + 505, + 383 + ], + "lines": [ + { + "bbox": [ + 106, + 316, + 506, + 329 + ], + "spans": [ + { + "bbox": [ + 106, + 316, + 506, + 329 + ], + "score": 1.0, + "content": "TypeWriter OSS. Some recent work has developed supervised machine learning approaches for", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 327, + 505, + 340 + ], + "spans": [ + { + "bbox": [ + 105, + 327, + 505, + 340 + ], + "score": 1.0, + "content": "predicting type annotations for dynamically-typed languages including Python (Xu et al., 2016;", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 104, + 336, + 505, + 352 + ], + "spans": [ + { + "bbox": [ + 104, + 336, + 505, + 352 + ], + "score": 1.0, + "content": "Allamanis et al., 2020; Pradel et al., 2020) and TypeScript (Hellendoorn et al., 2018; Wei et al.,", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 104, + 348, + 505, + 363 + ], + "spans": [ + { + "bbox": [ + 104, + 348, + 505, + 363 + ], + "score": 1.0, + "content": "2020; Jesse et al., 2021). We compare our zero-shot model to one such approach for Python, Type-", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 360, + 506, + 373 + ], + "spans": [ + { + "bbox": [ + 105, + 360, + 506, + 373 + ], + "score": 1.0, + "content": "Writer (Pradel et al., 2020), which combines a neural architecture for type hint prediction with a", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 372, + 316, + 383 + ], + "spans": [ + { + "bbox": [ + 106, + 372, + 316, + 383 + ], + "score": 1.0, + "content": "search-based incremental type validation procedure.", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 25.5, + "bbox_fs": [ + 104, + 316, + 506, + 383 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 388, + 505, + 487 + ], + "lines": [ + { + "bbox": [ + 106, + 387, + 505, + 401 + ], + "spans": [ + { + "bbox": [ + 106, + 387, + 505, + 401 + ], + "score": 1.0, + "content": "To compare to the supervised TypeWriter approach, we obtain its predictions on the open-source", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 399, + 505, + 411 + ], + "spans": [ + { + "bbox": [ + 106, + 399, + 505, + 411 + ], + "score": 1.0, + "content": "software (OSS) dataset used in that work (Pradel et al., 2020), consisting of Python functions from", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 409, + 505, + 423 + ], + "spans": [ + { + "bbox": [ + 105, + 409, + 505, + 423 + ], + "score": 1.0, + "content": "GitHub. Unfortunately, we could not evaluate on their full evaluation set since much of it was in-", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 420, + 505, + 434 + ], + "spans": [ + { + "bbox": [ + 105, + 420, + 505, + 434 + ], + "score": 1.0, + "content": "cluded in our model’s training data. We filter to instances that were not included in our training data,", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 431, + 506, + 445 + ], + "spans": [ + { + "bbox": [ + 105, + 431, + 506, + 445 + ], + "score": 1.0, + "content": "for which we were able to obtain files and extract functions and types from via AST parsing, and", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 442, + 506, + 456 + ], + "spans": [ + { + "bbox": [ + 105, + 442, + 410, + 456 + ], + "score": 1.0, + "content": "which have non-NONE return type hints. This leaves 2,092 examples (about", + "type": "text" + }, + { + "bbox": [ + 410, + 443, + 429, + 453 + ], + "score": 0.89, + "content": "1 2 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 430, + 442, + 506, + 456 + ], + "score": 1.0, + "content": "of their evaluation", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 453, + 505, + 467 + ], + "spans": [ + { + "bbox": [ + 105, + 453, + 505, + 467 + ], + "score": 1.0, + "content": "set). We otherwise emulate their exact setup, which allows our model to condition on file imports,", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 464, + 505, + 478 + ], + "spans": [ + { + "bbox": [ + 105, + 464, + 505, + 478 + ], + "score": 1.0, + "content": "the function body, and the function signature to predict return type hints. We use the same inference", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 476, + 370, + 488 + ], + "spans": [ + { + "bbox": [ + 105, + 476, + 370, + 488 + ], + "score": 1.0, + "content": "hyperparameters as we did for CodeXGLUE type hint prediction.", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 33, + "bbox_fs": [ + 105, + 387, + 506, + 488 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 493, + 505, + 539 + ], + "lines": [ + { + "bbox": [ + 105, + 492, + 505, + 506 + ], + "spans": [ + { + "bbox": [ + 105, + 492, + 505, + 506 + ], + "score": 1.0, + "content": "We present our results in two tables: Table 3b containing metrics across non-None types, and Ta-", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 505, + 505, + 518 + ], + "spans": [ + { + "bbox": [ + 105, + 505, + 505, + 518 + ], + "score": 1.0, + "content": "ble 10 in the Appendix, which includes None types as well (following Pradel et al. 2020).8 We again", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 516, + 505, + 530 + ], + "spans": [ + { + "bbox": [ + 105, + 516, + 505, + 530 + ], + "score": 1.0, + "content": "see benefits from causal masked infilling’s ability to condition on the function body when generating", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 528, + 482, + 540 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 482, + 540 + ], + "score": 1.0, + "content": "return types, and find that our zero-shot model outperforms the supervised TypeWriter model.", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 39.5, + "bbox_fs": [ + 105, + 492, + 505, + 540 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 552, + 261, + 563 + ], + "lines": [ + { + "bbox": [ + 106, + 552, + 263, + 565 + ], + "spans": [ + { + "bbox": [ + 106, + 552, + 263, + 565 + ], + "score": 1.0, + "content": "4.4 VARIABLE NAME PREDICTION", + "type": "text" + } + ], + "index": 42 + } + ], + "index": 42 + }, + { + "type": "text", + "bbox": [ + 106, + 573, + 505, + 684 + ], + "lines": [ + { + "bbox": [ + 105, + 572, + 505, + 585 + ], + "spans": [ + { + "bbox": [ + 105, + 572, + 505, + 585 + ], + "score": 1.0, + "content": "Variable name prediction is a less-constrained code generation task that requires modeling bidirec-", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 583, + 505, + 597 + ], + "spans": [ + { + "bbox": [ + 105, + 583, + 505, + 597 + ], + "score": 1.0, + "content": "tional context. We again use the test set from the CodexGlue code-to-text task (docstring generation)", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 595, + 505, + 608 + ], + "spans": [ + { + "bbox": [ + 105, + 595, + 505, + 608 + ], + "score": 1.0, + "content": "and run an AST transform to isolate and either mask all the occurrences of the variable name (in-", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 606, + 505, + 619 + ], + "spans": [ + { + "bbox": [ + 105, + 606, + 505, + 619 + ], + "score": 1.0, + "content": "filling) or take the left-most context from the first variable name (left-to-right mode). 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For our re-ranking, we con-", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 106, + 650, + 505, + 662 + ], + "spans": [ + { + "bbox": [ + 106, + 650, + 505, + 662 + ], + "score": 1.0, + "content": "sider a candidate set of 25 variables. We present our results in Table 4. We again see substantial", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 104, + 659, + 506, + 675 + ], + "spans": [ + { + "bbox": [ + 104, + 659, + 506, + 675 + ], + "score": 1.0, + "content": "benefits from using both left and right context: left-to-right reranking and causal-masked infilling", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 105, + 672, + 505, + 685 + ], + "spans": [ + { + "bbox": [ + 105, + 672, + 505, + 685 + ], + "score": 1.0, + "content": "both outperform the left-to-right single baseline (which uses only the left context). 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MethodAccuracy
Left-to-right single18.4
Left-to-right reranking23.5
Causal-masked infilling30.6
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Our", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 153, + 505, + 165 + ], + "spans": [ + { + "bbox": [ + 105, + 153, + 505, + 165 + ], + "score": 1.0, + "content": "model benefits from using the right-sided context in selecting (L-R reranking and CM infilling) and", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 164, + 273, + 176 + ], + "spans": [ + { + "bbox": [ + 105, + 164, + 273, + 176 + ], + "score": 1.0, + "content": "proposing (CM infilling) variable names.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 3 + }, + { + "type": "text", + "bbox": [ + 106, + 180, + 504, + 203 + ], + "lines": [ + { + "bbox": [ + 105, + 178, + 505, + 194 + ], + "spans": [ + { + "bbox": [ + 105, + 178, + 505, + 194 + ], + "score": 1.0, + "content": "infilling substantially on the left-to-right reranking method, demonstrating the value of conditioning", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 192, + 347, + 204 + ], + "spans": [ + { + "bbox": [ + 106, + 192, + 347, + 204 + ], + "score": 1.0, + "content": "on the right context when proposing candidate completions.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 5.5 + }, + { + "type": "title", + "bbox": [ + 108, + 219, + 257, + 231 + ], + "lines": [ + { + "bbox": [ + 105, + 218, + 258, + 233 + ], + "spans": [ + { + "bbox": [ + 105, + 218, + 258, + 233 + ], + "score": 1.0, + "content": "5 ABLATION EXPERIMENTS", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 7 + }, + { + "type": "text", + "bbox": [ + 107, + 243, + 505, + 287 + ], + "lines": [ + { + "bbox": [ + 105, + 244, + 505, + 255 + ], + "spans": [ + { + "bbox": [ + 105, + 244, + 505, + 255 + ], + "score": 1.0, + "content": "For an analysis of the effects of training a model with causal masking (rather than the standard", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 255, + 505, + 267 + ], + "spans": [ + { + "bbox": [ + 105, + 255, + 505, + 267 + ], + "score": 1.0, + "content": "language modeling objective, as well as model size and the training data, we train several variations", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 266, + 505, + 277 + ], + "spans": [ + { + "bbox": [ + 105, + 266, + 273, + 277 + ], + "score": 1.0, + "content": "of our model. We compare model pass", + "type": "text" + }, + { + "bbox": [ + 273, + 266, + 288, + 276 + ], + "score": 0.74, + "content": "@ 1", + "type": "inline_equation" + }, + { + "bbox": [ + 289, + 266, + 505, + 277 + ], + "score": 1.0, + "content": "scores on the HumanEval (Chen et al., 2021a) and", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 276, + 453, + 288 + ], + "spans": [ + { + "bbox": [ + 105, + 276, + 453, + 288 + ], + "score": 1.0, + "content": "MBPP (Austin et al., 2021) left-to-right synthesis benchmarks, with results in Table 5.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 9.5 + }, + { + "type": "text", + "bbox": [ + 107, + 299, + 505, + 366 + ], + "lines": [ + { + "bbox": [ + 106, + 300, + 505, + 311 + ], + "spans": [ + { + "bbox": [ + 106, + 300, + 505, + 311 + ], + "score": 1.0, + "content": "Objective. Comparing 1.3B parameter models trained on the same training data with the causal", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 310, + 505, + 323 + ], + "spans": [ + { + "bbox": [ + 105, + 310, + 505, + 323 + ], + "score": 1.0, + "content": "masked (CM) objective (row 2) and the standard left-to-right language modeling (LM) objective", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 321, + 505, + 334 + ], + "spans": [ + { + "bbox": [ + 106, + 321, + 505, + 334 + ], + "score": 1.0, + "content": "(row 3), we see that the causal-masked model obtains slightly higher performance on the HumanEval", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 332, + 505, + 345 + ], + "spans": [ + { + "bbox": [ + 105, + 332, + 203, + 345 + ], + "score": 1.0, + "content": "and MBPP tasks in pass", + "type": "text" + }, + { + "bbox": [ + 204, + 333, + 218, + 343 + ], + "score": 0.74, + "content": "@ 1", + "type": "inline_equation" + }, + { + "bbox": [ + 218, + 332, + 505, + 345 + ], + "score": 1.0, + "content": "score. This provides further evidence that causal masking training does", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 344, + 505, + 356 + ], + "spans": [ + { + "bbox": [ + 105, + 344, + 505, + 356 + ], + "score": 1.0, + "content": "not hurt the model’s ability to perform standard left-to-right generation, at least to the 1.3B parameter", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 354, + 331, + 367 + ], + "spans": [ + { + "bbox": [ + 105, + 354, + 331, + 367 + ], + "score": 1.0, + "content": "scale, in line with the findings of Bavarian et al. (2022).", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 14.5 + }, + { + "type": "text", + "bbox": [ + 106, + 378, + 504, + 400 + ], + "lines": [ + { + "bbox": [ + 105, + 376, + 505, + 391 + ], + "spans": [ + { + "bbox": [ + 105, + 376, + 505, + 391 + ], + "score": 1.0, + "content": "Model size. With data fixed, increasing model size consistently improves performance (comparing", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 388, + 505, + 401 + ], + "spans": [ + { + "bbox": [ + 105, + 388, + 505, + 401 + ], + "score": 1.0, + "content": "the 6.7B and 1.3B CM models in rows 1 and 2, and the 1.3B and 2.3B LM models in rows 3 and 6).", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 18.5 + }, + { + "type": "text", + "bbox": [ + 107, + 412, + 505, + 501 + ], + "lines": [ + { + "bbox": [ + 105, + 411, + 506, + 425 + ], + "spans": [ + { + "bbox": [ + 105, + 411, + 506, + 425 + ], + "score": 1.0, + "content": "Effects of data. We compare models trained on our entire dataset of multiple code languages", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 423, + 505, + 435 + ], + "spans": [ + { + "bbox": [ + 105, + 423, + 235, + 435 + ], + "score": 1.0, + "content": "and StackOverflow (multi lang", + "type": "text" + }, + { + "bbox": [ + 236, + 423, + 259, + 434 + ], + "score": 0.56, + "content": "+ \\ S O", + "type": "inline_equation" + }, + { + "bbox": [ + 260, + 423, + 505, + 435 + ], + "score": 1.0, + "content": ", described in Section A.1) to data ablations that train only", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 434, + 505, + 447 + ], + "spans": [ + { + "bbox": [ + 105, + 434, + 306, + 447 + ], + "score": 1.0, + "content": "on Python code files and StackOverflow (Python", + "type": "text" + }, + { + "bbox": [ + 307, + 434, + 331, + 445 + ], + "score": 0.62, + "content": "+ \\ S O", + "type": "inline_equation" + }, + { + "bbox": [ + 331, + 434, + 505, + 447 + ], + "score": 1.0, + "content": ") and only Python code files (Python). We", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 445, + 505, + 457 + ], + "spans": [ + { + "bbox": [ + 105, + 445, + 505, + 457 + ], + "score": 1.0, + "content": "find that training on multiple languages gives a slight reduction in performance on these Python", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 455, + 505, + 470 + ], + "spans": [ + { + "bbox": [ + 105, + 455, + 505, + 470 + ], + "score": 1.0, + "content": "evaluations. However, comparing rows 4 and 5, we see that including StackOverflow data in training", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 467, + 505, + 479 + ], + "spans": [ + { + "bbox": [ + 105, + 467, + 505, + 479 + ], + "score": 1.0, + "content": "substantially improves performance on both HumanEval and MBPP. This suggests that future work", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 478, + 505, + 491 + ], + "spans": [ + { + "bbox": [ + 105, + 478, + 505, + 491 + ], + "score": 1.0, + "content": "on generative code models for language-guided synthesis tasks should consider using StackOverflow", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 489, + 381, + 501 + ], + "spans": [ + { + "bbox": [ + 105, + 489, + 381, + 501 + ], + "score": 1.0, + "content": "or other corpora that mix natural language and code as training data.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 23.5 + }, + { + "type": "title", + "bbox": [ + 108, + 516, + 256, + 529 + ], + "lines": [ + { + "bbox": [ + 105, + 515, + 258, + 532 + ], + "spans": [ + { + "bbox": [ + 105, + 515, + 258, + 532 + ], + "score": 1.0, + "content": "6 QUALITATIVE EXAMPLES", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 28 + }, + { + "type": "table", + "bbox": [ + 123, + 592, + 487, + 685 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 108, + 540, + 505, + 586 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 540, + 505, + 554 + ], + "spans": [ + { + "bbox": [ + 105, + 540, + 505, + 554 + ], + "score": 1.0, + "content": "We show a variety of qualitative examples from our model in Section D.2 in both the infilling and", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 552, + 505, + 565 + ], + "spans": [ + { + "bbox": [ + 105, + 552, + 505, + 565 + ], + "score": 1.0, + "content": "left-to-right generation modes: docstring generation, metadata conditioning, class attribute inference", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 563, + 505, + 576 + ], + "spans": [ + { + "bbox": [ + 105, + 563, + 505, + 576 + ], + "score": 1.0, + "content": "from class usage, comment-conditioned code editing, StackOverflow title and tag generation, and", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 573, + 443, + 587 + ], + "spans": [ + { + "bbox": [ + 105, + 573, + 443, + 587 + ], + "score": 1.0, + "content": "zero-shot bidirectional translation of technical jargon between Chinese and English.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 30.5 + }, + { + "type": "table_body", + "bbox": [ + 123, + 592, + 487, + 685 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 123, + 592, + 487, + 685 + ], + "spans": [ + { + "bbox": [ + 123, + 592, + 487, + 685 + ], + "score": 0.982, + "html": "
