{ "pdf_info": [ { "preproc_blocks": [ { "type": "title", "bbox": [ 107, 78, 388, 116 ], "lines": [ { "bbox": [ 106, 77, 389, 97 ], "spans": [ { "bbox": [ 106, 77, 389, 97 ], "score": 1.0, "content": "ROBUST WEIGHT PERTURBATION FOR", "type": "text" } ], "index": 0 }, { "bbox": [ 106, 97, 297, 117 ], "spans": [ { "bbox": [ 106, 97, 297, 117 ], "score": 1.0, "content": "ADVERSARIAL TRAINING", "type": "text" } ], "index": 1 } ], "index": 0.5 }, { "type": "text", "bbox": [ 113, 135, 244, 157 ], "lines": [ { "bbox": [ 113, 136, 201, 147 ], "spans": [ { "bbox": [ 113, 136, 201, 147 ], "score": 1.0, "content": "Anonymous authors", "type": "text" } ], "index": 2 }, { "bbox": [ 111, 146, 245, 158 ], "spans": [ { "bbox": [ 111, 146, 245, 158 ], "score": 1.0, "content": "Paper under double-blind review", "type": "text" } ], "index": 3 } ], "index": 2.5 }, { "type": "title", "bbox": [ 278, 186, 333, 199 ], "lines": [ { "bbox": [ 277, 186, 335, 200 ], "spans": [ { "bbox": [ 277, 186, 335, 200 ], "score": 1.0, "content": "ABSTRACT", "type": "text" } ], "index": 4 } ], "index": 4 }, { "type": "text", "bbox": [ 143, 217, 468, 436 ], "lines": [ { "bbox": [ 142, 217, 469, 229 ], "spans": [ { "bbox": [ 142, 217, 469, 229 ], "score": 1.0, "content": "Overfitting widely exists in adversarial robust training of deep networks. An ef-", "type": "text" } ], "index": 5 }, { "bbox": [ 141, 227, 470, 240 ], "spans": [ { "bbox": [ 141, 227, 470, 240 ], "score": 1.0, "content": "fective and promising remedy is adversarial weight perturbation, which injects", "type": "text" } ], "index": 6 }, { "bbox": [ 141, 239, 469, 251 ], "spans": [ { "bbox": [ 141, 239, 469, 251 ], "score": 1.0, "content": "the worst-case weight perturbation during network training by maximizing the", "type": "text" } ], "index": 7 }, { "bbox": [ 141, 249, 469, 263 ], "spans": [ { "bbox": [ 141, 249, 469, 263 ], "score": 1.0, "content": "classification loss on adversarial examples. Adversarial weight perturbation helps", "type": "text" } ], "index": 8 }, { "bbox": [ 141, 261, 469, 273 ], "spans": [ { "bbox": [ 141, 261, 469, 273 ], "score": 1.0, "content": "reduce the robust generalization gap; however, it also undermines the robustness", "type": "text" } ], "index": 9 }, { "bbox": [ 142, 272, 469, 284 ], "spans": [ { "bbox": [ 142, 272, 469, 284 ], "score": 1.0, "content": "enhancement. A criterion that regulates the weight perturbation is therefore cru-", "type": "text" } ], "index": 10 }, { "bbox": [ 141, 282, 470, 295 ], "spans": [ { "bbox": [ 141, 282, 470, 295 ], "score": 1.0, "content": "cial for adversarial training. In this paper, we propose such a criterion, namely", "type": "text" } ], "index": 11 }, { "bbox": [ 142, 294, 469, 306 ], "spans": [ { "bbox": [ 142, 294, 469, 306 ], "score": 1.0, "content": "Loss Stationary Condition (LSC) for constrained perturbation. With LSC, we find", "type": "text" } ], "index": 12 }, { "bbox": [ 142, 305, 469, 317 ], "spans": [ { "bbox": [ 142, 305, 469, 317 ], "score": 1.0, "content": "that deep network first overfits the adversarial examples with small loss, and then", "type": "text" } ], "index": 13 }, { "bbox": [ 141, 315, 470, 329 ], "spans": [ { "bbox": [ 141, 315, 470, 329 ], "score": 1.0, "content": "gradually develops to overfit all adversarial examples in the later stage of training.", "type": "text" } ], "index": 14 }, { "bbox": [ 141, 326, 469, 339 ], "spans": [ { "bbox": [ 141, 326, 469, 339 ], "score": 1.0, "content": "Following this, we find that it is essential to conduct weight perturbation on ad-", "type": "text" } ], "index": 15 }, { "bbox": [ 142, 338, 469, 349 ], "spans": [ { "bbox": [ 142, 338, 469, 349 ], "score": 1.0, "content": "versarial data with small classification loss to eliminate overfitting in adversarial", "type": "text" } ], "index": 16 }, { "bbox": [ 141, 348, 469, 360 ], "spans": [ { "bbox": [ 141, 348, 469, 360 ], "score": 1.0, "content": "training. Weight perturbation on adversarial data with large classification loss is", "type": "text" } ], "index": 17 }, { "bbox": [ 141, 360, 470, 371 ], "spans": [ { "bbox": [ 141, 360, 470, 371 ], "score": 1.0, "content": "not necessary and may even lead to poor robustness. Based on these observations,", "type": "text" } ], "index": 18 }, { "bbox": [ 141, 371, 469, 383 ], "spans": [ { "bbox": [ 141, 371, 469, 383 ], "score": 1.0, "content": "we propose a robust perturbation strategy to constrain the extent of weight pertur-", "type": "text" } ], "index": 19 }, { "bbox": [ 141, 380, 470, 394 ], "spans": [ { "bbox": [ 141, 380, 470, 394 ], "score": 1.0, "content": "bation. The perturbation strategy prevents deep networks from overfitting while", "type": "text" } ], "index": 20 }, { "bbox": [ 142, 393, 469, 405 ], "spans": [ { "bbox": [ 142, 393, 469, 405 ], "score": 1.0, "content": "avoiding the side effect of excessive weight perturbation, significantly improv-", "type": "text" } ], "index": 21 }, { "bbox": [ 141, 403, 469, 415 ], "spans": [ { "bbox": [ 141, 403, 469, 415 ], "score": 1.0, "content": "ing the robustness of adversarial training. Extensive experiments demonstrate the", "type": "text" } ], "index": 22 }, { "bbox": [ 141, 414, 470, 428 ], "spans": [ { "bbox": [ 141, 414, 470, 428 ], "score": 1.0, "content": "superiority of the proposed method over the state-of-the-art adversarial training", "type": "text" } ], "index": 23 }, { "bbox": [ 141, 426, 181, 436 ], "spans": [ { "bbox": [ 141, 426, 181, 436 ], "score": 1.0, "content": "methods.", "type": "text" } ], "index": 24 } ], "index": 14.5 }, { "type": "title", "bbox": [ 108, 470, 205, 483 ], "lines": [ { "bbox": [ 105, 469, 208, 486 ], "spans": [ { "bbox": [ 105, 469, 208, 486 ], "score": 1.0, "content": "1 INTRODUCTION", "type": "text" } ], "index": 25 } ], "index": 25 }, { "type": "text", "bbox": [ 107, 500, 504, 555 ], "lines": [ { "bbox": [ 105, 500, 506, 514 ], "spans": [ { "bbox": [ 105, 500, 506, 514 ], "score": 1.0, "content": "Although deep neural networks (DNNs) have led to impressive breakthroughs in a number of fields", "type": "text" } ], "index": 26 }, { "bbox": [ 105, 511, 505, 524 ], "spans": [ { "bbox": [ 105, 511, 505, 524 ], "score": 1.0, "content": "such as computer vision (He et al., 2016), speech recognition (Wang et al., 2017), and natural lan-", "type": "text" } ], "index": 27 }, { "bbox": [ 105, 522, 506, 535 ], "spans": [ { "bbox": [ 105, 522, 506, 535 ], "score": 1.0, "content": "guage processing (Devlin et al., 2018), they are extremely vulnerable to adversarial examples that", "type": "text" } ], "index": 28 }, { "bbox": [ 105, 532, 505, 547 ], "spans": [ { "bbox": [ 105, 532, 505, 547 ], "score": 1.0, "content": "are crafted by adding small and human-imperceptible perturbation to normal examples (Szegedy", "type": "text" } ], "index": 29 }, { "bbox": [ 105, 543, 258, 558 ], "spans": [ { "bbox": [ 105, 543, 258, 558 ], "score": 1.0, "content": "et al., 2013; Goodfellow et al., 2014).", "type": "text" } ], "index": 30 } ], "index": 28 }, { "type": "text", "bbox": [ 107, 561, 505, 704 ], "lines": [ { "bbox": [ 106, 561, 505, 574 ], "spans": [ { "bbox": [ 106, 561, 505, 574 ], "score": 1.0, "content": "The vulnerability of DNNs has attracted extensive attention and led to a large number of defense", "type": "text" } ], "index": 31 }, { "bbox": [ 105, 571, 506, 586 ], "spans": [ { "bbox": [ 105, 571, 506, 586 ], "score": 1.0, "content": "techniques against adversarial examples. Across existing defenses, adversarial training (AT) is one", "type": "text" } ], "index": 32 }, { "bbox": [ 105, 582, 506, 597 ], "spans": [ { "bbox": [ 105, 582, 506, 597 ], "score": 1.0, "content": "of the strongest empirical defenses. AT directly incorporates adversarial examples into the training", "type": "text" } ], "index": 33 }, { "bbox": [ 104, 594, 506, 607 ], "spans": [ { "bbox": [ 104, 594, 506, 607 ], "score": 1.0, "content": "process to solve a min-max optimization problem (Madry et al., 2017), which can obtain models with", "type": "text" } ], "index": 34 }, { "bbox": [ 105, 605, 505, 618 ], "spans": [ { "bbox": [ 105, 605, 505, 618 ], "score": 1.0, "content": "moderate adversarial robustness and has not been comprehensively attacked (Athalye et al., 2018).", "type": "text" } ], "index": 35 }, { "bbox": [ 105, 615, 505, 629 ], "spans": [ { "bbox": [ 105, 615, 505, 629 ], "score": 1.0, "content": "However, different from the standard training scenario, overfitting is a dominant phenomenon in", "type": "text" } ], "index": 36 }, { "bbox": [ 105, 627, 506, 640 ], "spans": [ { "bbox": [ 105, 627, 506, 640 ], "score": 1.0, "content": "adversarial robust training of deep networks (Rice et al., 2020). After a certain point in AT, the robust", "type": "text" } ], "index": 37 }, { "bbox": [ 105, 637, 505, 650 ], "spans": [ { "bbox": [ 105, 637, 505, 650 ], "score": 1.0, "content": "performance on test data will continue to degrade with further training. This phenomenon, termed", "type": "text" } ], "index": 38 }, { "bbox": [ 105, 649, 506, 661 ], "spans": [ { "bbox": [ 105, 649, 506, 661 ], "score": 1.0, "content": "as robust overfitting, breaches the common practice in deep learning that using over-parameterized", "type": "text" } ], "index": 39 }, { "bbox": [ 105, 660, 505, 673 ], "spans": [ { "bbox": [ 105, 660, 505, 673 ], "score": 1.0, "content": "networks and training for as long as possible (Neyshabur et al., 2017; Belkin et al., 2019). Such", "type": "text" } ], "index": 40 }, { "bbox": [ 106, 671, 505, 683 ], "spans": [ { "bbox": [ 106, 671, 505, 683 ], "score": 1.0, "content": "anomaly in AT causes detrimental effects on the robust generalization performance and subsequent", "type": "text" } ], "index": 41 }, { "bbox": [ 106, 682, 505, 693 ], "spans": [ { "bbox": [ 106, 682, 505, 693 ], "score": 1.0, "content": "algorithm assessment (Rice et al., 2020; Chen et al., 2020b). Relief techniques that mitigate robust", "type": "text" } ], "index": 42 }, { "bbox": [ 105, 692, 375, 706 ], "spans": [ { "bbox": [ 105, 692, 375, 706 ], "score": 1.0, "content": "overfitting have thus become crucial for stable adversarial training.", "type": "text" } ], "index": 43 } ], "index": 37 }, { "type": "text", "bbox": [ 107, 709, 503, 731 ], "lines": [ { "bbox": [ 106, 709, 505, 722 ], "spans": [ { "bbox": [ 106, 709, 505, 722 ], "score": 1.0, "content": "An effective and promising remedy for robust overfitting is Adversarial Weight Perturbation", "type": "text" } ], "index": 44 }, { "bbox": [ 106, 720, 505, 733 ], "spans": [ { "bbox": [ 106, 720, 505, 733 ], "score": 1.0, "content": "(AWP) (Wu et al., 2020), which forms a double-perturbation mechanism in the adversarial train-", "type": "text" } ], "index": 45 } ], "index": 44.5 } ], "page_idx": 0, "page_size": [ 612, 792 ], "discarded_blocks": [ { "type": "discarded", "bbox": [ 107, 27, 308, 37 ], "lines": [ { "bbox": [ 106, 25, 308, 38 ], "spans": [ { "bbox": [ 106, 25, 308, 38 ], "score": 1.0, "content": "Under review 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, 78, 388, 116 ], "lines": [ { "bbox": [ 106, 77, 389, 97 ], "spans": [ { "bbox": [ 106, 77, 389, 97 ], "score": 1.0, "content": "ROBUST WEIGHT PERTURBATION FOR", "type": "text" } ], "index": 0 }, { "bbox": [ 106, 97, 297, 117 ], "spans": [ { "bbox": [ 106, 97, 297, 117 ], "score": 1.0, "content": "ADVERSARIAL TRAINING", "type": "text" } ], "index": 1 } ], "index": 0.5 }, { "type": "text", "bbox": [ 113, 135, 244, 157 ], "lines": [ { "bbox": [ 113, 136, 201, 147 ], "spans": [ { "bbox": [ 113, 136, 201, 147 ], "score": 1.0, "content": "Anonymous authors", "type": "text" } ], "index": 2 }, { "bbox": [ 111, 146, 245, 158 ], "spans": [ { "bbox": [ 111, 146, 245, 158 ], "score": 1.0, "content": "Paper under double-blind review", "type": "text" } ], "index": 3 } ], "index": 2.5, "bbox_fs": [ 111, 136, 245, 158 ] }, { "type": "title", "bbox": [ 278, 186, 333, 199 ], "lines": [ { "bbox": [ 277, 186, 335, 200 ], "spans": [ { "bbox": [ 277, 186, 335, 200 ], "score": 1.0, "content": "ABSTRACT", "type": "text" } ], "index": 4 } ], "index": 4 }, { "type": "text", "bbox": [ 143, 217, 468, 436 ], "lines": [ { "bbox": [ 142, 217, 469, 229 ], "spans": [ { "bbox": [ 142, 217, 469, 229 ], "score": 1.0, "content": "Overfitting widely exists in adversarial robust training of deep networks. An ef-", "type": "text" } ], "index": 5 }, { "bbox": [ 141, 227, 470, 240 ], "spans": [ { "bbox": [ 141, 227, 470, 240 ], "score": 1.0, "content": "fective and promising remedy is adversarial weight perturbation, which injects", "type": "text" } ], "index": 6 }, { "bbox": [ 141, 239, 469, 251 ], "spans": [ { "bbox": [ 141, 239, 469, 251 ], "score": 1.0, "content": "the worst-case weight perturbation during network training by maximizing the", "type": "text" } ], "index": 7 }, { "bbox": [ 141, 249, 469, 263 ], "spans": [ { "bbox": [ 141, 249, 469, 263 ], "score": 1.0, "content": "classification loss on adversarial examples. Adversarial weight perturbation helps", "type": "text" } ], "index": 8 }, { "bbox": [ 141, 261, 469, 273 ], "spans": [ { "bbox": [ 141, 261, 469, 273 ], "score": 1.0, "content": "reduce the robust generalization gap; however, it also undermines the robustness", "type": "text" } ], "index": 9 }, { "bbox": [ 142, 272, 469, 284 ], "spans": [ { "bbox": [ 142, 272, 469, 284 ], "score": 1.0, "content": "enhancement. A criterion that regulates the weight perturbation is therefore cru-", "type": "text" } ], "index": 10 }, { "bbox": [ 141, 282, 470, 295 ], "spans": [ { "bbox": [ 141, 282, 470, 295 ], "score": 1.0, "content": "cial for adversarial training. In this paper, we propose such a criterion, namely", "type": "text" } ], "index": 11 }, { "bbox": [ 142, 294, 469, 306 ], "spans": [ { "bbox": [ 142, 294, 469, 306 ], "score": 1.0, "content": "Loss Stationary Condition (LSC) for constrained perturbation. With LSC, we find", "type": "text" } ], "index": 12 }, { "bbox": [ 142, 305, 469, 317 ], "spans": [ { "bbox": [ 142, 305, 469, 317 ], "score": 1.0, "content": "that deep network first overfits the adversarial examples with small loss, and then", "type": "text" } ], "index": 13 }, { "bbox": [ 141, 315, 470, 329 ], "spans": [ { "bbox": [ 141, 315, 470, 329 ], "score": 1.0, "content": "gradually develops to overfit all adversarial examples in the later stage of training.", "type": "text" } ], "index": 14 }, { "bbox": [ 141, 326, 469, 339 ], "spans": [ { "bbox": [ 141, 326, 469, 339 ], "score": 1.0, "content": "Following this, we find that it is essential to conduct weight perturbation on ad-", "type": "text" } ], "index": 15 }, { "bbox": [ 142, 338, 469, 349 ], "spans": [ { "bbox": [ 142, 338, 469, 349 ], "score": 1.0, "content": "versarial data with small classification loss to eliminate overfitting in adversarial", "type": "text" } ], "index": 16 }, { "bbox": [ 141, 348, 469, 360 ], "spans": [ { "bbox": [ 141, 348, 469, 360 ], "score": 1.0, "content": "training. Weight perturbation on adversarial data with large classification loss is", "type": "text" } ], "index": 17 }, { "bbox": [ 141, 360, 470, 371 ], "spans": [ { "bbox": [ 141, 360, 470, 371 ], "score": 1.0, "content": "not necessary and may even lead to poor robustness. Based on these observations,", "type": "text" } ], "index": 18 }, { "bbox": [ 141, 371, 469, 383 ], "spans": [ { "bbox": [ 141, 371, 469, 383 ], "score": 1.0, "content": "we propose a robust perturbation strategy to constrain the extent of weight pertur-", "type": "text" } ], "index": 19 }, { "bbox": [ 141, 380, 470, 394 ], "spans": [ { "bbox": [ 141, 380, 470, 394 ], "score": 1.0, "content": "bation. The perturbation strategy prevents deep networks from overfitting while", "type": "text" } ], "index": 20 }, { "bbox": [ 142, 393, 469, 405 ], "spans": [ { "bbox": [ 142, 393, 469, 405 ], "score": 1.0, "content": "avoiding the side effect of excessive weight perturbation, significantly improv-", "type": "text" } ], "index": 21 }, { "bbox": [ 141, 403, 469, 415 ], "spans": [ { "bbox": [ 141, 403, 469, 415 ], "score": 1.0, "content": "ing the robustness of adversarial training. Extensive experiments demonstrate the", "type": "text" } ], "index": 22 }, { "bbox": [ 141, 414, 470, 428 ], "spans": [ { "bbox": [ 141, 414, 470, 428 ], "score": 1.0, "content": "superiority of the proposed method over the state-of-the-art adversarial training", "type": "text" } ], "index": 23 }, { "bbox": [ 141, 426, 181, 436 ], "spans": [ { "bbox": [ 141, 426, 181, 436 ], "score": 1.0, "content": "methods.", "type": "text" } ], "index": 24 } ], "index": 14.5, "bbox_fs": [ 141, 217, 470, 436 ] }, { "type": "title", "bbox": [ 108, 470, 205, 483 ], "lines": [ { "bbox": [ 105, 469, 208, 486 ], "spans": [ { "bbox": [ 105, 469, 208, 486 ], "score": 1.0, "content": "1 INTRODUCTION", "type": "text" } ], "index": 25 } ], "index": 25 }, { "type": "text", "bbox": [ 107, 500, 504, 555 ], "lines": [ { "bbox": [ 105, 500, 506, 514 ], "spans": [ { "bbox": [ 105, 500, 506, 514 ], "score": 1.0, "content": "Although deep neural networks (DNNs) have led to impressive breakthroughs in a number of fields", "type": "text" } ], "index": 26 }, { "bbox": [ 105, 511, 505, 524 ], "spans": [ { "bbox": [ 105, 511, 505, 524 ], "score": 1.0, "content": "such as computer vision (He et al., 2016), speech recognition (Wang et al., 2017), and natural lan-", "type": "text" } ], "index": 27 }, { "bbox": [ 105, 522, 506, 535 ], "spans": [ { "bbox": [ 105, 522, 506, 535 ], "score": 1.0, "content": "guage processing (Devlin et al., 2018), they are extremely vulnerable to adversarial examples that", "type": "text" } ], "index": 28 }, { "bbox": [ 105, 532, 505, 547 ], "spans": [ { "bbox": [ 105, 532, 505, 547 ], "score": 1.0, "content": "are crafted by adding small and human-imperceptible perturbation to normal examples (Szegedy", "type": "text" } ], "index": 29 }, { "bbox": [ 105, 543, 258, 558 ], "spans": [ { "bbox": [ 105, 543, 258, 558 ], "score": 1.0, "content": "et al., 2013; Goodfellow et al., 2014).", "type": "text" } ], "index": 30 } ], "index": 28, "bbox_fs": [ 105, 500, 506, 558 ] }, { "type": "text", "bbox": [ 107, 561, 505, 704 ], "lines": [ { "bbox": [ 106, 561, 505, 574 ], "spans": [ { "bbox": [ 106, 561, 505, 574 ], "score": 1.0, "content": "The vulnerability of DNNs has attracted extensive attention and led to a large number of defense", "type": "text" } ], "index": 31 }, { "bbox": [ 105, 571, 506, 586 ], "spans": [ { "bbox": [ 105, 571, 506, 586 ], "score": 1.0, "content": "techniques against adversarial examples. Across existing defenses, adversarial training (AT) is one", "type": "text" } ], "index": 32 }, { "bbox": [ 105, 582, 506, 597 ], "spans": [ { "bbox": [ 105, 582, 506, 597 ], "score": 1.0, "content": "of the strongest empirical defenses. AT directly incorporates adversarial examples into the training", "type": "text" } ], "index": 33 }, { "bbox": [ 104, 594, 506, 607 ], "spans": [ { "bbox": [ 104, 594, 506, 607 ], "score": 1.0, "content": "process to solve a min-max optimization problem (Madry et al., 2017), which can obtain models with", "type": "text" } ], "index": 34 }, { "bbox": [ 105, 605, 505, 618 ], "spans": [ { "bbox": [ 105, 605, 505, 618 ], "score": 1.0, "content": "moderate adversarial robustness and has not been comprehensively attacked (Athalye et al., 2018).", "type": "text" } ], "index": 35 }, { "bbox": [ 105, 615, 505, 629 ], "spans": [ { "bbox": [ 105, 615, 505, 629 ], "score": 1.0, "content": "However, different from the standard training scenario, overfitting is a dominant phenomenon in", "type": "text" } ], "index": 36 }, { "bbox": [ 105, 627, 506, 640 ], "spans": [ { "bbox": [ 105, 627, 506, 640 ], "score": 1.0, "content": "adversarial robust training of deep networks (Rice et al., 2020). After a certain point in AT, the robust", "type": "text" } ], "index": 37 }, { "bbox": [ 105, 637, 505, 650 ], "spans": [ { "bbox": [ 105, 637, 505, 650 ], "score": 1.0, "content": "performance on test data will continue to degrade with further training. This phenomenon, termed", "type": "text" } ], "index": 38 }, { "bbox": [ 105, 649, 506, 661 ], "spans": [ { "bbox": [ 105, 649, 506, 661 ], "score": 1.0, "content": "as robust overfitting, breaches the common practice in deep learning that using over-parameterized", "type": "text" } ], "index": 39 }, { "bbox": [ 105, 660, 505, 673 ], "spans": [ { "bbox": [ 105, 660, 505, 673 ], "score": 1.0, "content": "networks and training for as long as possible (Neyshabur et al., 2017; Belkin et al., 2019). Such", "type": "text" } ], "index": 40 }, { "bbox": [ 106, 671, 505, 683 ], "spans": [ { "bbox": [ 106, 671, 505, 683 ], "score": 1.0, "content": "anomaly in AT causes detrimental effects on the robust generalization performance and subsequent", "type": "text" } ], "index": 41 }, { "bbox": [ 106, 682, 505, 693 ], "spans": [ { "bbox": [ 106, 682, 505, 693 ], "score": 1.0, "content": "algorithm assessment (Rice et al., 2020; Chen et al., 2020b). Relief techniques that mitigate robust", "type": "text" } ], "index": 42 }, { "bbox": [ 105, 692, 375, 706 ], "spans": [ { "bbox": [ 105, 692, 375, 706 ], "score": 1.0, "content": "overfitting have thus become crucial for stable adversarial training.", "type": "text" } ], "index": 43 } ], "index": 37, "bbox_fs": [ 104, 561, 506, 706 ] }, { "type": "text", "bbox": [ 107, 709, 503, 731 ], "lines": [ { "bbox": [ 106, 709, 505, 722 ], "spans": [ { "bbox": [ 106, 709, 505, 722 ], "score": 1.0, "content": "An effective and promising remedy for robust overfitting is Adversarial Weight Perturbation", "type": "text" } ], "index": 44 }, { "bbox": [ 106, 720, 505, 733 ], "spans": [ { "bbox": [ 106, 720, 505, 733 ], "score": 1.0, "content": "(AWP) (Wu et al., 2020), which forms a double-perturbation mechanism in the adversarial train-", "type": "text" } ], "index": 45 }, { "bbox": [ 105, 81, 374, 97 ], "spans": [ { "bbox": [ 105, 81, 374, 97 ], "score": 1.0, "content": "ing framework that adversarially perturbs both inputs and weights:", "type": "text", "cross_page": true } ], "index": 0 } ], "index": 44.5, "bbox_fs": [ 106, 709, 505, 733 ] } ] }, { "preproc_blocks": [ { "type": "text", "bbox": [ 106, 82, 373, 94 ], "lines": [ { "bbox": [ 105, 81, 374, 97 ], "spans": [ { "bbox": [ 105, 81, 374, 97 ], "score": 1.0, "content": "ing framework that adversarially perturbs both inputs and weights:", "type": "text" } ], "index": 0 } ], "index": 0 }, { "type": "interline_equation", "bbox": [ 215, 100, 396, 133 ], "lines": [ { "bbox": [ 215, 100, 396, 133 ], "spans": [ { "bbox": [ 215, 100, 396, 133 ], "score": 0.94, "content": "\\operatorname* { m i n } _ { w } \\operatorname* { m a x } _ { v \\in \\mathcal { V } } \\frac { 1 } { n } \\sum _ { i = 1 } ^ { n } \\operatorname* { m a x } _ { | | x _ { i } ^ { \\prime } - x _ { i } | | _ { p } \\leq \\epsilon } \\ell ( f _ { w + v } ( x _ { i } ^ { \\prime } ) , y _ { i } ) ,", "type": "interline_equation", "image_path": "7291a5ecc48ec28aa86438dd16259ae630db3e03eae87e519da7d54998a58aef.jpg" } ] } ], "index": 1.5, "virtual_lines": [ { "bbox": [ 215, 100, 396, 116.5 ], "spans": [], "index": 1 }, { "bbox": [ 215, 116.5, 396, 133.0 ], "spans": [], "index": 2 } ] }, { "type": "text", "bbox": [ 106, 138, 505, 249 ], "lines": [ { "bbox": [ 106, 139, 505, 152 ], "spans": [ { "bbox": [ 106, 139, 134, 152 ], "score": 1.0, "content": "where", "type": "text" }, { "bbox": [ 134, 142, 141, 149 ], "score": 0.76, "content": "n", "type": "inline_equation" }, { "bbox": [ 142, 139, 291, 152 ], "score": 1.0, "content": "is the number of training examples,", "type": "text" }, { "bbox": [ 292, 139, 302, 151 ], "score": 0.89, "content": "\\boldsymbol { x } _ { i } ^ { \\prime }", "type": "inline_equation" }, { "bbox": [ 303, 139, 425, 152 ], "score": 1.0, "content": "is the adversarial example of", "type": "text" }, { "bbox": [ 425, 140, 453, 151 ], "score": 0.42, "content": "x _ { i } , f _ { w }", "type": "inline_equation" }, { "bbox": [ 454, 139, 505, 152 ], "score": 1.0, "content": "is the DNN", "type": "text" } ], "index": 3 }, { "bbox": [ 105, 149, 506, 163 ], "spans": [ { "bbox": [ 105, 149, 157, 163 ], "score": 1.0, "content": "with weight", "type": "text" }, { "bbox": [ 157, 150, 188, 162 ], "score": 0.54, "content": "w , \\ell ( \\cdot )", "type": "inline_equation" }, { "bbox": [ 188, 149, 272, 163 ], "score": 1.0, "content": "is the loss function,", "type": "text" }, { "bbox": [ 272, 153, 278, 160 ], "score": 0.7, "content": "\\epsilon", "type": "inline_equation" }, { "bbox": [ 279, 149, 506, 163 ], "score": 1.0, "content": "is the maximum perturbation constraint for inputs (i.e.,", "type": "text" } ], "index": 4 }, { "bbox": [ 107, 160, 505, 175 ], "spans": [ { "bbox": [ 107, 161, 179, 173 ], "score": 0.89, "content": "| | x _ { i } ^ { \\prime } - x _ { i } | | _ { p } \\leq \\epsilon )", "type": "inline_equation" }, { "bbox": [ 179, 160, 201, 175 ], "score": 1.0, "content": ", and", "type": "text" }, { "bbox": [ 201, 162, 210, 172 ], "score": 0.79, "content": "\\nu", "type": "inline_equation" }, { "bbox": [ 210, 160, 424, 175 ], "score": 1.0, "content": "is the feasible perturbation region for weights (i.e.,", "type": "text" }, { "bbox": [ 424, 161, 505, 173 ], "score": 0.89, "content": "\\{ v \\in \\mathcal { V } : | | v | | _ { 2 } \\leq", "type": "inline_equation" } ], "index": 5 }, { "bbox": [ 106, 172, 506, 185 ], "spans": [ { "bbox": [ 106, 173, 142, 184 ], "score": 0.89, "content": "\\gamma | | w | | _ { 2 } \\bigr \\}", "type": "inline_equation" }, { "bbox": [ 142, 172, 176, 185 ], "score": 1.0, "content": ", where", "type": "text" }, { "bbox": [ 176, 174, 184, 184 ], "score": 0.83, "content": "\\gamma", "type": "inline_equation" }, { "bbox": [ 184, 172, 506, 185 ], "score": 1.0, "content": "is the constraint on weight perturbation size). The inner maximization is to", "type": "text" } ], "index": 6 }, { "bbox": [ 105, 182, 506, 196 ], "spans": [ { "bbox": [ 105, 182, 212, 196 ], "score": 1.0, "content": "find adversarial examples", "type": "text" }, { "bbox": [ 213, 183, 223, 195 ], "score": 0.9, "content": "x _ { i } ^ { \\prime }", "type": "inline_equation" }, { "bbox": [ 223, 182, 268, 196 ], "score": 1.0, "content": "within the", "type": "text" }, { "bbox": [ 269, 185, 274, 193 ], "score": 0.69, "content": "\\epsilon", "type": "inline_equation" }, { "bbox": [ 275, 182, 413, 196 ], "score": 1.0, "content": "-ball centered at normal examples", "type": "text" }, { "bbox": [ 414, 185, 424, 194 ], "score": 0.86, "content": "x _ { i }", "type": "inline_equation" }, { "bbox": [ 424, 182, 506, 196 ], "score": 1.0, "content": "that maximizes the", "type": "text" } ], "index": 7 }, { "bbox": [ 106, 194, 505, 206 ], "spans": [ { "bbox": [ 106, 194, 179, 206 ], "score": 1.0, "content": "classification loss", "type": "text" }, { "bbox": [ 179, 195, 185, 204 ], "score": 0.6, "content": "\\ell", "type": "inline_equation" }, { "bbox": [ 185, 194, 479, 206 ], "score": 1.0, "content": ". On the other hand, the outer maximization is to find weight perturbation", "type": "text" }, { "bbox": [ 479, 196, 487, 204 ], "score": 0.68, "content": "\\textbf { { v } }", "type": "inline_equation" }, { "bbox": [ 487, 194, 505, 206 ], "score": 1.0, "content": "that", "type": "text" } ], "index": 8 }, { "bbox": [ 105, 205, 506, 217 ], "spans": [ { "bbox": [ 105, 205, 185, 217 ], "score": 1.0, "content": "maximizes the loss", "type": "text" }, { "bbox": [ 185, 206, 191, 215 ], "score": 0.7, "content": "\\ell", "type": "inline_equation" }, { "bbox": [ 191, 205, 506, 217 ], "score": 1.0, "content": "on adversarial examples to flatten the weight loss landscape and reduce robust", "type": "text" } ], "index": 9 }, { "bbox": [ 105, 216, 506, 228 ], "spans": [ { "bbox": [ 105, 216, 506, 228 ], "score": 1.0, "content": "generalization gap. This is the problem of training a weight-perturbed robust classifier on adversarial", "type": "text" } ], "index": 10 }, { "bbox": [ 106, 227, 506, 239 ], "spans": [ { "bbox": [ 106, 227, 506, 239 ], "score": 1.0, "content": "examples. Therefore, how well the weight perturbation is found directly affects the performance of", "type": "text" } ], "index": 11 }, { "bbox": [ 106, 239, 343, 250 ], "spans": [ { "bbox": [ 106, 239, 343, 250 ], "score": 1.0, "content": "the outer minimization, i.e., the robustness of the classifier.", "type": "text" } ], "index": 12 } ], "index": 7.5 }, { "type": "text", "bbox": [ 106, 254, 505, 365 ], "lines": [ { "bbox": [ 106, 255, 505, 267 ], "spans": [ { "bbox": [ 106, 255, 505, 267 ], "score": 1.0, "content": "Several attack methods have been used to solve the inner maximization problem in Eq.(1), such", "type": "text" } ], "index": 13 }, { "bbox": [ 106, 266, 505, 277 ], "spans": [ { "bbox": [ 106, 266, 505, 277 ], "score": 1.0, "content": "as Fast Gradient Sign Method (FGSM) (Goodfellow et al., 2014) and Projected Gradient Descent", "type": "text" } ], "index": 14 }, { "bbox": [ 106, 277, 505, 289 ], "spans": [ { "bbox": [ 106, 277, 505, 289 ], "score": 1.0, "content": "(PGD) (Madry et al., 2017). For the outer maximization problem, AWP (Wu et al., 2020) injects the", "type": "text" } ], "index": 15 }, { "bbox": [ 105, 288, 505, 300 ], "spans": [ { "bbox": [ 105, 288, 505, 300 ], "score": 1.0, "content": "worst-case weight perturbation to reduce robust generalization gap. However, the extent to which", "type": "text" } ], "index": 16 }, { "bbox": [ 105, 298, 505, 312 ], "spans": [ { "bbox": [ 105, 298, 505, 312 ], "score": 1.0, "content": "the weights should be perturbed has not been explored. Without an appropriate criterion to regulate", "type": "text" } ], "index": 17 }, { "bbox": [ 106, 309, 506, 322 ], "spans": [ { "bbox": [ 106, 309, 506, 322 ], "score": 1.0, "content": "the weight perturbation, the adversarial training procedure is difficult to unleash its full power. In", "type": "text" } ], "index": 18 }, { "bbox": [ 106, 321, 506, 334 ], "spans": [ { "bbox": [ 106, 321, 506, 334 ], "score": 1.0, "content": "this paper, we propose such a criterion, namely Loss Stationary Condition (LSC) for constrained", "type": "text" } ], "index": 19 }, { "bbox": [ 105, 332, 505, 344 ], "spans": [ { "bbox": [ 105, 332, 505, 344 ], "score": 1.0, "content": "perturbation, which sheds light on the nitty-gritty of robust overfitting in adversarial training, and", "type": "text" } ], "index": 20 }, { "bbox": [ 106, 343, 505, 356 ], "spans": [ { "bbox": [ 106, 343, 505, 356 ], "score": 1.0, "content": "this in turn motivates us to propose an improved weight perturbation strategy for better robustness.", "type": "text" } ], "index": 21 }, { "bbox": [ 106, 353, 251, 366 ], "spans": [ { "bbox": [ 106, 353, 251, 366 ], "score": 1.0, "content": "Our main contributions are follows:", "type": "text" } ], "index": 22 } ], "index": 17.5 }, { "type": "text", "bbox": [ 106, 375, 506, 495 ], "lines": [ { "bbox": [ 105, 374, 506, 388 ], "spans": [ { "bbox": [ 105, 374, 506, 388 ], "score": 1.0, "content": "• We propose a principled criterion LSC to monitor the training status of different adversarial ex-", "type": "text" } ], "index": 23 }, { "bbox": [ 114, 385, 505, 399 ], "spans": [ { "bbox": [ 114, 385, 505, 399 ], "score": 1.0, "content": "amples during network optimization. It provides a better understanding of robust overfitting in", "type": "text" } ], "index": 24 }, { "bbox": [ 114, 398, 448, 409 ], "spans": [ { "bbox": [ 114, 398, 448, 409 ], "score": 1.0, "content": "adversarial training, and it is also a good indicator for efficient weight perturbation.", "type": "text" } ], "index": 25 }, { "bbox": [ 105, 412, 505, 425 ], "spans": [ { "bbox": [ 105, 412, 505, 425 ], "score": 1.0, "content": "• With LSC, we find that deep network first overfits adversarial data with small classification loss", "type": "text" } ], "index": 26 }, { "bbox": [ 114, 423, 505, 437 ], "spans": [ { "bbox": [ 114, 423, 505, 437 ], "score": 1.0, "content": "and then gradually develops to overfit all adversarial data. Following this, we find that better per-", "type": "text" } ], "index": 27 }, { "bbox": [ 114, 435, 505, 447 ], "spans": [ { "bbox": [ 114, 435, 505, 447 ], "score": 1.0, "content": "turbation of model weights is associated with perturbing on adversarial data with small classifica-", "type": "text" } ], "index": 28 }, { "bbox": [ 114, 445, 505, 459 ], "spans": [ { "bbox": [ 114, 445, 505, 459 ], "score": 1.0, "content": "tion loss. For adversarial data with large classification loss, weight perturbation is not necessary", "type": "text" } ], "index": 29 }, { "bbox": [ 114, 457, 217, 468 ], "spans": [ { "bbox": [ 114, 457, 217, 468 ], "score": 1.0, "content": "and can even be harmful.", "type": "text" } ], "index": 30 }, { "bbox": [ 105, 472, 505, 485 ], "spans": [ { "bbox": [ 105, 472, 505, 485 ], "score": 1.0, "content": "• We propose a robust perturbation strategy to constrain the extent of weight perturbation. Experi-", "type": "text" } ], "index": 31 }, { "bbox": [ 113, 482, 501, 497 ], "spans": [ { "bbox": [ 113, 482, 501, 497 ], "score": 1.0, "content": "ments show that the robust strategy significantly improves the robustness of adversarial training.", "type": "text" } ], "index": 32 } ], "index": 27.5 }, { "type": "title", "bbox": [ 108, 512, 211, 525 ], "lines": [ { "bbox": [ 104, 511, 213, 528 ], "spans": [ { "bbox": [ 104, 511, 213, 528 ], "score": 1.0, "content": "2 RELATED WORK", "type": "text" } ], "index": 33 } ], "index": 33 }, { "type": "title", "bbox": [ 108, 538, 237, 549 ], "lines": [ { "bbox": [ 106, 538, 237, 550 ], "spans": [ { "bbox": [ 106, 538, 237, 550 ], "score": 1.0, "content": "2.1 ADVERSARIAL ATTACKS", "type": "text" } ], "index": 34 } ], "index": 34 }, { "type": "text", "bbox": [ 106, 558, 505, 614 ], "lines": [ { "bbox": [ 106, 558, 506, 572 ], "spans": [ { "bbox": [ 106, 558, 208, 572 ], "score": 1.0, "content": "Given a normal example", "type": "text" }, { "bbox": [ 208, 559, 231, 571 ], "score": 0.91, "content": "( x , y )", "type": "inline_equation" }, { "bbox": [ 232, 558, 267, 572 ], "score": 1.0, "content": ", a DNN", "type": "text" }, { "bbox": [ 268, 560, 280, 570 ], "score": 0.85, "content": "f _ { w }", "type": "inline_equation" }, { "bbox": [ 281, 558, 438, 572 ], "score": 1.0, "content": ", and maximum perturbation constraint", "type": "text" }, { "bbox": [ 438, 561, 444, 569 ], "score": 0.51, "content": "\\epsilon", "type": "inline_equation" }, { "bbox": [ 444, 558, 464, 572 ], "score": 1.0, "content": ". Let", "type": "text" }, { "bbox": [ 465, 560, 475, 569 ], "score": 0.8, "content": "\\mathcal { X }", "type": "inline_equation" }, { "bbox": [ 475, 558, 506, 572 ], "score": 1.0, "content": "denote", "type": "text" } ], "index": 35 }, { "bbox": [ 106, 569, 505, 583 ], "spans": [ { "bbox": [ 106, 569, 220, 583 ], "score": 1.0, "content": "the input feature space and", "type": "text" }, { "bbox": [ 221, 570, 381, 582 ], "score": 0.92, "content": "\\mathcal { B } _ { \\epsilon } ^ { p } ( x ) = \\{ x ^ { \\prime } \\in \\mathcal { X } : | | x ^ { \\prime } - x | | _ { p } \\leq \\epsilon \\}", "type": "inline_equation" }, { "bbox": [ 382, 569, 411, 583 ], "score": 1.0, "content": "be the", "type": "text" }, { "bbox": [ 411, 570, 421, 582 ], "score": 0.87, "content": "\\ell _ { p }", "type": "inline_equation" }, { "bbox": [ 422, 569, 505, 583 ], "score": 1.0, "content": "-norm ball of radius", "type": "text" } ], "index": 36 }, { "bbox": [ 107, 579, 504, 595 ], "spans": [ { "bbox": [ 107, 583, 112, 591 ], "score": 0.64, "content": "\\epsilon", "type": "inline_equation" }, { "bbox": [ 113, 579, 160, 595 ], "score": 1.0, "content": "centered at", "type": "text" }, { "bbox": [ 161, 583, 168, 591 ], "score": 0.75, "content": "x", "type": "inline_equation" }, { "bbox": [ 168, 579, 180, 595 ], "score": 1.0, "content": "in", "type": "text" }, { "bbox": [ 181, 582, 190, 591 ], "score": 0.81, "content": "\\mathcal { X }", "type": "inline_equation" }, { "bbox": [ 190, 579, 455, 595 ], "score": 1.0, "content": ". The goal of adversarial attack is to find an adversarial example", "type": "text" }, { "bbox": [ 455, 581, 504, 593 ], "score": 0.92, "content": "x ^ { \\prime } \\in B _ { \\epsilon } ^ { p } ( x )", "type": "inline_equation" } ], "index": 37 }, { "bbox": [ 106, 591, 505, 605 ], "spans": [ { "bbox": [ 106, 591, 326, 605 ], "score": 1.0, "content": "that can fool the DNN to produce an incorrect output (", "type": "text" }, { "bbox": [ 326, 592, 376, 604 ], "score": 0.89, "content": "f _ { w } ( x ^ { \\prime } ) \\ne y", "type": "inline_equation" }, { "bbox": [ 376, 591, 505, 605 ], "score": 1.0, "content": "). Here we selectively introduce", "type": "text" } ], "index": 38 }, { "bbox": [ 105, 603, 314, 615 ], "spans": [ { "bbox": [ 105, 603, 314, 615 ], "score": 1.0, "content": "several commonly used adversarial attack methods.", "type": "text" } ], "index": 39 } ], "index": 37 }, { "type": "text", "bbox": [ 106, 619, 502, 642 ], "lines": [ { "bbox": [ 106, 619, 504, 632 ], "spans": [ { "bbox": [ 106, 619, 504, 632 ], "score": 1.0, "content": "Fast Gradient Sign Method (FGSM). FGSM (Goodfellow et al., 2014) perturbs natural example", "type": "text" } ], "index": 40 }, { "bbox": [ 107, 631, 342, 644 ], "spans": [ { "bbox": [ 107, 633, 113, 641 ], "score": 0.74, "content": "x", "type": "inline_equation" }, { "bbox": [ 114, 631, 221, 644 ], "score": 1.0, "content": "for one step with step size", "type": "text" }, { "bbox": [ 221, 633, 226, 641 ], "score": 0.76, "content": "\\epsilon", "type": "inline_equation" }, { "bbox": [ 227, 631, 342, 644 ], "score": 1.0, "content": "along the gradient direction:", "type": "text" } ], "index": 41 } ], "index": 40.5 }, { "type": "interline_equation", "bbox": [ 234, 648, 376, 663 ], "lines": [ { "bbox": [ 234, 648, 376, 663 ], "spans": [ { "bbox": [ 234, 648, 376, 663 ], "score": 0.92, "content": "\\begin{array} { r } { x ^ { \\prime } = x + \\epsilon \\cdot \\mathrm { s i g n } \\bigl ( \\nabla _ { x } \\ell ( f _ { w } ( x ) , y ) \\bigr ) . } \\end{array}", "type": "interline_equation", "image_path": "952e1c47e1823c3227cdfaac7c6095e657112ff88a6291e8c8541528e5f252c1.jpg" } ] } ], "index": 42, "virtual_lines": [ { "bbox": [ 234, 648, 376, 663 ], "spans": [], "index": 42 } ] }, { "type": "text", "bbox": [ 105, 668, 506, 691 ], "lines": [ { "bbox": [ 106, 667, 505, 681 ], "spans": [ { "bbox": [ 106, 667, 505, 681 ], "score": 1.0, "content": "Projected Gradient Descent (PGD). PGD (Madry et al., 2017) is a stronger iterative variant of", "type": "text" } ], "index": 43 }, { "bbox": [ 106, 680, 467, 693 ], "spans": [ { "bbox": [ 106, 680, 267, 693 ], "score": 1.0, "content": "FGSM, which perturbs normal example", "type": "text" }, { "bbox": [ 268, 683, 274, 690 ], "score": 0.79, "content": "x", "type": "inline_equation" }, { "bbox": [ 275, 680, 348, 693 ], "score": 1.0, "content": "for multiple steps", "type": "text" }, { "bbox": [ 348, 680, 358, 690 ], "score": 0.84, "content": "K", "type": "inline_equation" }, { "bbox": [ 358, 680, 455, 693 ], "score": 1.0, "content": "with a smaller step size", "type": "text" }, { "bbox": [ 455, 682, 462, 690 ], "score": 0.74, "content": "\\alpha", "type": "inline_equation" }, { "bbox": [ 463, 680, 467, 693 ], "score": 1.0, "content": ":", "type": "text" } ], "index": 44 } ], "index": 43.5 }, { "type": "interline_equation", "bbox": [ 271, 696, 339, 711 ], "lines": [ { "bbox": [ 271, 696, 339, 711 ], "spans": [ { "bbox": [ 271, 696, 339, 711 ], "score": 0.74, "content": "x ^ { 0 } \\sim \\mathcal { U } ( B _ { \\epsilon } ^ { p } ( x ) ) ,", "type": "interline_equation", "image_path": "79264faa6ff45f1aef7f22fa537f2dd6fffda973b3d97ded9f3ec049a5982a2f.jpg" } ] } ], "index": 45, "virtual_lines": [ { "bbox": [ 271, 696, 339, 711 ], "spans": [], "index": 45 } ] }, { "type": "interline_equation", "bbox": [ 192, 718, 417, 734 ], "lines": [ { "bbox": [ 192, 718, 417, 734 ], "spans": [ { "bbox": [ 192, 718, 417, 734 ], "score": 0.77, "content": "\\boldsymbol { x } ^ { k } = \\Pi _ { \\mathcal { B } _ { \\epsilon } ^ { p } ( x ) } ( \\boldsymbol { x } ^ { k - 1 } + \\alpha \\cdot \\mathrm { s i g n } ( \\nabla _ { \\boldsymbol { x } ^ { k - 1 } } \\ell ( f _ { w } ( \\boldsymbol { x } ^ { k - 1 } ) , \\boldsymbol { y } ) ) ) ,", "type": "interline_equation", "image_path": "2a73b5ef623b75557caaff3282b72e798941ef060aaa0e6629ef5f7416d1598c.jpg" } ] } ], "index": 46, "virtual_lines": [ { "bbox": [ 192, 718, 417, 734 ], "spans": [], "index": 46 } ] } ], "page_idx": 1, "page_size": [ 612, 792 ], "discarded_blocks": [ { "type": "discarded", "bbox": [ 