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Code available here 1", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 16, + "bbox_fs": [ + 141, + 266, + 470, + 430 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 452, + 206, + 464 + ], + "lines": [ + { + "bbox": [ + 105, + 451, + 208, + 467 + ], + "spans": [ + { + "bbox": [ + 105, + 451, + 208, + 467 + ], + "score": 1.0, + "content": "1 INTRODUCTION", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 24 + }, + { + "type": "text", + "bbox": [ + 107, + 477, + 504, + 554 + ], + "lines": [ + { + "bbox": [ + 106, + 477, + 506, + 489 + ], + "spans": [ + { + "bbox": [ + 106, + 477, + 506, + 489 + ], + "score": 1.0, + "content": "One of the most challenging problems for Time Series Classification (TSC) tasks is how to tell", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 488, + 505, + 500 + ], + "spans": [ + { + "bbox": [ + 105, + 488, + 505, + 500 + ], + "score": 1.0, + "content": "models in what time scales 2 to extract features. Time series (TS) data is a series of data points", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 499, + 506, + 512 + ], + "spans": [ + { + "bbox": [ + 105, + 499, + 506, + 512 + ], + "score": 1.0, + "content": "ordered by time or other meaningful sequences such as frequency. Due to the variety of information", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 509, + 506, + 524 + ], + "spans": [ + { + "bbox": [ + 105, + 509, + 506, + 524 + ], + "score": 1.0, + "content": "sources (e.g., medical sensors, economic indicators, and logs) and record settings (e.g., sampling", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 521, + 506, + 533 + ], + "spans": [ + { + "bbox": [ + 105, + 521, + 506, + 533 + ], + "score": 1.0, + "content": "rate, record length, and bandwidth), TS data is naturally composed of various types of signals on", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 532, + 506, + 544 + ], + "spans": [ + { + "bbox": [ + 105, + 532, + 506, + 544 + ], + "score": 1.0, + "content": "various time scales (Hills et al., 2014; Schafer, 2015; Dau et al., 2018). Thus, in what time scales ¨", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 543, + 498, + 555 + ], + "spans": [ + { + "bbox": [ + 105, + 543, + 498, + 555 + ], + "score": 1.0, + "content": "can a model “see” from the TS input data has been a key for the performance of TS classification.", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 28, + "bbox_fs": [ + 105, + 477, + 506, + 555 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 560, + 505, + 691 + ], + "lines": [ + { + "bbox": [ + 105, + 559, + 506, + 573 + ], + "spans": [ + { + "bbox": [ + 105, + 559, + 506, + 573 + ], + "score": 1.0, + "content": "Traditional machine learning methods have taken huge efforts to capture important time scales, and", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 570, + 505, + 583 + ], + "spans": [ + { + "bbox": [ + 105, + 570, + 505, + 583 + ], + "score": 1.0, + "content": "the computational resource consumption increase exponentially with the length of TS increase. For", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 582, + 505, + 594 + ], + "spans": [ + { + "bbox": [ + 105, + 582, + 505, + 594 + ], + "score": 1.0, + "content": "example, for shapelet methods (Hills et al., 2014; Lines et al., 2012), whose discriminatory feature", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 593, + 505, + 605 + ], + "spans": [ + { + "bbox": [ + 105, + 593, + 505, + 605 + ], + "score": 1.0, + "content": "is obtained via finding sub-sequences from TS that can be representative of class membership, the", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 603, + 505, + 617 + ], + "spans": [ + { + "bbox": [ + 105, + 603, + 505, + 617 + ], + "score": 1.0, + "content": "time scale capture work is finding the proper sub-sequences length. To obtain the proper length,", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 615, + 505, + 627 + ], + "spans": [ + { + "bbox": [ + 105, + 615, + 505, + 627 + ], + "score": 1.0, + "content": "even for a dataset with length 512, (Hills et al., 2014) has to try 71 different sub-sequence lengths.", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 625, + 505, + 638 + ], + "spans": [ + { + "bbox": [ + 105, + 625, + 505, + 638 + ], + "score": 1.0, + "content": "For other methods, such as (Berndt & Clifford, 1994; Schafer, 2015; Lucas et al., 2019), despite ¨", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 636, + 506, + 650 + ], + "spans": [ + { + "bbox": [ + 105, + 636, + 506, + 650 + ], + "score": 1.0, + "content": "the time scale capture might be called by different names such as finding warping size or window", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 104, + 646, + 505, + 661 + ], + "spans": [ + { + "bbox": [ + 104, + 646, + 505, + 661 + ], + "score": 1.0, + "content": "length. They all need searching works to identify those important time scales. More recent deep", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 658, + 505, + 671 + ], + "spans": [ + { + "bbox": [ + 105, + 658, + 505, + 671 + ], + "score": 1.0, + "content": "learning based methods also showed that they had to pay a lot of attention to this time scale problem.", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 669, + 505, + 681 + ], + "spans": [ + { + "bbox": [ + 105, + 669, + 505, + 681 + ], + "score": 1.0, + "content": "MCNN (Cui et al., 2016) searches the kernel size to find the best RF of a 1D-CNN for every dataset.", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 106, + 680, + 505, + 693 + ], + "spans": [ + { + "bbox": [ + 106, + 680, + 505, + 693 + ], + "score": 1.0, + "content": "Tapnet (Zhang et al., 2020) additionally considers the dilation steps. Chen & Shi (2021) also take", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 236, + 505, + 249 + ], + "spans": [ + { + "bbox": [ + 106, + 236, + 505, + 249 + ], + "score": 1.0, + "content": "the number of layers into considerations. These are all important factors for the RF of CNNs and", + "type": "text", + "cross_page": true + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 247, + 211, + 260 + ], + "spans": [ + { + "bbox": [ + 106, + 247, + 211, + 260 + ], + "score": 1.0, + "content": "the performance for TSC.", + "type": "text", + "cross_page": true + } + ], + "index": 8 + } + ], + "index": 37.5, + "bbox_fs": [ + 104, + 559, + 506, + 693 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 107, + 80, + 503, + 167 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 107, + 80, + 503, + 167 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 107, + 80, + 503, + 167 + ], + "spans": [ + { + "bbox": [ + 107, + 80, + 503, + 167 + ], + "score": 0.928, + "type": "image", + "image_path": "0de81077afc0a14742088d5b94bd12b016a9cd78eeb745fcf515465d47d20a88.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 107, + 80, + 503, + 109.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 107, + 109.0, + 503, + 138.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 107, + 138.0, + 503, + 167.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 180, + 505, + 224 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 180, + 504, + 192 + ], + "spans": [ + { + "bbox": [ + 106, + 180, + 504, + 192 + ], + "score": 1.0, + "content": "Figure 1: Left: A model’s accuracy on the UCR 85 datasets changes by tuning the model’s receptive", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 190, + 505, + 204 + ], + "spans": [ + { + "bbox": [ + 104, + 190, + 505, + 204 + ], + "score": 1.0, + "content": "field sizes from 10 to 200. Right: The average rank results of each receptive field size are pretty", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 201, + 506, + 214 + ], + "spans": [ + { + "bbox": [ + 105, + 201, + 506, + 214 + ], + "score": 1.0, + "content": "similar, which means that no single receptive field size can significantly outperform others on most", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 213, + 144, + 225 + ], + "spans": [ + { + "bbox": [ + 105, + 213, + 144, + 225 + ], + "score": 1.0, + "content": "datasets.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 4.5 + } + ], + "index": 2.75 + }, + { + "type": "text", + "bbox": [ + 108, + 237, + 504, + 259 + ], + "lines": [ + { + "bbox": [ + 106, + 236, + 505, + 249 + ], + "spans": [ + { + "bbox": [ + 106, + 236, + 505, + 249 + ], + "score": 1.0, + "content": "the number of layers into considerations. These are all important factors for the RF of CNNs and", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 247, + 211, + 260 + ], + "spans": [ + { + "bbox": [ + 106, + 247, + 211, + 260 + ], + "score": 1.0, + "content": "the performance for TSC.", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 7.5 + }, + { + "type": "text", + "bbox": [ + 107, + 264, + 504, + 353 + ], + "lines": [ + { + "bbox": [ + 106, + 264, + 505, + 276 + ], + "spans": [ + { + "bbox": [ + 106, + 264, + 505, + 276 + ], + "score": 1.0, + "content": "Although a number of researchers have searched for the best RF of 1D-CNNs for TSC, there is still", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 276, + 506, + 287 + ], + "spans": [ + { + "bbox": [ + 105, + 276, + 506, + 287 + ], + "score": 1.0, + "content": "no agreed answer to 1) what size of the RF is the best? And 2) how many different RFs should be", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 287, + 505, + 299 + ], + "spans": [ + { + "bbox": [ + 105, + 287, + 505, + 299 + ], + "score": 1.0, + "content": "used? Models need to be equipped with different sizes and different numbers of RFs for a specific", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 298, + 505, + 310 + ], + "spans": [ + { + "bbox": [ + 106, + 298, + 505, + 310 + ], + "score": 1.0, + "content": "dataset. Using the same setup for every dataset can lead to a significant performance drop for some", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 308, + 505, + 321 + ], + "spans": [ + { + "bbox": [ + 105, + 308, + 505, + 321 + ], + "score": 1.0, + "content": "datasets. For example, as shown by the statistics on the University of California Riverside (UCR) 85", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 319, + 504, + 332 + ], + "spans": [ + { + "bbox": [ + 105, + 319, + 489, + 332 + ], + "score": 1.0, + "content": "“bake off” datasets in Figure 1a, the accuracy of most datasets can have a variance of more than", + "type": "text" + }, + { + "bbox": [ + 489, + 320, + 504, + 330 + ], + "score": 0.85, + "content": "5 \\%", + "type": "inline_equation" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 331, + 506, + 343 + ], + "spans": [ + { + "bbox": [ + 105, + 331, + 506, + 343 + ], + "score": 1.0, + "content": "just by changing the RF sizes of their model while keeping the rest of the configurations the same.", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 342, + 475, + 354 + ], + "spans": [ + { + "bbox": [ + 105, + 342, + 475, + 354 + ], + "score": 1.0, + "content": "As also shown in Figure 1b, no RF can consistently perform the best over different datasets.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 12.5 + }, + { + "type": "text", + "bbox": [ + 107, + 358, + 505, + 457 + ], + "lines": [ + { + "bbox": [ + 106, + 358, + 505, + 371 + ], + "spans": [ + { + "bbox": [ + 106, + 358, + 505, + 371 + ], + "score": 1.0, + "content": "To avoid those complicated and resource-consuming searching work, we propose Omni-Scale block", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 370, + 505, + 381 + ], + "spans": [ + { + "bbox": [ + 106, + 370, + 505, + 381 + ], + "score": 1.0, + "content": "(OS-block), where the kernel choices for 1D-CNNs are automatically set through a simple and", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 379, + 506, + 393 + ], + "spans": [ + { + "bbox": [ + 105, + 379, + 506, + 393 + ], + "score": 1.0, + "content": "universal rule that can cover the RF of all scales. The rule is inspired by Goldbach’s conjecture,", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 392, + 505, + 403 + ], + "spans": [ + { + "bbox": [ + 106, + 392, + 505, + 403 + ], + "score": 1.0, + "content": "where any positive even number can be written as the sum of two prime numbers. Therefore, the", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 402, + 506, + 415 + ], + "spans": [ + { + "bbox": [ + 105, + 402, + 506, + 415 + ], + "score": 1.0, + "content": "OS-block uses a set of prime numbers as the kernel sizes except for the last layer whose kernel", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 413, + 505, + 425 + ], + "spans": [ + { + "bbox": [ + 106, + 413, + 505, + 425 + ], + "score": 1.0, + "content": "sizes are 1 and 2. In this way, a 1D-CNN with these kernel sizes can cover the RF of all scales", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 424, + 505, + 436 + ], + "spans": [ + { + "bbox": [ + 105, + 424, + 505, + 436 + ], + "score": 1.0, + "content": "by transforming TS through different combinations of these prime size kernels. What’s more, the", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 434, + 506, + 448 + ], + "spans": [ + { + "bbox": [ + 105, + 434, + 506, + 448 + ], + "score": 1.0, + "content": "OS-block is easy to implement to various TS datasets via selecting the maximum prime number", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 446, + 243, + 459 + ], + "spans": [ + { + "bbox": [ + 105, + 446, + 243, + 459 + ], + "score": 1.0, + "content": "according to the length of the TS.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 21 + }, + { + "type": "text", + "bbox": [ + 107, + 463, + 505, + 540 + ], + "lines": [ + { + "bbox": [ + 105, + 462, + 505, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 462, + 505, + 475 + ], + "score": 1.0, + "content": "In experiments, we show consistent state-of-the-art performance on four TSC benchmarks. These", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 473, + 505, + 487 + ], + "spans": [ + { + "bbox": [ + 105, + 473, + 505, + 487 + ], + "score": 1.0, + "content": "benchmarks contain datasets from different domains, i.e., healthcare, human activity recognition,", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 485, + 505, + 497 + ], + "spans": [ + { + "bbox": [ + 105, + 485, + 505, + 497 + ], + "score": 1.0, + "content": "speech recognition, and spectrum analysis. Despite the dynamic patterns of these datasets, 1D-", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 495, + 505, + 508 + ], + "spans": [ + { + "bbox": [ + 106, + 495, + 505, + 508 + ], + "score": 1.0, + "content": "CNNs with our OS-block robustly outperform previous baselines with the unified training hyper-", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 507, + 506, + 519 + ], + "spans": [ + { + "bbox": [ + 105, + 507, + 506, + 519 + ], + "score": 1.0, + "content": "parameters for all datasets such as learning rate, batch size, and iteration numbers. We also did a", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 518, + 505, + 530 + ], + "spans": [ + { + "bbox": [ + 105, + 518, + 505, + 530 + ], + "score": 1.0, + "content": "comprehensive study to show our OS-block, the no time scale search solution, always matches the", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 529, + 333, + 541 + ], + "spans": [ + { + "bbox": [ + 105, + 529, + 333, + 541 + ], + "score": 1.0, + "content": "performance with the best RF size for different datasets.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 29 + }, + { + "type": "title", + "bbox": [ + 108, + 556, + 199, + 569 + ], + "lines": [ + { + "bbox": [ + 104, + 555, + 200, + 572 + ], + "spans": [ + { + "bbox": [ + 104, + 555, + 200, + 572 + ], + "score": 1.0, + "content": "2 MOTIVATIONS", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 33 + }, + { + "type": "text", + "bbox": [ + 107, + 581, + 504, + 604 + ], + "lines": [ + { + "bbox": [ + 106, + 581, + 505, + 594 + ], + "spans": [ + { + "bbox": [ + 106, + 581, + 505, + 594 + ], + "score": 1.0, + "content": "Two phenomena of 1D-CNNs inspire the design of the OS-block. In this section, we will introduce", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 592, + 495, + 604 + ], + "spans": [ + { + "bbox": [ + 106, + 592, + 495, + 604 + ], + "score": 1.0, + "content": "the two phenomena with examples in Figure 2 and more discussions can be found in Section 4.6.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 34.5 + }, + { + "type": "text", + "bbox": [ + 107, + 609, + 505, + 642 + ], + "lines": [ + { + "bbox": [ + 106, + 609, + 505, + 621 + ], + "spans": [ + { + "bbox": [ + 106, + 609, + 505, + 621 + ], + "score": 1.0, + "content": "Firstly, we found that, although the RF size is important, the 1D-CNNs are not sensitive to the", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 620, + 505, + 632 + ], + "spans": [ + { + "bbox": [ + 105, + 620, + 505, + 632 + ], + "score": 1.0, + "content": "specific kernel size configurations that we take to compose that RF size. An example is given in the", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 631, + 217, + 644 + ], + "spans": [ + { + "bbox": [ + 105, + 631, + 217, + 644 + ], + "score": 1.0, + "content": "right image of the Figure 2", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 37 + }, + { + "type": "text", + "bbox": [ + 107, + 648, + 505, + 703 + ], + "lines": [ + { + "bbox": [ + 106, + 648, + 505, + 660 + ], + "spans": [ + { + "bbox": [ + 106, + 648, + 505, + 660 + ], + "score": 1.0, + "content": "Secondly, the performance of 1D-CNNs is mainly determined by the best RF size it has. To be", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 659, + 505, + 671 + ], + "spans": [ + { + "bbox": [ + 105, + 659, + 505, + 671 + ], + "score": 1.0, + "content": "specific, supposing we have multiple single-RF-size-models which are of similar model size and", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 669, + 505, + 682 + ], + "spans": [ + { + "bbox": [ + 105, + 669, + 494, + 682 + ], + "score": 1.0, + "content": "layer numbers, but each of them has a unique RF size. Let’s denote the set of those RF sizes as", + "type": "text" + }, + { + "bbox": [ + 494, + 670, + 501, + 680 + ], + "score": 0.32, + "content": "\\mathbb { S }", + "type": "inline_equation" + }, + { + "bbox": [ + 502, + 669, + 505, + 682 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 680, + 505, + 694 + ], + "spans": [ + { + "bbox": [ + 105, + 680, + 505, + 694 + ], + "score": 1.0, + "content": "When testing those models on a dataset, we will have a set of accuracy results A. Then, supposing", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 691, + 506, + 704 + ], + "spans": [ + { + "bbox": [ + 105, + 691, + 467, + 704 + ], + "score": 1.0, + "content": "we have a multi-kernel model which has multiple RF sizes3 and set of those sizes is also", + "type": "text" + }, + { + "bbox": [ + 467, + 692, + 474, + 702 + ], + "score": 0.27, + "content": "\\mathbb { S }", + "type": "inline_equation" + }, + { + "bbox": [ + 475, + 691, + 506, + 704 + ], + "score": 1.0, + "content": ". Then,", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 41 + } + ], + "page_idx": 1, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 25, + 294, + 39 + ], + "spans": [ + { + "bbox": [ + 106, + 25, + 294, + 39 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2022", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 309, + 760 + ], + "lines": [ + { + "bbox": [ + 301, + 750, + 310, + 763 + ], + "spans": [ + { + "bbox": [ + 301, + 750, + 310, + 763 + ], + "score": 1.0, + "content": "2", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 106, + 711, + 504, + 731 + ], + "lines": [ + { + "bbox": [ + 118, + 709, + 505, + 723 + ], + "spans": [ + { + "bbox": [ + 118, + 709, + 505, + 723 + ], + "score": 1.0, + "content": "3A detailed discussion about how to calculate RF sizes for 1D-CNNs with multiple kernels in each layer", + "type": "text" + } + ] + }, + { + "bbox": [ + 105, + 721, + 208, + 731 + ], + "spans": [ + { + "bbox": [ + 105, + 721, + 208, + 731 + ], + "score": 1.0, + "content": "can be found in Section 3.2", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "image", + "bbox": [ + 107, + 80, + 503, + 167 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 107, + 80, + 503, + 167 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 107, + 80, + 503, + 167 + ], + "spans": [ + { + "bbox": [ + 107, + 80, + 503, + 167 + ], + "score": 0.928, + "type": "image", + "image_path": "0de81077afc0a14742088d5b94bd12b016a9cd78eeb745fcf515465d47d20a88.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 107, + 80, + 503, + 109.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 107, + 109.0, + 503, + 138.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 107, + 138.0, + 503, + 167.