#Size (B)Obj.Training DataData SizeTrain TokensTrain ComputeHumanEval Pass@1MBPP Pass@1
1)6.7CMmulti lang + SO204 GB52B3.0Z1519.4
2)1.3CMmulti lang + SO204 GB52B0.6Z810.9
3)1.3LMmulti lang + SO204 GB52B0.6Z68.9
4)1.3LMPython + SO104 GB25B0.3Z99.8
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MethodAccuracy
Left-to-right single18.4
Left-to-right reranking23.5
Causal-masked infilling30.6
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Our", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 153, + 505, + 165 + ], + "spans": [ + { + "bbox": [ + 105, + 153, + 505, + 165 + ], + "score": 1.0, + "content": "model benefits from using the right-sided context in selecting (L-R reranking and CM infilling) and", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 164, + 273, + 176 + ], + "spans": [ + { + "bbox": [ + 105, + 164, + 273, + 176 + ], + "score": 1.0, + "content": "proposing (CM infilling) variable names.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 3, + "bbox_fs": [ + 105, + 140, + 505, + 176 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 180, + 504, + 203 + ], + "lines": [ + { + "bbox": [ + 105, + 178, + 505, + 194 + ], + "spans": [ + { + "bbox": [ + 105, + 178, + 505, + 194 + ], + "score": 1.0, + "content": "infilling substantially on the left-to-right reranking method, demonstrating the value of conditioning", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 192, + 347, + 204 + ], + "spans": [ + { + "bbox": [ + 106, + 192, + 347, + 204 + ], + "score": 1.0, + "content": "on the right context when proposing candidate completions.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 5.5, + "bbox_fs": [ + 105, + 178, + 505, + 204 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 219, + 257, + 231 + ], + "lines": [ + { + "bbox": [ + 105, + 218, + 258, + 233 + ], + "spans": [ + { + "bbox": [ + 105, + 218, + 258, + 233 + ], + "score": 1.0, + "content": "5 ABLATION EXPERIMENTS", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 7 + }, + { + "type": "text", + "bbox": [ + 107, + 243, + 505, + 287 + ], + "lines": [ + { + "bbox": [ + 105, + 244, + 505, + 255 + ], + "spans": [ + { + "bbox": [ + 105, + 244, + 505, + 255 + ], + "score": 1.0, + "content": "For an analysis of the effects of training a model with causal masking (rather than the standard", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 255, + 505, + 267 + ], + "spans": [ + { + "bbox": [ + 105, + 255, + 505, + 267 + ], + "score": 1.0, + "content": "language modeling objective, as well as model size and the training data, we train several variations", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 266, + 505, + 277 + ], + "spans": [ + { + "bbox": [ + 105, + 266, + 273, + 277 + ], + "score": 1.0, + "content": "of our model. 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With data fixed, increasing model size consistently improves performance (comparing", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 388, + 505, + 401 + ], + "spans": [ + { + "bbox": [ + 105, + 388, + 505, + 401 + ], + "score": 1.0, + "content": "the 6.7B and 1.3B CM models in rows 1 and 2, and the 1.3B and 2.3B LM models in rows 3 and 6).", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 18.5, + "bbox_fs": [ + 105, + 376, + 505, + 401 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 412, + 505, + 501 + ], + "lines": [ + { + "bbox": [ + 105, + 411, + 506, + 425 + ], + "spans": [ + { + "bbox": [ + 105, + 411, + 506, + 425 + ], + "score": 1.0, + "content": "Effects of data. 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This suggests that future work", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 478, + 505, + 491 + ], + "spans": [ + { + "bbox": [ + 105, + 478, + 505, + 491 + ], + "score": 1.0, + "content": "on generative code models for language-guided synthesis tasks should consider using StackOverflow", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 489, + 381, + 501 + ], + "spans": [ + { + "bbox": [ + 105, + 489, + 381, + 501 + ], + "score": 1.0, + "content": "or other corpora that mix natural language and code as training data.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 23.5, + "bbox_fs": [ + 105, + 411, + 506, + 501 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 516, + 256, + 529 + ], + "lines": [ + { + "bbox": [ + 105, + 515, + 258, + 532 + ], + "spans": [ + { + "bbox": [ + 105, + 515, + 258, + 532 + ], + "score": 1.0, + "content": "6 QUALITATIVE EXAMPLES", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 28 + }, + { + "type": "table", + "bbox": [ + 123, + 592, + 487, + 685 + ], + "blocks": [ + { + "type": "table_caption", + "bbox": [ + 108, + 540, + 505, + 586 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 540, + 505, + 554 + ], + "spans": [ + { + "bbox": [ + 105, + 540, + 505, + 554 + ], + "score": 1.0, + "content": "We show a variety of qualitative examples from our model in Section D.2 in both the infilling and", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 552, + 505, + 565 + ], + "spans": [ + { + "bbox": [ + 105, + 552, + 505, + 565 + ], + "score": 1.0, + "content": "left-to-right generation modes: docstring generation, metadata conditioning, class attribute inference", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 563, + 505, + 576 + ], + "spans": [ + { + "bbox": [ + 105, + 563, + 505, + 576 + ], + "score": 1.0, + "content": "from class usage, comment-conditioned code editing, StackOverflow title and tag generation, and", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 573, + 443, + 587 + ], + "spans": [ + { + "bbox": [ + 105, + 573, + 443, + 587 + ], + "score": 1.0, + "content": "zero-shot bidirectional translation of technical jargon between Chinese and English.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 30.5 + }, + { + "type": "table_body", + "bbox": [ + 123, + 592, + 487, + 685 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 123, + 592, + 487, + 685 + ], + "spans": [ + { + "bbox": [ + 123, + 592, + 487, + 685 + ], + "score": 0.982, + "html": "
#Size (B)Obj.Training DataData SizeTrain TokensTrain ComputeHumanEval Pass@1MBPP Pass@1
1)6.7CMmulti lang + SO204 GB52B3.0Z1519.4
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4)1.3LMPython + SO104 GB25B0.3Z99.8
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We compare", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 715, + 505, + 727 + ], + "spans": [ + { + "bbox": [ + 105, + 715, + 505, + 727 + ], + "score": 1.0, + "content": "models by size (in billions of parameters), objective (causal masked, CM, versus standard left-to-", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 726, + 505, + 739 + ], + "spans": [ + { + "bbox": [ + 105, + 726, + 505, + 739 + ], + "score": 1.0, + "content": "right language modeling, LM), training data, and total amount of compute in training (in zettaflops).", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 37.5 + } + ], + "index": 34 + } + ] + }, + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 108, + 81, + 211, + 93 + ], + "lines": [ + { + "bbox": [ + 105, + 80, + 213, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 80, + 213, + 95 + ], + "score": 1.0, + "content": "7 RELATED WORK", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 107, + 105, + 505, + 205 + ], + "lines": [ + { + "bbox": [ + 106, + 106, + 505, + 118 + ], + "spans": [ + { + "bbox": [ + 106, + 106, + 505, + 118 + ], + "score": 1.0, + "content": "Language Models for Code There has been a flurry of recent work on training large-scale neural", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 115, + 506, + 131 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 506, + 131 + ], + "score": 1.0, + "content": "language models on source code. Existing models differ in their architectural design and training", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 128, + 506, + 141 + ], + "spans": [ + { + "bbox": [ + 105, + 128, + 506, + 141 + ], + "score": 1.0, + "content": "objectives, e.g., decoder-only language models (Austin et al., 2021; Chen et al., 2021a; Izadi et al.,", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 138, + 506, + 151 + ], + "spans": [ + { + "bbox": [ + 105, + 138, + 506, + 151 + ], + "score": 1.0, + "content": "2022; Xu et al., 2022; Nijkamp et al., 2022), encoder-only masked language models (Feng et al.,", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 149, + 506, + 162 + ], + "spans": [ + { + "bbox": [ + 105, + 149, + 506, + 162 + ], + "score": 1.0, + "content": "2020; Kanade et al., 2020), and encoder-decoder models (Ahmad et al., 2021; Li et al., 2022; Roziere", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 160, + 505, + 174 + ], + "spans": [ + { + "bbox": [ + 105, + 160, + 505, + 174 + ], + "score": 1.0, + "content": "et al., 2021; Wang et al., 2021). Decoder-only language models have grown in popularity as they", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 172, + 505, + 185 + ], + "spans": [ + { + "bbox": [ + 105, + 172, + 505, + 185 + ], + "score": 1.0, + "content": "can perform zero-shot program synthesis by generating in a left-to-right fashion. 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Similar to our findings in Section 5, they", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 359, + 505, + 372 + ], + "spans": [ + { + "bbox": [ + 105, + 359, + 505, + 372 + ], + "score": 1.0, + "content": "find that the infilling capability does not adversely affect left-to-right performance. Our objective,", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 369, + 506, + 383 + ], + "spans": [ + { + "bbox": [ + 105, + 369, + 506, + 383 + ], + "score": 1.0, + "content": "in contrast, allows infilling multiple regions of code, and we demonstrate the benefits of infilling", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 382, + 321, + 393 + ], + "spans": [ + { + "bbox": [ + 105, + 382, + 321, + 393 + ], + "score": 1.0, + "content": "across a broader range of natural programming tasks.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 17.5 + }, + { + "type": "text", + "bbox": [ + 107, + 404, + 504, + 470 + ], + "lines": [ + { + "bbox": [ + 105, + 403, + 505, + 417 + ], + "spans": [ + { + "bbox": [ + 105, + 403, + 505, + 417 + ], + "score": 1.0, + "content": "Machine Learning for Code Assistance There is an extensive literature on using machine learn-", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 415, + 505, + 428 + ], + "spans": [ + { + "bbox": [ + 105, + 415, + 505, + 428 + ], + "score": 1.0, + "content": "ing models to aid human programmers. This includes methods to infer variable types (Pradel et al.,", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 425, + 506, + 439 + ], + "spans": [ + { + "bbox": [ + 105, + 425, + 506, + 439 + ], + "score": 1.0, + "content": "2020; Wei et al., 2020), generate unit tests (Fraser & Arcuri, 2011), repair programs (Gupta et al.,", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 437, + 506, + 450 + ], + "spans": [ + { + "bbox": [ + 105, + 437, + 506, + 450 + ], + "score": 1.0, + "content": "2017; Yasunaga & Liang, 2020; Chen et al., 2021c; Yasunaga & Liang, 2021), and verify program", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 449, + 505, + 460 + ], + "spans": [ + { + "bbox": [ + 106, + 449, + 505, + 460 + ], + "score": 1.0, + "content": "correctness (Ryan et al., 2020). Our model can infill arbitrary spans of code, allowing it to complete", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 459, + 482, + 472 + ], + "spans": [ + { + "bbox": [ + 105, + 459, + 482, + 472 + ], + "score": 1.0, + "content": "many of these tasks, as well as perform standard left-to-right generation, in a single approach.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 28.5 + }, + { + "type": "text", + "bbox": [ + 107, + 482, + 505, + 560 + ], + "lines": [ + { + "bbox": [ + 105, + 482, + 505, + 495 + ], + "spans": [ + { + "bbox": [ + 105, + 482, + 505, + 495 + ], + "score": 1.0, + "content": "Machine Learning for Program Synthesis Program synthesis approaches directly generate pro-", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 493, + 505, + 507 + ], + "spans": [ + { + "bbox": [ + 105, + 493, + 505, + 507 + ], + "score": 1.0, + "content": "grams from a specification of functionality (Gulwani et al., 2017). 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Our InCoder model differs from this past work as it can both synthesize", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 547, + 491, + 562 + ], + "spans": [ + { + "bbox": [ + 105, + 547, + 491, + 562 + ], + "score": 1.0, + "content": "and infill arbitrary spans of code, conditioning on natural language and partial implementations.", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 35 + }, + { + "type": "title", + "bbox": [ + 108, + 575, + 195, + 588 + ], + "lines": [ + { + "bbox": [ + 104, + 573, + 197, + 591 + ], + "spans": [ + { + "bbox": [ + 104, + 573, + 197, + 591 + ], + "score": 1.0, + "content": "8 CONCLUSION", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 39 + }, + { + "type": "text", + "bbox": [ + 107, + 600, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 600, + 506, + 613 + ], + "spans": [ + { + "bbox": [ + 105, + 600, + 506, + 613 + ], + "score": 1.0, + "content": "We demonstrated that using a causal masking objective when training a generative model of code", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 610, + 505, + 624 + ], + "spans": [ + { + "bbox": [ + 105, + 610, + 505, + 624 + ], + "score": 1.0, + "content": "enables strong zero-shot performance on many challenging and practical code infilling and editing", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 621, + 505, + 635 + ], + "spans": [ + { + "bbox": [ + 105, + 621, + 505, + 635 + ], + "score": 1.0, + "content": "tasks. The model’s additional infilling capability does not appear to harm its ability to do standard", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 633, + 505, + 645 + ], + "spans": [ + { + "bbox": [ + 105, + 633, + 505, + 645 + ], + "score": 1.0, + "content": "left-to-right generation: ablation and comparison experiments show that our causal-masked models", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 643, + 505, + 657 + ], + "spans": [ + { + "bbox": [ + 105, + 643, + 505, + 657 + ], + "score": 1.0, + "content": "have comparable performance to similarly-resourced models on standard left-to-right language-to-", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 654, + 506, + 668 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 506, + 668 + ], + "score": 1.0, + "content": "code synthesis benchmarks. Looking forward, we expect our model performance to continue to", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 505, + 678 + ], + "score": 1.0, + "content": "increase with more parameters, data, and training steps (Kaplan et al., 2020; Henighan et al., 2020).", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 104, + 675, + 506, + 691 + ], + "spans": [ + { + "bbox": [ + 104, + 675, + 506, + 691 + ], + "score": 1.0, + "content": "Moreover, fine-tuning would allow our models to be better able to condition on natural language", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 104, + 685, + 506, + 702 + ], + "spans": [ + { + "bbox": [ + 104, + 685, + 506, + 702 + ], + "score": 1.0, + "content": "instructions and other indications of human intent (Zhong et al., 2021; Wei et al., 2022; Ouyang", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 698, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 505, + 712 + ], + "score": 1.0, + "content": "et al., 2022). 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Existing models differ in their architectural design and training", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 128, + 506, + 141 + ], + "spans": [ + { + "bbox": [ + 105, + 128, + 506, + 141 + ], + "score": 1.0, + "content": "objectives, e.g., decoder-only language models (Austin et al., 2021; Chen et al., 2021a; Izadi et al.,", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 138, + 506, + 151 + ], + "spans": [ + { + "bbox": [ + 105, + 138, + 506, + 151 + ], + "score": 1.0, + "content": "2022; Xu et al., 2022; Nijkamp et al., 2022), encoder-only masked language models (Feng et al.,", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 149, + 506, + 162 + ], + "spans": [ + { + "bbox": [ + 105, + 149, + 506, + 162 + ], + "score": 1.0, + "content": "2020; Kanade et al., 2020), and encoder-decoder models (Ahmad et al., 2021; Li et al., 2022; Roziere", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 160, + 505, + 174 + ], + "spans": [ + { + "bbox": [ + 105, + 160, + 505, + 174 + ], + "score": 1.0, + "content": "et al., 2021; Wang et al., 2021). 