106, 26, 308, 38 ], "lines": [ { "bbox": [ 106, 25, 309, 39 ], "spans": [ { "bbox": [ 106, 25, 309, 39 ], "score": 1.0, "content": "Under review 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, 373, 94 ], "lines": [], "index": 0, "bbox_fs": [ 105, 81, 374, 97 ], "lines_deleted": true }, { "type": "interline_equation", "bbox": [ 215, 100, 396, 133 ], "lines": [ { "bbox": [ 215, 100, 396, 133 ], "spans": [ { "bbox": [ 215, 100, 396, 133 ], "score": 0.94, "content": "\\operatorname* { m i n } _ { w } \\operatorname* { m a x } _ { v \\in \\mathcal { V } } \\frac { 1 } { n } \\sum _ { i = 1 } ^ { n } \\operatorname* { m a x } _ { | | x _ { i } ^ { \\prime } - x _ { i } | | _ { p } \\leq \\epsilon } \\ell ( f _ { w + v } ( x _ { i } ^ { \\prime } ) , y _ { i } ) ,", "type": "interline_equation", "image_path": "7291a5ecc48ec28aa86438dd16259ae630db3e03eae87e519da7d54998a58aef.jpg" } ] } ], "index": 1.5, "virtual_lines": [ { "bbox": [ 215, 100, 396, 116.5 ], "spans": [], "index": 1 }, { "bbox": [ 215, 116.5, 396, 133.0 ], "spans": [], "index": 2 } ] }, { "type": "text", "bbox": [ 106, 138, 505, 249 ], "lines": [ { "bbox": [ 106, 139, 505, 152 ], "spans": [ { "bbox": [ 106, 139, 134, 152 ], "score": 1.0, "content": "where", "type": "text" }, { "bbox": [ 134, 142, 141, 149 ], "score": 0.76, "content": "n", "type": "inline_equation" }, { "bbox": [ 142, 139, 291, 152 ], "score": 1.0, "content": "is the number of training examples,", "type": "text" }, { "bbox": [ 292, 139, 302, 151 ], "score": 0.89, "content": "\\boldsymbol { x } _ { i } ^ { \\prime }", "type": "inline_equation" }, { "bbox": [ 303, 139, 425, 152 ], "score": 1.0, "content": "is the adversarial example of", "type": "text" }, { "bbox": [ 425, 140, 453, 151 ], "score": 0.42, "content": "x _ { i } , f _ { w }", "type": "inline_equation" }, { "bbox": [ 454, 139, 505, 152 ], "score": 1.0, "content": "is the DNN", "type": "text" } ], "index": 3 }, { "bbox": [ 105, 149, 506, 163 ], "spans": [ { "bbox": [ 105, 149, 157, 163 ], "score": 1.0, "content": "with weight", "type": "text" }, { "bbox": [ 157, 150, 188, 162 ], "score": 0.54, "content": "w , \\ell ( \\cdot )", "type": "inline_equation" }, { "bbox": [ 188, 149, 272, 163 ], "score": 1.0, "content": "is the loss function,", "type": "text" }, { "bbox": [ 272, 153, 278, 160 ], "score": 0.7, "content": "\\epsilon", "type": "inline_equation" }, { "bbox": [ 279, 149, 506, 163 ], "score": 1.0, "content": "is the maximum perturbation constraint for inputs (i.e.,", "type": "text" } ], "index": 4 }, { "bbox": [ 107, 160, 505, 175 ], "spans": [ { "bbox": [ 107, 161, 179, 173 ], "score": 0.89, "content": "| | x _ { i } ^ { \\prime } - x _ { i } | | _ { p } \\leq \\epsilon )", "type": "inline_equation" }, { "bbox": [ 179, 160, 201, 175 ], "score": 1.0, "content": ", and", "type": "text" }, { "bbox": [ 201, 162, 210, 172 ], "score": 0.79, "content": "\\nu", "type": "inline_equation" }, { "bbox": [ 210, 160, 424, 175 ], "score": 1.0, "content": "is the feasible perturbation region for weights (i.e.,", "type": "text" }, { "bbox": [ 424, 161, 505, 173 ], "score": 0.89, "content": "\\{ v \\in \\mathcal { V } : | | v | | _ { 2 } \\leq", "type": "inline_equation" } ], "index": 5 }, { "bbox": [ 106, 172, 506, 185 ], "spans": [ { "bbox": [ 106, 173, 142, 184 ], "score": 0.89, "content": "\\gamma | | w | | _ { 2 } \\bigr \\}", "type": "inline_equation" }, { "bbox": [ 142, 172, 176, 185 ], "score": 1.0, "content": ", where", "type": "text" }, { "bbox": [ 176, 174, 184, 184 ], "score": 0.83, "content": "\\gamma", "type": "inline_equation" }, { "bbox": [ 184, 172, 506, 185 ], "score": 1.0, "content": "is the constraint on weight perturbation size). The inner maximization is to", "type": "text" } ], "index": 6 }, { "bbox": [ 105, 182, 506, 196 ], "spans": [ { "bbox": [ 105, 182, 212, 196 ], "score": 1.0, "content": "find adversarial examples", "type": "text" }, { "bbox": [ 213, 183, 223, 195 ], "score": 0.9, "content": "x _ { i } ^ { \\prime }", "type": "inline_equation" }, { "bbox": [ 223, 182, 268, 196 ], "score": 1.0, "content": "within the", "type": "text" }, { "bbox": [ 269, 185, 274, 193 ], "score": 0.69, "content": "\\epsilon", "type": "inline_equation" }, { "bbox": [ 275, 182, 413, 196 ], "score": 1.0, "content": "-ball centered at normal examples", "type": "text" }, { "bbox": [ 414, 185, 424, 194 ], "score": 0.86, "content": "x _ { i }", "type": "inline_equation" }, { "bbox": [ 424, 182, 506, 196 ], "score": 1.0, "content": "that maximizes the", "type": "text" } ], "index": 7 }, { "bbox": [ 106, 194, 505, 206 ], "spans": [ { "bbox": [ 106, 194, 179, 206 ], "score": 1.0, "content": "classification loss", "type": "text" }, { "bbox": [ 179, 195, 185, 204 ], "score": 0.6, "content": "\\ell", "type": "inline_equation" }, { "bbox": [ 185, 194, 479, 206 ], "score": 1.0, "content": ". On the other hand, the outer maximization is to find weight perturbation", "type": "text" }, { "bbox": [ 479, 196, 487, 204 ], "score": 0.68, "content": "\\textbf { { v } }", "type": "inline_equation" }, { "bbox": [ 487, 194, 505, 206 ], "score": 1.0, "content": "that", "type": "text" } ], "index": 8 }, { "bbox": [ 105, 205, 506, 217 ], "spans": [ { "bbox": [ 105, 205, 185, 217 ], "score": 1.0, "content": "maximizes the loss", "type": "text" }, { "bbox": [ 185, 206, 191, 215 ], "score": 0.7, "content": "\\ell", "type": "inline_equation" }, { "bbox": [ 191, 205, 506, 217 ], "score": 1.0, "content": "on adversarial examples to flatten the weight loss landscape and reduce robust", "type": "text" } ], "index": 9 }, { "bbox": [ 105, 216, 506, 228 ], "spans": [ { "bbox": [ 105, 216, 506, 228 ], "score": 1.0, "content": "generalization gap. This is the problem of training a weight-perturbed robust classifier on adversarial", "type": "text" } ], "index": 10 }, { "bbox": [ 106, 227, 506, 239 ], "spans": [ { "bbox": [ 106, 227, 506, 239 ], "score": 1.0, "content": "examples. Therefore, how well the weight perturbation is found directly affects the performance of", "type": "text" } ], "index": 11 }, { "bbox": [ 106, 239, 343, 250 ], "spans": [ { "bbox": [ 106, 239, 343, 250 ], "score": 1.0, "content": "the outer minimization, i.e., the robustness of the classifier.", "type": "text" } ], "index": 12 } ], "index": 7.5, "bbox_fs": [ 105, 139, 506, 250 ] }, { "type": "text", "bbox": [ 106, 254, 505, 365 ], "lines": [ { "bbox": [ 106, 255, 505, 267 ], "spans": [ { "bbox": [ 106, 255, 505, 267 ], "score": 1.0, "content": "Several attack methods have been used to solve the inner maximization problem in Eq.(1), such", "type": "text" } ], "index": 13 }, { "bbox": [ 106, 266, 505, 277 ], "spans": [ { "bbox": [ 106, 266, 505, 277 ], "score": 1.0, "content": "as Fast Gradient Sign Method (FGSM) (Goodfellow et al., 2014) and Projected Gradient Descent", "type": "text" } ], "index": 14 }, { "bbox": [ 106, 277, 505, 289 ], "spans": [ { "bbox": [ 106, 277, 505, 289 ], "score": 1.0, "content": "(PGD) (Madry et al., 2017). For the outer maximization problem, AWP (Wu et al., 2020) injects the", "type": "text" } ], "index": 15 }, { "bbox": [ 105, 288, 505, 300 ], "spans": [ { "bbox": [ 105, 288, 505, 300 ], "score": 1.0, "content": "worst-case weight perturbation to reduce robust generalization gap. However, the extent to which", "type": "text" } ], "index": 16 }, { "bbox": [ 105, 298, 505, 312 ], "spans": [ { "bbox": [ 105, 298, 505, 312 ], "score": 1.0, "content": "the weights should be perturbed has not been explored. Without an appropriate criterion to regulate", "type": "text" } ], "index": 17 }, { "bbox": [ 106, 309, 506, 322 ], "spans": [ { "bbox": [ 106, 309, 506, 322 ], "score": 1.0, "content": "the weight perturbation, the adversarial training procedure is difficult to unleash its full power. In", "type": "text" } ], "index": 18 }, { "bbox": [ 106, 321, 506, 334 ], "spans": [ { "bbox": [ 106, 321, 506, 334 ], "score": 1.0, "content": "this paper, we propose such a criterion, namely Loss Stationary Condition (LSC) for constrained", "type": "text" } ], "index": 19 }, { "bbox": [ 105, 332, 505, 344 ], "spans": [ { "bbox": [ 105, 332, 505, 344 ], "score": 1.0, "content": "perturbation, which sheds light on the nitty-gritty of robust overfitting in adversarial training, and", "type": "text" } ], "index": 20 }, { "bbox": [ 106, 343, 505, 356 ], "spans": [ { "bbox": [ 106, 343, 505, 356 ], "score": 1.0, "content": "this in turn motivates us to propose an improved weight perturbation strategy for better robustness.", "type": "text" } ], "index": 21 }, { "bbox": [ 106, 353, 251, 366 ], "spans": [ { "bbox": [ 106, 353, 251, 366 ], "score": 1.0, "content": "Our main contributions are follows:", "type": "text" } ], "index": 22 } ], "index": 17.5, "bbox_fs": [ 105, 255, 506, 366 ] }, { "type": "text", "bbox": [ 106, 375, 506, 495 ], "lines": [ { "bbox": [ 105, 374, 506, 388 ], "spans": [ { "bbox": [ 105, 374, 506, 388 ], "score": 1.0, "content": "• We propose a principled criterion LSC to monitor the training status of different adversarial ex-", "type": "text" } ], "index": 23 }, { "bbox": [ 114, 385, 505, 399 ], "spans": [ { "bbox": [ 114, 385, 505, 399 ], "score": 1.0, "content": "amples during network optimization. It provides a better understanding of robust overfitting in", "type": "text" } ], "index": 24 }, { "bbox": [ 114, 398, 448, 409 ], "spans": [ { "bbox": [ 114, 398, 448, 409 ], "score": 1.0, "content": "adversarial training, and it is also a good indicator for efficient weight perturbation.", "type": "text" } ], "index": 25 }, { "bbox": [ 105, 412, 505, 425 ], "spans": [ { "bbox": [ 105, 412, 505, 425 ], "score": 1.0, "content": "• With LSC, we find that deep network first overfits adversarial data with small classification loss", "type": "text" } ], "index": 26 }, { "bbox": [ 114, 423, 505, 437 ], "spans": [ { "bbox": [ 114, 423, 505, 437 ], "score": 1.0, "content": "and then gradually develops to overfit all adversarial data. Following this, we find that better per-", "type": "text" } ], "index": 27 }, { "bbox": [ 114, 435, 505, 447 ], "spans": [ { "bbox": [ 114, 435, 505, 447 ], "score": 1.0, "content": "turbation of model weights is associated with perturbing on adversarial data with small classifica-", "type": "text" } ], "index": 28 }, { "bbox": [ 114, 445, 505, 459 ], "spans": [ { "bbox": [ 114, 445, 505, 459 ], "score": 1.0, "content": "tion loss. For adversarial data with large classification loss, weight perturbation is not necessary", "type": "text" } ], "index": 29 }, { "bbox": [ 114, 457, 217, 468 ], "spans": [ { "bbox": [ 114, 457, 217, 468 ], "score": 1.0, "content": "and can even be harmful.", "type": "text" } ], "index": 30 }, { "bbox": [ 105, 472, 505, 485 ], "spans": [ { "bbox": [ 105, 472, 505, 485 ], "score": 1.0, "content": "• We propose a robust perturbation strategy to constrain the extent of weight perturbation. Experi-", "type": "text" } ], "index": 31 }, { "bbox": [ 113, 482, 501, 497 ], "spans": [ { "bbox": [ 113, 482, 501, 497 ], "score": 1.0, "content": "ments show that the robust strategy significantly improves the robustness of adversarial training.", "type": "text" } ], "index": 32 } ], "index": 27.5, "bbox_fs": [ 105, 374, 506, 497 ] }, { "type": "title", "bbox": [ 108, 512, 211, 525 ], "lines": [ { "bbox": [ 104, 511, 213, 528 ], "spans": [ { "bbox": [ 104, 511, 213, 528 ], "score": 1.0, "content": "2 RELATED WORK", "type": "text" } ], "index": 33 } ], "index": 33 }, { "type": "title", "bbox": [ 108, 538, 237, 549 ], "lines": [ { "bbox": [ 106, 538, 237, 550 ], "spans": [ { "bbox": [ 106, 538, 237, 550 ], "score": 1.0, "content": "2.1 ADVERSARIAL ATTACKS", "type": "text" } ], "index": 34 } ], "index": 34 }, { "type": "text", "bbox": [ 106, 558, 505, 614 ], "lines": [ { "bbox": [ 106, 558, 506, 572 ], "spans": [ { "bbox": [ 106, 558, 208, 572 ], "score": 1.0, "content": "Given a normal example", "type": "text" }, { "bbox": [ 208, 559, 231, 571 ], "score": 0.91, "content": "( x , y )", "type": "inline_equation" }, { "bbox": [ 232, 558, 267, 572 ], "score": 1.0, "content": ", a DNN", "type": "text" }, { "bbox": [ 268, 560, 280, 570 ], "score": 0.85, "content": "f _ { w }", "type": "inline_equation" }, { "bbox": [ 281, 558, 438, 572 ], "score": 1.0, "content": ", and maximum perturbation constraint", "type": "text" }, { "bbox": [ 438, 561, 444, 569 ], "score": 0.51, "content": "\\epsilon", "type": "inline_equation" }, { "bbox": [ 444, 558, 464, 572 ], "score": 1.0, "content": ". Let", "type": "text" }, { "bbox": [ 465, 560, 475, 569 ], "score": 0.8, "content": "\\mathcal { X }", "type": "inline_equation" }, { "bbox": [ 475, 558, 506, 572 ], "score": 1.0, "content": "denote", "type": "text" } ], "index": 35 }, { "bbox": [ 106, 569, 505, 583 ], "spans": [ { "bbox": [ 106, 569, 220, 583 ], "score": 1.0, "content": "the input feature space and", "type": "text" }, { "bbox": [ 221, 570, 381, 582 ], "score": 0.92, "content": "\\mathcal { B } _ { \\epsilon } ^ { p } ( x ) = \\{ x ^ { \\prime } \\in \\mathcal { X } : | | x ^ { \\prime } - x | | _ { p } \\leq \\epsilon \\}", "type": "inline_equation" }, { "bbox": [ 382, 569, 411, 583 ], "score": 1.0, "content": "be the", "type": "text" }, { "bbox": [ 411, 570, 421, 582 ], "score": 0.87, "content": "\\ell _ { p }", "type": "inline_equation" }, { "bbox": [ 422, 569, 505, 583 ], "score": 1.0, "content": "-norm ball of radius", "type": "text" } ], "index": 36 }, { "bbox": [ 107, 579, 504, 595 ], "spans": [ { "bbox": [ 107, 583, 112, 591 ], "score": 0.64, "content": "\\epsilon", "type": "inline_equation" }, { "bbox": [ 113, 579, 160, 595 ], "score": 1.0, "content": "centered at", "type": "text" }, { "bbox": [ 161, 583, 168, 591 ], "score": 0.75, "content": "x", "type": "inline_equation" }, { "bbox": [ 168, 579, 180, 595 ], "score": 1.0, "content": "in", "type": "text" }, { "bbox": [ 181, 582, 190, 591 ], "score": 0.81, "content": "\\mathcal { X }", "type": "inline_equation" }, { "bbox": [ 190, 579, 455, 595 ], "score": 1.0, "content": ". The goal of adversarial attack is to find an adversarial example", "type": "text" }, { "bbox": [ 455, 581, 504, 593 ], "score": 0.92, "content": "x ^ { \\prime } \\in B _ { \\epsilon } ^ { p } ( x )", "type": "inline_equation" } ], "index": 37 }, { "bbox": [ 106, 591, 505, 605 ], "spans": [ { "bbox": [ 106, 591, 326, 605 ], "score": 1.0, "content": "that can fool the DNN to produce an incorrect output (", "type": "text" }, { "bbox": [ 326, 592, 376, 604 ], "score": 0.89, "content": "f _ { w } ( x ^ { \\prime } ) \\ne y", "type": "inline_equation" }, { "bbox": [ 376, 591, 505, 605 ], "score": 1.0, "content": "). Here we selectively introduce", "type": "text" } ], "index": 38 }, { "bbox": [ 105, 603, 314, 615 ], "spans": [ { "bbox": [ 105, 603, 314, 615 ], "score": 1.0, "content": "several commonly used adversarial attack methods.", "type": "text" } ], "index": 39 } ], "index": 37, "bbox_fs": [ 105, 558, 506, 615 ] }, { "type": "text", "bbox": [ 106, 619, 502, 642 ], "lines": [ { "bbox": [ 106, 619, 504, 632 ], "spans": [ { "bbox": [ 106, 619, 504, 632 ], "score": 1.0, "content": "Fast Gradient Sign Method (FGSM). FGSM (Goodfellow et al., 2014) perturbs natural example", "type": "text" } ], "index": 40 }, { "bbox": [ 107, 631, 342, 644 ], "spans": [ { "bbox": [ 107, 633, 113, 641 ], "score": 0.74, "content": "x", "type": "inline_equation" }, { "bbox": [ 114, 631, 221, 644 ], "score": 1.0, "content": "for one step with step size", "type": "text" }, { "bbox": [ 221, 633, 226, 641 ], "score": 0.76, "content": "\\epsilon", "type": "inline_equation" }, { "bbox": [ 227, 631, 342, 644 ], "score": 1.0, "content": "along the gradient direction:", "type": "text" } ], "index": 41 } ], "index": 40.5, "bbox_fs": [ 106, 619, 504, 644 ] }, { "type": "interline_equation", "bbox": [ 234, 648, 376, 663 ], "lines": [ { "bbox": [ 234, 648, 376, 663 ], "spans": [ { "bbox": [ 234, 648, 376, 663 ], "score": 0.92, "content": "\\begin{array} { r } { x ^ { \\prime } = x + \\epsilon \\cdot \\mathrm { s i g n } \\bigl ( \\nabla _ { x } \\ell ( f _ { w } ( x ) , y ) \\bigr ) . } \\end{array}", "type": "interline_equation", "image_path": "952e1c47e1823c3227cdfaac7c6095e657112ff88a6291e8c8541528e5f252c1.jpg" } ] } ], "index": 42, "virtual_lines": [ { "bbox": [ 234, 648, 376, 663 ], "spans": [], "index": 42 } ] }, { "type": "text", "bbox": [ 105, 668, 506, 691 ], "lines": [ { "bbox": [ 106, 667, 505, 681 ], "spans": [ { "bbox": [ 106, 667, 505, 681 ], "score": 1.0, "content": "Projected Gradient Descent (PGD). PGD (Madry et al., 2017) is a stronger iterative variant of", "type": "text" } ], "index": 43 }, { "bbox": [ 106, 680, 467, 693 ], "spans": [ { "bbox": [ 106, 680, 267, 693 ], "score": 1.0, "content": "FGSM, which perturbs normal example", "type": "text" }, { "bbox": [ 268, 683, 274, 690 ], "score": 0.79, "content": "x", "type": "inline_equation" }, { "bbox": [ 275, 680, 348, 693 ], "score": 1.0, "content": "for multiple steps", "type": "text" }, { "bbox": [ 348, 680, 358, 690 ], "score": 0.84, "content": "K", "type": "inline_equation" }, { "bbox": [ 358, 680, 455, 693 ], "score": 1.0, "content": "with a smaller step size", "type": "text" }, { "bbox": [ 455, 682, 462, 690 ], "score": 0.74, "content": "\\alpha", "type": "inline_equation" }, { "bbox": [ 463, 680, 467, 693 ], "score": 1.0, "content": ":", "type": "text" } ], "index": 44 } ], "index": 43.5, "bbox_fs": [ 106, 667, 505, 693 ] }, { "type": "interline_equation", "bbox": [ 271, 696, 339, 711 ], "lines": [ { "bbox": [ 271, 696, 339, 711 ], "spans": [ { "bbox": [ 271, 696, 339, 711 ], "score": 0.74, "content": "x ^ { 0 } \\sim \\mathcal { U } ( B _ { \\epsilon } ^ { p } ( x ) ) ,", "type": "interline_equation", "image_path": "79264faa6ff45f1aef7f22fa537f2dd6fffda973b3d97ded9f3ec049a5982a2f.jpg" } ] } ], "index": 45, "virtual_lines": [ { "bbox": [ 271, 696, 339, 711 ], "spans": [], "index": 45 } ] }, { "type": "interline_equation", "bbox": [ 192, 718, 417, 734 ], "lines": [ { "bbox": [ 192, 718, 417, 734 ], "spans": [ { "bbox": [ 192, 718, 417, 734 ], "score": 0.77, "content": "\\boldsymbol { x } ^ { k } = \\Pi _ { \\mathcal { B } _ { \\epsilon } ^ { p } ( x ) } ( \\boldsymbol { x } ^ { k - 1 } + \\alpha \\cdot \\mathrm { s i g n } ( \\nabla _ { \\boldsymbol { x } ^ { k - 1 } } \\ell ( f _ { w } ( \\boldsymbol { x } ^ { k - 1 } ) , \\boldsymbol { y } ) ) ) ,", "type": "interline_equation", "image_path": "2a73b5ef623b75557caaff3282b72e798941ef060aaa0e6629ef5f7416d1598c.jpg" } ] } ], "index": 46, "virtual_lines": [ { "bbox": [ 192, 718, 417, 734 ], "spans": [], "index": 46 } ] } ] }, { "preproc_blocks": [ { "type": "text", "bbox": [ 107, 82, 504, 117 ], "lines": [ { "bbox": [ 106, 82, 504, 95 ], "spans": [ { "bbox": [ 106, 82, 133, 95 ], "score": 1.0, "content": "where", "type": "text" }, { "bbox": [ 133, 83, 142, 93 ], "score": 0.65, "content": "\\mathcal { U }", "type": "inline_equation" }, { "bbox": [ 142, 82, 276, 95 ], "score": 1.0, "content": "denotes the uniform distribution,", "type": "text" }, { "bbox": [ 276, 82, 288, 93 ], "score": 0.86, "content": "x ^ { 0 }", "type": "inline_equation" }, { "bbox": [ 288, 82, 504, 95 ], "score": 1.0, "content": "denotes the normal example disturbed by a small uni-", "type": "text" } ], "index": 0 }, { "bbox": [ 105, 92, 506, 108 ], "spans": [ { "bbox": [ 105, 92, 187, 108 ], "score": 1.0, "content": "form random noise,", "type": "text" }, { "bbox": [ 187, 93, 199, 104 ], "score": 0.87, "content": "x ^ { k }", "type": "inline_equation" }, { "bbox": [ 199, 92, 357, 108 ], "score": 1.0, "content": "denotes the adversarial example at step", "type": "text" }, { "bbox": [ 357, 94, 364, 104 ], "score": 0.71, "content": "k", "type": "inline_equation" }, { "bbox": [ 364, 92, 384, 108 ], "score": 1.0, "content": ", and", "type": "text" }, { "bbox": [ 384, 94, 413, 106 ], "score": 0.92, "content": "\\Pi _ { B _ { \\epsilon } ^ { p } ( x ) }", "type": "inline_equation" }, { "bbox": [ 414, 92, 506, 108 ], "score": 1.0, "content": "denotes the projection", "type": "text" } ], "index": 1 }, { "bbox": [ 105, 104, 437, 120 ], "spans": [ { "bbox": [ 105, 104, 358, 120 ], "score": 1.0, "content": "function that projects the adversarial example back into the set", "type": "text" }, { "bbox": [ 358, 106, 384, 118 ], "score": 0.92, "content": "B _ { \\epsilon } ^ { p } ( x )", "type": "inline_equation" }, { "bbox": [ 384, 104, 437, 120 ], "score": 1.0, "content": "if necessary.", "type": "text" } ], "index": 2 } ], "index": 1 }, { "type": "text", "bbox": [ 107, 122, 505, 178 ], "lines": [ { "bbox": [ 106, 123, 505, 135 ], "spans": [ { "bbox": [ 106, 123, 505, 135 ], "score": 1.0, "content": "AutoAttack (AA). AA (Croce & Hein, 2020b) is an ensemble of complementary attacks, which", "type": "text" } ], "index": 3 }, { "bbox": [ 105, 133, 505, 146 ], "spans": [ { "bbox": [ 105, 133, 505, 146 ], "score": 1.0, "content": "consists of three white-box attacks (APGD-CE (Croce & Hein, 2020b), APGD-DLR (Croce & Hein,", "type": "text" } ], "index": 4 }, { "bbox": [ 105, 145, 505, 157 ], "spans": [ { "bbox": [ 105, 145, 505, 157 ], "score": 1.0, "content": "2020b), and FAB (Croce & Hein, 2020a)) and a black-box attack (Square Attack (Andriushchenko", "type": "text" } ], "index": 5 }, { "bbox": [ 105, 155, 506, 168 ], "spans": [ { "bbox": [ 105, 155, 506, 168 ], "score": 1.0, "content": "et al., 2020)). AA regards models to be robust only if the models correctly classify all types of", "type": "text" } ], "index": 6 }, { "bbox": [ 105, 166, 505, 179 ], "spans": [ { "bbox": [ 105, 166, 505, 179 ], "score": 1.0, "content": "adversarial examples, which is among the most reliable evaluation of adversarial robustness to date.", "type": "text" } ], "index": 7 } ], "index": 5 }, { "type": "text", "bbox": [ 107, 183, 505, 227 ], "lines": [ { "bbox": [ 105, 183, 505, 196 ], "spans": [ { "bbox": [ 105, 183, 505, 196 ], "score": 1.0, "content": "There are also other types of attacking methods, e.g., the CW attack (Carlini & Wagner, 2017), de-", "type": "text" } ], "index": 8 }, { "bbox": [ 106, 195, 505, 207 ], "spans": [ { "bbox": [ 106, 195, 505, 207 ], "score": 1.0, "content": "formation attack (Engstrom et al., 2017; Xiao et al., 2018; Engstrom et al., 2019), Hamming distance", "type": "text" } ], "index": 9 }, { "bbox": [ 105, 205, 505, 217 ], "spans": [ { "bbox": [ 105, 205, 505, 217 ], "score": 1.0, "content": "based attack (Shamir et al., 2019), Frank-Wolfe based attack (Chen et al., 2020a) and adaptive attack", "type": "text" } ], "index": 10 }, { "bbox": [ 106, 217, 194, 228 ], "spans": [ { "bbox": [ 106, 217, 194, 228 ], "score": 1.0, "content": "(Tramer et al., 2020).", "type": "text" } ], "index": 11 } ], "index": 9.5 }, { "type": "title", "bbox": [ 108, 241, 237, 253 ], "lines": [ { "bbox": [ 106, 241, 238, 254 ], "spans": [ { "bbox": [ 106, 241, 238, 254 ], "score": 1.0, "content": "2.2 ADVERSARIAL DEFENSE", "type": "text" } ], "index": 12 } ], "index": 12 }, { "type": "text", "bbox": [ 106, 262, 505, 395 ], "lines": [ { "bbox": [ 105, 261, 505, 276 ], "spans": [ { "bbox": [ 105, 261, 505, 276 ], "score": 1.0, "content": "Since the discovery of adversarial examples, a large number of works have emerged for defending", "type": "text" } ], "index": 13 }, { "bbox": [ 104, 273, 506, 286 ], "spans": [ { "bbox": [ 104, 273, 506, 286 ], "score": 1.0, "content": "against adversarial attacks, such as input denoising (Guo et al., 2018; Liao et al., 2018; Wu et al.,", "type": "text" } ], "index": 14 }, { "bbox": [ 105, 283, 505, 297 ], "spans": [ { "bbox": [ 105, 283, 505, 297 ], "score": 1.0, "content": "2021), defensive distillation (Papernot et al., 2016; Carlini & Wagner, 2017), adversarial detection", "type": "text" } ], "index": 15 }, { "bbox": [ 106, 296, 504, 307 ], "spans": [ { "bbox": [ 106, 296, 504, 307 ], "score": 1.0, "content": "(Metzen et al., 2017; Tao et al., 2018), gradient regularization (Tramer et al., 2018; Ross & Doshi- `", "type": "text" } ], "index": 16 }, { "bbox": [ 106, 306, 505, 319 ], "spans": [ { "bbox": [ 106, 306, 505, 319 ], "score": 1.0, "content": "Velez, 2018) and adversarial training (Goodfellow et al., 2014; Madry et al., 2017). Among them,", "type": "text" } ], "index": 17 }, { "bbox": [ 106, 317, 505, 330 ], "spans": [ { "bbox": [ 106, 317, 505, 330 ], "score": 1.0, "content": "adversarial training has been demonstrated to be the most effective method (Athalye et al., 2018).", "type": "text" } ], "index": 18 }, { "bbox": [ 105, 328, 505, 341 ], "spans": [ { "bbox": [ 105, 328, 505, 341 ], "score": 1.0, "content": "Based on adversarial training, a wide range of subsequent works are then proposed to further im-", "type": "text" } ], "index": 19 }, { "bbox": [ 104, 338, 506, 353 ], "spans": [ { "bbox": [ 104, 338, 506, 353 ], "score": 1.0, "content": "prove the model robustness (Xie et al., 2019; Mosbach et al., 2018; Kannan et al., 2018; Zhang", "type": "text" } ], "index": 20 }, { "bbox": [ 105, 350, 505, 363 ], "spans": [ { "bbox": [ 105, 350, 505, 363 ], "score": 1.0, "content": "et al., 2019; Cai et al., 2018; Wang et al., 2019a; Zhang et al., 2020a; Dong et al., 2018; Yang et al.,", "type": "text" } ], "index": 21 }, { "bbox": [ 105, 361, 505, 373 ], "spans": [ { "bbox": [ 105, 361, 505, 373 ], "score": 1.0, "content": "2019; Wang et al., 2019b; Song et al., 2020; Carmon et al., 2019; Zhai et al., 2019; Uesato et al.,", "type": "text" } ], "index": 22 }, { "bbox": [ 105, 371, 505, 385 ], "spans": [ { "bbox": [ 105, 371, 505, 385 ], "score": 1.0, "content": "2019; Hendrycks et al., 2019; Yan et al., 2021; Du et al., 2021). Here, we introduce two currently", "type": "text" } ], "index": 23 }, { "bbox": [ 106, 384, 299, 395 ], "spans": [ { "bbox": [ 106, 384, 299, 395 ], "score": 1.0, "content": "state-of-the-art adversarial training frameworks.", "type": "text" } ], "index": 24 } ], "index": 18.5 }, { "type": "text", "bbox": [ 104, 399, 504, 422 ], "lines": [ { "bbox": [ 106, 399, 505, 412 ], "spans": [ { "bbox": [ 106, 399, 505, 412 ], "score": 1.0, "content": "TRADES. TRADES (Zhang et al., 2019) optimizes a regularized surrogate loss that is a trade-off", "type": "text" } ], "index": 25 }, { "bbox": [ 105, 410, 334, 423 ], "spans": [ { "bbox": [ 105, 410, 334, 423 ], "score": 1.0, "content": "between the natural accuracy and adversarial robustness:", "type": "text" } ], "index": 26 } ], "index": 25.5 }, { "type": "interline_equation", "bbox": [ 136, 428, 475, 461 ], "lines": [ { "bbox": [ 136, 428, 475, 461 ], "spans": [ { "bbox": [ 136, 428, 475, 461 ], "score": 0.94, "content": "\\ell ^ { { \\mathrm { T R A D E S } } } ( \\boldsymbol { w } ; \\boldsymbol { x } , \\boldsymbol { y } ) = \\frac { 1 } { n } \\sum _ { i = 1 } ^ { n } \\left\\{ \\operatorname { C E } ( f _ { w } ( x _ { i } ) , y _ { i } ) + \\beta \\cdot \\operatorname* { m a x } _ { \\boldsymbol { x } ^ { \\prime } \\in B _ { \\epsilon } ^ { p } ( \\boldsymbol { x } ) } \\operatorname { K L } ( f _ { w } ( x _ { i } ) | | f _ { w } ( x _ { i } ^ { \\prime } ) ) \\right\\} ,", "type": "interline_equation", "image_path": "5038702dda60b9f60e6298c190f52bf80e5d5a1bf4f001e081811522069bab56.jpg" } ] } ], "index": 28, "virtual_lines": [ { "bbox": [ 136, 428, 475, 439.0 ], "spans": [], "index": 27 }, { "bbox": [ 136, 439.0, 475, 450.0 ], "spans": [], "index": 28 }, { "bbox": [ 136, 450.0, 475, 461.0 ], "spans": [], "index": 29 } ] }, { "type": "text", "bbox": [ 107, 466, 504, 499 ], "lines": [ { "bbox": [ 105, 465, 506, 479 ], "spans": [ { "bbox": [ 105, 465, 506, 479 ], "score": 1.0, "content": "where CE is the cross-entropy loss that encourages the network to maximize the natural accuracy,", "type": "text" } ], "index": 30 }, { "bbox": [ 105, 477, 506, 490 ], "spans": [ { "bbox": [ 105, 477, 472, 490 ], "score": 1.0, "content": "KL is the Kullback-Leibler divergence that encourages to improve the robust accuracy, and", "type": "text" }, { "bbox": [ 473, 477, 480, 488 ], "score": 0.85, "content": "\\beta", "type": "inline_equation" }, { "bbox": [ 480, 477, 506, 490 ], "score": 1.0, "content": "is the", "type": "text" } ], "index": 31 }, { "bbox": [ 105, 488, 478, 501 ], "spans": [ { "bbox": [ 105, 488, 478, 501 ], "score": 1.0, "content": "hyperparameter to control the trade-off between natural accuracy and adversarial robustness.", "type": "text" } ], "index": 32 } ], "index": 31 }, { "type": "text", "bbox": [ 107, 504, 504, 560 ], "lines": [ { "bbox": [ 106, 505, 506, 517 ], "spans": [ { "bbox": [ 106, 505, 506, 517 ], "score": 1.0, "content": "Robust Self-Training (RST). RST (Carmon et al., 2019) utilize additional 500K unlabeled data", "type": "text" } ], "index": 33 }, { "bbox": [ 106, 516, 505, 528 ], "spans": [ { "bbox": [ 106, 516, 505, 528 ], "score": 1.0, "content": "extracted from the 80 Million Tiny Images dataset (Torralba et al., 2008). RST first leverages the", "type": "text" } ], "index": 34 }, { "bbox": [ 105, 526, 505, 540 ], "spans": [ { "bbox": [ 105, 526, 505, 540 ], "score": 1.0, "content": "surrogate natural model to generate pseudo-labels for these unlabeled data, and then adversarially", "type": "text" } ], "index": 35 }, { "bbox": [ 105, 537, 506, 550 ], "spans": [ { "bbox": [ 105, 537, 395, 550 ], "score": 1.0, "content": "trains the network with both additional pseudo-labeled unlabeled data", "type": "text" }, { "bbox": [ 396, 538, 419, 550 ], "score": 0.93, "content": "( \\tilde { x } , \\tilde { y } )", "type": "inline_equation" }, { "bbox": [ 420, 537, 506, 550 ], "score": 1.0, "content": "and original labeled", "type": "text" } ], "index": 36 }, { "bbox": [ 105, 547, 245, 563 ], "spans": [ { "bbox": [ 105, 547, 126, 563 ], "score": 1.0, "content": "data", "type": "text" }, { "bbox": [ 126, 549, 150, 561 ], "score": 0.92, "content": "( x , y )", "type": "inline_equation" }, { "bbox": [ 150, 547, 245, 563 ], "score": 1.0, "content": "in a supervised setting:", "type": "text" } ], "index": 37 } ], "index": 35 }, { "type": "interline_equation", "bbox": [ 171, 565, 439, 581 ], "lines": [ { "bbox": [ 171, 565, 439, 581 ], "spans": [ { "bbox": [ 171, 565, 439, 581 ], "score": 0.88, "content": "\\ell ^ { \\mathrm { R S T } } ( \\boldsymbol { w } ; x , y , \\tilde { x } , \\tilde { y } ) = \\ell ^ { \\mathrm { T R A D E S } } ( \\boldsymbol { w } ; x , y ) + \\lambda \\cdot \\ell ^ { \\mathrm { T R A D E S } } ( \\boldsymbol { w } ; \\tilde { x } , \\tilde { y } ) ,", "type": "interline_equation", "image_path": "51daceb8a8209ae90ce8723bce03d88fd94b9ff19aa9e7b78ad84ff7d7640980.jpg" } ] } ], "index": 38, "virtual_lines": [ { "bbox": [ 171, 565, 439, 581 ], "spans": [], "index": 38 } ] }, { "type": "text", "bbox": [ 107, 587, 269, 598 ], "lines": [ { "bbox": [ 106, 586, 270, 599 ], "spans": [ { "bbox": [ 106, 586, 133, 599 ], "score": 1.0, "content": "where", "type": "text" }, { "bbox": [ 133, 587, 140, 597 ], "score": 0.82, "content": "\\lambda", "type": "inline_equation" }, { "bbox": [ 141, 586, 270, 599 ], "score": 1.0, "content": "is the weight on unlabeled data.", "type": "text" } ], "index": 39 } ], "index": 39 }, { "type": "title", "bbox": [ 108, 612, 228, 623 ], "lines": [ { "bbox": [ 105, 610, 230, 625 ], "spans": [ { "bbox": [ 105, 610, 230, 625 ], "score": 1.0, "content": "2.3 ROBUST OVERFITTING", "type": "text" } ], "index": 40 } ], "index": 40 }, { "type": "text", "bbox": [ 106, 632, 505, 732 ], "lines": [ { "bbox": [ 106, 632, 505, 645 ], "spans": [ { "bbox": [ 106, 632, 505, 645 ], "score": 1.0, "content": "Nowadays, there are effective countermeasures to alleviate the overfitting in standard training. But", "type": "text" } ], "index": 41 }, { "bbox": [ 106, 644, 505, 655 ], "spans": [ { "bbox": [ 106, 644, 505, 655 ], "score": 1.0, "content": "in adversarial training, robust overfitting widely exists and those common countermeasures used in", "type": "text" } ], "index": 42 }, { "bbox": [ 104, 653, 506, 669 ], "spans": [ { "bbox": [ 104, 653, 506, 669 ], "score": 1.0, "content": "standard training help little (Rice et al., 2020). Schmidt et al. (2018) explains robust overfitting", "type": "text" } ], "index": 43 }, { "bbox": [ 105, 666, 505, 678 ], "spans": [ { "bbox": [ 105, 666, 505, 678 ], "score": 1.0, "content": "partially from the perspective of sample complexity, and is supported by empirical results in deriva-", "type": "text" } ], "index": 44 }, { "bbox": [ 105, 677, 506, 690 ], "spans": [ { "bbox": [ 105, 677, 506, 690 ], "score": 1.0, "content": "tive works, such as adversarial training with semi-supervised learning (Carmon et al., 2019; Uesato", "type": "text" } ], "index": 45 }, { "bbox": [ 104, 686, 506, 702 ], "spans": [ { "bbox": [ 104, 686, 506, 702 ], "score": 1.0, "content": "et al., 2019; Zhai et al., 2019), robust local feature (Song et al., 2020) and data interpolation (Zhang", "type": "text" } ], "index": 46 }, { "bbox": [ 105, 698, 506, 712 ], "spans": [ { "bbox": [ 105, 698, 506, 712 ], "score": 1.0, "content": "& Xu, 2019; Lee et al., 2020; Chen et al., 2021). Separate works have also attempt to mitigate robust", "type": "text" } ], "index": 47 }, { "bbox": [ 105, 709, 505, 722 ], "spans": [ { "bbox": [ 105, 709, 505, 722 ], "score": 1.0, "content": "overfitting by the unequal treatment of data (Zhang et al., 2020b) and weight smoothing (Chen et al.,", "type": "text" } ], "index": 48 }, { "bbox": [ 106, 720, 505, 733 ], "spans": [ { "bbox": [ 106, 720, 505, 733 ], "score": 1.0, "content": "2020b). Recent study (Wu et al., 2020) reveals the connection between the flatness of weight loss", "type": "text" } ], "index": 49 } ], "index": 45 } ], "page_idx": 2, "page_size": [ 612, 792 ], "discarded_blocks": [ { "type": "discarded", "bbox": [ 107, 27, 308, 37 ], "lines": [ { "bbox": [ 106, 25, 308, 38 ], "spans": [ { "bbox": [ 106, 25, 308, 38 ], "score": 1.0, "content": "Under review 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": "3", "type": "text" } ] } ] } ], "para_blocks": [ { "type": "text", "bbox": [ 107, 82, 504, 117 ], "lines": [ { "bbox": [ 106, 82, 504, 95 ], "spans": [ { "bbox": [ 106, 82, 133, 95 ], "score": 1.0, "content": "where", "type": "text" }, { "bbox": [ 133, 83, 142, 93 ], "score": 0.65, "content": "\\mathcal { U }", "type": "inline_equation" }, { "bbox": [ 142, 82, 276, 95 ], "score": 1.0, "content": "denotes the uniform distribution,", "type": "text" }, { "bbox": [ 276, 82, 288, 93 ], "score": 0.86, "content": "x ^ { 0 }", "type": "inline_equation" }, { "bbox": [ 288, 82, 504, 95 ], "score": 1.0, "content": "denotes the normal example disturbed by a small uni-", "type": "text" } ], "index": 0 }, { "bbox": [ 105, 92, 506, 108 ], "spans": [ { "bbox": [ 105, 92, 187, 108 ], "score": 1.0, "content": "form random noise,", "type": "text" }, { "bbox": [ 187, 93, 199, 104 ], "score": 0.87, "content": "x ^ { k }", "type": "inline_equation" }, { "bbox": [ 199, 92, 357, 108 ], "score": 1.0, "content": "denotes the adversarial example at step", "type": "text" }, { "bbox": [ 357, 94, 364, 104 ], "score": 0.71, "content": "k", "type": "inline_equation" }, { "bbox": [ 364, 92, 384, 108 ], "score": 1.0, "content": ", and", "type": "text" }, { "bbox": [ 384, 94, 413, 106 ], "score": 0.92, "content": "\\Pi _ { B _ { \\epsilon } ^ { p } ( x ) }", "type": "inline_equation" }, { "bbox": [ 414, 92, 506, 108 ], "score": 1.0, "content": "denotes the projection", "type": "text" } ], "index": 1 }, { "bbox": [ 105, 104, 437, 120 ], "spans": [ { "bbox": [ 105, 104, 358, 120 ], "score": 1.0, "content": "function that projects the adversarial example back into the set", "type": "text" }, { "bbox": [ 358, 106, 384, 118 ], "score": 0.92, "content": "B _ { \\epsilon } ^ { p } ( x )", "type": "inline_equation" }, { "bbox": [ 384, 104, 437, 120 ], "score": 1.0, "content": "if necessary.", "type": "text" } ], "index": 2 } ], "index": 1, "bbox_fs": [ 105, 82, 506, 120 ] }, { "type": "text", "bbox": [ 107, 122, 505, 178 ], "lines": [ { "bbox": [ 106, 123, 505, 135 ], "spans": [ { "bbox": [ 106, 123, 505, 135 ], "score": 1.0, "content": "AutoAttack (AA). AA (Croce & Hein, 2020b) is an ensemble of complementary attacks, which", "type": "text" } ], "index": 3 }, { "bbox": [ 105, 133, 505, 146 ], "spans": [ { "bbox": [ 105, 133, 505, 146 ], "score": 1.0, "content": "consists of three white-box attacks (APGD-CE (Croce & Hein, 2020b), APGD-DLR (Croce & Hein,", "type": "text" } ], "index": 4 }, { "bbox": [ 105, 145, 505, 157 ], "spans": [ { "bbox": [ 105, 145, 505, 157 ], "score": 1.0, "content": "2020b), and FAB (Croce & Hein, 2020a)) and a black-box attack (Square Attack (Andriushchenko", "type": "text" } ], "index": 5 }, { "bbox": [ 105, 155, 506, 168 ], "spans": [ { "bbox": [ 105, 155, 506, 168 ], "score": 1.0, "content": "et al., 2020)). AA regards models to be robust only if the models correctly classify all types of", "type": "text" } ], "index": 6 }, { "bbox": [ 105, 166, 505, 179 ], "spans": [ { "bbox": [ 105, 166, 505, 179 ], "score": 1.0, "content": "adversarial examples, which is among the most reliable evaluation of adversarial robustness to date.", "type": "text" } ], "index": 7 } ], "index": 5, "bbox_fs": [ 105, 123, 506, 179 ] }, { "type": "text", "bbox": [ 107, 183, 505, 227 ], "lines": [ { "bbox": [ 105, 183, 505, 196 ], "spans": [ { "bbox": [ 105, 183, 505, 196 ], "score": 1.0, "content": "There are also other types of attacking methods, e.g., the CW attack (Carlini & Wagner, 2017), de-", "type": "text" } ], "index": 8 }, { "bbox": [ 106, 195, 505, 207 ], "spans": [ { "bbox": [ 106, 195, 505, 207 ], "score": 1.0, "content": "formation attack (Engstrom et al., 2017; Xiao et al., 2018; Engstrom et al., 2019), Hamming distance", "type": "text" } ], "index": 9 }, { "bbox": [ 105, 205, 505, 217 ], "spans": [ { "bbox": [ 105, 205, 505, 217 ], "score": 1.0, "content": "based attack (Shamir et al., 2019), Frank-Wolfe based attack (Chen et al., 2020a) and adaptive attack", "type": "text" } ], "index": 10 }, { "bbox": [ 106, 217, 194, 228 ], "spans": [ { "bbox": [ 106, 217, 194, 228 ], "score": 1.0, "content": "(Tramer et al., 2020).", "type": "text" } ], "index": 11 } ], "index": 9.5, "bbox_fs": [ 105, 183, 505, 228 ] }, { "type": "title", "bbox": [ 108, 241, 237, 253 ], "lines": [ { "bbox": [ 106, 241, 238, 254 ], "spans": [ { "bbox": [ 106, 241, 238, 254 ], "score": 1.0, "content": "2.2 ADVERSARIAL DEFENSE", "type": "text" } ], "index": 12 } ], "index": 12 }, { "type": "text", "bbox": [ 106, 262, 505, 395 ], "lines": [ { "bbox": [ 105, 261, 505, 276 ], "spans": [ { "bbox": [ 105, 261, 505, 276 ], "score": 1.0, "content": "Since the discovery of adversarial examples, a large number of works have emerged for defending", "type": "text" } ], "index": 13 }, { "bbox": [ 104, 273, 506, 286 ], "spans": [ { "bbox": [ 104, 273, 506, 286 ], "score": 1.0, "content": "against adversarial attacks, such as input denoising (Guo et al., 2018; Liao et al., 2018; Wu et al.,", "type": "text" } ], "index": 14 }, { "bbox": [ 105, 283, 505, 297 ], "spans": [ { "bbox": [ 105, 283, 505, 297 ], "score": 1.0, "content": "2021), defensive distillation (Papernot et al., 2016; Carlini & Wagner, 2017), adversarial detection", "type": "text" } ], "index": 15 }, { "bbox": [ 106, 296, 504, 307 ], "spans": [ { "bbox": [ 106, 296, 504, 307 ], "score": 1.0, "content": "(Metzen et al., 2017; Tao et al., 2018), gradient regularization (Tramer et al., 2018; Ross & Doshi- `", "type": "text" } ], "index": 16 }, { "bbox": [ 106, 306, 505, 319 ], "spans": [ { "bbox": [ 106, 306, 505, 319 ], "score": 1.0, "content": "Velez, 2018) and adversarial training (Goodfellow et al., 2014; Madry et al., 2017). Among them,", "type": "text" } ], "index": 17 }, { "bbox": [ 106, 317, 505, 330 ], "spans": [ { "bbox": [ 106, 317, 505, 330 ], "score": 1.0, "content": "adversarial training has been demonstrated to be the most effective method (Athalye et al., 2018).", "type": "text" } ], "index": 18 }, { "bbox": [ 105, 328, 505, 341 ], "spans": [ { "bbox": [ 105, 328, 505, 341 ], "score": 1.0, "content": "Based on adversarial training, a wide range of subsequent works are then proposed to further im-", "type": "text" } ], "index": 19 }, { "bbox": [ 104, 338, 506, 353 ], "spans": [ { "bbox": [ 104, 338, 506, 353 ], "score": 1.0, "content": "prove the model robustness (Xie et al., 2019; Mosbach et al., 2018; Kannan et al., 2018; Zhang", "type": "text" } ], "index": 20 }, { "bbox": [ 105, 350, 505, 363 ], "spans": [ { "bbox": [ 105, 350, 505, 363 ], "score": 1.0, "content": "et al., 2019; Cai et al., 2018; Wang et al., 2019a; Zhang et al., 2020a; Dong et al., 2018; Yang et