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 180, + 505, + 224 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 180, + 504, + 192 + ], + "spans": [ + { + "bbox": [ + 106, + 180, + 504, + 192 + ], + "score": 1.0, + "content": "Figure 1: Left: A model’s accuracy on the UCR 85 datasets changes by tuning the model’s receptive", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 104, + 190, + 505, + 204 + ], + "spans": [ + { + "bbox": [ + 104, + 190, + 505, + 204 + ], + "score": 1.0, + "content": "field sizes from 10 to 200. Right: The average rank results of each receptive field size are pretty", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 201, + 506, + 214 + ], + "spans": [ + { + "bbox": [ + 105, + 201, + 506, + 214 + ], + "score": 1.0, + "content": "similar, which means that no single receptive field size can significantly outperform others on most", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 213, + 144, + 225 + ], + "spans": [ + { + "bbox": [ + 105, + 213, + 144, + 225 + ], + "score": 1.0, + "content": "datasets.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 4.5 + } + ], + "index": 2.75 + }, + { + "type": "text", + "bbox": [ + 108, + 237, + 504, + 259 + ], + "lines": [], + "index": 7.5, + "bbox_fs": [ + 106, + 236, + 505, + 260 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 107, + 264, + 504, + 353 + ], + "lines": [ + { + "bbox": [ + 106, + 264, + 505, + 276 + ], + "spans": [ + { + "bbox": [ + 106, + 264, + 505, + 276 + ], + "score": 1.0, + "content": "Although a number of researchers have searched for the best RF of 1D-CNNs for TSC, there is still", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 276, + 506, + 287 + ], + "spans": [ + { + "bbox": [ + 105, + 276, + 506, + 287 + ], + "score": 1.0, + "content": "no agreed answer to 1) what size of the RF is the best? And 2) how many different RFs should be", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 287, + 505, + 299 + ], + "spans": [ + { + "bbox": [ + 105, + 287, + 505, + 299 + ], + "score": 1.0, + "content": "used? Models need to be equipped with different sizes and different numbers of RFs for a specific", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 298, + 505, + 310 + ], + "spans": [ + { + "bbox": [ + 106, + 298, + 505, + 310 + ], + "score": 1.0, + "content": "dataset. Using the same setup for every dataset can lead to a significant performance drop for some", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 308, + 505, + 321 + ], + "spans": [ + { + "bbox": [ + 105, + 308, + 505, + 321 + ], + "score": 1.0, + "content": "datasets. For example, as shown by the statistics on the University of California Riverside (UCR) 85", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 319, + 504, + 332 + ], + "spans": [ + { + "bbox": [ + 105, + 319, + 489, + 332 + ], + "score": 1.0, + "content": "“bake off” datasets in Figure 1a, the accuracy of most datasets can have a variance of more than", + "type": "text" + }, + { + "bbox": [ + 489, + 320, + 504, + 330 + ], + "score": 0.85, + "content": "5 \\%", + "type": "inline_equation" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 331, + 506, + 343 + ], + "spans": [ + { + "bbox": [ + 105, + 331, + 506, + 343 + ], + "score": 1.0, + "content": "just by changing the RF sizes of their model while keeping the rest of the configurations the same.", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 342, + 475, + 354 + ], + "spans": [ + { + "bbox": [ + 105, + 342, + 475, + 354 + ], + "score": 1.0, + "content": "As also shown in Figure 1b, no RF can consistently perform the best over different datasets.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 12.5, + "bbox_fs": [ + 105, + 264, + 506, + 354 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 358, + 505, + 457 + ], + "lines": [ + { + "bbox": [ + 106, + 358, + 505, + 371 + ], + "spans": [ + { + "bbox": [ + 106, + 358, + 505, + 371 + ], + "score": 1.0, + "content": "To avoid those complicated and resource-consuming searching work, we propose Omni-Scale block", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 370, + 505, + 381 + ], + "spans": [ + { + "bbox": [ + 106, + 370, + 505, + 381 + ], + "score": 1.0, + "content": "(OS-block), where the kernel choices for 1D-CNNs are automatically set through a simple and", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 379, + 506, + 393 + ], + "spans": [ + { + "bbox": [ + 105, + 379, + 506, + 393 + ], + "score": 1.0, + "content": "universal rule that can cover the RF of all scales. The rule is inspired by Goldbach’s conjecture,", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 392, + 505, + 403 + ], + "spans": [ + { + "bbox": [ + 106, + 392, + 505, + 403 + ], + "score": 1.0, + "content": "where any positive even number can be written as the sum of two prime numbers. Therefore, the", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 402, + 506, + 415 + ], + "spans": [ + { + "bbox": [ + 105, + 402, + 506, + 415 + ], + "score": 1.0, + "content": "OS-block uses a set of prime numbers as the kernel sizes except for the last layer whose kernel", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 413, + 505, + 425 + ], + "spans": [ + { + "bbox": [ + 106, + 413, + 505, + 425 + ], + "score": 1.0, + "content": "sizes are 1 and 2. In this way, a 1D-CNN with these kernel sizes can cover the RF of all scales", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 424, + 505, + 436 + ], + "spans": [ + { + "bbox": [ + 105, + 424, + 505, + 436 + ], + "score": 1.0, + "content": "by transforming TS through different combinations of these prime size kernels. What’s more, the", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 434, + 506, + 448 + ], + "spans": [ + { + "bbox": [ + 105, + 434, + 506, + 448 + ], + "score": 1.0, + "content": "OS-block is easy to implement to various TS datasets via selecting the maximum prime number", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 446, + 243, + 459 + ], + "spans": [ + { + "bbox": [ + 105, + 446, + 243, + 459 + ], + "score": 1.0, + "content": "according to the length of the TS.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 21, + "bbox_fs": [ + 105, + 358, + 506, + 459 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 463, + 505, + 540 + ], + "lines": [ + { + "bbox": [ + 105, + 462, + 505, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 462, + 505, + 475 + ], + "score": 1.0, + "content": "In experiments, we show consistent state-of-the-art performance on four TSC benchmarks. These", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 473, + 505, + 487 + ], + "spans": [ + { + "bbox": [ + 105, + 473, + 505, + 487 + ], + "score": 1.0, + "content": "benchmarks contain datasets from different domains, i.e., healthcare, human activity recognition,", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 485, + 505, + 497 + ], + "spans": [ + { + "bbox": [ + 105, + 485, + 505, + 497 + ], + "score": 1.0, + "content": "speech recognition, and spectrum analysis. Despite the dynamic patterns of these datasets, 1D-", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 495, + 505, + 508 + ], + "spans": [ + { + "bbox": [ + 106, + 495, + 505, + 508 + ], + "score": 1.0, + "content": "CNNs with our OS-block robustly outperform previous baselines with the unified training hyper-", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 507, + 506, + 519 + ], + "spans": [ + { + "bbox": [ + 105, + 507, + 506, + 519 + ], + "score": 1.0, + "content": "parameters for all datasets such as learning rate, batch size, and iteration numbers. We also did a", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 518, + 505, + 530 + ], + "spans": [ + { + "bbox": [ + 105, + 518, + 505, + 530 + ], + "score": 1.0, + "content": "comprehensive study to show our OS-block, the no time scale search solution, always matches the", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 529, + 333, + 541 + ], + "spans": [ + { + "bbox": [ + 105, + 529, + 333, + 541 + ], + "score": 1.0, + "content": "performance with the best RF size for different datasets.", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 29, + "bbox_fs": [ + 105, + 462, + 506, + 541 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 556, + 199, + 569 + ], + "lines": [ + { + "bbox": [ + 104, + 555, + 200, + 572 + ], + "spans": [ + { + "bbox": [ + 104, + 555, + 200, + 572 + ], + "score": 1.0, + "content": "2 MOTIVATIONS", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 33 + }, + { + "type": "text", + "bbox": [ + 107, + 581, + 504, + 604 + ], + "lines": [ + { + "bbox": [ + 106, + 581, + 505, + 594 + ], + "spans": [ + { + "bbox": [ + 106, + 581, + 505, + 594 + ], + "score": 1.0, + "content": "Two phenomena of 1D-CNNs inspire the design of the OS-block. In this section, we will introduce", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 592, + 495, + 604 + ], + "spans": [ + { + "bbox": [ + 106, + 592, + 495, + 604 + ], + "score": 1.0, + "content": "the two phenomena with examples in Figure 2 and more discussions can be found in Section 4.6.", + "type": "text" + } + ], + "index": 35 + } + ], + "index": 34.5, + "bbox_fs": [ + 106, + 581, + 505, + 604 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 609, + 505, + 642 + ], + "lines": [ + { + "bbox": [ + 106, + 609, + 505, + 621 + ], + "spans": [ + { + "bbox": [ + 106, + 609, + 505, + 621 + ], + "score": 1.0, + "content": "Firstly, we found that, although the RF size is important, the 1D-CNNs are not sensitive to the", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 620, + 505, + 632 + ], + "spans": [ + { + "bbox": [ + 105, + 620, + 505, + 632 + ], + "score": 1.0, + "content": "specific kernel size configurations that we take to compose that RF size. An example is given in the", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 631, + 217, + 644 + ], + "spans": [ + { + "bbox": [ + 105, + 631, + 217, + 644 + ], + "score": 1.0, + "content": "right image of the Figure 2", + "type": "text" + } + ], + "index": 38 + } + ], + "index": 37, + "bbox_fs": [ + 105, + 609, + 505, + 644 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 648, + 505, + 703 + ], + "lines": [ + { + "bbox": [ + 106, + 648, + 505, + 660 + ], + "spans": [ + { + "bbox": [ + 106, + 648, + 505, + 660 + ], + "score": 1.0, + "content": "Secondly, the performance of 1D-CNNs is mainly determined by the best RF size it has. To be", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 659, + 505, + 671 + ], + "spans": [ + { + "bbox": [ + 105, + 659, + 505, + 671 + ], + "score": 1.0, + "content": "specific, supposing we have multiple single-RF-size-models which are of similar model size and", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 669, + 505, + 682 + ], + "spans": [ + { + "bbox": [ + 105, + 669, + 494, + 682 + ], + "score": 1.0, + "content": "layer numbers, but each of them has a unique RF size. Let’s denote the set of those RF sizes as", + "type": "text" + }, + { + "bbox": [ + 494, + 670, + 501, + 680 + ], + "score": 0.32, + "content": "\\mathbb { S }", + "type": "inline_equation" + }, + { + "bbox": [ + 502, + 669, + 505, + 682 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 105, + 680, + 505, + 694 + ], + "spans": [ + { + "bbox": [ + 105, + 680, + 505, + 694 + ], + "score": 1.0, + "content": "When testing those models on a dataset, we will have a set of accuracy results A. Then, supposing", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 691, + 506, + 704 + ], + "spans": [ + { + "bbox": [ + 105, + 691, + 467, + 704 + ], + "score": 1.0, + "content": "we have a multi-kernel model which has multiple RF sizes3 and set of those sizes is also", + "type": "text" + }, + { + "bbox": [ + 467, + 692, + 474, + 702 + ], + "score": 0.27, + "content": "\\mathbb { S }", + "type": "inline_equation" + }, + { + "bbox": [ + 475, + 691, + 506, + 704 + ], + "score": 1.0, + "content": ". Then,", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 106, + 290, + 505, + 303 + ], + "spans": [ + { + "bbox": [ + 106, + 290, + 505, + 303 + ], + "score": 1.0, + "content": "the accuracy of the multiple-RF-sizes-model will be similar to the highest value of A. An example is", + "type": "text", + "cross_page": true + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 301, + 506, + 314 + ], + "spans": [ + { + "bbox": [ + 105, + 301, + 506, + 314 + ], + "score": 1.0, + "content": "given in the left image of Figure 2. Specifically, when testing single-RF-size-models on the Google", + "type": "text", + "cross_page": true + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 313, + 505, + 324 + ], + "spans": [ + { + "bbox": [ + 105, + 313, + 505, + 324 + ], + "score": 1.0, + "content": "Speechcommands dataset, the model’s performance is positive correlation with the model’s RF", + "type": "text", + "cross_page": true + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 324, + 505, + 336 + ], + "spans": [ + { + "bbox": [ + 105, + 324, + 353, + 336 + ], + "score": 1.0, + "content": "size. For example, the light blue line whose set of RF size is", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 353, + 324, + 374, + 336 + ], + "score": 0.89, + "content": "\\{ 9 9 \\}", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 374, + 324, + 505, + 336 + ], + "score": 1.0, + "content": "outperforms the light green line", + "type": "text", + "cross_page": true + } + ], + "index": 14 + }, + { + "bbox": [ + 107, + 334, + 506, + 347 + ], + "spans": [ + { + "bbox": [ + 107, + 334, + 128, + 347 + ], + "score": 0.9, + "content": "\\{ 3 9 \\}", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 128, + 334, + 199, + 347 + ], + "score": 1.0, + "content": "and light red line", + "type": "text", + "cross_page": true + }, + { + "bbox": [ + 199, + 334, + 214, + 347 + ], + "score": 0.84, + "content": "\\{ \\bar { 9 } \\}", + "type": "inline_equation", + "cross_page": true + }, + { + "bbox": [ + 215, + 334, + 506, + 347 + ], + "score": 1.0, + "content": ". For those multiple-RF-sizes-models which has more than one element", + "type": "text", + "cross_page": true + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 345, + 506, + 358 + ], + "spans": [ + { + "bbox": [ + 105, + 345, + 506, + 358 + ], + "score": 1.0, + "content": "in their set of RF sizes, their performance are determined by the best (also the largest because of", + "type": "text", + "cross_page": true + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 357, + 505, + 369 + ], + "spans": [ + { + "bbox": [ + 106, + 357, + 505, + 369 + ], + "score": 1.0, + "content": "the positive correlation) RF size it has. 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For example, the light blue line whose set of RF size is", + "type": "text" + }, + { + "bbox": [ + 353, + 324, + 374, + 336 + ], + "score": 0.89, + "content": "\\{ 9 9 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 374, + 324, + 505, + 336 + ], + "score": 1.0, + "content": "outperforms the light green line", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 107, + 334, + 506, + 347 + ], + "spans": [ + { + "bbox": [ + 107, + 334, + 128, + 347 + ], + "score": 0.9, + "content": "\\{ 3 9 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 128, + 334, + 199, + 347 + ], + "score": 1.0, + "content": "and light red line", + "type": "text" + }, + { + "bbox": [ + 199, + 334, + 214, + 347 + ], + "score": 0.84, + "content": "\\{ \\bar { 9 } \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 215, + 334, + 506, + 347 + ], + "score": 1.0, + "content": ". For those multiple-RF-sizes-models which has more than one element", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 345, + 506, + 358 + ], + "spans": [ + { + "bbox": [ + 105, + 345, + 506, + 358 + ], + "score": 1.0, + "content": "in their set of RF sizes, their performance are determined by the best (also the largest because of", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 357, + 505, + 369 + ], + "spans": [ + { + "bbox": [ + 106, + 357, + 505, + 369 + ], + "score": 1.0, + "content": "the positive correlation) RF size it has. 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It is a three-layer multi-kernel structure, and", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 679, + 505, + 693 + ], + "spans": [ + { + "bbox": [ + 105, + 679, + 505, + 693 + ], + "score": 1.0, + "content": "each kernel does the same padding convolution with input. 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For example, (9):5 5 1 1 1 means the 1D-CNN has five layers and the receptive", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 211, + 505, + 224 + ], + "spans": [ + { + "bbox": [ + 105, + 211, + 505, + 224 + ], + "score": 1.0, + "content": "field size is 9, and from the first layer to the last layer, kernel sizes of each layer are 5, 5, 1, 1,", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 223, + 506, + 235 + ], + "spans": [ + { + "bbox": [ + 105, + 223, + 506, + 235 + ], + "score": 1.0, + "content": "and 1. Lines of similar color are 1D-CNNs with the same receptive field size, and they are also of", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 233, + 505, + 246 + ], + "spans": [ + { + "bbox": [ + 105, + 233, + 505, + 246 + ], + "score": 1.0, + "content": "similar performance. Right: Lines with similar colors are models which have the same best receptive", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 244, + 505, + 257 + ], + "spans": [ + { + "bbox": [ + 105, + 244, + 505, + 257 + ], + "score": 1.0, + "content": "field size. For example, all (red/green/blue) lines have the receptive field size (9/39/99), and their", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 255, + 505, + 268 + ], + "spans": [ + { + "bbox": [ + 105, + 255, + 505, + 268 + ], + "score": 1.0, + "content": "performances are similar to the bright (red/green/blue) line which denotes the model only has the", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 266, + 225, + 279 + ], + "spans": [ + { + "bbox": [ + 105, + 266, + 225, + 279 + ], + "score": 1.0, + "content": "receptive field size (9/39/99).", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 6.5 + } + ], + "index": 3.75 + }, + { + "type": "text", + "bbox": [ + 106, + 290, + 505, + 379 + ], + "lines": [], + "index": 14.5, + "bbox_fs": [ + 105, + 290, + 506, + 380 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 107, + 384, + 505, + 462 + ], + "lines": [ + { + "bbox": [ + 106, + 385, + 504, + 396 + ], + "spans": [ + { + "bbox": [ + 106, + 385, + 504, + 396 + ], + "score": 1.0, + "content": "The second phenomenon means that, instead of searching for the best time scales, if the model", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 394, + 506, + 408 + ], + "spans": [ + { + "bbox": [ + 105, + 394, + 506, + 408 + ], + "score": 1.0, + "content": "covers all RF sizes, its performance will be similar to that of a model with the best RF size. However,", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 406, + 505, + 418 + ], + "spans": [ + { + "bbox": [ + 105, + 406, + 505, + 418 + ], + "score": 1.0, + "content": "there are many designs that can cover all RF sizes. Which one should be preferred? Based on the", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 417, + 505, + 430 + ], + "spans": [ + { + "bbox": [ + 105, + 417, + 505, + 430 + ], + "score": 1.0, + "content": "first phenomenon, from the performance perspective, we could choose any design that we want.", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 428, + 505, + 440 + ], + "spans": [ + { + "bbox": [ + 105, + 428, + 505, + 440 + ], + "score": 1.0, + "content": "However, as we will show in Section 3.3, those candidate designs are not of the same characteristics", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 439, + 504, + 451 + ], + "spans": [ + { + "bbox": [ + 106, + 439, + 504, + 451 + ], + "score": 1.0, + "content": "such as the model size or the expandability for long TS data. Therefore, the design of the OS-block", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 450, + 381, + 462 + ], + "spans": [ + { + "bbox": [ + 105, + 450, + 381, + 462 + ], + "score": 1.0, + "content": "that we propose aims at covering all RF sizes in an efficient manner.