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Recent work addresses this by chang-", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 271, + 506, + 285 + ], + "spans": [ + { + "bbox": [ + 105, + 271, + 506, + 285 + ], + "score": 1.0, + "content": "ing model architectures, inference procedures, and training objectives (Aghajanyan et al., 2022a;", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 283, + 505, + 295 + ], + "spans": [ + { + "bbox": [ + 105, + 283, + 505, + 295 + ], + "score": 1.0, + "content": "Stern et al., 2019; West et al., 2021; Aghajanyan et al., 2022b). Most related to our approach is the", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 292, + 506, + 307 + ], + "spans": [ + { + "bbox": [ + 105, + 292, + 506, + 307 + ], + "score": 1.0, + "content": "work of Donahue et al. 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Similar to our findings in Section 5, they", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 359, + 505, + 372 + ], + "spans": [ + { + "bbox": [ + 105, + 359, + 505, + 372 + ], + "score": 1.0, + "content": "find that the infilling capability does not adversely affect left-to-right performance. 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This includes methods to infer variable types (Pradel et al.,", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 425, + 506, + 439 + ], + "spans": [ + { + "bbox": [ + 105, + 425, + 506, + 439 + ], + "score": 1.0, + "content": "2020; Wei et al., 2020), generate unit tests (Fraser & Arcuri, 2011), repair programs (Gupta et al.,", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 437, + 506, + 450 + ], + "spans": [ + { + "bbox": [ + 105, + 437, + 506, + 450 + ], + "score": 1.0, + "content": "2017; Yasunaga & Liang, 2020; Chen et al., 2021c; Yasunaga & Liang, 2021), and verify program", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 449, + 505, + 460 + ], + "spans": [ + { + "bbox": [ + 106, + 449, + 505, + 460 + ], + "score": 1.0, + "content": "correctness (Ryan et al., 2020). 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Such models work by taking", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 104, + 504, + 505, + 518 + ], + "spans": [ + { + "bbox": [ + 104, + 504, + 505, + 518 + ], + "score": 1.0, + "content": "e.g., input-output examples (Balog et al., 2017; Gulwani, 2011; Chen et al., 2021b; Bavishi et al.,", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 515, + 505, + 528 + ], + "spans": [ + { + "bbox": [ + 105, + 515, + 505, + 528 + ], + "score": 1.0, + "content": "2019), partial implementations (Solar-Lezama et al., 2006), or natural language descriptions (Zelle", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 526, + 505, + 539 + ], + "spans": [ + { + "bbox": [ + 105, + 526, + 505, + 539 + ], + "score": 1.0, + "content": "& Mooney, 1996; Yu et al., 2018; Yin et al., 2018; Kulal et al., 2019; Chen et al., 2021a) of the", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 537, + 505, + 550 + ], + "spans": [ + { + "bbox": [ + 105, + 537, + 505, + 550 + ], + "score": 1.0, + "content": "desired program as input. Our InCoder model differs from this past work as it can both synthesize", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 547, + 491, + 562 + ], + "spans": [ + { + "bbox": [ + 105, + 547, + 491, + 562 + ], + "score": 1.0, + "content": "and infill arbitrary spans of code, conditioning on natural language and partial implementations.", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 35, + "bbox_fs": [ + 104, + 482, + 505, + 562 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 575, + 195, + 588 + ], + "lines": [ + { + "bbox": [ + 104, + 573, + 197, + 591 + ], + "spans": [ + { + "bbox": [ + 104, + 573, + 197, + 591 + ], + "score": 1.0, + "content": "8 CONCLUSION", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 39 + }, + { + "type": "text", + "bbox": [ + 107, + 600, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 600, + 506, + 613 + ], + "spans": [ + { + "bbox": [ + 105, + 600, + 506, + 613 + ], + "score": 1.0, + "content": "We demonstrated that using a causal masking objective when training a generative model of code", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 610, + 505, + 624 + ], + "spans": [ + { + "bbox": [ + 105, + 610, + 505, + 624 + ], + "score": 1.0, + "content": "enables strong zero-shot performance on many challenging and practical code infilling and editing", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 621, + 505, + 635 + ], + "spans": [ + { + "bbox": [ + 105, + 621, + 505, + 635 + ], + "score": 1.0, + "content": "tasks. 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In EMNLP, 2021.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 10.5 + }, + { + "type": "title", + "bbox": [ + 108, + 267, + 157, + 280 + ], + "lines": [ + { + "bbox": [ + 105, + 266, + 159, + 283 + ], + "spans": [ + { + "bbox": [ + 105, + 266, + 159, + 283 + ], + "score": 1.0, + "content": "A DATA", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 12 + }, + { + "type": "title", + "bbox": [ + 108, + 292, + 185, + 304 + ], + "lines": [ + { + "bbox": [ + 105, + 290, + 187, + 306 + ], + "spans": [ + { + "bbox": [ + 105, + 290, + 187, + 306 + ], + "score": 1.0, + "content": "A.1 CODE DATA", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 13 + }, + { + "type": "text", + "bbox": [ + 106, + 313, + 505, + 427 + ], + "lines": [ + { + "bbox": [ + 106, + 313, + 505, + 325 + ], + "spans": [ + { + "bbox": [ + 106, + 313, + 505, + 325 + ], + "score": 1.0, + "content": "Sources. 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We obtained approximately", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 334, + 506, + 348 + ], + "spans": [ + { + "bbox": [ + 105, + 334, + 506, + 348 + ], + "score": 1.0, + "content": "670,000 public non-fork repositories which GitHub/GitLab detected as containing primarily Python,", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 345, + 506, + 358 + ], + "spans": [ + { + "bbox": [ + 105, + 345, + 506, + 358 + ], + "score": 1.0, + "content": "JavaScript, or Jupyter Notebook files, and with either an MIT, Apache 2.0, BSD-2, or BSD-3 clause", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 356, + 505, + 369 + ], + "spans": [ + { + "bbox": [ + 105, + 356, + 505, + 369 + ], + "score": 1.0, + "content": "license. We included all code from a list of 28 languages (determined by file extension) contained in", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 369, + 505, + 383 + ], + "spans": [ + { + "bbox": [ + 105, + 369, + 505, + 383 + ], + "score": 1.0, + "content": "these repositories.9 Since Python files can also be contained in non-majority-Python repositories, we", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 104, + 379, + 505, + 395 + ], + "spans": [ + { + "bbox": [ + 104, + 379, + 505, + 395 + ], + "score": 1.0, + "content": "also included all other Python and Jupyter files obtainable through the GitHub archive on BigQuery", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 104, + 390, + 506, + 407 + ], + "spans": [ + { + "bbox": [ + 104, + 390, + 506, + 407 + ], + "score": 1.0, + "content": "that we did not already obtain from GitHub directly.10 We preprocess Jupyter notebooks by includ-", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 404, + 505, + 419 + ], + "spans": [ + { + "bbox": [ + 105, + 404, + 505, + 419 + ], + "score": 1.0, + "content": "ing all text and code (with Markdown formatting removed from text cells), with cells demarcated by", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 416, + 245, + 429 + ], + "spans": [ + { + "bbox": [ + 106, + 416, + 245, + 429 + ], + "score": 1.0, + "content": "XML-style tags (see Section A.3).", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 18.5 + }, + { + "type": "text", + "bbox": [ + 106, + 439, + 505, + 543 + ], + "lines": [ + { + "bbox": [ + 105, + 438, + 505, + 453 + ], + "spans": [ + { + "bbox": [ + 105, + 438, + 505, + 453 + ], + "score": 1.0, + "content": "Deduplication. Recent work has shown that deduplicating training data can improve model per-", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 450, + 505, + 463 + ], + "spans": [ + { + "bbox": [ + 105, + 450, + 505, + 463 + ], + "score": 1.0, + "content": "formance and reduce the risk of memorizing training data (Allamanis, 2019; Lee et al., 2022; Kand-", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 461, + 505, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 461, + 505, + 475 + ], + "score": 1.0, + "content": "pal et al., 2022). Our deduplication scheme removes code files using exact match on the sequence", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 473, + 505, + 488 + ], + "spans": [ + { + "bbox": [ + 105, + 473, + 379, + 488 + ], + "score": 1.0, + "content": "of alphanumeric tokens in the file.11 This removed approximately", + "type": "text" + }, + { + "bbox": [ + 379, + 474, + 399, + 485 + ], + "score": 0.87, + "content": "7 5 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 399, + 473, + 505, + 488 + ], + "score": 1.0, + "content": "of the corpus by file size", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 486, + 505, + 498 + ], + "spans": [ + { + "bbox": [ + 106, + 486, + 505, + 498 + ], + "score": 1.0, + "content": "(reducing from 1 TB to 250 GB) as there are numerous duplicated repositories, library dependen-", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 497, + 505, + 509 + ], + "spans": [ + { + "bbox": [ + 105, + 497, + 505, + 509 + ], + "score": 1.0, + "content": "cies included as source files, and common boilerplate code files (e.g., for Python web frameworks).", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 508, + 506, + 519 + ], + "spans": [ + { + "bbox": [ + 106, + 508, + 506, + 519 + ], + "score": 1.0, + "content": "We also use regular expressions to detect email addresses in the code files and replace them with a", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 520, + 505, + 533 + ], + "spans": [ + { + "bbox": [ + 105, + 520, + 505, + 533 + ], + "score": 1.0, + "content": "dummy address,12 to reduce the risks of the model memorizing real email addresses or hallucinating", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 531, + 150, + 543 + ], + "spans": [ + { + "bbox": [ + 105, + 531, + 150, + 543 + ], + "score": 1.0, + "content": "fake ones.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 28 + }, + { + "type": "text", + "bbox": [ + 107, + 555, + 505, + 588 + ], + "lines": [ + { + "bbox": [ + 106, + 555, + 506, + 568 + ], + "spans": [ + { + "bbox": [ + 106, + 555, + 506, + 568 + ], + "score": 1.0, + "content": "Decontamination. 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We remove any repositories contained in", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 34 + } + ], + "page_idx": 13, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 106, + 625, + 506, + 732 + ], + "lines": [ + { + "bbox": [ + 118, + 623, + 506, + 640 + ], + "spans": [ + { + "bbox": [ + 118, + 623, + 243, + 640 + ], + "score": 1.0, + "content": "9We include source files from C,", + "type": "text" + }, + { + "bbox": [ + 244, + 627, + 261, + 636 + ], + "score": 0.83, + "content": "\\mathrm { C } { + + }", + "type": "inline_equation" + }, + { + "bbox": [ + 262, + 623, + 506, + 640 + ], + "score": 1.0, + "content": ", CSS, C#, Common Lisp, Dart, Forth, Go, HTML, Haskell, Java,", + "type": "text" + } + ] + }, + { + "bbox": [ + 106, + 636, + 505, + 648 + ], + "spans": [ + { + "bbox": [ + 106, + 636, + 505, + 648 + ], + "score": 1.0, + "content": "JavaScript, Julia, Jupyter, Kotlin, Lua, Matlab, PHP, Perl, Python, R, Ruby, Rust, SQL, Scala, Shell, Swift, and", + "type": "text" + } + ] + }, + { + "bbox": [ + 106, + 646, + 425, + 659 + ], + "spans": [ + { + "bbox": [ + 106, + 646, + 425, + 659 + ], + "score": 1.0, + "content": "TypeScript, although the great majority of files are Python and JavaScript. See Figure 3.", + "type": "text" + } + ] + }, + { + "bbox": [ + 117, + 656, + 505, + 670 + ], + "spans": [ + { + "bbox": [ + 117, + 656, + 138, + 669 + ], + "score": 1.0, + "content": "10We", + "type": "text" + }, + { + "bbox": [ + 193, + 659, + 209, + 669 + ], + "score": 1.0, + "content": "use", + "type": "text" + }, + { + "bbox": [ + 263, + 659, + 505, + 670 + ], + "score": 1.0, + "content": "https://cloud.google.com/blog/topics/public-datasets/", + "type": "text" + } + ] + }, + { + "bbox": [ + 105, + 667, + 506, + 681 + ], + "spans": [ + { + "bbox": [ + 105, + 667, + 506, + 681 + ], + "score": 1.0, + "content": "github-on-bigquery-analyze-all-the-open-source-code. We only include repositories with one", + "type": "text" + } + ] + }, + { + "bbox": [ + 105, + 678, + 227, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 678, + 227, + 690 + ], + "score": 1.0, + "content": "of the above permissive licenses.", + "type": "text" + } + ] + }, + { + "bbox": [ + 116, + 686, + 506, + 704 + ], + "spans": [ + { + "bbox": [ + 116, + 686, + 506, + 704 + ], + "score": 1.0, + "content": "11We implement match checking using a Bloom filter Bloom (1970) whose keys are: the file extension,", + "type": "text" + } + ] + }, + { + "bbox": [ + 105, + 699, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 505, + 712 + ], + "score": 1.0, + "content": "number of tokens in the file, and an MD5 hash Rivest (1992) of the sequence of tokens, which is highly", + "type": "text" + } + ] + }, + { + "bbox": [ + 105, + 709, + 351, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 351, + 722 + ], + "score": 1.0, + "content": "accurate at identifying files with exactly matching token sequences.", + "type": "text" + } + ] + }, + { + "bbox": [ + 117, + 717, + 366, + 736 + ], + "spans": [ + { + "bbox": [ + 117, + 717, + 366, + 736 + ], + "score": 1.0, + "content": "12We replace detected email addresses with removed@example.com.", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 293, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2023", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 300, + 752, + 311, + 760 + ], + "lines": [ + { + "bbox": [ + 299, + 750, + 313, + 764 + ], + "spans": [ + { + "bbox": [ + 299, + 750, + 313, + 764 + ], + "score": 1.0, + "content": "", + "type": "text", + "height": 14, + "width": 14 + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 106, + 82, + 504, + 105 + ], + "lines": [ + { + "bbox": [ + 105, + 81, + 506, + 96 + ], + "spans": [ + { + "bbox": [ + 105, + 81, + 506, + 96 + ], + "score": 1.0, + "content": "Pengcheng Yin, Bowen Deng, Edgar Chen, Bogdan Vasilescu, and Graham Neubig. 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We obtained approximately", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 334, + 506, + 348 + ], + "spans": [ + { + "bbox": [ + 105, + 334, + 506, + 348 + ], + "score": 1.0, + "content": "670,000 public non-fork repositories which GitHub/GitLab detected as containing primarily Python,", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 345, + 506, + 358 + ], + "spans": [ + { + "bbox": [ + 105, + 345, + 506, + 358 + ], + "score": 1.0, + "content": "JavaScript, or Jupyter Notebook files, and with either an MIT, Apache 2.0, BSD-2, or BSD-3 clause", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 356, + 505, + 369 + ], + "spans": [ + { + "bbox": [ + 105, + 356, + 505, + 369 + ], + "score": 1.0, + "content": "license. We included all code from a list of 28 languages (determined by file extension) contained in", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 369, + 505, + 383 + ], + "spans": [ + { + "bbox": [ + 105, + 369, + 505, + 383 + ], + "score": 1.0, + "content": "these repositories.9 Since Python files can also be contained in non-majority-Python repositories, we", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 104, + 379, + 505, + 395 + ], + "spans": [ + { + "bbox": [ + 104, + 379, + 505, + 395 + ], + "score": 1.0, + "content": "also included all other Python and Jupyter files obtainable through the GitHub archive on BigQuery", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 104, + 390, + 506, + 407 + ], + "spans": [ + { + "bbox": [ + 104, + 390, + 506, + 407 + ], + "score": 1.0, + "content": "that we did not already obtain from GitHub directly.10 We preprocess Jupyter notebooks by includ-", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 404, + 505, + 419 + ], + "spans": [ + { + "bbox": [ + 105, + 404, + 505, + 419 + ], + "score": 1.0, + "content": "ing all text and code (with Markdown formatting removed from text cells), with cells demarcated by", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 416, + 245, + 429 + ], + "spans": [ + { + "bbox": [ + 106, + 416, + 245, + 429 + ], + "score": 1.0, + "content": "XML-style tags (see Section A.3).", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 18.5, + "bbox_fs": [ + 104, + 313, + 506, + 429 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 439, + 505, + 543 + ], + "lines": [ + { + "bbox": [ + 105, + 438, + 505, + 453 + ], + "spans": [ + { + "bbox": [ + 105, + 438, + 505, + 453 + ], + "score": 1.0, + "content": "Deduplication. Recent work has shown that deduplicating training data can improve model per-", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 450, + 505, + 463 + ], + "spans": [ + { + "bbox": [ + 105, + 450, + 505, + 463 + ], + "score": 1.0, + "content": "formance and reduce the risk of memorizing training data (Allamanis, 2019; Lee et al., 2022; Kand-", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 461, + 505, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 461, + 505, + 475 + ], + "score": 1.0, + "content": "pal et al., 2022). Our deduplication scheme removes code files using exact match on the sequence", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 473, + 505, + 488 + ], + "spans": [ + { + "bbox": [ + 105, + 473, + 379, + 488 + ], + "score": 1.0, + "content": "of alphanumeric tokens in the file.11 This removed approximately", + "type": "text" + }, + { + "bbox": [ + 379, + 474, + 399, + 485 + ], + "score": 0.87, + "content": "7 5 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 399, + 473, + 505, + 488 + ], + "score": 1.0, + "content": "of the corpus by file size", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 486, + 505, + 498 + ], + "spans": [ + { + "bbox": [ + 106, + 486, + 505, + 498 + ], + "score": 1.0, + "content": "(reducing from 1 TB to 250 GB) as there are numerous duplicated repositories, library dependen-", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 497, + 505, + 509 + ], + "spans": [ + { + "bbox": [ + 105, + 497, + 505, + 509 + ], + "score": 1.0, + "content": "cies included as source files, and common boilerplate code files (e.g., for Python web frameworks).", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 508, + 506, + 519 + ], + "spans": [ + { + "bbox": [ + 106, + 508, + 506, + 519 + ], + "score": 1.0, + "content": "We also use regular expressions to detect email addresses in the code files and replace them with a", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 520, + 505, + 533 + ], + "spans": [ + { + "bbox": [ + 105, + 520, + 505, + 533 + ], + "score": 1.0, + "content": "dummy address,12 to reduce the risks of the model memorizing real email addresses or hallucinating", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 531, + 150, + 543 + ], + "spans": [ + { + "bbox": [ + 105, + 531, + 150, + 543 + ], + "score": 1.0, + "content": "fake ones.