al.,", "type": "text" } ], "index": 21 }, { "bbox": [ 105, 361, 505, 373 ], "spans": [ { "bbox": [ 105, 361, 505, 373 ], "score": 1.0, "content": "2019; Wang et al., 2019b; Song et al., 2020; Carmon et al., 2019; Zhai et al., 2019; Uesato et al.,", "type": "text" } ], "index": 22 }, { "bbox": [ 105, 371, 505, 385 ], "spans": [ { "bbox": [ 105, 371, 505, 385 ], "score": 1.0, "content": "2019; Hendrycks et al., 2019; Yan et al., 2021; Du et al., 2021). Here, we introduce two currently", "type": "text" } ], "index": 23 }, { "bbox": [ 106, 384, 299, 395 ], "spans": [ { "bbox": [ 106, 384, 299, 395 ], "score": 1.0, "content": "state-of-the-art adversarial training frameworks.", "type": "text" } ], "index": 24 } ], "index": 18.5, "bbox_fs": [ 104, 261, 506, 395 ] }, { "type": "text", "bbox": [ 104, 399, 504, 422 ], "lines": [ { "bbox": [ 106, 399, 505, 412 ], "spans": [ { "bbox": [ 106, 399, 505, 412 ], "score": 1.0, "content": "TRADES. TRADES (Zhang et al., 2019) optimizes a regularized surrogate loss that is a trade-off", "type": "text" } ], "index": 25 }, { "bbox": [ 105, 410, 334, 423 ], "spans": [ { "bbox": [ 105, 410, 334, 423 ], "score": 1.0, "content": "between the natural accuracy and adversarial robustness:", "type": "text" } ], "index": 26 } ], "index": 25.5, "bbox_fs": [ 105, 399, 505, 423 ] }, { "type": "interline_equation", "bbox": [ 136, 428, 475, 461 ], "lines": [ { "bbox": [ 136, 428, 475, 461 ], "spans": [ { "bbox": [ 136, 428, 475, 461 ], "score": 0.94, "content": "\\ell ^ { { \\mathrm { T R A D E S } } } ( \\boldsymbol { w } ; \\boldsymbol { x } , \\boldsymbol { y } ) = \\frac { 1 } { n } \\sum _ { i = 1 } ^ { n } \\left\\{ \\operatorname { C E } ( f _ { w } ( x _ { i } ) , y _ { i } ) + \\beta \\cdot \\operatorname* { m a x } _ { \\boldsymbol { x } ^ { \\prime } \\in B _ { \\epsilon } ^ { p } ( \\boldsymbol { x } ) } \\operatorname { K L } ( f _ { w } ( x _ { i } ) | | f _ { w } ( x _ { i } ^ { \\prime } ) ) \\right\\} ,", "type": "interline_equation", "image_path": "5038702dda60b9f60e6298c190f52bf80e5d5a1bf4f001e081811522069bab56.jpg" } ] } ], "index": 28, "virtual_lines": [ { "bbox": [ 136, 428, 475, 439.0 ], "spans": [], "index": 27 }, { "bbox": [ 136, 439.0, 475, 450.0 ], "spans": [], "index": 28 }, { "bbox": [ 136, 450.0, 475, 461.0 ], "spans": [], "index": 29 } ] }, { "type": "text", "bbox": [ 107, 466, 504, 499 ], "lines": [ { "bbox": [ 105, 465, 506, 479 ], "spans": [ { "bbox": [ 105, 465, 506, 479 ], "score": 1.0, "content": "where CE is the cross-entropy loss that encourages the network to maximize the natural accuracy,", "type": "text" } ], "index": 30 }, { "bbox": [ 105, 477, 506, 490 ], "spans": [ { "bbox": [ 105, 477, 472, 490 ], "score": 1.0, "content": "KL is the Kullback-Leibler divergence that encourages to improve the robust accuracy, and", "type": "text" }, { "bbox": [ 473, 477, 480, 488 ], "score": 0.85, "content": "\\beta", "type": "inline_equation" }, { "bbox": [ 480, 477, 506, 490 ], "score": 1.0, "content": "is the", "type": "text" } ], "index": 31 }, { "bbox": [ 105, 488, 478, 501 ], "spans": [ { "bbox": [ 105, 488, 478, 501 ], "score": 1.0, "content": "hyperparameter to control the trade-off between natural accuracy and adversarial robustness.", "type": "text" } ], "index": 32 } ], "index": 31, "bbox_fs": [ 105, 465, 506, 501 ] }, { "type": "text", "bbox": [ 107, 504, 504, 560 ], "lines": [ { "bbox": [ 106, 505, 506, 517 ], "spans": [ { "bbox": [ 106, 505, 506, 517 ], "score": 1.0, "content": "Robust Self-Training (RST). RST (Carmon et al., 2019) utilize additional 500K unlabeled data", "type": "text" } ], "index": 33 }, { "bbox": [ 106, 516, 505, 528 ], "spans": [ { "bbox": [ 106, 516, 505, 528 ], "score": 1.0, "content": "extracted from the 80 Million Tiny Images dataset (Torralba et al., 2008). RST first leverages the", "type": "text" } ], "index": 34 }, { "bbox": [ 105, 526, 505, 540 ], "spans": [ { "bbox": [ 105, 526, 505, 540 ], "score": 1.0, "content": "surrogate natural model to generate pseudo-labels for these unlabeled data, and then adversarially", "type": "text" } ], "index": 35 }, { "bbox": [ 105, 537, 506, 550 ], "spans": [ { "bbox": [ 105, 537, 395, 550 ], "score": 1.0, "content": "trains the network with both additional pseudo-labeled unlabeled data", "type": "text" }, { "bbox": [ 396, 538, 419, 550 ], "score": 0.93, "content": "( \\tilde { x } , \\tilde { y } )", "type": "inline_equation" }, { "bbox": [ 420, 537, 506, 550 ], "score": 1.0, "content": "and original labeled", "type": "text" } ], "index": 36 }, { "bbox": [ 105, 547, 245, 563 ], "spans": [ { "bbox": [ 105, 547, 126, 563 ], "score": 1.0, "content": "data", "type": "text" }, { "bbox": [ 126, 549, 150, 561 ], "score": 0.92, "content": "( x , y )", "type": "inline_equation" }, { "bbox": [ 150, 547, 245, 563 ], "score": 1.0, "content": "in a supervised setting:", "type": "text" } ], "index": 37 } ], "index": 35, "bbox_fs": [ 105, 505, 506, 563 ] }, { "type": "interline_equation", "bbox": [ 171, 565, 439, 581 ], "lines": [ { "bbox": [ 171, 565, 439, 581 ], "spans": [ { "bbox": [ 171, 565, 439, 581 ], "score": 0.88, "content": "\\ell ^ { \\mathrm { R S T } } ( \\boldsymbol { w } ; x , y , \\tilde { x } , \\tilde { y } ) = \\ell ^ { \\mathrm { T R A D E S } } ( \\boldsymbol { w } ; x , y ) + \\lambda \\cdot \\ell ^ { \\mathrm { T R A D E S } } ( \\boldsymbol { w } ; \\tilde { x } , \\tilde { y } ) ,", "type": "interline_equation", "image_path": "51daceb8a8209ae90ce8723bce03d88fd94b9ff19aa9e7b78ad84ff7d7640980.jpg" } ] } ], "index": 38, "virtual_lines": [ { "bbox": [ 171, 565, 439, 581 ], "spans": [], "index": 38 } ] }, { "type": "text", "bbox": [ 107, 587, 269, 598 ], "lines": [ { "bbox": [ 106, 586, 270, 599 ], "spans": [ { "bbox": [ 106, 586, 133, 599 ], "score": 1.0, "content": "where", "type": "text" }, { "bbox": [ 133, 587, 140, 597 ], "score": 0.82, "content": "\\lambda", "type": "inline_equation" }, { "bbox": [ 141, 586, 270, 599 ], "score": 1.0, "content": "is the weight on unlabeled data.", "type": "text" } ], "index": 39 } ], "index": 39, "bbox_fs": [ 106, 586, 270, 599 ] }, { "type": "title", "bbox": [ 108, 612, 228, 623 ], "lines": [ { "bbox": [ 105, 610, 230, 625 ], "spans": [ { "bbox": [ 105, 610, 230, 625 ], "score": 1.0, "content": "2.3 ROBUST OVERFITTING", "type": "text" } ], "index": 40 } ], "index": 40 }, { "type": "text", "bbox": [ 106, 632, 505, 732 ], "lines": [ { "bbox": [ 106, 632, 505, 645 ], "spans": [ { "bbox": [ 106, 632, 505, 645 ], "score": 1.0, "content": "Nowadays, there are effective countermeasures to alleviate the overfitting in standard training. But", "type": "text" } ], "index": 41 }, { "bbox": [ 106, 644, 505, 655 ], "spans": [ { "bbox": [ 106, 644, 505, 655 ], "score": 1.0, "content": "in adversarial training, robust overfitting widely exists and those common countermeasures used in", "type": "text" } ], "index": 42 }, { "bbox": [ 104, 653, 506, 669 ], "spans": [ { "bbox": [ 104, 653, 506, 669 ], "score": 1.0, "content": "standard training help little (Rice et al., 2020). Schmidt et al. (2018) explains robust overfitting", "type": "text" } ], "index": 43 }, { "bbox": [ 105, 666, 505, 678 ], "spans": [ { "bbox": [ 105, 666, 505, 678 ], "score": 1.0, "content": "partially from the perspective of sample complexity, and is supported by empirical results in deriva-", "type": "text" } ], "index": 44 }, { "bbox": [ 105, 677, 506, 690 ], "spans": [ { "bbox": [ 105, 677, 506, 690 ], "score": 1.0, "content": "tive works, such as adversarial training with semi-supervised learning (Carmon et al., 2019; Uesato", "type": "text" } ], "index": 45 }, { "bbox": [ 104, 686, 506, 702 ], "spans": [ { "bbox": [ 104, 686, 506, 702 ], "score": 1.0, "content": "et al., 2019; Zhai et al., 2019), robust local feature (Song et al., 2020) and data interpolation (Zhang", "type": "text" } ], "index": 46 }, { "bbox": [ 105, 698, 506, 712 ], "spans": [ { "bbox": [ 105, 698, 506, 712 ], "score": 1.0, "content": "& Xu, 2019; Lee et al., 2020; Chen et al., 2021). Separate works have also attempt to mitigate robust", "type": "text" } ], "index": 47 }, { "bbox": [ 105, 709, 505, 722 ], "spans": [ { "bbox": [ 105, 709, 505, 722 ], "score": 1.0, "content": "overfitting by the unequal treatment of data (Zhang et al., 2020b) and weight smoothing (Chen et al.,", "type": "text" } ], "index": 48 }, { "bbox": [ 106, 720, 505, 733 ], "spans": [ { "bbox": [ 106, 720, 505, 733 ], "score": 1.0, "content": "2020b). Recent study (Wu et al., 2020) reveals the connection between the flatness of weight loss", "type": "text" } ], "index": 49 }, { "bbox": [ 106, 350, 504, 362 ], "spans": [ { "bbox": [ 106, 350, 504, 362 ], "score": 1.0, "content": "landscape and robust generalization gap, and proposes to incorporate adversarial weight perturba-", "type": "text", "cross_page": true } ], "index": 5 }, { "bbox": [ 106, 360, 505, 373 ], "spans": [ { "bbox": [ 106, 360, 505, 373 ], "score": 1.0, "content": "tion mechanism in the adversarial training framework. Despite the efficacy of adversarial weight", "type": "text", "cross_page": true } ], "index": 6 }, { "bbox": [ 105, 372, 506, 384 ], "spans": [ { "bbox": [ 105, 372, 506, 384 ], "score": 1.0, "content": "perturbation in suppressing the robust overfitting in adversarial training, a deeper understanding of", "type": "text", "cross_page": true } ], "index": 7 }, { "bbox": [ 105, 381, 505, 396 ], "spans": [ { "bbox": [ 105, 381, 505, 396 ], "score": 1.0, "content": "the cause of robust overfitting and a clear direction for valid weight perturbation is largely missing.", "type": "text", "cross_page": true } ], "index": 8 }, { "bbox": [ 106, 393, 506, 407 ], "spans": [ { "bbox": [ 106, 393, 506, 407 ], "score": 1.0, "content": "The outer maximization in Eq.(1) lacks an effective criterion to regulate and constrain the extent of", "type": "text", "cross_page": true } ], "index": 9 }, { "bbox": [ 106, 405, 505, 417 ], "spans": [ { "bbox": [ 106, 405, 505, 417 ], "score": 1.0, "content": "weight perturbation, which in turn influences the optimization of the outer minimization problem. In", "type": "text", "cross_page": true } ], "index": 10 }, { "bbox": [ 105, 416, 505, 428 ], "spans": [ { "bbox": [ 105, 416, 505, 428 ], "score": 1.0, "content": "this paper, we propose such a criterion and provide new understanding of the robust overfitting in ad-", "type": "text", "cross_page": true } ], "index": 11 }, { "bbox": [ 106, 426, 505, 439 ], "spans": [ { "bbox": [ 106, 426, 505, 439 ], "score": 1.0, "content": "versarial training. Following this, we design a robust weight perturbation strategy that significantly", "type": "text", "cross_page": true } ], "index": 12 }, { "bbox": [ 105, 437, 297, 451 ], "spans": [ { "bbox": [ 105, 437, 297, 451 ], "score": 1.0, "content": "improves the robustness of adversarial training.", "type": "text", "cross_page": true } ], "index": 13 } ], "index": 45, "bbox_fs": [ 104, 632, 506, 733 ] } ] }, { "preproc_blocks": [ { "type": "image", "bbox": [ 109, 80, 500, 306 ], "blocks": [ { "type": "image_body", "bbox": [ 109, 80, 500, 306 ], "group_id": 0, "lines": [ { "bbox": [ 109, 80, 500, 306 ], "spans": [ { "bbox": [ 109, 80, 500, 306 ], "score": 0.972, "type": "image", "image_path": "cf8c9c1611ba4804d2a3319c5b7ff65a8e692709372051083b7ff11770673d20.jpg" } ] } ], "index": 1, "virtual_lines": [ { "bbox": [ 109, 80, 500, 155.33333333333331 ], "spans": [], "index": 0 }, { "bbox": [ 109, 155.33333333333331, 500, 230.66666666666663 ], "spans": [], "index": 1 }, { "bbox": [ 109, 230.66666666666663, 500, 305.99999999999994 ], "spans": [], "index": 2 } ] }, { "type": "image_caption", "bbox": [ 105, 318, 504, 342 ], "group_id": 0, "lines": [ { "bbox": [ 105, 318, 505, 333 ], "spans": [ { "bbox": [ 105, 318, 505, 333 ], "score": 1.0, "content": "Figure 1: (a): Test robustness of AWP with varying weight perturbation size; (b): The learning curve", "type": "text" } ], "index": 3 }, { "bbox": [ 105, 328, 379, 344 ], "spans": [ { "bbox": [ 105, 328, 379, 344 ], "score": 1.0, "content": "of vanilla AT; (c): Test robustness of AWP with varying LSC range.", "type": "text" } ], "index": 4 } ], "index": 3.5 } ], "index": 2.25 }, { "type": "text", "bbox": [ 106, 349, 505, 449 ], "lines": [ { "bbox": [ 106, 350, 504, 362 ], "spans": [ { "bbox": [ 106, 350, 504, 362 ], "score": 1.0, "content": "landscape and robust generalization gap, and proposes to incorporate adversarial weight perturba-", "type": "text" } ], "index": 5 }, { "bbox": [ 106, 360, 505, 373 ], "spans": [ { "bbox": [ 106, 360, 505, 373 ], "score": 1.0, "content": "tion mechanism in the adversarial training framework. Despite the efficacy of adversarial weight", "type": "text" } ], "index": 6 }, { "bbox": [ 105, 372, 506, 384 ], "spans": [ { "bbox": [ 105, 372, 506, 384 ], "score": 1.0, "content": "perturbation in suppressing the robust overfitting in adversarial training, a deeper understanding of", "type": "text" } ], "index": 7 }, { "bbox": [ 105, 381, 505, 396 ], "spans": [ { "bbox": [ 105, 381, 505, 396 ], "score": 1.0, "content": "the cause of robust overfitting and a clear direction for valid weight perturbation is largely missing.", "type": "text" } ], "index": 8 }, { "bbox": [ 106, 393, 506, 407 ], "spans": [ { "bbox": [ 106, 393, 506, 407 ], "score": 1.0, "content": "The outer maximization in Eq.(1) lacks an effective criterion to regulate and constrain the extent of", "type": "text" } ], "index": 9 }, { "bbox": [ 106, 405, 505, 417 ], "spans": [ { "bbox": [ 106, 405, 505, 417 ], "score": 1.0, "content": "weight perturbation, which in turn influences the optimization of the outer minimization problem. In", "type": "text" } ], "index": 10 }, { "bbox": [ 105, 416, 505, 428 ], "spans": [ { "bbox": [ 105, 416, 505, 428 ], "score": 1.0, "content": "this paper, we propose such a criterion and provide new understanding of the robust overfitting in ad-", "type": "text" } ], "index": 11 }, { "bbox": [ 106, 426, 505, 439 ], "spans": [ { "bbox": [ 106, 426, 505, 439 ], "score": 1.0, "content": "versarial training. Following this, we design a robust weight perturbation strategy that significantly", "type": "text" } ], "index": 12 }, { "bbox": [ 105, 437, 297, 451 ], "spans": [ { "bbox": [ 105, 437, 297, 451 ], "score": 1.0, "content": "improves the robustness of adversarial training.", "type": "text" } ], "index": 13 } ], "index": 9 }, { "type": "title", "bbox": [ 108, 464, 284, 477 ], "lines": [ { "bbox": [ 104, 462, 286, 480 ], "spans": [ { "bbox": [ 104, 462, 286, 480 ], "score": 1.0, "content": "3 LOSS STATIONARY CONDITION", "type": "text" } ], "index": 14 } ], "index": 14 }, { "type": "text", "bbox": [ 107, 489, 505, 544 ], "lines": [ { "bbox": [ 106, 489, 505, 501 ], "spans": [ { "bbox": [ 106, 489, 505, 501 ], "score": 1.0, "content": "In this section, we first empirically investigate the relationship between weight perturbation robust-", "type": "text" } ], "index": 15 }, { "bbox": [ 105, 501, 505, 513 ], "spans": [ { "bbox": [ 105, 501, 505, 513 ], "score": 1.0, "content": "ness and adversarial robustness, and then propose a new criterion to monitor the training status of", "type": "text" } ], "index": 16 }, { "bbox": [ 105, 510, 505, 524 ], "spans": [ { "bbox": [ 105, 510, 505, 524 ], "score": 1.0, "content": "different adversarial examples in the learning process of adversarial training, which leads to a new", "type": "text" } ], "index": 17 }, { "bbox": [ 105, 522, 506, 536 ], "spans": [ { "bbox": [ 105, 522, 506, 536 ], "score": 1.0, "content": "perspective of robust overfitting. To this end, some discussions about robust overfitting and adver-", "type": "text" } ], "index": 18 }, { "bbox": [ 106, 534, 266, 546 ], "spans": [ { "bbox": [ 106, 534, 266, 546 ], "score": 1.0, "content": "sarial weight perturbation are provided.", "type": "text" } ], "index": 19 } ], "index": 17 }, { "type": "text", "bbox": [ 106, 550, 505, 682 ], "lines": [ { "bbox": [ 105, 550, 505, 563 ], "spans": [ { "bbox": [ 105, 550, 505, 563 ], "score": 1.0, "content": "Does Weight Perturbation Robustness Lead to Better Adversarial Robustness? First, we inves-", "type": "text" } ], "index": 20 }, { "bbox": [ 106, 561, 505, 574 ], "spans": [ { "bbox": [ 106, 561, 505, 574 ], "score": 1.0, "content": "tigate whether the robustness against weight perturbation is beneficial to the adversarial robustness.", "type": "text" } ], "index": 21 }, { "bbox": [ 105, 572, 505, 585 ], "spans": [ { "bbox": [ 105, 572, 505, 585 ], "score": 1.0, "content": "In particular, we train PreAct ResNet-18 with AWP on CIFAR-10 using varying weight perturbation", "type": "text" } ], "index": 22 }, { "bbox": [ 105, 583, 506, 596 ], "spans": [ { "bbox": [ 105, 583, 146, 596 ], "score": 1.0, "content": "size from", "type": "text" }, { "bbox": [ 147, 583, 270, 595 ], "score": 0.53, "content": "0 \\gamma , \\gamma / 8 , \\gamma / 4 , \\gamma / 2 , \\gamma , 2 \\gamma , 4 \\gamma", "type": "inline_equation" }, { "bbox": [ 271, 583, 282, 596 ], "score": 1.0, "content": "to", "type": "text" }, { "bbox": [ 283, 583, 295, 595 ], "score": 0.86, "content": "8 \\gamma", "type": "inline_equation" }, { "bbox": [ 295, 583, 506, 596 ], "score": 1.0, "content": ". In each setting, we evaluate the robustness of the", "type": "text" } ], "index": 23 }, { "bbox": [ 105, 593, 505, 607 ], "spans": [ { "bbox": [ 105, 593, 505, 607 ], "score": 1.0, "content": "model against 20-step PGD (PGD-20) attacks on CIFAR-10 test images. As shown in Figure 1(a),", "type": "text" } ], "index": 24 }, { "bbox": [ 105, 605, 506, 617 ], "spans": [ { "bbox": [ 105, 605, 506, 617 ], "score": 1.0, "content": "when varying weight perturbation size, the best adversarial robustness has a certain improvement", "type": "text" } ], "index": 25 }, { "bbox": [ 105, 617, 505, 629 ], "spans": [ { "bbox": [ 105, 617, 505, 629 ], "score": 1.0, "content": "in the early stage. When weight perturbation size is large, the best adversarial robustness begins", "type": "text" } ], "index": 26 }, { "bbox": [ 105, 627, 506, 639 ], "spans": [ { "bbox": [ 105, 627, 506, 639 ], "score": 1.0, "content": "to decrease significantly as the size of the perturbation increases. It might be explained by the fact", "type": "text" } ], "index": 27 }, { "bbox": [ 105, 637, 505, 651 ], "spans": [ { "bbox": [ 105, 637, 505, 651 ], "score": 1.0, "content": "that the network has to sacrifice adversarial robustness to allocate more capacity to defend against", "type": "text" } ], "index": 28 }, { "bbox": [ 106, 649, 505, 661 ], "spans": [ { "bbox": [ 106, 649, 505, 661 ], "score": 1.0, "content": "weight perturbation, which implies that weight perturbation robustness and adversarial robustness", "type": "text" } ], "index": 29 }, { "bbox": [ 105, 659, 506, 674 ], "spans": [ { "bbox": [ 105, 659, 506, 674 ], "score": 1.0, "content": "are not actually mutually beneficial. The performance gain of AWP is mainly due to suppressing", "type": "text" } ], "index": 30 }, { "bbox": [ 105, 670, 180, 684 ], "spans": [ { "bbox": [ 105, 670, 180, 684 ], "score": 1.0, "content": "robust overfitting.", "type": "text" } ], "index": 31 } ], "index": 25.5 }, { "type": "text", "bbox": [ 107, 687, 504, 720 ], "lines": [ { "bbox": [ 105, 686, 506, 701 ], "spans": [ { "bbox": [ 105, 686, 506, 701 ], "score": 1.0, "content": "Loss Stationary Condition. In order to further understand the robust overfitting, we propose a", "type": "text" } ], "index": 32 }, { "bbox": [ 105, 698, 505, 712 ], "spans": [ { "bbox": [ 105, 698, 505, 712 ], "score": 1.0, "content": "criterion that divides the training adversarial examples into different groups according to their clas-", "type": "text" } ], "index": 33 }, { "bbox": [ 105, 708, 167, 722 ], "spans": [ { "bbox": [ 105, 708, 167, 722 ], "score": 1.0, "content": "sification loss:", "type": "text" } ], "index": 34 } ], "index": 33 }, { "type": "interline_equation", "bbox": [ 209, 719, 400, 733 ], "lines": [ { "bbox": [ 209, 719, 400, 733 ], "spans": [ { "bbox": [ 209, 719, 400, 733 ], "score": 0.91, "content": "\\mathrm { L S C } [ p , q ] = \\{ x ^ { \\prime } \\in \\mathcal { X } \\mid p \\leq \\ell ( f _ { w } ( x ^ { \\prime } ) , y ) \\leq q \\} ,", "type": "interline_equation", "image_path": "bb5610cf813f89d661a182e85eec8c7f431ffac34cd888580cdada2d5705a4f1.jpg" } ] } ], "index": 35, "virtual_lines": [ { "bbox": [ 209, 719, 400, 733 ], "spans": [], "index": 35 } ] } ], "page_idx": 3, "page_size": [ 612, 792 ], "discarded_blocks": [ { "type": "discarded", "bbox": [ 106, 27, 308, 37 ], "lines": [ { "bbox": [ 106, 26, 309, 38 ], "spans": [ { "bbox": [ 106, 26, 309, 38 ], "score": 1.0, "content": "Under review as a conference paper at ICLR 2022", "type": "text" } ] } ] }, { "type": "discarded", "bbox": [ 302, 752, 308, 759 ], "lines": [] } ], "para_blocks": [ { "type": "image", "bbox": [ 109, 80, 500, 306 ], "blocks": [ { "type": "image_body", "bbox": [ 109, 80, 500, 306 ], "group_id": 0, "lines": [ { "bbox": [ 109, 80, 500, 306 ], "spans": [ { "bbox": [ 109, 80, 500, 306 ], "score": 0.972, "type": "image", "image_path": "cf8c9c1611ba4804d2a3319c5b7ff65a8e692709372051083b7ff11770673d20.jpg" } ] } ], "index": 1, "virtual_lines": [ { "bbox": [ 109, 80, 500, 155.33333333333331 ], "spans": [], "index": 0 }, { "bbox": [ 109, 155.33333333333331, 500, 230.66666666666663 ], "spans": [], "index": 1 }, { "bbox": [ 109, 230.66666666666663, 500, 305.99999999999994 ], "spans": [], "index": 2 } ] }, { "type": "image_caption", "bbox": [ 105, 318, 504, 342 ], "group_id": 0, "lines": [ { "bbox": [ 105, 318, 505, 333 ], "spans": [ { "bbox": [ 105, 318, 505, 333 ], "score": 1.0, "content": "Figure 1: (a): Test robustness of AWP with varying weight perturbation size; (b): The learning curve", "type": "text" } ], "index": 3 }, { "bbox": [ 105, 328, 379, 344 ], "spans": [ { "bbox": [ 105, 328, 379, 344 ], "score": 1.0, "content": "of vanilla AT; (c): Test robustness of AWP with varying LSC range.", "type": "text" } ], "index": 4 } ], "index": 3.5 } ], "index": 2.25 }, { "type": "text", "bbox": [ 106, 349, 505, 449 ], "lines": [], "index": 9, "bbox_fs": [ 105, 350, 506, 451 ], "lines_deleted": true }, { "type": "title", "bbox": [ 108, 464, 284, 477 ], "lines": [ { "bbox": [ 104, 462, 286, 480 ], "spans": [ { "bbox": [ 104, 462, 286, 480 ], "score": 1.0, "content": "3 LOSS STATIONARY CONDITION", "type": "text" } ], "index": 14 } ], "index": 14 }, { "type": "text", "bbox": [ 107, 489, 505, 544 ], "lines": [ { "bbox": [ 106, 489, 505, 501 ], "spans": [ { "bbox": [ 106, 489, 505, 501 ], "score": 1.0, "content": "In this section, we first empirically investigate the relationship between weight perturbation robust-", "type": "text" } ], "index": 15 }, { "bbox": [ 105, 501, 505, 513 ], "spans": [ { "bbox": [ 105, 501, 505, 513 ], "score": 1.0, "content": "ness and adversarial robustness, and then propose a new criterion to monitor the training status of", "type": "text" } ], "index": 16 }, { "bbox": [ 105, 510, 505, 524 ], "spans": [ { "bbox": [ 105, 510, 505, 524 ], "score": 1.0, "content": "different adversarial examples in the learning process of adversarial training, which leads to a new", "type": "text" } ], "index": 17 }, { "bbox": [ 105, 522, 506, 536 ], "spans": [ { "bbox": [ 105, 522, 506, 536 ], "score": 1.0, "content": "perspective of robust overfitting. To this end, some discussions about robust overfitting and adver-", "type": "text" } ], "index": 18 }, { "bbox": [ 106, 534, 266, 546 ], "spans": [ { "bbox": [ 106, 534, 266, 546 ], "score": 1.0, "content": "sarial weight perturbation are provided.", "type": "text" } ], "index": 19 } ], "index": 17, "bbox_fs": [ 105, 489, 506, 546 ] }, { "type": "text", "bbox": [ 106, 550, 505, 682 ], "lines": [ { "bbox": [ 105, 550, 505, 563 ], "spans": [ { "bbox": [ 105, 550, 505, 563 ], "score": 1.0, "content": "Does Weight Perturbation Robustness Lead to Better Adversarial Robustness? First, we inves-", "type": "text" } ], "index": 20 }, { "bbox": [ 106, 561, 505, 574 ], "spans": [ { "bbox": [ 106, 561, 505, 574 ], "score": 1.0, "content": "tigate whether the robustness against weight perturbation is beneficial to the adversarial robustness.", "type": "text" } ], "index": 21 }, { "bbox": [ 105, 572, 505, 585 ], "spans": [ { "bbox": [ 105, 572, 505, 585 ], "score": 1.0, "content": "In particular, we train PreAct ResNet-18 with AWP on CIFAR-10 using varying weight perturbation", "type": "text" } ], "index": 22 }, { "bbox": [ 105, 583, 506, 596 ], "spans": [ { "bbox": [ 105, 583, 146, 596 ], "score": 1.0, "content": "size from", "type": "text" }, { "bbox": [ 147, 583, 270, 595 ], "score": 0.53, "content": "0 \\gamma , \\gamma / 8 , \\gamma / 4 , \\gamma / 2 , \\gamma , 2 \\gamma , 4 \\gamma", "type": "inline_equation" }, { "bbox": [ 271, 583, 282, 596 ], "score": 1.0, "content": "to", "type": "text" }, { "bbox": [ 283, 583, 295, 595 ], "score": 0.86, "content": "8 \\gamma", "type": "inline_equation" }, { "bbox": [ 295, 583, 506, 596 ], "score": 1.0, "content": ". In each setting, we evaluate the robustness of the", "type": "text" } ], "index": 23 }, { "bbox": [ 105, 593, 505, 607 ], "spans": [ { "bbox": [ 105, 593, 505, 607 ], "score": 1.0, "content": "model against 20-step PGD (PGD-20) attacks on CIFAR-10 test images. As shown in Figure 1(a),", "type": "text" } ], "index": 24 }, { "bbox": [ 105, 605, 506, 617 ], "spans": [ { "bbox": [ 105, 605, 506, 617 ], "score": 1.0, "content": "when varying weight perturbation size, the best adversarial robustness has a certain improvement", "type": "text" } ], "index": 25 }, { "bbox": [ 105, 617, 505, 629 ], "spans": [ { "bbox": [ 105, 617, 505, 629 ], "score": 1.0, "content": "in the early stage. When weight perturbation size is large, the best adversarial robustness begins", "type": "text" } ], "index": 26 }, { "bbox": [ 105, 627, 506, 639 ], "spans": [ { "bbox": [ 105, 627, 506, 639 ], "score": 1.0, "content": "to decrease significantly as the size of the perturbation increases. It might be explained by the fact", "type": "text" } ], "index": 27 }, { "bbox": [ 105, 637, 505, 651 ], "spans": [ { "bbox": [ 105, 637, 505, 651 ], "score": 1.0, "content": "that the network has to sacrifice adversarial robustness to allocate more capacity to defend against", "type": "text" } ], "index": 28 }, { "bbox": [ 106, 649, 505, 661 ], "spans": [ { "bbox": [ 106, 649, 505, 661 ], "score": 1.0, "content": "weight perturbation, which implies that weight perturbation robustness and adversarial robustness", "type": "text" } ], "index": 29 }, { "bbox": [ 105, 659, 506, 674 ], "spans": [ { "bbox": [ 105, 659, 506, 674 ], "score": 1.0, "content": "are not actually mutually beneficial. The performance gain of AWP is mainly due to suppressing", "type": "text" } ], "index": 30 }, { "bbox": [ 105, 670, 180, 684 ], "spans": [ { "bbox": [ 105, 670, 180, 684 ], "score": 1.0, "content": "robust overfitting.", "type": "text" } ], "index": 31 } ], "index": 25.5, "bbox_fs": [ 105, 550, 506, 684 ] }, { "type": "text", "bbox": [ 107, 687, 504, 720 ], "lines": [ { "bbox": [ 105, 686, 506, 701 ], "spans": [ { "bbox": [ 105, 686, 506, 701 ], "score": 1.0, "content": "Loss Stationary Condition. In order to further understand the robust overfitting, we propose a", "type": "text" } ], "index": 32 }, { "bbox": [ 105, 698, 505, 712 ], "spans": [ { "bbox": [ 105, 698, 505, 712 ], "score": 1.0, "content": "criterion that divides the training adversarial examples into different groups according to their clas-", "type": "text" } ], "index": 33 }, { "bbox": [ 105, 708, 167, 722 ], "spans": [ { "bbox": [ 105, 708, 167, 722 ], "score": 1.0, "content": "sification loss:", "type": "text" } ], "index": 34 } ], "index": 33, "bbox_fs": [ 105, 686, 506, 722 ] }, { "type": "interline_equation", "bbox": [ 209, 719, 400, 733 ], "lines": [ { "bbox": [ 209, 719, 400, 733 ], "spans": [ { "bbox": [ 209, 719, 400, 733 ], "score": 0.91, "content": "\\mathrm { L S C } [ p , q ] = \\{ x ^ { \\prime } \\in \\mathcal { X } \\mid p \\leq \\ell ( f _ { w } ( x ^ { \\prime } ) , y ) \\leq q \\} ,", "type": "interline_equation", "image_path": "bb5610cf813f89d661a182e85eec8c7f431ffac34cd888580cdada2d5705a4f1.jpg" } ] } ], "index": 35, "virtual_lines": [ { "bbox": [ 209, 719, 400, 733 ], "spans": [], "index": 35 } ] } ] }, { "preproc_blocks": [ { "type": "image", "bbox": [ 119, 83, 491, 339 ], "blocks": [ { "type": "image_body", "bbox": [ 119, 83, 491, 339 ], "group_id": 0, "lines": [ { "bbox": [ 119, 83, 491, 339 ], "spans": [ { "bbox": [ 119, 83, 491, 339 ], "score": 0.976, "type": "image", "image_path": "029122678a72cbfbbe80142edc40947c335d750d1a999a146521906d2088d916.jpg" } ] } ], "index": 1, "virtual_lines": [ { "bbox": [ 119, 83, 491, 168.33333333333331 ], "spans": [], "index": 0 }, { "bbox": [ 119, 168.33333333333331, 491, 253.66666666666663 ], "spans": [], "index": 1 }, { "bbox": [ 119, 253.66666666666663, 491, 338.99999999999994 ], "spans": [], "index": 2 } ] }, { "type": "image_caption", "bbox": [ 132, 351, 478, 363 ], "group_id": 0, "lines": [ { "bbox": [ 131, 349, 479, 365 ], "spans": [ { "bbox": [ 131, 349, 479, 365 ], "score": 1.0, "content": "Figure 2: The weight loss landscape of different LSC groups on different checkpoints.", "type": "text" } ], "index": 3 } ], "index": 3 } ], "index": 2.0 }, { "type": "text", "bbox": [ 107, 372, 505, 417 ], "lines": [ { "bbox": [ 105, 372, 506, 385 ], "spans": [ { "bbox": [ 105, 372, 134, 385 ], "score": 1.0, "content": "where", "type": "text" }, { "bbox": [ 134, 373, 162, 384 ], "score": 0.9, "content": "p \\leq q", "type": "inline_equation" }, { "bbox": [ 163, 372, 506, 385 ], "score": 1.0, "content": ". The adversarial examples in the group all satisfy their classification loss within a", "type": "text" } ], "index": 4 }, { "bbox": [ 105, 384, 505, 395 ], "spans": [ { "bbox": [ 105, 384, 505, 395 ], "score": 1.0, "content": "certain range, which is termed Loss Stationary Condition (LSC). The proposed criterion LSC allows", "type": "text" } ], "index": 5 }, { "bbox": [ 106, 394, 505, 407 ], "spans": [ { "bbox": [ 106, 394, 505, 407 ], "score": 1.0, "content": "the analysis of training status of different adversarial examples independently, and provides more", "type": "text" } ], "index": 6 }, { "bbox": [ 105, 405, 245, 418 ], "spans": [ { "bbox": [ 105, 405, 245, 418 ], "score": 1.0, "content": "insights into the robust overfitting.", "type": "text" } ], "index": 7 } ], "index": 5.5 }, { "type": "text", "bbox": [ 106, 421, 505, 521 ], "lines": [ { "bbox": [ 105, 421, 505, 435 ], "spans": [ { "bbox": [ 105, 421, 505, 435 ], "score": 1.0, "content": "LSC View of Robust Overfitting. To provide details of the robust overfitting in adversarial train-", "type": "text" } ], "index": 8 }, { "bbox": [ 105, 433, 505, 446 ], "spans": [ { "bbox": [ 105, 433, 486, 446 ], "score": 1.0, "content": "ing, we train a PreAct ResNet-18 for 200 epochs on CIFAR-10 using PGD-10 with step size", "type": "text" }, { "bbox": [ 486, 433, 501, 445 ], "score": 0.85, "content": "\\epsilon / 4", "type": "inline_equation" }, { "bbox": [ 501, 433, 505, 446 ], "score": 1.0, "content": ",", "type": "text" } ], "index": 9 }, { "bbox": [ 105, 444, 505, 458 ], "spans": [ { "bbox": [ 105, 444, 200, 458 ], "score": 1.0, "content": "maximum perturbation", "type": "text" }, { "bbox": [ 200, 444, 244, 456 ], "score": 0.88, "content": "\\epsilon = 8 / 2 5 5", "type": "inline_equation" }, { "bbox": [ 244, 444, 505, 458 ], "score": 1.0, "content": ", following the standard setting in Madry et al. (2017). The learn-", "type": "text" } ], "index": 10 }, { "bbox": [ 105, 455, 505, 468 ], "spans": [ { "bbox": [ 105, 455, 505, 468 ], "score": 1.0, "content": "ing curve is shown in Figure 1(b). For each intermediate model, we then apply the same PGD-10", "type": "text" } ], "index": 11 }, { "bbox": [ 105, 466, 506, 479 ], "spans": [ { "bbox": [ 105, 466, 506, 479 ], "score": 1.0, "content": "attack on CIFAR-10 training images to craft adversarial examples, and divide the crafted adversarial", "type": "text" } ], "index": 12 }, { "bbox": [ 106, 477, 504, 489 ], "spans": [ { "bbox": [ 106, 477, 504, 489 ], "score": 1.0, "content": "examples into 6 consecutive LSC groups ranging from 0.0 to 3.0. Then, we use the weight loss", "type": "text" } ], "index": 13 }, { "bbox": [ 105, 488, 505, 501 ], "spans": [ { "bbox": [ 105, 488, 505, 501 ], "score": 1.0, "content": "landscape to characterize the training status of the adversarial examples in each LSC group, which", "type": "text" } ], "index": 14 }, { "bbox": [ 105, 498, 505, 511 ], "spans": [ { "bbox": [ 105, 498, 388, 511 ], "score": 1.0, "content": "plots the classification loss change when perturbing the model weight", "type": "text" }, { "bbox": [ 388, 501, 398, 509 ], "score": 0.73, "content": "\\pmb { w }", "type": "inline_equation" }, { "bbox": [ 398, 498, 476, 511 ], "score": 1.0, "content": "by a random noise", "type": "text" }, { "bbox": [ 476, 500, 484, 509 ], "score": 0.79, "content": "^ d", "type": "inline_equation" }, { "bbox": [ 484, 498, 505, 511 ], "score": 1.0, "content": "with", "type": "text" } ], "index": 15 }, { "bbox": [ 105, 510, 163, 524 ], "spans": [ { "bbox": [ 105, 510, 151, 524 ], "score": 1.0, "content": "magnitude", "type": "text" }, { "bbox": [ 151, 512, 158, 522 ], "score": 0.77, "content": "\\mu", "type": "inline_equation" }, { "bbox": [ 159, 510, 163, 524 ], "score": 1.0, "content": ":", "type": "text" } ], "index": 16 } ], "index": 12 }, { "type": "interline_equation", "bbox": [ 192, 521, 418, 554 ], "lines": [ { "bbox": [ 192, 521, 418, 554 ], "spans": [ { "bbox": [ 192, 521, 418, 554 ], "score": 0.94, "content": "g _ { j } ( \\mu ) = \\frac { 1 } { n _ { j } } \\sum _ { i = 1 } ^ { n _ { j } } \\ell ( f _ { w + \\mu d } ( x _ { i j } ^ { \\prime } ) , y _ { i j } ) , \\ x _ { i j } ^ { \\prime } \\in \\mathrm { L S C } [ p _ { j } , q _ { j } ] ,", "type": "interline_equation", "image_path": "75abf559daaca9833f7b426bdcb43c93e5379ab29bce5e90e5fdaed3dd53c7a8.jpg" } ] } ], "index": 17.5, "virtual_lines": [ { "bbox": [ 192, 521, 418, 537.5 ], "spans": [], "index": 17 }, { "bbox": [ 192, 537.5, 418, 554.0 ], "spans": [], "index": 18 } ] }, { "type": "text", "bbox": [ 106, 556, 505, 661 ], "lines": [ { "bbox": [ 106, 557, 506, 570 ], "spans": [ { "bbox": [ 106, 557, 133, 570 ], "score": 1.0, "content": "where", "type": "text" }, { "bbox": [ 133, 558, 140, 569 ], "score": 0.83, "content": "j", "type": "inline_equation" }, { "bbox": [ 140, 557, 242, 570 ], "score": 1.0, "content": "is the number of groups,", "type": "text" }, { "bbox": [ 242, 559, 253, 570 ], "score": 0.81, "content": "n _ { j }", "type": "inline_equation" }, { "bbox": [ 253, 557, 420, 570 ], "score": 1.0, "content": "is the number of adversarial examples in", "type": "text" }, { "bbox": [ 420, 558, 426, 569 ], "score": 0.83, "content": "j", "type": "inline_equation" }, { "bbox": [ 426, 557, 506, 570 ], "score": 1.0, "content": "-th LSC group, and", "type": "text" } ], "index": 19 }, { "bbox": [ 107, 565, 509, 589 ], "spans": [ { "bbox": [ 107, 570, 114, 580 ], "score": 0.77, "content": "^ d", "type": "inline_equation" }, { "bbox": [ 114, 565, 209, 589 ], "score": 1.0, "content": "is filter normalized by", "type": "text" }, { "bbox": [ 209, 570, 270, 585 ], "score": 0.93, "content": "\\begin{array} { r } { d \\gets \\frac { d } { | | d | | } | | \\boldsymbol { w } | | } \\end{array}", "type": "inline_equation" }, { "bbox": [ 270, 565, 509, 589 ], "score": 1.0, "content": "following Li et al. (2017). It is worth noting that weight", "type": "text" } ], "index": 20 }, { "bbox": [ 105, 582, 506, 596 ], "spans": [ { "bbox": [ 105, 582, 506, 596 ], "score": 1.0, "content": "loss landscape has been widely used to characterize the generalization gap (Neyshabur et al., 2017;", "type": "text" } ], "index": 21 }, { "bbox": [ 105, 594, 505, 606 ], "spans": [ { "bbox": [ 105, 594, 505, 606 ], "score": 1.0, "content": "Foret et al., 2020; Wu et al., 2020). Here, we use it to characterize the training status of different", "type": "text" } ], "index": 22 }, { "bbox": [ 105, 604, 506, 618 ], "spans": [ { "bbox": [ 105, 604, 506, 618 ], "score": 1.0, "content": "adversarial examples. For training adversarial examples, the higher the degree of overfitting by the", "type": "text" } ], "index": 23 }, { "bbox": [ 105, 615, 505, 628 ], "spans": [ { "bbox": [ 105, 615, 505, 628 ], "score": 1.0, "content": "model, the more sensitive its loss is to model weight perturbations, thus making the weight loss", "type": "text" } ], "index": 24 }, { "bbox": [ 105, 627, 506, 640 ], "spans": [ { "bbox": [ 105, 627, 506, 640 ], "score": 1.0, "content": "landscape sharper. Here the weight loss curve sharpness is served as a comparable measurement", "type": "text" } ], "index": 25 }, { "bbox": [ 106, 638, 505, 650 ], "spans": [ { "bbox": [ 106, 638, 505, 650 ], "score": 1.0, "content": "of overfitting strength. Besides, another key difference to previous works lies on the LSC criterion", "type": "text" } ], "index": 26 }, { "bbox": [ 105, 649, 423, 662 ], "spans": [ { "bbox": [ 105, 649, 423, 662 ], "score": 1.0, "content": "used for visualization, which provides more insights into the robust overfitting.", "type": "text" } ], "index": 27 } ], "index": 23 }, { "type": "text", "bbox": [ 106, 665, 505, 732 ], "lines": [ { "bbox": [ 106, 666, 505, 678 ], "spans": [ { "bbox": [ 106, 666, 505, 678 ], "score": 1.0, "content": "We show the weight loss curve of each LSC group on different checkpoints in Figure 2. In the", "type": "text" } ], "index": 28 }, { "bbox": [ 106, 677, 505, 689 ], "spans": [ { "bbox": [ 106, 677, 505, 689 ], "score": 1.0, "content": "early stage of training (between 100 and 120 epoch), it can be seen that the weight loss curve of", "type": "text" } ], "index": 29 }, { "bbox": [ 105, 687, 506, 700 ], "spans": [ { "bbox": [ 105, 687, 506, 700 ], "score": 1.0, "content": "the LSC group with small loss is obviously sharper than that of the LSC group with large loss,", "type": "text" } ], "index": 30 }, { "bbox": [ 105, 698, 506, 711 ], "spans": [ { "bbox": [ 105, 698, 506, 711 ], "score": 1.0, "content": "which indicates that the adversarial examples with small classification loss were first overfitted. As", "type": "text" } ], "index": 31 }, { "bbox": [ 105, 709, 505, 722 ], "spans": [ { "bbox": [ 105, 709, 505, 722 ], "score": 1.0, "content": "the training progresses, the weight loss curves of all LSC groups become very sharp, which shows", "type": "text" } ], "index": 32 }, { "bbox": [ 105, 718, 505, 734 ], "spans": [ { "bbox": [ 105, 718, 505, 734 ], "score": 1.0, "content": "that the network overfits all adversarial examples. These observations suggest that robust overfitting", "type": "text" } ], "index": 33 } ], "index": 30.5 } ], "page_idx": 4, "page_size": [ 612, 792 ], "discarded_blocks": [ { "type": "discarded", "bbox": [ 107, 27, 308, 37 ], "lines": [ { "bbox": [ 106, 25, 309, 39 ], "spans": [ { "bbox": [ 106, 25, 309, 39 ], "score": 1.0, "content": "Under review as a conference paper at ICLR 2022", "type": "text" } ] } ] }, { "type": "discarded", "bbox": [ 302, 751, 308, 760 ], "lines": [ { "bbox": [ 302, 750, 309, 763 ], "spans": [ { "bbox": [ 302, 750, 309, 763 ], "score": 1.0, "content": "5", "type": "text" } ] } ] } ], "para_blocks": [ { "type": "image", "bbox": [ 119, 83, 491, 339 ], "blocks": [ { "type": "image_body", "bbox": [ 119, 83, 491, 339 ], "group_id": 0, "lines": [ { "bbox": [ 119, 83, 491, 339 ], "spans": [ { "bbox": [ 119, 83, 491, 339 ], "score": 0.976, "type": "image", "image_path": "029122678a72cbfbbe80142edc40947c335d750d1a999a146521906d2088d916.jpg" } ] } ], "index": 1, "virtual_lines": [ { "bbox": [ 119, 83, 491, 168.33333333333331 ], "spans": [], "index": 0 }, { "bbox": [ 119, 168.33333333333331, 491, 253.66666666666663 ], "spans": [], "index": 1 }, { "bbox": [ 119, 253.66666666666663, 491, 338.99999999999994 ], "spans": [], "index": 2 } ] }, { "type": "image_caption", "bbox": [ 132, 351, 478, 363 ], "group_id": 0, "lines": [ { "bbox": [ 131, 349, 479, 365 ], "spans": [ { "bbox": [ 131, 349, 479, 365 ], "score": 1.0, "content": "Figure 2: The weight loss landscape of different LSC groups on different checkpoints.", "type": "text" } ], "index": 3 } ], "index": 3 } ], "index": 2.0 }, { "type": "text", "bbox": [ 107, 372, 505, 417 ], "lines": [ { "bbox": [ 105, 372, 506, 385 ], "spans": [ { "bbox": [ 105, 372, 134, 385 ], "score": 1.0, "content": "where", "type": "text" }, { "bbox": [ 134, 373, 162, 384 ], "score": 