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 22, + "bbox_fs": [ + 105, + 385, + 506, + 462 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 477, + 173, + 489 + ], + "lines": [ + { + "bbox": [ + 104, + 474, + 175, + 493 + ], + "spans": [ + { + "bbox": [ + 104, + 474, + 175, + 493 + ], + "score": 1.0, + "content": "3 METHOD", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 26 + }, + { + "type": "text", + "bbox": [ + 107, + 501, + 505, + 546 + ], + "lines": [ + { + "bbox": [ + 105, + 501, + 505, + 514 + ], + "spans": [ + { + "bbox": [ + 105, + 501, + 505, + 514 + ], + "score": 1.0, + "content": "The section is organized as follows: Firstly, we give the problem definition in Section 3.1. Then,", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 105, + 513, + 506, + 525 + ], + "spans": [ + { + "bbox": [ + 105, + 513, + 506, + 525 + ], + "score": 1.0, + "content": "we will explain how to construct the Omni-scale block (OS-block) which covers all receptive field", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 106, + 524, + 505, + 536 + ], + "spans": [ + { + "bbox": [ + 106, + 524, + 505, + 536 + ], + "score": 1.0, + "content": "sizes in Section 3.2. Section 3.3 will explain the reason why OS-block can cover RF of all sizes in", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 106, + 534, + 488, + 546 + ], + "spans": [ + { + "bbox": [ + 106, + 534, + 488, + 546 + ], + "score": 1.0, + "content": "an efficient manner. In Section 3.4, we will introduce how to apply the OS-block on TSC tasks.", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 28.5, + "bbox_fs": [ + 105, + 501, + 506, + 546 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 559, + 227, + 570 + ], + "lines": [ + { + "bbox": [ + 105, + 559, + 228, + 572 + ], + "spans": [ + { + "bbox": [ + 105, + 559, + 228, + 572 + ], + "score": 1.0, + "content": "3.1 PROBLEM DEFINITION", + "type": "text" + } + ], + "index": 31 + } + ], + "index": 31 + }, + { + "type": "text", + "bbox": [ + 107, + 579, + 505, + 635 + ], + "lines": [ + { + "bbox": [ + 105, + 578, + 505, + 592 + ], + "spans": [ + { + "bbox": [ + 105, + 578, + 204, + 592 + ], + "score": 1.0, + "content": "TS data is denoted as", + "type": "text" + }, + { + "bbox": [ + 205, + 579, + 300, + 591 + ], + "score": 0.91, + "content": "\\textbf { \\textit { X } } = ~ [ \\pmb { x } _ { 1 } , \\pmb { x } _ { 2 } , . . . , \\pmb { x } _ { m } ]", + "type": "inline_equation" + }, + { + "bbox": [ + 301, + 578, + 335, + 592 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 336, + 582, + 346, + 590 + ], + "score": 0.72, + "content": "m", + "type": "inline_equation" + }, + { + "bbox": [ + 347, + 578, + 505, + 592 + ], + "score": 1.0, + "content": "is the number of variates. For uni-", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 590, + 505, + 603 + ], + "spans": [ + { + "bbox": [ + 106, + 590, + 179, + 603 + ], + "score": 1.0, + "content": "variate TS data,", + "type": "text" + }, + { + "bbox": [ + 179, + 591, + 216, + 601 + ], + "score": 0.9, + "content": "\\textit { m } = \\textit { 1 }", + "type": "inline_equation" + }, + { + "bbox": [ + 216, + 590, + 255, + 603 + ], + "score": 1.0, + "content": "and for", + "type": "text" + }, + { + "bbox": [ + 255, + 592, + 291, + 601 + ], + "score": 0.89, + "content": "m \\ > \\ 1", + "type": "inline_equation" + }, + { + "bbox": [ + 291, + 590, + 505, + 603 + ], + "score": 1.0, + "content": ", the TS are multivariate. Each variate is a vec-", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 600, + 505, + 614 + ], + "spans": [ + { + "bbox": [ + 105, + 600, + 164, + 614 + ], + "score": 1.0, + "content": "tor of length", + "type": "text" + }, + { + "bbox": [ + 164, + 602, + 169, + 611 + ], + "score": 0.53, + "content": "l", + "type": "inline_equation" + }, + { + "bbox": [ + 170, + 600, + 291, + 614 + ], + "score": 1.0, + "content": ". A TS dataset, which has", + "type": "text" + }, + { + "bbox": [ + 291, + 604, + 299, + 612 + ], + "score": 0.78, + "content": "n", + "type": "inline_equation" + }, + { + "bbox": [ + 299, + 600, + 480, + 614 + ], + "score": 1.0, + "content": "data and label pairs, can be denoted as:", + "type": "text" + }, + { + "bbox": [ + 480, + 602, + 505, + 613 + ], + "score": 0.86, + "content": "\\mathbb { D } =", + "type": "inline_equation" + } + ], + "index": 34 + }, + { + "bbox": [ + 106, + 611, + 506, + 626 + ], + "spans": [ + { + "bbox": [ + 106, + 612, + 251, + 625 + ], + "score": 0.89, + "content": "\\{ ( \\boldsymbol { X } ^ { 1 } , \\boldsymbol { y } ^ { 1 } ) , \\overbar { ( \\boldsymbol { X } ^ { 2 } , \\boldsymbol { y } ^ { 2 } ) } , . . . , ( \\boldsymbol { X } ^ { n } , \\boldsymbol { y } ^ { n } ) \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 252, + 611, + 283, + 626 + ], + "score": 1.0, + "content": ", where", + "type": "text" + }, + { + "bbox": [ + 283, + 613, + 320, + 624 + ], + "score": 0.91, + "content": "( X ^ { * } , y ^ { * } )", + "type": "inline_equation" + }, + { + "bbox": [ + 321, + 611, + 405, + 626 + ], + "score": 1.0, + "content": "denotes the TS data", + "type": "text" + }, + { + "bbox": [ + 406, + 613, + 421, + 623 + ], + "score": 0.87, + "content": "x ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 421, + 611, + 506, + 626 + ], + "score": 1.0, + "content": "belongs to the class", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 107, + 623, + 400, + 636 + ], + "spans": [ + { + "bbox": [ + 107, + 625, + 117, + 635 + ], + "score": 0.87, + "content": "y ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 118, + 623, + 298, + 636 + ], + "score": 1.0, + "content": ". The task of TSC is to predict the class label", + "type": "text" + }, + { + "bbox": [ + 298, + 625, + 309, + 635 + ], + "score": 0.88, + "content": "y ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 309, + 623, + 379, + 636 + ], + "score": 1.0, + "content": "when given a TS", + "type": "text" + }, + { + "bbox": [ + 380, + 624, + 395, + 634 + ], + "score": 0.87, + "content": "x ^ { * }", + "type": "inline_equation" + }, + { + "bbox": [ + 396, + 623, + 400, + 636 + ], + "score": 1.0, + "content": ".", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 34, + "bbox_fs": [ + 105, + 578, + 506, + 636 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 648, + 262, + 659 + ], + "lines": [ + { + "bbox": [ + 106, + 648, + 263, + 660 + ], + "spans": [ + { + "bbox": [ + 106, + 648, + 263, + 660 + ], + "score": 1.0, + "content": "3.2 ARCHITECTURE OF OS-BLOCK", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 37 + }, + { + "type": "text", + "bbox": [ + 107, + 668, + 505, + 703 + ], + "lines": [ + { + "bbox": [ + 106, + 668, + 505, + 681 + ], + "spans": [ + { + "bbox": [ + 106, + 668, + 505, + 681 + ], + "score": 1.0, + "content": "The architecture of the OS-block is shown in Figure 3. It is a three-layer multi-kernel structure, and", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 679, + 505, + 693 + ], + "spans": [ + { + "bbox": [ + 105, + 679, + 505, + 693 + ], + "score": 1.0, + "content": "each kernel does the same padding convolution with input. For the kernel size configuration, we use", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 106, + 689, + 305, + 706 + ], + "spans": [ + { + "bbox": [ + 106, + 691, + 123, + 702 + ], + "score": 0.89, + "content": "\\mathbb { P } ^ { ( i ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 123, + 689, + 263, + 706 + ], + "score": 1.0, + "content": "to denote the kernel size set of the", + "type": "text" + }, + { + "bbox": [ + 263, + 693, + 267, + 701 + ], + "score": 0.76, + "content": "i", + "type": "inline_equation" + }, + { + "bbox": [ + 268, + 689, + 305, + 706 + ], + "score": 1.0, + "content": "-th layer:", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 39, + "bbox_fs": [ + 105, + 668, + 505, + 706 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 217, + 707, + 389, + 735 + ], + "lines": [ + { + "bbox": [ + 217, + 707, + 389, + 735 + ], + "spans": [ + { + "bbox": [ + 217, + 707, + 389, + 735 + ], + "score": 0.94, + "content": "\\mathbb { P } ^ { ( i ) } = \\left\\{ \\begin{array} { l l } { \\{ 1 , 2 , 3 , 5 , . . . , p _ { k } \\} ~ } & { , i \\in \\{ 1 , 2 \\} } \\\\ { \\{ 1 , 2 \\} ~ } & { , i = 3 } \\end{array} \\right.", + "type": "interline_equation", + "image_path": "235f0eac9ec4db855af6264a0cefa6a125dc9adc30d84563a049b4c6f1c43e45.jpg" + } + ] + } + ], + "index": 41.5, + "virtual_lines": [ + { + "bbox": [ + 217, + 707, + 389, + 721.0 + ], + "spans": [], + "index": 41 + }, + { + "bbox": [ + 217, + 721.0, + 389, + 735.0 + ], + "spans": [], + "index": 42 + } + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 118, + 80, + 501, + 236 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 118, + 80, + 501, + 236 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 118, + 80, + 501, + 236 + ], + "spans": [ + { + "bbox": [ + 118, + 80, + 501, + 236 + ], + "score": 0.97, + "type": "image", + "image_path": "9233984bbc86d0cc295e7b0d82cf4d5c4614b52e390f439f9702504bfb0f06ab.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 118, + 80, + 501, + 132.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 118, + 132.0, + 501, + 184.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 118, + 184.0, + 501, + 236.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 249, + 505, + 338 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 250, + 506, + 262 + ], + "spans": [ + { + "bbox": [ + 106, + 250, + 506, + 262 + ], + "score": 1.0, + "content": "Figure 3: The left image shows that every even number from 2 to 38 can be composed via two", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 261, + 505, + 272 + ], + "spans": [ + { + "bbox": [ + 105, + 261, + 505, + 272 + ], + "score": 1.0, + "content": "prime numbers from 1 to 19. This phenomenon can be extended to all even numbers. Based on this", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 272, + 505, + 284 + ], + "spans": [ + { + "bbox": [ + 106, + 272, + 505, + 284 + ], + "score": 1.0, + "content": "phenomenon, with the OS-block structure in the middle image, we could cover all receptive field", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 282, + 505, + 295 + ], + "spans": [ + { + "bbox": [ + 105, + 282, + 404, + 295 + ], + "score": 1.0, + "content": "sizes. Specifically, the first two layers have prime-sized kernels from 1 to", + "type": "text" + }, + { + "bbox": [ + 404, + 284, + 415, + 294 + ], + "score": 0.84, + "content": "p _ { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 416, + 282, + 505, + 295 + ], + "score": 1.0, + "content": ". Thus, the two layers", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 294, + 506, + 306 + ], + "spans": [ + { + "bbox": [ + 106, + 294, + 506, + 306 + ], + "score": 1.0, + "content": "can cover all even number receptive field sizes. With kernels of sizes 1 and 2 in the third layer, we", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 304, + 505, + 316 + ], + "spans": [ + { + "bbox": [ + 105, + 304, + 419, + 316 + ], + "score": 1.0, + "content": "could cover all integer receptive field sizes in a range via selecting the value", + "type": "text" + }, + { + "bbox": [ + 419, + 306, + 430, + 316 + ], + "score": 0.85, + "content": "p _ { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 430, + 304, + 505, + 316 + ], + "score": 1.0, + "content": ". The OS-block is", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 315, + 505, + 327 + ], + "spans": [ + { + "bbox": [ + 105, + 315, + 505, + 327 + ], + "score": 1.0, + "content": "easy to be applied on time series classification tasks. A simple classifier with the OS-block, namely", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 326, + 451, + 339 + ], + "spans": [ + { + "bbox": [ + 105, + 326, + 451, + 339 + ], + "score": 1.0, + "content": "OS-CNN, is given in the right image, which achieves a series of SOTA performances.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 6.5 + } + ], + "index": 3.75 + }, + { + "type": "text", + "bbox": [ + 106, + 357, + 505, + 456 + ], + "lines": [ + { + "bbox": [ + 105, + 356, + 506, + 371 + ], + "spans": [ + { + "bbox": [ + 105, + 356, + 136, + 371 + ], + "score": 1.0, + "content": "Where", + "type": "text" + }, + { + "bbox": [ + 136, + 357, + 217, + 370 + ], + "score": 0.92, + "content": "\\{ 1 , 2 , 3 , 5 , 7 , . . . , p _ { k } \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 217, + 356, + 362, + 371 + ], + "score": 1.0, + "content": "is a set of prime numbers from 1 to", + "type": "text" + }, + { + "bbox": [ + 363, + 359, + 374, + 369 + ], + "score": 0.85, + "content": "p _ { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 374, + 356, + 433, + 371 + ], + "score": 1.0, + "content": ". The value of", + "type": "text" + }, + { + "bbox": [ + 433, + 359, + 444, + 369 + ], + "score": 0.86, + "content": "p _ { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 444, + 356, + 506, + 371 + ], + "score": 1.0, + "content": "is the smallest", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 368, + 505, + 381 + ], + "spans": [ + { + "bbox": [ + 105, + 368, + 505, + 381 + ], + "score": 1.0, + "content": "prime number that can cover all sizes of RF in a range. Here, the range that we mentioned is all", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 379, + 506, + 392 + ], + "spans": [ + { + "bbox": [ + 105, + 379, + 327, + 392 + ], + "score": 1.0, + "content": "meaningful scales. For example, since the TS length is", + "type": "text" + }, + { + "bbox": [ + 327, + 380, + 331, + 389 + ], + "score": 0.53, + "content": "l", + "type": "inline_equation" + }, + { + "bbox": [ + 332, + 379, + 506, + 392 + ], + "score": 1.0, + "content": ", we don’t need to cover RFs that are larger", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 389, + 506, + 403 + ], + "spans": [ + { + "bbox": [ + 105, + 389, + 126, + 403 + ], + "score": 1.0, + "content": "than", + "type": "text" + }, + { + "bbox": [ + 127, + 391, + 131, + 401 + ], + "score": 0.55, + "content": "l", + "type": "inline_equation" + }, + { + "bbox": [ + 132, + 389, + 266, + 403 + ], + "score": 1.0, + "content": "or smaller than 1. Therefore, the", + "type": "text" + }, + { + "bbox": [ + 266, + 392, + 277, + 402 + ], + "score": 0.87, + "content": "p _ { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 278, + 389, + 506, + 403 + ], + "score": 1.0, + "content": "is the smallest prime number that can cover the RF size", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 401, + 506, + 414 + ], + "spans": [ + { + "bbox": [ + 105, + 401, + 148, + 414 + ], + "score": 1.0, + "content": "from 1 to", + "type": "text" + }, + { + "bbox": [ + 148, + 402, + 153, + 411 + ], + "score": 0.31, + "content": "l", + "type": "inline_equation" + }, + { + "bbox": [ + 153, + 401, + 506, + 414 + ], + "score": 1.0, + "content": ". If we have prior knowledge, such as that we know there are cycles in the TS, or we", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 412, + 505, + 424 + ], + "spans": [ + { + "bbox": [ + 106, + 412, + 505, + 424 + ], + "score": 1.0, + "content": "know the length range of the hidden representative pattern. We could change the RF size range of", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 424, + 505, + 435 + ], + "spans": [ + { + "bbox": [ + 106, + 424, + 505, + 435 + ], + "score": 1.0, + "content": "the OS-block by simply changing the prime number list. An example is given in the left image in", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 433, + 506, + 447 + ], + "spans": [ + { + "bbox": [ + 105, + 433, + 506, + 447 + ], + "score": 1.0, + "content": "Figure 3, which uses the prime number list in the blue block to cover the RF size range from 10 to", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 444, + 122, + 458 + ], + "spans": [ + { + "bbox": [ + 105, + 444, + 122, + 458 + ], + "score": 1.0, + "content": "26.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 15 + }, + { + "type": "text", + "bbox": [ + 106, + 461, + 505, + 528 + ], + "lines": [ + { + "bbox": [ + 105, + 461, + 505, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 461, + 505, + 475 + ], + "score": 1.0, + "content": "RF sizes of the OS-block: The RF is defined as the size of the region in the input that produces", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 473, + 504, + 485 + ], + "spans": [ + { + "bbox": [ + 106, + 473, + 504, + 485 + ], + "score": 1.0, + "content": "the feature. Because each layer of the OS-block has more than one convolution kernel, there will", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 484, + 506, + 497 + ], + "spans": [ + { + "bbox": [ + 106, + 484, + 506, + 497 + ], + "score": 1.0, + "content": "be several different paths from the input signal to the final output feature (Araujo et al., 2019; Luo", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 104, + 493, + 505, + 509 + ], + "spans": [ + { + "bbox": [ + 104, + 493, + 505, + 509 + ], + "score": 1.0, + "content": "et al., 2016), and each path will have a RF size. For the 3-layer OS-block, which has no pooling", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 505, + 506, + 519 + ], + "spans": [ + { + "bbox": [ + 105, + 505, + 305, + 519 + ], + "score": 1.0, + "content": "layer and the stride size is 1, the set of RF sizes", + "type": "text" + }, + { + "bbox": [ + 305, + 506, + 313, + 516 + ], + "score": 0.79, + "content": "\\mathbb { S }", + "type": "inline_equation" + }, + { + "bbox": [ + 313, + 505, + 506, + 519 + ], + "score": 1.0, + "content": "is the set of RF size of all paths, and it can be", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 516, + 161, + 529 + ], + "spans": [ + { + "bbox": [ + 105, + 516, + 161, + 529 + ], + "score": 1.0, + "content": "described as:", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 22.5 + }, + { + "type": "interline_equation", + "bbox": [ + 190, + 542, + 420, + 558 + ], + "lines": [ + { + "bbox": [ + 190, + 542, + 420, + 558 + ], + "spans": [ + { + "bbox": [ + 190, + 542, + 420, + 558 + ], + "score": 0.91, + "content": "\\mathbb { S } = \\{ p ^ { ( 1 ) } + p ^ { ( 2 ) } + p ^ { ( 3 ) } - 2 \\ | \\ p ^ { ( i ) } \\in \\mathbb { P } ^ { ( i ) } , i \\in \\{ 1 , 2 , 3 \\} \\} .", + "type": "interline_equation", + "image_path": "7fe0eca125404a28165f1c41eea2702cb392f9a726d3671ac7bec9c7facdfb94.jpg" + } + ] + } + ], + "index": 26, + "virtual_lines": [ + { + "bbox": [ + 190, + 542, + 420, + 558 + ], + "spans": [], + "index": 26 + } + ] + }, + { + "type": "text", + "bbox": [ + 105, + 565, + 504, + 589 + ], + "lines": [ + { + "bbox": [ + 104, + 564, + 506, + 579 + ], + "spans": [ + { + "bbox": [ + 104, + 564, + 187, + 579 + ], + "score": 1.0, + "content": "For the reasons that", + "type": "text" + }, + { + "bbox": [ + 187, + 565, + 204, + 577 + ], + "score": 0.91, + "content": "\\mathbb { P } ^ { ( i ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 204, + 564, + 317, + 579 + ], + "score": 1.0, + "content": "are prime number list when", + "type": "text" + }, + { + "bbox": [ + 318, + 567, + 359, + 579 + ], + "score": 0.94, + "content": "i \\in \\{ 1 , 2 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 359, + 564, + 391, + 579 + ], + "score": 1.0, + "content": ", the set", + "type": "text" + }, + { + "bbox": [ + 392, + 565, + 506, + 579 + ], + "score": 0.91, + "content": "\\{ p ^ { ( 1 ) } + p ^ { ( 2 ) } | p ^ { ( i ) } \\in \\mathbb { P } ^ { ( i ) } , i \\in", + "type": "inline_equation" + } + ], + "index": 27 + }, + { + "bbox": [ + 107, + 576, + 334, + 591 + ], + "spans": [ + { + "bbox": [ + 107, + 578, + 137, + 590 + ], + "score": 0.92, + "content": "\\{ 1 , 2 \\} \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 137, + 576, + 256, + 591 + ], + "score": 1.0, + "content": "is the set of all even numbers", + "type": "text" + }, + { + "bbox": [ + 257, + 578, + 264, + 588 + ], + "score": 0.52, + "content": "\\mathbb { E }", + "type": "inline_equation" + }, + { + "bbox": [ + 265, + 576, + 334, + 591 + ], + "score": 1.0, + "content": ".4 Thus, we have", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 27.5 + }, + { + "type": "interline_equation", + "bbox": [ + 222, + 603, + 388, + 618 + ], + "lines": [ + { + "bbox": [ + 222, + 603, + 388, + 618 + ], + "spans": [ + { + "bbox": [ + 222, + 603, + 388, + 618 + ], + "score": 0.91, + "content": "\\mathbb { S } = \\{ e + p ^ { ( 3 ) } - 2 \\mid p ^ { ( 3 ) } \\in \\mathbb { P } ^ { ( 3 ) } , e \\in \\mathbb { E } \\} .", + "type": "interline_equation", + "image_path": "779814a2496b431c3b26fdddebd44a0d8bddc1be84c5f79963792e9577de12a7.jpg" + } + ] + } + ], + "index": 29, + "virtual_lines": [ + { + "bbox": [ + 222, + 603, + 388, + 618 + ], + "spans": [], + "index": 29 + } + ] + }, + { + "type": "text", + "bbox": [ + 108, + 626, + 274, + 637 + ], + "lines": [ + { + "bbox": [ + 106, + 624, + 275, + 640 + ], + "spans": [ + { + "bbox": [ + 106, + 624, + 275, + 640 + ], + "score": 1.0, + "content": "With Equation 3 and Equation 1, we have", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 30 + }, + { + "type": "interline_equation", + "bbox": [ + 225, + 642, + 386, + 656 + ], + "lines": [ + { + "bbox": [ + 225, + 642, + 386, + 656 + ], + "spans": [ + { + "bbox": [ + 225, + 642, + 386, + 656 + ], + "score": 0.91, + "content": "\\mathbb { S } = \\{ e | e \\in \\mathbb { E } \\} \\cup \\{ e - 1 | e \\in \\mathbb { E } \\} \\equiv \\mathbb { N } ^ { + } .", + "type": "interline_equation", + "image_path": "62b398a9f23ad63303d85141df9a4486f888ea7d5d40626c9b0420e68adb65a8.jpg" + } + ] + } + ], + "index": 31, + "virtual_lines": [ + { + "bbox": [ + 225, + 642, + 386, + 656 + ], + "spans": [], + "index": 31 + } + ] + }, + { + "type": "text", + "bbox": [ + 108, + 660, + 503, + 683 + ], + "lines": [ + { + "bbox": [ + 106, + 659, + 506, + 673 + ], + "spans": [ + { + "bbox": [ + 106, + 659, + 135, + 673 + ], + "score": 1.0, + "content": "Where", + "type": "text" + }, + { + "bbox": [ + 135, + 660, + 151, + 671 + ], + "score": 0.88, + "content": "\\mathbb { N } ^ { + }", + "type": "inline_equation" + }, + { + "bbox": [ + 151, + 659, + 400, + 673 + ], + "score": 1.0, + "content": "is the set of all integer numbers in the range. Specifically, the", + "type": "text" + }, + { + "bbox": [ + 401, + 660, + 435, + 671 + ], + "score": 0.91, + "content": "\\mathbb { S } \\equiv \\mathbb { N } ^ { + }", + "type": "inline_equation" + }, + { + "bbox": [ + 436, + 659, + 506, + 673 + ], + "score": 1.0, + "content": "is because a real", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 671, + 505, + 684 + ], + "spans": [ + { + "bbox": [ + 106, + 671, + 336, + 684 + ], + "score": 1.0, + "content": "number must be an odd number or an even number, while", + "type": "text" + }, + { + "bbox": [ + 336, + 672, + 344, + 681 + ], + "score": 0.8, + "content": "\\mathbb { E }", + "type": "inline_equation" + }, + { + "bbox": [ + 344, + 671, + 438, + 684 + ], + "score": 1.0, + "content": "is the even number set,", + "type": "text" + }, + { + "bbox": [ + 438, + 671, + 495, + 684 + ], + "score": 0.93, + "content": "\\{ e - 1 | e \\in \\mathbb { E } \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 495, + 671, + 505, + 684 + ], + "score": 1.0, + "content": "is", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 32.5 + } + ], + "page_idx": 3, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 106, + 691, + 505, + 732 + ], + "lines": [ + { + "bbox": [ + 118, + 688, + 505, + 705 + ], + "spans": [ + { + "bbox": [ + 118, + 688, + 505, + 705 + ], + "score": 1.0, + "content": "4This is according to Goldbach’s conjecture. 