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 28, + "bbox_fs": [ + 105, + 438, + 506, + 543 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 555, + 505, + 588 + ], + "lines": [ + { + "bbox": [ + 106, + 555, + 506, + 568 + ], + "spans": [ + { + "bbox": [ + 106, + 555, + 506, + 568 + ], + "score": 1.0, + "content": "Decontamination. To ensure that our code generation models can be evaluated on several current", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 567, + 505, + 579 + ], + "spans": [ + { + "bbox": [ + 106, + 567, + 505, + 579 + ], + "score": 1.0, + "content": "code generation benchmarks, we perform data decontamination: removing overlap between our", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 577, + 505, + 590 + ], + "spans": [ + { + "bbox": [ + 106, + 577, + 505, + 590 + ], + "score": 1.0, + "content": "training data and the evaluation sets of these benchmarks. We remove any repositories contained in", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 106, + 82, + 505, + 94 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 505, + 94 + ], + "score": 1.0, + "content": "the validation and test sets of CodeSearchNet (Husain et al., 2019), as these are used to construct", + "type": "text", + "cross_page": true + } + ], + "index": 0 + }, + { + "bbox": [ + 103, + 90, + 439, + 111 + ], + "spans": [ + { + "bbox": [ + 103, + 90, + 439, + 111 + ], + "score": 1.0, + "content": "validation and test sets for several of the tasks in CodeXGLUE (Lu et al., 2021).13", + "type": "text", + "cross_page": true + } + ], + "index": 1 + } + ], + "index": 34, + "bbox_fs": [ + 106, + 555, + 506, + 590 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 105, + 82, + 504, + 106 + ], + "lines": [ + { + "bbox": [ + 106, + 82, + 505, + 94 + ], + "spans": [ + { + "bbox": [ + 106, + 82, + 505, + 94 + ], + "score": 1.0, + "content": "the validation and test sets of CodeSearchNet (Husain et al., 2019), as these are used to construct", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 103, + 90, + 439, + 111 + ], + "spans": [ + { + "bbox": [ + 103, + 90, + 439, + 111 + ], + "score": 1.0, + "content": "validation and test sets for several of the tasks in CodeXGLUE (Lu et al., 2021).13", + "type": "text" + } + ], + "index": 1 + } + ], + "index": 0.5 + }, + { + "type": "text", + "bbox": [ + 107, + 146, + 505, + 226 + ], + "lines": [ + { + "bbox": [ + 105, + 145, + 505, + 159 + ], + "spans": [ + { + "bbox": [ + 105, + 145, + 505, + 159 + ], + "score": 1.0, + "content": "Filtering. Our filtering is similar to past work on generative models of code Chen et al. (2021a);", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 157, + 505, + 170 + ], + "spans": [ + { + "bbox": [ + 106, + 157, + 505, + 170 + ], + "score": 1.0, + "content": "Nijkamp et al. (2022); Xu et al. (2022): we remove files that contain any line longer than 3000", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 168, + 505, + 181 + ], + "spans": [ + { + "bbox": [ + 106, + 168, + 406, + 181 + ], + "score": 1.0, + "content": "tokens or an average line length greater than 100 tokens, have less than", + "type": "text" + }, + { + "bbox": [ + 406, + 168, + 426, + 179 + ], + "score": 0.85, + "content": "40 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 426, + 168, + 505, + 181 + ], + "score": 1.0, + "content": "of their characters", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 179, + 506, + 193 + ], + "spans": [ + { + "bbox": [ + 105, + 179, + 506, + 193 + ], + "score": 1.0, + "content": "being alphanumeric or underscores, or appear to be automatically generated, which we determine", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 190, + 506, + 203 + ], + "spans": [ + { + "bbox": [ + 105, + 190, + 506, + 203 + ], + "score": 1.0, + "content": "using substring match on a small number of phrases produced by automatic code and documentation", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 202, + 506, + 217 + ], + "spans": [ + { + "bbox": [ + 105, + 202, + 196, + 216 + ], + "score": 1.0, + "content": "generation systems.14", + "type": "text" + }, + { + "bbox": [ + 199, + 202, + 472, + 217 + ], + "score": 1.0, + "content": "Our decontamination and filtering steps together remove roughly", + "type": "text" + }, + { + "bbox": [ + 473, + 203, + 492, + 214 + ], + "score": 0.84, + "content": "10 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 492, + 202, + 506, + 217 + ], + "score": 1.0, + "content": "of", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 214, + 160, + 227 + ], + "spans": [ + { + "bbox": [ + 106, + 214, + 160, + 227 + ], + "score": 1.0, + "content": "Python files.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 5 + }, + { + "type": "title", + "bbox": [ + 108, + 266, + 210, + 278 + ], + "lines": [ + { + "bbox": [ + 106, + 266, + 212, + 279 + ], + "spans": [ + { + "bbox": [ + 106, + 266, + 212, + 279 + ], + "score": 1.0, + "content": "A.2 STACKOVERFLOW", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 9 + }, + { + "type": "text", + "bbox": [ + 107, + 298, + 505, + 376 + ], + "lines": [ + { + "bbox": [ + 105, + 298, + 505, + 310 + ], + "spans": [ + { + "bbox": [ + 105, + 298, + 505, + 310 + ], + "score": 1.0, + "content": "The second component of our corpus consists of questions, answers, and comments from Stack-", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 308, + 506, + 321 + ], + "spans": [ + { + "bbox": [ + 105, + 308, + 506, + 321 + ], + "score": 1.0, + "content": "Overflow. The Pile (Gao et al., 2020), which was used to train recent generative code models that", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 320, + 506, + 333 + ], + "spans": [ + { + "bbox": [ + 105, + 320, + 506, + 333 + ], + "score": 1.0, + "content": "we compare to in Section 5, also contains these questions and answers but does not contain com-", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 331, + 505, + 344 + ], + "spans": [ + { + "bbox": [ + 105, + 331, + 505, + 344 + ], + "score": 1.0, + "content": "ments. We include all questions that have at least one answer, up to ten answers with a non-negative", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 342, + 505, + 355 + ], + "spans": [ + { + "bbox": [ + 105, + 342, + 505, + 355 + ], + "score": 1.0, + "content": "score (sorted by score) per question, and up to five comments per question/answer. Qualitatively, we", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 353, + 505, + 366 + ], + "spans": [ + { + "bbox": [ + 105, + 353, + 505, + 366 + ], + "score": 1.0, + "content": "find that comments, together with the infilling ability of the model, allow our model to have some", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 364, + 412, + 377 + ], + "spans": [ + { + "bbox": [ + 105, + 364, + 412, + 377 + ], + "score": 1.0, + "content": "capability to do interactive code editing guided by language (see Figure 11).", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 13 + }, + { + "type": "title", + "bbox": [ + 108, + 416, + 181, + 427 + ], + "lines": [ + { + "bbox": [ + 106, + 415, + 182, + 429 + ], + "spans": [ + { + "bbox": [ + 106, + 415, + 182, + 429 + ], + "score": 1.0, + "content": "A.3 METADATA", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 17 + }, + { + "type": "text", + "bbox": [ + 106, + 448, + 505, + 582 + ], + "lines": [ + { + "bbox": [ + 106, + 448, + 505, + 461 + ], + "spans": [ + { + "bbox": [ + 106, + 448, + 505, + 461 + ], + "score": 1.0, + "content": "We include some metadata on the code files and StackOverflow questions/answers directly in our", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 459, + 505, + 471 + ], + "spans": [ + { + "bbox": [ + 105, + 459, + 505, + 471 + ], + "score": 1.0, + "content": "training data to allow attribute-conditioned generation (Keskar et al., 2019; Zellers et al., 2019) and", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 470, + 506, + 483 + ], + "spans": [ + { + "bbox": [ + 106, + 470, + 506, + 483 + ], + "score": 1.0, + "content": "attribute prediction. For code file data, our attributes are the code filename, the file extension (as a", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 481, + 506, + 494 + ], + "spans": [ + { + "bbox": [ + 105, + 481, + 506, + 494 + ], + "score": 1.0, + "content": "proxy for language), the file source (GitHub or GitLab), and, for GitHub repositories, the number", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 104, + 491, + 506, + 507 + ], + "spans": [ + { + "bbox": [ + 104, + 491, + 506, + 507 + ], + "score": 1.0, + "content": "of stars binned into six buckets.15 To allow this metadata to be optional when performing left-", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 505, + 506, + 517 + ], + "spans": [ + { + "bbox": [ + 106, + 505, + 506, + 517 + ], + "score": 1.0, + "content": "to-right prompting of the model, we insert each attribute it the beginning of its document with a", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 515, + 506, + 529 + ], + "spans": [ + { + "bbox": [ + 105, + 515, + 164, + 529 + ], + "score": 1.0, + "content": "probability of", + "type": "text" + }, + { + "bbox": [ + 165, + 516, + 184, + 527 + ], + "score": 0.87, + "content": "50 \\%", + "type": "inline_equation" + }, + { + "bbox": [ + 185, + 515, + 506, + 529 + ], + "score": 1.0, + "content": "(allowing the model to learn metadata conditioning); otherwise, we insert it at", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 528, + 504, + 539 + ], + "spans": [ + { + "bbox": [ + 106, + 528, + 504, + 539 + ], + "score": 1.0, + "content": "the end of its document (allowing metadata prediction). See Figure 6a and Figure 6b for examples.", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 537, + 505, + 551 + ], + "spans": [ + { + "bbox": [ + 105, + 537, + 505, + 551 + ], + "score": 1.0, + "content": "For StackOverflow, our metadata attributes are the question tags for the topic (e.g., python,django)", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 548, + 505, + 561 + ], + "spans": [ + { + "bbox": [ + 105, + 548, + 505, + 561 + ], + "score": 1.0, + "content": "and the number of votes for each question and answer, binned in the same way as repository stars.", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 560, + 506, + 573 + ], + "spans": [ + { + "bbox": [ + 105, + 560, + 506, + 573 + ], + "score": 1.0, + "content": "We insert comments directly after the questions or answers they were written for. See Figure 6c for", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 571, + 150, + 583 + ], + "spans": [ + { + "bbox": [ + 105, + 571, + 150, + 583 + ], + "score": 1.0, + "content": "examples.", + "type": "text" + } + ], + "index": 29 + } + ], + "index": 23.5 + }, + { + "type": "title", + "bbox": [ + 108, + 623, + 199, + 634 + ], + "lines": [ + { + "bbox": [ + 106, + 622, + 201, + 636 + ], + "spans": [ + { + "bbox": [ + 106, + 622, + 201, + 636 + ], + "score": 1.0, + "content": "A.4 TOKENIZATION", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 30 + }, + { + "type": "text", + "bbox": [ + 107, + 654, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 655, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 106, + 655, + 505, + 667 + ], + "score": 1.0, + "content": "To increase the amount of context that our code model can condition on, the length of documents", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 665, + 506, + 678 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 506, + 678 + ], + "score": 1.0, + "content": "that the model can generate, and the efficiency of training and inference, we train a byte-level BPE", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 676, + 505, + 690 + ], + "spans": [ + { + "bbox": [ + 105, + 676, + 505, + 690 + ], + "score": 1.0, + "content": "tokenizer Sennrich et al. (2016); Radford et al. (2019). We allow tokens to extend across whitespace", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 687, + 505, + 701 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 505, + 701 + ], + "score": 1.0, + "content": "(excluding newline characters) so that common code idioms (e.g., import numpy as np) are rep-", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 698, + 504, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 698, + 504, + 711 + ], + "score": 1.0, + "content": "resented as single tokens in the vocabulary. 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Our models have", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 449, + 505, + 462 + ], + "spans": [ + { + "bbox": [ + 105, + 449, + 505, + 462 + ], + "score": 1.0, + "content": "also not yet saturated and would benefit from further training; we report the performance of the 6.7B", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 460, + 506, + 473 + ], + "spans": [ + { + "bbox": [ + 105, + 460, + 506, + 473 + ], + "score": 1.0, + "content": "model on the HumanEval Python function synthesis benchmark (Chen et al., 2021a) (see Section C.6", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 471, + 506, + 484 + ], + "spans": [ + { + "bbox": [ + 106, + 471, + 506, + 484 + ], + "score": 1.0, + "content": "for a description of this benchmark) and see a consistent increase in performance over the course of", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 483, + 185, + 495 + ], + "spans": [ + { + "bbox": [ + 106, + 483, + 185, + 495 + ], + "score": 1.0, + "content": "training (Figure 5).", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 40 + }, + { + "type": "title", + "bbox": [ + 107, + 539, + 220, + 550 + ], + "lines": [ + { + "bbox": [ + 105, + 538, + 222, + 552 + ], + "spans": [ + { + "bbox": [ + 105, + 538, + 222, + 552 + ], + "score": 1.0, + "content": "B.2 INFERENCE DETAILS", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 44 + }, + { + "type": "text", + "bbox": [ + 106, + 572, + 505, + 649 + ], + "lines": [ + { + "bbox": [ + 104, + 571, + 505, + 585 + ], + "spans": [ + { + "bbox": [ + 104, + 571, + 468, + 585 + ], + "score": 1.0, + "content": "In practice, to generate a single infill we sample from the distribution", + "type": "text" + }, + { + "bbox": [ + 468, + 571, + 505, + 583 + ], + "score": 0.55, + "content": "\\begin{array} { r l } { P ( \\cdot } & { { } \\ l } \\end{array}", + "type": "inline_equation" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 582, + 505, + 595 + ], + "spans": [ + { + "bbox": [ + 105, + 582, + 171, + 595 + ], + "score": 1.0, + "content": "[Left; ", + "type": "inline_equation" + }, + { + "bbox": [ + 183, + 582, + 255, + 595 + ], + "score": 1.0, + "content": "; Right; ", + "type": "inline_equation" + }, + { + "bbox": [ + 268, + 582, + 276, + 595 + ], + "score": 1.0, + "content": ";", + "type": "text" + }, + { + "bbox": [ + 276, + 583, + 323, + 595 + ], + "score": 0.6, + "content": "\\angle M a s k : 0 > ]", + "type": "inline_equation" + }, + { + "bbox": [ + 323, + 582, + 462, + 595 + ], + "score": 1.0, + "content": "), where we insert an artificial", + "type": "text" + }, + { + "bbox": [ + 462, + 584, + 505, + 594 + ], + "score": 0.27, + "content": "\\angle M a s k : 1 >", + "type": "inline_equation" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 594, + 505, + 606 + ], + "spans": [ + { + "bbox": [ + 106, + 594, + 224, + 606 + ], + "score": 1.0, + "content": "token. 