0.9, "content": "p \\leq q", "type": "inline_equation" }, { "bbox": [ 163, 372, 506, 385 ], "score": 1.0, "content": ". The adversarial examples in the group all satisfy their classification loss within a", "type": "text" } ], "index": 4 }, { "bbox": [ 105, 384, 505, 395 ], "spans": [ { "bbox": [ 105, 384, 505, 395 ], "score": 1.0, "content": "certain range, which is termed Loss Stationary Condition (LSC). The proposed criterion LSC allows", "type": "text" } ], "index": 5 }, { "bbox": [ 106, 394, 505, 407 ], "spans": [ { "bbox": [ 106, 394, 505, 407 ], "score": 1.0, "content": "the analysis of training status of different adversarial examples independently, and provides more", "type": "text" } ], "index": 6 }, { "bbox": [ 105, 405, 245, 418 ], "spans": [ { "bbox": [ 105, 405, 245, 418 ], "score": 1.0, "content": "insights into the robust overfitting.", "type": "text" } ], "index": 7 } ], "index": 5.5, "bbox_fs": [ 105, 372, 506, 418 ] }, { "type": "text", "bbox": [ 106, 421, 505, 521 ], "lines": [ { "bbox": [ 105, 421, 505, 435 ], "spans": [ { "bbox": [ 105, 421, 505, 435 ], "score": 1.0, "content": "LSC View of Robust Overfitting. To provide details of the robust overfitting in adversarial train-", "type": "text" } ], "index": 8 }, { "bbox": [ 105, 433, 505, 446 ], "spans": [ { "bbox": [ 105, 433, 486, 446 ], "score": 1.0, "content": "ing, we train a PreAct ResNet-18 for 200 epochs on CIFAR-10 using PGD-10 with step size", "type": "text" }, { "bbox": [ 486, 433, 501, 445 ], "score": 0.85, "content": "\\epsilon / 4", "type": "inline_equation" }, { "bbox": [ 501, 433, 505, 446 ], "score": 1.0, "content": ",", "type": "text" } ], "index": 9 }, { "bbox": [ 105, 444, 505, 458 ], "spans": [ { "bbox": [ 105, 444, 200, 458 ], "score": 1.0, "content": "maximum perturbation", "type": "text" }, { "bbox": [ 200, 444, 244, 456 ], "score": 0.88, "content": "\\epsilon = 8 / 2 5 5", "type": "inline_equation" }, { "bbox": [ 244, 444, 505, 458 ], "score": 1.0, "content": ", following the standard setting in Madry et al. (2017). The learn-", "type": "text" } ], "index": 10 }, { "bbox": [ 105, 455, 505, 468 ], "spans": [ { "bbox": [ 105, 455, 505, 468 ], "score": 1.0, "content": "ing curve is shown in Figure 1(b). For each intermediate model, we then apply the same PGD-10", "type": "text" } ], "index": 11 }, { "bbox": [ 105, 466, 506, 479 ], "spans": [ { "bbox": [ 105, 466, 506, 479 ], "score": 1.0, "content": "attack on CIFAR-10 training images to craft adversarial examples, and divide the crafted adversarial", "type": "text" } ], "index": 12 }, { "bbox": [ 106, 477, 504, 489 ], "spans": [ { "bbox": [ 106, 477, 504, 489 ], "score": 1.0, "content": "examples into 6 consecutive LSC groups ranging from 0.0 to 3.0. Then, we use the weight loss", "type": "text" } ], "index": 13 }, { "bbox": [ 105, 488, 505, 501 ], "spans": [ { "bbox": [ 105, 488, 505, 501 ], "score": 1.0, "content": "landscape to characterize the training status of the adversarial examples in each LSC group, which", "type": "text" } ], "index": 14 }, { "bbox": [ 105, 498, 505, 511 ], "spans": [ { "bbox": [ 105, 498, 388, 511 ], "score": 1.0, "content": "plots the classification loss change when perturbing the model weight", "type": "text" }, { "bbox": [ 388, 501, 398, 509 ], "score": 0.73, "content": "\\pmb { w }", "type": "inline_equation" }, { "bbox": [ 398, 498, 476, 511 ], "score": 1.0, "content": "by a random noise", "type": "text" }, { "bbox": [ 476, 500, 484, 509 ], "score": 0.79, "content": "^ d", "type": "inline_equation" }, { "bbox": [ 484, 498, 505, 511 ], "score": 1.0, "content": "with", "type": "text" } ], "index": 15 }, { "bbox": [ 105, 510, 163, 524 ], "spans": [ { "bbox": [ 105, 510, 151, 524 ], "score": 1.0, "content": "magnitude", "type": "text" }, { "bbox": [ 151, 512, 158, 522 ], "score": 0.77, "content": "\\mu", "type": "inline_equation" }, { "bbox": [ 159, 510, 163, 524 ], "score": 1.0, "content": ":", "type": "text" } ], "index": 16 } ], "index": 12, "bbox_fs": [ 105, 421, 506, 524 ] }, { "type": "interline_equation", "bbox": [ 192, 521, 418, 554 ], "lines": [ { "bbox": [ 192, 521, 418, 554 ], "spans": [ { "bbox": [ 192, 521, 418, 554 ], "score": 0.94, "content": "g _ { j } ( \\mu ) = \\frac { 1 } { n _ { j } } \\sum _ { i = 1 } ^ { n _ { j } } \\ell ( f _ { w + \\mu d } ( x _ { i j } ^ { \\prime } ) , y _ { i j } ) , \\ x _ { i j } ^ { \\prime } \\in \\mathrm { L S C } [ p _ { j } , q _ { j } ] ,", "type": "interline_equation", "image_path": "75abf559daaca9833f7b426bdcb43c93e5379ab29bce5e90e5fdaed3dd53c7a8.jpg" } ] } ], "index": 17.5, "virtual_lines": [ { "bbox": [ 192, 521, 418, 537.5 ], "spans": [], "index": 17 }, { "bbox": [ 192, 537.5, 418, 554.0 ], "spans": [], "index": 18 } ] }, { "type": "text", "bbox": [ 106, 556, 505, 661 ], "lines": [ { "bbox": [ 106, 557, 506, 570 ], "spans": [ { "bbox": [ 106, 557, 133, 570 ], "score": 1.0, "content": "where", "type": "text" }, { "bbox": [ 133, 558, 140, 569 ], "score": 0.83, "content": "j", "type": "inline_equation" }, { "bbox": [ 140, 557, 242, 570 ], "score": 1.0, "content": "is the number of groups,", "type": "text" }, { "bbox": [ 242, 559, 253, 570 ], "score": 0.81, "content": "n _ { j }", "type": "inline_equation" }, { "bbox": [ 253, 557, 420, 570 ], "score": 1.0, "content": "is the number of adversarial examples in", "type": "text" }, { "bbox": [ 420, 558, 426, 569 ], "score": 0.83, "content": "j", "type": "inline_equation" }, { "bbox": [ 426, 557, 506, 570 ], "score": 1.0, "content": "-th LSC group, and", "type": "text" } ], "index": 19 }, { "bbox": [ 107, 565, 509, 589 ], "spans": [ { "bbox": [ 107, 570, 114, 580 ], "score": 0.77, "content": "^ d", "type": "inline_equation" }, { "bbox": [ 114, 565, 209, 589 ], "score": 1.0, "content": "is filter normalized by", "type": "text" }, { "bbox": [ 209, 570, 270, 585 ], "score": 0.93, "content": "\\begin{array} { r } { d \\gets \\frac { d } { | | d | | } | | \\boldsymbol { w } | | } \\end{array}", "type": "inline_equation" }, { "bbox": [ 270, 565, 509, 589 ], "score": 1.0, "content": "following Li et al. (2017). It is worth noting that weight", "type": "text" } ], "index": 20 }, { "bbox": [ 105, 582, 506, 596 ], "spans": [ { "bbox": [ 105, 582, 506, 596 ], "score": 1.0, "content": "loss landscape has been widely used to characterize the generalization gap (Neyshabur et al., 2017;", "type": "text" } ], "index": 21 }, { "bbox": [ 105, 594, 505, 606 ], "spans": [ { "bbox": [ 105, 594, 505, 606 ], "score": 1.0, "content": "Foret et al., 2020; Wu et al., 2020). Here, we use it to characterize the training status of different", "type": "text" } ], "index": 22 }, { "bbox": [ 105, 604, 506, 618 ], "spans": [ { "bbox": [ 105, 604, 506, 618 ], "score": 1.0, "content": "adversarial examples. For training adversarial examples, the higher the degree of overfitting by the", "type": "text" } ], "index": 23 }, { "bbox": [ 105, 615, 505, 628 ], "spans": [ { "bbox": [ 105, 615, 505, 628 ], "score": 1.0, "content": "model, the more sensitive its loss is to model weight perturbations, thus making the weight loss", "type": "text" } ], "index": 24 }, { "bbox": [ 105, 627, 506, 640 ], "spans": [ { "bbox": [ 105, 627, 506, 640 ], "score": 1.0, "content": "landscape sharper. Here the weight loss curve sharpness is served as a comparable measurement", "type": "text" } ], "index": 25 }, { "bbox": [ 106, 638, 505, 650 ], "spans": [ { "bbox": [ 106, 638, 505, 650 ], "score": 1.0, "content": "of overfitting strength. Besides, another key difference to previous works lies on the LSC criterion", "type": "text" } ], "index": 26 }, { "bbox": [ 105, 649, 423, 662 ], "spans": [ { "bbox": [ 105, 649, 423, 662 ], "score": 1.0, "content": "used for visualization, which provides more insights into the robust overfitting.", "type": "text" } ], "index": 27 } ], "index": 23, "bbox_fs": [ 105, 557, 509, 662 ] }, { "type": "text", "bbox": [ 106, 665, 505, 732 ], "lines": [ { "bbox": [ 106, 666, 505, 678 ], "spans": [ { "bbox": [ 106, 666, 505, 678 ], "score": 1.0, "content": "We show the weight loss curve of each LSC group on different checkpoints in Figure 2. In the", "type": "text" } ], "index": 28 }, { "bbox": [ 106, 677, 505, 689 ], "spans": [ { "bbox": [ 106, 677, 505, 689 ], "score": 1.0, "content": "early stage of training (between 100 and 120 epoch), it can be seen that the weight loss curve of", "type": "text" } ], "index": 29 }, { "bbox": [ 105, 687, 506, 700 ], "spans": [ { "bbox": [ 105, 687, 506, 700 ], "score": 1.0, "content": "the LSC group with small loss is obviously sharper than that of the LSC group with large loss,", "type": "text" } ], "index": 30 }, { "bbox": [ 105, 698, 506, 711 ], "spans": [ { "bbox": [ 105, 698, 506, 711 ], "score": 1.0, "content": "which indicates that the adversarial examples with small classification loss were first overfitted. As", "type": "text" } ], "index": 31 }, { "bbox": [ 105, 709, 505, 722 ], "spans": [ { "bbox": [ 105, 709, 505, 722 ], "score": 1.0, "content": "the training progresses, the weight loss curves of all LSC groups become very sharp, which shows", "type": "text" } ], "index": 32 }, { "bbox": [ 105, 718, 505, 734 ], "spans": [ { "bbox": [ 105, 718, 505, 734 ], "score": 1.0, "content": "that the network overfits all adversarial examples. These observations suggest that robust overfitting", "type": "text" } ], "index": 33 }, { "bbox": [ 105, 352, 505, 367 ], "spans": [ { "bbox": [ 105, 352, 505, 367 ], "score": 1.0, "content": "exists a diffusion process: the model will first memorize some easy-to-learn adversarial examples,", "type": "text", "cross_page": true } ], "index": 4 }, { "bbox": [ 106, 365, 288, 377 ], "spans": [ { "bbox": [ 106, 365, 288, 377 ], "score": 1.0, "content": "and then spread to the entire training dataset.", "type": "text", "cross_page": true } ], "index": 5 } ], "index": 30.5, "bbox_fs": [ 105, 666, 506, 734 ] } ] }, { "preproc_blocks": [ { "type": "table", "bbox": [ 110, 88, 505, 332 ], "blocks": [ { "type": "table_caption", "bbox": [ 109, 82, 273, 93 ], "group_id": 0, "lines": [ { "bbox": [ 107, 81, 274, 95 ], "spans": [ { "bbox": [ 107, 81, 274, 95 ], "score": 1.0, "content": "Algorithm 1 Robust Weight Perturbation", "type": "text" } ], "index": 0 } ], "index": 0 }, { "type": "table_body", "bbox": [ 110, 88, 505, 332 ], "group_id": 0, "lines": [ { "bbox": [ 110, 88, 505, 332 ], "spans": [ { "bbox": [ 110, 88, 505, 332 ], "score": 0.866, "html": "
igorlhhTKobustWergntFerturbaton Input: Network fw, training data S,mini-batch B,batch size n,learning rate n,PGD step size α,
PGD steps K1,PGD constraint ε, RWP steps K2, RWP constraint γ, minimum LSC value Cmin· Output: Adversarially robust model fw · repeat
Read mini-batch xp from training set S. xB ← xB +δ,where δ ~ Uniform(-∈,∈) for k=1 to K1 do
x' ←II(xB+α·sign(Vxsl(fw(xB),y)))
end for
Initialize v = 0
for k=1 to K2 do
V = 1B(l(fw+u(xs),y)≤ Cmin)
if∑V=0 then
break
else
v ← v+ Vu(V ·l(fw+v(xs),y))
U←Yw
end if
w ←(w+v)-nVw+vn∑i=1l(fw+u(x'g),y(i))-v
end for
", "type": "table", "image_path": "169fb02ee0a43a98b3db59ea741d4fd545c4822786f0625739702233feece071.jpg" } ] } ], "index": 2, "virtual_lines": [ { "bbox": [ 110, 88, 505, 169.33333333333331 ], "spans": [], "index": 1 }, { "bbox": [ 110, 169.33333333333331, 505, 250.66666666666663 ], "spans": [], "index": 2 }, { "bbox": [ 110, 250.66666666666663, 505, 331.99999999999994 ], "spans": [], "index": 3 } ] } ], "index": 1.0 }, { "type": "text", "bbox": [ 108, 353, 503, 376 ], "lines": [ { "bbox": [ 105, 352, 505, 367 ], "spans": [ { "bbox": [ 105, 352, 505, 367 ], "score": 1.0, "content": "exists a diffusion process: the model will first memorize some easy-to-learn adversarial examples,", "type": "text" } ], "index": 4 }, { "bbox": [ 106, 365, 288, 377 ], "spans": [ { "bbox": [ 106, 365, 288, 377 ], "score": 1.0, "content": "and then spread to the entire training dataset.", "type": "text" } ], "index": 5 } ], "index": 4.5 }, { "type": "text", "bbox": [ 106, 381, 505, 513 ], "lines": [ { "bbox": [ 105, 380, 505, 395 ], "spans": [ { "bbox": [ 105, 380, 505, 395 ], "score": 1.0, "content": "LSC view of Adversarial Weight Perturbation. To provide more insight into how AWP suppresses", "type": "text" } ], "index": 6 }, { "bbox": [ 105, 392, 505, 406 ], "spans": [ { "bbox": [ 105, 392, 505, 406 ], "score": 1.0, "content": "robust overfitting, we train PreAct ResNet-18 on CIFAR-10 by varying the LSC group that performs", "type": "text" } ], "index": 7 }, { "bbox": [ 105, 403, 505, 416 ], "spans": [ { "bbox": [ 105, 403, 505, 416 ], "score": 1.0, "content": "adversarial weight perturbation. In each setting, we evaluate the robustness of the model against", "type": "text" } ], "index": 8 }, { "bbox": [ 105, 413, 506, 428 ], "spans": [ { "bbox": [ 105, 413, 506, 428 ], "score": 1.0, "content": "PGD-20 attacks on CIFAR-10 test images. As shown in Figure 1(c), when varying the LSC range,", "type": "text" } ], "index": 9 }, { "bbox": [ 105, 425, 505, 437 ], "spans": [ { "bbox": [ 105, 425, 505, 437 ], "score": 1.0, "content": "we can observe that conducting adversarial weight perturbation on adversarial examples with small", "type": "text" } ], "index": 10 }, { "bbox": [ 106, 437, 506, 449 ], "spans": [ { "bbox": [ 106, 437, 506, 449 ], "score": 1.0, "content": "classification loss is sufficient to suppress robust overfitting. Recalling the diffusion process in robust", "type": "text" } ], "index": 11 }, { "bbox": [ 106, 448, 505, 460 ], "spans": [ { "bbox": [ 106, 448, 505, 460 ], "score": 1.0, "content": "overfitting, we can infer that to eliminate robust overfitting, it is essential to prevent the model", "type": "text" } ], "index": 12 }, { "bbox": [ 105, 457, 506, 472 ], "spans": [ { "bbox": [ 105, 457, 506, 472 ], "score": 1.0, "content": "from memorizing the easy-to-learn adversarial examples. Besides, it is observed that conducting", "type": "text" } ], "index": 13 }, { "bbox": [ 106, 469, 506, 482 ], "spans": [ { "bbox": [ 106, 469, 506, 482 ], "score": 1.0, "content": "adversarial weight perturbation on adversarial examples with large classification loss leads to worse", "type": "text" } ], "index": 14 }, { "bbox": [ 105, 480, 506, 492 ], "spans": [ { "bbox": [ 105, 480, 506, 492 ], "score": 1.0, "content": "adversarial robustness, which again verifies that the robustness against weight perturbation will not", "type": "text" } ], "index": 15 }, { "bbox": [ 105, 491, 506, 504 ], "spans": [ { "bbox": [ 105, 491, 506, 504 ], "score": 1.0, "content": "bring adversarial robustness gain, or even on the contrary, it undermines the adversarial robustness", "type": "text" } ], "index": 16 }, { "bbox": [ 106, 502, 164, 514 ], "spans": [ { "bbox": [ 106, 502, 164, 514 ], "score": 1.0, "content": "enhancement.", "type": "text" } ], "index": 17 } ], "index": 11.5 }, { "type": "text", "bbox": [ 107, 519, 505, 585 ], "lines": [ { "bbox": [ 105, 518, 506, 532 ], "spans": [ { "bbox": [ 105, 518, 506, 532 ], "score": 1.0, "content": "Do We Really Need the Worst-case Weight Perturbation? As aforementioned, the robustness", "type": "text" } ], "index": 18 }, { "bbox": [ 105, 530, 506, 542 ], "spans": [ { "bbox": [ 105, 530, 506, 542 ], "score": 1.0, "content": "against weight perturbation is detrimental to the adversarial robustness enhancement. Therefore, to", "type": "text" } ], "index": 19 }, { "bbox": [ 104, 540, 506, 554 ], "spans": [ { "bbox": [ 104, 540, 506, 554 ], "score": 1.0, "content": "purely prevent the network from memorizing the adversarial examples with small classification loss,", "type": "text" } ], "index": 20 }, { "bbox": [ 105, 552, 505, 564 ], "spans": [ { "bbox": [ 105, 552, 505, 564 ], "score": 1.0, "content": "conducting worst-case weight perturbation on these adversarial examples is not necessary, since", "type": "text" } ], "index": 21 }, { "bbox": [ 105, 563, 505, 575 ], "spans": [ { "bbox": [ 105, 563, 505, 575 ], "score": 1.0, "content": "it will also deteriorate the adversarial robustness. In the next section, we will propose a robust", "type": "text" } ], "index": 22 }, { "bbox": [ 105, 574, 276, 587 ], "spans": [ { "bbox": [ 105, 574, 276, 587 ], "score": 1.0, "content": "perturbation strategy to address this issue.", "type": "text" } ], "index": 23 } ], "index": 20.5 }, { "type": "title", "bbox": [ 108, 601, 298, 614 ], "lines": [ { "bbox": [ 105, 601, 299, 615 ], "spans": [ { "bbox": [ 105, 601, 299, 615 ], "score": 1.0, "content": "4 ROBUST WEIGHT PERTURBATION", "type": "text" } ], "index": 24 } ], "index": 24 }, { "type": "text", "bbox": [ 106, 626, 504, 649 ], "lines": [ { "bbox": [ 105, 626, 505, 639 ], "spans": [ { "bbox": [ 105, 626, 505, 639 ], "score": 1.0, "content": "In this section, we introduce the proposed robust weight perturbation strategy and its algorithmic", "type": "text" } ], "index": 25 }, { "bbox": [ 105, 638, 154, 650 ], "spans": [ { "bbox": [ 105, 638, 154, 650 ], "score": 1.0, "content": "realization.", "type": "text" } ], "index": 26 } ], "index": 25.5 }, { "type": "text", "bbox": [ 107, 654, 505, 732 ], "lines": [ { "bbox": [ 105, 655, 505, 667 ], "spans": [ { "bbox": [ 105, 655, 505, 667 ], "score": 1.0, "content": "As mentioned in Section 3, conducting adversarial weight perturbation on adversarial examples with", "type": "text" } ], "index": 27 }, { "bbox": [ 105, 665, 505, 678 ], "spans": [ { "bbox": [ 105, 665, 505, 678 ], "score": 1.0, "content": "small classification loss is enough to prevent robust overfitting and leads to higher robustness. How-", "type": "text" } ], "index": 28 }, { "bbox": [ 105, 677, 505, 690 ], "spans": [ { "bbox": [ 105, 677, 505, 690 ], "score": 1.0, "content": "ever, conducting adversarial weight perturbation on adversarial examples with large classification", "type": "text" } ], "index": 29 }, { "bbox": [ 105, 688, 506, 700 ], "spans": [ { "bbox": [ 105, 688, 506, 700 ], "score": 1.0, "content": "loss may not be helpful. Recalling the criterion LSC proposed in Section 3, we have seen that it is", "type": "text" } ], "index": 30 }, { "bbox": [ 105, 699, 505, 711 ], "spans": [ { "bbox": [ 105, 699, 505, 711 ], "score": 1.0, "content": "closely correlated with the tendency of adversarial example to be overfitted. Thus, it can be used", "type": "text" } ], "index": 31 }, { "bbox": [ 105, 710, 505, 722 ], "spans": [ { "bbox": [ 105, 710, 505, 722 ], "score": 1.0, "content": "to regulate the extent of weight perturbation at a fine-grained level. Therefore, we propose to train", "type": "text" } ], "index": 32 }, { "bbox": [ 105, 721, 505, 732 ], "spans": [ { "bbox": [ 105, 721, 505, 732 ], "score": 1.0, "content": "network with adversarial examples that are all above a minimum LSC value, so as to ensure that no", "type": "text" } ], "index": 33 } ], "index": 30 } ], "page_idx": 5, "page_size": [ 612, 792 ], "discarded_blocks": [ { "type": "discarded", "bbox": [ 107, 27, 308, 37 ], "lines": [ { "bbox": [ 107, 26, 308, 38 ], "spans": [ { "bbox": [ 107, 26, 308, 38 ], "score": 1.0, "content": "Under review as a conference paper at ICLR 2022", "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": [ 110, 88, 505, 332 ], "blocks": [ { "type": "table_caption", "bbox": [ 109, 82, 273, 93 ], "group_id": 0, "lines": [ { "bbox": [ 107, 81, 274, 95 ], "spans": [ { "bbox": [ 107, 81, 274, 95 ], "score": 1.0, "content": "Algorithm 1 Robust Weight Perturbation", "type": "text" } ], "index": 0 } ], "index": 0 }, { "type": "table_body", "bbox": [ 110, 88, 505, 332 ], "group_id": 0, "lines": [ { "bbox": [ 110, 88, 505, 332 ], "spans": [ { "bbox": [ 110, 88, 505, 332 ], "score": 0.866, "html": "
igorlhhTKobustWergntFerturbaton Input: Network fw, training data S,mini-batch B,batch size n,learning rate n,PGD step size α,
PGD steps K1,PGD constraint ε, RWP steps K2, RWP constraint γ, minimum LSC value Cmin· Output: Adversarially robust model fw · repeat
Read mini-batch xp from training set S. xB ← xB +δ,where δ ~ Uniform(-∈,∈) for k=1 to K1 do
x' ←II(xB+α·sign(Vxsl(fw(xB),y)))
end for
Initialize v = 0
for k=1 to K2 do
V = 1B(l(fw+u(xs),y)≤ Cmin)
if∑V=0 then
break
else
v ← v+ Vu(V ·l(fw+v(xs),y))
U←Yw
end if
w ←(w+v)-nVw+vn∑i=1l(fw+u(x'g),y(i))-v
end for
", "type": "table", "image_path": "169fb02ee0a43a98b3db59ea741d4fd545c4822786f0625739702233feece071.jpg" } ] } ], "index": 2, "virtual_lines": [ { "bbox": [ 110, 88, 505, 169.33333333333331 ], "spans": [], "index": 1 }, { "bbox": [ 110, 169.33333333333331, 505, 250.66666666666663 ], "spans": [], "index": 2 }, { "bbox": [ 110, 250.66666666666663, 505, 331.99999999999994 ], "spans": [], "index": 3 } ] } ], "index": 1.0 }, { "type": "text", "bbox": [ 108, 353, 503, 376 ], "lines": [], "index": 4.5, "bbox_fs": [ 105, 352, 505, 377 ], "lines_deleted": true }, { "type": "text", "bbox": [ 106, 381, 505, 513 ], "lines": [ { "bbox": [ 105, 380, 505, 395 ], "spans": [ { "bbox": [ 105, 380, 505, 395 ], "score": 1.0, "content": "LSC view of Adversarial Weight Perturbation. To provide more insight into how AWP suppresses", "type": "text" } ], "index": 6 }, { "bbox": [ 105, 392, 505, 406 ], "spans": [ { "bbox": [ 105, 392, 505, 406 ], "score": 1.0, "content": "robust overfitting, we train PreAct ResNet-18 on CIFAR-10 by varying the LSC group that performs", "type": "text" } ], "index": 7 }, { "bbox": [ 105, 403, 505, 416 ], "spans": [ { "bbox": [ 105, 403, 505, 416 ], "score": 1.0, "content": "adversarial weight perturbation. In each setting, we evaluate the robustness of the model against", "type": "text" } ], "index": 8 }, { "bbox": [ 105, 413, 506, 428 ], "spans": [ { "bbox": [ 105, 413, 506, 428 ], "score": 1.0, "content": "PGD-20 attacks on CIFAR-10 test images. As shown in Figure 1(c), when varying the LSC range,", "type": "text" } ], "index": 9 }, { "bbox": [ 105, 425, 505, 437 ], "spans": [ { "bbox": [ 105, 425, 505, 437 ], "score": 1.0, "content": "we can observe that conducting adversarial weight perturbation on adversarial examples with small", "type": "text" } ], "index": 10 }, { "bbox": [ 106, 437, 506, 449 ], "spans": [ { "bbox": [ 106, 437, 506, 449 ], "score": 1.0, "content": "classification loss is sufficient to suppress robust overfitting. Recalling the diffusion process in robust", "type": "text" } ], "index": 11 }, { "bbox": [ 106, 448, 505, 460 ], "spans": [ { "bbox": [ 106, 448, 505, 460 ], "score": 1.0, "content": "overfitting, we can infer that to eliminate robust overfitting, it is essential to prevent the model", "type": "text" } ], "index": 12 }, { "bbox": [ 105, 457, 506, 472 ], "spans": [ { "bbox": [ 105, 457, 506, 472 ], "score": 1.0, "content": "from memorizing the easy-to-learn adversarial examples. Besides, it is observed that conducting", "type": "text" } ], "index": 13 }, { "bbox": [ 106, 469, 506, 482 ], "spans": [ { "bbox": [ 106, 469, 506, 482 ], "score": 1.0, "content": "adversarial weight perturbation on adversarial examples with large classification loss leads to worse", "type": "text" } ], "index": 14 }, { "bbox": [ 105, 480, 506, 492 ], "spans": [ { "bbox": [ 105, 480, 506, 492 ], "score": 1.0, "content": "adversarial robustness, which again verifies that the robustness against weight perturbation will not", "type": "text" } ], "index": 15 }, { "bbox": [ 105, 491, 506, 504 ], "spans": [ { "bbox": [ 105, 491, 506, 504 ], "score": 1.0, "content": "bring adversarial robustness gain, or even on the contrary, it undermines the adversarial robustness", "type": "text" } ], "index": 16 }, { "bbox": [ 106, 502, 164, 514 ], "spans": [ { "bbox": [ 106, 502, 164, 514 ], "score": 1.0, "content": "enhancement.", "type": "text" } ], "index": 17 } ], "index": 11.5, "bbox_fs": [ 105, 380, 506, 514 ] }, { "type": "text", "bbox": [ 107, 519, 505, 585 ], "lines": [ { "bbox": [ 105, 518, 506, 532 ], "spans": [ { "bbox": [ 105, 518, 506, 532 ], "score": 1.0, "content": "Do We Really Need the Worst-case Weight Perturbation? As aforementioned, the robustness", "type": "text" } ], "index": 18 }, { "bbox": [ 105, 530, 506, 542 ], "spans": [ { "bbox": [ 105, 530, 506, 542 ], "score": 1.0, "content": "against weight perturbation is detrimental to the adversarial robustness enhancement. Therefore, to", "type": "text" } ], "index": 19 }, { "bbox": [ 104, 540, 506, 554 ], "spans": [ { "bbox": [ 104, 540, 506, 554 ], "score": 1.0, "content": "purely prevent the network from memorizing the adversarial examples with small classification loss,", "type": "text" } ], "index": 20 }, { "bbox": [ 105, 552, 505, 564 ], "spans": [ { "bbox": [ 105, 552, 505, 564 ], "score": 1.0, "content": "conducting worst-case weight perturbation on these adversarial examples is not necessary, since", "type": "text" } ], "index": 21 }, { "bbox": [ 105, 563, 505, 575 ], "spans": [ { "bbox": [ 105, 563, 505, 575 ], "score": 1.0, "content": "it will also deteriorate the adversarial robustness. In the next section, we will propose a robust", "type": "text" } ], "index": 22 }, { "bbox": [ 105, 574, 276, 587 ], "spans": [ { "bbox": [ 105, 574, 276, 587 ], "score": 1.0, "content": "perturbation strategy to address this issue.", "type": "text" } ], "index": 23 } ], "index": 20.5, "bbox_fs": [ 104, 518, 506, 587 ] }, { "type": "title", "bbox": [ 108, 601, 298, 614 ], "lines": [ { "bbox": [ 105, 601, 299, 615 ], "spans": [ { "bbox": [ 105, 601, 299, 615 ], "score": 1.0, "content": "4 ROBUST WEIGHT PERTURBATION", "type": "text" } ], "index": 24 } ], "index": 24 }, { "type": "text", "bbox": [ 106, 626, 504, 649 ], "lines": [ { "bbox": [ 105, 626, 505, 639 ], "spans": [ { "bbox": [ 105, 626, 505, 639 ], "score": 1.0, "content": "In this section, we introduce the proposed robust weight perturbation strategy and its algorithmic", "type": "text" } ], "index": 25 }, { "bbox": [ 105, 638, 154, 650 ], "spans": [ { "bbox": [ 105, 638, 154, 650 ], "score": 1.0, "content": "realization.", "type": "text" } ], "index": 26 } ], "index": 25.5, "bbox_fs": [ 105, 626, 505, 650 ] }, { "type": "text", "bbox": [ 107, 654, 505, 732 ], "lines": [ { "bbox": [ 105, 655, 505, 667 ], "spans": [ { "bbox": [ 105, 655, 505, 667 ], "score": 1.0, "content": "As mentioned in Section 3, conducting adversarial weight perturbation on adversarial examples with", "type": "text" } ], "index": 27 }, { "bbox": [ 105, 665, 505, 678 ], "spans": [ { "bbox": [ 105, 665, 505, 678 ], "score": 1.0, "content": "small classification loss is enough to prevent robust overfitting and leads to higher robustness. How-", "type": "text" } ], "index": 28 }, { "bbox": [ 105, 677, 505, 690 ], "spans": [ { "bbox": [ 105, 677, 505, 690 ], "score": 1.0, "content": "ever, conducting adversarial weight perturbation on adversarial examples with large classification", "type": "text" } ], "index": 29 }, { "bbox": [ 105, 688, 506, 700 ], "spans": [ { "bbox": [ 105, 688, 506, 700 ], "score": 1.0, "content": "loss may not be helpful. Recalling the criterion LSC proposed in Section 3, we have seen that it is", "type": "text" } ], "index": 30 }, { "bbox": [ 105, 699, 505, 711 ], "spans": [ { "bbox": [ 105, 699, 505, 711 ], "score": 1.0, "content": "closely correlated with the tendency of adversarial example to be overfitted. Thus, it can be used", "type": "text" } ], "index": 31 }, { "bbox": [ 105, 710, 505, 722 ], "spans": [ { "bbox": [ 105, 710, 505, 722 ], "score": 1.0, "content": "to regulate the extent of weight perturbation at a fine-grained level. Therefore, we propose to train", "type": "text" } ], "index": 32 }, { "bbox": [ 105, 721, 505, 732 ], "spans": [ { "bbox": [ 105, 721, 505, 732 ], "score": 1.0, "content": "network with adversarial examples that are all above a minimum LSC value, so as to ensure that no", "type": "text" } ], "index": 33 }, { "bbox": [ 104, 80, 504, 97 ], "spans": [ { "bbox": [ 104, 80, 483, 97 ], "score": 1.0, "content": "robust overfitting occurs while avoiding the side effect of excessive weight perturbation. Let", "type": "text", "cross_page": true }, { "bbox": [ 483, 84, 504, 94 ], "score": 0.85, "content": "c _ { m i n }", "type": "inline_equation", "cross_page": true } ], "index": 0 }, { "bbox": [ 105, 93, 505, 106 ], "spans": [ { "bbox": [ 105, 93, 391, 106 ], "score": 1.0, "content": "be the minimum LSC value. Instead of generating weight perturbation", "type": "text", "cross_page": true }, { "bbox": [ 391, 96, 398, 104 ], "score": 0.73, "content": "\\textbf { { v } }", "type": "inline_equation", "cross_page": true }, { "bbox": [ 398, 93, 505, 106 ], "score": 1.0, "content": "via outer maximization in", "type": "text", "cross_page": true } ], "index": 1 }, { "bbox": [ 105, 104, 242, 118 ], "spans": [ { "bbox": [ 105, 104, 187, 118 ], "score": 1.0, "content": "Eq.(1), we generate", "type": "text", "cross_page": true }, { "bbox": [ 187, 106, 194, 114 ], "score": 0.75, "content": "\\pmb { v }", "type": "inline_equation", "cross_page": true }, { "bbox": [ 195, 104, 242, 118 ], "score": 1.0, "content": "as follows:", "type": "text", "cross_page": true } ], "index": 2 } ], "index": 30, "bbox_fs": [ 105, 655, 506, 732 ] } ] }, { "preproc_blocks": [ { "type": "text", "bbox": [ 106, 82, 505, 116 ], "lines": [ { "bbox": [ 104, 80, 504, 97 ], "spans": [ { "bbox": [ 104, 80, 483, 97 ], "score": 1.0, "content": "robust overfitting occurs while avoiding the side effect of excessive weight perturbation. Let", "type": "text" }, { "bbox": [ 483, 84, 504, 94 ], "score": 0.85, "content": "c _ { m i n }", "type": "inline_equation" } ], "index": 0 }, { "bbox": [ 105, 93, 505, 106 ], "spans": [ { "bbox": [ 105, 93, 391, 106 ], "score": 1.0, "content": "be the minimum LSC value. Instead of generating weight perturbation", "type": "text" }, { "bbox": [ 391, 96, 398, 104 ], "score": 0.73, "content": "\\textbf { { v } }", "type": "inline_equation" }, { "bbox": [ 398, 93, 505, 106 ], "score": 1.0, "content": "via outer maximization in", "type": "text" } ], "index": 1 }, { "bbox": [ 105, 104, 242, 118 ], "spans": [ { "bbox": [ 105, 104, 187, 118 ], "score": 1.0, "content": "Eq.(1), we generate", "type": "text" }, { "bbox": [ 187, 106, 194, 114 ], "score": 0.75, "content": "\\pmb { v }", "type": "inline_equation" }, { "bbox": [ 195, 104, 242, 118 ], "score": 1.0, "content": "as follows:", "type": "text" } ], "index": 2 } ], "index": 1 }, { "type": "interline_equation", "bbox": [ 194, 121, 417, 185 ], "lines": [ { "bbox": [ 194, 121, 417, 185 ], "spans": [ { "bbox": [ 194, 121, 417, 185 ], "score": 0.89, "content": "\\begin{array} { r l } { \\pmb { v } ^ { k + 1 } = \\pmb { v } ^ { k } + \\nabla _ { \\pmb { v } ^ { k } } \\cfrac { 1 } { n } \\displaystyle \\sum _ { i = 1 } ^ { n } \\mathbb { 1 } ( x _ { i } ^ { \\prime } , y _ { i } ) \\ell ( f _ { \\pmb { w + v } ^ { k } } ( x _ { i } ^ { \\prime } ) , y _ { i } ) , } & { } \\\\ { \\mathrm { w h e r e } \\quad \\mathbb { 1 } ( x _ { i } ^ { \\prime } , y _ { i } ) = \\left\\{ \\begin{array} { l l } { 0 } & { \\mathrm { i f ~ } \\ell ( f _ { \\pmb { w + v } ^ { k } } ( x _ { i } ^ { \\prime } ) , y _ { i } ) > c _ { m i n } } \\\\ { 1 } & { \\mathrm { i f ~ } \\ell ( f _ { \\pmb { w + v } ^ { k } } ( x _ { i } ^ { \\prime } ) , y _ { i } ) \\leq c _ { m i n } } \\end{array} \\right. } \\end{array}", "type": "interline_equation", "image_path": "7d0912a7f1e94c34b52730fda58bc81a07a4b7a8a81559896aed4b3e0f410fc9.jpg" } ] } ], "index": 4.5, "virtual_lines": [ { "bbox": [ 194, 121, 417, 137.0 ], "spans": [], "index": 3 }, { "bbox": [ 194, 137.0, 417, 153.0 ], "spans": [], "index": 4 }, { "bbox": [ 194, 153.0, 417, 169.0 ], "spans": [], "index": 5 }, { "bbox": [ 194, 169.0, 417, 185.0 ], "spans": [], "index": 6 } ] }, { "type": "text", "bbox": [ 106, 189, 505, 343 ], "lines": [ { "bbox": [ 106, 189, 505, 201 ], "spans": [ { "bbox": [ 106, 189, 505, 201 ], "score": 1.0, "content": "The proposed Robust Weight Perturbation (RWP) algorithm is shown in Algorithm 1. We use PGD", "type": "text" } ], "index": 7 }, { "bbox": [ 106, 200, 505, 213 ], "spans": [ { "bbox": [ 106, 200, 505, 213 ], "score": 1.0, "content": "attack (Madry et al., 2017) to generate the training adversarial examples, which can be also ex-", "type": "text" } ], "index": 8 }, { "bbox": [ 106, 212, 504, 223 ], "spans": [ { "bbox": [ 106, 212, 504, 223 ], "score": 1.0, "content": "tended to other variants such as TRADES (Zhang et al., 2019) and RST (Carmon et al., 2019). The", "type": "text" } ], "index": 9 }, { "bbox": [ 105, 222, 505, 235 ], "spans": [ { "bbox": [ 105, 222, 195, 235 ], "score": 1.0, "content": "mimimum LSC value", "type": "text" }, { "bbox": [ 195, 223, 216, 233 ], "score": 0.89, "content": "c _ { m i n }", "type": "inline_equation" }, { "bbox": [ 216, 222, 505, 235 ], "score": 1.0, "content": "controls the minimum classification loss (minimum weight perturbation", "type": "text" } ], "index": 10 }, { "bbox": [ 105, 233, 506, 246 ], "spans": [ { "bbox": [ 105, 233, 506, 246 ], "score": 1.0, "content": "strength) of the adversarial examples during network training. In the early stages of training, the", "type": "text" } ], "index": 11 }, { "bbox": [ 105, 243, 505, 257 ], "spans": [ { "bbox": [ 105, 243, 369, 257 ], "score": 1.0, "content": "classification loss of adversarial example is generally larger than", "type": "text" }, { "bbox": [ 370, 245, 390, 255 ], "score": 0.88, "content": "c _ { m i n }", "type": "inline_equation" }, { "bbox": [ 390, 243, 505, 257 ], "score": 1.0, "content": "corresponding to no weight", "type": "text" } ], "index": 12 }, { "bbox": [ 104, 254, 506, 268 ], "spans": [ { "bbox": [ 104, 254, 506, 268 ], "score": 1.0, "content": "perturbation process. The classification loss of adversarial examples then decreases as training pro-", "type": "text" } ], "index": 13 }, { "bbox": [ 104, 266, 506, 278 ], "spans": [ { "bbox": [ 104, 266, 506, 278 ], "score": 1.0, "content": "gresses. At each optimization step, we monitor the classification loss of the adversarial example and", "type": "text" } ], "index": 14 }, { "bbox": [ 105, 277, 505, 290 ], "spans": [ { "bbox": [ 105, 277, 505, 290 ], "score": 1.0, "content": "conduct the weight perturbation process for adversarial examples whose classification loss is already", "type": "text" } ], "index": 15 }, { "bbox": [ 105, 288, 505, 300 ], "spans": [ { "bbox": [ 105, 288, 158, 300 ], "score": 1.0, "content": "smaller than", "type": "text" }, { "bbox": [ 159, 289, 179, 299 ], "score": 0.89, "content": "c _ { m i n }", "type": "inline_equation" }, { "bbox": [ 180, 288, 339, 300 ], "score": 1.0, "content": ", enabled by an indicator control vector", "type": "text" }, { "bbox": [ 339, 288, 348, 298 ], "score": 0.64, "content": "V", "type": "inline_equation" }, { "bbox": [ 349, 288, 505, 300 ], "score": 1.0, "content": ". At each perturbation step, the weight", "type": "text" } ], "index": 16 }, { "bbox": [ 104, 298, 506, 312 ], "spans": [ { "bbox": [ 104, 298, 158, 312 ], "score": 1.0, "content": "perturbation", "type": "text" }, { "bbox": [ 159, 301, 166, 308 ], "score": 0.68, "content": "\\pmb { v }", "type": "inline_equation" }, { "bbox": [ 166, 298, 506, 312 ], "score": 1.0, "content": "will be updated to increase the classification loss of the corresponding adversarial", "type": "text" } ], "index": 17 }, { "bbox": [ 105, 310, 505, 322 ], "spans": [ { "bbox": [ 105, 310, 457, 322 ], "score": 1.0, "content": "example. When the classification loss of training adversarial examples is all higher than", "type": "text" }, { "bbox": [ 457, 311, 478, 321 ], "score": 0.89, "content": "c _ { m i n }", "type": "inline_equation" }, { "bbox": [ 479, 310, 505, 322 ], "score": 1.0, "content": "or the", "type": "text" } ], "index": 18 }, { "bbox": [ 105, 320, 506, 333 ], "spans": [ { "bbox": [ 105, 320, 506, 333 ], "score": 1.0, "content": "number of perturbation step reaches the defined value, we stop the weight perturbation process and", "type": "text" } ], "index": 19 }, { "bbox": [ 105, 331, 373, 346 ], "spans": [ { "bbox": [ 105, 331, 268, 346 ], "score": 1.0, "content": "inject the generated weight perturbation", "type": "text" }, { "bbox": [ 268, 334, 275, 342 ], "score": 0.68, "content": "\\textbf { { v } }", "type": "inline_equation" }, { "bbox": [ 275, 331, 373, 346 ], "score": 1.0, "content": "for adversarial training.", "type": "text" } ], "index": 20 } ], "index": 13.5 }, { "type": "title", "bbox": [ 108, 359, 200, 372 ], "lines": [ { "bbox": [ 104, 357, 202, 374 ], "spans": [ { "bbox": [ 104, 357, 202, 374 ], "score": 1.0, "content": "5 EXPERIMENTS", "type": "text" } ], "index": 21 } ], "index": 21 }, { "type": "text", "bbox": [ 107, 384, 503, 406 ], "lines": [ { "bbox": [ 105, 383, 504, 396 ], "spans": [ { "bbox": [ 105, 383, 504, 396 ], "score": 1.0, "content": "In this section, we conduct comprehensive experiments to evaluate the effectiveness of RWP includ-", "type": "text" } ], "index": 22 }, { "bbox": [ 105, 395, 395, 407 ], "spans": [ { "bbox": [ 105, 395, 395, 407 ], "score": 1.0, "content": "ing its experimental settings, robustness evaluation and ablation studies.", "type": "text" } ], "index": 23 } ], "index": 22.5 }, { "type": "title", "bbox": [ 107, 420, 230, 431 ], "lines": [ { "bbox": [ 106, 419, 231, 432 ], "spans": [ { "bbox": [ 106, 419, 231, 432 ], "score": 1.0, "content": "5.1 EXPERIMENTAL SETUP", "type": "text" } ], "index": 24 } ], "index": 24 }, { "type": "text", "bbox": [ 106, 440, 505, 649 ], "lines": [ { "bbox": [ 106, 440, 505, 453 ], "spans": [ { "bbox": [ 106, 440, 505, 453 ], "score": 1.0, "content": "Baselines and Implementation Details. Our implementation is based on PyTorch and the code", "type": "text" } ], "index": 25 }, { "bbox": [ 106, 452, 505, 463 ], "spans": [ { "bbox": [ 106, 452, 505, 463 ], "score": 1.0, "content": "as well as other related resources will be released for public use and verification. We conduct ex-", "type": "text" } ], "index": 26 }, { "bbox": [ 105, 462, 505, 474 ], "spans": [ { "bbox": [ 105, 462, 505, 474 ], "score": 1.0, "content": "tensive experiments across three benchmark datasets (CIFAR-10 (Krizhevsky et al., 2009), CIFAR-", "type": "text" } ], "index": 27 }, { "bbox": [ 106, 473, 506, 486 ], "spans": [ { "bbox": [ 106, 473, 469, 486 ], "score": 1.0, "content": "100 (Krizhevsky et al., 2009) and SVHN (Netzer et al., 2011)) and two threat models", "type": "text" }, { "bbox": [ 469, 474, 486, 484 ], "score": 0.87, "content": "L _ { \\infty }", "type": "inline_equation" }, { "bbox": [ 486, 473, 506, 486 ], "score": 1.0, "content": "and", "type": "text" } ], "index": 28 }, { "bbox": [ 106, 484, 505, 497 ], "spans": [ { "bbox": [ 106, 485, 119, 496 ], "score": 0.78, "content": "L _ { 2 }", "type": "inline_equation" }, { "bbox": [ 120, 484, 505, 497 ], "score": 1.0, "content": "). We use PreAct ResNet-18 (He et al., 2016) and Wide ResNet (WRN-28-10 and WRN-34-10)", "type": "text" } ], "index": 29 }, { "bbox": [ 106, 496, 505, 507 ], "spans": [ { "bbox": [ 106, 496, 505, 507 ], "score": 1.0, "content": "(Zagoruyko & Komodakis, 2016) as the network structure following Wu et al. (2020). We compare", "type": "text" } ], "index": 30 }, { "bbox": [ 106, 506, 505, 519 ], "spans": [ { "bbox": [ 106, 506, 505, 519 ], "score": 1.0, "content": "the performance of the proposed method on a number of baseline methods: 1) standard adversarial", "type": "text" } ], "index": 31 }, { "bbox": [ 105, 515, 506, 532 ], "spans": [ { "bbox": [ 105, 515, 506, 532 ], "score": 1.0, "content": "training without weight perturbation, including vanilla AT (Madry et al., 2017), TRADES (Zhang", "type": "text" } ], "index": 32 }, { "bbox": [ 104, 527, 505, 542 ], "spans": [ { "bbox": [ 104, 527, 505, 542 ], "score": 1.0, "content": "et al., 2019) and RST (Carmon et al., 2019); 2) adversarial training with adversarial weight per-", "type": "text" } ], "index": 33 }, { "bbox": [ 104, 538, 506, 552 ], "spans": [ { "bbox": [ 104, 538, 506, 552 ], "score": 1.0, "content": "turbation (AWP) (Wu et al., 2020). For training, the network is trained for 200 epochs using SGD", "type": "text" } ], "index": 34 }, { "bbox": [ 105, 549, 505, 563 ], "spans": [ { "bbox": [ 105, 549, 247, 563 ], "score": 1.0, "content": "with momentum 0.9, weight decay", "type": "text" }, { "bbox": [ 247, 550, 286, 561 ], "score": 0.91, "content": "5 \\times 1 0 ^ { - 4 }", "type": "inline_equation" }, { "bbox": [ 286, 549, 505, 563 ], "score": 1.0, "content": ", and an initial learning rate of 0.1. The learning rate is", "type": "text" } ], "index": 35 }, { "bbox": [ 105, 561, 505, 574 ], "spans": [ { "bbox": [ 105, 561, 505, 574 ], "score": 1.0, "content": "divided by 10 at the 100-th and 150-th epoch. Standard data augmentation including random crops", "type": "text" } ], "index": 36 }, { "bbox": [ 106, 572, 504, 583 ], "spans": [ { "bbox": [ 106, 572, 504, 583 ], "score": 1.0, "content": "with 4 pixels of padding and random horizontal flips are applied. For testing, model robustness is", "type": "text" } ], "index": 37 }, { "bbox": [ 105, 583, 505, 596 ], "spans": [ { "bbox": [ 105, 583, 505, 596 ], "score": 1.0, "content": "evaluated by measuring the accuracy of the model under different adversarial attacks. For hyper-", "type": "text" } ], "index": 38 }, { "bbox": [ 105, 594, 506, 606 ], "spans": [ { "bbox": [ 105, 594, 290, 606 ], "score": 1.0, "content": "parameters in RWP, we set perturbation step", "type": "text" }, { "bbox": [ 290, 594, 330, 605 ], "score": 0.91, "content": "K _ { 2 } = 1 0", "type": "inline_equation" }, { "bbox": [ 331, 594, 506, 606 ], "score": 1.0, "content": "for all datasets. The minimum LSC value", "type": "text" } ], "index": 39 }, { "bbox": [ 106, 604, 506, 619 ], "spans": [ { "bbox": [ 106, 605, 156, 617 ], "score": 0.89, "content": "c _ { m i n } = 1 . 