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This phenomenon can be extended to all even numbers. Based on this", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 272, + 505, + 284 + ], + "spans": [ + { + "bbox": [ + 106, + 272, + 505, + 284 + ], + "score": 1.0, + "content": "phenomenon, with the OS-block structure in the middle image, we could cover all receptive field", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 282, + 505, + 295 + ], + "spans": [ + { + "bbox": [ + 105, + 282, + 404, + 295 + ], + "score": 1.0, + "content": "sizes. Specifically, the first two layers have prime-sized kernels from 1 to", + "type": "text" + }, + { + "bbox": [ + 404, + 284, + 415, + 294 + ], + "score": 0.84, + "content": "p _ { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 416, + 282, + 505, + 295 + ], + "score": 1.0, + "content": ". Thus, the two layers", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 294, + 506, + 306 + ], + "spans": [ + { + "bbox": [ + 106, + 294, + 506, + 306 + ], + "score": 1.0, + "content": "can cover all even number receptive field sizes. With kernels of sizes 1 and 2 in the third layer, we", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 304, + 505, + 316 + ], + "spans": [ + { + "bbox": [ + 105, + 304, + 419, + 316 + ], + "score": 1.0, + "content": "could cover all integer receptive field sizes in a range via selecting the value", + "type": "text" + }, + { + "bbox": [ + 419, + 306, + 430, + 316 + ], + "score": 0.85, + "content": "p _ { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 430, + 304, + 505, + 316 + ], + "score": 1.0, + "content": ". The OS-block is", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 315, + 505, + 327 + ], + "spans": [ + { + "bbox": [ + 105, + 315, + 505, + 327 + ], + "score": 1.0, + "content": "easy to be applied on time series classification tasks. A simple classifier with the OS-block, namely", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 326, + 451, + 339 + ], + "spans": [ + { + "bbox": [ + 105, + 326, + 451, + 339 + ], + "score": 1.0, + "content": "OS-CNN, is given in the right image, which achieves a series of SOTA performances.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 6.5 + } + ], + "index": 3.75 + }, + { + "type": "text", + "bbox": [ + 106, + 357, + 505, + 456 + ], + "lines": [ + { + "bbox": [ + 105, + 356, + 506, + 371 + ], + "spans": [ + { + "bbox": [ + 105, + 356, + 136, + 371 + ], + "score": 1.0, + "content": "Where", + "type": "text" + }, + { + "bbox": [ + 136, + 357, + 217, + 370 + ], + "score": 0.92, + "content": "\\{ 1 , 2 , 3 , 5 , 7 , . . . , p _ { k } \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 217, + 356, + 362, + 371 + ], + "score": 1.0, + "content": "is a set of prime numbers from 1 to", + "type": "text" + }, + { + "bbox": [ + 363, + 359, + 374, + 369 + ], + "score": 0.85, + "content": "p _ { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 374, + 356, + 433, + 371 + ], + "score": 1.0, + "content": ". The value of", + "type": "text" + }, + { + "bbox": [ + 433, + 359, + 444, + 369 + ], + "score": 0.86, + "content": "p _ { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 444, + 356, + 506, + 371 + ], + "score": 1.0, + "content": "is the smallest", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 368, + 505, + 381 + ], + "spans": [ + { + "bbox": [ + 105, + 368, + 505, + 381 + ], + "score": 1.0, + "content": "prime number that can cover all sizes of RF in a range. Here, the range that we mentioned is all", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 379, + 506, + 392 + ], + "spans": [ + { + "bbox": [ + 105, + 379, + 327, + 392 + ], + "score": 1.0, + "content": "meaningful scales. For example, since the TS length is", + "type": "text" + }, + { + "bbox": [ + 327, + 380, + 331, + 389 + ], + "score": 0.53, + "content": "l", + "type": "inline_equation" + }, + { + "bbox": [ + 332, + 379, + 506, + 392 + ], + "score": 1.0, + "content": ", we don’t need to cover RFs that are larger", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 389, + 506, + 403 + ], + "spans": [ + { + "bbox": [ + 105, + 389, + 126, + 403 + ], + "score": 1.0, + "content": "than", + "type": "text" + }, + { + "bbox": [ + 127, + 391, + 131, + 401 + ], + "score": 0.55, + "content": "l", + "type": "inline_equation" + }, + { + "bbox": [ + 132, + 389, + 266, + 403 + ], + "score": 1.0, + "content": "or smaller than 1. Therefore, the", + "type": "text" + }, + { + "bbox": [ + 266, + 392, + 277, + 402 + ], + "score": 0.87, + "content": "p _ { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 278, + 389, + 506, + 403 + ], + "score": 1.0, + "content": "is the smallest prime number that can cover the RF size", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 401, + 506, + 414 + ], + "spans": [ + { + "bbox": [ + 105, + 401, + 148, + 414 + ], + "score": 1.0, + "content": "from 1 to", + "type": "text" + }, + { + "bbox": [ + 148, + 402, + 153, + 411 + ], + "score": 0.31, + "content": "l", + "type": "inline_equation" + }, + { + "bbox": [ + 153, + 401, + 506, + 414 + ], + "score": 1.0, + "content": ". If we have prior knowledge, such as that we know there are cycles in the TS, or we", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 106, + 412, + 505, + 424 + ], + "spans": [ + { + "bbox": [ + 106, + 412, + 505, + 424 + ], + "score": 1.0, + "content": "know the length range of the hidden representative pattern. We could change the RF size range of", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 106, + 424, + 505, + 435 + ], + "spans": [ + { + "bbox": [ + 106, + 424, + 505, + 435 + ], + "score": 1.0, + "content": "the OS-block by simply changing the prime number list. An example is given in the left image in", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 433, + 506, + 447 + ], + "spans": [ + { + "bbox": [ + 105, + 433, + 506, + 447 + ], + "score": 1.0, + "content": "Figure 3, which uses the prime number list in the blue block to cover the RF size range from 10 to", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 444, + 122, + 458 + ], + "spans": [ + { + "bbox": [ + 105, + 444, + 122, + 458 + ], + "score": 1.0, + "content": "26.", + "type": "text" + } + ], + "index": 19 + } + ], + "index": 15, + "bbox_fs": [ + 105, + 356, + 506, + 458 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 461, + 505, + 528 + ], + "lines": [ + { + "bbox": [ + 105, + 461, + 505, + 475 + ], + "spans": [ + { + "bbox": [ + 105, + 461, + 505, + 475 + ], + "score": 1.0, + "content": "RF sizes of the OS-block: The RF is defined as the size of the region in the input that produces", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 106, + 473, + 504, + 485 + ], + "spans": [ + { + "bbox": [ + 106, + 473, + 504, + 485 + ], + "score": 1.0, + "content": "the feature. Because each layer of the OS-block has more than one convolution kernel, there will", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 106, + 484, + 506, + 497 + ], + "spans": [ + { + "bbox": [ + 106, + 484, + 506, + 497 + ], + "score": 1.0, + "content": "be several different paths from the input signal to the final output feature (Araujo et al., 2019; Luo", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 104, + 493, + 505, + 509 + ], + "spans": [ + { + "bbox": [ + 104, + 493, + 505, + 509 + ], + "score": 1.0, + "content": "et al., 2016), and each path will have a RF size. For the 3-layer OS-block, which has no pooling", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 505, + 506, + 519 + ], + "spans": [ + { + "bbox": [ + 105, + 505, + 305, + 519 + ], + "score": 1.0, + "content": "layer and the stride size is 1, the set of RF sizes", + "type": "text" + }, + { + "bbox": [ + 305, + 506, + 313, + 516 + ], + "score": 0.79, + "content": "\\mathbb { S }", + "type": "inline_equation" + }, + { + "bbox": [ + 313, + 505, + 506, + 519 + ], + "score": 1.0, + "content": "is the set of RF size of all paths, and it can be", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 516, + 161, + 529 + ], + "spans": [ + { + "bbox": [ + 105, + 516, + 161, + 529 + ], + "score": 1.0, + "content": "described as:", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 22.5, + "bbox_fs": [ + 104, + 461, + 506, + 529 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 190, + 542, + 420, + 558 + ], + "lines": [ + { + "bbox": [ + 190, + 542, + 420, + 558 + ], + "spans": [ + { + "bbox": [ + 190, + 542, + 420, + 558 + ], + "score": 0.91, + "content": "\\mathbb { S } = \\{ p ^ { ( 1 ) } + p ^ { ( 2 ) } + p ^ { ( 3 ) } - 2 \\ | \\ p ^ { ( i ) } \\in \\mathbb { P } ^ { ( i ) } , i \\in \\{ 1 , 2 , 3 \\} \\} .", + "type": "interline_equation", + "image_path": "7fe0eca125404a28165f1c41eea2702cb392f9a726d3671ac7bec9c7facdfb94.jpg" + } + ] + } + ], + "index": 26, + "virtual_lines": [ + { + "bbox": [ + 190, + 542, + 420, + 558 + ], + "spans": [], + "index": 26 + } + ] + }, + { + "type": "text", + "bbox": [ + 105, + 565, + 504, + 589 + ], + "lines": [ + { + "bbox": [ + 104, + 564, + 506, + 579 + ], + "spans": [ + { + "bbox": [ + 104, + 564, + 187, + 579 + ], + "score": 1.0, + "content": "For the reasons that", + "type": "text" + }, + { + "bbox": [ + 187, + 565, + 204, + 577 + ], + "score": 0.91, + "content": "\\mathbb { P } ^ { ( i ) }", + "type": "inline_equation" + }, + { + "bbox": [ + 204, + 564, + 317, + 579 + ], + "score": 1.0, + "content": "are prime number list when", + "type": "text" + }, + { + "bbox": [ + 318, + 567, + 359, + 579 + ], + "score": 0.94, + "content": "i \\in \\{ 1 , 2 \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 359, + 564, + 391, + 579 + ], + "score": 1.0, + "content": ", the set", + "type": "text" + }, + { + "bbox": [ + 392, + 565, + 506, + 579 + ], + "score": 0.91, + "content": "\\{ p ^ { ( 1 ) } + p ^ { ( 2 ) } | p ^ { ( i ) } \\in \\mathbb { P } ^ { ( i ) } , i \\in", + "type": "inline_equation" + } + ], + "index": 27 + }, + { + "bbox": [ + 107, + 576, + 334, + 591 + ], + "spans": [ + { + "bbox": [ + 107, + 578, + 137, + 590 + ], + "score": 0.92, + "content": "\\{ 1 , 2 \\} \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 137, + 576, + 256, + 591 + ], + "score": 1.0, + "content": "is the set of all even numbers", + "type": "text" + }, + { + "bbox": [ + 257, + 578, + 264, + 588 + ], + "score": 0.52, + "content": "\\mathbb { E }", + "type": "inline_equation" + }, + { + "bbox": [ + 265, + 576, + 334, + 591 + ], + "score": 1.0, + "content": ".4 Thus, we have", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 27.5, + "bbox_fs": [ + 104, + 564, + 506, + 591 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 222, + 603, + 388, + 618 + ], + "lines": [ + { + "bbox": [ + 222, + 603, + 388, + 618 + ], + "spans": [ + { + "bbox": [ + 222, + 603, + 388, + 618 + ], + "score": 0.91, + "content": "\\mathbb { S } = \\{ e + p ^ { ( 3 ) } - 2 \\mid p ^ { ( 3 ) } \\in \\mathbb { P } ^ { ( 3 ) } , e \\in \\mathbb { E } \\} .", + "type": "interline_equation", + "image_path": "779814a2496b431c3b26fdddebd44a0d8bddc1be84c5f79963792e9577de12a7.jpg" + } + ] + } + ], + "index": 29, + "virtual_lines": [ + { + "bbox": [ + 222, + 603, + 388, + 618 + ], + "spans": [], + "index": 29 + } + ] + }, + { + "type": "text", + "bbox": [ + 108, + 626, + 274, + 637 + ], + "lines": [ + { + "bbox": [ + 106, + 624, + 275, + 640 + ], + "spans": [ + { + "bbox": [ + 106, + 624, + 275, + 640 + ], + "score": 1.0, + "content": "With Equation 3 and Equation 1, we have", + "type": "text" + } + ], + "index": 30 + } + ], + "index": 30, + "bbox_fs": [ + 106, + 624, + 275, + 640 + ] + }, + { + "type": "interline_equation", + "bbox": [ + 225, + 642, + 386, + 656 + ], + "lines": [ + { + "bbox": [ + 225, + 642, + 386, + 656 + ], + "spans": [ + { + "bbox": [ + 225, + 642, + 386, + 656 + ], + "score": 0.91, + "content": "\\mathbb { S } = \\{ e | e \\in \\mathbb { E } \\} \\cup \\{ e - 1 | e \\in \\mathbb { E } \\} \\equiv \\mathbb { N } ^ { + } .", + "type": "interline_equation", + "image_path": "62b398a9f23ad63303d85141df9a4486f888ea7d5d40626c9b0420e68adb65a8.jpg" + } + ] + } + ], + "index": 31, + "virtual_lines": [ + { + "bbox": [ + 225, + 642, + 386, + 656 + ], + "spans": [], + "index": 31 + } + ] + }, + { + "type": "text", + "bbox": [ + 108, + 660, + 503, + 683 + ], + "lines": [ + { + "bbox": [ + 106, + 659, + 506, + 673 + ], + "spans": [ + { + "bbox": [ + 106, + 659, + 135, + 673 + ], + "score": 1.0, + "content": "Where", + "type": "text" + }, + { + "bbox": [ + 135, + 660, + 151, + 671 + ], + "score": 0.88, + "content": "\\mathbb { N } ^ { + }", + "type": "inline_equation" + }, + { + "bbox": [ + 151, + 659, + 400, + 673 + ], + "score": 1.0, + "content": "is the set of all integer numbers in the range. Specifically, the", + "type": "text" + }, + { + "bbox": [ + 401, + 660, + 435, + 671 + ], + "score": 0.91, + "content": "\\mathbb { S } \\equiv \\mathbb { N } ^ { + }", + "type": "inline_equation" + }, + { + "bbox": [ + 436, + 659, + 506, + 673 + ], + "score": 1.0, + "content": "is because a real", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 671, + 505, + 684 + ], + "spans": [ + { + "bbox": [ + 106, + 671, + 336, + 684 + ], + "score": 1.0, + "content": "number must be an odd number or an even number, while", + "type": "text" + }, + { + "bbox": [ + 336, + 672, + 344, + 681 + ], + "score": 0.8, + "content": "\\mathbb { E }", + "type": "inline_equation" + }, + { + "bbox": [ + 344, + 671, + 438, + 684 + ], + "score": 1.0, + "content": "is the even number set,", + "type": "text" + }, + { + "bbox": [ + 438, + 671, + 495, + 684 + ], + "score": 0.93, + "content": "\\{ e - 1 | e \\in \\mathbb { E } \\}", + "type": "inline_equation" + }, + { + "bbox": [ + 495, + 671, + 505, + 684 + ], + "score": 1.0, + "content": "is", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 32.5, + "bbox_fs": [ + 106, + 659, + 506, + 684 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 115, + 83, + 498, + 203 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 115, + 83, + 498, + 203 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 115, + 83, + 498, + 203 + ], + "spans": [ + { + "bbox": [ + 115, + 83, + 498, + 203 + ], + "score": 0.828, + "type": "image", + "image_path": "5c37dd4e643525b376a8b285e8a193ac043160aba88198a014638ff0eeadc244.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 115, + 83, + 498, + 123.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 115, + 123.0, + 498, + 163.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 115, + 163.0, + 498, + 203.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 154, + 215, + 454, + 227 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 154, + 214, + 456, + 230 + ], + "spans": [ + { + "bbox": [ + 154, + 214, + 456, + 230 + ], + "score": 1.0, + "content": "Figure 4: Examples of using OS-block with other deep learning structures.", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 3 + } + ], + "index": 2.0 + }, + { + "type": "text", + "bbox": [ + 107, + 249, + 504, + 281 + ], + "lines": [ + { + "bbox": [ + 105, + 248, + 506, + 262 + ], + "spans": [ + { + "bbox": [ + 105, + 248, + 346, + 262 + ], + "score": 1.0, + "content": "the odd number set. Therefore, with the proper selection of", + "type": "text" + }, + { + "bbox": [ + 346, + 251, + 357, + 261 + ], + "score": 0.86, + "content": "p _ { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 358, + 248, + 506, + 262 + ], + "score": 1.0, + "content": ", we could cover any integer RF size", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 260, + 505, + 272 + ], + "spans": [ + { + "bbox": [ + 105, + 260, + 505, + 272 + ], + "score": 1.0, + "content": "in a range. It should be noticed that, there might be many options to cover all RF sizes, we use the", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 271, + 344, + 282 + ], + "spans": [ + { + "bbox": [ + 106, + 271, + 344, + 282 + ], + "score": 1.0, + "content": "Godlach’s conjecture to make sure that we could all scales.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 5 + }, + { + "type": "title", + "bbox": [ + 107, + 297, + 377, + 308 + ], + "lines": [ + { + "bbox": [ + 105, + 295, + 379, + 310 + ], + "spans": [ + { + "bbox": [ + 105, + 295, + 379, + 310 + ], + "score": 1.0, + "content": "3.3 OS-BLOCK COVER ALL SCALES IN AN EFFICIENT MANNER", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 7 + }, + { + "type": "text", + "bbox": [ + 107, + 318, + 505, + 372 + ], + "lines": [ + { + "bbox": [ + 106, + 318, + 505, + 330 + ], + "spans": [ + { + "bbox": [ + 106, + 318, + 505, + 330 + ], + "score": 1.0, + "content": "From the model size perspective, using prime numbers is more efficient than using even numbers", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 329, + 505, + 341 + ], + "spans": [ + { + "bbox": [ + 106, + 329, + 505, + 341 + ], + "score": 1.0, + "content": "or odd numbers. To be specific, to cover receptive fields up to size r, the model size complexity of", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 338, + 505, + 353 + ], + "spans": [ + { + "bbox": [ + 105, + 338, + 217, + 353 + ], + "score": 1.0, + "content": "using prime size kernels is", + "type": "text" + }, + { + "bbox": [ + 217, + 339, + 273, + 352 + ], + "score": 0.92, + "content": "O ( r ^ { 2 } / l o g ( r ) )", + "type": "inline_equation" + }, + { + "bbox": [ + 273, + 338, + 505, + 353 + ], + "score": 1.0, + "content": ". On the other hand, no matter we use even number pairs", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 349, + 505, + 365 + ], + "spans": [ + { + "bbox": [ + 105, + 349, + 310, + 365 + ], + "score": 1.0, + "content": "or odd number pairs, the model size complexity is", + "type": "text" + }, + { + "bbox": [ + 311, + 350, + 336, + 362 + ], + "score": 0.92, + "content": "O ( r ^ { 2 } )", + "type": "inline_equation" + }, + { + "bbox": [ + 336, + 349, + 505, + 365 + ], + "score": 1.0, + "content": ". We also empirically show the advantage", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 361, + 493, + 374 + ], + "spans": [ + { + "bbox": [ + 105, + 361, + 493, + 374 + ], + "score": 1.0, + "content": "of our model on efficiency in the following table and this table has been added to Appendix A.7:", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 10 + }, + { + "type": "title", + "bbox": [ + 107, + 387, + 313, + 399 + ], + "lines": [ + { + "bbox": [ + 105, + 386, + 314, + 401 + ], + "spans": [ + { + "bbox": [ + 105, + 386, + 314, + 401 + ], + "score": 1.0, + "content": "3.4 HOW TO APPLY OS-BLOCK ON TSC TASKS", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 13 + }, + { + "type": "text", + "bbox": [ + 107, + 408, + 505, + 529 + ], + "lines": [ + { + "bbox": [ + 105, + 409, + 505, + 421 + ], + "spans": [ + { + "bbox": [ + 105, + 409, + 505, + 421 + ], + "score": 1.0, + "content": "Firstly, the OS-block could take both univariate and multivariate TS data by adjusting the input", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 420, + 505, + 432 + ], + "spans": [ + { + "bbox": [ + 105, + 420, + 505, + 432 + ], + "score": 1.0, + "content": "channel the same as the variate number of input TS data. A simple example classifier with OS-", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 430, + 505, + 443 + ], + "spans": [ + { + "bbox": [ + 105, + 430, + 505, + 443 + ], + "score": 1.0, + "content": "block, namely OS-CNN, is given in Figure 3. The OS-CNN is composed of an OS-block with one", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 441, + 506, + 455 + ], + "spans": [ + { + "bbox": [ + 105, + 441, + 506, + 455 + ], + "score": 1.0, + "content": "global average pooling layer as the dimensional reduction module and one fully connected layer", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 453, + 505, + 465 + ], + "spans": [ + { + "bbox": [ + 105, + 453, + 505, + 465 + ], + "score": 1.0, + "content": "as the classification module. Other than OS-CNN, the OS-block is flexible and easy to extend.", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 465, + 505, + 476 + ], + "spans": [ + { + "bbox": [ + 106, + 465, + 505, + 476 + ], + "score": 1.0, + "content": "Specifically, convolution layers of OS-block can be calculated parallelly. Thus, each layer can be", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 474, + 505, + 487 + ], + "spans": [ + { + "bbox": [ + 105, + 474, + 505, + 487 + ], + "score": 1.0, + "content": "viewed as one convolutional layer with zero masks. Therefore, both the multi-kernel layers or the", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 485, + 505, + 498 + ], + "spans": [ + { + "bbox": [ + 105, + 485, + 505, + 498 + ], + "score": 1.0, + "content": "OS-block itself are easy to extend with more complicated structures (such as dilation (Oord et al.,", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 496, + 505, + 509 + ], + "spans": [ + { + "bbox": [ + 105, + 496, + 505, + 509 + ], + "score": 1.0, + "content": "2016), attention or transformer (Shen et al., 2018a), and bottleneck) that are normally used in 1D-", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 506, + 506, + 521 + ], + "spans": [ + { + "bbox": [ + 105, + 506, + 506, + 521 + ], + "score": 1.0, + "content": "CNN for performance gain. In Figure 4, we give three examples which uses OS-block with other", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 520, + 150, + 530 + ], + "spans": [ + { + "bbox": [ + 105, + 520, + 150, + 530 + ], + "score": 1.0, + "content": "structures.