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See Aghajanyan et al. (2022a) for more.", + "type": "text" + } + ], + "index": 51 + } + ], + "index": 48 + }, + { + "type": "text", + "bbox": [ + 107, + 654, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "score": 1.0, + "content": "More generally, when inserting at multiple locations, we condition on the document with mul-", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 105, + 666, + 506, + 677 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 506, + 677 + ], + "score": 1.0, + "content": "tiple mask sentinel tokens inserted and a final mask token appended. 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Our models have", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 449, + 505, + 462 + ], + "spans": [ + { + "bbox": [ + 105, + 449, + 505, + 462 + ], + "score": 1.0, + "content": "also not yet saturated and would benefit from further training; we report the performance of the 6.7B", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 460, + 506, + 473 + ], + "spans": [ + { + "bbox": [ + 105, + 460, + 506, + 473 + ], + "score": 1.0, + "content": "model on the HumanEval Python function synthesis benchmark (Chen et al., 2021a) (see Section C.6", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 471, + 506, + 484 + ], + "spans": [ + { + "bbox": [ + 106, + 471, + 506, + 484 + ], + "score": 1.0, + "content": "for a description of this benchmark) and see a consistent increase in performance over the course of", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 483, + 185, + 495 + ], + "spans": [ + { + "bbox": [ + 106, + 483, + 185, + 495 + ], + "score": 1.0, + "content": "training (Figure 5).", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 40, + "bbox_fs": [ + 105, + 415, + 506, + 495 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 539, + 220, + 550 + ], + "lines": [ + { + "bbox": [ + 105, + 538, + 222, + 552 + ], + "spans": [ + { + "bbox": [ + 105, + 538, + 222, + 552 + ], + "score": 1.0, + "content": "B.2 INFERENCE DETAILS", + "type": "text" + } + ], + "index": 44 + } + ], + "index": 44 + }, + { + "type": "text", + "bbox": [ + 106, + 572, + 505, + 649 + ], + "lines": [ + { + "bbox": [ + 104, + 571, + 505, + 585 + ], + "spans": [ + { + "bbox": [ + 104, + 571, + 468, + 585 + ], + "score": 1.0, + "content": "In practice, to generate a single infill we sample from the distribution", + "type": "text" + }, + { + "bbox": [ + 468, + 571, + 505, + 583 + ], + "score": 0.55, + "content": "\\begin{array} { r l } { P ( \\cdot } & { { } \\ l } \\end{array}", + "type": "inline_equation" + } + ], + "index": 45 + }, + { + "bbox": [ + 105, + 582, + 505, + 595 + ], + "spans": [ + { + "bbox": [ + 105, + 582, + 171, + 595 + ], + "score": 1.0, + "content": "[Left; ", + "type": "inline_equation" + }, + { + "bbox": [ + 183, + 582, + 255, + 595 + ], + "score": 1.0, + "content": "; Right; ", + "type": "inline_equation" + }, + { + "bbox": [ + 268, + 582, + 276, + 595 + ], + "score": 1.0, + "content": ";", + "type": "text" + }, + { + "bbox": [ + 276, + 583, + 323, + 595 + ], + "score": 0.6, + "content": "\\angle M a s k : 0 > ]", + "type": "inline_equation" + }, + { + "bbox": [ + 323, + 582, + 462, + 595 + ], + "score": 1.0, + "content": "), where we insert an artificial", + "type": "text" + }, + { + "bbox": [ + 462, + 584, + 505, + 594 + ], + "score": 0.27, + "content": "\\angle M a s k : 1 >", + "type": "inline_equation" + } + ], + "index": 46 + }, + { + "bbox": [ + 106, + 594, + 505, + 606 + ], + "spans": [ + { + "bbox": [ + 106, + 594, + 224, + 606 + ], + "score": 1.0, + "content": "token. Not inserting ", + "type": "inline_equation" + }, + { + "bbox": [ + 236, + 594, + 466, + 606 + ], + "score": 1.0, + "content": "gives an implicit size hint to the model that the ", + "type": "inline_equation" + }, + { + "bbox": [ + 479, + 594, + 505, + 606 + ], + "score": 1.0, + "content": "token", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 604, + 505, + 617 + ], + "spans": [ + { + "bbox": [ + 105, + 604, + 492, + 617 + ], + "score": 1.0, + "content": "should be expanded to fill the rest of the 2048 token context window. Instead, inserting a ", + "type": "inline_equation" + } + ], + "index": 48 + }, + { + "bbox": [ + 105, + 615, + 505, + 628 + ], + "spans": [ + { + "bbox": [ + 105, + 615, + 505, + 628 + ], + "score": 1.0, + "content": "token indicates to the model that some amount of the document is omitted after the right context.", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 106, + 627, + 504, + 639 + ], + "spans": [ + { + "bbox": [ + 106, + 627, + 477, + 639 + ], + "score": 1.0, + "content": "We found that including this substantially improved the ability of the model to predict", + "type": "text" + }, + { + "bbox": [ + 477, + 627, + 504, + 637 + ], + "score": 0.68, + "content": "\\tt { < E O M > }", + "type": "inline_equation" + } + ], + "index": 50 + }, + { + "bbox": [ + 105, + 638, + 486, + 651 + ], + "spans": [ + { + "bbox": [ + 105, + 638, + 308, + 651 + ], + "score": 1.0, + "content": "appropriately when generating an infill for ", + "type": "inline_equation" + }, + { + "bbox": [ + 320, + 638, + 486, + 651 + ], + "score": 1.0, + "content": ". See Aghajanyan et al. (2022a) for more.", + "type": "text" + } + ], + "index": 51 + } + ], + "index": 48, + "bbox_fs": [ + 104, + 571, + 505, + 651 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 654, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "score": 1.0, + "content": "More generally, when inserting at multiple locations, we condition on the document with mul-", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 105, + 666, + 506, + 677 + ], + "spans": [ + { + "bbox": [ + 105, + 666, + 506, + 677 + ], + "score": 1.0, + "content": "tiple mask sentinel tokens inserted and a final mask token appended. 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We pre- and post-process each HumanEval infilling example as needed for", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 104, + 199, + 506, + 213 + ], + "spans": [ + { + "bbox": [ + 104, + 199, + 506, + 213 + ], + "score": 1.0, + "content": "PLBART: we represent each example as a stream of space-separated tokens (as identified by", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 211, + 506, + 223 + ], + "spans": [ + { + "bbox": [ + 106, + 211, + 506, + 223 + ], + "score": 1.0, + "content": "Python’s built-in lexer) with newlines and indentations replaced by control characters, and use a", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 221, + 505, + 235 + ], + "spans": [ + { + "bbox": [ + 105, + 221, + 505, + 235 + ], + "score": 1.0, + "content": " token to represent the line to be infilled. We extract the infilled region from the output by", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 106, + 233, + 505, + 245 + ], + "spans": [ + { + "bbox": [ + 106, + 233, + 505, + 245 + ], + "score": 1.0, + "content": "searching for the longest suffix of the left context contained in the output, and (as in our left-to-right", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 244, + 479, + 255 + ], + "spans": [ + { + "bbox": [ + 105, + 244, + 479, + 255 + ], + "score": 1.0, + "content": "baselines) take the ground-truth number of lines following this left context suffix as the infill.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 7.5 + }, + { + "type": "text", + "bbox": [ + 106, + 270, + 503, + 303 + ], + "lines": [ + { + "bbox": [ + 104, + 269, + 505, + 283 + ], + "spans": [ + { + "bbox": [ + 104, + 269, + 505, + 283 + ], + "score": 1.0, + "content": "Left-to-right with templated prompting (Codex). 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We evaluate on", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 433, + 506, + 446 + ], + "spans": [ + { + "bbox": [ + 106, + 433, + 506, + 446 + ], + "score": 1.0, + "content": "the max/min subtask, where the model has to decide if the given mask should be filled with either", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 444, + 505, + 456 + ], + "spans": [ + { + "bbox": [ + 105, + 444, + 505, + 456 + ], + "score": 1.0, + "content": "max or min. 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Using the causal-masked infill format with a single token (con-", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 494, + 505, + 506 + ], + "spans": [ + { + "bbox": [ + 105, + 494, + 505, + 506 + ], + "score": 1.0, + "content": "taining min/max) as the masked region (CM infill-token) performs better than using just the left", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 505, + 505, + 518 + ], + "spans": [ + { + "bbox": [ + 105, + 505, + 505, + 518 + ], + "score": 1.0, + "content": "context, but not as well as scoring the entire sequence left to right. Masking a larger region (CM", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 516, + 505, + 529 + ], + "spans": [ + { + "bbox": [ + 105, + 516, + 505, + 529 + ], + "score": 1.0, + "content": "infill-region), containing the left prefix and 10 right-side tokens in the masked region, performs", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 527, + 505, + 540 + ], + "spans": [ + { + "bbox": [ + 105, + 527, + 505, + 540 + ], + "score": 1.0, + "content": "comparably to scoring the whole sequence. Infill region length and tokenization can affect the per-", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 538, + 342, + 551 + ], + "spans": [ + { + "bbox": [ + 105, + 538, + 342, + 551 + ], + "score": 1.0, + "content": "formance, see C.3 for more details and more comparisons.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 28.5 + }, + { + "type": "table", + "bbox": [ + 144, + 570, + 465, + 654 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 144, + 570, + 465, + 654 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 144, + 570, + 465, + 654 + ], + "spans": [ + { + "bbox": [ + 144, + 570, + 465, + 654 + ], + "score": 0.977, + "html": "
MethodPython JavaScriptRubyGoJavaPHP
Left-to-right single76.977.665.870.474.177.1
Left-to-right reranking87.990.176.392.891.790.4
CM infill-token81.873.981.695.477.687.0
CM infill-region86.291.278.994.789.891.4
CodeBERT82.286.486.890.890.588.2
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We perform zero-shot prompting on the", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 281, + 504, + 294 + ], + "spans": [ + { + "bbox": [ + 105, + 281, + 504, + 294 + ], + "score": 1.0, + "content": "Codex code-cushman-001 and code-davinci-001 OpenAI API models using the following tem-", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 292, + 133, + 305 + ], + "spans": [ + { + "bbox": [ + 105, + 292, + 133, + 305 + ], + "score": 1.0, + "content": "plate:", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 13, + "bbox_fs": [ + 104, + 269, + 505, + 305 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 316, + 442, + 349 + ], + "lines": [ + { + "bbox": [ + 106, + 316, + 443, + 328 + ], + "spans": [ + { + "bbox": [ + 106, + 316, + 443, + 328 + ], + "score": 1.0, + "content": "[code before the infill mask] [code after the infill mask]", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 104, + 325, + 389, + 341 + ], + "spans": [ + { + "bbox": [ + 104, + 325, + 389, + 341 + ], + "score": 1.0, + "content": "# Complete the above code by replacing the tag.", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 338, + 254, + 349 + ], + "spans": [ + { + "bbox": [ + 106, + 338, + 254, + 349 + ], + "score": 1.0, + "content": "[code before the infill mask]", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 16, + "bbox_fs": [ + 104, + 316, + 443, + 349 + ] + }, + { + "type": "text", + "bbox": [ + 108, + 362, + 405, + 373 + ], + "lines": [ + { + "bbox": [ + 106, + 360, + 407, + 375 + ], + "spans": [ + { + "bbox": [ + 106, + 360, + 407, + 375 + ], + "score": 1.0, + "content": "We take [code after the infill mask] as the indicator of completion.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 18, + "bbox_fs": [ + 106, + 360, + 407, + 375 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 389, + 262, + 401 + ], + "lines": [ + { + "bbox": [ + 105, + 388, + 263, + 404 + ], + "spans": [ + { + "bbox": [ + 105, + 388, + 263, + 404 + ], + "score": 1.0, + "content": "C.2 CODE CLOZE (CODEXGLUE)", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 19 + }, + { + "type": "text", + "bbox": [ + 106, + 411, + 505, + 477 + ], + "lines": [ + { + "bbox": [ + 105, + 411, + 506, + 424 + ], + "spans": [ + { + "bbox": [ + 105, + 411, + 506, + 424 + ], + "score": 1.0, + "content": "CodeXGLUE cloze is created from CodeSearchNet to evaluate CodeBERT and consists of a short", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 423, + 506, + 435 + ], + "spans": [ + { + "bbox": [ + 105, + 423, + 506, + 435 + ], + "score": 1.0, + "content": "natural language description followed by code in several programming languages. We evaluate on", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 433, + 506, + 446 + ], + "spans": [ + { + "bbox": [ + 106, + 433, + 506, + 446 + ], + "score": 1.0, + "content": "the max/min subtask, where the model has to decide if the given mask should be filled with either", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 444, + 505, + 456 + ], + "spans": [ + { + "bbox": [ + 105, + 444, + 505, + 456 + ], + "score": 1.0, + "content": "max or min. 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Using the causal-masked infill format with a single token (con-", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 494, + 505, + 506 + ], + "spans": [ + { + "bbox": [ + 105, + 494, + 505, + 506 + ], + "score": 1.0, + "content": "taining min/max) as the masked region (CM infill-token) performs better than using just the left", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 505, + 505, + 518 + ], + "spans": [ + { + "bbox": [ + 105, + 505, + 505, + 518 + ], + "score": 1.0, + "content": "context, but not as well as scoring the entire sequence left to right. 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MethodPython JavaScriptRubyGoJavaPHP
Left-to-right single76.977.665.870.474.177.1
Left-to-right reranking87.990.176.392.891.790.4
CM infill-token81.873.981.695.477.687.0
CM infill-region86.291.278.994.789.891.4
CodeBERT82.286.486.890.890.588.2
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PythonJavascriptRubyGoJavaPHP
Left-break72.472.168.471.774.176.9
Left-token76.977.665.870.474.177.1
Left-region84.288.673.785.587.687.0
Left-right-break77.979.463.289.582.085.3
Left-right87.990.176.392.891.790.4
Infill-break79.183.184.290.184.085.3
Infill-token81.873.981.695.477.687.0
Infill-region86.291.278.994.789.891.4
CodeBERT82.286.486.890.890.588.2
Codex*93.693.494.799.395.094.3
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PythonJavascriptRubyGoJavaPHP
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Left-token76.977.665.870.474.177.1
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CodeBERT82.286.486.890.890.588.2
Codex*93.693.494.799.395.094.3
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ModelInferencePass RateExact Match
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INCODER-6.7BLeft-to-right reranking54.944.1
INCODER-6.7BInfilling69.056.3
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MethodPrecisionRecallF1
Ours: Left-to-right single20.020.020.0
Ours: Left-to-right rerank24.224.224.2
Ours: Infill46.846.846.8
Ours: Left-to-right single + Return checks63.263.263.2
Ours: Left-to-right rerank + Return checks64.364.364.3
Ours: Infill + Return checks76.776.776.7
TypeWriter (Supervised)78.869.974.1
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ModelInferencePass RateExact Match
INCODER-6.7BLeft-to-right single48.238.7
INCODER-6.7BLeft-to-right reranking54.944.1
INCODER-6.7BInfilling69.056.3
code-davinci-002Left-to-right single63.748.4
code-davinci-002Left-to-right reranking71.852.0
code-davinci-002Infilling87.469.6
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MethodPrecisionRecallF1
Ours: Left-to-right single20.020.020.0
Ours: Left-to-right rerank24.224.224.2
Ours: Infill46.846.846.8
Ours: Left-to-right single + Return checks63.263.263.2
Ours: Left-to-right rerank + Return checks64.364.364.3
Ours: Infill + Return checks76.776.776.7
TypeWriter (Supervised)78.869.974.1