7", "type": "inline_equation" }, { "bbox": [ 157, 604, 221, 619 ], "score": 1.0, "content": "for CIFAR-10,", "type": "text" }, { "bbox": [ 221, 605, 271, 616 ], "score": 0.89, "content": "c _ { m i n } = 2 . 2", "type": "inline_equation" }, { "bbox": [ 271, 604, 335, 619 ], "score": 1.0, "content": "for SVHN and", "type": "text" }, { "bbox": [ 335, 605, 385, 616 ], "score": 0.9, "content": "c _ { m i n } = 4 . 0", "type": "inline_equation" }, { "bbox": [ 386, 604, 506, 619 ], "score": 1.0, "content": "for CIFAR-100. The weight", "type": "text" } ], "index": 40 }, { "bbox": [ 105, 616, 505, 628 ], "spans": [ { "bbox": [ 105, 616, 197, 628 ], "score": 1.0, "content": "perturbation budget of", "type": "text" }, { "bbox": [ 198, 617, 235, 627 ], "score": 0.91, "content": "\\gamma = 0 . 0 1", "type": "inline_equation" }, { "bbox": [ 235, 616, 289, 628 ], "score": 1.0, "content": "for AT-RWP,", "type": "text" }, { "bbox": [ 289, 616, 333, 628 ], "score": 0.89, "content": "\\gamma = 0 . 0 0 5", "type": "inline_equation" }, { "bbox": [ 333, 616, 505, 628 ], "score": 1.0, "content": "for TRADES-RWP and RST-RWP follow-", "type": "text" } ], "index": 41 }, { "bbox": [ 105, 627, 505, 640 ], "spans": [ { "bbox": [ 105, 627, 505, 640 ], "score": 1.0, "content": "ing literature (Wu et al., 2020). Other hyper-parameters of the baselines are configured as per their", "type": "text" } ], "index": 42 }, { "bbox": [ 105, 638, 171, 651 ], "spans": [ { "bbox": [ 105, 638, 171, 651 ], "score": 1.0, "content": "original papers.", "type": "text" } ], "index": 43 } ], "index": 34 }, { "type": "text", "bbox": [ 106, 654, 505, 732 ], "lines": [ { "bbox": [ 105, 654, 505, 667 ], "spans": [ { "bbox": [ 105, 654, 505, 667 ], "score": 1.0, "content": "Adversarial Setting. The training attack is 10-step PGD attack with random start. We follow the", "type": "text" } ], "index": 44 }, { "bbox": [ 105, 666, 505, 678 ], "spans": [ { "bbox": [ 105, 666, 273, 678 ], "score": 1.0, "content": "same settings in Rice et al. (2020) : for", "type": "text" }, { "bbox": [ 273, 666, 290, 677 ], "score": 0.89, "content": "L _ { \\infty }", "type": "inline_equation" }, { "bbox": [ 290, 666, 349, 678 ], "score": 1.0, "content": "threat model,", "type": "text" }, { "bbox": [ 349, 666, 396, 677 ], "score": 0.9, "content": "\\epsilon = 8 / 2 5 5", "type": "inline_equation" }, { "bbox": [ 396, 666, 439, 678 ], "score": 1.0, "content": ", step size", "type": "text" }, { "bbox": [ 439, 666, 489, 677 ], "score": 0.9, "content": "\\alpha = 1 / 2 5 5", "type": "inline_equation" }, { "bbox": [ 489, 666, 505, 678 ], "score": 1.0, "content": "for", "type": "text" } ], "index": 45 }, { "bbox": [ 106, 677, 505, 689 ], "spans": [ { "bbox": [ 106, 677, 157, 689 ], "score": 1.0, "content": "SVHN, and", "type": "text" }, { "bbox": [ 158, 677, 208, 688 ], "score": 0.89, "content": "\\alpha = 2 / 2 5 5", "type": "inline_equation" }, { "bbox": [ 208, 677, 371, 689 ], "score": 1.0, "content": "for both CIFAR10 and CIFAR100; for", "type": "text" }, { "bbox": [ 372, 677, 384, 688 ], "score": 0.87, "content": "L _ { 2 }", "type": "inline_equation" }, { "bbox": [ 384, 677, 444, 689 ], "score": 1.0, "content": "threat model,", "type": "text" }, { "bbox": [ 444, 677, 501, 689 ], "score": 0.82, "content": "\\epsilon = 1 2 8 / 2 5 5", "type": "inline_equation" }, { "bbox": [ 502, 677, 505, 689 ], "score": 1.0, "content": ",", "type": "text" } ], "index": 46 }, { "bbox": [ 105, 688, 505, 700 ], "spans": [ { "bbox": [ 105, 688, 143, 700 ], "score": 1.0, "content": "step size", "type": "text" }, { "bbox": [ 144, 688, 195, 699 ], "score": 0.85, "content": "\\alpha = 1 5 / 2 5 5", "type": "inline_equation" }, { "bbox": [ 195, 688, 505, 700 ], "score": 1.0, "content": "for all datasets. The test attacks used for robustness evaluation are generated", "type": "text" } ], "index": 47 }, { "bbox": [ 105, 699, 505, 711 ], "spans": [ { "bbox": [ 105, 699, 505, 711 ], "score": 1.0, "content": "from the original test set images by attacking the defense models using different attacking methods,", "type": "text" } ], "index": 48 }, { "bbox": [ 105, 709, 506, 723 ], "spans": [ { "bbox": [ 105, 709, 266, 723 ], "score": 1.0, "content": "including: FGSM, PGD-20, PGD-100,", "type": "text" }, { "bbox": [ 266, 710, 300, 721 ], "score": 0.64, "content": "\\mathrm { C } \\& \\mathbf { W } _ { \\infty }", "type": "inline_equation" }, { "bbox": [ 300, 709, 305, 723 ], "score": 0.0, "content": "", "type": "text" }, { "bbox": [ 305, 710, 321, 721 ], "score": 0.86, "content": "L _ { \\infty }", "type": "inline_equation" }, { "bbox": [ 322, 709, 506, 723 ], "score": 1.0, "content": "version of C&W optimized by PGD for 100", "type": "text" } ], "index": 49 }, { "bbox": [ 105, 721, 227, 733 ], "spans": [ { "bbox": [ 105, 721, 227, 733 ], "score": 1.0, "content": "steps) and Auto Attack (AA).", "type": "text" } ], "index": 50 } ], "index": 47 } ], "page_idx": 6, "page_size": [ 612, 792 ], "discarded_blocks": [ { "type": "discarded", "bbox": [ 107, 27, 308, 37 ], "lines": [ { "bbox": [ 107, 26, 308, 38 ], "spans": [ { "bbox": [ 107, 26, 308, 38 ], "score": 1.0, "content": "Under review as a conference paper at ICLR 2022", "type": "text" } ] } ] }, { "type": "discarded", "bbox": [ 303, 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": "text", "bbox": [ 106, 82, 505, 116 ], "lines": [], "index": 1, "bbox_fs": [ 104, 80, 505, 118 ], "lines_deleted": true }, { "type": "interline_equation", "bbox": [ 194, 121, 417, 185 ], "lines": [ { "bbox": [ 194, 121, 417, 185 ], "spans": [ { "bbox": [ 194, 121, 417, 185 ], "score": 0.89, "content": "\\begin{array} { r l } { \\pmb { v } ^ { k + 1 } = \\pmb { v } ^ { k } + \\nabla _ { \\pmb { v } ^ { k } } \\cfrac { 1 } { n } \\displaystyle \\sum _ { i = 1 } ^ { n } \\mathbb { 1 } ( x _ { i } ^ { \\prime } , y _ { i } ) \\ell ( f _ { \\pmb { w + v } ^ { k } } ( x _ { i } ^ { \\prime } ) , y _ { i } ) , } & { } \\\\ { \\mathrm { w h e r e } \\quad \\mathbb { 1 } ( x _ { i } ^ { \\prime } , y _ { i } ) = \\left\\{ \\begin{array} { l l } { 0 } & { \\mathrm { i f ~ } \\ell ( f _ { \\pmb { w + v } ^ { k } } ( x _ { i } ^ { \\prime } ) , y _ { i } ) > c _ { m i n } } \\\\ { 1 } & { \\mathrm { i f ~ } \\ell ( f _ { \\pmb { w + v } ^ { k } } ( x _ { i } ^ { \\prime } ) , y _ { i } ) \\leq c _ { m i n } } \\end{array} \\right. } \\end{array}", "type": "interline_equation", "image_path": "7d0912a7f1e94c34b52730fda58bc81a07a4b7a8a81559896aed4b3e0f410fc9.jpg" } ] } ], "index": 4.5, "virtual_lines": [ { "bbox": [ 194, 121, 417, 137.0 ], "spans": [], "index": 3 }, { "bbox": [ 194, 137.0, 417, 153.0 ], "spans": [], "index": 4 }, { "bbox": [ 194, 153.0, 417, 169.0 ], "spans": [], "index": 5 }, { "bbox": [ 194, 169.0, 417, 185.0 ], "spans": [], "index": 6 } ] }, { "type": "text", "bbox": [ 106, 189, 505, 343 ], "lines": [ { "bbox": [ 106, 189, 505, 201 ], "spans": [ { "bbox": [ 106, 189, 505, 201 ], "score": 1.0, "content": "The proposed Robust Weight Perturbation (RWP) algorithm is shown in Algorithm 1. We use PGD", "type": "text" } ], "index": 7 }, { "bbox": [ 106, 200, 505, 213 ], "spans": [ { "bbox": [ 106, 200, 505, 213 ], "score": 1.0, "content": "attack (Madry et al., 2017) to generate the training adversarial examples, which can be also ex-", "type": "text" } ], "index": 8 }, { "bbox": [ 106, 212, 504, 223 ], "spans": [ { "bbox": [ 106, 212, 504, 223 ], "score": 1.0, "content": "tended to other variants such as TRADES (Zhang et al., 2019) and RST (Carmon et al., 2019). The", "type": "text" } ], "index": 9 }, { "bbox": [ 105, 222, 505, 235 ], "spans": [ { "bbox": [ 105, 222, 195, 235 ], "score": 1.0, "content": "mimimum LSC value", "type": "text" }, { "bbox": [ 195, 223, 216, 233 ], "score": 0.89, "content": "c _ { m i n }", "type": "inline_equation" }, { "bbox": [ 216, 222, 505, 235 ], "score": 1.0, "content": "controls the minimum classification loss (minimum weight perturbation", "type": "text" } ], "index": 10 }, { "bbox": [ 105, 233, 506, 246 ], "spans": [ { "bbox": [ 105, 233, 506, 246 ], "score": 1.0, "content": "strength) of the adversarial examples during network training. In the early stages of training, the", "type": "text" } ], "index": 11 }, { "bbox": [ 105, 243, 505, 257 ], "spans": [ { "bbox": [ 105, 243, 369, 257 ], "score": 1.0, "content": "classification loss of adversarial example is generally larger than", "type": "text" }, { "bbox": [ 370, 245, 390, 255 ], "score": 0.88, "content": "c _ { m i n }", "type": "inline_equation" }, { "bbox": [ 390, 243, 505, 257 ], "score": 1.0, "content": "corresponding to no weight", "type": "text" } ], "index": 12 }, { "bbox": [ 104, 254, 506, 268 ], "spans": [ { "bbox": [ 104, 254, 506, 268 ], "score": 1.0, "content": "perturbation process. The classification loss of adversarial examples then decreases as training pro-", "type": "text" } ], "index": 13 }, { "bbox": [ 104, 266, 506, 278 ], "spans": [ { "bbox": [ 104, 266, 506, 278 ], "score": 1.0, "content": "gresses. At each optimization step, we monitor the classification loss of the adversarial example and", "type": "text" } ], "index": 14 }, { "bbox": [ 105, 277, 505, 290 ], "spans": [ { "bbox": [ 105, 277, 505, 290 ], "score": 1.0, "content": "conduct the weight perturbation process for adversarial examples whose classification loss is already", "type": "text" } ], "index": 15 }, { "bbox": [ 105, 288, 505, 300 ], "spans": [ { "bbox": [ 105, 288, 158, 300 ], "score": 1.0, "content": "smaller than", "type": "text" }, { "bbox": [ 159, 289, 179, 299 ], "score": 0.89, "content": "c _ { m i n }", "type": "inline_equation" }, { "bbox": [ 180, 288, 339, 300 ], "score": 1.0, "content": ", enabled by an indicator control vector", "type": "text" }, { "bbox": [ 339, 288, 348, 298 ], "score": 0.64, "content": "V", "type": "inline_equation" }, { "bbox": [ 349, 288, 505, 300 ], "score": 1.0, "content": ". At each perturbation step, the weight", "type": "text" } ], "index": 16 }, { "bbox": [ 104, 298, 506, 312 ], "spans": [ { "bbox": [ 104, 298, 158, 312 ], "score": 1.0, "content": "perturbation", "type": "text" }, { "bbox": [ 159, 301, 166, 308 ], "score": 0.68, "content": "\\pmb { v }", "type": "inline_equation" }, { "bbox": [ 166, 298, 506, 312 ], "score": 1.0, "content": "will be updated to increase the classification loss of the corresponding adversarial", "type": "text" } ], "index": 17 }, { "bbox": [ 105, 310, 505, 322 ], "spans": [ { "bbox": [ 105, 310, 457, 322 ], "score": 1.0, "content": "example. When the classification loss of training adversarial examples is all higher than", "type": "text" }, { "bbox": [ 457, 311, 478, 321 ], "score": 0.89, "content": "c _ { m i n }", "type": "inline_equation" }, { "bbox": [ 479, 310, 505, 322 ], "score": 1.0, "content": "or the", "type": "text" } ], "index": 18 }, { "bbox": [ 105, 320, 506, 333 ], "spans": [ { "bbox": [ 105, 320, 506, 333 ], "score": 1.0, "content": "number of perturbation step reaches the defined value, we stop the weight perturbation process and", "type": "text" } ], "index": 19 }, { "bbox": [ 105, 331, 373, 346 ], "spans": [ { "bbox": [ 105, 331, 268, 346 ], "score": 1.0, "content": "inject the generated weight perturbation", "type": "text" }, { "bbox": [ 268, 334, 275, 342 ], "score": 0.68, "content": "\\textbf { { v } }", "type": "inline_equation" }, { "bbox": [ 275, 331, 373, 346 ], "score": 1.0, "content": "for adversarial training.", "type": "text" } ], "index": 20 } ], "index": 13.5, "bbox_fs": [ 104, 189, 506, 346 ] }, { "type": "title", "bbox": [ 108, 359, 200, 372 ], "lines": [ { "bbox": [ 104, 357, 202, 374 ], "spans": [ { "bbox": [ 104, 357, 202, 374 ], "score": 1.0, "content": "5 EXPERIMENTS", "type": "text" } ], "index": 21 } ], "index": 21 }, { "type": "text", "bbox": [ 107, 384, 503, 406 ], "lines": [ { "bbox": [ 105, 383, 504, 396 ], "spans": [ { "bbox": [ 105, 383, 504, 396 ], "score": 1.0, "content": "In this section, we conduct comprehensive experiments to evaluate the effectiveness of RWP includ-", "type": "text" } ], "index": 22 }, { "bbox": [ 105, 395, 395, 407 ], "spans": [ { "bbox": [ 105, 395, 395, 407 ], "score": 1.0, "content": "ing its experimental settings, robustness evaluation and ablation studies.", "type": "text" } ], "index": 23 } ], "index": 22.5, "bbox_fs": [ 105, 383, 504, 407 ] }, { "type": "title", "bbox": [ 107, 420, 230, 431 ], "lines": [ { "bbox": [ 106, 419, 231, 432 ], "spans": [ { "bbox": [ 106, 419, 231, 432 ], "score": 1.0, "content": "5.1 EXPERIMENTAL SETUP", "type": "text" } ], "index": 24 } ], "index": 24 }, { "type": "text", "bbox": [ 106, 440, 505, 649 ], "lines": [ { "bbox": [ 106, 440, 505, 453 ], "spans": [ { "bbox": [ 106, 440, 505, 453 ], "score": 1.0, "content": "Baselines and Implementation Details. Our implementation is based on PyTorch and the code", "type": "text" } ], "index": 25 }, { "bbox": [ 106, 452, 505, 463 ], "spans": [ { "bbox": [ 106, 452, 505, 463 ], "score": 1.0, "content": "as well as other related resources will be released for public use and verification. We conduct ex-", "type": "text" } ], "index": 26 }, { "bbox": [ 105, 462, 505, 474 ], "spans": [ { "bbox": [ 105, 462, 505, 474 ], "score": 1.0, "content": "tensive experiments across three benchmark datasets (CIFAR-10 (Krizhevsky et al., 2009), CIFAR-", "type": "text" } ], "index": 27 }, { "bbox": [ 106, 473, 506, 486 ], "spans": [ { "bbox": [ 106, 473, 469, 486 ], "score": 1.0, "content": "100 (Krizhevsky et al., 2009) and SVHN (Netzer et al., 2011)) and two threat models", "type": "text" }, { "bbox": [ 469, 474, 486, 484 ], "score": 0.87, "content": "L _ { \\infty }", "type": "inline_equation" }, { "bbox": [ 486, 473, 506, 486 ], "score": 1.0, "content": "and", "type": "text" } ], "index": 28 }, { "bbox": [ 106, 484, 505, 497 ], "spans": [ { "bbox": [ 106, 485, 119, 496 ], "score": 0.78, "content": "L _ { 2 }", "type": "inline_equation" }, { "bbox": [ 120, 484, 505, 497 ], "score": 1.0, "content": "). We use PreAct ResNet-18 (He et al., 2016) and Wide ResNet (WRN-28-10 and WRN-34-10)", "type": "text" } ], "index": 29 }, { "bbox": [ 106, 496, 505, 507 ], "spans": [ { "bbox": [ 106, 496, 505, 507 ], "score": 1.0, "content": "(Zagoruyko & Komodakis, 2016) as the network structure following Wu et al. (2020). We compare", "type": "text" } ], "index": 30 }, { "bbox": [ 106, 506, 505, 519 ], "spans": [ { "bbox": [ 106, 506, 505, 519 ], "score": 1.0, "content": "the performance of the proposed method on a number of baseline methods: 1) standard adversarial", "type": "text" } ], "index": 31 }, { "bbox": [ 105, 515, 506, 532 ], "spans": [ { "bbox": [ 105, 515, 506, 532 ], "score": 1.0, "content": "training without weight perturbation, including vanilla AT (Madry et al., 2017), TRADES (Zhang", "type": "text" } ], "index": 32 }, { "bbox": [ 104, 527, 505, 542 ], "spans": [ { "bbox": [ 104, 527, 505, 542 ], "score": 1.0, "content": "et al., 2019) and RST (Carmon et al., 2019); 2) adversarial training with adversarial weight per-", "type": "text" } ], "index": 33 }, { "bbox": [ 104, 538, 506, 552 ], "spans": [ { "bbox": [ 104, 538, 506, 552 ], "score": 1.0, "content": "turbation (AWP) (Wu et al., 2020). For training, the network is trained for 200 epochs using SGD", "type": "text" } ], "index": 34 }, { "bbox": [ 105, 549, 505, 563 ], "spans": [ { "bbox": [ 105, 549, 247, 563 ], "score": 1.0, "content": "with momentum 0.9, weight decay", "type": "text" }, { "bbox": [ 247, 550, 286, 561 ], "score": 0.91, "content": "5 \\times 1 0 ^ { - 4 }", "type": "inline_equation" }, { "bbox": [ 286, 549, 505, 563 ], "score": 1.0, "content": ", and an initial learning rate of 0.1. The learning rate is", "type": "text" } ], "index": 35 }, { "bbox": [ 105, 561, 505, 574 ], "spans": [ { "bbox": [ 105, 561, 505, 574 ], "score": 1.0, "content": "divided by 10 at the 100-th and 150-th epoch. Standard data augmentation including random crops", "type": "text" } ], "index": 36 }, { "bbox": [ 106, 572, 504, 583 ], "spans": [ { "bbox": [ 106, 572, 504, 583 ], "score": 1.0, "content": "with 4 pixels of padding and random horizontal flips are applied. For testing, model robustness is", "type": "text" } ], "index": 37 }, { "bbox": [ 105, 583, 505, 596 ], "spans": [ { "bbox": [ 105, 583, 505, 596 ], "score": 1.0, "content": "evaluated by measuring the accuracy of the model under different adversarial attacks. For hyper-", "type": "text" } ], "index": 38 }, { "bbox": [ 105, 594, 506, 606 ], "spans": [ { "bbox": [ 105, 594, 290, 606 ], "score": 1.0, "content": "parameters in RWP, we set perturbation step", "type": "text" }, { "bbox": [ 290, 594, 330, 605 ], "score": 0.91, "content": "K _ { 2 } = 1 0", "type": "inline_equation" }, { "bbox": [ 331, 594, 506, 606 ], "score": 1.0, "content": "for all datasets. The minimum LSC value", "type": "text" } ], "index": 39 }, { "bbox": [ 106, 604, 506, 619 ], "spans": [ { "bbox": [ 106, 605, 156, 617 ], "score": 0.89, "content": "c _ { m i n } = 1 . 7", "type": "inline_equation" }, { "bbox": [ 157, 604, 221, 619 ], "score": 1.0, "content": "for CIFAR-10,", "type": "text" }, { "bbox": [ 221, 605, 271, 616 ], "score": 0.89, "content": "c _ { m i n } = 2 . 2", "type": "inline_equation" }, { "bbox": [ 271, 604, 335, 619 ], "score": 1.0, "content": "for SVHN and", "type": "text" }, { "bbox": [ 335, 605, 385, 616 ], "score": 0.9, "content": "c _ { m i n } = 4 . 0", "type": "inline_equation" }, { "bbox": [ 386, 604, 506, 619 ], "score": 1.0, "content": "for CIFAR-100. The weight", "type": "text" } ], "index": 40 }, { "bbox": [ 105, 616, 505, 628 ], "spans": [ { "bbox": [ 105, 616, 197, 628 ], "score": 1.0, "content": "perturbation budget of", "type": "text" }, { "bbox": [ 198, 617, 235, 627 ], "score": 0.91, "content": "\\gamma = 0 . 0 1", "type": "inline_equation" }, { "bbox": [ 235, 616, 289, 628 ], "score": 1.0, "content": "for AT-RWP,", "type": "text" }, { "bbox": [ 289, 616, 333, 628 ], "score": 0.89, "content": "\\gamma = 0 . 0 0 5", "type": "inline_equation" }, { "bbox": [ 333, 616, 505, 628 ], "score": 1.0, "content": "for TRADES-RWP and RST-RWP follow-", "type": "text" } ], "index": 41 }, { "bbox": [ 105, 627, 505, 640 ], "spans": [ { "bbox": [ 105, 627, 505, 640 ], "score": 1.0, "content": "ing literature (Wu et al., 2020). Other hyper-parameters of the baselines are configured as per their", "type": "text" } ], "index": 42 }, { "bbox": [ 105, 638, 171, 651 ], "spans": [ { "bbox": [ 105, 638, 171, 651 ], "score": 1.0, "content": "original papers.", "type": "text" } ], "index": 43 } ], "index": 34, "bbox_fs": [ 104, 440, 506, 651 ] }, { "type": "text", "bbox": [ 106, 654, 505, 732 ], "lines": [ { "bbox": [ 105, 654, 505, 667 ], "spans": [ { "bbox": [ 105, 654, 505, 667 ], "score": 1.0, "content": "Adversarial Setting. The training attack is 10-step PGD attack with random start. We follow the", "type": "text" } ], "index": 44 }, { "bbox": [ 105, 666, 505, 678 ], "spans": [ { "bbox": [ 105, 666, 273, 678 ], "score": 1.0, "content": "same settings in Rice et al. (2020) : for", "type": "text" }, { "bbox": [ 273, 666, 290, 677 ], "score": 0.89, "content": "L _ { \\infty }", "type": "inline_equation" }, { "bbox": [ 290, 666, 349, 678 ], "score": 1.0, "content": "threat model,", "type": "text" }, { "bbox": [ 349, 666, 396, 677 ], "score": 0.9, "content": "\\epsilon = 8 / 2 5 5", "type": "inline_equation" }, { "bbox": [ 396, 666, 439, 678 ], "score": 1.0, "content": ", step size", "type": "text" }, { "bbox": [ 439, 666, 489, 677 ], "score": 0.9, "content": "\\alpha = 1 / 2 5 5", "type": "inline_equation" }, { "bbox": [ 489, 666, 505, 678 ], "score": 1.0, "content": "for", "type": "text" } ], "index": 45 }, { "bbox": [ 106, 677, 505, 689 ], "spans": [ { "bbox": [ 106, 677, 157, 689 ], "score": 1.0, "content": "SVHN, and", "type": "text" }, { "bbox": [ 158, 677, 208, 688 ], "score": 0.89, "content": "\\alpha = 2 / 2 5 5", "type": "inline_equation" }, { "bbox": [ 208, 677, 371, 689 ], "score": 1.0, "content": "for both CIFAR10 and CIFAR100; for", "type": "text" }, { "bbox": [ 372, 677, 384, 688 ], "score": 0.87, "content": "L _ { 2 }", "type": "inline_equation" }, { "bbox": [ 384, 677, 444, 689 ], "score": 1.0, "content": "threat model,", "type": "text" }, { "bbox": [ 444, 677, 501, 689 ], "score": 0.82, "content": "\\epsilon = 1 2 8 / 2 5 5", "type": "inline_equation" }, { "bbox": [ 502, 677, 505, 689 ], "score": 1.0, "content": ",", "type": "text" } ], "index": 46 }, { "bbox": [ 105, 688, 505, 700 ], "spans": [ { "bbox": [ 105, 688, 143, 700 ], "score": 1.0, "content": "step size", "type": "text" }, { "bbox": [ 144, 688, 195, 699 ], "score": 0.85, "content": "\\alpha = 1 5 / 2 5 5", "type": "inline_equation" }, { "bbox": [ 195, 688, 505, 700 ], "score": 1.0, "content": "for all datasets. The test attacks used for robustness evaluation are generated", "type": "text" } ], "index": 47 }, { "bbox": [ 105, 699, 505, 711 ], "spans": [ { "bbox": [ 105, 699, 505, 711 ], "score": 1.0, "content": "from the original test set images by attacking the defense models using different attacking methods,", "type": "text" } ], "index": 48 }, { "bbox": [ 105, 709, 506, 723 ], "spans": [ { "bbox": [ 105, 709, 266, 723 ], "score": 1.0, "content": "including: FGSM, PGD-20, PGD-100,", "type": "text" }, { "bbox": [ 266, 710, 300, 721 ], "score": 0.64, "content": "\\mathrm { C } \\& \\mathbf { W } _ { \\infty }", "type": "inline_equation" }, { "bbox": [ 300, 709, 305, 723 ], "score": 0.0, "content": "", "type": "text" }, { "bbox": [ 305, 710, 321, 721 ], "score": 0.86, "content": "L _ { \\infty }", "type": "inline_equation" }, { "bbox": [ 322, 709, 506, 723 ], "score": 1.0, "content": "version of C&W optimized by PGD for 100", "type": "text" } ], "index": 49 }, { "bbox": [ 105, 721, 227, 733 ], "spans": [ { "bbox": [ 105, 721, 227, 733 ], "score": 1.0, "content": "steps) and Auto Attack (AA).", "type": "text" } ], "index": 50 } ], "index": 47, "bbox_fs": [ 105, 654, 506, 733 ] } ] }, { "preproc_blocks": [ { "type": "title", "bbox": [ 108, 82, 246, 93 ], "lines": [ { "bbox": [ 105, 81, 249, 95 ], "spans": [ { "bbox": [ 105, 81, 249, 95 ], "score": 1.0, "content": "5.2 ROBUSTNESS EVALUATION", "type": "text" } ], "index": 0 } ], "index": 0 }, { "type": "text", "bbox": [ 106, 107, 505, 261 ], "lines": [ { "bbox": [ 105, 106, 505, 120 ], "spans": [ { "bbox": [ 105, 106, 505, 120 ], "score": 1.0, "content": "Performance Evaluations. To validate the effectiveness of the proposed RWP, we conduct per-", "type": "text" } ], "index": 1 }, { "bbox": [ 106, 119, 506, 130 ], "spans": [ { "bbox": [ 106, 119, 506, 130 ], "score": 1.0, "content": "formance evaluation on vanilla AT, AT-AWP and AT-RWP across different benchmark datasets and", "type": "text" } ], "index": 2 }, { "bbox": [ 105, 128, 506, 142 ], "spans": [ { "bbox": [ 105, 128, 506, 142 ], "score": 1.0, "content": "threat models using PreAct ResNet-18. We report the accuracy on the test images under PGD-20", "type": "text" } ], "index": 3 }, { "bbox": [ 106, 141, 505, 152 ], "spans": [ { "bbox": [ 106, 141, 505, 152 ], "score": 1.0, "content": "attack. The evaluation results are summarized in Table 1. “Best” denotes the highest robustness that", "type": "text" } ], "index": 4 }, { "bbox": [ 106, 151, 504, 163 ], "spans": [ { "bbox": [ 106, 151, 504, 163 ], "score": 1.0, "content": "ever achieved at different checkpoints and ”last” denotes the robustness at the last epoch checkpoint.", "type": "text" } ], "index": 5 }, { "bbox": [ 105, 162, 505, 174 ], "spans": [ { "bbox": [ 105, 162, 505, 174 ], "score": 1.0, "content": "It is observed vanilla AT suffers from severe robust overfitting (the performance gap between ”best”", "type": "text" } ], "index": 6 }, { "bbox": [ 105, 172, 505, 186 ], "spans": [ { "bbox": [ 105, 172, 505, 186 ], "score": 1.0, "content": "and ”last” is very large). AT-AWP and AT-RWP method narrow the performance gap significantly", "type": "text" } ], "index": 7 }, { "bbox": [ 105, 184, 506, 196 ], "spans": [ { "bbox": [ 105, 184, 506, 196 ], "score": 1.0, "content": "over the vanilla AT model due to suppression of robust overfitting. Moreover, on CIFAR-10 dataset", "type": "text" } ], "index": 8 }, { "bbox": [ 106, 195, 505, 208 ], "spans": [ { "bbox": [ 106, 195, 147, 208 ], "score": 1.0, "content": "under the", "type": "text" }, { "bbox": [ 148, 195, 164, 206 ], "score": 0.9, "content": "L _ { \\infty }", "type": "inline_equation" }, { "bbox": [ 165, 195, 279, 208 ], "score": 1.0, "content": "attack, vanilla AT achieves", "type": "text" }, { "bbox": [ 279, 195, 311, 206 ], "score": 0.88, "content": "5 2 . 7 9 \\%", "type": "inline_equation" }, { "bbox": [ 312, 195, 505, 208 ], "score": 1.0, "content": "”best” test robustness. The AT-AWP approach", "type": "text" } ], "index": 9 }, { "bbox": [ 106, 206, 505, 219 ], "spans": [ { "bbox": [ 106, 206, 215, 219 ], "score": 1.0, "content": "boosts the performance to", "type": "text" }, { "bbox": [ 215, 206, 247, 217 ], "score": 0.88, "content": "5 5 . 3 9 \\%", "type": "inline_equation" }, { "bbox": [ 248, 206, 505, 219 ], "score": 1.0, "content": ". The proposed approach further outperforms both methods by", "type": "text" } ], "index": 10 }, { "bbox": [ 104, 216, 506, 231 ], "spans": [ { "bbox": [ 104, 216, 291, 231 ], "score": 1.0, "content": "a large margin, improving over vanilla AT by", "type": "text" }, { "bbox": [ 292, 217, 319, 228 ], "score": 0.88, "content": "5 . 7 6 \\%", "type": "inline_equation" }, { "bbox": [ 319, 216, 349, 231 ], "score": 1.0, "content": ", and is", "type": "text" }, { "bbox": [ 349, 217, 377, 228 ], "score": 0.88, "content": "3 . 1 6 \\%", "type": "inline_equation" }, { "bbox": [ 378, 216, 506, 231 ], "score": 1.0, "content": "better than AT-AWP, achieving", "type": "text" } ], "index": 11 }, { "bbox": [ 106, 227, 506, 240 ], "spans": [ { "bbox": [ 106, 228, 138, 239 ], "score": 0.87, "content": "5 8 . 5 5 \\%", "type": "inline_equation" }, { "bbox": [ 139, 227, 506, 240 ], "score": 1.0, "content": "accuracy under the standard 20 steps PGD attack. Similar patten has been observed on other", "type": "text" } ], "index": 12 }, { "bbox": [ 106, 239, 506, 252 ], "spans": [ { "bbox": [ 106, 239, 506, 252 ], "score": 1.0, "content": "datasets and threat model. AT-RWP consistently improves the test robustness across a wide range of", "type": "text" } ], "index": 13 }, { "bbox": [ 105, 249, 450, 263 ], "spans": [ { "bbox": [ 105, 249, 450, 263 ], "score": 1.0, "content": "datasets and threat models, demonstrating the effectiveness of the proposed approach.", "type": "text" } ], "index": 14 } ], "index": 7.5 }, { "type": "table", "bbox": [ 131, 302, 478, 412 ], "blocks": [ { "type": "table_caption", "bbox": [ 135, 290, 474, 302 ], "group_id": 0, "lines": [ { "bbox": [ 135, 289, 475, 303 ], "spans": [ { "bbox": [ 135, 289, 235, 303 ], "score": 1.0, "content": "Table 1: Test robustness", "type": "text" }, { "bbox": [ 236, 291, 251, 301 ], "score": 0.67, "content": "( \\% )", "type": "inline_equation" }, { "bbox": [ 252, 289, 475, 303 ], "score": 1.0, "content": "of AT, AT-AWP and AT-RWP using PreAct ResNet-18.", "type": "text" } ], "index": 15 } ], "index": 15 }, { "type": "table_body", "bbox": [ 131, 302, 478, 412 ], "group_id": 0, "lines": [ { "bbox": [ 131, 302, 478, 412 ], "spans": [ { "bbox": [ 131, 302, 478, 412 ], "score": 0.984, "html": "
Threat ModelMethodSVHNCIFAR-10CIFAR-100
BestLastBestLastBestLast
L8AT53.3644.4952.7944.4427.2220.82
AT-AWP59.1255.8755.3954.7330.7130.28
AT-RWP61.1557.4558.5558.0131.1730.64
L2AT66.8765.0369.1565.9341.3335.27
AT-AWP72.5767.7372.6972.0845.6044.66
AT-RWP73.3569.4874.4773.8445.7145.05
", "type": "table", "image_path": "45802b10bc18e868a421b53cff82ff389c7a141952169fe23eae3703c4e7ad74.jpg" } ] } ], "index": 17, "virtual_lines": [ { "bbox": [ 131, 302, 478, 338.6666666666667 ], "spans": [], "index": 16 }, { "bbox": [ 131, 338.6666666666667, 478, 375.33333333333337 ], "spans": [], "index": 17 }, { "bbox": [ 131, 375.33333333333337, 478, 412.00000000000006 ], "spans": [], "index": 18 } ] } ], "index": 16.0 }, { "type": "text", "bbox": [ 106, 421, 505, 553 ], "lines": [ { "bbox": [ 105, 420, 505, 434 ], "spans": [ { "bbox": [ 105, 420, 505, 434 ], "score": 1.0, "content": "Benchmarking the state-of-the-art Robustness. To manifest the full power of our proposed per-", "type": "text" } ], "index": 19 }, { "bbox": [ 105, 431, 506, 445 ], "spans": [ { "bbox": [ 105, 431, 462, 445 ], "score": 1.0, "content": "turbation strategy and also benchmark the state-of-the-art robustness on CIFAR-10 under", "type": "text" }, { "bbox": [ 462, 433, 478, 443 ], "score": 0.9, "content": "\\mathrm { L } _ { \\infty }", "type": "inline_equation" }, { "bbox": [ 479, 431, 506, 445 ], "score": 1.0, "content": "threat", "type": "text" } ], "index": 20 }, { "bbox": [ 105, 443, 506, 456 ], "spans": [ { "bbox": [ 105, 443, 506, 456 ], "score": 1.0, "content": "model, we conduct experiments on the large capacity network with different baseline methods. We", "type": "text" } ], "index": 21 }, { "bbox": [ 106, 454, 506, 466 ], "spans": [ { "bbox": [ 106, 454, 506, 466 ], "score": 1.0, "content": "train Wide ResNet-34-10 for AT and TRADES, and Wide ResNet-28-10 for RST following their", "type": "text" } ], "index": 22 }, { "bbox": [ 105, 465, 506, 477 ], "spans": [ { "bbox": [ 105, 465, 506, 477 ], "score": 1.0, "content": "original papers. We evaluate the adversarial robustness of trained model with various test attack", "type": "text" } ], "index": 23 }, { "bbox": [ 106, 476, 505, 488 ], "spans": [ { "bbox": [ 106, 476, 505, 488 ], "score": 1.0, "content": "and report the “best” test robustness, with the results shown in Table 2. “Natural” denotes the accu-", "type": "text" } ], "index": 24 }, { "bbox": [ 105, 487, 505, 500 ], "spans": [ { "bbox": [ 105, 487, 505, 500 ], "score": 1.0, "content": "racy on natural test data. First, it is observed that the natural accuracy of RWP model consistently", "type": "text" } ], "index": 25 }, { "bbox": [ 106, 498, 505, 510 ], "spans": [ { "bbox": [ 106, 498, 505, 510 ], "score": 1.0, "content": "outperforms AWP by a large margin. It is due to the benefits that our RWP avoids the excessive", "type": "text" } ], "index": 26 }, { "bbox": [ 106, 509, 506, 521 ], "spans": [ { "bbox": [ 106, 509, 506, 521 ], "score": 1.0, "content": "weight perturbation. Moreover, RWP achieves the best adversarial robustness against all types of", "type": "text" } ], "index": 27 }, { "bbox": [ 106, 520, 505, 532 ], "spans": [ { "bbox": [ 106, 520, 505, 532 ], "score": 1.0, "content": "attack across a wide range of baseline methods, which verifies that RWP is effective in general and", "type": "text" } ], "index": 28 }, { "bbox": [ 106, 531, 505, 543 ], "spans": [ { "bbox": [ 106, 531, 505, 543 ], "score": 1.0, "content": "improves adversarial robustness reliably rather than improper tuning of hyper-parameters of attacks,", "type": "text" } ], "index": 29 }, { "bbox": [ 105, 541, 241, 555 ], "spans": [ { "bbox": [ 105, 541, 241, 555 ], "score": 1.0, "content": "gradient obfuscation or masking.", "type": "text" } ], "index": 30 } ], "index": 24.5 }, { "type": "table", "bbox": [ 138, 583, 473, 714 ], "blocks": [ { "type": "table_caption", "bbox": [ 128, 571, 479, 582 ], "group_id": 1, "lines": [ { "bbox": [ 129, 570, 480, 584 ], "spans": [ { "bbox": [ 129, 570, 229, 584 ], "score": 1.0, "content": "Table 2: Test robustness", "type": "text" }, { "bbox": [ 230, 572, 245, 582 ], "score": 0.72, "content": "( \\% )", "type": "inline_equation" }, { "bbox": [ 246, 570, 408, 584 ], "score": 1.0, "content": "on CIFAR-10 using Wide ResNet under", "type": "text" }, { "bbox": [ 408, 572, 424, 582 ], "score": 0.89, "content": "L _ { \\infty }", "type": "inline_equation" }, { "bbox": [ 424, 570, 480, 584 ], "score": 1.0, "content": "threat model.", "type": "text" } ], "index": 31 } ], "index": 31 }, { "type": "table_body", "bbox": [ 138, 583, 473, 714 ], "group_id": 1, "lines": [ { "bbox": [ 138, 583, 473, 714 ], "spans": [ { "bbox": [ 138, 583, 473, 714 ], "score": 0.985, "html": "
DefenseNaturalFGSMPGD-20PGD-100C&WAA
AT86.0761.7656.1055.7954.1952.60
AT-AWP85.5762.9058.1457.9455.9654.04
AT-RWP86.8666.2262.8762.8756.6254.61
TRADES84.6561.3256.3356.0754.2053.08
TRADES-AWP85.3663.4959.2759.1257.0756.17
TRADES-RWP86.1464.7060.4560.3058.0757.20
RST89.6969.6062.6062.2260.4759.53
RST-AWP88.2567.9463.7363.5861.6260.05
RST-RWP88.8769.7164.1163.9262.0360.36
", "type": "table", "image_path": "c358e97c8b763776c5cf4fa2be767217492a15a71f8f43feb9865a88292bf574.jpg" } ] } ], "index": 33, "virtual_lines": [ { "bbox": [ 138, 583, 473, 626.6666666666666 ], "spans": [], "index": 32 }, { "bbox": [ 138, 626.6666666666666, 473, 670.3333333333333 ], "spans": [], "index": 33 }, { "bbox": [ 138, 670.3333333333333, 473, 713.9999999999999 ], "spans": [], "index": 34 } ] } ], "index": 32.0 } ], "page_idx": 7, "page_size": [ 612, 792 ], "discarded_blocks": [ { "type": "discarded", "bbox": [ 107, 27, 308, 37 ], "lines": [ { "bbox": [ 107, 26, 308, 38 ], "spans": [ { "bbox": [ 107, 26, 308, 38 ], "score": 1.0, "content": "Under review as a conference paper at ICLR 2022", "type": "text" } ] } ] }, { "type": "discarded", "bbox": [ 302, 751, 309, 760 ], "lines": [ { "bbox": [ 302, 750, 309, 761 ], "spans": [ { "bbox": [ 302, 750, 309, 761 ], "score": 1.0, "content": "8", "type": "text" } ] } ] } ], "para_blocks": [ { "type": "title", "bbox": [ 108, 82, 246, 93 ], "lines": [ { "bbox": [ 105, 81, 249, 95 ], "spans": [ { "bbox": [ 105, 81, 249, 95 ], "score": 1.0, "content": "5.2 ROBUSTNESS EVALUATION", "type": "text" } ], "index": 0 } ], "index": 0 }, { "type": "text", "bbox": [ 106, 107, 505, 261 ], "lines": [ { "bbox": [ 105, 106, 505, 120 ], "spans": [ { "bbox": [ 105, 106, 505, 120 ], "score": 1.0, "content": "Performance Evaluations. To validate the effectiveness of the proposed RWP, we conduct per-", "type": "text" } ], "index": 1 }, { "bbox": [ 106, 119, 506, 130 ], "spans": [ { "bbox": [ 106, 119, 506, 130 ], "score": 1.0, "content": "formance evaluation on vanilla AT, AT-AWP and AT-RWP across different benchmark datasets and", "type": "text" } ], "index": 2 }, { "bbox": [ 105, 128, 506, 142 ], "spans": [ { "bbox": [ 105, 128, 506, 142 ], "score": 1.0, "content": "threat models using PreAct ResNet-18. We report the accuracy on the test images under PGD-20", "type": "text" } ], "index": 3 }, { "bbox": [ 106, 141, 505, 152 ], "spans": [ { "bbox": [ 106, 141, 505, 152 ], "score": 1.0, "content": "attack. The evaluation results are summarized in Table 1. “Best” denotes the highest robustness that", "type": "text" } ], "index": 4 }, { "bbox": [ 106, 151, 504, 163 ], "spans": [ { "bbox": [ 106, 151, 504, 163 ], "score": 1.0, "content": "ever achieved at different checkpoints and ”last” denotes the robustness at the last epoch checkpoint.", "type": "text" } ], "index": 5 }, { "bbox": [ 105, 162, 505, 174 ], "spans": [ { "bbox": [ 105, 162, 505, 174 ], "score": 1.0, "content": "It is observed vanilla AT suffers from severe robust overfitting (the performance gap between ”best”", "type": "text" } ], "index": 6 }, { "bbox": [ 105, 172, 505, 186 ], "spans": [ { "bbox": [ 105, 172, 505, 186 ], "score": 1.0, "content": "and ”last” is very large). AT-AWP and AT-RWP method narrow the performance gap significantly", "type": "text" } ], "index": 7 }, { "bbox": [ 105, 184, 506, 196 ], "spans": [ { "bbox": [ 105, 184, 506, 196 ], "score": 1.0, "content": "over the vanilla AT model due to suppression of robust overfitting. Moreover, on CIFAR-10 dataset", "type": "text" } ], "index": 8 }, { "bbox": [ 106, 195, 505, 208 ], "spans": [ { "bbox": [ 106, 195, 147, 208 ], "score": 1.0, "content": "under the", "type": "text" }, { "bbox": [ 148, 195, 164, 206 ], "score": 0.9, "content": "L _ { \\infty }", "type": "inline_equation" }, { "bbox": [ 165, 195, 279, 208 ], "score": 1.0, "content": "attack, vanilla AT achieves", "type": "text" }, { "bbox": [ 279, 195, 311, 206 ], "score": 0.88, "content": "5 2 . 7 9 \\%", "type": "inline_equation" }, { "bbox": [ 312, 195, 505, 208 ], "score": 1.0, "content": "”best” test robustness. The AT-AWP approach", "type": "text" } ], "index": 9 }, { "bbox": [ 106, 206, 505, 219 ], "spans": [ { "bbox": [ 106, 206, 215, 219 ], "score": 1.0, "content": "boosts the performance to", "type": "text" }, { "bbox": [ 215, 206, 247, 217 ], "score": 0.88, "content": "5 5 . 3 9 \\%", "type": "inline_equation" }, { "bbox": [ 248, 206, 505, 219 ], "score": 1.0, "content": ". The proposed approach further outperforms both methods by", "type": "text" } ], "index": 10 }, { "bbox": [ 104, 216, 506, 231 ], "spans": [ { "bbox": [ 104, 216, 291, 231 ], "score": 1.0, "content": "a large margin, improving over vanilla AT by", "type": "text" }, { "bbox": [ 292, 217, 319, 228 ], "score": 0.88, "content": "5 . 7 6 \\%", "type": "inline_equation" }, { "bbox": [ 319, 216, 349, 231 ], "score": 1.0, "content": ", and is", "type": "text" }, { "bbox": [ 349, 217, 377, 228 ], "score": 0.88, "content": "3 . 1 6 \\%", "type": "inline_equation" }, { "bbox": [ 378, 216, 506, 231 ], "score": 1.0, "content": "better than AT-AWP, achieving", "type": "text" } ], "index": 11 }, { "bbox": [ 106, 227, 506, 240 ], "spans": [ { "bbox": [ 106, 228, 138, 239 ], "score": 0.87, "content": "5 8 . 5 5 \\%", "type": "inline_equation" }, { "bbox": [ 139, 227, 506, 240 ], "score": 1.0, "content": "accuracy under the standard 20 steps PGD attack. Similar patten has been observed on other", "type": "text" } ], "index": 12 }, { "bbox": [ 106, 239, 506, 252 ], "spans": [ { "bbox": [ 106, 239, 506, 252 ], "score": 1.0, "content": "datasets and threat model. AT-RWP consistently improves the test robustness across a wide range of", "type": "text" } ], "index": 13 }, { "bbox": [ 105, 249, 450, 263 ], "spans": [ { "bbox": [ 105, 249, 450, 263 ], "score": 1.0, "content": "datasets and threat models, demonstrating the effectiveness of the proposed approach.", "type": "text" } ], "index": 14 } ], "index": 7.5, "bbox_fs": [ 104, 106, 506, 263 ] }, { "type": "table", "bbox": [ 131, 302, 478, 412 ], "blocks": [ { "type": "table_caption", "bbox": [ 135, 290, 474, 302 ], "group_id": 0, "lines": [ { "bbox": [ 135, 289, 475, 303 ], "spans": [ { "bbox": [ 135, 289, 235, 303 ], "score": 1.0, "content": "Table 1: Test robustness", "type": "text" }, { "bbox": [ 236, 291, 251, 301 ], "score": 0.67, "content": "( \\% )", "type": "inline_equation" }, { "bbox": [ 252, 289, 475, 303 ], "score": 1.0, "content": "of AT, AT-AWP and AT-RWP using PreAct ResNet-18.", "type": "text" } ], "index": 15 } ], "index": 15 }, { "type": "table_body", "bbox": [ 131, 302, 478, 412 ], "group_id": 0, "lines": [ { "bbox": [ 131, 302, 478, 412 ], "spans": [ { "bbox": [ 131, 302, 478, 412 ], "score": 0.984, "html": "
Threat ModelMethodSVHNCIFAR-10CIFAR-100
BestLastBestLastBestLast
L8AT53.3644.4952.7944.4427.2220.82
AT-AWP59.1255.8755.3954.7330.7130.28
AT-RWP61.1557.4558.5558.0131.1730.64
L2AT66.8765.0369.1565.9341.3335.27
AT-AWP72.5767.7372.6972.0845.6044.66
AT-RWP73.3569.4874.4773.8445.7145.05