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 19 + }, + { + "type": "title", + "bbox": [ + 108, + 547, + 194, + 560 + ], + "lines": [ + { + "bbox": [ + 105, + 546, + 196, + 561 + ], + "spans": [ + { + "bbox": [ + 105, + 546, + 196, + 561 + ], + "score": 1.0, + "content": "4 EXPERIMENT", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 25 + }, + { + "type": "title", + "bbox": [ + 107, + 573, + 193, + 584 + ], + "lines": [ + { + "bbox": [ + 105, + 572, + 194, + 585 + ], + "spans": [ + { + "bbox": [ + 105, + 572, + 194, + 585 + ], + "score": 1.0, + "content": "4.1 BENCHMARKS", + "type": "text" + } + ], + "index": 26 + } + ], + "index": 26 + }, + { + "type": "text", + "bbox": [ + 108, + 594, + 504, + 616 + ], + "lines": [ + { + "bbox": [ + 107, + 594, + 505, + 605 + ], + "spans": [ + { + "bbox": [ + 107, + 594, + 505, + 605 + ], + "score": 1.0, + "content": "We evaluate OS-block on 4 TSC benchmarks which include, in total, 159 datasets. The details of", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 605, + 229, + 618 + ], + "spans": [ + { + "bbox": [ + 106, + 605, + 229, + 618 + ], + "score": 1.0, + "content": "each benchmark is as follows:", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 27.5 + }, + { + "type": "text", + "bbox": [ + 132, + 628, + 505, + 731 + ], + "lines": [ + { + "bbox": [ + 136, + 628, + 505, + 641 + ], + "spans": [ + { + "bbox": [ + 136, + 628, + 505, + 641 + ], + "score": 1.0, + "content": "• Magnetoencephalography recording for Temporal Lobe Epilepsy diagnosis (MEG-", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 141, + 638, + 506, + 651 + ], + "spans": [ + { + "bbox": [ + 141, + 638, + 506, + 651 + ], + "score": 1.0, + "content": "TLE) dataset (Gu et al., 2020): The Magnetoencephalography dataset was recorded from", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 141, + 649, + 506, + 663 + ], + "spans": [ + { + "bbox": [ + 141, + 649, + 506, + 663 + ], + "score": 1.0, + "content": "epilepsy patients and was introduced to classify two subtypes (simple and complex) of", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 141, + 660, + 506, + 673 + ], + "spans": [ + { + "bbox": [ + 141, + 660, + 506, + 673 + ], + "score": 1.0, + "content": "temporal Lobe Epilepsy. The dataset contains 2877 recordings which were obtained at the", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 141, + 671, + 505, + 685 + ], + "spans": [ + { + "bbox": [ + 141, + 671, + 224, + 685 + ], + "score": 1.0, + "content": "sampling frequency", + "type": "text" + }, + { + "bbox": [ + 224, + 672, + 259, + 682 + ], + "score": 0.59, + "content": "1 2 0 0 \\mathrm { H z }", + "type": "inline_equation" + }, + { + "bbox": [ + 259, + 671, + 505, + 685 + ], + "score": 1.0, + "content": ". Each recording is approximately 2 sec. Therefore the length", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 141, + 683, + 200, + 694 + ], + "spans": [ + { + "bbox": [ + 141, + 683, + 200, + 694 + ], + "score": 1.0, + "content": "is about 2400.", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 137, + 698, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 137, + 698, + 506, + 712 + ], + "score": 1.0, + "content": "University of East Anglia (UEA) 30 archive (Bagnall et al., 2018): This formulation of", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 142, + 710, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 142, + 710, + 505, + 722 + ], + "score": 1.0, + "content": "the archive was a collaborative effort between researchers at the University of East Anglia", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 141, + 720, + 506, + 733 + ], + "spans": [ + { + "bbox": [ + 141, + 720, + 506, + 733 + ], + "score": 1.0, + "content": "and the University of California, Riverside. It is an archive of 30 multivariate TS datasets", + "type": "text" + } + ], + "index": 37 + } + ], + "index": 33 + } + ], + "page_idx": 4, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 25, + 294, + 39 + ], + "spans": [ + { + "bbox": [ + 106, + 25, + 294, + 39 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2022", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 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": [ + 115, + 83, + 498, + 203 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 115, + 83, + 498, + 203 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 115, + 83, + 498, + 203 + ], + "spans": [ + { + "bbox": [ + 115, + 83, + 498, + 203 + ], + "score": 0.828, + "type": "image", + "image_path": "5c37dd4e643525b376a8b285e8a193ac043160aba88198a014638ff0eeadc244.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 115, + 83, + 498, + 123.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 115, + 123.0, + 498, + 163.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 115, + 163.0, + 498, + 203.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 154, + 215, + 454, + 227 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 154, + 214, + 456, + 230 + ], + "spans": [ + { + "bbox": [ + 154, + 214, + 456, + 230 + ], + "score": 1.0, + "content": "Figure 4: Examples of using OS-block with other deep learning structures.", + "type": "text" + } + ], + "index": 3 + } + ], + "index": 3 + } + ], + "index": 2.0 + }, + { + "type": "text", + "bbox": [ + 107, + 249, + 504, + 281 + ], + "lines": [ + { + "bbox": [ + 105, + 248, + 506, + 262 + ], + "spans": [ + { + "bbox": [ + 105, + 248, + 346, + 262 + ], + "score": 1.0, + "content": "the odd number set. Therefore, with the proper selection of", + "type": "text" + }, + { + "bbox": [ + 346, + 251, + 357, + 261 + ], + "score": 0.86, + "content": "p _ { k }", + "type": "inline_equation" + }, + { + "bbox": [ + 358, + 248, + 506, + 262 + ], + "score": 1.0, + "content": ", we could cover any integer RF size", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 260, + 505, + 272 + ], + "spans": [ + { + "bbox": [ + 105, + 260, + 505, + 272 + ], + "score": 1.0, + "content": "in a range. It should be noticed that, there might be many options to cover all RF sizes, we use the", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 106, + 271, + 344, + 282 + ], + "spans": [ + { + "bbox": [ + 106, + 271, + 344, + 282 + ], + "score": 1.0, + "content": "Godlach’s conjecture to make sure that we could all scales.", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 5, + "bbox_fs": [ + 105, + 248, + 506, + 282 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 297, + 377, + 308 + ], + "lines": [ + { + "bbox": [ + 105, + 295, + 379, + 310 + ], + "spans": [ + { + "bbox": [ + 105, + 295, + 379, + 310 + ], + "score": 1.0, + "content": "3.3 OS-BLOCK COVER ALL SCALES IN AN EFFICIENT MANNER", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 7 + }, + { + "type": "text", + "bbox": [ + 107, + 318, + 505, + 372 + ], + "lines": [ + { + "bbox": [ + 106, + 318, + 505, + 330 + ], + "spans": [ + { + "bbox": [ + 106, + 318, + 505, + 330 + ], + "score": 1.0, + "content": "From the model size perspective, using prime numbers is more efficient than using even numbers", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 329, + 505, + 341 + ], + "spans": [ + { + "bbox": [ + 106, + 329, + 505, + 341 + ], + "score": 1.0, + "content": "or odd numbers. To be specific, to cover receptive fields up to size r, the model size complexity of", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 338, + 505, + 353 + ], + "spans": [ + { + "bbox": [ + 105, + 338, + 217, + 353 + ], + "score": 1.0, + "content": "using prime size kernels is", + "type": "text" + }, + { + "bbox": [ + 217, + 339, + 273, + 352 + ], + "score": 0.92, + "content": "O ( r ^ { 2 } / l o g ( r ) )", + "type": "inline_equation" + }, + { + "bbox": [ + 273, + 338, + 505, + 353 + ], + "score": 1.0, + "content": ". On the other hand, no matter we use even number pairs", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 349, + 505, + 365 + ], + "spans": [ + { + "bbox": [ + 105, + 349, + 310, + 365 + ], + "score": 1.0, + "content": "or odd number pairs, the model size complexity is", + "type": "text" + }, + { + "bbox": [ + 311, + 350, + 336, + 362 + ], + "score": 0.92, + "content": "O ( r ^ { 2 } )", + "type": "inline_equation" + }, + { + "bbox": [ + 336, + 349, + 505, + 365 + ], + "score": 1.0, + "content": ". We also empirically show the advantage", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 361, + 493, + 374 + ], + "spans": [ + { + "bbox": [ + 105, + 361, + 493, + 374 + ], + "score": 1.0, + "content": "of our model on efficiency in the following table and this table has been added to Appendix A.7:", + "type": "text" + } + ], + "index": 12 + } + ], + "index": 10, + "bbox_fs": [ + 105, + 318, + 505, + 374 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 387, + 313, + 399 + ], + "lines": [ + { + "bbox": [ + 105, + 386, + 314, + 401 + ], + "spans": [ + { + "bbox": [ + 105, + 386, + 314, + 401 + ], + "score": 1.0, + "content": "3.4 HOW TO APPLY OS-BLOCK ON TSC TASKS", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 13 + }, + { + "type": "text", + "bbox": [ + 107, + 408, + 505, + 529 + ], + "lines": [ + { + "bbox": [ + 105, + 409, + 505, + 421 + ], + "spans": [ + { + "bbox": [ + 105, + 409, + 505, + 421 + ], + "score": 1.0, + "content": "Firstly, the OS-block could take both univariate and multivariate TS data by adjusting the input", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 420, + 505, + 432 + ], + "spans": [ + { + "bbox": [ + 105, + 420, + 505, + 432 + ], + "score": 1.0, + "content": "channel the same as the variate number of input TS data. A simple example classifier with OS-", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 430, + 505, + 443 + ], + "spans": [ + { + "bbox": [ + 105, + 430, + 505, + 443 + ], + "score": 1.0, + "content": "block, namely OS-CNN, is given in Figure 3. The OS-CNN is composed of an OS-block with one", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 441, + 506, + 455 + ], + "spans": [ + { + "bbox": [ + 105, + 441, + 506, + 455 + ], + "score": 1.0, + "content": "global average pooling layer as the dimensional reduction module and one fully connected layer", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 453, + 505, + 465 + ], + "spans": [ + { + "bbox": [ + 105, + 453, + 505, + 465 + ], + "score": 1.0, + "content": "as the classification module. Other than OS-CNN, the OS-block is flexible and easy to extend.", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 465, + 505, + 476 + ], + "spans": [ + { + "bbox": [ + 106, + 465, + 505, + 476 + ], + "score": 1.0, + "content": "Specifically, convolution layers of OS-block can be calculated parallelly. Thus, each layer can be", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 474, + 505, + 487 + ], + "spans": [ + { + "bbox": [ + 105, + 474, + 505, + 487 + ], + "score": 1.0, + "content": "viewed as one convolutional layer with zero masks. Therefore, both the multi-kernel layers or the", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 485, + 505, + 498 + ], + "spans": [ + { + "bbox": [ + 105, + 485, + 505, + 498 + ], + "score": 1.0, + "content": "OS-block itself are easy to extend with more complicated structures (such as dilation (Oord et al.,", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 496, + 505, + 509 + ], + "spans": [ + { + "bbox": [ + 105, + 496, + 505, + 509 + ], + "score": 1.0, + "content": "2016), attention or transformer (Shen et al., 2018a), and bottleneck) that are normally used in 1D-", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 506, + 506, + 521 + ], + "spans": [ + { + "bbox": [ + 105, + 506, + 506, + 521 + ], + "score": 1.0, + "content": "CNN for performance gain. 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The dataset contains 2877 recordings which were obtained at the", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 141, + 671, + 505, + 685 + ], + "spans": [ + { + "bbox": [ + 141, + 671, + 224, + 685 + ], + "score": 1.0, + "content": "sampling frequency", + "type": "text" + }, + { + "bbox": [ + 224, + 672, + 259, + 682 + ], + "score": 0.59, + "content": "1 2 0 0 \\mathrm { H z }", + "type": "inline_equation" + }, + { + "bbox": [ + 259, + 671, + 505, + 685 + ], + "score": 1.0, + "content": ". Each recording is approximately 2 sec. Therefore the length", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 141, + 683, + 200, + 694 + ], + "spans": [ + { + "bbox": [ + 141, + 683, + 200, + 694 + ], + "score": 1.0, + "content": "is about 2400.", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 137, + 698, + 506, + 712 + ], + "spans": [ + { + "bbox": [ + 137, + 698, + 506, + 712 + ], + "score": 1.0, + "content": "University of East Anglia (UEA) 30 archive (Bagnall et al., 2018): This formulation of", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 142, + 710, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 142, + 710, + 505, + 722 + ], + "score": 1.0, + "content": "the archive was a collaborative effort between researchers at the University of East Anglia", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 141, + 720, + 506, + 733 + ], + "spans": [ + { + "bbox": [ + 141, + 720, + 506, + 733 + ], + "score": 1.0, + "content": "and the University of California, Riverside. It is an archive of 30 multivariate TS datasets", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 141, + 421, + 505, + 434 + ], + "spans": [ + { + "bbox": [ + 141, + 421, + 505, + 434 + ], + "score": 1.0, + "content": "from various domains such as motion detection, physiological data, audio spectra classi-", + "type": "text", + "cross_page": true + } + ], + "index": 12 + }, + { + "bbox": [ + 141, + 430, + 505, + 445 + ], + "spans": [ + { + "bbox": [ + 141, + 430, + 505, + 445 + ], + "score": 1.0, + "content": "fication. Besides domains, those datasets also have various characteristics. For instance,", + "type": "text", + "cross_page": true + } + ], + "index": 13 + }, + { + "bbox": [ + 141, + 443, + 505, + 455 + ], + "spans": [ + { + "bbox": [ + 141, + 443, + 505, + 455 + ], + "score": 1.0, + "content": "among those datasets, the class number various from 2 to 39, the length of each dataset", + "type": "text", + "cross_page": true + } + ], + "index": 14 + }, + { + "bbox": [ + 143, + 454, + 445, + 465 + ], + "spans": [ + { + "bbox": [ + 143, + 454, + 445, + 465 + ], + "score": 1.0, + "content": "various from 8 to 17,894, and the number of variates various from 2 to 963.", + "type": "text", + "cross_page": true + } + ], + "index": 15 + } + ], + "index": 33, + "bbox_fs": [ + 136, + 628, + 506, + 733 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "table", + "bbox": [ + 108, + 81, + 504, + 155 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 108, + 81, + 504, + 155 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 108, + 81, + 504, + 155 + ], + "spans": [ + { + "bbox": [ + 108, + 81, + 504, + 155 + ], + "score": 0.285, + "html": "
Individual dataset benchmark
DatasetMethodAccuracy(%)F1-score# parameters
MEG-TLE (Gu et al.,2020)CNN(Gu et al.,2020)83.282.33.8M
PF(Gu et al.,2020)82.668.21
SVM (Gu et al.,2020)55.285.2-
MSAM (Gu et al.,2020)83.683.42.3M
Rocket (Dempster et al., 2020)87.789.9
OS-CNN (Ours)91.391.6235k
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ArchiveMethodBaseline winsOS-CNN(Ours) winsTieAverage Rank
UEA 30 archive (Bagnall et al., 2018)DTW-1NND(norm) (Zhang et al.,2020)72305.68
DTW-1NN-I(norm) (Zhang et al.,2020)516.70
ED-1NN(norm) (Zhang et al.,2020)507.45
DTW-1NND (Zhang et al.,2020)705.28
DTW-1NN-I (Zhang et al.,2020) ED-1NN (Zhang et al., 2020)7 5242523225116.07
WEASEL+MUSE(Schäfer& Leser,2017)1007.12
MLSTM-FCN(Karim et al.,2019)72314.15
92005.62
TapNet (Zhang et al.,2020) OS-CNN (Ours)-=1 =3.80 3.13
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ArchiveMethodBaselinewinsOS-CNN(Ours) winsTieAverage rank
UCR 85 archive (Chen et al.,2015)PF (Lucas et al.,2019)136756.57
ResNet (Wang et al.,2017)196155.41
STC (Hameurlain et al., 2017)275625.05
InceptionTime (Ismail Fawaz et al.,2019)344294.05
ROCKET (Dempster et al.,2020)334483.64
HIVE-COTE(Lines et al., 2016) TS-CHIEF(Shifaz et al.,2020)34 42438 43.99
OS-CNN (Ours)139 -3.68 3.59
UCR128 archive (Dau et al., 2018)ResNet (Wang et al.,2017)1983- 26
InceptionTime (Ismail Fawaz et al.,2019)3059393.21
ROCKET (Dempster et al.,2020)4362232.41
OS-CNN (Ours)---2.36 2.02
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It is the updated version of the UCR 85 archive.", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 141, + 560, + 505, + 573 + ], + "spans": [ + { + "bbox": [ + 141, + 560, + 505, + 573 + ], + "score": 1.0, + "content": "However, the new archive cannot be viewed as a replacement for the former because they", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 141, + 570, + 505, + 584 + ], + "spans": [ + { + "bbox": [ + 141, + 570, + 505, + 584 + ], + "score": 1.0, + "content": "have different characteristics. 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Specifically, for the", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 105, + 665, + 505, + 677 + ], + "spans": [ + { + "bbox": [ + 105, + 665, + 505, + 677 + ], + "score": 1.0, + "content": "MEG-TLE dataset, following Multi-Head Self-Attention Model (MSAM) (Gu et al., 2020), models", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 677, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 105, + 677, + 505, + 689 + ], + "score": 1.0, + "content": "are evaluated by test accuracy and f1 score. Besides using recommended metrics of each benchmark,", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 106, + 688, + 505, + 699 + ], + "spans": [ + { + "bbox": [ + 106, + 688, + 505, + 699 + ], + "score": 1.0, + "content": "we also compare the model size of OS-block with other deep learning methods. For UEA 30, UCR", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 104, + 698, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 104, + 698, + 505, + 712 + ], + "score": 1.0, + "content": "85 archives, and UCR 128 archives, following the evaluation advice from the archive (Dau et al.,", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "2018; Bagnall et al., 2018), count of wins, and critical difference diagrams (cd-diagram) (Dau et al.,", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 720, + 505, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 505, + 734 + ], + "score": 1.0, + "content": "2018) were selected as the evaluation method. 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Individual dataset benchmark