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Given an overrepresentation of functions with None in this dataset, and the", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 104, + 561, + 506, + 577 + ], + "spans": [ + { + "bbox": [ + 104, + 561, + 506, + 577 + ], + "score": 1.0, + "content": "static analysis capabilities of TypeWriter, we also give results using a simple post-processing step", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 573, + 431, + 587 + ], + "spans": [ + { + "bbox": [ + 106, + 573, + 431, + 587 + ], + "score": 1.0, + "content": "that predicts None if the function does not have any non-trivial return statements.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 25, + "bbox_fs": [ + 104, + 529, + 506, + 587 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 606, + 467, + 618 + ], + "lines": [ + { + "bbox": [ + 105, + 605, + 469, + 618 + ], + "spans": [ + { + "bbox": [ + 105, + 605, + 469, + 618 + ], + "score": 1.0, + "content": "C.6 COMPARISON TO LEFT-TO-RIGHT GENERATIVE MODELS ON CODE SYNTHESIS", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 28 + }, + { + "type": "text", + "bbox": [ + 107, + 626, + 505, + 682 + ], + "lines": [ + { + "bbox": [ + 106, + 626, + 505, + 640 + ], + "spans": [ + { + "bbox": [ + 106, + 626, + 505, + 640 + ], + "score": 1.0, + "content": "We compare to past published work on generative code models on the HumanEval (Chen et al.,", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 637, + 505, + 651 + ], + "spans": [ + { + "bbox": [ + 105, + 637, + 505, + 651 + ], + "score": 1.0, + "content": "2021a) and MBPP (Austin et al., 2021) benchmarks, which require models to condition on natural", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 649, + 505, + 661 + ], + "spans": [ + { + "bbox": [ + 105, + 649, + 505, + 661 + ], + "score": 1.0, + "content": "language descriptions (docstrings) to produce Python programs (typically a single function), and", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 659, + 506, + 674 + ], + "spans": [ + { + "bbox": [ + 105, + 659, + 506, + 674 + ], + "score": 1.0, + "content": "evaluates overall functional accuracy (pass rate) across examples using several test cases for each", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 104, + 672, + 145, + 684 + ], + "spans": [ + { + "bbox": [ + 104, + 672, + 145, + 684 + ], + "score": 1.0, + "content": "program.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 31, + "bbox_fs": [ + 104, + 626, + 506, + 684 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 687, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 687, + 505, + 699 + ], + "spans": [ + { + "bbox": [ + 106, + 687, + 505, + 699 + ], + "score": 1.0, + "content": "We evaluate our INCODER-6.7B model in zero-shot evaluation on both of these benchmarks. For", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 699, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 505, + 711 + ], + "score": 1.0, + "content": "HumanEval, we follow past work by prompting with function signatures and docstring descrip-", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 709, + 504, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 384, + 722 + ], + "score": 1.0, + "content": "tions, sample 200 candidate program completions, and compute pass", + "type": "text" + }, + { + "bbox": [ + 384, + 710, + 398, + 720 + ], + "score": 0.71, + "content": "@ 1", + "type": "inline_equation" + }, + { + "bbox": [ + 398, + 709, + 420, + 722 + ], + "score": 1.0, + "content": ", pass", + "type": "text" + }, + { + "bbox": [ + 421, + 710, + 440, + 720 + ], + "score": 0.65, + "content": "@ 1 0", + "type": "inline_equation" + }, + { + "bbox": [ + 440, + 709, + 479, + 722 + ], + "score": 1.0, + "content": ", and pass", + "type": "text" + }, + { + "bbox": [ + 480, + 710, + 504, + 720 + ], + "score": 0.73, + "content": "@ 1 0 0", + "type": "inline_equation" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 721, + 506, + 732 + ], + "spans": [ + { + "bbox": [ + 105, + 721, + 506, + 732 + ], + "score": 1.0, + "content": "using the unbiased sampling estimator of Chen et al. (Chen et al., 2021a). For MBPP, which", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 35.5, + "bbox_fs": [ + 105, + 687, + 506, + 732 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 108, + 80, + 502, + 234 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 108, + 80, + 502, + 234 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 108, + 80, + 502, + 234 + ], + "spans": [ + { + "bbox": [ + 108, + 80, + 502, + 234 + ], + "score": 0.982, + "html": "
ModelSize (B)Python Code (GB)Other Code (GB)OtherCode LicenseInfill?HE @1HE @10HEMBPP @1
(GB)@100
Released
CodeParrot (Tunstall et al.,2022)1.550NoneNone4.08.717.9
PolyCoder (Xu et al.,2022)2.716238None5.69.817.7
GPT-J(Wang & Komatsuzaki,2021; Chen et al.,2021a)669073011.615.727.7
INCODER-6.7B6.75210757Permissive√15.227.847.019.4
GPT-NeoX (Black et al., 2022)2069073015.425.641.2
CodeGen-Multi (Nijkamp et al.,2022)6.162375120018.228.744.9
CodeGen-Mono (Nijkamp et al.,2022)6.1279375120026.142.365.8
CodeGen-Mono (Nijkamp et al.,2022)16.1279375120029.349.975.0
Unreleased
LaMDA (Austin et al.,2021; Thoppilan137NoneNone？?？14.047.314.8
et al.,2022; Chowdhery et al.,2022) AlphaCode (Li et al.,2022)
Codex-2.5B (Chen et al.,2021a)1.154660None17.128.2 35.445.3
2.5180None None> 57021.459.5
Codex-12B (Chen et al.,2021a)12180> 57028.8 36.046.872.3 88.4
PaLM-Coder (Chowdhery et al.,2022)540~20~200~4000Permissive一47.0
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All models are", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 264, + 504, + 276 + ], + "spans": [ + { + "bbox": [ + 106, + 264, + 504, + 276 + ], + "score": 1.0, + "content": "decoder-only transformer models. A “Permissive” code license indicates models trained on only", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 275, + 506, + 287 + ], + "spans": [ + { + "bbox": [ + 105, + 275, + 506, + 287 + ], + "score": 1.0, + "content": "open-source repositories with non-copyleft licenses. 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(Austin et al., 2021) and Chowdhery et al. 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ModelSize (B)Python Code (GB)Other Code (GB)OtherCode LicenseInfill?HE @1HE @10HEMBPP @1
(GB)@100
Released
CodeParrot (Tunstall et al.,2022)1.550NoneNone4.08.717.9
PolyCoder (Xu et al.,2022)2.716238None5.69.817.7
GPT-J(Wang & Komatsuzaki,2021; Chen et al.,2021a)669073011.615.727.7
INCODER-6.7B6.75210757Permissive√15.227.847.019.4
GPT-NeoX (Black et al., 2022)2069073015.425.641.2
CodeGen-Multi (Nijkamp et al.,2022)6.162375120018.228.744.9
CodeGen-Mono (Nijkamp et al.,2022)6.1279375120026.142.365.8
CodeGen-Mono (Nijkamp et al.,2022)16.1279375120029.349.975.0
Unreleased
LaMDA (Austin et al.,2021; Thoppilan137NoneNone？?？14.047.314.8
et al.,2022; Chowdhery et al.,2022) AlphaCode (Li et al.,2022)
Codex-2.5B (Chen et al.,2021a)1.154660None17.128.2 35.445.3
2.5180None None> 57021.459.5
Codex-12B (Chen et al.,2021a)12180> 57028.8 36.046.872.3 88.4
PaLM-Coder (Chowdhery et al.,2022)540~20~200~4000Permissive一47.0
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Here's a description:", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 113, + 111, + 457, + 125 + ], + "spans": [ + { + "bbox": [ + 113, + 111, + 457, + 125 + ], + "score": 1.0, + "content": "\"Write a function to convert a snake case string to a camel case string.\"", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 113, + 124, + 206, + 137 + ], + "spans": [ + { + "bbox": [ + 113, + 124, + 206, + 137 + ], + "score": 1.0, + "content": "<| q tags=python |>", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 112, + 136, + 151, + 148 + ], + "spans": [ + { + "bbox": [ + 112, + 136, + 151, + 148 + ], + "score": 1.0, + "content": "<| a |>", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 113, + 147, + 219, + 159 + ], + "spans": [ + { + "bbox": [ + 113, + 147, + 219, + 159 + ], + "score": 1.0, + "content": "You can use str.title:", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 113, + 159, + 146, + 171 + ], + "spans": [ + { + "bbox": [ + 113, + 159, + 146, + 171 + ], + "score": 1.0, + "content": "", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 111, + 169, + 243, + 184 + ], + "spans": [ + { + "bbox": [ + 111, + 169, + 243, + 184 + ], + "score": 1.0, + "content": ">>> 'my_snake_case'.title()", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 114, + 182, + 177, + 195 + ], + "spans": [ + { + "bbox": [ + 114, + 182, + 177, + 195 + ], + "score": 1.0, + "content": "'MySnakeCase'", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 113, + 194, + 150, + 206 + ], + "spans": [ + { + "bbox": [ + 113, + 194, + 150, + 206 + ], + "score": 1.0, + "content": "", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 114, + 206, + 248, + 218 + ], + "spans": [ + { + "bbox": [ + 114, + 206, + 219, + 218 + ], + "score": 1.0, + "content": "", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 5.5 + }, + { + "type": "title", + "bbox": [ + 107, + 240, + 160, + 249 + ], + "lines": [ + { + "bbox": [ + 107, + 240, + 160, + 249 + ], + "spans": [ + { + "bbox": [ + 107, + 240, + 160, + 249 + ], + "score": 1.0, + "content": "2. Add comment", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 11 + }, + { + "type": "text", + "bbox": [ + 111, + 258, + 493, + 452 + ], + "lines": [ + { + "bbox": [ + 112, + 258, + 489, + 271 + ], + "spans": [ + { + "bbox": [ + 112, + 258, + 489, + 271 + ], + "score": 1.0, + "content": "I need to write a Python function called `snake_to_camel`. Here's a description:", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 113, + 270, + 457, + 284 + ], + "spans": [ + { + "bbox": [ + 113, + 270, + 457, + 284 + ], + "score": 1.0, + "content": "\"Write a function to convert a snake case string to a camel case string.\"", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 113, + 282, + 205, + 295 + ], + "spans": [ + { + "bbox": [ + 113, + 282, + 155, + 295 + ], + "score": 1.0, + "content": "<| q tags", + "type": "text" + }, + { + "bbox": [ + 156, + 285, + 162, + 292 + ], + "score": 0.33, + "content": "{ } , = { }", + "type": "inline_equation" + }, + { + "bbox": [ + 162, + 282, + 205, + 295 + ], + "score": 1.0, + "content": "python |>", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 111, + 293, + 151, + 307 + ], + "spans": [ + { + "bbox": [ + 111, + 293, + 151, + 307 + ], + "score": 1.0, + "content": "<| a |>", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 111, + 304, + 219, + 319 + ], + "spans": [ + { + "bbox": [ + 111, + 304, + 219, + 319 + ], + "score": 1.0, + "content": "You can use str.title:", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 112, + 318, + 145, + 329 + ], + "spans": [ + { + "bbox": [ + 112, + 318, + 145, + 329 + ], + "score": 1.0, + "content": "", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 111, + 328, + 242, + 342 + ], + "spans": [ + { + "bbox": [ + 111, + 328, + 242, + 342 + ], + "score": 1.0, + "content": ">>> 'my_snake_case'.title()", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 114, + 339, + 176, + 353 + ], + "spans": [ + { + "bbox": [ + 114, + 339, + 176, + 353 + ], + "score": 1.0, + "content": "'MySnakeCase'", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 112, + 352, + 150, + 365 + ], + "spans": [ + { + "bbox": [ + 112, + 352, + 150, + 365 + ], + "score": 1.0, + "content": "", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 112, + 364, + 248, + 376 + ], + "spans": [ + { + "bbox": [ + 112, + 364, + 155, + 376 + ], + "score": 1.0, + "content": "", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 113, + 376, + 150, + 388 + ], + "spans": [ + { + "bbox": [ + 113, + 376, + 150, + 388 + ], + "score": 1.0, + "content": "<| c |>", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 111, + 386, + 433, + 401 + ], + "spans": [ + { + "bbox": [ + 111, + 386, + 433, + 401 + ], + "score": 1.0, + "content": "Close, but you need to replace the underscores with an empty string.", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 112, + 399, + 155, + 412 + ], + "spans": [ + { + "bbox": [ + 112, + 399, + 155, + 412 + ], + "score": 1.0, + "content": "<|/ c |>", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 112, + 411, + 150, + 424 + ], + "spans": [ + { + "bbox": [ + 112, + 411, + 150, + 424 + ], + "score": 1.0, + "content": "<| c |>", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 112, + 421, + 186, + 435 + ], + "spans": [ + { + "bbox": [ + 112, + 421, + 186, + 435 + ], + "score": 1.0, + "content": "Thanks, edited!", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 112, + 434, + 155, + 447 + ], + "spans": [ + { + "bbox": [ + 112, + 434, + 155, + 447 + ], + "score": 1.0, + "content": "<|/ c |>", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 19.5 + }, + { + "type": "title", + "bbox": [ + 111, + 467, + 250, + 476 + ], + "lines": [ + { + "bbox": [ + 110, + 467, + 251, + 477 + ], + "spans": [ + { + "bbox": [ + 110, + 467, + 251, + 477 + ], + "score": 1.0, + "content": "3. Regenerate ¼nfill cond¼t¼oned on comment", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 28 + }, + { + "type": "text", + "bbox": [ + 111, + 482, + 493, + 663 + ], + "lines": [ + { + "bbox": [ + 112, + 481, + 489, + 494 + ], + "spans": [ + { + "bbox": [ + 112, + 481, + 489, + 494 + ], + "score": 1.0, + "content": "I need to write a Python function called `snake_to_camel`. Here's a description:", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 113, + 492, + 457, + 506 + ], + "spans": [ + { + "bbox": [ + 113, + 492, + 457, + 506 + ], + "score": 1.0, + "content": "\"Write a function to convert a snake case string to a camel case string.\"", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 113, + 505, + 206, + 518 + ], + "spans": [ + { + "bbox": [ + 113, + 505, + 155, + 518 + ], + "score": 1.0, + "content": "<| q tags", + "type": "text" + }, + { + "bbox": [ + 155, + 508, + 162, + 515 + ], + "score": 0.41, + "content": "; =", + "type": "inline_equation" + }, + { + "bbox": [ + 162, + 505, + 206, + 518 + ], + "score": 1.0, + "content": "python |>", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 111, + 516, + 151, + 530 + ], + "spans": [ + { + "bbox": [ + 111, + 516, + 151, + 530 + ], + "score": 1.0, + "content": "<| a |>", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 111, + 528, + 146, + 541 + ], + "spans": [ + { + "bbox": [ + 111, + 528, + 146, + 541 + ], + "score": 1.0, + "content": "", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 111, + 540, + 233, + 552 + ], + "spans": [ + { + "bbox": [ + 111, + 540, + 233, + 552 + ], + "score": 1.0, + "content": "def snake_to_camel(name):", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 116, + 551, + 354, + 564 + ], + "spans": [ + { + "bbox": [ + 116, + 551, + 354, + 564 + ], + "score": 1.0, + "content": "return ''.join(x.title() for x in name.split('_'))", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 112, + 563, + 150, + 576 + ], + "spans": [ + { + "bbox": [ + 112, + 563, + 150, + 576 + ], + "score": 1.0, + "content": "", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 114, + 574, + 248, + 588 + ], + "spans": [ + { + "bbox": [ + 114, + 577, + 125, + 585 + ], + "score": 0.29, + "content": "< /", + "type": "inline_equation" + }, + { + "bbox": [ + 125, + 574, + 153, + 588 + ], + "score": 1.0, + "content": "a tag", + "type": "text" + }, + { + "bbox": [ + 154, + 578, + 162, + 585 + ], + "score": 0.36, + "content": "{ \\sf S } ^ { \\sf = }", + "type": "inline_equation" + }, + { + "bbox": [ + 162, + 574, + 217, + 588 + ], + "score": 1.0, + "content": "python dscor", + "type": "text" + }, + { + "bbox": [ + 217, + 577, + 232, + 585 + ], + "score": 0.55, + "content": "e = 3", + "type": "inline_equation" + }, + { + "bbox": [ + 232, + 574, + 248, + 588 + ], + "score": 1.0, + "content": "|>", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 112, + 586, + 151, + 600 + ], + "spans": [ + { + "bbox": [ + 112, + 586, + 151, + 600 + ], + "score": 1.0, + "content": "<| c |>", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 111, + 597, + 433, + 611 + ], + "spans": [ + { + "bbox": [ + 111, + 597, + 433, + 611 + ], + "score": 1.0, + "content": "Close, but you need to replace the underscores with an empty string.", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 111, + 609, + 155, + 623 + ], + "spans": [ + { + "bbox": [ + 111, + 609, + 155, + 623 + ], + "score": 1.0, + "content": "<|/ c |>", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 111, + 621, + 151, + 635 + ], + "spans": [ + { + "bbox": [ + 111, + 621, + 151, + 635 + ], + "score": 1.0, + "content": "<| c |>", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 111, + 632, + 187, + 646 + ], + "spans": [ + { + "bbox": [ + 111, + 632, + 187, + 646 + ], + "score": 1.0, + "content": "Thanks, edited!", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 112, + 644, + 155, + 659 + ], + "spans": [ + { + "bbox": [ + 112, + 644, + 155, + 659 + ], + "score": 1.0, + "content": "<|/ c |>", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 36 + }, + { + "type": "text", + "bbox": [ + 106, + 687, + 505, + 743 + ], + "lines": [ + { + "bbox": [ + 105, + 686, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 686, + 505, + 700 + ], + "score": 1.0, + "content": "Figure 11: Pretraining on StackOverflow, and our model’s infilling capability, allows it to perform", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 106, + 699, + 505, + 711 + ], + "spans": [ + { + "bbox": [ + 106, + 699, + 505, + 711 + ], + "score": 1.0, + "content": "zero-shot interactive refinement of a function. 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Add comment", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 11 + }, + { + "type": "list", + "bbox": [ + 111, + 258, + 493, + 452 + ], + "lines": [ + { + "bbox": [ + 112, + 258, + 489, + 271 + ], + "spans": [ + { + "bbox": [ + 112, + 258, + 489, + 271 + ], + "score": 1.0, + "content": "I need to write a Python function called `snake_to_camel`. Here's a description:", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 113, + 270, + 457, + 284 + ], + "spans": [ + { + "bbox": [ + 113, + 270, + 457, + 284 + ], + "score": 1.0, + "content": "\"Write a function to convert a snake case string to a camel case string.