", "type": "table", "image_path": "45802b10bc18e868a421b53cff82ff389c7a141952169fe23eae3703c4e7ad74.jpg" } ] } ], "index": 17, "virtual_lines": [ { "bbox": [ 131, 302, 478, 338.6666666666667 ], "spans": [], "index": 16 }, { "bbox": [ 131, 338.6666666666667, 478, 375.33333333333337 ], "spans": [], "index": 17 }, { "bbox": [ 131, 375.33333333333337, 478, 412.00000000000006 ], "spans": [], "index": 18 } ] } ], "index": 16.0 }, { "type": "text", "bbox": [ 106, 421, 505, 553 ], "lines": [ { "bbox": [ 105, 420, 505, 434 ], "spans": [ { "bbox": [ 105, 420, 505, 434 ], "score": 1.0, "content": "Benchmarking the state-of-the-art Robustness. To manifest the full power of our proposed per-", "type": "text" } ], "index": 19 }, { "bbox": [ 105, 431, 506, 445 ], "spans": [ { "bbox": [ 105, 431, 462, 445 ], "score": 1.0, "content": "turbation strategy and also benchmark the state-of-the-art robustness on CIFAR-10 under", "type": "text" }, { "bbox": [ 462, 433, 478, 443 ], "score": 0.9, "content": "\\mathrm { L } _ { \\infty }", "type": "inline_equation" }, { "bbox": [ 479, 431, 506, 445 ], "score": 1.0, "content": "threat", "type": "text" } ], "index": 20 }, { "bbox": [ 105, 443, 506, 456 ], "spans": [ { "bbox": [ 105, 443, 506, 456 ], "score": 1.0, "content": "model, we conduct experiments on the large capacity network with different baseline methods. We", "type": "text" } ], "index": 21 }, { "bbox": [ 106, 454, 506, 466 ], "spans": [ { "bbox": [ 106, 454, 506, 466 ], "score": 1.0, "content": "train Wide ResNet-34-10 for AT and TRADES, and Wide ResNet-28-10 for RST following their", "type": "text" } ], "index": 22 }, { "bbox": [ 105, 465, 506, 477 ], "spans": [ { "bbox": [ 105, 465, 506, 477 ], "score": 1.0, "content": "original papers. We evaluate the adversarial robustness of trained model with various test attack", "type": "text" } ], "index": 23 }, { "bbox": [ 106, 476, 505, 488 ], "spans": [ { "bbox": [ 106, 476, 505, 488 ], "score": 1.0, "content": "and report the “best” test robustness, with the results shown in Table 2. “Natural” denotes the accu-", "type": "text" } ], "index": 24 }, { "bbox": [ 105, 487, 505, 500 ], "spans": [ { "bbox": [ 105, 487, 505, 500 ], "score": 1.0, "content": "racy on natural test data. First, it is observed that the natural accuracy of RWP model consistently", "type": "text" } ], "index": 25 }, { "bbox": [ 106, 498, 505, 510 ], "spans": [ { "bbox": [ 106, 498, 505, 510 ], "score": 1.0, "content": "outperforms AWP by a large margin. It is due to the benefits that our RWP avoids the excessive", "type": "text" } ], "index": 26 }, { "bbox": [ 106, 509, 506, 521 ], "spans": [ { "bbox": [ 106, 509, 506, 521 ], "score": 1.0, "content": "weight perturbation. Moreover, RWP achieves the best adversarial robustness against all types of", "type": "text" } ], "index": 27 }, { "bbox": [ 106, 520, 505, 532 ], "spans": [ { "bbox": [ 106, 520, 505, 532 ], "score": 1.0, "content": "attack across a wide range of baseline methods, which verifies that RWP is effective in general and", "type": "text" } ], "index": 28 }, { "bbox": [ 106, 531, 505, 543 ], "spans": [ { "bbox": [ 106, 531, 505, 543 ], "score": 1.0, "content": "improves adversarial robustness reliably rather than improper tuning of hyper-parameters of attacks,", "type": "text" } ], "index": 29 }, { "bbox": [ 105, 541, 241, 555 ], "spans": [ { "bbox": [ 105, 541, 241, 555 ], "score": 1.0, "content": "gradient obfuscation or masking.", "type": "text" } ], "index": 30 } ], "index": 24.5, "bbox_fs": [ 105, 420, 506, 555 ] }, { "type": "table", "bbox": [ 138, 583, 473, 714 ], "blocks": [ { "type": "table_caption", "bbox": [ 128, 571, 479, 582 ], "group_id": 1, "lines": [ { "bbox": [ 129, 570, 480, 584 ], "spans": [ { "bbox": [ 129, 570, 229, 584 ], "score": 1.0, "content": "Table 2: Test robustness", "type": "text" }, { "bbox": [ 230, 572, 245, 582 ], "score": 0.72, "content": "( \\% )", "type": "inline_equation" }, { "bbox": [ 246, 570, 408, 584 ], "score": 1.0, "content": "on CIFAR-10 using Wide ResNet under", "type": "text" }, { "bbox": [ 408, 572, 424, 582 ], "score": 0.89, "content": "L _ { \\infty }", "type": "inline_equation" }, { "bbox": [ 424, 570, 480, 584 ], "score": 1.0, "content": "threat model.", "type": "text" } ], "index": 31 } ], "index": 31 }, { "type": "table_body", "bbox": [ 138, 583, 473, 714 ], "group_id": 1, "lines": [ { "bbox": [ 138, 583, 473, 714 ], "spans": [ { "bbox": [ 138, 583, 473, 714 ], "score": 0.985, "html": "
DefenseNaturalFGSMPGD-20PGD-100C&WAA
AT86.0761.7656.1055.7954.1952.60
AT-AWP85.5762.9058.1457.9455.9654.04
AT-RWP86.8666.2262.8762.8756.6254.61
TRADES84.6561.3256.3356.0754.2053.08
TRADES-AWP85.3663.4959.2759.1257.0756.17
TRADES-RWP86.1464.7060.4560.3058.0757.20
RST89.6969.6062.6062.2260.4759.53
RST-AWP88.2567.9463.7363.5861.6260.05
RST-RWP88.8769.7164.1163.9262.0360.36
", "type": "table", "image_path": "c358e97c8b763776c5cf4fa2be767217492a15a71f8f43feb9865a88292bf574.jpg" } ] } ], "index": 33, "virtual_lines": [ { "bbox": [ 138, 583, 473, 626.6666666666666 ], "spans": [], "index": 32 }, { "bbox": [ 138, 626.6666666666666, 473, 670.3333333333333 ], "spans": [], "index": 33 }, { "bbox": [ 138, 670.3333333333333, 473, 713.9999999999999 ], "spans": [], "index": 34 } ] } ], "index": 32.0 } ] }, { "preproc_blocks": [ { "type": "image", "bbox": [ 117, 61, 493, 206 ], "blocks": [ { "type": "image_body", "bbox": [ 117, 61, 493, 206 ], "group_id": 0, "lines": [ { "bbox": [ 117, 61, 491, 206 ], "spans": [ { "bbox": [ 117, 61, 491, 206 ], "score": 0.97, "type": "image", "image_path": "05cc9a011b1b361f1fc69f9f40b1f1f4a73327c2b02695b658d3ce690a694601.jpg" } ] } ], "index": 1, "virtual_lines": [ { "bbox": [ 117, 61, 493, 109.33333333333334 ], "spans": [], "index": 0 }, { "bbox": [ 117, 109.33333333333334, 493, 157.66666666666669 ], "spans": [], "index": 1 }, { "bbox": [ 117, 157.66666666666669, 493, 206.00000000000003 ], "spans": [], "index": 2 } ] }, { "type": "image_caption", "bbox": [ 192, 213, 418, 225 ], "group_id": 0, "lines": [ { "bbox": [ 192, 213, 418, 227 ], "spans": [ { "bbox": [ 192, 213, 418, 227 ], "score": 1.0, "content": "Figure 3: The ablation study experiments on CIFAR-10.", "type": "text" } ], "index": 3 } ], "index": 3 } ], "index": 2.0 }, { "type": "title", "bbox": [ 107, 234, 217, 245 ], "lines": [ { "bbox": [ 105, 233, 218, 247 ], "spans": [ { "bbox": [ 105, 233, 218, 247 ], "score": 1.0, "content": "5.3 ABLATION STUDIES", "type": "text" } ], "index": 4 } ], "index": 4 }, { "type": "text", "bbox": [ 107, 255, 504, 288 ], "lines": [ { "bbox": [ 105, 255, 505, 267 ], "spans": [ { "bbox": [ 105, 255, 505, 267 ], "score": 1.0, "content": "In this part, we investigate the impacts of algorithmic components using AT-RWP on PreAct ResNet-", "type": "text" } ], "index": 5 }, { "bbox": [ 105, 265, 505, 279 ], "spans": [ { "bbox": [ 105, 265, 145, 279 ], "score": 1.0, "content": "18 under", "type": "text" }, { "bbox": [ 145, 267, 162, 277 ], "score": 0.9, "content": "L _ { \\infty }", "type": "inline_equation" }, { "bbox": [ 162, 265, 238, 279 ], "score": 1.0, "content": "threat model with", "type": "text" }, { "bbox": [ 238, 266, 284, 278 ], "score": 0.9, "content": "\\epsilon = 8 / 2 5 5", "type": "inline_equation" }, { "bbox": [ 285, 265, 303, 279 ], "score": 1.0, "content": "and", "type": "text" }, { "bbox": [ 303, 266, 352, 278 ], "score": 0.89, "content": "\\alpha = 2 / 2 5 5", "type": "inline_equation" }, { "bbox": [ 352, 265, 505, 279 ], "score": 1.0, "content": "following the same setting in section", "type": "text" } ], "index": 6 }, { "bbox": [ 105, 277, 361, 290 ], "spans": [ { "bbox": [ 105, 277, 361, 290 ], "score": 1.0, "content": "5.1. The training/test attacks are PGD-10/PGD-20 respectively.", "type": "text" } ], "index": 7 } ], "index": 6 }, { "type": "text", "bbox": [ 106, 294, 505, 425 ], "lines": [ { "bbox": [ 105, 293, 505, 307 ], "spans": [ { "bbox": [ 105, 293, 505, 307 ], "score": 1.0, "content": "The Importance of Minimum LSC Value. We empirically verify the effectiveness of minimum", "type": "text" } ], "index": 8 }, { "bbox": [ 104, 303, 505, 319 ], "spans": [ { "bbox": [ 104, 303, 153, 319 ], "score": 1.0, "content": "LSC value", "type": "text" }, { "bbox": [ 153, 307, 173, 316 ], "score": 0.87, "content": "c _ { m i n }", "type": "inline_equation" }, { "bbox": [ 174, 303, 505, 319 ], "score": 1.0, "content": ", by comparing the performance of models trained using different weight pertur-", "type": "text" } ], "index": 9 }, { "bbox": [ 104, 315, 506, 329 ], "spans": [ { "bbox": [ 104, 315, 506, 329 ], "score": 1.0, "content": "bation schemes: 1) AT: standard adversarial training without weight perturbation (equivalent to", "type": "text" } ], "index": 10 }, { "bbox": [ 106, 326, 506, 340 ], "spans": [ { "bbox": [ 106, 327, 147, 338 ], "score": 0.85, "content": "c _ { m i n } = 0 \\mathrm { { . } }", "type": "inline_equation" }, { "bbox": [ 147, 326, 506, 340 ], "score": 1.0, "content": "); 2) AWP: weight perturbation generated via outer maximization in Eq.(1) (equivalent to", "type": "text" } ], "index": 11 }, { "bbox": [ 106, 338, 505, 351 ], "spans": [ { "bbox": [ 106, 339, 151, 349 ], "score": 0.84, "content": "c _ { m i n } = \\infty", "type": "inline_equation" }, { "bbox": [ 152, 338, 505, 351 ], "score": 1.0, "content": "); 3) RWP: weight perturbation generated using the proposed robust strategy with differ-", "type": "text" } ], "index": 12 }, { "bbox": [ 104, 349, 506, 361 ], "spans": [ { "bbox": [ 104, 349, 121, 361 ], "score": 1.0, "content": "ent", "type": "text" }, { "bbox": [ 122, 351, 143, 360 ], "score": 0.88, "content": "c _ { m i n }", "type": "inline_equation" }, { "bbox": [ 143, 349, 506, 361 ], "score": 1.0, "content": "values. All other hyper-parameters are kept exactly the same other than the perturbation", "type": "text" } ], "index": 13 }, { "bbox": [ 106, 361, 505, 371 ], "spans": [ { "bbox": [ 106, 361, 505, 371 ], "score": 1.0, "content": "scheme used. The results are summarized in Table 3(a). It is observed that the test robustness of", "type": "text" } ], "index": 14 }, { "bbox": [ 105, 371, 505, 382 ], "spans": [ { "bbox": [ 105, 371, 505, 382 ], "score": 1.0, "content": "RWP model first increases and then decreases as the minimum LSC value increases, and the best test", "type": "text" } ], "index": 15 }, { "bbox": [ 105, 381, 505, 395 ], "spans": [ { "bbox": [ 105, 381, 206, 395 ], "score": 1.0, "content": "robustness is obtained at", "type": "text" }, { "bbox": [ 207, 382, 253, 393 ], "score": 0.91, "content": "c _ { m i n } = 1 . 7", "type": "inline_equation" }, { "bbox": [ 254, 381, 432, 395 ], "score": 1.0, "content": ". It is evident that RWP with a wide range of", "type": "text" }, { "bbox": [ 432, 383, 453, 393 ], "score": 0.89, "content": "c _ { m i n }", "type": "inline_equation" }, { "bbox": [ 453, 381, 505, 395 ], "score": 1.0, "content": "outperforms", "type": "text" } ], "index": 16 }, { "bbox": [ 105, 392, 505, 405 ], "spans": [ { "bbox": [ 105, 392, 505, 405 ], "score": 1.0, "content": "both AT and AWP model, demonstrating its effectiveness. Furthermore, as it is the major component", "type": "text" } ], "index": 17 }, { "bbox": [ 105, 404, 505, 416 ], "spans": [ { "bbox": [ 105, 404, 505, 416 ], "score": 1.0, "content": "that is different from the AWP pipeline, this result suggests that LSC criterion constraints is the main", "type": "text" } ], "index": 18 }, { "bbox": [ 105, 415, 311, 427 ], "spans": [ { "bbox": [ 105, 415, 311, 427 ], "score": 1.0, "content": "contributor to the improved adversarial robustness.", "type": "text" } ], "index": 19 } ], "index": 13.5 }, { "type": "text", "bbox": [ 107, 431, 505, 520 ], "lines": [ { "bbox": [ 105, 430, 505, 445 ], "spans": [ { "bbox": [ 105, 430, 428, 445 ], "score": 1.0, "content": "The Impact of Step Number. We further investigate the effect of step number", "type": "text" }, { "bbox": [ 429, 432, 443, 443 ], "score": 0.89, "content": "K _ { 2 }", "type": "inline_equation" }, { "bbox": [ 443, 430, 505, 445 ], "score": 1.0, "content": ", by comparing", "type": "text" } ], "index": 20 }, { "bbox": [ 105, 443, 505, 455 ], "spans": [ { "bbox": [ 105, 443, 474, 455 ], "score": 1.0, "content": "the performances of model trained using different perturbation steps. The step number", "type": "text" }, { "bbox": [ 474, 443, 488, 453 ], "score": 0.88, "content": "K _ { 2 }", "type": "inline_equation" }, { "bbox": [ 488, 443, 505, 455 ], "score": 1.0, "content": "for", "type": "text" } ], "index": 21 }, { "bbox": [ 105, 453, 505, 466 ], "spans": [ { "bbox": [ 105, 453, 452, 466 ], "score": 1.0, "content": "RWP varies from 1 to 10. The results are shown in Figure 3(b). As expected, when", "type": "text" }, { "bbox": [ 452, 453, 467, 464 ], "score": 0.89, "content": "K _ { 2 }", "type": "inline_equation" }, { "bbox": [ 467, 453, 505, 466 ], "score": 1.0, "content": "is small,", "type": "text" } ], "index": 22 }, { "bbox": [ 105, 464, 506, 478 ], "spans": [ { "bbox": [ 105, 464, 149, 478 ], "score": 1.0, "content": "increasing", "type": "text" }, { "bbox": [ 150, 465, 164, 475 ], "score": 0.88, "content": "K _ { 2 }", "type": "inline_equation" }, { "bbox": [ 164, 464, 304, 478 ], "score": 1.0, "content": "leads higher test robustness. When", "type": "text" }, { "bbox": [ 304, 465, 318, 475 ], "score": 0.88, "content": "K _ { 2 }", "type": "inline_equation" }, { "bbox": [ 319, 464, 506, 478 ], "score": 1.0, "content": "increases from 7 to 10, the performance is flat,", "type": "text" } ], "index": 23 }, { "bbox": [ 106, 476, 506, 488 ], "spans": [ { "bbox": [ 106, 476, 506, 488 ], "score": 1.0, "content": "which suggests that the generating weight perturbation is sufficient to comprehensively avoid robust", "type": "text" } ], "index": 24 }, { "bbox": [ 105, 487, 505, 498 ], "spans": [ { "bbox": [ 105, 487, 505, 498 ], "score": 1.0, "content": "overfitting. Note that extra iterations will not bring computational overhead when classification loss", "type": "text" } ], "index": 25 }, { "bbox": [ 105, 497, 506, 510 ], "spans": [ { "bbox": [ 105, 497, 375, 510 ], "score": 1.0, "content": "of adversarial examples in the batch exceeds minimum LSC value", "type": "text" }, { "bbox": [ 375, 498, 396, 509 ], "score": 0.88, "content": "c _ { m i n }", "type": "inline_equation" }, { "bbox": [ 396, 497, 506, 510 ], "score": 1.0, "content": ", as shown in Algorithm 1.", "type": "text" } ], "index": 26 }, { "bbox": [ 106, 508, 355, 521 ], "spans": [ { "bbox": [ 106, 508, 223, 521 ], "score": 1.0, "content": "Therefore, we uniformly use", "type": "text" }, { "bbox": [ 223, 509, 261, 519 ], "score": 0.91, "content": "K _ { 2 } = 1 0", "type": "inline_equation" }, { "bbox": [ 261, 508, 355, 521 ], "score": 1.0, "content": "in our implementation.", "type": "text" } ], "index": 27 } ], "index": 23.5 }, { "type": "text", "bbox": [ 107, 525, 504, 580 ], "lines": [ { "bbox": [ 105, 525, 505, 537 ], "spans": [ { "bbox": [ 105, 525, 505, 537 ], "score": 1.0, "content": "Effect on Adversarial Robustness and Robust Overfitting. We then visualize the learning curve", "type": "text" } ], "index": 28 }, { "bbox": [ 105, 535, 506, 549 ], "spans": [ { "bbox": [ 105, 535, 506, 549 ], "score": 1.0, "content": "of AT, AWP and RWP in Figure 3(c). We observe that the test robustness of RWP model continues", "type": "text" } ], "index": 29 }, { "bbox": [ 105, 546, 506, 560 ], "spans": [ { "bbox": [ 105, 546, 506, 560 ], "score": 1.0, "content": "to increase as the training progresses. In addition, RWP outperforms AWP with a clear margin in", "type": "text" } ], "index": 30 }, { "bbox": [ 105, 557, 506, 571 ], "spans": [ { "bbox": [ 105, 557, 506, 571 ], "score": 1.0, "content": "the later stage of training. Such observations exactly reflect the nature of our approach which aims", "type": "text" } ], "index": 31 }, { "bbox": [ 105, 569, 389, 582 ], "spans": [ { "bbox": [ 105, 569, 389, 582 ], "score": 1.0, "content": "to prevent robust overfitting as well as enhance adversarial robustness.", "type": "text" } ], "index": 32 } ], "index": 30 }, { "type": "title", "bbox": [ 107, 596, 195, 609 ], "lines": [ { "bbox": [ 105, 594, 198, 613 ], "spans": [ { "bbox": [ 105, 594, 198, 613 ], "score": 1.0, "content": "6 CONCLUSION", "type": "text" } ], "index": 33 } ], "index": 33 }, { "type": "text", "bbox": [ 107, 621, 505, 731 ], "lines": [ { "bbox": [ 105, 622, 505, 634 ], "spans": [ { "bbox": [ 105, 622, 505, 634 ], "score": 1.0, "content": "In this paper, we proposed a criterion, Loss Stationary Condition (LSC) for constrained perturba-", "type": "text" } ], "index": 34 }, { "bbox": [ 105, 632, 505, 646 ], "spans": [ { "bbox": [ 105, 632, 505, 646 ], "score": 1.0, "content": "tion, to monitor the training status of different adversarial examples during network optimization.", "type": "text" } ], "index": 35 }, { "bbox": [ 105, 642, 505, 658 ], "spans": [ { "bbox": [ 105, 642, 505, 658 ], "score": 1.0, "content": "The proposed criterion provides a new understanding of robust overfitting in adversarial training.", "type": "text" } ], "index": 36 }, { "bbox": [ 106, 655, 504, 667 ], "spans": [ { "bbox": [ 106, 655, 504, 667 ], "score": 1.0, "content": "Based on LSC, we found that elimination of robust overfitting and higher robustness of adversarial", "type": "text" } ], "index": 37 }, { "bbox": [ 105, 666, 505, 678 ], "spans": [ { "bbox": [ 105, 666, 505, 678 ], "score": 1.0, "content": "training can be achieved by weight perturbation on adversarial examples with small classification", "type": "text" } ], "index": 38 }, { "bbox": [ 105, 677, 506, 690 ], "spans": [ { "bbox": [ 105, 677, 506, 690 ], "score": 1.0, "content": "loss, rather than adversarial examples with large classification loss. Following this, we proposed a", "type": "text" } ], "index": 39 }, { "bbox": [ 104, 686, 505, 701 ], "spans": [ { "bbox": [ 104, 686, 505, 701 ], "score": 1.0, "content": "Robust Weight Perturbation (RWP) strategy to monitor and regulate the extent of weight perturba-", "type": "text" } ], "index": 40 }, { "bbox": [ 105, 698, 505, 712 ], "spans": [ { "bbox": [ 105, 698, 505, 712 ], "score": 1.0, "content": "tion. Comprehensive experiments show that RWP is generic and can improve the state-of-the-art", "type": "text" } ], "index": 41 }, { "bbox": [ 105, 710, 505, 722 ], "spans": [ { "bbox": [ 105, 710, 505, 722 ], "score": 1.0, "content": "adversarial robustness across different adversarial training approaches, network architectures, threat", "type": "text" } ], "index": 42 }, { "bbox": [ 106, 720, 238, 732 ], "spans": [ { "bbox": [ 106, 720, 238, 732 ], "score": 1.0, "content": "models and benchmark datasets.", "type": "text" } ], "index": 43 } ], "index": 38.5 } ], "page_idx": 8, "page_size": [ 612, 792 ], "discarded_blocks": [ { "type": "discarded", "bbox": [ 106, 27, 308, 37 ], "lines": [ { "bbox": [ 106, 26, 308, 38 ], "spans": [ { "bbox": [ 106, 26, 308, 38 ], "score": 1.0, "content": "Under review 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": "image", "bbox": [ 117, 61, 493, 206 ], "blocks": [ { "type": "image_body", "bbox": [ 117, 61, 493, 206 ], "group_id": 0, "lines": [ { "bbox": [ 117, 61, 491, 206 ], "spans": [ { "bbox": [ 117, 61, 491, 206 ], "score": 0.97, "type": "image", "image_path": "05cc9a011b1b361f1fc69f9f40b1f1f4a73327c2b02695b658d3ce690a694601.jpg" } ] } ], "index": 1, "virtual_lines": [ { "bbox": [ 117, 61, 493, 109.33333333333334 ], "spans": [], "index": 0 }, { "bbox": [ 117, 109.33333333333334, 493, 157.66666666666669 ], "spans": [], "index": 1 }, { "bbox": [ 117, 157.66666666666669, 493, 206.00000000000003 ], "spans": [], "index": 2 } ] }, { "type": "image_caption", "bbox": [ 192, 213, 418, 225 ], "group_id": 0, "lines": [ { "bbox": [ 192, 213, 418, 227 ], "spans": [ { "bbox": [ 192, 213, 418, 227 ], "score": 1.0, "content": "Figure 3: The ablation study experiments on CIFAR-10.", "type": "text" } ], "index": 3 } ], "index": 3 } ], "index": 2.0 }, { "type": "title", "bbox": [ 107, 234, 217, 245 ], "lines": [ { "bbox": [ 105, 233, 218, 247 ], "spans": [ { "bbox": [ 105, 233, 218, 247 ], "score": 1.0, "content": "5.3 ABLATION STUDIES", "type": "text" } ], "index": 4 } ], "index": 4 }, { "type": "text", "bbox": [ 107, 255, 504, 288 ], "lines": [ { "bbox": [ 105, 255, 505, 267 ], "spans": [ { "bbox": [ 105, 255, 505, 267 ], "score": 1.0, "content": "In this part, we investigate the impacts of algorithmic components using AT-RWP on PreAct ResNet-", "type": "text" } ], "index": 5 }, { "bbox": [ 105, 265, 505, 279 ], "spans": [ { "bbox": [ 105, 265, 145, 279 ], "score": 1.0, "content": "18 under", "type": "text" }, { "bbox": [ 145, 267, 162, 277 ], "score": 0.9, "content": "L _ { \\infty }", "type": "inline_equation" }, { "bbox": [ 162, 265, 238, 279 ], "score": 1.0, "content": "threat model with", "type": "text" }, { "bbox": [ 238, 266, 284, 278 ], "score": 0.9, "content": "\\epsilon = 8 / 2 5 5", "type": "inline_equation" }, { "bbox": [ 285, 265, 303, 279 ], "score": 1.0, "content": "and", "type": "text" }, { "bbox": [ 303, 266, 352, 278 ], "score": 0.89, "content": "\\alpha = 2 / 2 5 5", "type": "inline_equation" }, { "bbox": [ 352, 265, 505, 279 ], "score": 1.0, "content": "following the same setting in section", "type": "text" } ], "index": 6 }, { "bbox": [ 105, 277, 361, 290 ], "spans": [ { "bbox": [ 105, 277, 361, 290 ], "score": 1.0, "content": "5.1. The training/test attacks are PGD-10/PGD-20 respectively.", "type": "text" } ], "index": 7 } ], "index": 6, "bbox_fs": [ 105, 255, 505, 290 ] }, { "type": "text", "bbox": [ 106, 294, 505, 425 ], "lines": [ { "bbox": [ 105, 293, 505, 307 ], "spans": [ { "bbox": [ 105, 293, 505, 307 ], "score": 1.0, "content": "The Importance of Minimum LSC Value. We empirically verify the effectiveness of minimum", "type": "text" } ], "index": 8 }, { "bbox": [ 104, 303, 505, 319 ], "spans": [ { "bbox": [ 104, 303, 153, 319 ], "score": 1.0, "content": "LSC value", "type": "text" }, { "bbox": [ 153, 307, 173, 316 ], "score": 0.87, "content": "c _ { m i n }", "type": "inline_equation" }, { "bbox": [ 174, 303, 505, 319 ], "score": 1.0, "content": ", by comparing the performance of models trained using different weight pertur-", "type": "text" } ], "index": 9 }, { "bbox": [ 104, 315, 506, 329 ], "spans": [ { "bbox": [ 104, 315, 506, 329 ], "score": 1.0, "content": "bation schemes: 1) AT: standard adversarial training without weight perturbation (equivalent to", "type": "text" } ], "index": 10 }, { "bbox": [ 106, 326, 506, 340 ], "spans": [ { "bbox": [ 106, 327, 147, 338 ], "score": 0.85, "content": "c _ { m i n } = 0 \\mathrm { { . } }", "type": "inline_equation" }, { "bbox": [ 147, 326, 506, 340 ], "score": 1.0, "content": "); 2) AWP: weight perturbation generated via outer maximization in Eq.(1) (equivalent to", "type": "text" } ], "index": 11 }, { "bbox": [ 106, 338, 505, 351 ], "spans": [ { "bbox": [ 106, 339, 151, 349 ], "score": 0.84, "content": "c _ { m i n } = \\infty", "type": "inline_equation" }, { "bbox": [ 152, 338, 505, 351 ], "score": 1.0, "content": "); 3) RWP: weight perturbation generated using the proposed robust strategy with differ-", "type": "text" } ], "index": 12 }, { "bbox": [ 104, 349, 506, 361 ], "spans": [ { "bbox": [ 104, 349, 121, 361 ], "score": 1.0, "content": "ent", "type": "text" }, { "bbox": [ 122, 351, 143, 360 ], "score": 0.88, "content": "c _ { m i n }", "type": "inline_equation" }, { "bbox": [ 143, 349, 506, 361 ], "score": 1.0, "content": "values. All other hyper-parameters are kept exactly the same other than the perturbation", "type": "text" } ], "index": 13 }, { "bbox": [ 106, 361, 505, 371 ], "spans": [ { "bbox": [ 106, 361, 505, 371 ], "score": 1.0, "content": "scheme used. The results are summarized in Table 3(a). It is observed that the test robustness of", "type": "text" } ], "index": 14 }, { "bbox": [ 105, 371, 505, 382 ], "spans": [ { "bbox": [ 105, 371, 505, 382 ], "score": 1.0, "content": "RWP model first increases and then decreases as the minimum LSC value increases, and the best test", "type": "text" } ], "index": 15 }, { "bbox": [ 105, 381, 505, 395 ], "spans": [ { "bbox": [ 105, 381, 206, 395 ], "score": 1.0, "content": "robustness is obtained at", "type": "text" }, { "bbox": [ 207, 382, 253, 393 ], "score": 0.91, "content": "c _ { m i n } = 1 . 7", "type": "inline_equation" }, { "bbox": [ 254, 381, 432, 395 ], "score": 1.0, "content": ". It is evident that RWP with a wide range of", "type": "text" }, { "bbox": [ 432, 383, 453, 393 ], "score": 0.89, "content": "c _ { m i n }", "type": "inline_equation" }, { "bbox": [ 453, 381, 505, 395 ], "score": 1.0, "content": "outperforms", "type": "text" } ], "index": 16 }, { "bbox": [ 105, 392, 505, 405 ], "spans": [ { "bbox": [ 105, 392, 505, 405 ], "score": 1.0, "content": "both AT and AWP model, demonstrating its effectiveness. Furthermore, as it is the major component", "type": "text" } ], "index": 17 }, { "bbox": [ 105, 404, 505, 416 ], "spans": [ { "bbox": [ 105, 404, 505, 416 ], "score": 1.0, "content": "that is different from the AWP pipeline, this result suggests that LSC criterion constraints is the main", "type": "text" } ], "index": 18 }, { "bbox": [ 105, 415, 311, 427 ], "spans": [ { "bbox": [ 105, 415, 311, 427 ], "score": 1.0, "content": "contributor to the improved adversarial robustness.", "type": "text" } ], "index": 19 } ], "index": 13.5, "bbox_fs": [ 104, 293, 506, 427 ] }, { "type": "text", "bbox": [ 107, 431, 505, 520 ], "lines": [ { "bbox": [ 105, 430, 505, 445 ], "spans": [ { "bbox": [ 105, 430, 428, 445 ], "score": 1.0, "content": "The Impact of Step Number. We further investigate the effect of step number", "type": "text" }, { "bbox": [ 429, 432, 443, 443 ], "score": 0.89, "content": "K _ { 2 }", "type": "inline_equation" }, { "bbox": [ 443, 430, 505, 445 ], "score": 1.0, "content": ", by comparing", "type": "text" } ], "index": 20 }, { "bbox": [ 105, 443, 505, 455 ], "spans": [ { "bbox": [ 105, 443, 474, 455 ], "score": 1.0, "content": "the performances of model trained using different perturbation steps. The step number", "type": "text" }, { "bbox": [ 474, 443, 488, 453 ], "score": 0.88, "content": "K _ { 2 }", "type": "inline_equation" }, { "bbox": [ 488, 443, 505, 455 ], "score": 1.0, "content": "for", "type": "text" } ], "index": 21 }, { "bbox": [ 105, 453, 505, 466 ], "spans": [ { "bbox": [ 105, 453, 452, 466 ], "score": 1.0, "content": "RWP varies from 1 to 10. The results are shown in Figure 3(b). As expected, when", "type": "text" }, { "bbox": [ 452, 453, 467, 464 ], "score": 0.89, "content": "K _ { 2 }", "type": "inline_equation" }, { "bbox": [ 467, 453, 505, 466 ], "score": 1.0, "content": "is small,", "type": "text" } ], "index": 22 }, { "bbox": [ 105, 464, 506, 478 ], "spans": [ { "bbox": [ 105, 464, 149, 478 ], "score": 1.0, "content": "increasing", "type": "text" }, { "bbox": [ 150, 465, 164, 475 ], "score": 0.88, "content": "K _ { 2 }", "type": "inline_equation" }, { "bbox": [ 164, 464, 304, 478 ], "score": 1.0, "content": "leads higher test robustness. When", "type": "text" }, { "bbox": [ 304, 465, 318, 475 ], "score": 0.88, "content": "K _ { 2 }", "type": "inline_equation" }, { "bbox": [ 319, 464, 506, 478 ], "score": 1.0, "content": "increases from 7 to 10, the performance is flat,", "type": "text" } ], "index": 23 }, { "bbox": [ 106, 476, 506, 488 ], "spans": [ { "bbox": [ 106, 476, 506, 488 ], "score": 1.0, "content": "which suggests that the generating weight perturbation is sufficient to comprehensively avoid robust", "type": "text" } ], "index": 24 }, { "bbox": [ 105, 487, 505, 498 ], "spans": [ { "bbox": [ 105, 487, 505, 498 ], "score": 1.0, "content": "overfitting. Note that extra iterations will not bring computational overhead when classification loss", "type": "text" } ], "index": 25 }, { "bbox": [ 105, 497, 506, 510 ], "spans": [ { "bbox": [ 105, 497, 375, 510 ], "score": 1.0, "content": "of adversarial examples in the batch exceeds minimum LSC value", "type": "text" }, { "bbox": [ 375, 498, 396, 509 ], "score": 0.88, "content": "c _ { m i n }", "type": "inline_equation" }, { "bbox": [ 396, 497, 506, 510 ], "score": 1.0, "content": ", as shown in Algorithm 1.", "type": "text" } ], "index": 26 }, { "bbox": [ 106, 508, 355, 521 ], "spans": [ { "bbox": [ 106, 508, 223, 521 ], "score": 1.0, "content": "Therefore, we uniformly use", "type": "text" }, { "bbox": [ 223, 509, 261, 519 ], "score": 0.91, "content": "K _ { 2 } = 1 0", "type": "inline_equation" }, { "bbox": [ 261, 508, 355, 521 ], "score": 1.0, "content": "in our implementation.", "type": "text" } ], "index": 27 } ], "index": 23.5, "bbox_fs": [ 105, 430, 506, 521 ] }, { "type": "text", "bbox": [ 107, 525, 504, 580 ], "lines": [ { "bbox": [ 105, 525, 505, 537 ], "spans": [ { "bbox": [ 105, 525, 505, 537 ], "score": 1.0, "content": "Effect on Adversarial Robustness and Robust Overfitting. We then visualize the learning curve", "type": "text" } ], "index": 28 }, { "bbox": [ 105, 535, 506, 549 ], "spans": [ { "bbox": [ 105, 535, 506, 549 ], "score": 1.0, "content": "of AT, AWP and RWP in Figure 3(c). We observe that the test robustness of RWP model continues", "type": "text" } ], "index": 29 }, { "bbox": [ 105, 546, 506, 560 ], "spans": [ { "bbox": [ 105, 546, 506, 560 ], "score": 1.0, "content": "to increase as the training progresses. In addition, RWP outperforms AWP with a clear margin in", "type": "text" } ], "index": 30 }, { "bbox": [ 105, 557, 506, 571 ], "spans": [ { "bbox": [ 105, 557, 506, 571 ], "score": 1.0, "content": "the later stage of training. Such observations exactly reflect the nature of our approach which aims", "type": "text" } ], "index": 31 }, { "bbox": [ 105, 569, 389, 582 ], "spans": [ { "bbox": [ 105, 569, 389, 582 ], "score": 1.0, "content": "to prevent robust overfitting as well as enhance adversarial robustness.", "type": "text" } ], "index": 32 } ], "index": 30, "bbox_fs": [ 105, 525, 506, 582 ] }, { "type": "title", "bbox": [ 107, 596, 195, 609 ], "lines": [ { "bbox": [ 105, 594, 198, 613 ], "spans": [ { "bbox": [ 105, 594, 198, 613 ], "score": 1.0, "content": "6 CONCLUSION", "type": "text" } ], "index": 33 } ], "index": 33 }, { "type": "text", "bbox": [ 107, 621, 505, 731 ], "lines": [ { "bbox": [ 105, 622, 505, 634 ], "spans": [ { "bbox": [ 105, 622, 505, 634 ], "score": 1.0, "content": "In this paper, we proposed a criterion, Loss Stationary Condition (LSC) for constrained perturba-", "type": "text" } ], "index": 34 }, { "bbox": [ 105, 632, 505, 646 ], "spans": [ { "bbox": [ 105, 632, 505, 646 ], "score": 1.0, "content": "tion, to monitor the training status of different adversarial examples during network optimization.", "type": "text" } ], "index": 35 }, { "bbox": [ 105, 642, 505, 658 ], "spans": [ { "bbox": [ 105, 642, 505, 658 ], "score": 1.0, "content": "The proposed criterion provides a new understanding of robust overfitting in adversarial training.", "type": "text" } ], "index": 36 }, { "bbox": [ 106, 655, 504, 667 ], "spans": [ { "bbox": [ 106, 655, 504, 667 ], "score": 1.0, "content": "Based on LSC, we found that elimination of robust overfitting and higher robustness of adversarial", "type": "text" } ], "index": 37 }, { "bbox": [ 105, 666, 505, 678 ], "spans": [ { "bbox": [ 105, 666, 505, 678 ], "score": 1.0, "content": "training can be achieved by weight perturbation on adversarial examples with small classification", "type": "text" } ], "index": 38 }, { "bbox": [ 105, 677, 506, 690 ], "spans": [ { "bbox": [ 105, 677, 506, 690 ], "score": 1.0, "content": "loss, rather than adversarial examples with large classification loss. Following this, we proposed a", "type": "text" } ], "index": 39 }, { "bbox": [ 104, 686, 505, 701 ], "spans": [ { "bbox": [ 104, 686, 505, 701 ], "score": 1.0, "content": "Robust Weight Perturbation (RWP) strategy to monitor and regulate the extent of weight perturba-", "type": "text" } ], "index": 40 }, { "bbox": [ 105, 698, 505, 712 ], "spans": [ { "bbox": [ 105, 698, 505, 712 ], "score": 1.0, "content": "tion. Comprehensive experiments show that RWP is generic and can improve the state-of-the-art", "type": "text" } ], "index": 41 }, { "bbox": [ 105, 710, 505, 722 ], "spans": [ { "bbox": [ 105, 710, 505, 722 ], "score": 1.0, "content": "adversarial robustness across different adversarial training approaches, network architectures, threat", "type": "text" } ], "index": 42 }, { "bbox": [ 106, 720, 238, 732 ], "spans": [ { "bbox": [ 106, 720, 238, 732 ], "score": 1.0, "content": "models and benchmark datasets.", "type": "text" } ], "index": 43 } ], "index": 38.5, "bbox_fs": [ 104, 622, 506, 732 ] } ] }, { "preproc_blocks": [ { "type": "title", "bbox": [ 108, 81, 267, 94 ], "lines": [ { "bbox": [ 106, 81, 270, 95 ], "spans": [ { "bbox": [ 106, 81, 270, 95 ], "score": 1.0, "content": "REPRODUCIBILITY STATEMENT", "type": "text" } ], "index": 0 } ], "index": 0 }, { "type": "text", "bbox": [ 107, 106, 505, 173 ], "lines": [ { "bbox": [ 105, 106, 506, 119 ], "spans": [ { "bbox": [ 105, 106, 506, 119 ], "score": 1.0, "content": "For sake of reproducibility of our algorithm, we make the following efforts: (i) In Section 5.1, we", "type": "text" } ], "index": 1 }, { "bbox": [ 106, 118, 505, 130 ], "spans": [ { "bbox": [ 106, 118, 505, 130 ], "score": 1.0, "content": "clearly state the implementation details, including benchmark datasets, network structure, baselines,", "type": "text" } ], "index": 2 }, { "bbox": [ 105, 128, 505, 141 ], "spans": [ { "bbox": [ 105, 128, 505, 141 ], "score": 1.0, "content": "training and test parameter setting as well as training and test attack setting. (ii) In Section 5.3,", "type": "text" } ], "index": 3 }, { "bbox": [ 105, 140, 505, 153 ], "spans": [ { "bbox": [ 105, 140, 505, 153 ], "score": 1.0, "content": "we evaluate the sensitivity of the algorithm to hyperparameters and show the detailed hyperparam-", "type": "text" } ], "index": 4 }, { "bbox": [ 106, 151, 505, 163 ], "spans": [ { "bbox": [ 106, 151, 505, 163 ], "score": 1.0, "content": "eter tuning process. (iii) At last, we open-source the source code of RWP algorithm, available at", "type": "text" } ], "index": 5 }, { "bbox": [ 105, 162, 205, 174 ], "spans": [ { "bbox": [ 105, 162, 205, 174 ], "score": 1.0, "content": "supplementary material.", "type": "text" } ], "index": 6 } ], "index": 3.5 }, { "type": "title", "bbox": [ 107, 191, 175, 203 ], "lines": [ { "bbox": [ 106, 191, 176, 204 ], "spans": [ { "bbox": [ 106, 191, 176, 204 ], "score": 1.0, "content": "REFERENCES", "type": "text" } ], "index": 7 } ], "index": 7 }, { "type": "text", "bbox": [ 108, 210, 504, 243 ], "lines": [ { "bbox": [ 105, 209, 505, 223 ], "spans": [ { "bbox": [ 105, 209, 505, 223 ], "score": 1.0, "content": "Maksym Andriushchenko, Francesco Croce, Nicolas Flammarion, and Matthias Hein. Square at-", "type": "text" } ], "index": 8 }, { "bbox": [ 115, 221, 505, 234 ], "spans": [ { "bbox": [ 115, 221, 505, 234 ], "score": 1.0, "content": "tack: a query-efficient black-box adversarial attack via random search. In European Conference", "type": "text" } ], "index": 9 }, { "bbox": [ 116, 232, 319, 244 ], "spans": [ { "bbox": [ 116, 232, 319, 244 ], "score": 1.0, "content": "on Computer Vision, pp. 484–501. Springer, 2020.", "type": "text" } ], "index": 10 } ], "index": 9 }, { "type": "text", "bbox": [ 107, 252, 503, 286 ], "lines": [ { "bbox": [ 105, 252, 505, 265 ], "spans": [ { "bbox": [ 105, 252, 505, 265 ], "score": 1.0, "content": "Anish Athalye, Nicholas Carlini, and David Wagner. Obfuscated gradients give a false sense of se-", "type": "text" } ], "index": 11 }, { "bbox": [ 116, 264, 505, 276 ], "spans": [ { "bbox": [ 116, 264, 505, 276 ], "score": 1.0, "content": "curity: Circumventing defenses to adversarial examples. In International conference on machine", "type": "text" } ], "index": 12 }, { "bbox": [ 116, 274, 268, 288 ], "spans": [ { "bbox": [ 116, 274, 268, 288 ], "score": 1.0, "content": "learning, pp. 274–283. PMLR, 2018.", "type": "text" } ], "index": 13 } ], "index": 12 }, { "type": "text", "bbox": [ 106, 295, 503, 329 ], "lines": [ { "bbox": [ 105, 294, 505, 308 ], "spans": [ { "bbox": [ 105, 294, 505, 308 ], "score": 1.0, "content": "Mikhail Belkin, Daniel Hsu, Siyuan Ma, and Soumik Mandal. Reconciling modern machine-", "type": "text" } ], "index": 14 }, { "bbox": [ 115, 306, 505, 320 ], "spans": [ { "bbox": [ 115, 306, 505, 320 ], "score": 1.0, "content": "learning practice and the classical bias–variance trade-off. Proceedings of the National Academy", "type": "text" } ], "index": 15 }, { "bbox": [ 115, 317, 285, 329 ], "spans": [ { "bbox": [ 115, 317, 285, 329 ], "score": 1.0, "content": "of Sciences, 116(32):15849–15854, 2019.", "type": "text" } ], "index": 16 } ], "index": 15 }, { "type": "text", "bbox": [ 105, 337, 504, 361 ], "lines": [ { "bbox": [ 105, 336, 506, 351 ], "spans": [ { "bbox": [ 105, 336, 506, 351 ], "score": 1.0, "content": "Qi-Zhi Cai, Min Du, Chang Liu, and Dawn Song. Curriculum adversarial training. arXiv preprint", "type": "text" } ], "index": 17 }, { "bbox": [ 115, 348, 220, 361 ], "spans": [ { "bbox": [ 115, 348, 220, 361 ], "score": 1.0, "content": "arXiv:1805.04807, 2018.", "type": "text" } ], "index": 18 } ], "index": 17.5 }, { "type": "text", "bbox": [ 104, 369, 505, 393 ], "lines": [ { "bbox": [ 106, 369, 505, 382 ], "spans": [ { "bbox": [ 106, 369, 505, 382 ], "score": 1.0, "content": "Nicholas Carlini and David Wagner. Towards evaluating the robustness of neural networks. In 2017", "type": "text" } ], "index": 19 }, { "bbox": [ 115, 380, 395, 393 ], "spans": [ { "bbox": [ 115, 380, 395, 393 ], "score": 1.0, "content": "ieee symposium on security and privacy (sp), pp. 39–57. IEEE, 2017.", "type": "text" } ], "index": 20 } ], "index": 19.5 }, { "type": "text", "bbox": [ 106, 400, 504, 424 ], "lines": [ { "bbox": [ 106, 400, 505, 414 ], "spans": [ { "bbox": [ 106, 400, 505, 414 ], "score": 1.0, "content": "Yair Carmon, Aditi Raghunathan, Ludwig Schmidt, Percy Liang, and John C Duchi. Unlabeled data", "type": "text" } ], "index": 21 }, { "bbox": [ 115, 412, 412, 424 ], "spans": [ { "bbox": [ 115, 412, 412, 424 ], "score": 1.0, "content": "improves adversarial robustness. arXiv preprint arXiv:1905.13736, 2019.", "type": "text" } ], "index": 22 } ], "index": 21.5 }, { "type": "text", "bbox": [ 106, 432, 504, 456 ], "lines": [ { "bbox": [ 106, 431, 505, 446 ], "spans": [ { "bbox": [ 106, 431, 505, 446 ], "score": 1.0, "content": "Chen Chen, Jingfeng Zhang, Xilie Xu, Tianlei Hu, Gang Niu, Gang Chen, and Masashi Sugiyama.", "type": "text" } ], "index": 23 }, { "bbox": [ 116, 443, 460, 456 ], "spans": [ { "bbox": [ 116, 443, 460, 456 ], "score": 1.0, "content": "Guided interpolation for adversarial training. arXiv preprint arXiv:2102.07327, 2021.", "type": "text" } ], "index": 24 } ], "index": 23.5 }, { "type": "text", "bbox": [ 105, 464, 504, 487 ], "lines": [ { "bbox": [ 105, 464, 505, 477 ], "spans": [ { "bbox": [ 105, 464, 505, 477 ], "score": 1.0, "content": "Jinghui Chen, Dongruo Zhou, Jinfeng Yi, and Quanquan Gu. A frank-wolfe framework for efficient", "type": "text" } ], "index": 25 }, { "bbox": [ 116, 475, 382, 488 ], "spans": [ { "bbox": [ 116, 475, 382, 488 ], "score": 1.0, "content": "and effective adversarial attacks. In AAAI, pp. 3486–3494, 2020a.", "type": "text" } ], "index": 26 } ], "index": 25.5 }, { "type": "text", "bbox": [ 106, 495, 503, 529 ], "lines": [ { "bbox": [ 106, 495, 505, 509 ], "spans": [ { "bbox": [ 106, 495, 505, 509 ], "score": 1.0, "content": "Tianlong Chen, Zhenyu Zhang, Sijia Liu, Shiyu Chang, and Zhangyang Wang. Robust overfitting", "type": "text" } ], "index": 27 }, { "bbox": [ 115, 506, 505, 521 ], "spans": [ { "bbox": [ 115, 506, 505, 521 ], "score": 1.0, "content": "may be mitigated by properly learned smoothening. In International Conference on Learning", "type": "text" } ], "index": 28 }, { "bbox": [ 116, 518, 216, 530 ], "spans": [ { "bbox": [ 116, 518, 216, 530 ], "score": 1.0, "content": "Representations, 2020b.", "type": "text" } ], "index": 29 } ], "index": 28 }, { "type": "text", "bbox": [ 107, 538, 503, 572 ], "lines": [ { "bbox": [ 105, 538, 505, 551 ], "spans": [ { "bbox": [ 105, 538, 505, 551 ], "score": 1.0, "content": "Francesco Croce and Matthias Hein. Minimally distorted adversarial examples with a fast adaptive", "type": "text" } ], "index": 30 }, { "bbox": [ 116, 550, 505, 562 ], "spans": [ { "bbox": [ 116, 550, 505, 562 ], "score": 1.0, "content": "boundary attack. In International Conference on Machine Learning, pp. 2196–2205. PMLR,", "type": "text" } ], "index": 31 }, { "bbox": [ 115, 559, 147, 574 ], "spans": [ { "bbox": [ 115, 559, 147, 574 ], "score": 1.0, "content": "2020a.", "type": "text" } ], "index": 32 } ], "index": 31 }, { "type": "text", "bbox": [ 106, 581, 505, 615 ], "lines": [ { "bbox": [ 105, 581, 505, 593 ], "spans": [ { "bbox": [ 105, 581, 505, 593 ], "score": 1.0, "content": "Francesco Croce and Matthias Hein. Reliable evaluation of adversarial