DatasetMethodAccuracy(%)F1-score# parameters
MEG-TLE (Gu et al.,2020)CNN(Gu et al.,2020)83.282.33.8M
PF(Gu et al.,2020)82.668.21
SVM (Gu et al.,2020)55.285.2-
MSAM (Gu et al.,2020)83.683.42.3M
Rocket (Dempster et al., 2020)87.789.9
OS-CNN (Ours)91.391.6235k
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ArchiveMethodBaseline winsOS-CNN(Ours) winsTieAverage Rank
UEA 30 archive (Bagnall et al., 2018)DTW-1NND(norm) (Zhang et al.,2020)72305.68
DTW-1NN-I(norm) (Zhang et al.,2020)516.70
ED-1NN(norm) (Zhang et al.,2020)507.45
DTW-1NND (Zhang et al.,2020)705.28
DTW-1NN-I (Zhang et al.,2020) ED-1NN (Zhang et al., 2020)7 5242523225116.07
WEASEL+MUSE(Schäfer& Leser,2017)1007.12
MLSTM-FCN(Karim et al.,2019)72314.15
92005.62
TapNet (Zhang et al.,2020) OS-CNN (Ours)-=1 =3.80 3.13
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ArchiveMethodBaselinewinsOS-CNN(Ours) winsTieAverage rank
UCR 85 archive (Chen et al.,2015)PF (Lucas et al.,2019)136756.57
ResNet (Wang et al.,2017)196155.41
STC (Hameurlain et al., 2017)275625.05
InceptionTime (Ismail Fawaz et al.,2019)344294.05
ROCKET (Dempster et al.,2020)334483.64
HIVE-COTE(Lines et al., 2016) TS-CHIEF(Shifaz et al.,2020)34 42438 43.99
OS-CNN (Ours)139 -3.68 3.59
UCR128 archive (Dau et al., 2018)ResNet (Wang et al.,2017)1983- 26
InceptionTime (Ismail Fawaz et al.,2019)3059393.21
ROCKET (Dempster et al.,2020)4362232.41
OS-CNN (Ours)---2.36 2.02
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For UEA 30, UCR", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 104, + 698, + 505, + 712 + ], + "spans": [ + { + "bbox": [ + 104, + 698, + 505, + 712 + ], + "score": 1.0, + "content": "85 archives, and UCR 128 archives, following the evaluation advice from the archive (Dau et al.,", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "2018; Bagnall et al., 2018), count of wins, and critical difference diagrams (cd-diagram) (Dau et al.,", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 720, + 505, + 734 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 505, + 734 + ], + "score": 1.0, + "content": "2018) were selected as the evaluation method. Due to the page limitation, we list the average rank", + "type": "text" + } + ], + "index": 36 + } + ], + "index": 33, + "bbox_fs": [ + 104, + 655, + 505, + 734 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 108, + 79, + 502, + 215 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 108, + 79, + 502, + 215 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 108, + 79, + 502, + 215 + ], + "spans": [ + { + "bbox": [ + 108, + 79, + 502, + 215 + ], + "score": 0.961, + "type": "image", + "image_path": "1690ddc86abcdb74ef91fcafda3f877cb182a9803b493d66dcbc21aebb97508a.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 108, + 79, + 502, + 124.33333333333334 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 108, + 124.33333333333334, + 502, + 169.66666666666669 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 108, + 169.66666666666669, + 502, + 215.00000000000003 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 226, + 505, + 260 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 106, + 226, + 505, + 239 + ], + "spans": [ + { + "bbox": [ + 106, + 226, + 505, + 239 + ], + "score": 1.0, + "content": "Figure 5: Classification accuracies for OS-CNN vs. accuracies from 20 1D-CNNs with receptiveCount of datasets by the RF tuning's percentile range that OS result belongs to", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 236, + 505, + 250 + ], + "spans": [ + { + "bbox": [ + 105, + 236, + 505, + 250 + ], + "score": 1.0, + "content": "50 field size. As we can see, for most of the dataset, the orange points (accuracy of OS-CNN) are near", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 106, + 249, + 458, + 261 + ], + "spans": [ + { + "bbox": [ + 106, + 249, + 458, + 261 + ], + "score": 1.0, + "content": "40 the top of blue points. More analysis for this comparison can be found in Appendix A.1", + "type": "text" + } + ], + "index": 5 + } + ], + "index": 4 + } + ], + "index": 2.5 + }, + { + "type": "text", + "bbox": [ + 105, + 282, + 504, + 304 + ], + "lines": [ + { + "bbox": [ + 105, + 280, + 506, + 296 + ], + "spans": [ + { + "bbox": [ + 105, + 280, + 506, + 296 + ], + "score": 1.0, + "content": "0 3 (3.53%) 2 (2.35%) 5 (5.88%) 2 (2.35%) 3 (3.53%) 3 (3.53%) 1 (1.18%) 5 (5.88%) 4 (4.71%) in the result table because it is the main criteria of the cd-diagram. The full cd-diagram results are", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 106, + 293, + 203, + 306 + ], + "spans": [ + { + "bbox": [ + 106, + 293, + 203, + 306 + ], + "score": 1.0, + "content": "< 0.5 0.55 listed in Appendix A.3.", + "type": "text" + } + ], + "index": 7 + } + ], + "index": 6.5 + }, + { + "type": "title", + "bbox": [ + 108, + 320, + 217, + 331 + ], + "lines": [ + { + "bbox": [ + 106, + 320, + 218, + 332 + ], + "spans": [ + { + "bbox": [ + 106, + 320, + 218, + 332 + ], + "score": 1.0, + "content": "4.3 EXPERIMENT SETUP", + "type": "text" + } + ], + "index": 8 + } + ], + "index": 8 + }, + { + "type": "text", + "bbox": [ + 107, + 341, + 505, + 374 + ], + "lines": [ + { + "bbox": [ + 105, + 341, + 505, + 353 + ], + "spans": [ + { + "bbox": [ + 105, + 341, + 505, + 353 + ], + "score": 1.0, + "content": "For the MEG-TLE dataset, they were normalized by z-normalization (Chen et al., 2015). 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As we can see,", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 495, + 505, + 507 + ], + "spans": [ + { + "bbox": [ + 106, + 495, + 505, + 507 + ], + "score": 1.0, + "content": "for the MIT-TLE dataset, OS-CNN outperforms baselines in a ten times smaller model size. For", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 506, + 505, + 518 + ], + "spans": [ + { + "bbox": [ + 105, + 506, + 505, + 518 + ], + "score": 1.0, + "content": "all dataset archives, the OS-block achieves the best average rank, which means that, in general, the", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 516, + 306, + 529 + ], + "spans": [ + { + "bbox": [ + 105, + 516, + 306, + 529 + ], + "score": 1.0, + "content": "OS-block design can achieve better performance.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 20.5 + }, + { + "type": "title", + "bbox": [ + 107, + 544, + 339, + 555 + ], + "lines": [ + { + "bbox": [ + 106, + 543, + 341, + 556 + ], + "spans": [ + { + "bbox": [ + 106, + 543, + 341, + 556 + ], + "score": 1.0, + "content": "4.5 OS-BLOCK CAN CAPTURE THE BEST TIME SCALE", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 23 + }, + { + "type": "text", + "bbox": [ + 107, + 582, + 505, + 626 + ], + "lines": [ + { + "bbox": [ + 105, + 582, + 505, + 595 + ], + "spans": [ + { + "bbox": [ + 105, + 582, + 416, + 595 + ], + "score": 1.0, + "content": "To demonstrate that the OS-block can capture the best time scale, we build", + "type": "text" + }, + { + "bbox": [ + 417, + 582, + 452, + 593 + ], + "score": 0.28, + "content": "2 0 ~ \\mathrm { F C N }", + "type": "inline_equation" + }, + { + "bbox": [ + 452, + 582, + 505, + 595 + ], + "score": 1.0, + "content": "models with", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 592, + 505, + 606 + ], + "spans": [ + { + "bbox": [ + 105, + 592, + 505, + 606 + ], + "score": 1.0, + "content": "different RF sizes (from 10 to 200 with step 10), and compare their performance with OS-CNN on", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 604, + 506, + 617 + ], + "spans": [ + { + "bbox": [ + 105, + 604, + 506, + 617 + ], + "score": 1.0, + "content": "the UCR 85 archive. 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For the", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 353, + 505, + 365 + ], + "spans": [ + { + "bbox": [ + 105, + 353, + 505, + 365 + ], + "score": 1.0, + "content": "other archives, we take the raw dataset without processing for datasets in those archives already", + "type": "text" + } + ], + "index": 10 + }, + { + "bbox": [ + 105, + 364, + 242, + 376 + ], + "spans": [ + { + "bbox": [ + 105, + 364, + 242, + 376 + ], + "score": 1.0, + "content": "normalized with z-normalization.", + "type": "text" + } + ], + "index": 11 + } + ], + "index": 10, + "bbox_fs": [ + 105, + 341, + 505, + 376 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 380, + 505, + 446 + ], + "lines": [ + { + "bbox": [ + 105, + 380, + 505, + 393 + ], + "spans": [ + { + "bbox": [ + 105, + 380, + 505, + 393 + ], + "score": 1.0, + "content": "Following the setup of (Wang et al., 2017), we use the learning rate of 0.001, batch size of 16, and", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 392, + 505, + 404 + ], + "spans": [ + { + "bbox": [ + 105, + 392, + 505, + 404 + ], + "score": 1.0, + "content": "Adam (Kingma & Ba, 2014) optimizer. 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We use PyTorch 6 to implement our method and run our experiments on Nvidia Titan", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 435, + 124, + 447 + ], + "spans": [ + { + "bbox": [ + 105, + 435, + 124, + 447 + ], + "score": 1.0, + "content": "XP.", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 14.5, + "bbox_fs": [ + 105, + 380, + 506, + 447 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 463, + 360, + 474 + ], + "lines": [ + { + "bbox": [ + 106, + 462, + 361, + 475 + ], + "spans": [ + { + "bbox": [ + 106, + 462, + 361, + 475 + ], + "score": 1.0, + "content": "4.4 STATE-OF-THE-ART PERFORMANCE ON BENCHMARKS", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 18 + }, + { + "type": "text", + "bbox": [ + 107, + 484, + 505, + 528 + ], + "lines": [ + { + "bbox": [ + 105, + 483, + 506, + 497 + ], + "spans": [ + { + "bbox": [ + 105, + 483, + 506, + 497 + ], + "score": 1.0, + "content": "We show consistent state-of-the-art performance on four benchmarks as in Table 1. As we can see,", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 106, + 495, + 505, + 507 + ], + "spans": [ + { + "bbox": [ + 106, + 495, + 505, + 507 + ], + "score": 1.0, + "content": "for the MIT-TLE dataset, OS-CNN outperforms baselines in a ten times smaller model size. For", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 506, + 505, + 518 + ], + "spans": [ + { + "bbox": [ + 105, + 506, + 505, + 518 + ], + "score": 1.0, + "content": "all dataset archives, the OS-block achieves the best average rank, which means that, in general, the", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 516, + 306, + 529 + ], + "spans": [ + { + "bbox": [ + 105, + 516, + 306, + 529 + ], + "score": 1.0, + "content": "OS-block design can achieve better performance.", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 20.5, + "bbox_fs": [ + 105, + 483, + 506, + 529 + ] + }, + { + "type": "title", + "bbox": [ + 107, + 544, + 339, + 555 + ], + "lines": [ + { + "bbox": [ + 106, + 543, + 341, + 556 + ], + "spans": [ + { + "bbox": [ + 106, + 543, + 341, + 556 + ], + "score": 1.0, + "content": "4.5 OS-BLOCK CAN CAPTURE THE BEST TIME SCALE", + "type": "text" + } + ], + "index": 23 + } + ], + "index": 23 + }, + { + "type": "text", + "bbox": [ + 107, + 582, + 505, + 626 + ], + "lines": [ + { + "bbox": [ + 105, + 582, + 505, + 595 + ], + "spans": [ + { + "bbox": [ + 105, + 582, + 416, + 595 + ], + "score": 1.0, + "content": "To demonstrate that the OS-block can capture the best time scale, we build", + "type": "text" + }, + { + "bbox": [ + 417, + 582, + 452, + 593 + ], + "score": 0.28, + "content": "2 0 ~ \\mathrm { F C N }", + "type": "inline_equation" + }, + { + "bbox": [ + 452, + 582, + 505, + 595 + ], + "score": 1.0, + "content": "models with", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 592, + 505, + 606 + ], + "spans": [ + { + "bbox": [ + 105, + 592, + 505, + 606 + ], + "score": 1.0, + "content": "different RF sizes (from 10 to 200 with step 10), and compare their performance with OS-CNN on", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 604, + 506, + 617 + ], + "spans": [ + { + "bbox": [ + 105, + 604, + 506, + 617 + ], + "score": 1.0, + "content": "the UCR 85 archive. Specifically, the FCN (Wang et al., 2017) is selected as the backbone model", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 615, + 272, + 627 + ], + "spans": [ + { + "bbox": [ + 106, + 615, + 272, + 627 + ], + "score": 1.0, + "content": "for it has a similar structure as OS-CNN.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 25.5, + "bbox_fs": [ + 105, + 582, + 506, + 627 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 632, + 505, + 698 + ], + "lines": [ + { + "bbox": [ + 106, + 632, + 505, + 644 + ], + "spans": [ + { + "bbox": [ + 106, + 632, + 505, + 644 + ], + "score": 1.0, + "content": "To obtain FCN with various RF sizes, we change the kernel size of each layer proportionally. To be", + "type": "text" + } + ], + "index": 28 + }, + { + "bbox": [ + 105, + 643, + 506, + 655 + ], + "spans": [ + { + "bbox": [ + 105, + 643, + 506, + 655 + ], + "score": 1.0, + "content": "specific, the kernel sizes of the original three layer FCN are 8, 5, and 3, and the RF size is 14. To", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 653, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 653, + 505, + 667 + ], + "score": 1.0, + "content": "obtain the RF size 30, we will set kernel sizes of each layer as 16,10, and 6. To control variables,", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 665, + 504, + 677 + ], + "spans": [ + { + "bbox": [ + 106, + 665, + 504, + 677 + ], + "score": 1.0, + "content": "when the kernel size increases, we will reduce the channel number to keep the model size constant.", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 675, + 505, + 688 + ], + "spans": [ + { + "bbox": [ + 105, + 675, + 505, + 688 + ], + "score": 1.0, + "content": "This will not influence the conclusion. To check that, in Appendix A.2, we also provide the static", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 687, + 424, + 699 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 424, + 699 + ], + "score": 1.0, + "content": "result comparison between OS-CNN and FCNs with the fixed channel number.", + "type": "text" + } + ], + "index": 33 + } + ], + "index": 30.5, + "bbox_fs": [ + 105, + 632, + 506, + 699 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "image", + "bbox": [ + 108, + 81, + 503, + 153 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 108, + 81, + 503, + 153 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 108, + 81, + 503, + 153 + ], + "spans": [ + { + "bbox": [ + 108, + 81, + 503, + 153 + ], + "score": 0.931, + "type": "image", + "image_path": "a84164c9eb086966cd032e99b14e2ab863246890ce6932e92da955183fe232b0.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 108, + 81, + 503, + 105.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 108, + 105.0, + 503, + 129.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 108, + 129.0, + 503, + 153.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 107, + 166, + 505, + 211 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 166, + 506, + 179 + ], + "spans": [ + { + "bbox": [ + 105, + 166, + 506, + 179 + ], + "score": 1.0, + "content": "Figure 6: The class activation map of OS-CNN is similar to that of the model which has a better", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 178, + 505, + 190 + ], + "spans": [ + { + "bbox": [ + 105, + 178, + 505, + 190 + ], + "score": 1.0, + "content": "performance. For the ScreenType dataset, FCN(10) outperforms FCN(200), and the class activation", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 189, + 505, + 201 + ], + "spans": [ + { + "bbox": [ + 105, + 189, + 505, + 201 + ], + "score": 1.0, + "content": "map of OS-CNN (green) is similar to FCN(10)(blue). For the InsectWingbeatSound dataset, the", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 199, + 432, + 212 + ], + "spans": [ + { + "bbox": [ + 105, + 199, + 432, + 212 + ], + "score": 1.0, + "content": "class activation map is similar to FCN(200) for FCN(200) outperforms FCN(10).", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 4.5 + } + ], + "index": 2.75 + }, + { + "type": "text", + "bbox": [ + 108, + 232, + 504, + 265 + ], + "lines": [ + { + "bbox": [ + 106, + 232, + 505, + 244 + ], + "spans": [ + { + "bbox": [ + 106, + 232, + 505, + 244 + ], + "score": 1.0, + "content": "Due to the page limitation, the full result can be found in the supplementary material. And in", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 244, + 505, + 255 + ], + "spans": [ + { + "bbox": [ + 106, + 244, + 505, + 255 + ], + "score": 1.0, + "content": "Figure 5, a simple result comparison is given, and we could see that for most of the datasets, OS-", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 253, + 381, + 266 + ], + "spans": [ + { + "bbox": [ + 106, + 253, + 381, + 266 + ], + "score": 1.0, + "content": "CNN can achieve a similar result as models with the best time scale.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 8 + }, + { + "type": "title", + "bbox": [ + 113, + 281, + 373, + 291 + ], + "lines": [ + { + "bbox": [ + 111, + 280, + 375, + 293 + ], + "spans": [ + { + "bbox": [ + 111, + 280, + 375, + 293 + ], + "score": 1.0, + "content": ".6 DISCUSSION ABOUT BEST TIME SCALE CAPTURE ABILITY", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 10 + }, + { + "type": "text", + "bbox": [ + 107, + 300, + 505, + 367 + ], + "lines": [ + { + "bbox": [ + 106, + 301, + 505, + 313 + ], + "spans": [ + { + "bbox": [ + 106, + 301, + 505, + 313 + ], + "score": 1.0, + "content": "The result in Figure 5 empirically verifies two phenomena that we mentioned in Section 2 with", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 312, + 505, + 325 + ], + "spans": [ + { + "bbox": [ + 106, + 312, + 505, + 325 + ], + "score": 1.0, + "content": "multiple datasets from multiple domains. Firstly, the OS-block covers all scales. Therefore, besides", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 323, + 505, + 336 + ], + "spans": [ + { + "bbox": [ + 105, + 323, + 505, + 336 + ], + "score": 1.0, + "content": "the important size, it also covers many redundant sizes, but those redundancies will not pull down", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 333, + 505, + 346 + ], + "spans": [ + { + "bbox": [ + 105, + 333, + 505, + 346 + ], + "score": 1.0, + "content": "the performance. Secondly, OS-block composes the RF size via the prime design while the FCN", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 345, + 505, + 358 + ], + "spans": [ + { + "bbox": [ + 105, + 345, + 505, + 358 + ], + "score": 1.0, + "content": "uses a different design. It means that the performances of 1D-CNNs are determined mainly by the", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 356, + 346, + 368 + ], + "spans": [ + { + "bbox": [ + 105, + 356, + 346, + 368 + ], + "score": 1.0, + "content": "RF size instead of the kernel configuration to compose that.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 13.5 + }, + { + "type": "title", + "bbox": [ + 108, + 382, + 383, + 393 + ], + "lines": [ + { + "bbox": [ + 105, + 380, + 385, + 394 + ], + "spans": [ + { + "bbox": [ + 105, + 380, + 385, + 394 + ], + "score": 1.0, + "content": "4.7 CASE STUDY FOR THE BEST TIME SCALE CAPTURE ABILITY", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 17 + }, + { + "type": "text", + "bbox": [ + 107, + 402, + 505, + 512 + ], + "lines": [ + { + "bbox": [ + 105, + 402, + 505, + 415 + ], + "spans": [ + { + "bbox": [ + 105, + 402, + 505, + 415 + ], + "score": 1.0, + "content": "To further demonstrate the RF size capture ability, we will give a case study that compares the class", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 414, + 505, + 425 + ], + "spans": [ + { + "bbox": [ + 106, + 414, + 505, + 425 + ], + "score": 1.0, + "content": "activation map (Zhou et al., 2016) of OS-CNN with that of models with the best RF size. We select", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 424, + 506, + 437 + ], + "spans": [ + { + "bbox": [ + 105, + 424, + 506, + 437 + ], + "score": 1.0, + "content": "the ScreenType and InsectWingbeatSound datasets for the case study. They were selected because", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 435, + 505, + 448 + ], + "spans": [ + { + "bbox": [ + 105, + 435, + 505, + 448 + ], + "score": 1.0, + "content": "they are of the largest and the smallest accuracy difference calculated by the accuracy of FCN with", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 446, + 506, + 460 + ], + "spans": [ + { + "bbox": [ + 105, + 446, + 506, + 460 + ], + "score": 1.0, + "content": "RF size 10 (FCN(10)) minus accuracy of FCN with RF size 200 (FCN(200)). Specifically, it can", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 457, + 505, + 470 + ], + "spans": [ + { + "bbox": [ + 105, + 457, + 505, + 470 + ], + "score": 1.0, + "content": "be seen as, among UCR 85 datasets, the ScreenType is the dataset which the FCN(10) outperform", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 468, + 505, + 481 + ], + "spans": [ + { + "bbox": [ + 105, + 468, + 505, + 481 + ], + "score": 1.0, + "content": "FCN(200) most, and InsectWingbeatSound is the dataset which the FCN(200) outperforms FCN(10)", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 479, + 505, + 491 + ], + "spans": [ + { + "bbox": [ + 105, + 479, + 505, + 491 + ], + "score": 1.0, + "content": "most. We visualize the class activation map of the first instance in the two datasets, and the results", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 491, + 505, + 502 + ], + "spans": [ + { + "bbox": [ + 106, + 491, + 505, + 502 + ], + "score": 1.0, + "content": "are shown in Figure 6. As we can see in Figure 6, the class activation map of the OS-block is similar", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 501, + 275, + 513 + ], + "spans": [ + { + "bbox": [ + 106, + 501, + 275, + 513 + ], + "score": 1.0, + "content": "to that of the model with the best RF size.