\"", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 113, + 282, + 205, + 295 + ], + "spans": [ + { + "bbox": [ + 113, + 282, + 155, + 295 + ], + "score": 1.0, + "content": "<| q tags", + "type": "text" + }, + { + "bbox": [ + 156, + 285, + 162, + 292 + ], + "score": 0.33, + "content": "{ } , = { }", + "type": "inline_equation" + }, + { + "bbox": [ + 162, + 282, + 205, + 295 + ], + "score": 1.0, + "content": "python |>", + "type": "text" + } + ], + "index": 14, + "is_list_end_line": true + }, + { + "bbox": [ + 111, + 293, + 151, + 307 + ], + "spans": [ + { + "bbox": [ + 111, + 293, + 151, + 307 + ], + "score": 1.0, + "content": "<| a |>", + "type": "text" + } + ], + "index": 15, + "is_list_start_line": true, + "is_list_end_line": true + }, + { + "bbox": [ + 111, + 304, + 219, + 319 + ], + "spans": [ + { + "bbox": [ + 111, + 304, + 219, + 319 + ], + "score": 1.0, + "content": "You can use str.title:", + "type": "text" + } + ], + "index": 16, + "is_list_start_line": true, + "is_list_end_line": true + }, + { + "bbox": [ + 112, + 318, + 145, + 329 + ], + "spans": [ + { + "bbox": [ + 112, + 318, + 145, + 329 + ], + "score": 1.0, + "content": "", + "type": "text" + } + ], + "index": 17, + "is_list_start_line": true, + "is_list_end_line": true + }, + { + "bbox": [ + 111, + 328, + 242, + 342 + ], + "spans": [ + { + "bbox": [ + 111, + 328, + 242, + 342 + ], + "score": 1.0, + "content": ">>> 'my_snake_case'.title()", + "type": "text" + } + ], + "index": 18, + "is_list_start_line": true, + "is_list_end_line": true + }, + { + "bbox": [ + 114, + 339, + 176, + 353 + ], + "spans": [ + { + "bbox": [ + 114, + 339, + 176, + 353 + ], + "score": 1.0, + "content": "'MySnakeCase'", + "type": "text" + } + ], + "index": 19, + "is_list_start_line": true, + "is_list_end_line": true + }, + { + "bbox": [ + 112, + 352, + 150, + 365 + ], + "spans": [ + { + "bbox": [ + 112, + 352, + 150, + 365 + ], + "score": 1.0, + "content": "", + "type": "text" + } + ], + "index": 20, + "is_list_start_line": true, + "is_list_end_line": true + }, + { + "bbox": [ + 112, + 364, + 248, + 376 + ], + "spans": [ + { + "bbox": [ + 112, + 364, + 155, + 376 + ], + "score": 1.0, + "content": "", + "type": "text" + } + ], + "index": 21, + "is_list_start_line": true, + "is_list_end_line": true + }, + { + "bbox": [ + 113, + 376, + 150, + 388 + ], + "spans": [ + { + "bbox": [ + 113, + 376, + 150, + 388 + ], + "score": 1.0, + "content": "<| c |>", + "type": "text" + } + ], + "index": 22, + "is_list_start_line": true, + "is_list_end_line": true + }, + { + "bbox": [ + 111, + 386, + 433, + 401 + ], + "spans": [ + { + "bbox": [ + 111, + 386, + 433, + 401 + ], + "score": 1.0, + "content": "Close, but you need to replace the underscores with an empty string.", + "type": "text" + } + ], + "index": 23, + "is_list_start_line": true, + "is_list_end_line": true + }, + { + "bbox": [ + 112, + 399, + 155, + 412 + ], + "spans": [ + { + "bbox": [ + 112, + 399, + 155, + 412 + ], + "score": 1.0, + "content": "<|/ c |>", + "type": "text" + } + ], + "index": 24, + "is_list_start_line": true, + "is_list_end_line": true + }, + { + "bbox": [ + 112, + 411, + 150, + 424 + ], + "spans": [ + { + "bbox": [ + 112, + 411, + 150, + 424 + ], + "score": 1.0, + "content": "<| c |>", + "type": "text" + } + ], + "index": 25, + "is_list_start_line": true, + "is_list_end_line": true + }, + { + "bbox": [ + 112, + 421, + 186, + 435 + ], + "spans": [ + { + "bbox": [ + 112, + 421, + 186, + 435 + ], + "score": 1.0, + "content": "Thanks, edited!", + "type": "text" + } + ], + "index": 26, + "is_list_start_line": true, + "is_list_end_line": true + }, + { + "bbox": [ + 112, + 434, + 155, + 447 + ], + "spans": [ + { + "bbox": [ + 112, + 434, + 155, + 447 + ], + "score": 1.0, + "content": "<|/ c |>", + "type": "text" + } + ], + "index": 27, + "is_list_start_line": true, + "is_list_end_line": true + } + ], + "index": 19.5, + "bbox_fs": [ + 111, + 258, + 489, + 447 + ] + }, + { + "type": "title", + "bbox": [ + 111, + 467, + 250, + 476 + ], + "lines": [ + { + "bbox": [ + 110, + 467, + 251, + 477 + ], + "spans": [ + { + "bbox": [ + 110, + 467, + 251, + 477 + ], + "score": 1.0, + "content": "3. Regenerate ¼nfill cond¼t¼oned on comment", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 28 + }, + { + "type": "list", + "bbox": [ + 111, + 482, + 493, + 663 + ], + "lines": [ + { + "bbox": [ + 112, + 481, + 489, + 494 + ], + "spans": [ + { + "bbox": [ + 112, + 481, + 489, + 494 + ], + "score": 1.0, + "content": "I need to write a Python function called `snake_to_camel`. Here's a description:", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 113, + 492, + 457, + 506 + ], + "spans": [ + { + "bbox": [ + 113, + 492, + 457, + 506 + ], + "score": 1.0, + "content": "\"Write a function to convert a snake case string to a camel case string.\"", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 113, + 505, + 206, + 518 + ], + "spans": [ + { + "bbox": [ + 113, + 505, + 155, + 518 + ], + "score": 1.0, + "content": "<| q tags", + "type": "text" + }, + { + "bbox": [ + 155, + 508, + 162, + 515 + ], + "score": 0.41, + "content": "; =", + "type": "inline_equation" + }, + { + "bbox": [ + 162, + 505, + 206, + 518 + ], + "score": 1.0, + "content": "python |>", + "type": "text" + } + ], + "index": 31, + "is_list_end_line": true + }, + { + "bbox": [ + 111, + 516, + 151, + 530 + ], + "spans": [ + { + "bbox": [ + 111, + 516, + 151, + 530 + ], + "score": 1.0, + "content": "<| a |>", + "type": "text" + } + ], + "index": 32, + "is_list_start_line": true, + "is_list_end_line": true + }, + { + "bbox": [ + 111, + 528, + 146, + 541 + ], + "spans": [ + { + "bbox": [ + 111, + 528, + 146, + 541 + ], + "score": 1.0, + "content": "", + "type": "text" + } + ], + "index": 33, + "is_list_start_line": true, + "is_list_end_line": true + }, + { + "bbox": [ + 111, + 540, + 233, + 552 + ], + "spans": [ + { + "bbox": [ + 111, + 540, + 233, + 552 + ], + "score": 1.0, + "content": "def snake_to_camel(name):", + "type": "text" + } + ], + "index": 34, + "is_list_start_line": true, + "is_list_end_line": true + }, + { + "bbox": [ + 116, + 551, + 354, + 564 + ], + "spans": [ + { + "bbox": [ + 116, + 551, + 354, + 564 + ], + "score": 1.0, + "content": "return ''.join(x.title() for x in name.split('_'))", + "type": "text" + } + ], + "index": 35, + "is_list_start_line": true, + "is_list_end_line": true + }, + { + "bbox": [ + 112, + 563, + 150, + 576 + ], + "spans": [ + { + "bbox": [ + 112, + 563, + 150, + 576 + ], + "score": 1.0, + "content": "", + "type": 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Re-", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 682, + 389, + 695 + ], + "spans": [ + { + "bbox": [ + 105, + 682, + 389, + 695 + ], + "score": 1.0, + "content": "gions in orange are infill generations from our INCODER-6.7B model.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 8.5 + } + ], + "index": 7.25 + } + ] + } + ], + "_backend": "pipeline", + "_version_name": "2.2.2" +} \ No newline at end of file diff --git a/parse/dev/xT5rDp5VqKO/xT5rDp5VqKO.md b/parse/dev/xT5rDp5VqKO/xT5rDp5VqKO.md new file mode 100644 index 0000000000000000000000000000000000000000..2ab776891d34500eb736878b30b5301bb7d3e1b2 --- /dev/null +++ b/parse/dev/xT5rDp5VqKO/xT5rDp5VqKO.md @@ -0,0 +1,134 @@ +# Coincidence Detection Is All You Need + +Anonymous Author(s) +Affiliation +Address +email + +# Abstract + +1 This paper demonstrates that the performance of coincidence detection - a classic +2 neuromorphic signal processing method found in Rosenblatt’s perceptrons with +3 distributed transmission times, can be competitive to a state-of-the-art deep learning +4 method for pattern recognition. Hence, we cannot remain comfortably numb to the +5 prevailing dogma that efficient matrix-vector operations is all we need; but should +6 enquire with greater vigour if more advanced continual learning methods (running +7 on spiking neural network hardware with neuromodulatory mechanisms at multiple +8 timescales) can beat the accuracy of task-specific deep learning methods. + +# 9 1 Introduction + +10 Frank Rosenblatt and his team (1957-1971) built and analyzed several kinds of perceptrons [1, 2, 3, 4] +11 - networks of sensory, association and receptor neurons; which in contemporary deep learning termi +12 nology relates to the input, hidden and output layers. The propagating signals were binary (compatible +13 with a spike-based view), the synaptic delays (transmission times) and weights (memory states) could +14 be analog, the network could be recurrent and was often randomly interconnected, and learning +15 often meant tuning the weights of the association-receptor subnetwork by some error-corrective +16 reinforcement. The synaptic delays were not learnt but instead randomly distributed in Rosenblatt’s +17 Tobermory perceptrons [5], and this was rich enough to realize concentration-invariant and uniform +18 time-warp invariant spatiotemporal classification by logarithmic encoding and coincidence detection. +19 However, the processing speed of commercial Von Neumann computers advanced exponentially +20 and outperformed neuromorphic hardware on yesterdecade’s benchmarks [6]. The Tobermory per +21 ceptron was forgotten, nevertheless, the utility of logarithmic encoding and coincidence detection +22 was formalized by John Hopfield [7] as an efficient solution to the analog match problem in pattern +23 recognition. +24 Now, half a century after the accidental demise of Rosenblatt, neuromorphic signal processors are +25 making a comeback. For example, (1) Intel’s Loihi with spike-time dependent plasticity mechanisms +26 for learning olfactory pattern recognizers [8]; (2) Physical reservoir computing networks [9] where +27 the interconnectivity of the hidden layer is unchanged, closer to the spirit of Rosenblatt’s randomly +28 interconnected sensory-association subnetwork. +29 Here, to strengthen the case for revisiting classic methods on novel and modern hardware, we evaluate +30 the performance of coincidence detection in comparison to a deep learning method. Nothing more, +31 nothing less, although this work was triggered by a rabid interest in employing artificial intelligence +32 to sniff out infections and prevent future pandemics. + +Table 1: Test accuracy $( \% )$ + +
ResNet-26Coincidence detection
82.2±0.3 (from [10])82.7 (this work)
+ +# 33 2 Methods + +34 Here, we consider the work [10] of an interdisciplinary team, where a 26 layer convolutional neural +35 network with residual connections (ResNet-26) was successfully trained for classifying pathogenic +36 bacteria by Raman spectroscopy. In their work, there are $N = 3 0$ classes of bacterial isolates and +37 they begin with a ResNet-26 pre-trained on $N { \times } 2 0 0 0$ spectra, then for each class $n = 1 : N$ there are +38 $M = 1 0 0$ training spectra, and similarly $N \times M = 3 0 0 0$ test spectra. Each spectrum $_ { \textbf { \em x } }$ contains 1000 +39 floating-point numbers ranging between 0 and 1. Although compute intensive, their deep learning +40 method proved to be a tool of great convenience for pattern recognition in a challenging dataset, +41 where intra-isolate spectra were often more dissimilar than inter-isolate spectra. +42 Our method to tackle the above dataset, is inspired by the theory of how coincidence detection [7] +43 in animal brains is fundamental for odour classification in complex and turbulent mixtures. Each +44 class $n$ has a vector representation ${ \pmb w } _ { n }$ that is learnt, and an input vector $_ { \textbf { \em x } }$ results in an output +45 class $y ( \pmb { x } ) = \arg _ { n } \operatorname* { m a x } ( \pmb { x } \wedge \pmb { w } _ { n } )$ where we introduce the operator $\Lambda$ to represent the coincidence +46 between two signals. The analytical nature of coincidence detection depends on the specificities of the +47 ion-channels and the membranes involved [11], and may even incorporate nonlinear leaky-integrate +48 [12] multiple timescale mechanisms. We do not yet have a complete theory of neuromorphic signal +49 processing, so here we introduce an approximation for the translation and scale-invariant property of +50 coincidence detection as + +$$ +\operatorname { a r g } _ { n } \operatorname * { m a x } ( { \pmb x } \bigwedge { \pmb w } _ { n } ) \approx \arg _ { n } \operatorname * { m a x } ( { \pmb w } _ { n } \cdot { \hat { \pmb x } } ) , +$$ + +51 where $\hat { \pmb x }$ is the zero-mean unit-variance normalization of $_ { \textbf { \em x } }$ . + +52 Thus, the approximation in Eq. (1) allows $y ( \pmb { x } )$ to be learnt by a logistic regression on the normalized +53 dataset. We discard the pre-training data, pre-process the training and test spectra by a range-1 mean +54 filter, and use the default method for logistic regression in Wolfram Mathematica (L2-regularization +55 $= 0 . 0 0 0 1$ , optimization method $=$ limited-memory BFGS). Code is provided in the supplemental +56 material for reproducibility. + +# 57 3 Result and outlook + +58 The coincidence detection (via normalized logistic regression) method introduced here achieves a test +59 accuracy greater than ResNet-26 (see Table 1), and it took less than 3 seconds to train the classifier +60 on a modern desktop (without any special-purpose GPUs). Check the Appendix for a confusion +61 matrix plot of the training and test data. Note that the training data was fit all at once to a $100 \%$ +62 accuracy. With a more neuromorphic coincidence detection method and a learning method that adapts +63 the synaptic delays $\pmb { w }$ continually, to keep track under changing environmental conditions, we may +64 achieve even greater accuracies. + +# 5 References + +6 [1] Frank Rosenblatt. The perceptron, a perceiving and recognizing automaton Project Para. +Cornell Aeronautical Laboratory, Inc. Report no. 85-460-1, 1957. +8 [2] Frank Rosenblatt. The perceptron: A theory of statistical separability in cognitive systems. +9 Cornell Aeronautical Laboratory, Inc. Report no. VG-1196-G-1, 1958. +0 [3] Frank Rosenblatt. Principles of neurodynamics. perceptrons and the theory of brain mechanisms. +1 Cornell Aeronautical Laboratory, Inc. Report no. 1196-G-8, 1961. + +[4] Frank Rosenblatt. Cognitive systems research program. Technical report, Cornell University, Ithaca, New York, 1971. [5] Frank Rosenblatt. A description of the tobermory perceptron. In Collected Technical Papers, volume 2. Cornell University, Ithaca, New York, 1963. [6] George Nagy. Neural networks-then and now. IEEE Transactions on Neural Networks, 2(2):316– 318, 1991. +[7] John J Hopfield. Pattern recognition computation using action potential timing for stimulus representation. Nature, 376(6535):33–36, 1995. [8] Nabil Imam and Thomas A Cleland. Rapid online learning and robust recall in a neuromorphic olfactory circuit. Nature Machine Intelligence, 2(3):181–191, 2020. [9] G. Tanaka, T. Yamane, J.B. Héroux, R. Nakane, N. Kanazawa, S. Takeda, H. Numata, D. Nakano, and A. Hirose. Recent advances in physical reservoir computing: A review. Neural Networks, 115:100–123, 2019. +[10] Chi-Sing Ho, Neal Jean, Catherine A Hogan, Lena Blackmon, Stefanie S Jeffrey, Mark Holodniy, Niaz Banaei, Amr AE Saleh, Stefano Ermon, and Jennifer Dionne. Rapid identification of pathogenic bacteria using raman spectroscopy and deep learning. Nature communications, 10(1):1–8, 2019. +[11] Nelson Spruston. Pyramidal neurons: dendritic structure and synaptic integration. Nature Reviews Neuroscience, 9(3):206–221, 2008. +[12] Wondimu Teka, Toma M Marinov, and Fidel Santamaria. Neuronal spike timing adaptation described with a fractional leaky integrate-and-fire model. PLoS computational biology, 10(3):e1003526, 2014. + +# 94 Checklist + +1. For all authors... + +(a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? [Yes] See Table 1. +(b) Did you describe the limitations of your work? [Yes] Equation (1) makes it clear that we employ an approximation for coincidence detection. +(c) Did you discuss any potential negative societal impacts of your work? [N/A] +(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes] + +2. If you are including theoretical results... + +(a) Did you state the full set of assumptions of all theoretical results? [N/A] (b) Did you include complete proofs of all theoretical results? [N/A] + +3. If you ran experiments... + +(a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [Yes] Check supplemental material +(b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [Yes] +(c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? [N/A] +(d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)? [Yes] qualitatively, in the results section + +4. If you are using existing assets (e.g., code, data, models) or curating/releasing new assets... + +(a) If your work uses existing assets, did you cite the creators? [Yes] + +
118(b） Did you mention the license of the assets? [Yes] In the supplemental information
119(c） Did you include any new assets either in the supplemental material or as a URL? [No]
120 121(d) Did you discuss whether and how consent was obtained from people whose data you're using/curating?[N/A]
122 123(e） Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content? [N/A]
124 5. If you used crowdsourcing or conducted research with human subjects...