robustness with an ensemble", "type": "text" } ], "index": 33 }, { "bbox": [ 115, 592, 505, 605 ], "spans": [ { "bbox": [ 115, 592, 505, 605 ], "score": 1.0, "content": "of diverse parameter-free attacks. In International conference on machine learning, pp. 2206–", "type": "text" } ], "index": 34 }, { "bbox": [ 116, 602, 203, 615 ], "spans": [ { "bbox": [ 116, 602, 203, 615 ], "score": 1.0, "content": "2216. PMLR, 2020b.", "type": "text" } ], "index": 35 } ], "index": 34 }, { "type": "text", "bbox": [ 105, 624, 504, 647 ], "lines": [ { "bbox": [ 105, 622, 505, 637 ], "spans": [ { "bbox": [ 105, 622, 505, 637 ], "score": 1.0, "content": "Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. Bert: Pre-training of deep", "type": "text" } ], "index": 36 }, { "bbox": [ 115, 635, 499, 648 ], "spans": [ { "bbox": [ 115, 635, 499, 648 ], "score": 1.0, "content": "bidirectional transformers for language understanding. arXiv preprint arXiv:1810.04805, 2018.", "type": "text" } ], "index": 37 } ], "index": 36.5 }, { "type": "text", "bbox": [ 107, 655, 504, 690 ], "lines": [ { "bbox": [ 106, 655, 505, 669 ], "spans": [ { "bbox": [ 106, 655, 505, 669 ], "score": 1.0, "content": "Yinpeng Dong, Fangzhou Liao, Tianyu Pang, Hang Su, Jun Zhu, Xiaolin Hu, and Jianguo Li. Boost-", "type": "text" } ], "index": 38 }, { "bbox": [ 115, 666, 506, 680 ], "spans": [ { "bbox": [ 115, 666, 506, 680 ], "score": 1.0, "content": "ing adversarial attacks with momentum. In Proceedings of the IEEE conference on computer", "type": "text" } ], "index": 39 }, { "bbox": [ 116, 678, 331, 690 ], "spans": [ { "bbox": [ 116, 678, 331, 690 ], "score": 1.0, "content": "vision and pattern recognition, pp. 9185–9193, 2018.", "type": "text" } ], "index": 40 } ], "index": 39 }, { "type": "text", "bbox": [ 108, 699, 505, 731 ], "lines": [ { "bbox": [ 106, 698, 505, 712 ], "spans": [ { "bbox": [ 106, 698, 505, 712 ], "score": 1.0, "content": "Xuefeng Du, Jingfeng Zhang, Bo Han, Tongliang Liu, Yu Rong, Gang Niu, Junzhou Huang, and", "type": "text" } ], "index": 41 }, { "bbox": [ 116, 710, 505, 722 ], "spans": [ { "bbox": [ 116, 710, 505, 722 ], "score": 1.0, "content": "Masashi Sugiyama. Learning diverse-structured networks for adversarial robustness. arXiv", "type": "text" } ], "index": 42 }, { "bbox": [ 115, 721, 254, 732 ], "spans": [ { "bbox": [ 115, 721, 254, 732 ], "score": 1.0, "content": "preprint arXiv:2102.01886, 2021.", "type": "text" } ], "index": 43 } ], "index": 42 } ], "page_idx": 9, "page_size": [ 612, 792 ], "discarded_blocks": [ { "type": "discarded", "bbox": [ 107, 27, 308, 37 ], "lines": [ { "bbox": [ 107, 26, 308, 38 ], "spans": [ { "bbox": [ 107, 26, 308, 38 ], "score": 1.0, "content": "Under review as a conference paper at ICLR 2022", "type": "text" } ] } ] }, { "type": "discarded", "bbox": [ 301, 751, 311, 760 ], "lines": [ { "bbox": [ 299, 750, 313, 765 ], "spans": [ { "bbox": [ 299, 750, 313, 765 ], "score": 1.0, "content": "", "type": "text", "height": 15, "width": 14 } ] } ] } ], "para_blocks": [ { "type": "title", "bbox": [ 108, 81, 267, 94 ], "lines": [ { "bbox": [ 106, 81, 270, 95 ], "spans": [ { "bbox": [ 106, 81, 270, 95 ], "score": 1.0, "content": "REPRODUCIBILITY STATEMENT", "type": "text" } ], "index": 0 } ], "index": 0 }, { "type": "text", "bbox": [ 107, 106, 505, 173 ], "lines": [ { "bbox": [ 105, 106, 506, 119 ], "spans": [ { "bbox": [ 105, 106, 506, 119 ], "score": 1.0, "content": "For sake of reproducibility of our algorithm, we make the following efforts: (i) In Section 5.1, we", "type": "text" } ], "index": 1 }, { "bbox": [ 106, 118, 505, 130 ], "spans": [ { "bbox": [ 106, 118, 505, 130 ], "score": 1.0, "content": "clearly state the implementation details, including benchmark datasets, network structure, baselines,", "type": "text" } ], "index": 2 }, { "bbox": [ 105, 128, 505, 141 ], "spans": [ { "bbox": [ 105, 128, 505, 141 ], "score": 1.0, "content": "training and test parameter setting as well as training and test attack setting. (ii) In Section 5.3,", "type": "text" } ], "index": 3 }, { "bbox": [ 105, 140, 505, 153 ], "spans": [ { "bbox": [ 105, 140, 505, 153 ], "score": 1.0, "content": "we evaluate the sensitivity of the algorithm to hyperparameters and show the detailed hyperparam-", "type": "text" } ], "index": 4 }, { "bbox": [ 106, 151, 505, 163 ], "spans": [ { "bbox": [ 106, 151, 505, 163 ], "score": 1.0, "content": "eter tuning process. (iii) At last, we open-source the source code of RWP algorithm, available at", "type": "text" } ], "index": 5 }, { "bbox": [ 105, 162, 205, 174 ], "spans": [ { "bbox": [ 105, 162, 205, 174 ], "score": 1.0, "content": "supplementary material.", "type": "text" } ], "index": 6 } ], "index": 3.5, "bbox_fs": [ 105, 106, 506, 174 ] }, { "type": "title", "bbox": [ 107, 191, 175, 203 ], "lines": [ { "bbox": [ 106, 191, 176, 204 ], "spans": [ { "bbox": [ 106, 191, 176, 204 ], "score": 1.0, "content": "REFERENCES", "type": "text" } ], "index": 7 } ], "index": 7 }, { "type": "text", "bbox": [ 108, 210, 504, 243 ], "lines": [ { "bbox": [ 105, 209, 505, 223 ], "spans": [ { "bbox": [ 105, 209, 505, 223 ], "score": 1.0, "content": "Maksym Andriushchenko, Francesco Croce, Nicolas Flammarion, and Matthias Hein. Square at-", "type": "text" } ], "index": 8 }, { "bbox": [ 115, 221, 505, 234 ], "spans": [ { "bbox": [ 115, 221, 505, 234 ], "score": 1.0, "content": "tack: a query-efficient black-box adversarial attack via random search. In European Conference", "type": "text" } ], "index": 9 }, { "bbox": [ 116, 232, 319, 244 ], "spans": [ { "bbox": [ 116, 232, 319, 244 ], "score": 1.0, "content": "on Computer Vision, pp. 484–501. Springer, 2020.", "type": "text" } ], "index": 10 } ], "index": 9, "bbox_fs": [ 105, 209, 505, 244 ] }, { "type": "text", "bbox": [ 107, 252, 503, 286 ], "lines": [ { "bbox": [ 105, 252, 505, 265 ], "spans": [ { "bbox": [ 105, 252, 505, 265 ], "score": 1.0, "content": "Anish Athalye, Nicholas Carlini, and David Wagner. Obfuscated gradients give a false sense of se-", "type": "text" } ], "index": 11 }, { "bbox": [ 116, 264, 505, 276 ], "spans": [ { "bbox": [ 116, 264, 505, 276 ], "score": 1.0, "content": "curity: Circumventing defenses to adversarial examples. In International conference on machine", "type": "text" } ], "index": 12 }, { "bbox": [ 116, 274, 268, 288 ], "spans": [ { "bbox": [ 116, 274, 268, 288 ], "score": 1.0, "content": "learning, pp. 274–283. PMLR, 2018.", "type": "text" } ], "index": 13 } ], "index": 12, "bbox_fs": [ 105, 252, 505, 288 ] }, { "type": "text", "bbox": [ 106, 295, 503, 329 ], "lines": [ { "bbox": [ 105, 294, 505, 308 ], "spans": [ { "bbox": [ 105, 294, 505, 308 ], "score": 1.0, "content": "Mikhail Belkin, Daniel Hsu, Siyuan Ma, and Soumik Mandal. Reconciling modern machine-", "type": "text" } ], "index": 14 }, { "bbox": [ 115, 306, 505, 320 ], "spans": [ { "bbox": [ 115, 306, 505, 320 ], "score": 1.0, "content": "learning practice and the classical bias–variance trade-off. Proceedings of the National Academy", "type": "text" } ], "index": 15 }, { "bbox": [ 115, 317, 285, 329 ], "spans": [ { "bbox": [ 115, 317, 285, 329 ], "score": 1.0, "content": "of Sciences, 116(32):15849–15854, 2019.", "type": "text" } ], "index": 16 } ], "index": 15, "bbox_fs": [ 105, 294, 505, 329 ] }, { "type": "text", "bbox": [ 105, 337, 504, 361 ], "lines": [ { "bbox": [ 105, 336, 506, 351 ], "spans": [ { "bbox": [ 105, 336, 506, 351 ], "score": 1.0, "content": "Qi-Zhi Cai, Min Du, Chang Liu, and Dawn Song. Curriculum adversarial training. arXiv preprint", "type": "text" } ], "index": 17 }, { "bbox": [ 115, 348, 220, 361 ], "spans": [ { "bbox": [ 115, 348, 220, 361 ], "score": 1.0, "content": "arXiv:1805.04807, 2018.", "type": "text" } ], "index": 18 } ], "index": 17.5, "bbox_fs": [ 105, 336, 506, 361 ] }, { "type": "text", "bbox": [ 104, 369, 505, 393 ], "lines": [ { "bbox": [ 106, 369, 505, 382 ], "spans": [ { "bbox": [ 106, 369, 505, 382 ], "score": 1.0, "content": "Nicholas Carlini and David Wagner. Towards evaluating the robustness of neural networks. In 2017", "type": "text" } ], "index": 19 }, { "bbox": [ 115, 380, 395, 393 ], "spans": [ { "bbox": [ 115, 380, 395, 393 ], "score": 1.0, "content": "ieee symposium on security and privacy (sp), pp. 39–57. IEEE, 2017.", "type": "text" } ], "index": 20 } ], "index": 19.5, "bbox_fs": [ 106, 369, 505, 393 ] }, { "type": "text", "bbox": [ 106, 400, 504, 424 ], "lines": [ { "bbox": [ 106, 400, 505, 414 ], "spans": [ { "bbox": [ 106, 400, 505, 414 ], "score": 1.0, "content": "Yair Carmon, Aditi Raghunathan, Ludwig Schmidt, Percy Liang, and John C Duchi. Unlabeled data", "type": "text" } ], "index": 21 }, { "bbox": [ 115, 412, 412, 424 ], "spans": [ { "bbox": [ 115, 412, 412, 424 ], "score": 1.0, "content": "improves adversarial robustness. arXiv preprint arXiv:1905.13736, 2019.", "type": "text" } ], "index": 22 } ], "index": 21.5, "bbox_fs": [ 106, 400, 505, 424 ] }, { "type": "text", "bbox": [ 106, 432, 504, 456 ], "lines": [ { "bbox": [ 106, 431, 505, 446 ], "spans": [ { "bbox": [ 106, 431, 505, 446 ], "score": 1.0, "content": "Chen Chen, Jingfeng Zhang, Xilie Xu, Tianlei Hu, Gang Niu, Gang Chen, and Masashi Sugiyama.", "type": "text" } ], "index": 23 }, { "bbox": [ 116, 443, 460, 456 ], "spans": [ { "bbox": [ 116, 443, 460, 456 ], "score": 1.0, "content": "Guided interpolation for adversarial training. arXiv preprint arXiv:2102.07327, 2021.", "type": "text" } ], "index": 24 } ], "index": 23.5, "bbox_fs": [ 106, 431, 505, 456 ] }, { "type": "text", "bbox": [ 105, 464, 504, 487 ], "lines": [ { "bbox": [ 105, 464, 505, 477 ], "spans": [ { "bbox": [ 105, 464, 505, 477 ], "score": 1.0, "content": "Jinghui Chen, Dongruo Zhou, Jinfeng Yi, and Quanquan Gu. A frank-wolfe framework for efficient", "type": "text" } ], "index": 25 }, { "bbox": [ 116, 475, 382, 488 ], "spans": [ { "bbox": [ 116, 475, 382, 488 ], "score": 1.0, "content": "and effective adversarial attacks. In AAAI, pp. 3486–3494, 2020a.", "type": "text" } ], "index": 26 } ], "index": 25.5, "bbox_fs": [ 105, 464, 505, 488 ] }, { "type": "text", "bbox": [ 106, 495, 503, 529 ], "lines": [ { "bbox": [ 106, 495, 505, 509 ], "spans": [ { "bbox": [ 106, 495, 505, 509 ], "score": 1.0, "content": "Tianlong Chen, Zhenyu Zhang, Sijia Liu, Shiyu Chang, and Zhangyang Wang. Robust overfitting", "type": "text" } ], "index": 27 }, { "bbox": [ 115, 506, 505, 521 ], "spans": [ { "bbox": [ 115, 506, 505, 521 ], "score": 1.0, "content": "may be mitigated by properly learned smoothening. In International Conference on Learning", "type": "text" } ], "index": 28 }, { "bbox": [ 116, 518, 216, 530 ], "spans": [ { "bbox": [ 116, 518, 216, 530 ], "score": 1.0, "content": "Representations, 2020b.", "type": "text" } ], "index": 29 } ], "index": 28, "bbox_fs": [ 106, 495, 505, 530 ] }, { "type": "text", "bbox": [ 107, 538, 503, 572 ], "lines": [ { "bbox": [ 105, 538, 505, 551 ], "spans": [ { "bbox": [ 105, 538, 505, 551 ], "score": 1.0, "content": "Francesco Croce and Matthias Hein. Minimally distorted adversarial examples with a fast adaptive", "type": "text" } ], "index": 30 }, { "bbox": [ 116, 550, 505, 562 ], "spans": [ { "bbox": [ 116, 550, 505, 562 ], "score": 1.0, "content": "boundary attack. In International Conference on Machine Learning, pp. 2196–2205. PMLR,", "type": "text" } ], "index": 31 }, { "bbox": [ 115, 559, 147, 574 ], "spans": [ { "bbox": [ 115, 559, 147, 574 ], "score": 1.0, "content": "2020a.", "type": "text" } ], "index": 32 } ], "index": 31, "bbox_fs": [ 105, 538, 505, 574 ] }, { "type": "text", "bbox": [ 106, 581, 505, 615 ], "lines": [ { "bbox": [ 105, 581, 505, 593 ], "spans": [ { "bbox": [ 105, 581, 505, 593 ], "score": 1.0, "content": "Francesco Croce and Matthias Hein. Reliable evaluation of adversarial robustness with an ensemble", "type": "text" } ], "index": 33 }, { "bbox": [ 115, 592, 505, 605 ], "spans": [ { "bbox": [ 115, 592, 505, 605 ], "score": 1.0, "content": "of diverse parameter-free attacks. In International conference on machine learning, pp. 2206–", "type": "text" } ], "index": 34 }, { "bbox": [ 116, 602, 203, 615 ], "spans": [ { "bbox": [ 116, 602, 203, 615 ], "score": 1.0, "content": "2216. PMLR, 2020b.", "type": "text" } ], "index": 35 } ], "index": 34, "bbox_fs": [ 105, 581, 505, 615 ] }, { "type": "text", "bbox": [ 105, 624, 504, 647 ], "lines": [ { "bbox": [ 105, 622, 505, 637 ], "spans": [ { "bbox": [ 105, 622, 505, 637 ], "score": 1.0, "content": "Jacob Devlin, Ming-Wei Chang, Kenton Lee, and Kristina Toutanova. Bert: Pre-training of deep", "type": "text" } ], "index": 36 }, { "bbox": [ 115, 635, 499, 648 ], "spans": [ { "bbox": [ 115, 635, 499, 648 ], "score": 1.0, "content": "bidirectional transformers for language understanding. arXiv preprint arXiv:1810.04805, 2018.", "type": "text" } ], "index": 37 } ], "index": 36.5, "bbox_fs": [ 105, 622, 505, 648 ] }, { "type": "text", "bbox": [ 107, 655, 504, 690 ], "lines": [ { "bbox": [ 106, 655, 505, 669 ], "spans": [ { "bbox": [ 106, 655, 505, 669 ], "score": 1.0, "content": "Yinpeng Dong, Fangzhou Liao, Tianyu Pang, Hang Su, Jun Zhu, Xiaolin Hu, and Jianguo Li. Boost-", "type": "text" } ], "index": 38 }, { "bbox": [ 115, 666, 506, 680 ], "spans": [ { "bbox": [ 115, 666, 506, 680 ], "score": 1.0, "content": "ing adversarial attacks with momentum. In Proceedings of the IEEE conference on computer", "type": "text" } ], "index": 39 }, { "bbox": [ 116, 678, 331, 690 ], "spans": [ { "bbox": [ 116, 678, 331, 690 ], "score": 1.0, "content": "vision and pattern recognition, pp. 9185–9193, 2018.", "type": "text" } ], "index": 40 } ], "index": 39, "bbox_fs": [ 106, 655, 506, 690 ] }, { "type": "text", "bbox": [ 108, 699, 505, 731 ], "lines": [ { "bbox": [ 106, 698, 505, 712 ], "spans": [ { "bbox": [ 106, 698, 505, 712 ], "score": 1.0, "content": "Xuefeng Du, Jingfeng Zhang, Bo Han, Tongliang Liu, Yu Rong, Gang Niu, Junzhou Huang, and", "type": "text" } ], "index": 41 }, { "bbox": [ 116, 710, 505, 722 ], "spans": [ { "bbox": [ 116, 710, 505, 722 ], "score": 1.0, "content": "Masashi Sugiyama. Learning diverse-structured networks for adversarial robustness. arXiv", "type": "text" } ], "index": 42 }, { "bbox": [ 115, 721, 254, 732 ], "spans": [ { "bbox": [ 115, 721, 254, 732 ], "score": 1.0, "content": "preprint arXiv:2102.01886, 2021.", "type": "text" } ], "index": 43 } ], "index": 42, "bbox_fs": [ 106, 698, 505, 732 ] } ] }, { "preproc_blocks": [ { "type": "text", "bbox": [ 106, 82, 504, 116 ], "lines": [ { "bbox": [ 105, 82, 506, 95 ], "spans": [ { "bbox": [ 105, 82, 506, 95 ], "score": 1.0, "content": "Logan Engstrom, Dimitris Tsipras, Ludwig Schmidt, and Aleksander Madry. A rotation and a", "type": "text" } ], "index": 0 }, { "bbox": [ 116, 93, 505, 106 ], "spans": [ { "bbox": [ 116, 93, 505, 106 ], "score": 1.0, "content": "translation suffice: Fooling cnns with simple transformations. arXiv preprint arXiv:1712.02779,", "type": "text" } ], "index": 1 }, { "bbox": [ 115, 104, 171, 116 ], "spans": [ { "bbox": [ 115, 104, 171, 116 ], "score": 1.0, "content": "1(2):3, 2017.", "type": "text" } ], "index": 2 } ], "index": 1 }, { "type": "text", "bbox": [ 108, 123, 504, 157 ], "lines": [ { "bbox": [ 105, 123, 505, 136 ], "spans": [ { "bbox": [ 105, 123, 505, 136 ], "score": 1.0, "content": "Logan Engstrom, Brandon Tran, Dimitris Tsipras, Ludwig Schmidt, and Aleksander Madry. Ex-", "type": "text" } ], "index": 3 }, { "bbox": [ 115, 133, 506, 148 ], "spans": [ { "bbox": [ 115, 133, 506, 148 ], "score": 1.0, "content": "ploring the landscape of spatial robustness. In International Conference on Machine Learning,", "type": "text" } ], "index": 4 }, { "bbox": [ 115, 145, 238, 157 ], "spans": [ { "bbox": [ 115, 145, 238, 157 ], "score": 1.0, "content": "pp. 1802–1811. PMLR, 2019.", "type": "text" } ], "index": 5 } ], "index": 4 }, { "type": "text", "bbox": [ 106, 163, 503, 187 ], "lines": [ { "bbox": [ 105, 163, 505, 177 ], "spans": [ { "bbox": [ 105, 163, 505, 177 ], "score": 1.0, "content": "Pierre Foret, Ariel Kleiner, Hossein Mobahi, and Behnam Neyshabur. Sharpness-aware minimiza-", "type": "text" } ], "index": 6 }, { "bbox": [ 115, 175, 459, 188 ], "spans": [ { "bbox": [ 115, 175, 459, 188 ], "score": 1.0, "content": "tion for efficiently improving generalization. arXiv preprint arXiv:2010.01412, 2020.", "type": "text" } ], "index": 7 } ], "index": 6.5 }, { "type": "text", "bbox": [ 106, 194, 503, 217 ], "lines": [ { "bbox": [ 106, 194, 505, 207 ], "spans": [ { "bbox": [ 106, 194, 505, 207 ], "score": 1.0, "content": "Ian J Goodfellow, Jonathon Shlens, and Christian Szegedy. Explaining and harnessing adversarial", "type": "text" } ], "index": 8 }, { "bbox": [ 115, 205, 317, 217 ], "spans": [ { "bbox": [ 115, 205, 317, 217 ], "score": 1.0, "content": "examples. arXiv preprint arXiv:1412.6572, 2014.", "type": "text" } ], "index": 9 } ], "index": 8.5 }, { "type": "text", "bbox": [ 106, 223, 505, 258 ], "lines": [ { "bbox": [ 107, 224, 505, 236 ], "spans": [ { "bbox": [ 107, 224, 505, 236 ], "score": 1.0, "content": "Chuan Guo, Mayank Rana, Moustapha Cisse, and Laurens Van Der Maaten. Countering adversarial", "type": "text" } ], "index": 10 }, { "bbox": [ 115, 235, 505, 248 ], "spans": [ { "bbox": [ 115, 235, 505, 248 ], "score": 1.0, "content": "images using input transformations. In International Conference on Learning Representations,", "type": "text" } ], "index": 11 }, { "bbox": [ 115, 244, 144, 259 ], "spans": [ { "bbox": [ 115, 244, 144, 259 ], "score": 1.0, "content": "2018.", "type": "text" } ], "index": 12 } ], "index": 11 }, { "type": "text", "bbox": [ 106, 264, 505, 299 ], "lines": [ { "bbox": [ 105, 264, 504, 279 ], "spans": [ { "bbox": [ 105, 264, 504, 279 ], "score": 1.0, "content": "Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recog-", "type": "text" } ], "index": 13 }, { "bbox": [ 115, 275, 505, 290 ], "spans": [ { "bbox": [ 115, 275, 505, 290 ], "score": 1.0, "content": "nition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp.", "type": "text" } ], "index": 14 }, { "bbox": [ 116, 287, 181, 298 ], "spans": [ { "bbox": [ 116, 287, 181, 298 ], "score": 1.0, "content": "770–778, 2016.", "type": "text" } ], "index": 15 } ], "index": 14 }, { "type": "text", "bbox": [ 106, 305, 504, 329 ], "lines": [ { "bbox": [ 105, 305, 505, 318 ], "spans": [ { "bbox": [ 105, 305, 505, 318 ], "score": 1.0, "content": "Dan Hendrycks, Kimin Lee, and Mantas Mazeika. Using pre-training can improve model robustness", "type": "text" } ], "index": 16 }, { "bbox": [ 115, 317, 505, 329 ], "spans": [ { "bbox": [ 115, 317, 505, 329 ], "score": 1.0, "content": "and uncertainty. In International Conference on Machine Learning, pp. 2712–2721. PMLR, 2019.", "type": "text" } ], "index": 17 } ], "index": 16.5 }, { "type": "text", "bbox": [ 106, 335, 504, 358 ], "lines": [ { "bbox": [ 104, 334, 505, 350 ], "spans": [ { "bbox": [ 104, 334, 505, 350 ], "score": 1.0, "content": "Harini Kannan, Alexey Kurakin, and Ian Goodfellow. Adversarial logit pairing. arXiv preprint", "type": "text" } ], "index": 18 }, { "bbox": [ 115, 347, 219, 358 ], "spans": [ { "bbox": [ 115, 347, 219, 358 ], "score": 1.0, "content": "arXiv:1803.06373, 2018.", "type": "text" } ], "index": 19 } ], "index": 18.5 }, { "type": "text", "bbox": [ 106, 366, 504, 388 ], "lines": [ { "bbox": [ 105, 364, 505, 380 ], "spans": [ { "bbox": [ 105, 364, 505, 380 ], "score": 1.0, "content": "Alex Krizhevsky, Geoffrey Hinton, et al. Learning multiple layers of features from tiny images.", "type": "text" } ], "index": 20 }, { "bbox": [ 114, 375, 143, 389 ], "spans": [ { "bbox": [ 114, 375, 143, 389 ], "score": 1.0, "content": "2009.", "type": "text" } ], "index": 21 } ], "index": 20.5 }, { "type": "text", "bbox": [ 106, 396, 504, 430 ], "lines": [ { "bbox": [ 106, 396, 505, 409 ], "spans": [ { "bbox": [ 106, 396, 505, 409 ], "score": 1.0, "content": "Saehyung Lee, Hyungyu Lee, and Sungroh Yoon. Adversarial vertex mixup: Toward better adver-", "type": "text" } ], "index": 22 }, { "bbox": [ 116, 406, 505, 420 ], "spans": [ { "bbox": [ 116, 406, 505, 420 ], "score": 1.0, "content": "sarially robust generalization. In Proceedings of the IEEE/CVF Conference on Computer Vision", "type": "text" } ], "index": 23 }, { "bbox": [ 116, 417, 299, 431 ], "spans": [ { "bbox": [ 116, 417, 299, 431 ], "score": 1.0, "content": "and Pattern Recognition, pp. 272–281, 2020.", "type": "text" } ], "index": 24 } ], "index": 23 }, { "type": "text", "bbox": [ 106, 436, 504, 460 ], "lines": [ { "bbox": [ 106, 437, 505, 450 ], "spans": [ { "bbox": [ 106, 437, 505, 450 ], "score": 1.0, "content": "Hao Li, Zheng Xu, Gavin Taylor, Christoph Studer, and Tom Goldstein. Visualizing the loss land-", "type": "text" } ], "index": 25 }, { "bbox": [ 116, 448, 364, 459 ], "spans": [ { "bbox": [ 116, 448, 364, 459 ], "score": 1.0, "content": "scape of neural nets. arXiv preprint arXiv:1712.09913, 2017.", "type": "text" } ], "index": 26 } ], "index": 25.5 }, { "type": "text", "bbox": [ 106, 466, 504, 501 ], "lines": [ { "bbox": [ 106, 466, 506, 480 ], "spans": [ { "bbox": [ 106, 466, 506, 480 ], "score": 1.0, "content": "Fangzhou Liao, Ming Liang, Yinpeng Dong, Tianyu Pang, Xiaolin Hu, and Jun Zhu. Defense against", "type": "text" } ], "index": 27 }, { "bbox": [ 115, 478, 505, 490 ], "spans": [ { "bbox": [ 115, 478, 505, 490 ], "score": 1.0, "content": "adversarial attacks using high-level representation guided denoiser. In Proceedings of the IEEE", "type": "text" } ], "index": 28 }, { "bbox": [ 117, 488, 438, 502 ], "spans": [ { "bbox": [ 117, 488, 438, 502 ], "score": 1.0, "content": "Conference on Computer Vision and Pattern Recognition, pp. 1778–1787, 2018.", "type": "text" } ], "index": 29 } ], "index": 28 }, { "type": "text", "bbox": [ 107, 507, 504, 541 ], "lines": [ { "bbox": [ 106, 507, 504, 520 ], "spans": [ { "bbox": [ 106, 507, 504, 520 ], "score": 1.0, "content": "Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, and Adrian Vladu.", "type": "text" } ], "index": 30 }, { "bbox": [ 116, 518, 505, 531 ], "spans": [ { "bbox": [ 116, 518, 505, 531 ], "score": 1.0, "content": "Towards deep learning models resistant to adversarial attacks. arXiv preprint arXiv:1706.06083,", "type": "text" } ], "index": 31 }, { "bbox": [ 114, 528, 144, 541 ], "spans": [ { "bbox": [ 114, 528, 144, 541 ], "score": 1.0, "content": "2017.", "type": "text" } ], "index": 32 } ], "index": 31 }, { "type": "text", "bbox": [ 105, 548, 505, 572 ], "lines": [ { "bbox": [ 105, 548, 505, 561 ], "spans": [ { "bbox": [ 105, 548, 505, 561 ], "score": 1.0, "content": "Jan Hendrik Metzen, Tim Genewein, Volker Fischer, and Bastian Bischoff. On detecting adversarial", "type": "text" } ], "index": 33 }, { "bbox": [ 115, 559, 434, 572 ], "spans": [ { "bbox": [ 115, 559, 434, 572 ], "score": 1.0, "content": "perturbations. In International Conference on Learning Representations, 2017.", "type": "text" } ], "index": 34 } ], "index": 33.5 }, { "type": "text", "bbox": [ 105, 578, 503, 602 ], "lines": [ { "bbox": [ 106, 579, 504, 591 ], "spans": [ { "bbox": [ 106, 579, 504, 591 ], "score": 1.0, "content": "Marius Mosbach, Maksym Andriushchenko, Thomas Trost, Matthias Hein, and Dietrich Klakow.", "type": "text" } ], "index": 35 }, { "bbox": [ 116, 590, 500, 603 ], "spans": [ { "bbox": [ 116, 590, 500, 603 ], "score": 1.0, "content": "Logit pairing methods can fool gradient-based attacks. arXiv preprint arXiv:1810.12042, 2018.", "type": "text" } ], "index": 36 } ], "index": 35.5 }, { "type": "text", "bbox": [ 105, 608, 504, 631 ], "lines": [ { "bbox": [ 106, 606, 506, 623 ], "spans": [ { "bbox": [ 106, 606, 506, 623 ], "score": 1.0, "content": "Yuval Netzer, Tao Wang, Adam Coates, Alessandro Bissacco, Bo Wu, and Andrew Y Ng. Reading", "type": "text" } ], "index": 37 }, { "bbox": [ 116, 619, 382, 631 ], "spans": [ { "bbox": [ 116, 619, 382, 631 ], "score": 1.0, "content": "digits in natural images with unsupervised feature learning. 2011.", "type": "text" } ], "index": 38 } ], "index": 37.5 }, { "type": "text", "bbox": [ 105, 638, 504, 661 ], "lines": [ { "bbox": [ 105, 637, 504, 652 ], "spans": [ { "bbox": [ 105, 637, 504, 652 ], "score": 1.0, "content": "Behnam Neyshabur, Srinadh Bhojanapalli, David McAllester, and Nathan Srebro. Exploring gener-", "type": "text" } ], "index": 39 }, { "bbox": [ 115, 649, 386, 662 ], "spans": [ { "bbox": [ 115, 649, 386, 662 ], "score": 1.0, "content": "alization in deep learning. arXiv preprint arXiv:1706.08947, 2017.", "type": "text" } ], "index": 40 } ], "index": 39.5 }, { "type": "text", "bbox": [ 107, 668, 503, 702 ], "lines": [ { "bbox": [ 105, 668, 506, 681 ], "spans": [ { "bbox": [ 105, 668, 506, 681 ], "score": 1.0, "content": "Nicolas Papernot, Patrick McDaniel, Xi Wu, Somesh Jha, and Ananthram Swami. Distillation as a", "type": "text" } ], "index": 41 }, { "bbox": [ 116, 679, 505, 693 ], "spans": [ { "bbox": [ 116, 679, 505, 693 ], "score": 1.0, "content": "defense to adversarial perturbations against deep neural networks. In 2016 IEEE Symposium on", "type": "text" } ], "index": 42 }, { "bbox": [ 116, 691, 331, 703 ], "spans": [ { "bbox": [ 116, 691, 203, 703 ], "score": 1.0, "content": "Security and Privacy", "type": "text" }, { "bbox": [ 203, 691, 220, 702 ], "score": 0.26, "content": "( S P )", "type": "inline_equation" }, { "bbox": [ 220, 691, 331, 703 ], "score": 1.0, "content": "), pp. 582–597. IEEE, 2016.", "type": "text" } ], "index": 43 } ], "index": 42 }, { "type": "text", "bbox": [ 106, 709, 503, 732 ], "lines": [ { "bbox": [ 105, 708, 505, 722 ], "spans": [ { "bbox": [ 105, 708, 505, 722 ], "score": 1.0, "content": "Leslie Rice, Eric Wong, and Zico Kolter. Overfitting in adversarially robust deep learning. In", "type": "text" } ], "index": 44 }, { "bbox": [ 115, 720, 432, 733 ], "spans": [ { "bbox": [ 115, 720, 432, 733 ], "score": 1.0, "content": "International Conference on Machine Learning, pp. 8093–8104. PMLR, 2020.", "type": "text" } ], "index": 45 } ], "index": 44.5 } ], "page_idx": 10, "page_size": [ 612, 792 ], "discarded_blocks": [ { "type": "discarded", "bbox": [ 300, 751, 310, 760 ], "lines": [ { "bbox": [ 299, 750, 312, 765 ], "spans": [ { "bbox": [ 299, 750, 312, 765 ], "score": 1.0, "content": "", "type": "text", "height": 15, "width": 13 } ] } ] }, { "type": "discarded", "bbox": [ 107, 27, 308, 37 ], "lines": [ { "bbox": [ 107, 26, 308, 38 ], "spans": [ { "bbox": [ 107, 26, 308, 38 ], "score": 1.0, "content": "Under review as a conference paper at ICLR 2022", "type": "text" } ] } ] } ], "para_blocks": [ { "type": "text", "bbox": [ 106, 82, 504, 116 ], "lines": [ { "bbox": [ 105, 82, 506, 95 ], "spans": [ { "bbox": [ 105, 82, 506, 95 ], "score": 1.0, "content": "Logan Engstrom, Dimitris Tsipras, Ludwig Schmidt, and Aleksander Madry. A rotation and a", "type": "text" } ], "index": 0 }, { "bbox": [ 116, 93, 505, 106 ], "spans": [ { "bbox": [ 116, 93, 505, 106 ], "score": 1.0, "content": "translation suffice: Fooling cnns with simple transformations. arXiv preprint arXiv:1712.02779,", "type": "text" } ], "index": 1 }, { "bbox": [ 115, 104, 171, 116 ], "spans": [ { "bbox": [ 115, 104, 171, 116 ], "score": 1.0, "content": "1(2):3, 2017.", "type": "text" } ], "index": 2 } ], "index": 1, "bbox_fs": [ 105, 82, 506, 116 ] }, { "type": "text", "bbox": [ 108, 123, 504, 157 ], "lines": [ { "bbox": [ 105, 123, 505, 136 ], "spans": [ { "bbox": [ 105, 123, 505, 136 ], "score": 1.0, "content": "Logan Engstrom, Brandon Tran, Dimitris Tsipras, Ludwig Schmidt, and Aleksander Madry. Ex-", "type": "text" } ], "index": 3 }, { "bbox": [ 115, 133, 506, 148 ], "spans": [ { "bbox": [ 115, 133, 506, 148 ], "score": 1.0, "content": "ploring the landscape of spatial robustness. In International Conference on Machine Learning,", "type": "text" } ], "index": 4 }, { "bbox": [ 115, 145, 238, 157 ], "spans": [ { "bbox": [ 115, 145, 238, 157 ], "score": 1.0, "content": "pp. 1802–1811. PMLR, 2019.", "type": "text" } ], "index": 5 } ], "index": 4, "bbox_fs": [ 105, 123, 506, 157 ] }, { "type": "text", "bbox": [ 106, 163, 503, 187 ], "lines": [ { "bbox": [ 105, 163, 505, 177 ], "spans": [ { "bbox": [ 105, 163, 505, 177 ], "score": 1.0, "content": "Pierre Foret, Ariel Kleiner, Hossein Mobahi, and Behnam Neyshabur. Sharpness-aware minimiza-", "type": "text" } ], "index": 6 }, { "bbox": [ 115, 175, 459, 188 ], "spans": [ { "bbox": [ 115, 175, 459, 188 ], "score": 1.0, "content": "tion for efficiently improving generalization. arXiv preprint arXiv:2010.01412, 2020.", "type": "text" } ], "index": 7 } ], "index": 6.5, "bbox_fs": [ 105, 163, 505, 188 ] }, { "type": "text", "bbox": [ 106, 194, 503, 217 ], "lines": [ { "bbox": [ 106, 194, 505, 207 ], "spans": [ { "bbox": [ 106, 194, 505, 207 ], "score": 1.0, "content": "Ian J Goodfellow, Jonathon Shlens, and Christian Szegedy. Explaining and harnessing adversarial", "type": "text" } ], "index": 8 }, { "bbox": [ 115, 205, 317, 217 ], "spans": [ { "bbox": [ 115, 205, 317, 217 ], "score": 1.0, "content": "examples. arXiv preprint arXiv:1412.6572, 2014.", "type": "text" } ], "index": 9 } ], "index": 8.5, "bbox_fs": [ 106, 194, 505, 217 ] }, { "type": "text", "bbox": [ 106, 223, 505, 258 ], "lines": [ { "bbox": [ 107, 224, 505, 236 ], "spans": [ { "bbox": [ 107, 224, 505, 236 ], "score": 1.0, "content": "Chuan Guo, Mayank Rana, Moustapha Cisse, and Laurens Van Der Maaten. Countering adversarial", "type": "text" } ], "index": 10 }, { "bbox": [ 115, 235, 505, 248 ], "spans": [ { "bbox": [ 115, 235, 505, 248 ], "score": 1.0, "content": "images using input transformations. In International Conference on Learning Representations,", "type": "text" } ], "index": 11 }, { "bbox": [ 115, 244, 144, 259 ], "spans": [ { "bbox": [ 115, 244, 144, 259 ], "score": 1.0, "content": "2018.", "type": "text" } ], "index": 12 } ], "index": 11, "bbox_fs": [ 107, 224, 505, 259 ] }, { "type": "text", "bbox": [ 106, 264, 505, 299 ], "lines": [ { "bbox": [ 105, 264, 504, 279 ], "spans": [ { "bbox": [ 105, 264, 504, 279 ], "score": 1.0, "content": "Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recog-", "type": "text" } ], "index": 13 }, { "bbox": [ 115, 275, 505, 290 ], "spans": [ { "bbox": [ 115, 275, 505, 290 ], "score": 1.0, "content": "nition. In Proceedings of the IEEE conference on computer vision and pattern recognition, pp.", "type": "text" } ], "index": 14 }, { "bbox": [ 116, 287, 181, 298 ], "spans": [ { "bbox": [ 116, 287, 181, 298 ], "score": 1.0, "content": "770–778, 2016.", "type": "text" } ], "index": 15 } ], "index": 14, "bbox_fs": [ 105, 264, 505, 298 ] }, { "type": "text", "bbox": [ 106, 305, 504, 329 ], "lines": [ { "bbox": [ 105, 305, 505, 318 ], "spans": [ { "bbox": [ 105, 305, 505, 318 ], "score": 1.0, "content": "Dan Hendrycks, Kimin Lee, and Mantas Mazeika. Using pre-training can improve model robustness", "type": "text" } ], "index": 16 }, { "bbox": [ 115, 317, 505, 329 ], "spans": [ { "bbox": [ 115, 317, 505, 329 ], "score": 1.0, "content": "and uncertainty. In International Conference on Machine Learning, pp. 2712–2721. PMLR, 2019.", "type": "text" } ], "index": 17 } ], "index": 16.5, "bbox_fs": [ 105, 305, 505, 329 ] }, { "type": "text", "bbox": [ 106, 335, 504, 358 ], "lines": [ { "bbox": [ 104, 334, 505, 350 ], "spans": [ { "bbox": [ 104, 334, 505, 350 ], "score": 1.0, "content": "Harini Kannan, Alexey Kurakin, and Ian Goodfellow. Adversarial logit pairing. arXiv preprint", "type": "text" } ], "index": 18 }, { "bbox": [ 115, 347, 219, 358 ], "spans": [ { "bbox": [ 115, 347, 219, 358 ], "score": 1.0, "content": "arXiv:1803.06373, 2018.", "type": "text" } ], "index": 19 } ], "index": 18.5, "bbox_fs": [ 104, 334, 505, 358 ] }, { "type": "text", "bbox": [ 106, 366, 504, 388 ], "lines": [ { "bbox": [ 105, 364, 505, 380 ], "spans": [ { "bbox": [ 105, 364, 505, 380 ], "score": 1.0, "content": "Alex Krizhevsky, Geoffrey Hinton, et al. Learning multiple layers of features from tiny images.", "type": "text" } ], "index": 20 }, { "bbox": [ 114, 375, 143, 389 ], "spans": [ { "bbox": [ 114, 375, 143, 389 ], "score": 1.0, "content": "2009.", "type": "text" } ], "index": 21 } ], "index": 20.5, "bbox_fs": [ 105, 364, 505, 389 ] }, { "type": "text", "bbox": [ 106, 396, 504, 430 ], "lines": [ { "bbox": [ 106, 396, 505, 409 ], "spans": [ { "bbox": [ 106, 396, 505, 409 ], "score": 1.0, "content": "Saehyung Lee, Hyungyu Lee, and Sungroh Yoon. Adversarial vertex mixup: Toward better adver-", "type": "text" } ], "index": 22 }, { "bbox": [ 116, 406, 505, 420 ], "spans": [ { "bbox": [ 116, 406, 505, 420 ], "score": 1.0, "content": "sarially robust generalization. In Proceedings of the IEEE/CVF Conference on Computer Vision", "type": "text" } ], "index": 23 }, { "bbox": [ 116, 417, 299, 431 ], "spans": [ { "bbox": [ 116, 417, 299, 431 ], "score": 1.0, "content": "and Pattern Recognition, pp. 272–281, 2020.", "type": "text" } ], "index": 24 } ], "index": 23, "bbox_fs": [ 106, 396, 505, 431 ] }, { "type": "text", "bbox": [ 106, 436, 504, 460 ], "lines": [ { "bbox": [ 106, 437, 505, 450 ], "spans": [ { "bbox": [ 106, 437, 505, 450 ], "score": 1.0, "content": "Hao Li, Zheng Xu, Gavin Taylor, Christoph Studer, and Tom Goldstein. Visualizing the loss land-", "type": "text" } ], "index": 25 }, { "bbox": [ 116, 448, 364, 459 ], "spans": [ { "bbox": [ 116, 448, 364, 459 ], "score": 1.0, "content": "scape of neural nets. arXiv preprint arXiv:1712.09913, 2017.", "type": "text" } ], "index": 26 } ], "index": 25.5, "bbox_fs": [ 106, 437, 505, 459 ] }, { "type": "text", "bbox": [ 106, 466, 504, 501 ], "lines": [ { "bbox": [ 106, 466, 506, 480 ], "spans": [ { "bbox": [ 106, 466, 506, 480 ], "score": 1.0, "content": "Fangzhou Liao, Ming Liang, Yinpeng Dong, Tianyu Pang, Xiaolin Hu, and Jun Zhu. Defense against", "type": "text" } ], "index": 27 }, { "bbox": [ 115, 478, 505, 490 ], "spans": [ { "bbox": [ 115, 478, 505, 490 ], "score": 1.0, "content": "adversarial attacks using high-level representation guided denoiser. In Proceedings of the IEEE", "type": "text" } ], "index": 28 }, { "bbox": [ 117, 488, 438, 502 ], "spans": [ { "bbox": [ 117, 488, 438, 502 ], "score": 1.0, "content": "Conference on Computer Vision and Pattern Recognition, pp. 1778–1787, 2018.", "type": "text" } ], "index": 29 } ], "index": 28, "bbox_fs": [ 106, 466, 506, 502 ] }, { "type": "text", "bbox": [ 107, 507, 504, 541 ], "lines": [ { "bbox": [ 106, 507, 504, 520 ], "spans": [ { "bbox": [ 106, 507, 504, 520 ], "score": 1.0, "content": "Aleksander Madry, Aleksandar Makelov, Ludwig Schmidt, Dimitris Tsipras, and Adrian Vladu.", "type": "text" } ], "index": 30 }, { "bbox": [ 116, 518, 505, 531 ], "spans": [ { "bbox": [ 116, 518, 505, 531 ], "score": 1.0, "content": "Towards deep learning models resistant to adversarial attacks. arXiv preprint arXiv:1706.06083,", "type": "text" } ], "index": 31 }, { "bbox": [ 114, 528, 144, 541 ], "spans": [ { "bbox": [ 114, 528, 144, 541 ], "score": 1.0, "content": "2017.", "type": "text" } ], "index": 32 } ], "index": 31, "bbox_fs": [ 106, 507, 505, 541 ] }, { "type": "text", "bbox": [ 105, 548, 505, 572 ], "lines": [ { "bbox": [ 105, 548, 505, 561 ], "spans": [ { "bbox": [ 105, 548, 505, 561 ], "score": 1.0, "content": "Jan Hendrik Metzen, Tim Genewein, Volker Fischer, and Bastian Bischoff. On detecting adversarial", "type": "text" } ], "index": 33 }, { "bbox": [ 115, 559, 434, 572 ], "spans": [ { "bbox": [ 115, 559, 434, 572 ], "score": 1.0, "content": "perturbations. In International Conference on Learning Representations, 2017.", "type": "text" } ], "index": 34 } ], "index": 33.5, "bbox_fs": [ 105, 548, 505, 572 ] }, { "type": "text", "bbox": [ 105, 578, 503, 602 ], "lines": [ { "bbox": [ 106, 579, 504, 591 ], "spans": [ { "bbox": [ 106, 579, 504, 591 ], "score": 1.0, "content": "Marius Mosbach, Maksym Andriushchenko, Thomas Trost, Matthias Hein, and Dietrich Klakow.", "type": "text" } ], "index": 35 }, { "bbox": [ 116, 590, 500, 603 ], "spans": [ { "bbox": [ 116, 590, 500, 603 ], "score": 1.0, "content": "Logit pairing methods can fool gradient-based attacks. arXiv preprint arXiv:1810.12042, 2018.", "type": "text" } ], "index": 36 } ], "index": 35.5, "bbox_fs": [ 106, 579, 504, 603 ] }, { "type": "text", "bbox": [ 105, 608, 504, 631 ], "lines": [ { "bbox": [ 106, 606, 506, 623 ], "spans": [ { "bbox": [ 106, 606, 506, 623 ], "score": 1.0, "content": "Yuval Netzer, Tao Wang, Adam Coates, Alessandro Bissacco, Bo Wu, and Andrew Y Ng. Reading", "type": "text" } ], "index": 37 }, { "bbox": [ 116, 619, 382, 631 ], "spans": [ { "bbox": [ 116, 619, 382, 631 ], "score": 1.0, "content": "digits in natural images with unsupervised feature learning. 2011.", "type": "text" } ], "index": 38 } ], "index": 37.5, "bbox_fs": [ 106, 606, 506, 631 ] }, { "type": "text", "bbox": [ 105, 638, 504, 661 ], "lines": [ { "bbox": [ 105, 637, 504, 652 ], "spans": [ { "bbox": [ 105, 637, 504, 652 ], "score": 1.0, "content": "Behnam Neyshabur, Srinadh Bhojanapalli, David McAllester, and Nathan Srebro. Exploring gener-", "type": "text" } ], "index": 39 }, { "bbox": [ 115, 649, 386, 662 ], "spans": [ { "bbox": [ 115, 649, 386, 662 ], "score": 1.0, "content": "alization in deep learning. arXiv preprint arXiv:1706.08947, 2017.", "type": "text" } ], "index": 40 } ], "index": 39.5, "bbox_fs": [ 105, 637, 504, 662 ] }, { "type": "text", "bbox": [ 107, 668, 503, 702 ], "lines": [ { "bbox": [ 105, 668, 506, 681 ], "spans": [ { "bbox": [ 105, 668, 506, 681 ], "score": 1.0, "content": "Nicolas Papernot, Patrick McDaniel, Xi Wu, Somesh Jha, and Ananthram Swami. Distillation as a", "type": "text" } ], "index": 41 }, { "bbox": [ 116, 679, 505, 693 ], "spans": [ { "bbox": [ 116, 679, 505, 693 ], "score": 1.0, "content": "defense to adversarial perturbations against deep neural networks. In 2016 IEEE Symposium on", "type": "text" } ], "index": 42 }, { "bbox": [ 116, 691, 331, 703 ], "spans": [ { "bbox": [ 116, 691, 203, 703 ], "score": 1.0, "content": "Security and Privacy", "type": "text" }, { "bbox": [ 203, 691, 220, 702 ], "score": 0.26, "content": "( S P )", "type": "inline_equation" }, { "bbox": [ 220, 691, 331, 703 ], "score": 1.0, "content": "), pp. 582–597. IEEE, 2016.", "type": "text" } ], "index": 43 } ], "index": 42, "bbox_fs": [ 105, 668, 506, 703 ] }, { "type": "text", "bbox": [ 106, 709, 503, 732 ], "lines": [ { "bbox": [ 105, 708, 505, 722 ], "spans": [ { "bbox": [ 105, 708, 505, 722 ], "score": 1.0, "content": "Leslie Rice, Eric Wong, and Zico Kolter. Overfitting in adversarially robust deep learning. In", "type": "text" } ], "index": 44 }, { "bbox": [ 115, 720, 432, 733 ], "spans": [ { "bbox": [ 115, 720, 432, 733 ], "score": 1.0, "content": "International Conference on Machine Learning, pp. 8093–8104. PMLR, 2020.", "type": "text" } ], "index": 45 } ], "index": 44.5, "bbox_fs": [ 105, 708, 505, 733 ] } ] }, { "preproc_blocks": [ { "type": "text", "bbox": [ 108, 82, 504, 116 ], "lines": [ { "bbox": [ 105, 81, 506, 95 ], "spans": [ { "bbox": [ 105, 81, 506, 95 ], "score": 1.0, "content": "Andrew Ross and Finale Doshi-Velez. Improving the adversarial robustness and interpretability of", "type": "text" } ], "index": 0 }, { "bbox": [ 116, 93, 505, 107 ], "spans": [ { "bbox": [ 116, 93, 505, 107 ], "score": 1.0, "content": "deep neural networks by regularizing their input gradients. In Proceedings of the AAAI Conference", "type": "text" } ], "index": 1 }, { "bbox": [ 116, 105, 291, 116 ], "spans": [ { "bbox": [ 116, 105, 291, 116 ], "score": 1.0, "content": "on Artificial Intelligence, volume 32, 2018.", "type": "text" } ], "index": 2 } ], "index": 1 }, { "type": "text", "bbox": [ 108, 123, 503, 157 ], "lines": [ { "bbox": [ 106, 124, 504, 136 ], "spans": [ { "bbox": [ 106, 124, 504, 136 ], "score": 1.0, "content": "Ludwig Schmidt, Shibani Santurkar, Dimitris Tsipras, Kunal Talwar, and Aleksander Madry. Ad-", "type": "text" } ], "index": 3 }, { "bbox": [ 115, 134, 505, 149 ], "spans": [ { "bbox": [ 115, 134, 505, 149 ], "score": 1.0, "content": "versarially robust generalization requires more data. Advances in Neural Information Processing", "type": "text" } ], "index": 4 }, { "bbox": [ 116, 146, 241, 158 ], "spans": [ { "bbox": [ 116, 146, 241, 158 ], "score": 1.0, "content": "Systems, 31:5014–5026, 2018.", "type": "text" } ], "index": 5 } ], "index": 4 }, { "type": "text", "bbox": [ 107, 164, 503, 188 ], "lines": [ { "bbox": [ 105, 165, 505, 178 ], "spans": [ { "bbox": [ 105, 165, 505, 178 ], "score": 1.0, "content": "Adi Shamir, Itay Safran, Eyal Ronen, and Orr Dunkelman. A simple explanation for the existence", "type": "text" } ], "index": 6 }, { "bbox": [ 115, 176, 499, 189 ], "spans": [ { "bbox": [ 115, 176, 499, 189 ], "score": 1.0, "content": "of adversarial examples with small hamming distance. arXiv preprint arXiv:1901.10861, 2019.", "type": "text" } ], "index": 7 } ], "index": 6.5 }, { "type": "text", "bbox": [ 106, 195, 506, 229 ], "lines": [ { "bbox": [ 106, 195, 506, 209 ], "spans": [ { "bbox": [ 106, 195, 506, 209 ], "score": 1.0, "content": "Chubiao Song, Kun He, Jiadong Lin, Liwei Wang, and John E Hopcroft. Robust local features for", "type": "text" } ], "index": 8 }, { "bbox": [ 115, 205, 506, 221 ], "spans": [ { "bbox": [ 115, 205, 506, 221 ], "score": 1.0, "content": "improving the generalization of adversarial training. In International Conference on Learning", "type": "text" } ], "index": 9 }, { "bbox": [ 115, 218, 210, 230 ], "spans": [ { "bbox": [ 115, 218, 210, 230 ], "score": 1.0, "content": "Representations, 2020.", "type": "text" } ], "index": 10 } ], "index": 9 }, { "type": "text", "bbox": [ 105, 236, 505, 260 ], "lines": [ { "bbox": [ 105, 237, 505, 250 ], "spans": [ { "bbox": [ 105, 237, 505, 250 ], "score": 1.0, "content": "Christian Szegedy, Wojciech Zaremba, Ilya Sutskever, Joan Bruna, Dumitru Erhan, Ian Goodfellow,", "type": "text" } ], "index": 11 }, { "bbox": [ 115, 248, 505, 261 ], "spans": [ { "bbox": [ 115, 248, 505, 261 ], "score": 1.0, "content": "and Rob Fergus. Intriguing properties of neural networks. arXiv preprint arXiv:1312.6199, 2013.", "type": "text" } ], "index": 12 } ], "index": 11.5 }, { "type": "text", "bbox": [ 106, 267, 505, 301 ], "lines": [ { "bbox": [ 106, 266, 505, 281 ], "spans": [ { "bbox": [ 106, 266, 505, 281 ], "score": 1.0, "content": "Guanhong Tao, Shiqing Ma, Yingqi Liu, and Xiangyu Zhang. Attacks meet interpretability:", "type": "text" } ], "index": 13 }, { "bbox": [ 115, 277, 505, 292 ], "spans": [ { "bbox": [ 115, 277, 505, 292 ], "score": 1.0, "content": "Attribute-steered detection of adversarial samples. In Advances in Neural Information Processing", "type": "text" } ], "index": 14 }, { "bbox": [ 115, 289, 243, 302 ], "spans": [ { "bbox": [ 115, 289, 243, 302 ], "score": 1.0, "content": "Systems, pp. 7717–7728, 2018.", "type": "text" } ], "index": 15 } ], "index": 14 }, { "type": "text", "bbox": [ 107, 308, 504, 342 ], "lines": [ { "bbox": [ 106, 309, 505, 321 ], "spans": [ { "bbox": [ 106, 309, 505, 321 ], "score": 1.0, "content": "Antonio Torralba, Rob Fergus, and William T Freeman. 