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 22.5 + }, + { + "type": "title", + "bbox": [ + 108, + 529, + 214, + 542 + ], + "lines": [ + { + "bbox": [ + 105, + 528, + 217, + 544 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 217, + 544 + ], + "score": 1.0, + "content": "5 RELATED WORKS", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 28 + }, + { + "type": "text", + "bbox": [ + 107, + 555, + 505, + 621 + ], + "lines": [ + { + "bbox": [ + 105, + 554, + 505, + 568 + ], + "spans": [ + { + "bbox": [ + 105, + 554, + 505, + 568 + ], + "score": 1.0, + "content": "A TS data is a series of data points. TSC aims at labeling unseen TS data via a model trained by", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 565, + 505, + 578 + ], + "spans": [ + { + "bbox": [ + 105, + 565, + 505, + 578 + ], + "score": 1.0, + "content": "labeled data (Dau et al., 2018; Chen et al., 2015). One well-known challenge for TSC is telling the", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 577, + 505, + 589 + ], + "spans": [ + { + "bbox": [ + 106, + 577, + 505, + 589 + ], + "score": 1.0, + "content": "model in what time scale to extract features (Hills et al., 2014; Schafer, 2015; Berndt & Clifford, ¨", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 587, + 505, + 600 + ], + "spans": [ + { + "bbox": [ + 105, + 587, + 505, + 600 + ], + "score": 1.0, + "content": "1994). This is because TS data is naturally composed of multiple signals on different scales (Hills", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 599, + 505, + 611 + ], + "spans": [ + { + "bbox": [ + 105, + 599, + 505, + 611 + ], + "score": 1.0, + "content": "et al., 2014; Schafer, 2015; Dau et al., 2018) but, without prior knowledge, it is hard to find those ¨", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 609, + 168, + 623 + ], + "spans": [ + { + "bbox": [ + 105, + 609, + 168, + 623 + ], + "score": 1.0, + "content": "scales directly.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 31.5 + }, + { + "type": "text", + "bbox": [ + 107, + 627, + 505, + 704 + ], + "lines": [ + { + "bbox": [ + 105, + 627, + 505, + 639 + ], + "spans": [ + { + "bbox": [ + 105, + 627, + 505, + 639 + ], + "score": 1.0, + "content": "The success of deep learning encourages researchers to explore its application on TS data (Langkvist ¨", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 638, + 505, + 650 + ], + "spans": [ + { + "bbox": [ + 105, + 638, + 505, + 650 + ], + "score": 1.0, + "content": "et al., 2014; Fawaz et al., 2019; Dong et al., 2021). The Recurrent Neural Network (RNN) is de-", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 649, + 505, + 662 + ], + "spans": [ + { + "bbox": [ + 105, + 649, + 505, + 662 + ], + "score": 1.0, + "content": "signed for temporal sequence. In general, it does not need extra hyper-parameters to identify infor-", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 660, + 505, + 672 + ], + "spans": [ + { + "bbox": [ + 105, + 660, + 505, + 672 + ], + "score": 1.0, + "content": "mation extraction scales. However, RNN is rarely applied on TS classification (Fawaz et al., 2019).", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 669, + 506, + 684 + ], + "spans": [ + { + "bbox": [ + 105, + 669, + 506, + 684 + ], + "score": 1.0, + "content": "There are many reasons for this situation. One widely accepted reason is that when faced with long", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 681, + 506, + 694 + ], + "spans": [ + { + "bbox": [ + 105, + 681, + 506, + 694 + ], + "score": 1.0, + "content": "TS data, RNN models suffer from vanishing gradient and exploding gradient (Pascanu et al., 2013;", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 693, + 268, + 705 + ], + "spans": [ + { + "bbox": [ + 105, + 693, + 268, + 705 + ], + "score": 1.0, + "content": "Fawaz et al., 2019; Bengio et al., 1994).", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 38 + }, + { + "type": "text", + "bbox": [ + 107, + 709, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 709, + 504, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 504, + 722 + ], + "score": 1.0, + "content": "Nowadays, the most popular deep-learning method for TSC is 1D-CNN. However, for 1D-CNNs,", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 720, + 504, + 732 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 504, + 732 + ], + "score": 1.0, + "content": "the feature extraction scale is still a problem. For example, there is an unresolved challenge with", + "type": "text" + } + ], + "index": 43 + } + ], + "index": 42.5 + } + ], + "page_idx": 7, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 107, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 25, + 294, + 39 + ], + "spans": [ + { + "bbox": [ + 106, + 25, + 294, + 39 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2022", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 752, + 308, + 759 + ], + "lines": [ + { + "bbox": [ + 302, + 750, + 309, + 761 + ], + "spans": [ + { + "bbox": [ + 302, + 750, + 309, + 761 + ], + "score": 1.0, + "content": "8", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "image", + "bbox": [ + 108, + 81, + 503, + 153 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 108, + 81, + 503, + 153 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 108, + 81, + 503, + 153 + ], + "spans": [ + { + "bbox": [ + 108, + 81, + 503, + 153 + ], + "score": 0.931, + "type": "image", + "image_path": "a84164c9eb086966cd032e99b14e2ab863246890ce6932e92da955183fe232b0.jpg" + } + ] + } + ], + "index": 1, + "virtual_lines": [ + { + "bbox": [ + 108, + 81, + 503, + 105.0 + ], + "spans": [], + "index": 0 + }, + { + "bbox": [ + 108, + 105.0, + 503, + 129.0 + ], + "spans": [], + "index": 1 + }, + { + "bbox": [ + 108, + 129.0, + 503, + 153.0 + ], + "spans": [], + "index": 2 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 107, + 166, + 505, + 211 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 166, + 506, + 179 + ], + "spans": [ + { + "bbox": [ + 105, + 166, + 506, + 179 + ], + "score": 1.0, + "content": "Figure 6: The class activation map of OS-CNN is similar to that of the model which has a better", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 178, + 505, + 190 + ], + "spans": [ + { + "bbox": [ + 105, + 178, + 505, + 190 + ], + "score": 1.0, + "content": "performance. For the ScreenType dataset, FCN(10) outperforms FCN(200), and the class activation", + "type": "text" + } + ], + "index": 4 + }, + { + "bbox": [ + 105, + 189, + 505, + 201 + ], + "spans": [ + { + "bbox": [ + 105, + 189, + 505, + 201 + ], + "score": 1.0, + "content": "map of OS-CNN (green) is similar to FCN(10)(blue). For the InsectWingbeatSound dataset, the", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 199, + 432, + 212 + ], + "spans": [ + { + "bbox": [ + 105, + 199, + 432, + 212 + ], + "score": 1.0, + "content": "class activation map is similar to FCN(200) for FCN(200) outperforms FCN(10).", + "type": "text" + } + ], + "index": 6 + } + ], + "index": 4.5 + } + ], + "index": 2.75 + }, + { + "type": "text", + "bbox": [ + 108, + 232, + 504, + 265 + ], + "lines": [ + { + "bbox": [ + 106, + 232, + 505, + 244 + ], + "spans": [ + { + "bbox": [ + 106, + 232, + 505, + 244 + ], + "score": 1.0, + "content": "Due to the page limitation, the full result can be found in the supplementary material. And in", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 106, + 244, + 505, + 255 + ], + "spans": [ + { + "bbox": [ + 106, + 244, + 505, + 255 + ], + "score": 1.0, + "content": "Figure 5, a simple result comparison is given, and we could see that for most of the datasets, OS-", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 253, + 381, + 266 + ], + "spans": [ + { + "bbox": [ + 106, + 253, + 381, + 266 + ], + "score": 1.0, + "content": "CNN can achieve a similar result as models with the best time scale.", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 8, + "bbox_fs": [ + 106, + 232, + 505, + 266 + ] + }, + { + "type": "title", + "bbox": [ + 113, + 281, + 373, + 291 + ], + "lines": [ + { + "bbox": [ + 111, + 280, + 375, + 293 + ], + "spans": [ + { + "bbox": [ + 111, + 280, + 375, + 293 + ], + "score": 1.0, + "content": ".6 DISCUSSION ABOUT BEST TIME SCALE CAPTURE ABILITY", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 10 + }, + { + "type": "text", + "bbox": [ + 107, + 300, + 505, + 367 + ], + "lines": [ + { + "bbox": [ + 106, + 301, + 505, + 313 + ], + "spans": [ + { + "bbox": [ + 106, + 301, + 505, + 313 + ], + "score": 1.0, + "content": "The result in Figure 5 empirically verifies two phenomena that we mentioned in Section 2 with", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 106, + 312, + 505, + 325 + ], + "spans": [ + { + "bbox": [ + 106, + 312, + 505, + 325 + ], + "score": 1.0, + "content": "multiple datasets from multiple domains. Firstly, the OS-block covers all scales. Therefore, besides", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 323, + 505, + 336 + ], + "spans": [ + { + "bbox": [ + 105, + 323, + 505, + 336 + ], + "score": 1.0, + "content": "the important size, it also covers many redundant sizes, but those redundancies will not pull down", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 105, + 333, + 505, + 346 + ], + "spans": [ + { + "bbox": [ + 105, + 333, + 505, + 346 + ], + "score": 1.0, + "content": "the performance. Secondly, OS-block composes the RF size via the prime design while the FCN", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 345, + 505, + 358 + ], + "spans": [ + { + "bbox": [ + 105, + 345, + 505, + 358 + ], + "score": 1.0, + "content": "uses a different design. It means that the performances of 1D-CNNs are determined mainly by the", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 356, + 346, + 368 + ], + "spans": [ + { + "bbox": [ + 105, + 356, + 346, + 368 + ], + "score": 1.0, + "content": "RF size instead of the kernel configuration to compose that.", + "type": "text" + } + ], + "index": 16 + } + ], + "index": 13.5, + "bbox_fs": [ + 105, + 301, + 505, + 368 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 382, + 383, + 393 + ], + "lines": [ + { + "bbox": [ + 105, + 380, + 385, + 394 + ], + "spans": [ + { + "bbox": [ + 105, + 380, + 385, + 394 + ], + "score": 1.0, + "content": "4.7 CASE STUDY FOR THE BEST TIME SCALE CAPTURE ABILITY", + "type": "text" + } + ], + "index": 17 + } + ], + "index": 17 + }, + { + "type": "text", + "bbox": [ + 107, + 402, + 505, + 512 + ], + "lines": [ + { + "bbox": [ + 105, + 402, + 505, + 415 + ], + "spans": [ + { + "bbox": [ + 105, + 402, + 505, + 415 + ], + "score": 1.0, + "content": "To further demonstrate the RF size capture ability, we will give a case study that compares the class", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 106, + 414, + 505, + 425 + ], + "spans": [ + { + "bbox": [ + 106, + 414, + 505, + 425 + ], + "score": 1.0, + "content": "activation map (Zhou et al., 2016) of OS-CNN with that of models with the best RF size. We select", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 424, + 506, + 437 + ], + "spans": [ + { + "bbox": [ + 105, + 424, + 506, + 437 + ], + "score": 1.0, + "content": "the ScreenType and InsectWingbeatSound datasets for the case study. They were selected because", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 435, + 505, + 448 + ], + "spans": [ + { + "bbox": [ + 105, + 435, + 505, + 448 + ], + "score": 1.0, + "content": "they are of the largest and the smallest accuracy difference calculated by the accuracy of FCN with", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 446, + 506, + 460 + ], + "spans": [ + { + "bbox": [ + 105, + 446, + 506, + 460 + ], + "score": 1.0, + "content": "RF size 10 (FCN(10)) minus accuracy of FCN with RF size 200 (FCN(200)). Specifically, it can", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 105, + 457, + 505, + 470 + ], + "spans": [ + { + "bbox": [ + 105, + 457, + 505, + 470 + ], + "score": 1.0, + "content": "be seen as, among UCR 85 datasets, the ScreenType is the dataset which the FCN(10) outperform", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 105, + 468, + 505, + 481 + ], + "spans": [ + { + "bbox": [ + 105, + 468, + 505, + 481 + ], + "score": 1.0, + "content": "FCN(200) most, and InsectWingbeatSound is the dataset which the FCN(200) outperforms FCN(10)", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 479, + 505, + 491 + ], + "spans": [ + { + "bbox": [ + 105, + 479, + 505, + 491 + ], + "score": 1.0, + "content": "most. We visualize the class activation map of the first instance in the two datasets, and the results", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 106, + 491, + 505, + 502 + ], + "spans": [ + { + "bbox": [ + 106, + 491, + 505, + 502 + ], + "score": 1.0, + "content": "are shown in Figure 6. As we can see in Figure 6, the class activation map of the OS-block is similar", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 106, + 501, + 275, + 513 + ], + "spans": [ + { + "bbox": [ + 106, + 501, + 275, + 513 + ], + "score": 1.0, + "content": "to that of the model with the best RF size.", + "type": "text" + } + ], + "index": 27 + } + ], + "index": 22.5, + "bbox_fs": [ + 105, + 402, + 506, + 513 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 529, + 214, + 542 + ], + "lines": [ + { + "bbox": [ + 105, + 528, + 217, + 544 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 217, + 544 + ], + "score": 1.0, + "content": "5 RELATED WORKS", + "type": "text" + } + ], + "index": 28 + } + ], + "index": 28 + }, + { + "type": "text", + "bbox": [ + 107, + 555, + 505, + 621 + ], + "lines": [ + { + "bbox": [ + 105, + 554, + 505, + 568 + ], + "spans": [ + { + "bbox": [ + 105, + 554, + 505, + 568 + ], + "score": 1.0, + "content": "A TS data is a series of data points. TSC aims at labeling unseen TS data via a model trained by", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 105, + 565, + 505, + 578 + ], + "spans": [ + { + "bbox": [ + 105, + 565, + 505, + 578 + ], + "score": 1.0, + "content": "labeled data (Dau et al., 2018; Chen et al., 2015). One well-known challenge for TSC is telling the", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 577, + 505, + 589 + ], + "spans": [ + { + "bbox": [ + 106, + 577, + 505, + 589 + ], + "score": 1.0, + "content": "model in what time scale to extract features (Hills et al., 2014; Schafer, 2015; Berndt & Clifford, ¨", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 587, + 505, + 600 + ], + "spans": [ + { + "bbox": [ + 105, + 587, + 505, + 600 + ], + "score": 1.0, + "content": "1994). This is because TS data is naturally composed of multiple signals on different scales (Hills", + "type": "text" + } + ], + "index": 32 + }, + { + "bbox": [ + 105, + 599, + 505, + 611 + ], + "spans": [ + { + "bbox": [ + 105, + 599, + 505, + 611 + ], + "score": 1.0, + "content": "et al., 2014; Schafer, 2015; Dau et al., 2018) but, without prior knowledge, it is hard to find those ¨", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 105, + 609, + 168, + 623 + ], + "spans": [ + { + "bbox": [ + 105, + 609, + 168, + 623 + ], + "score": 1.0, + "content": "scales directly.", + "type": "text" + } + ], + "index": 34 + } + ], + "index": 31.5, + "bbox_fs": [ + 105, + 554, + 505, + 623 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 627, + 505, + 704 + ], + "lines": [ + { + "bbox": [ + 105, + 627, + 505, + 639 + ], + "spans": [ + { + "bbox": [ + 105, + 627, + 505, + 639 + ], + "score": 1.0, + "content": "The success of deep learning encourages researchers to explore its application on TS data (Langkvist ¨", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 638, + 505, + 650 + ], + "spans": [ + { + "bbox": [ + 105, + 638, + 505, + 650 + ], + "score": 1.0, + "content": "et al., 2014; Fawaz et al., 2019; Dong et al., 2021). The Recurrent Neural Network (RNN) is de-", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 649, + 505, + 662 + ], + "spans": [ + { + "bbox": [ + 105, + 649, + 505, + 662 + ], + "score": 1.0, + "content": "signed for temporal sequence. In general, it does not need extra hyper-parameters to identify infor-", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 660, + 505, + 672 + ], + "spans": [ + { + "bbox": [ + 105, + 660, + 505, + 672 + ], + "score": 1.0, + "content": "mation extraction scales. However, RNN is rarely applied on TS classification (Fawaz et al., 2019).", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 105, + 669, + 506, + 684 + ], + "spans": [ + { + "bbox": [ + 105, + 669, + 506, + 684 + ], + "score": 1.0, + "content": "There are many reasons for this situation. One widely accepted reason is that when faced with long", + "type": "text" + } + ], + "index": 39 + }, + { + "bbox": [ + 105, + 681, + 506, + 694 + ], + "spans": [ + { + "bbox": [ + 105, + 681, + 506, + 694 + ], + "score": 1.0, + "content": "TS data, RNN models suffer from vanishing gradient and exploding gradient (Pascanu et al., 2013;", + "type": "text" + } + ], + "index": 40 + }, + { + "bbox": [ + 105, + 693, + 268, + 705 + ], + "spans": [ + { + "bbox": [ + 105, + 693, + 268, + 705 + ], + "score": 1.0, + "content": "Fawaz et al., 2019; Bengio et al., 1994).", + "type": "text" + } + ], + "index": 41 + } + ], + "index": 38, + "bbox_fs": [ + 105, + 627, + 506, + 705 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 709, + 504, + 732 + ], + "lines": [ + { + "bbox": [ + 106, + 709, + 504, + 722 + ], + "spans": [ + { + "bbox": [ + 106, + 709, + 504, + 722 + ], + "score": 1.0, + "content": "Nowadays, the most popular deep-learning method for TSC is 1D-CNN. However, for 1D-CNNs,", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 720, + 504, + 732 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 504, + 732 + ], + "score": 1.0, + "content": "the feature extraction scale is still a problem. For example, there is an unresolved challenge with", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 83, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 83, + 505, + 95 + ], + "score": 1.0, + "content": "kernel size selection where there exists different approaches but non consensus on which is best.", + "type": "text", + "cross_page": true + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 93, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 106, + 93, + 505, + 106 + ], + "score": 1.0, + "content": "To date, the selection of feature extraction scales for 1D-CNN is regarded as a hyper-parameter", + "type": "text", + "cross_page": true + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 103, + 506, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 103, + 506, + 118 + ], + "score": 1.0, + "content": "selection problem e.g., (Cui et al., 2016) uses a grid search to find kernel sizes, while the following", + "type": "text", + "cross_page": true + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 506, + 128 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 506, + 128 + ], + "score": 1.0, + "content": "methods tune it empirically (Zheng et al., 2014; Wang et al., 2017; Rajpurkar et al., 2017; Serra`", + "type": "text", + "cross_page": true + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 127, + 366, + 138 + ], + "spans": [ + { + "bbox": [ + 105, + 127, + 366, + 138 + ], + "score": 1.0, + "content": "et al., 2018; Ismail Fawaz et al., 2019; Kashiparekh et al., 2019).", + "type": "text", + "cross_page": true + } + ], + "index": 4 + } + ], + "index": 42.5, + "bbox_fs": [ + 105, + 709, + 504, + 732 + ] + } + ] + }, + { + "preproc_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 504, + 138 + ], + "lines": [ + { + "bbox": [ + 105, + 83, + 505, + 95 + ], + "spans": [ + { + "bbox": [ + 105, + 83, + 505, + 95 + ], + "score": 1.0, + "content": "kernel size selection where there exists different approaches but non consensus on which is best.", + "type": "text" + } + ], + "index": 0 + }, + { + "bbox": [ + 106, + 93, + 505, + 106 + ], + "spans": [ + { + "bbox": [ + 106, + 93, + 505, + 106 + ], + "score": 1.0, + "content": "To date, the selection of feature extraction scales for 1D-CNN is regarded as a hyper-parameter", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 105, + 103, + 506, + 118 + ], + "spans": [ + { + "bbox": [ + 105, + 103, + 506, + 118 + ], + "score": 1.0, + "content": "selection problem e.g., (Cui et al., 2016) uses a grid search to find kernel sizes, while the following", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 105, + 115, + 506, + 128 + ], + "spans": [ + { + "bbox": [ + 105, + 115, + 506, + 128 + ], + "score": 1.0, + "content": "methods tune it empirically (Zheng et al., 2014; Wang et al., 2017; Rajpurkar et al., 2017; Serra`", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 105, + 127, + 366, + 138 + ], + "spans": [ + { + "bbox": [ + 105, + 127, + 366, + 138 + ], + "score": 1.0, + "content": "et al., 2018; Ismail Fawaz et al., 2019; Kashiparekh et al., 2019).", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 2 + }, + { + "type": "text", + "bbox": [ + 107, + 143, + 505, + 209 + ], + "lines": [ + { + "bbox": [ + 105, + 142, + 506, + 156 + ], + "spans": [ + { + "bbox": [ + 105, + 142, + 506, + 156 + ], + "score": 1.0, + "content": "Dilated convolution (Oord et al., 2016) is widely adopted in 1D-CNN to improve generalization", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 153, + 505, + 168 + ], + "spans": [ + { + "bbox": [ + 105, + 153, + 505, + 168 + ], + "score": 1.0, + "content": "ability for TS tasks (Oord et al., 2016; Zhang et al., 2020; Li et al., 2021). It takes a lower sampling", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 165, + 505, + 178 + ], + "spans": [ + { + "bbox": [ + 105, + 165, + 505, + 178 + ], + "score": 1.0, + "content": "frequency than the raw signal input thus can be viewed as a structure-based low bandpass filter.", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 176, + 505, + 189 + ], + "spans": [ + { + "bbox": [ + 105, + 176, + 505, + 189 + ], + "score": 1.0, + "content": "Compared with the OS-block, the dilated convolution also needs prior knowledge or searching work", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 187, + 505, + 199 + ], + "spans": [ + { + "bbox": [ + 105, + 187, + 505, + 199 + ], + "score": 1.0, + "content": "to set the dilation size which will determine the threshold to filter out redundant information from", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 196, + 143, + 210 + ], + "spans": [ + { + "bbox": [ + 105, + 196, + 143, + 210 + ], + "score": 1.0, + "content": "TS data.