125 126(a) Did you include the full text of instructions given to participants and screenshots, if applicable? [N/A]
127 128(b） Did you describe any potential participant risks,with links to Institutional Review Board (IRB) approvals, if applicable?[N/A]
129 130(c） Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? [N/A]
+ +# 131 A Appendix + +![](images/5c386ac8dd4daa9b49b79785dc9443ed5b441416b3248608eedd54357405a51b.jpg) \ No newline at end of file diff --git a/parse/dev/xT5rDp5VqKO/xT5rDp5VqKO_content_list.json b/parse/dev/xT5rDp5VqKO/xT5rDp5VqKO_content_list.json new file mode 100644 index 0000000000000000000000000000000000000000..412d5a27019b660e90a0b5e9b82fc9d982b9a2f0 --- /dev/null +++ b/parse/dev/xT5rDp5VqKO/xT5rDp5VqKO_content_list.json @@ -0,0 +1,374 @@ +[ + { + "type": "text", + "text": "Coincidence Detection Is All You Need ", + "text_level": 1, + "bbox": [ + 264, + 122, + 732, + 146 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Anonymous Author(s) \nAffiliation \nAddress \nemail ", + "bbox": [ + 423, + 196, + 580, + 252 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "Abstract ", + "text_level": 1, + "bbox": [ + 462, + 287, + 535, + 304 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "1 This paper demonstrates that the performance of coincidence detection - a classic \n2 neuromorphic signal processing method found in Rosenblatt’s perceptrons with \n3 distributed transmission times, can be competitive to a state-of-the-art deep learning \n4 method for pattern recognition. Hence, we cannot remain comfortably numb to the \n5 prevailing dogma that efficient matrix-vector operations is all we need; but should \n6 enquire with greater vigour if more advanced continual learning methods (running \n7 on spiking neural network hardware with neuromodulatory mechanisms at multiple \n8 timescales) can beat the accuracy of task-specific deep learning methods. ", + "bbox": [ + 150, + 329, + 766, + 440 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "9 1 Introduction ", + "text_level": 1, + "bbox": [ + 151, + 512, + 338, + 532 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "10 Frank Rosenblatt and his team (1957-1971) built and analyzed several kinds of perceptrons [1, 2, 3, 4] \n11 - networks of sensory, association and receptor neurons; which in contemporary deep learning termi \n12 nology relates to the input, hidden and output layers. The propagating signals were binary (compatible \n13 with a spike-based view), the synaptic delays (transmission times) and weights (memory states) could \n14 be analog, the network could be recurrent and was often randomly interconnected, and learning \n15 often meant tuning the weights of the association-receptor subnetwork by some error-corrective \n16 reinforcement. The synaptic delays were not learnt but instead randomly distributed in Rosenblatt’s \n17 Tobermory perceptrons [5], and this was rich enough to realize concentration-invariant and uniform \n18 time-warp invariant spatiotemporal classification by logarithmic encoding and coincidence detection. \n19 However, the processing speed of commercial Von Neumann computers advanced exponentially \n20 and outperformed neuromorphic hardware on yesterdecade’s benchmarks [6]. The Tobermory per \n21 ceptron was forgotten, nevertheless, the utility of logarithmic encoding and coincidence detection \n22 was formalized by John Hopfield [7] as an efficient solution to the analog match problem in pattern \n23 recognition. \n24 Now, half a century after the accidental demise of Rosenblatt, neuromorphic signal processors are \n25 making a comeback. For example, (1) Intel’s Loihi with spike-time dependent plasticity mechanisms \n26 for learning olfactory pattern recognizers [8]; (2) Physical reservoir computing networks [9] where \n27 the interconnectivity of the hidden layer is unchanged, closer to the spirit of Rosenblatt’s randomly \n28 interconnected sensory-association subnetwork. \n29 Here, to strengthen the case for revisiting classic methods on novel and modern hardware, we evaluate \n30 the performance of coincidence detection in comparison to a deep learning method. Nothing more, \n31 nothing less, although this work was triggered by a rabid interest in employing artificial intelligence \n32 to sniff out infections and prevent future pandemics. ", + "bbox": [ + 147, + 558, + 825, + 750 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "", + "bbox": [ + 147, + 756, + 825, + 825 + ], + "page_idx": 0 + }, + { + "type": "text", + "text": "", + "bbox": [ + 147, + 832, + 825, + 888 + ], + "page_idx": 0 + }, + { + "type": "table", + "img_path": "images/652089d176df3cac32600cfc9074e1ab496373b1c6181602a93c29960ad2ed13.jpg", + "table_caption": [ + "Table 1: Test accuracy $( \\% )$ " + ], + "table_footnote": [], + "table_body": "
ResNet-26Coincidence detection
82.2±0.3 (from [10])82.7 (this work)
", + "bbox": [ + 333, + 109, + 663, + 155 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "33 2 Methods ", + "text_level": 1, + "bbox": [ + 147, + 175, + 299, + 195 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "34 Here, we consider the work [10] of an interdisciplinary team, where a 26 layer convolutional neural \n35 network with residual connections (ResNet-26) was successfully trained for classifying pathogenic \n36 bacteria by Raman spectroscopy. In their work, there are $N = 3 0$ classes of bacterial isolates and \n37 they begin with a ResNet-26 pre-trained on $N { \\times } 2 0 0 0$ spectra, then for each class $n = 1 : N$ there are \n38 $M = 1 0 0$ training spectra, and similarly $N \\times M = 3 0 0 0$ test spectra. Each spectrum $_ { \\textbf { \\em x } }$ contains 1000 \n39 floating-point numbers ranging between 0 and 1. Although compute intensive, their deep learning \n40 method proved to be a tool of great convenience for pattern recognition in a challenging dataset, \n41 where intra-isolate spectra were often more dissimilar than inter-isolate spectra. \n42 Our method to tackle the above dataset, is inspired by the theory of how coincidence detection [7] \n43 in animal brains is fundamental for odour classification in complex and turbulent mixtures. Each \n44 class $n$ has a vector representation ${ \\pmb w } _ { n }$ that is learnt, and an input vector $_ { \\textbf { \\em x } }$ results in an output \n45 class $y ( \\pmb { x } ) = \\arg _ { n } \\operatorname* { m a x } ( \\pmb { x } \\wedge \\pmb { w } _ { n } )$ where we introduce the operator $\\Lambda$ to represent the coincidence \n46 between two signals. The analytical nature of coincidence detection depends on the specificities of the \n47 ion-channels and the membranes involved [11], and may even incorporate nonlinear leaky-integrate \n48 [12] multiple timescale mechanisms. We do not yet have a complete theory of neuromorphic signal \n49 processing, so here we introduce an approximation for the translation and scale-invariant property of \n50 coincidence detection as ", + "bbox": [ + 145, + 213, + 825, + 325 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "", + "bbox": [ + 147, + 330, + 825, + 455 + ], + "page_idx": 1 + }, + { + "type": "equation", + "img_path": "images/47034e52b12da81112f808e1a0b9eb8beeb7452f9b1bf3394fcb5a7e623378a3.jpg", + "text": "$$\n\\operatorname { a r g } _ { n } \\operatorname * { m a x } ( { \\pmb x } \\bigwedge { \\pmb w } _ { n } ) \\approx \\arg _ { n } \\operatorname * { m a x } ( { \\pmb w } _ { n } \\cdot { \\hat { \\pmb x } } ) ,\n$$", + "text_format": "latex", + "bbox": [ + 354, + 462, + 642, + 483 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "51 where $\\hat { \\pmb x }$ is the zero-mean unit-variance normalization of $_ { \\textbf { \\em x } }$ . ", + "bbox": [ + 147, + 491, + 563, + 506 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "52 Thus, the approximation in Eq. (1) allows $y ( \\pmb { x } )$ to be learnt by a logistic regression on the normalized \n53 dataset. We discard the pre-training data, pre-process the training and test spectra by a range-1 mean \n54 filter, and use the default method for logistic regression in Wolfram Mathematica (L2-regularization \n55 $= 0 . 0 0 0 1$ , optimization method $=$ limited-memory BFGS). Code is provided in the supplemental \n56 material for reproducibility. ", + "bbox": [ + 147, + 511, + 825, + 582 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "57 3 Result and outlook ", + "text_level": 1, + "bbox": [ + 150, + 609, + 400, + 630 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "58 The coincidence detection (via normalized logistic regression) method introduced here achieves a test \n59 accuracy greater than ResNet-26 (see Table 1), and it took less than 3 seconds to train the classifier \n60 on a modern desktop (without any special-purpose GPUs). Check the Appendix for a confusion \n61 matrix plot of the training and test data. Note that the training data was fit all at once to a $100 \\%$ \n62 accuracy. With a more neuromorphic coincidence detection method and a learning method that adapts \n63 the synaptic delays $\\pmb { w }$ continually, to keep track under changing environmental conditions, we may \n64 achieve even greater accuracies. ", + "bbox": [ + 147, + 648, + 825, + 746 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "5 References ", + "text_level": 1, + "bbox": [ + 156, + 775, + 284, + 794 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "6 [1] Frank Rosenblatt. The perceptron, a perceiving and recognizing automaton Project Para. \nCornell Aeronautical Laboratory, Inc. Report no. 85-460-1, 1957. \n8 [2] Frank Rosenblatt. The perceptron: A theory of statistical separability in cognitive systems. \n9 Cornell Aeronautical Laboratory, Inc. Report no. VG-1196-G-1, 1958. \n0 [3] Frank Rosenblatt. Principles of neurodynamics. perceptrons and the theory of brain mechanisms. \n1 Cornell Aeronautical Laboratory, Inc. Report no. 1196-G-8, 1961. ", + "bbox": [ + 156, + 806, + 830, + 912 + ], + "page_idx": 1 + }, + { + "type": "text", + "text": "[4] Frank Rosenblatt. Cognitive systems research program. Technical report, Cornell University, Ithaca, New York, 1971. [5] Frank Rosenblatt. A description of the tobermory perceptron. In Collected Technical Papers, volume 2. Cornell University, Ithaca, New York, 1963. [6] George Nagy. Neural networks-then and now. IEEE Transactions on Neural Networks, 2(2):316– 318, 1991. \n[7] John J Hopfield. Pattern recognition computation using action potential timing for stimulus representation. Nature, 376(6535):33–36, 1995. [8] Nabil Imam and Thomas A Cleland. Rapid online learning and robust recall in a neuromorphic olfactory circuit. Nature Machine Intelligence, 2(3):181–191, 2020. [9] G. Tanaka, T. Yamane, J.B. Héroux, R. Nakane, N. Kanazawa, S. Takeda, H. Numata, D. Nakano, and A. Hirose. Recent advances in physical reservoir computing: A review. Neural Networks, 115:100–123, 2019. \n[10] Chi-Sing Ho, Neal Jean, Catherine A Hogan, Lena Blackmon, Stefanie S Jeffrey, Mark Holodniy, Niaz Banaei, Amr AE Saleh, Stefano Ermon, and Jennifer Dionne. Rapid identification of pathogenic bacteria using raman spectroscopy and deep learning. Nature communications, 10(1):1–8, 2019. \n[11] Nelson Spruston. Pyramidal neurons: dendritic structure and synaptic integration. Nature Reviews Neuroscience, 9(3):206–221, 2008. \n[12] Wondimu Teka, Toma M Marinov, and Fidel Santamaria. Neuronal spike timing adaptation described with a fractional leaky integrate-and-fire model. PLoS computational biology, 10(3):e1003526, 2014. ", + "bbox": [ + 158, + 93, + 828, + 477 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "94 Checklist ", + "text_level": 1, + "bbox": [ + 148, + 508, + 269, + 527 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "1. For all authors... ", + "bbox": [ + 214, + 542, + 339, + 556 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "(a) Do the main claims made in the abstract and introduction accurately reflect the paper’s contributions and scope? [Yes] See Table 1. \n(b) Did you describe the limitations of your work? [Yes] Equation (1) makes it clear that we employ an approximation for coincidence detection. \n(c) Did you discuss any potential negative societal impacts of your work? [N/A] \n(d) Have you read the ethics review guidelines and ensured that your paper conforms to them? [Yes] ", + "bbox": [ + 238, + 560, + 825, + 666 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "2. If you are including theoretical results... ", + "bbox": [ + 214, + 670, + 493, + 684 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "(a) Did you state the full set of assumptions of all theoretical results? [N/A] (b) Did you include complete proofs of all theoretical results? [N/A] ", + "bbox": [ + 238, + 688, + 736, + 719 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "3. If you ran experiments... ", + "bbox": [ + 214, + 724, + 393, + 738 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "(a) Did you include the code, data, and instructions needed to reproduce the main experimental results (either in the supplemental material or as a URL)? [Yes] Check supplemental material \n(b) Did you specify all the training details (e.g., data splits, hyperparameters, how they were chosen)? [Yes] \n(c) Did you report error bars (e.g., with respect to the random seed after running experiments multiple times)? [N/A] \n(d) Did you include the total amount of compute and the type of resources used (e.g., type of GPUs, internal cluster, or cloud provider)? [Yes] qualitatively, in the results section ", + "bbox": [ + 238, + 742, + 825, + 875 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "4. If you are using existing assets (e.g., code, data, models) or curating/releasing new assets... ", + "bbox": [ + 220, + 878, + 825, + 893 + ], + "page_idx": 2 + }, + { + "type": "text", + "text": "(a) If your work uses existing assets, did you cite the creators? [Yes] ", + "bbox": [ + 235, + 897, + 694, + 911 + ], + "page_idx": 2 + }, + { + "type": "table", + "img_path": "images/bbde7388781d76919dd279438b8326026bd9d7e50f61bcf96f594a7c30ade3ff.jpg", + "table_caption": [], + "table_footnote": [], + "table_body": "
118(b） Did you mention the license of the assets? [Yes] In the supplemental information
119(c） Did you include any new assets either in the supplemental material or as a URL? [No]
120 121(d) Did you discuss whether and how consent was obtained from people whose data you're using/curating?[N/A]
122 123(e） Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content? [N/A]
124 5. If you used crowdsourcing or conducted research with human subjects...
125 126(a) Did you include the full text of instructions given to participants and screenshots, if applicable? [N/A]
127 128(b） Did you describe any potential participant risks,with links to Institutional Review Board (IRB) approvals, if applicable?[N/A]
129 130(c） Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? [N/A]
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ResNet-26Coincidence detection
82.2±0.3 (from [10])82.7 (this work)
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The perceptron, a perceiving and recognizing automaton Project Para.", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 127, + 650, + 393, + 663 + ], + "spans": [ + { + "bbox": [ + 127, + 650, + 393, + 663 + ], + "score": 1.0, + "content": "Cornell Aeronautical Laboratory, Inc. Report no. 85-460-1, 1957.", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 94, + 669, + 506, + 683 + ], + "spans": [ + { + "bbox": [ + 94, + 673, + 100, + 680 + ], + "score": 1.0, + "content": "8", + "type": "text" + }, + { + "bbox": [ + 109, + 669, + 506, + 683 + ], + "score": 1.0, + "content": "[2] Frank Rosenblatt. The perceptron: A theory of statistical separability in cognitive systems.", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 94, + 680, + 412, + 694 + ], + "spans": [ + { + "bbox": [ + 94, + 684, + 99, + 691 + ], + "score": 1.0, + "content": "9", + "type": "text" + }, + { + "bbox": [ + 127, + 680, + 412, + 694 + ], + "score": 1.0, + "content": "Cornell Aeronautical Laboratory, Inc. Report no. VG-1196-G-1, 1958.", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 94, + 699, + 506, + 713 + ], + "spans": [ + { + "bbox": [ + 94, + 704, + 100, + 710 + ], + "score": 1.0, + "content": "0", + "type": "text" + }, + { + "bbox": [ + 109, + 699, + 506, + 713 + ], + "score": 1.0, + "content": "[3] Frank Rosenblatt. Principles of neurodynamics. perceptrons and the theory of brain mechanisms.", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 94, + 711, + 394, + 724 + ], + "spans": [ + { + "bbox": [ + 94, + 715, + 99, + 722 + ], + "score": 1.0, + "content": "1", + "type": "text" + }, + { + "bbox": [ + 127, + 711, + 394, + 724 + ], + "score": 1.0, + "content": "Cornell Aeronautical Laboratory, Inc. 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118(b） Did you mention the license of the assets? [Yes] In the supplemental information
119(c） Did you include any new assets either in the supplemental material or as a URL? [No]
120 121(d) Did you discuss whether and how consent was obtained from people whose data you're using/curating?[N/A]
122 123(e） Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content? [N/A]
124 5. If you used crowdsourcing or conducted research with human subjects...
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127 128(b） Did you describe any potential participant risks,with links to Institutional Review Board (IRB) approvals, if applicable?[N/A]
129 130(c） Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? [N/A]
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118(b） Did you mention the license of the assets? [Yes] In the supplemental information
119(c） Did you include any new assets either in the supplemental material or as a URL? [No]
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124 5. If you used crowdsourcing or conducted research with human subjects...
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127 128(b） Did you describe any potential participant risks,with links to Institutional Review Board (IRB) approvals, if applicable?[N/A]
129 130(c） Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? [N/A]
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ResNet-26Coincidence detection
82.2±0.3 (from [10])82.7 (this work)
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118(b） Did you mention the license of the assets? [Yes] In the supplemental information
119(c） Did you include any new assets either in the supplemental material or as a URL? [No]
120 121(d) Did you discuss whether and how consent was obtained from people whose data you're using/curating?[N/A]
122 123(e） Did you discuss whether the data you are using/curating contains personally identifiable information or offensive content? [N/A]
124 5. If you used crowdsourcing or conducted research with human subjects...
125 126(a) Did you include the full text of instructions given to participants and screenshots, if applicable? [N/A]
127 128(b） Did you describe any potential participant risks,with links to Institutional Review Board (IRB) approvals, if applicable?[N/A]
129 130(c） Did you include the estimated hourly wage paid to participants and the total amount spent on participant compensation? [N/A]
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