80 million tiny images: A large data set for", "type": "text" } ], "index": 16 }, { "bbox": [ 116, 320, 505, 333 ], "spans": [ { "bbox": [ 116, 320, 505, 333 ], "score": 1.0, "content": "nonparametric object and scene recognition. IEEE transactions on pattern analysis and machine", "type": "text" } ], "index": 17 }, { "bbox": [ 117, 331, 272, 343 ], "spans": [ { "bbox": [ 117, 331, 272, 343 ], "score": 1.0, "content": "intelligence, 30(11):1958–1970, 2008.", "type": "text" } ], "index": 18 } ], "index": 17 }, { "type": "text", "bbox": [ 108, 349, 504, 384 ], "lines": [ { "bbox": [ 105, 349, 506, 363 ], "spans": [ { "bbox": [ 105, 349, 506, 363 ], "score": 1.0, "content": "Florian Tramer, Alexey Kurakin, Nicolas Papernot, Ian Goodfellow, Dan Boneh, and Patrick Mc- `", "type": "text" } ], "index": 19 }, { "bbox": [ 115, 361, 505, 374 ], "spans": [ { "bbox": [ 115, 361, 505, 374 ], "score": 1.0, "content": "Daniel. Ensemble adversarial training: Attacks and defenses. In International Conference on", "type": "text" } ], "index": 20 }, { "bbox": [ 116, 372, 249, 384 ], "spans": [ { "bbox": [ 116, 372, 249, 384 ], "score": 1.0, "content": "Learning Representations, 2018.", "type": "text" } ], "index": 21 } ], "index": 20 }, { "type": "text", "bbox": [ 106, 391, 504, 415 ], "lines": [ { "bbox": [ 105, 390, 506, 405 ], "spans": [ { "bbox": [ 105, 390, 506, 405 ], "score": 1.0, "content": "Florian Tramer, Nicholas Carlini, Wieland Brendel, and Aleksander Madry. On adaptive attacks to", "type": "text" } ], "index": 22 }, { "bbox": [ 116, 402, 401, 415 ], "spans": [ { "bbox": [ 116, 402, 401, 415 ], "score": 1.0, "content": "adversarial example defenses. arXiv preprint arXiv:2002.08347, 2020.", "type": "text" } ], "index": 23 } ], "index": 22.5 }, { "type": "text", "bbox": [ 106, 421, 505, 456 ], "lines": [ { "bbox": [ 106, 422, 505, 434 ], "spans": [ { "bbox": [ 106, 422, 505, 434 ], "score": 1.0, "content": "Jonathan Uesato, Jean-Baptiste Alayrac, Po-Sen Huang, Robert Stanforth, Alhussein Fawzi, and", "type": "text" } ], "index": 24 }, { "bbox": [ 115, 432, 505, 446 ], "spans": [ { "bbox": [ 115, 432, 505, 446 ], "score": 1.0, "content": "Pushmeet Kohli. Are labels required for improving adversarial robustness? arXiv preprint", "type": "text" } ], "index": 25 }, { "bbox": [ 115, 444, 219, 455 ], "spans": [ { "bbox": [ 115, 444, 219, 455 ], "score": 1.0, "content": "arXiv:1905.13725, 2019.", "type": "text" } ], "index": 26 } ], "index": 25 }, { "type": "text", "bbox": [ 106, 463, 504, 486 ], "lines": [ { "bbox": [ 107, 464, 505, 477 ], "spans": [ { "bbox": [ 107, 464, 505, 477 ], "score": 1.0, "content": "Yisen Wang, Xuejiao Deng, Songbai Pu, and Zhiheng Huang. Residual convolutional ctc networks", "type": "text" } ], "index": 27 }, { "bbox": [ 115, 475, 416, 487 ], "spans": [ { "bbox": [ 115, 475, 416, 487 ], "score": 1.0, "content": "for automatic speech recognition. arXiv preprint arXiv:1702.07793, 2017.", "type": "text" } ], "index": 28 } ], "index": 27.5 }, { "type": "text", "bbox": [ 106, 493, 505, 517 ], "lines": [ { "bbox": [ 106, 493, 505, 506 ], "spans": [ { "bbox": [ 106, 493, 505, 506 ], "score": 1.0, "content": "Yisen Wang, Xingjun Ma, James Bailey, Jinfeng Yi, Bowen Zhou, and Quanquan Gu. On the", "type": "text" } ], "index": 29 }, { "bbox": [ 115, 505, 462, 518 ], "spans": [ { "bbox": [ 115, 505, 462, 518 ], "score": 1.0, "content": "convergence and robustness of adversarial training. In ICML, volume 1, pp. 2, 2019a.", "type": "text" } ], "index": 30 } ], "index": 29.5 }, { "type": "text", "bbox": [ 107, 524, 505, 558 ], "lines": [ { "bbox": [ 105, 522, 505, 539 ], "spans": [ { "bbox": [ 105, 522, 505, 539 ], "score": 1.0, "content": "Yisen Wang, Difan Zou, Jinfeng Yi, James Bailey, Xingjun Ma, and Quanquan Gu. Improving", "type": "text" } ], "index": 31 }, { "bbox": [ 116, 536, 505, 548 ], "spans": [ { "bbox": [ 116, 536, 505, 548 ], "score": 1.0, "content": "adversarial robustness requires revisiting misclassified examples. In International Conference on", "type": "text" } ], "index": 32 }, { "bbox": [ 116, 546, 254, 559 ], "spans": [ { "bbox": [ 116, 546, 254, 559 ], "score": 1.0, "content": "Learning Representations, 2019b.", "type": "text" } ], "index": 33 } ], "index": 32 }, { "type": "text", "bbox": [ 104, 565, 504, 589 ], "lines": [ { "bbox": [ 106, 565, 505, 578 ], "spans": [ { "bbox": [ 106, 565, 505, 578 ], "score": 1.0, "content": "Boxi Wu, Heng Pan, Li Shen, Jindong Gu, Shuai Zhao, Zhifeng Li, Deng Cai, Xiaofei He, and Wei", "type": "text" } ], "index": 34 }, { "bbox": [ 116, 577, 471, 590 ], "spans": [ { "bbox": [ 116, 577, 471, 590 ], "score": 1.0, "content": "Liu. Attacking adversarial attacks as a defense. arXiv preprint arXiv:2106.04938, 2021.", "type": "text" } ], "index": 35 } ], "index": 34.5 }, { "type": "text", "bbox": [ 104, 595, 504, 619 ], "lines": [ { "bbox": [ 105, 595, 505, 609 ], "spans": [ { "bbox": [ 105, 595, 505, 609 ], "score": 1.0, "content": "Dongxian Wu, Shu-Tao Xia, and Yisen Wang. Adversarial weight perturbation helps robust gener-", "type": "text" } ], "index": 36 }, { "bbox": [ 115, 607, 319, 619 ], "spans": [ { "bbox": [ 115, 607, 319, 619 ], "score": 1.0, "content": "alization. arXiv preprint arXiv:2004.05884, 2020.", "type": "text" } ], "index": 37 } ], "index": 36.5 }, { "type": "text", "bbox": [ 104, 626, 504, 650 ], "lines": [ { "bbox": [ 106, 626, 505, 639 ], "spans": [ { "bbox": [ 106, 626, 505, 639 ], "score": 1.0, "content": "Chaowei Xiao, Jun-Yan Zhu, Bo Li, Warren He, Mingyan Liu, and Dawn Song. Spatially trans-", "type": "text" } ], "index": 38 }, { "bbox": [ 116, 637, 497, 650 ], "spans": [ { "bbox": [ 116, 637, 497, 650 ], "score": 1.0, "content": "formed adversarial examples. In International Conference on Learning Representations, 2018.", "type": "text" } ], "index": 39 } ], "index": 38.5 }, { "type": "text", "bbox": [ 107, 657, 504, 691 ], "lines": [ { "bbox": [ 105, 655, 506, 671 ], "spans": [ { "bbox": [ 105, 655, 506, 671 ], "score": 1.0, "content": "Cihang Xie, Yuxin Wu, Laurens van der Maaten, Alan L Yuille, and Kaiming He. Feature denoising", "type": "text" } ], "index": 40 }, { "bbox": [ 116, 668, 505, 680 ], "spans": [ { "bbox": [ 116, 668, 505, 680 ], "score": 1.0, "content": "for improving adversarial robustness. In Proceedings of the IEEE Conference on Computer Vision", "type": "text" } ], "index": 41 }, { "bbox": [ 116, 679, 298, 691 ], "spans": [ { "bbox": [ 116, 679, 298, 691 ], "score": 1.0, "content": "and Pattern Recognition, pp. 501–509, 2019.", "type": "text" } ], "index": 42 } ], "index": 41 }, { "type": "text", "bbox": [ 107, 699, 505, 732 ], "lines": [ { "bbox": [ 106, 699, 505, 711 ], "spans": [ { "bbox": [ 106, 699, 505, 711 ], "score": 1.0, "content": "Hanshu Yan, Jingfeng Zhang, Gang Niu, Jiashi Feng, Vincent YF Tan, and Masashi Sugiyama. Cifs:", "type": "text" } ], "index": 43 }, { "bbox": [ 116, 710, 505, 722 ], "spans": [ { "bbox": [ 116, 710, 505, 722 ], "score": 1.0, "content": "Improving adversarial robustness of cnns via channel-wise importance-based feature selection.", "type": "text" } ], "index": 44 }, { "bbox": [ 116, 720, 279, 732 ], "spans": [ { "bbox": [ 116, 720, 279, 732 ], "score": 1.0, "content": "arXiv preprint arXiv:2102.05311, 2021.", "type": "text" } ], "index": 45 } ], "index": 44 } ], "page_idx": 11, "page_size": [ 612, 792 ], "discarded_blocks": [ { "type": "discarded", "bbox": [ 300, 751, 311, 760 ], "lines": [ { "bbox": [ 299, 750, 313, 764 ], "spans": [ { "bbox": [ 299, 750, 313, 764 ], "score": 1.0, "content": "12", "type": "text" } ] } ] }, { "type": "discarded", "bbox": [ 107, 27, 308, 37 ], "lines": [ { "bbox": [ 107, 26, 308, 38 ], "spans": [ { "bbox": [ 107, 26, 308, 38 ], "score": 1.0, "content": "Under review as a conference paper at ICLR 2022", "type": "text" } ] } ] } ], "para_blocks": [ { "type": "text", "bbox": [ 108, 82, 504, 116 ], "lines": [ { "bbox": [ 105, 81, 506, 95 ], "spans": [ { "bbox": [ 105, 81, 506, 95 ], "score": 1.0, "content": "Andrew Ross and Finale Doshi-Velez. Improving the adversarial robustness and interpretability of", "type": "text" } ], "index": 0 }, { "bbox": [ 116, 93, 505, 107 ], "spans": [ { "bbox": [ 116, 93, 505, 107 ], "score": 1.0, "content": "deep neural networks by regularizing their input gradients. In Proceedings of the AAAI Conference", "type": "text" } ], "index": 1 }, { "bbox": [ 116, 105, 291, 116 ], "spans": [ { "bbox": [ 116, 105, 291, 116 ], "score": 1.0, "content": "on Artificial Intelligence, volume 32, 2018.", "type": "text" } ], "index": 2 } ], "index": 1, "bbox_fs": [ 105, 81, 506, 116 ] }, { "type": "text", "bbox": [ 108, 123, 503, 157 ], "lines": [ { "bbox": [ 106, 124, 504, 136 ], "spans": [ { "bbox": [ 106, 124, 504, 136 ], "score": 1.0, "content": "Ludwig Schmidt, Shibani Santurkar, Dimitris Tsipras, Kunal Talwar, and Aleksander Madry. Ad-", "type": "text" } ], "index": 3 }, { "bbox": [ 115, 134, 505, 149 ], "spans": [ { "bbox": [ 115, 134, 505, 149 ], "score": 1.0, "content": "versarially robust generalization requires more data. Advances in Neural Information Processing", "type": "text" } ], "index": 4 }, { "bbox": [ 116, 146, 241, 158 ], "spans": [ { "bbox": [ 116, 146, 241, 158 ], "score": 1.0, "content": "Systems, 31:5014–5026, 2018.", "type": "text" } ], "index": 5 } ], "index": 4, "bbox_fs": [ 106, 124, 505, 158 ] }, { "type": "text", "bbox": [ 107, 164, 503, 188 ], "lines": [ { "bbox": [ 105, 165, 505, 178 ], "spans": [ { "bbox": [ 105, 165, 505, 178 ], "score": 1.0, "content": "Adi Shamir, Itay Safran, Eyal Ronen, and Orr Dunkelman. A simple explanation for the existence", "type": "text" } ], "index": 6 }, { "bbox": [ 115, 176, 499, 189 ], "spans": [ { "bbox": [ 115, 176, 499, 189 ], "score": 1.0, "content": "of adversarial examples with small hamming distance. arXiv preprint arXiv:1901.10861, 2019.", "type": "text" } ], "index": 7 } ], "index": 6.5, "bbox_fs": [ 105, 165, 505, 189 ] }, { "type": "text", "bbox": [ 106, 195, 506, 229 ], "lines": [ { "bbox": [ 106, 195, 506, 209 ], "spans": [ { "bbox": [ 106, 195, 506, 209 ], "score": 1.0, "content": "Chubiao Song, Kun He, Jiadong Lin, Liwei Wang, and John E Hopcroft. Robust local features for", "type": "text" } ], "index": 8 }, { "bbox": [ 115, 205, 506, 221 ], "spans": [ { "bbox": [ 115, 205, 506, 221 ], "score": 1.0, "content": "improving the generalization of adversarial training. In International Conference on Learning", "type": "text" } ], "index": 9 }, { "bbox": [ 115, 218, 210, 230 ], "spans": [ { "bbox": [ 115, 218, 210, 230 ], "score": 1.0, "content": "Representations, 2020.", "type": "text" } ], "index": 10 } ], "index": 9, "bbox_fs": [ 106, 195, 506, 230 ] }, { "type": "text", "bbox": [ 105, 236, 505, 260 ], "lines": [ { "bbox": [ 105, 237, 505, 250 ], "spans": [ { "bbox": [ 105, 237, 505, 250 ], "score": 1.0, "content": "Christian Szegedy, Wojciech Zaremba, Ilya Sutskever, Joan Bruna, Dumitru Erhan, Ian Goodfellow,", "type": "text" } ], "index": 11 }, { "bbox": [ 115, 248, 505, 261 ], "spans": [ { "bbox": [ 115, 248, 505, 261 ], "score": 1.0, "content": "and Rob Fergus. Intriguing properties of neural networks. arXiv preprint arXiv:1312.6199, 2013.", "type": "text" } ], "index": 12 } ], "index": 11.5, "bbox_fs": [ 105, 237, 505, 261 ] }, { "type": "text", "bbox": [ 106, 267, 505, 301 ], "lines": [ { "bbox": [ 106, 266, 505, 281 ], "spans": [ { "bbox": [ 106, 266, 505, 281 ], "score": 1.0, "content": "Guanhong Tao, Shiqing Ma, Yingqi Liu, and Xiangyu Zhang. Attacks meet interpretability:", "type": "text" } ], "index": 13 }, { "bbox": [ 115, 277, 505, 292 ], "spans": [ { "bbox": [ 115, 277, 505, 292 ], "score": 1.0, "content": "Attribute-steered detection of adversarial samples. In Advances in Neural Information Processing", "type": "text" } ], "index": 14 }, { "bbox": [ 115, 289, 243, 302 ], "spans": [ { "bbox": [ 115, 289, 243, 302 ], "score": 1.0, "content": "Systems, pp. 7717–7728, 2018.", "type": "text" } ], "index": 15 } ], "index": 14, "bbox_fs": [ 106, 266, 505, 302 ] }, { "type": "text", "bbox": [ 107, 308, 504, 342 ], "lines": [ { "bbox": [ 106, 309, 505, 321 ], "spans": [ { "bbox": [ 106, 309, 505, 321 ], "score": 1.0, "content": "Antonio Torralba, Rob Fergus, and William T Freeman. 80 million tiny images: A large data set for", "type": "text" } ], "index": 16 }, { "bbox": [ 116, 320, 505, 333 ], "spans": [ { "bbox": [ 116, 320, 505, 333 ], "score": 1.0, "content": "nonparametric object and scene recognition. IEEE transactions on pattern analysis and machine", "type": "text" } ], "index": 17 }, { "bbox": [ 117, 331, 272, 343 ], "spans": [ { "bbox": [ 117, 331, 272, 343 ], "score": 1.0, "content": "intelligence, 30(11):1958–1970, 2008.", "type": "text" } ], "index": 18 } ], "index": 17, "bbox_fs": [ 106, 309, 505, 343 ] }, { "type": "text", "bbox": [ 108, 349, 504, 384 ], "lines": [ { "bbox": [ 105, 349, 506, 363 ], "spans": [ { "bbox": [ 105, 349, 506, 363 ], "score": 1.0, "content": "Florian Tramer, Alexey Kurakin, Nicolas Papernot, Ian Goodfellow, Dan Boneh, and Patrick Mc- `", "type": "text" } ], "index": 19 }, { "bbox": [ 115, 361, 505, 374 ], "spans": [ { "bbox": [ 115, 361, 505, 374 ], "score": 1.0, "content": "Daniel. Ensemble adversarial training: Attacks and defenses. In International Conference on", "type": "text" } ], "index": 20 }, { "bbox": [ 116, 372, 249, 384 ], "spans": [ { "bbox": [ 116, 372, 249, 384 ], "score": 1.0, "content": "Learning Representations, 2018.", "type": "text" } ], "index": 21 } ], "index": 20, "bbox_fs": [ 105, 349, 506, 384 ] }, { "type": "text", "bbox": [ 106, 391, 504, 415 ], "lines": [ { "bbox": [ 105, 390, 506, 405 ], "spans": [ { "bbox": [ 105, 390, 506, 405 ], "score": 1.0, "content": "Florian Tramer, Nicholas Carlini, Wieland Brendel, and Aleksander Madry. On adaptive attacks to", "type": "text" } ], "index": 22 }, { "bbox": [ 116, 402, 401, 415 ], "spans": [ { "bbox": [ 116, 402, 401, 415 ], "score": 1.0, "content": "adversarial example defenses. arXiv preprint arXiv:2002.08347, 2020.", "type": "text" } ], "index": 23 } ], "index": 22.5, "bbox_fs": [ 105, 390, 506, 415 ] }, { "type": "text", "bbox": [ 106, 421, 505, 456 ], "lines": [ { "bbox": [ 106, 422, 505, 434 ], "spans": [ { "bbox": [ 106, 422, 505, 434 ], "score": 1.0, "content": "Jonathan Uesato, Jean-Baptiste Alayrac, Po-Sen Huang, Robert Stanforth, Alhussein Fawzi, and", "type": "text" } ], "index": 24 }, { "bbox": [ 115, 432, 505, 446 ], "spans": [ { "bbox": [ 115, 432, 505, 446 ], "score": 1.0, "content": "Pushmeet Kohli. Are labels required for improving adversarial robustness? arXiv preprint", "type": "text" } ], "index": 25 }, { "bbox": [ 115, 444, 219, 455 ], "spans": [ { "bbox": [ 115, 444, 219, 455 ], "score": 1.0, "content": "arXiv:1905.13725, 2019.", "type": "text" } ], "index": 26 } ], "index": 25, "bbox_fs": [ 106, 422, 505, 455 ] }, { "type": "text", "bbox": [ 106, 463, 504, 486 ], "lines": [ { "bbox": [ 107, 464, 505, 477 ], "spans": [ { "bbox": [ 107, 464, 505, 477 ], "score": 1.0, "content": "Yisen Wang, Xuejiao Deng, Songbai Pu, and Zhiheng Huang. Residual convolutional ctc networks", "type": "text" } ], "index": 27 }, { "bbox": [ 115, 475, 416, 487 ], "spans": [ { "bbox": [ 115, 475, 416, 487 ], "score": 1.0, "content": "for automatic speech recognition. arXiv preprint arXiv:1702.07793, 2017.", "type": "text" } ], "index": 28 } ], "index": 27.5, "bbox_fs": [ 107, 464, 505, 487 ] }, { "type": "text", "bbox": [ 106, 493, 505, 517 ], "lines": [ { "bbox": [ 106, 493, 505, 506 ], "spans": [ { "bbox": [ 106, 493, 505, 506 ], "score": 1.0, "content": "Yisen Wang, Xingjun Ma, James Bailey, Jinfeng Yi, Bowen Zhou, and Quanquan Gu. On the", "type": "text" } ], "index": 29 }, { "bbox": [ 115, 505, 462, 518 ], "spans": [ { "bbox": [ 115, 505, 462, 518 ], "score": 1.0, "content": "convergence and robustness of adversarial training. In ICML, volume 1, pp. 2, 2019a.", "type": "text" } ], "index": 30 } ], "index": 29.5, "bbox_fs": [ 106, 493, 505, 518 ] }, { "type": "text", "bbox": [ 107, 524, 505, 558 ], "lines": [ { "bbox": [ 105, 522, 505, 539 ], "spans": [ { "bbox": [ 105, 522, 505, 539 ], "score": 1.0, "content": "Yisen Wang, Difan Zou, Jinfeng Yi, James Bailey, Xingjun Ma, and Quanquan Gu. Improving", "type": "text" } ], "index": 31 }, { "bbox": [ 116, 536, 505, 548 ], "spans": [ { "bbox": [ 116, 536, 505, 548 ], "score": 1.0, "content": "adversarial robustness requires revisiting misclassified examples. In International Conference on", "type": "text" } ], "index": 32 }, { "bbox": [ 116, 546, 254, 559 ], "spans": [ { "bbox": [ 116, 546, 254, 559 ], "score": 1.0, "content": "Learning Representations, 2019b.", "type": "text" } ], "index": 33 } ], "index": 32, "bbox_fs": [ 105, 522, 505, 559 ] }, { "type": "text", "bbox": [ 104, 565, 504, 589 ], "lines": [ { "bbox": [ 106, 565, 505, 578 ], "spans": [ { "bbox": [ 106, 565, 505, 578 ], "score": 1.0, "content": "Boxi Wu, Heng Pan, Li Shen, Jindong Gu, Shuai Zhao, Zhifeng Li, Deng Cai, Xiaofei He, and Wei", "type": "text" } ], "index": 34 }, { "bbox": [ 116, 577, 471, 590 ], "spans": [ { "bbox": [ 116, 577, 471, 590 ], "score": 1.0, "content": "Liu. Attacking adversarial attacks as a defense. arXiv preprint arXiv:2106.04938, 2021.", "type": "text" } ], "index": 35 } ], "index": 34.5, "bbox_fs": [ 106, 565, 505, 590 ] }, { "type": "text", "bbox": [ 104, 595, 504, 619 ], "lines": [ { "bbox": [ 105, 595, 505, 609 ], "spans": [ { "bbox": [ 105, 595, 505, 609 ], "score": 1.0, "content": "Dongxian Wu, Shu-Tao Xia, and Yisen Wang. Adversarial weight perturbation helps robust gener-", "type": "text" } ], "index": 36 }, { "bbox": [ 115, 607, 319, 619 ], "spans": [ { "bbox": [ 115, 607, 319, 619 ], "score": 1.0, "content": "alization. arXiv preprint arXiv:2004.05884, 2020.", "type": "text" } ], "index": 37 } ], "index": 36.5, "bbox_fs": [ 105, 595, 505, 619 ] }, { "type": "text", "bbox": [ 104, 626, 504, 650 ], "lines": [ { "bbox": [ 106, 626, 505, 639 ], "spans": [ { "bbox": [ 106, 626, 505, 639 ], "score": 1.0, "content": "Chaowei Xiao, Jun-Yan Zhu, Bo Li, Warren He, Mingyan Liu, and Dawn Song. Spatially trans-", "type": "text" } ], "index": 38 }, { "bbox": [ 116, 637, 497, 650 ], "spans": [ { "bbox": [ 116, 637, 497, 650 ], "score": 1.0, "content": "formed adversarial examples. In International Conference on Learning Representations, 2018.", "type": "text" } ], "index": 39 } ], "index": 38.5, "bbox_fs": [ 106, 626, 505, 650 ] }, { "type": "text", "bbox": [ 107, 657, 504, 691 ], "lines": [ { "bbox": [ 105, 655, 506, 671 ], "spans": [ { "bbox": [ 105, 655, 506, 671 ], "score": 1.0, "content": "Cihang Xie, Yuxin Wu, Laurens van der Maaten, Alan L Yuille, and Kaiming He. Feature denoising", "type": "text" } ], "index": 40 }, { "bbox": [ 116, 668, 505, 680 ], "spans": [ { "bbox": [ 116, 668, 505, 680 ], "score": 1.0, "content": "for improving adversarial robustness. In Proceedings of the IEEE Conference on Computer Vision", "type": "text" } ], "index": 41 }, { "bbox": [ 116, 679, 298, 691 ], "spans": [ { "bbox": [ 116, 679, 298, 691 ], "score": 1.0, "content": "and Pattern Recognition, pp. 501–509, 2019.", "type": "text" } ], "index": 42 } ], "index": 41, "bbox_fs": [ 105, 655, 506, 691 ] }, { "type": "text", "bbox": [ 107, 699, 505, 732 ], "lines": [ { "bbox": [ 106, 699, 505, 711 ], "spans": [ { "bbox": [ 106, 699, 505, 711 ], "score": 1.0, "content": "Hanshu Yan, Jingfeng Zhang, Gang Niu, Jiashi Feng, Vincent YF Tan, and Masashi Sugiyama. Cifs:", "type": "text" } ], "index": 43 }, { "bbox": [ 116, 710, 505, 722 ], "spans": [ { "bbox": [ 116, 710, 505, 722 ], "score": 1.0, "content": "Improving adversarial robustness of cnns via channel-wise importance-based feature selection.", "type": "text" } ], "index": 44 }, { "bbox": [ 116, 720, 279, 732 ], "spans": [ { "bbox": [ 116, 720, 279, 732 ], "score": 1.0, "content": "arXiv preprint arXiv:2102.05311, 2021.", "type": "text" } ], "index": 45 } ], "index": 44, "bbox_fs": [ 106, 699, 505, 732 ] } ] }, { "preproc_blocks": [ { "type": "text", "bbox": [ 108, 82, 503, 116 ], "lines": [ { "bbox": [ 106, 81, 505, 95 ], "spans": [ { "bbox": [ 106, 81, 505, 95 ], "score": 1.0, "content": "Yuzhe Yang, Guo Zhang, Dina Katabi, and Zhi Xu. Me-net: Towards effective adversarial robust-", "type": "text" } ], "index": 0 }, { "bbox": [ 115, 93, 505, 106 ], "spans": [ { "bbox": [ 115, 93, 505, 106 ], "score": 1.0, "content": "ness with matrix estimation. In International Conference on Machine Learning, pp. 7025–7034.", "type": "text" } ], "index": 1 }, { "bbox": [ 116, 104, 173, 115 ], "spans": [ { "bbox": [ 116, 104, 173, 115 ], "score": 1.0, "content": "PMLR, 2019.", "type": "text" } ], "index": 2 } ], "index": 1 }, { "type": "text", "bbox": [ 106, 123, 504, 145 ], "lines": [ { "bbox": [ 105, 122, 505, 136 ], "spans": [ { "bbox": [ 105, 122, 298, 136 ], "score": 1.0, "content": "Sergey Zagoruyko and Nikos Komodakis.", "type": "text" }, { "bbox": [ 313, 123, 428, 136 ], "score": 1.0, "content": "Wide residual networks.", "type": "text" }, { "bbox": [ 437, 123, 505, 136 ], "score": 1.0, "content": "arXiv preprint", "type": "text" } ], "index": 3 }, { "bbox": [ 115, 133, 220, 146 ], "spans": [ { "bbox": [ 115, 133, 220, 146 ], "score": 1.0, "content": "arXiv:1605.07146, 2016.", "type": "text" } ], "index": 4 } ], "index": 3.5 }, { "type": "text", "bbox": [ 106, 153, 504, 176 ], "lines": [ { "bbox": [ 106, 153, 504, 165 ], "spans": [ { "bbox": [ 106, 153, 504, 165 ], "score": 1.0, "content": "Runtian Zhai, Tianle Cai, Di He, Chen Dan, Kun He, John Hopcroft, and Liwei Wang. Adversarially", "type": "text" } ], "index": 5 }, { "bbox": [ 116, 164, 504, 177 ], "spans": [ { "bbox": [ 116, 164, 504, 177 ], "score": 1.0, "content": "robust generalization just requires more unlabeled data. arXiv preprint arXiv:1906.00555, 2019.", "type": "text" } ], "index": 6 } ], "index": 5.5 }, { "type": "text", "bbox": [ 107, 183, 504, 205 ], "lines": [ { "bbox": [ 105, 181, 506, 197 ], "spans": [ { "bbox": [ 105, 181, 506, 197 ], "score": 1.0, "content": "Haichao Zhang and Wei Xu. Adversarial interpolation training: A simple approach for improving", "type": "text" } ], "index": 7 }, { "bbox": [ 116, 193, 217, 206 ], "spans": [ { "bbox": [ 116, 193, 217, 206 ], "score": 1.0, "content": "model robustness. 2019.", "type": "text" } ], "index": 8 } ], "index": 7.5 }, { "type": "text", "bbox": [ 107, 212, 503, 246 ], "lines": [ { "bbox": [ 105, 212, 504, 226 ], "spans": [ { "bbox": [ 105, 212, 504, 226 ], "score": 1.0, "content": "Hongyang Zhang, Yaodong Yu, Jiantao Jiao, Eric Xing, Laurent El Ghaoui, and Michael Jordan.", "type": "text" } ], "index": 9 }, { "bbox": [ 117, 224, 505, 236 ], "spans": [ { "bbox": [ 117, 224, 505, 236 ], "score": 1.0, "content": "Theoretically principled trade-off between robustness and accuracy. In International Conference", "type": "text" } ], "index": 10 }, { "bbox": [ 116, 235, 330, 247 ], "spans": [ { "bbox": [ 116, 235, 330, 247 ], "score": 1.0, "content": "on Machine Learning, pp. 7472–7482. PMLR, 2019.", "type": "text" } ], "index": 11 } ], "index": 10 }, { "type": "text", "bbox": [ 107, 253, 504, 288 ], "lines": [ { "bbox": [ 105, 253, 505, 267 ], "spans": [ { "bbox": [ 105, 253, 505, 267 ], "score": 1.0, "content": "Jingfeng Zhang, Xilie Xu, Bo Han, Gang Niu, Lizhen Cui, Masashi Sugiyama, and Mohan Kankan-", "type": "text" } ], "index": 12 }, { "bbox": [ 115, 264, 506, 278 ], "spans": [ { "bbox": [ 115, 264, 506, 278 ], "score": 1.0, "content": "halli. Attacks which do not kill training make adversarial learning stronger. In International", "type": "text" } ], "index": 13 }, { "bbox": [ 116, 275, 393, 289 ], "spans": [ { "bbox": [ 116, 275, 393, 289 ], "score": 1.0, "content": "Conference on Machine Learning, pp. 11278–11287. PMLR, 2020a.", "type": "text" } ], "index": 14 } ], "index": 13 }, { "type": "text", "bbox": [ 106, 294, 506, 327 ], "lines": [ { "bbox": [ 106, 294, 504, 307 ], "spans": [ { "bbox": [ 106, 294, 504, 307 ], "score": 1.0, "content": "Jingfeng Zhang, Jianing Zhu, Gang Niu, Bo Han, Masashi Sugiyama, and Mohan Kankanhalli.", "type": "text" } ], "index": 15 }, { "bbox": [ 116, 306, 505, 318 ], "spans": [ { "bbox": [ 116, 306, 505, 318 ], "score": 1.0, "content": "Geometry-aware instance-reweighted adversarial training. arXiv preprint arXiv:2010.01736,", "type": "text" } ], "index": 16 }, { "bbox": [ 115, 315, 147, 328 ], "spans": [ { "bbox": [ 115, 315, 147, 328 ], "score": 1.0, "content": "2020b.", "type": "text" } ], "index": 17 } ], "index": 16 }, { "type": "title", "bbox": [ 108, 349, 182, 361 ], "lines": [ { "bbox": [ 105, 347, 185, 365 ], "spans": [ { "bbox": [ 105, 347, 185, 365 ], "score": 1.0, "content": "A APPENDIX", "type": "text" } ], "index": 18 } ], "index": 18 }, { "type": "text", "bbox": [ 106, 374, 506, 451 ], "lines": [ { "bbox": [ 106, 374, 506, 387 ], "spans": [ { "bbox": [ 106, 374, 506, 387 ], "score": 1.0, "content": "In this part, we verify the generalities of diffusion process in robust overfitting (the model will first", "type": "text" } ], "index": 19 }, { "bbox": [ 105, 385, 505, 398 ], "spans": [ { "bbox": [ 105, 385, 505, 398 ], "score": 1.0, "content": "memorize some easy-to-learn adversarial examples, and then spread to the entire training dataset)", "type": "text" } ], "index": 20 }, { "bbox": [ 105, 396, 505, 408 ], "spans": [ { "bbox": [ 105, 396, 505, 408 ], "score": 1.0, "content": "across different threat models, datasets and network architectures. Specifically, we remove the train-", "type": "text" } ], "index": 21 }, { "bbox": [ 105, 406, 506, 421 ], "spans": [ { "bbox": [ 105, 406, 506, 421 ], "score": 1.0, "content": "ing examples whose loss value is lower than the LSC value during adversarial training. The learning", "type": "text" } ], "index": 22 }, { "bbox": [ 105, 418, 505, 430 ], "spans": [ { "bbox": [ 105, 418, 505, 430 ], "score": 1.0, "content": "curve and the rate of removal are shown in Figure 4. We can observe that if these easy-to-learn", "type": "text" } ], "index": 23 }, { "bbox": [ 105, 428, 506, 443 ], "spans": [ { "bbox": [ 105, 428, 506, 443 ], "score": 1.0, "content": "adversarial examples are not included in the training data, robust overfitting will not occur during", "type": "text" } ], "index": 24 }, { "bbox": [ 106, 441, 312, 452 ], "spans": [ { "bbox": [ 106, 441, 312, 452 ], "score": 1.0, "content": "adversarial training, which verified our conclusion.", "type": "text" } ], "index": 25 } ], "index": 22 }, { "type": "image", "bbox": [ 113, 466, 499, 687 ], "blocks": [ { "type": "image_body", "bbox": [ 113, 466, 499, 687 ], "group_id": 0, "lines": [ { "bbox": [ 113, 466, 499, 687 ], "spans": [ { "bbox": [ 113, 466, 499, 687 ], "score": 0.974, "type": "image", "image_path": "63a545c53b23ec9d26c6ce6938c8f965e1898870c7e3b47b57c0bcfb4fd6b0cf.jpg" } ] } ], "index": 27, "virtual_lines": [ { "bbox": [ 113, 466, 499, 539.6666666666666 ], "spans": [], "index": 26 }, { "bbox": [ 113, 539.6666666666666, 499, 613.3333333333333 ], "spans": [], "index": 27 }, { "bbox": [ 113, 613.3333333333333, 499, 686.9999999999999 ], "spans": [], "index": 28 } ] }, { "type": "image_caption", "bbox": [ 107, 700, 504, 734 ], "group_id": 0, "lines": [ { "bbox": [ 105, 698, 505, 713 ], "spans": [ { "bbox": [ 105, 698, 480, 713 ], "score": 1.0, "content": "Figure 4: The learning curve and removing rate of adversarial training under (a) Cifar10 -", "type": "text" }, { "bbox": [ 480, 700, 497, 711 ], "score": 0.77, "content": "L _ { \\infty }", "type": "inline_equation" }, { "bbox": [ 497, 698, 505, 713 ], "score": 1.0, "content": "-", "type": "text" } ], "index": 29 }, { "bbox": [ 105, 710, 505, 724 ], "spans": [ { "bbox": [ 105, 710, 236, 724 ], "score": 1.0, "content": "PreAct ResNet18; (b) Cifar10 -", "type": "text" }, { "bbox": [ 236, 711, 249, 722 ], "score": 0.65, "content": "L _ { 2 }", "type": "inline_equation" }, { "bbox": [ 249, 710, 368, 724 ], "score": 1.0, "content": "- PreAct ResNet18; (c) Cifar", "type": "text" }, { "bbox": [ 368, 711, 407, 722 ], "score": 0.46, "content": "1 0 0 - L _ { \\infty }", "type": "inline_equation" }, { "bbox": [ 408, 710, 505, 724 ], "score": 1.0, "content": "- PreAct ResNet18; (d)", "type": "text" } ], "index": 30 }, { "bbox": [ 106, 722, 232, 734 ], "spans": [ { "bbox": [ 106, 722, 129, 734 ], "score": 1.0, "content": "Cifar", "type": "text" }, { "bbox": [ 130, 722, 167, 733 ], "score": 0.67, "content": "1 0 0 - L _ { \\infty }", "type": "inline_equation" }, { "bbox": [ 167, 722, 232, 734 ], "score": 1.0, "content": "- Wide ResNet.", "type": "text" } ], "index": 31 } ], "index": 30 } ], "index": 28.5 } ], "page_idx": 12, "page_size": [ 612, 792 ], "discarded_blocks": [ { "type": "discarded", "bbox": [ 107, 27, 308, 37 ], "lines": [ { "bbox": [ 107, 26, 308, 38 ], "spans": [ { "bbox": [ 107, 26, 308, 38 ], "score": 1.0, "content": "Under review as a conference paper at ICLR 2022", "type": "text" } ] } ] }, { "type": "discarded", "bbox": [ 300, 751, 311, 760 ], "lines": [ { "bbox": [ 299, 750, 313, 764 ], "spans": [ { "bbox": [ 299, 750, 313, 764 ], "score": 1.0, "content": "13", "type": "text" } ] } ] } ], "para_blocks": [ { "type": "text", "bbox": [ 108, 82, 503, 116 ], "lines": [ { "bbox": [ 106, 81, 505, 95 ], "spans": [ { "bbox": [ 106, 81, 505, 95 ], "score": 1.0, "content": "Yuzhe Yang, Guo Zhang, Dina Katabi, and Zhi Xu. Me-net: Towards effective adversarial robust-", "type": "text" } ], "index": 0 }, { "bbox": [ 115, 93, 505, 106 ], "spans": [ { "bbox": [ 115, 93, 505, 106 ], "score": 1.0, "content": "ness with matrix estimation. In International Conference on Machine Learning, pp. 7025–7034.", "type": "text" } ], "index": 1 }, { "bbox": [ 116, 104, 173, 115 ], "spans": [ { "bbox": [ 116, 104, 173, 115 ], "score": 1.0, "content": "PMLR, 2019.", "type": "text" } ], "index": 2 } ], "index": 1, "bbox_fs": [ 106, 81, 505, 115 ] }, { "type": "text", "bbox": [ 106, 123, 504, 145 ], "lines": [ { "bbox": [ 105, 122, 505, 136 ], "spans": [ { "bbox": [ 105, 122, 298, 136 ], "score": 1.0, "content": "Sergey Zagoruyko and Nikos Komodakis.", "type": "text" }, { "bbox": [ 313, 123, 428, 136 ], "score": 1.0, "content": "Wide residual networks.", "type": "text" }, { "bbox": [ 437, 123, 505, 136 ], "score": 1.0, "content": "arXiv preprint", "type": "text" } ], "index": 3 }, { "bbox": [ 115, 133, 220, 146 ], "spans": [ { "bbox": [ 115, 133, 220, 146 ], "score": 1.0, "content": "arXiv:1605.07146, 2016.", "type": "text" } ], "index": 4 } ], "index": 3.5, "bbox_fs": [ 105, 122, 505, 146 ] }, { "type": "text", "bbox": [ 106, 153, 504, 176 ], "lines": [ { "bbox": [ 106, 153, 504, 165 ], "spans": [ { "bbox": [ 106, 153, 504, 165 ], "score": 1.0, "content": "Runtian Zhai, Tianle Cai, Di He, Chen Dan, Kun He, John Hopcroft, and Liwei Wang. Adversarially", "type": "text" } ], "index": 5 }, { "bbox": [ 116, 164, 504, 177 ], "spans": [ { "bbox": [ 116, 164, 504, 177 ], "score": 1.0, "content": "robust generalization just requires more unlabeled data. arXiv preprint arXiv:1906.00555, 2019.", "type": "text" } ], "index": 6 } ], "index": 5.5, "bbox_fs": [ 106, 153, 504, 177 ] }, { "type": "text", "bbox": [ 107, 183, 504, 205 ], "lines": [ { "bbox": [ 105, 181, 506, 197 ], "spans": [ { "bbox": [ 105, 181, 506, 197 ], "score": 1.0, "content": "Haichao Zhang and Wei Xu. Adversarial interpolation training: A simple approach for improving", "type": "text" } ], "index": 7 }, { "bbox": [ 116, 193, 217, 206 ], "spans": [ { "bbox": [ 116, 193, 217, 206 ], "score": 1.0, "content": "model robustness. 2019.", "type": "text" } ], "index": 8 } ], "index": 7.5, "bbox_fs": [ 105, 181, 506, 206 ] }, { "type": "text", "bbox": [ 107, 212, 503, 246 ], "lines": [ { "bbox": [ 105, 212, 504, 226 ], "spans": [ { "bbox": [ 105, 212, 504, 226 ], "score": 1.0, "content": "Hongyang Zhang, Yaodong Yu, Jiantao Jiao, Eric Xing, Laurent El Ghaoui, and Michael Jordan.", "type": "text" } ], "index": 9 }, { "bbox": [ 117, 224, 505, 236 ], "spans": [ { "bbox": [ 117, 224, 505, 236 ], "score": 1.0, "content": "Theoretically principled trade-off between robustness and accuracy. In International Conference", "type": "text" } ], "index": 10 }, { "bbox": [ 116, 235, 330, 247 ], "spans": [ { "bbox": [ 116, 235, 330, 247 ], "score": 1.0, "content": "on Machine Learning, pp. 7472–7482. PMLR, 2019.", "type": "text" } ], "index": 11 } ], "index": 10, "bbox_fs": [ 105, 212, 505, 247 ] }, { "type": "text", "bbox": [ 107, 253, 504, 288 ], "lines": [ { "bbox": [ 105, 253, 505, 267 ], "spans": [ { "bbox": [ 105, 253, 505, 267 ], "score": 1.0, "content": "Jingfeng Zhang, Xilie Xu, Bo Han, Gang Niu, Lizhen Cui, Masashi Sugiyama, and Mohan Kankan-", "type": "text" } ], "index": 12 }, { "bbox": [ 115, 264, 506, 278 ], "spans": [ { "bbox": [ 115, 264, 506, 278 ], "score": 1.0, "content": "halli. Attacks which do not kill training make adversarial learning stronger. In International", "type": "text" } ], "index": 13 }, { "bbox": [ 116, 275, 393, 289 ], "spans": [ { "bbox": [ 116, 275, 393, 289 ], "score": 1.0, "content": "Conference on Machine Learning, pp. 11278–11287. PMLR, 2020a.", "type": "text" } ], "index": 14 } ], "index": 13, "bbox_fs": [ 105, 253, 506, 289 ] }, { "type": "text", "bbox": [ 106, 294, 506, 327 ], "lines": [ { "bbox": [ 106, 294, 504, 307 ], "spans": [ { "bbox": [ 106, 294, 504, 307 ], "score": 1.0, "content": "Jingfeng Zhang, Jianing Zhu, Gang Niu, Bo Han, Masashi Sugiyama, and Mohan Kankanhalli.", "type": "text" } ], "index": 15 }, { "bbox": [ 116, 306, 505, 318 ], "spans": [ { "bbox": [ 116, 306, 505, 318 ], "score": 1.0, "content": "Geometry-aware instance-reweighted adversarial training. arXiv preprint arXiv:2010.01736,", "type": "text" } ], "index": 16 }, { "bbox": [ 115, 315, 147, 328 ], "spans": [ { "bbox": [ 115, 315, 147, 328 ], "score": 1.0, "content": "2020b.", "type": "text" } ], "index": 17 } ], "index": 16, "bbox_fs": [ 106, 294, 505, 328 ] }, { "type": "title", "bbox": [ 108, 349, 182, 361 ], "lines": [ { "bbox": [ 105, 347, 185, 365 ], "spans": [ { "bbox": [ 105, 347, 185, 365 ], "score": 1.0, "content": "A APPENDIX", "type": "text" } ], "index": 18 } ], "index": 18 }, { "type": "text", "bbox": [ 106, 374, 506, 451 ], "lines": [ { "bbox": [ 106, 374, 506, 387 ], "spans": [ { "bbox": [ 106, 374, 506, 387 ], "score": 1.0, "content": "In this part, we verify the generalities of diffusion process in robust overfitting (the model will first", "type": "text" } ], "index": 19 }, { "bbox": [ 105, 385, 505, 398 ], "spans": [ { "bbox": [ 105, 385, 505, 398 ], "score": 1.0, "content": "memorize some easy-to-learn adversarial examples, and then spread to the entire training dataset)", "type": "text" } ], "index": 20 }, { "bbox": [ 105, 396, 505, 408 ], "spans": [ { "bbox": [ 105, 396, 505, 408 ], "score": 1.0, "content": "across different threat models, datasets and network architectures. Specifically, we remove the train-", "type": "text" } ], "index": 21 }, { "bbox": [ 105, 406, 506, 421 ], "spans": [ { "bbox": [ 105, 406, 506, 421 ], "score": 1.0, "content": "ing examples whose loss value is lower than the LSC value during adversarial training. The learning", "type": "text" } ], "index": 22 }, { "bbox": [ 105, 418, 505, 430 ], "spans": [ { "bbox": [ 105, 418, 505, 430 ], "score": 1.0, "content": "curve and the rate of removal are shown in Figure 4. We can observe that if these easy-to-learn", "type": "text" } ], "index": 23 }, { "bbox": [ 105, 428, 506, 443 ], "spans": [ { "bbox": [ 105, 428, 506, 443 ], "score": 1.0, "content": "adversarial examples are not included in the training data, robust overfitting will not occur during", "type": "text" } ], "index": 24 }, { "bbox": [ 106, 441, 312, 452 ], "spans": [ { "bbox": [ 106, 441, 312, 452 ], "score": 1.0, "content": "adversarial training, which verified our conclusion.", "type": "text" } ], "index": 25 } ], "index": 22, "bbox_fs": [ 105, 374, 506, 452 ] }, { "type": "image", "bbox": [ 113, 466, 499, 687 ], "blocks": [ { "type": "image_body", "bbox": [ 113, 466, 499, 687 ], "group_id": 0, "lines": [ { "bbox": [ 113, 466, 499, 687 ], "spans": [ { "bbox": [ 113, 466, 499, 687 ], "score": 0.974, "type": "image", "image_path": "63a545c53b23ec9d26c6ce6938c8f965e1898870c7e3b47b57c0bcfb4fd6b0cf.jpg" } ] } ], "index": 27, "virtual_lines": [ { "bbox": [ 113, 466, 499, 539.6666666666666 ], "spans": [], "index": 26 }, { "bbox": [ 113, 539.6666666666666, 499, 613.3333333333333 ], "spans": [], "index": 27 }, { "bbox": [ 113, 613.3333333333333, 499, 686.9999999999999 ], "spans": [], "index": 28 } ] }, { "type": "image_caption", "bbox": [ 107, 700, 504, 734 ], "group_id": 0, "lines": [ { "bbox": [ 105, 698, 505, 713 ], "spans": [ { "bbox": [ 105, 698, 480, 713 ], "score": 1.0, "content": "Figure 4: The learning curve and removing rate of adversarial training under (a) Cifar10 -", "type": "text" }, { "bbox": [ 480, 700, 497, 711 ], "score": 0.77, "content": "L _ { \\infty }", "type": "inline_equation" }, { "bbox": [ 497, 698, 505, 713 ], "score": 1.0, "content": "-", "type": "text" } ], "index": 29 }, { "bbox": [ 105, 710, 505, 724 ], "spans": [ { "bbox": [ 105, 710, 236, 724 ], "score": 1.0, "content": "PreAct ResNet18; (b) Cifar10 -", "type": "text" }, { "bbox": [ 236, 711, 249, 722 ], "score": 0.65, "content": "L _ { 2 }", "type": "inline_equation" }, { "bbox": [ 249, 710, 368, 724 ], "score": 1.0, "content": "- PreAct ResNet18; (c) Cifar", "type": "text" }, { "bbox": [ 368, 711, 407, 722 ], "score": 0.46, "content": "1 0 0 - L _ { \\infty }", "type": "inline_equation" }, { "bbox": [ 408, 710, 505, 724 ], "score": 1.0, "content": "- PreAct ResNet18; (d)", "type": "text" } ], "index": 30 }, { "bbox": [ 106, 722, 232, 734 ], "spans": [ { "bbox": [ 106, 722, 129, 734 ], "score": 1.0, "content": "Cifar", "type": "text" }, { "bbox": [ 130, 722, 167, 733 ], "score": 0.67, "content": "1 0 0 - L _ { \\infty }", "type": "inline_equation" }, { "bbox": [ 167, 722, 232, 734 ], "score": 1.0, "content": "- Wide ResNet.", "type": "text" } ], "index": 31 } ], "index": 30 } ], "index": 28.5 } ] } ], "_backend": "pipeline", "_version_name": "2.2.2" }