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 7.5 + }, + { + "type": "text", + "bbox": [ + 107, + 214, + 505, + 347 + ], + "lines": [ + { + "bbox": [ + 106, + 215, + 506, + 227 + ], + "spans": [ + { + "bbox": [ + 106, + 215, + 506, + 227 + ], + "score": 1.0, + "content": "Inception structure (Szegedy et al., 2015) is widely used in 1D-CNN for TSC tasks (Ismail Fawaz", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 226, + 505, + 238 + ], + "spans": [ + { + "bbox": [ + 105, + 226, + 505, + 238 + ], + "score": 1.0, + "content": "et al., 2019; Kashiparekh et al., 2019; Chen & Shi, 2021; Dong et al., 2021). The design of the", + "type": "text" + } + ], + "index": 12 + }, + { + "bbox": [ + 105, + 236, + 505, + 249 + ], + "spans": [ + { + "bbox": [ + 105, + 236, + 505, + 249 + ], + "score": 1.0, + "content": "multi-kernel structure of OS-block is inspired from the inception structure (Szegedy et al., 2015).", + "type": "text" + } + ], + "index": 13 + }, + { + "bbox": [ + 106, + 248, + 506, + 260 + ], + "spans": [ + { + "bbox": [ + 106, + 248, + 506, + 260 + ], + "score": 1.0, + "content": "Compared with existing works, the OS-block has two differences. Firstly, the OS-block does not", + "type": "text" + } + ], + "index": 14 + }, + { + "bbox": [ + 105, + 259, + 505, + 271 + ], + "spans": [ + { + "bbox": [ + 105, + 259, + 505, + 271 + ], + "score": 1.0, + "content": "need to assign weight to important scales via complicated methods such as pre-train (Kashiparekh", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 271, + 505, + 281 + ], + "spans": [ + { + "bbox": [ + 105, + 271, + 505, + 281 + ], + "score": 1.0, + "content": "et al., 2019), attention (Chen & Shi, 2021; Shen et al., 2018b), or a series of modifications such as", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 280, + 505, + 293 + ], + "spans": [ + { + "bbox": [ + 105, + 280, + 505, + 293 + ], + "score": 1.0, + "content": "bias removal and bottleneck for convolutions (Ismail Fawaz et al., 2019). Secondly, OS-block does", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 291, + 506, + 304 + ], + "spans": [ + { + "bbox": [ + 105, + 291, + 506, + 304 + ], + "score": 1.0, + "content": "not need to search for candidate scales. Specifically, those methods can only assign weight to a", + "type": "text" + } + ], + "index": 18 + }, + { + "bbox": [ + 105, + 302, + 505, + 315 + ], + "spans": [ + { + "bbox": [ + 105, + 302, + 505, + 315 + ], + "score": 1.0, + "content": "limited number of scales. Thus, they still need searching works to answer a series of questions. For", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 314, + 505, + 326 + ], + "spans": [ + { + "bbox": [ + 105, + 314, + 505, + 326 + ], + "score": 1.0, + "content": "example, Which sequence, such as geometric or arithmetic, should be preferred? 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And how do they select the", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 336, + 297, + 348 + ], + "spans": [ + { + "bbox": [ + 105, + 336, + 297, + 348 + ], + "score": 1.0, + "content": "common difference or ratio for their sequence?", + "type": "text" + } + ], + "index": 22 + } + ], + "index": 16.5 + }, + { + "type": "text", + "bbox": [ + 107, + 352, + 505, + 451 + ], + "lines": [ + { + "bbox": [ + 106, + 353, + 504, + 365 + ], + "spans": [ + { + "bbox": [ + 106, + 353, + 504, + 365 + ], + "score": 1.0, + "content": "Adaptive receptive field (Han et al., 2018; Tabernik et al., 2020; Xiong et al., 2020; Pintea et al.,", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 363, + 505, + 375 + ], + "spans": [ + { + "bbox": [ + 106, + 363, + 505, + 375 + ], + "score": 1.0, + "content": "2021; Liu et al., 2021; Tomen et al., 2021; Dong et al., 2021), has been proposed to learn the optimal", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 105, + 374, + 505, + 388 + ], + "spans": [ + { + "bbox": [ + 105, + 374, + 505, + 388 + ], + "score": 1.0, + "content": "kernel sizes during the training stage. Generally, it can be viewed as learning a weight mask on", + "type": "text" + } + ], + "index": 25 + }, + { + "bbox": [ + 105, + 383, + 506, + 399 + ], + "spans": [ + { + "bbox": [ + 105, + 383, + 506, + 399 + ], + "score": 1.0, + "content": "kernels to control the receptive field size. The weight of the mask can be learned during the training", + "type": "text" + } + ], + "index": 26 + }, + { + "bbox": [ + 105, + 397, + 505, + 409 + ], + "spans": [ + { + "bbox": [ + 105, + 397, + 505, + 409 + ], + "score": 1.0, + "content": "step. On the other hand, OS-block learns the linkage between kernels and uses kernels of different", + "type": "text" + } + ], + "index": 27 + }, + { + "bbox": [ + 106, + 408, + 505, + 420 + ], + "spans": [ + { + "bbox": [ + 106, + 408, + 505, + 420 + ], + "score": 1.0, + "content": "sizes to compose different receptive field sizes. 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This is because the video classification task", + "type": "text" + } + ], + "index": 33 + }, + { + "bbox": [ + 106, + 479, + 504, + 490 + ], + "spans": [ + { + "bbox": [ + 106, + 479, + 504, + 490 + ], + "score": 1.0, + "content": "and time series classification task share the same challenge (Xie et al., 2018; Bian et al., 2017; Tan", + "type": "text" + } + ], + "index": 34 + }, + { + "bbox": [ + 105, + 489, + 505, + 502 + ], + "spans": [ + { + "bbox": [ + 105, + 489, + 505, + 502 + ], + "score": 1.0, + "content": "et al., 2021; Liu et al., 2020; Li et al., 2020), which is the same region of interest might of different", + "type": "text" + } + ], + "index": 35 + }, + { + "bbox": [ + 105, + 500, + 505, + 514 + ], + "spans": [ + { + "bbox": [ + 105, + 500, + 505, + 514 + ], + "score": 1.0, + "content": "time scales for different data. Thus, using the kernel of various sizes will increase the probability to", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 512, + 505, + 524 + ], + "spans": [ + { + "bbox": [ + 105, + 512, + 505, + 524 + ], + "score": 1.0, + "content": "catch proper scales. 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It does not need any feature extrac-", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 601, + 505, + 612 + ], + "spans": [ + { + "bbox": [ + 106, + 601, + 505, + 612 + ], + "score": 1.0, + "content": "tion scale tuning and can achieve a similar performance as models with the best feature extraction", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 610, + 506, + 625 + ], + "spans": [ + { + "bbox": [ + 105, + 610, + 506, + 625 + ], + "score": 1.0, + "content": "scales. The key idea is using prime number design to cover all RF sizes in an efficient manner. We", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 622, + 505, + 634 + ], + "spans": [ + { + "bbox": [ + 105, + 622, + 505, + 634 + ], + "score": 1.0, + "content": "conduct experiments to demonstrate that the OS-block can robustly capture the best time scale on", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 633, + 504, + 645 + ], + "spans": [ + { + "bbox": [ + 105, + 633, + 504, + 645 + ], + "score": 1.0, + "content": "datasets from multiple domains. Due to the strong scale capture ability, it achieves a series SOTA", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 644, + 505, + 656 + ], + "spans": [ + { + "bbox": [ + 106, + 644, + 505, + 656 + ], + "score": 1.0, + "content": "performance on multiple TSC benchmarks. Besides that, the OS-CNN results reveal two charac-", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "score": 1.0, + "content": "teristics of 1D-CNN models, which will benefit the development of the domain. In the future, we", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 664, + 505, + 679 + ], + "spans": [ + { + "bbox": [ + 105, + 664, + 505, + 679 + ], + "score": 1.0, + "content": "could extend our work in the following aspects. Firstly, other than the prime kernel size design,", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "score": 1.0, + "content": "there might be a more efficient design to cover all RF sizes. Secondly, the OS-block can work with", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "score": 1.0, + "content": "existing deep neural structures to achieve better performance, but there might be unique structures", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 105, + 699, + 504, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 504, + 711 + ], + "score": 1.0, + "content": "or variants of those existing structures that are more suitable for the OS-block. Besides that, char-", + "type": "text" + } + ], + "index": 51 + }, + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "spans": [ + { + "bbox": [ + 105, + 709, + 505, + 722 + ], + "score": 1.0, + "content": "acteristics of OS-block are empirically analyzed via the way there must be a theoretical explanation", + "type": "text" + } + ], + "index": 52 + }, + { + "bbox": [ + 105, + 720, + 194, + 733 + ], + "spans": [ + { + "bbox": [ + 105, + 720, + 194, + 733 + ], + "score": 1.0, + "content": "of the characteristics.", + "type": "text" + } + ], + "index": 53 + } + ], + "index": 47 + } + ], + "page_idx": 8, + "page_size": [ + 612, + 792 + ], + "discarded_blocks": [ + { + "type": "discarded", + "bbox": [ + 108, + 27, + 293, + 37 + ], + "lines": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "spans": [ + { + "bbox": [ + 106, + 26, + 294, + 38 + ], + "score": 1.0, + "content": "Published as a conference paper at ICLR 2022", + "type": "text" + } + ] + } + ] + }, + { + "type": "discarded", + "bbox": [ + 302, + 751, + 308, + 759 + ], + "lines": [ + { + "bbox": [ + 302, + 751, + 309, + 762 + ], + "spans": [ + { + "bbox": [ + 302, + 751, + 309, + 762 + ], + "score": 1.0, + "content": "9", + "type": "text" + } + ] + } + ] + } + ], + "para_blocks": [ + { + "type": "text", + "bbox": [ + 107, + 82, + 504, + 138 + ], + "lines": [], + "index": 2, + "bbox_fs": [ + 105, + 83, + 506, + 138 + ], + "lines_deleted": true + }, + { + "type": "text", + "bbox": [ + 107, + 143, + 505, + 209 + ], + "lines": [ + { + "bbox": [ + 105, + 142, + 506, + 156 + ], + "spans": [ + { + "bbox": [ + 105, + 142, + 506, + 156 + ], + "score": 1.0, + "content": "Dilated convolution (Oord et al., 2016) is widely adopted in 1D-CNN to improve generalization", + "type": "text" + } + ], + "index": 5 + }, + { + "bbox": [ + 105, + 153, + 505, + 168 + ], + "spans": [ + { + "bbox": [ + 105, + 153, + 505, + 168 + ], + "score": 1.0, + "content": "ability for TS tasks (Oord et al., 2016; Zhang et al., 2020; Li et al., 2021). It takes a lower sampling", + "type": "text" + } + ], + "index": 6 + }, + { + "bbox": [ + 105, + 165, + 505, + 178 + ], + "spans": [ + { + "bbox": [ + 105, + 165, + 505, + 178 + ], + "score": 1.0, + "content": "frequency than the raw signal input thus can be viewed as a structure-based low bandpass filter.", + "type": "text" + } + ], + "index": 7 + }, + { + "bbox": [ + 105, + 176, + 505, + 189 + ], + "spans": [ + { + "bbox": [ + 105, + 176, + 505, + 189 + ], + "score": 1.0, + "content": "Compared with the OS-block, the dilated convolution also needs prior knowledge or searching work", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 105, + 187, + 505, + 199 + ], + "spans": [ + { + "bbox": [ + 105, + 187, + 505, + 199 + ], + "score": 1.0, + "content": "to set the dilation size which will determine the threshold to filter out redundant information from", + "type": "text" + } + ], + "index": 9 + }, + { + "bbox": [ + 105, + 196, + 143, + 210 + ], + "spans": [ + { + "bbox": [ + 105, + 196, + 143, + 210 + ], + "score": 1.0, + "content": "TS data.", + "type": "text" + } + ], + "index": 10 + } + ], + "index": 7.5, + "bbox_fs": [ + 105, + 142, + 506, + 210 + ] + }, + { + "type": "text", + "bbox": [ + 107, + 214, + 505, + 347 + ], + "lines": [ + { + "bbox": [ + 106, + 215, + 506, + 227 + ], + "spans": [ + { + "bbox": [ + 106, + 215, + 506, + 227 + ], + "score": 1.0, + "content": "Inception structure (Szegedy et al., 2015) is widely used in 1D-CNN for TSC tasks (Ismail Fawaz", + "type": "text" + } + ], + "index": 11 + }, + { + "bbox": [ + 105, + 226, + 505, + 238 + ], + "spans": [ + { + "bbox": [ + 105, + 226, + 505, + 238 + ], + "score": 1.0, + "content": "et al., 2019; Kashiparekh et al., 2019; Chen & Shi, 2021; Dong et al., 2021). 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Thus, using the kernel of various sizes will increase the probability to", + "type": "text" + } + ], + "index": 36 + }, + { + "bbox": [ + 105, + 512, + 505, + 524 + ], + "spans": [ + { + "bbox": [ + 105, + 512, + 505, + 524 + ], + "score": 1.0, + "content": "catch proper scales. However, in this paper, we mainly target the classic 1D time series classification,", + "type": "text" + } + ], + "index": 37 + }, + { + "bbox": [ + 105, + 522, + 505, + 536 + ], + "spans": [ + { + "bbox": [ + 105, + 522, + 505, + 536 + ], + "score": 1.0, + "content": "which is an active research area with many open problems (Fawaz et al., 2019; Zhang et al., 2020;", + "type": "text" + } + ], + "index": 38 + }, + { + "bbox": [ + 106, + 534, + 238, + 546 + ], + "spans": [ + { + "bbox": [ + 106, + 534, + 238, + 546 + ], + "score": 1.0, + "content": "Dempster et al., 2020) unsolven.", + "type": "text" + } + ], + "index": 39 + } + ], + "index": 35.5, + "bbox_fs": [ + 105, + 457, + 506, + 546 + ] + }, + { + "type": "title", + "bbox": [ + 108, + 563, + 195, + 576 + ], + "lines": [ + { + "bbox": [ + 104, + 561, + 197, + 579 + ], + "spans": [ + { + "bbox": [ + 104, + 561, + 197, + 579 + ], + "score": 1.0, + "content": "6 CONCLUSION", + "type": "text" + } + ], + "index": 40 + } + ], + "index": 40 + }, + { + "type": "text", + "bbox": [ + 107, + 589, + 505, + 731 + ], + "lines": [ + { + "bbox": [ + 106, + 590, + 504, + 601 + ], + "spans": [ + { + "bbox": [ + 106, + 590, + 504, + 601 + ], + "score": 1.0, + "content": "The paper presents a simple 1D-CNN block, namely OS-block. It does not need any feature extrac-", + "type": "text" + } + ], + "index": 41 + }, + { + "bbox": [ + 106, + 601, + 505, + 612 + ], + "spans": [ + { + "bbox": [ + 106, + 601, + 505, + 612 + ], + "score": 1.0, + "content": "tion scale tuning and can achieve a similar performance as models with the best feature extraction", + "type": "text" + } + ], + "index": 42 + }, + { + "bbox": [ + 105, + 610, + 506, + 625 + ], + "spans": [ + { + "bbox": [ + 105, + 610, + 506, + 625 + ], + "score": 1.0, + "content": "scales. The key idea is using prime number design to cover all RF sizes in an efficient manner. We", + "type": "text" + } + ], + "index": 43 + }, + { + "bbox": [ + 105, + 622, + 505, + 634 + ], + "spans": [ + { + "bbox": [ + 105, + 622, + 505, + 634 + ], + "score": 1.0, + "content": "conduct experiments to demonstrate that the OS-block can robustly capture the best time scale on", + "type": "text" + } + ], + "index": 44 + }, + { + "bbox": [ + 105, + 633, + 504, + 645 + ], + "spans": [ + { + "bbox": [ + 105, + 633, + 504, + 645 + ], + "score": 1.0, + "content": "datasets from multiple domains. Due to the strong scale capture ability, it achieves a series SOTA", + "type": "text" + } + ], + "index": 45 + }, + { + "bbox": [ + 106, + 644, + 505, + 656 + ], + "spans": [ + { + "bbox": [ + 106, + 644, + 505, + 656 + ], + "score": 1.0, + "content": "performance on multiple TSC benchmarks. Besides that, the OS-CNN results reveal two charac-", + "type": "text" + } + ], + "index": 46 + }, + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "spans": [ + { + "bbox": [ + 105, + 654, + 505, + 667 + ], + "score": 1.0, + "content": "teristics of 1D-CNN models, which will benefit the development of the domain. In the future, we", + "type": "text" + } + ], + "index": 47 + }, + { + "bbox": [ + 105, + 664, + 505, + 679 + ], + "spans": [ + { + "bbox": [ + 105, + 664, + 505, + 679 + ], + "score": 1.0, + "content": "could extend our work in the following aspects. Firstly, other than the prime kernel size design,", + "type": "text" + } + ], + "index": 48 + }, + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "spans": [ + { + "bbox": [ + 106, + 677, + 505, + 689 + ], + "score": 1.0, + "content": "there might be a more efficient design to cover all RF sizes. Secondly, the OS-block can work with", + "type": "text" + } + ], + "index": 49 + }, + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "spans": [ + { + "bbox": [ + 105, + 687, + 505, + 700 + ], + "score": 1.0, + "content": "existing deep neural structures to achieve better performance, but there might be unique structures", + "type": "text" + } + ], + "index": 50 + }, + { + "bbox": [ + 105, + 699, + 504, + 711 + ], + "spans": [ + { + "bbox": [ + 105, + 699, + 504, + 711 + ], + "score": 1.0, + "content": "or variants of those existing structures that are more suitable for the OS-block. 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We could see that the best", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 106, + 409, + 455, + 421 + ], + "spans": [ + { + "bbox": [ + 106, + 409, + 455, + 421 + ], + "score": 1.0, + "content": "receptive field size mainly dominates the performance in the set of receptive fieldsizes.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 17 + } + ], + "index": 15.5 + }, + { + "type": "image", + "bbox": [ + 108, + 430, + 503, + 523 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 108, + 430, + 503, + 523 + ], + "group_id": 2, + "lines": [ + { + "bbox": [ + 108, + 430, + 503, + 523 + ], + "spans": [ + { + "bbox": [ + 108, + 430, + 503, + 523 + ], + "score": 0.963, + "type": "image", + "image_path": "d6d0b86b0bf7571ff2267b5610e54825894aa424380e4027b92f9387c71e496f.jpg" + } + ] + } + ], + "index": 20, + "virtual_lines": [ + { + "bbox": [ + 108, + 430, + 503, + 461.0 + ], + "spans": [], + "index": 19 + }, + { + "bbox": [ + 108, + 461.0, + 503, + 492.0 + ], + "spans": [], + "index": 20 + }, + { + "bbox": [ + 108, + 492.0, + 503, + 523.0 + ], + "spans": [], + "index": 21 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 536, + 506, + 581 + ], + "group_id": 2, + "lines": [ + { + "bbox": [ + 105, + 535, + 506, + 549 + ], + "spans": [ + { + "bbox": [ + 105, + 535, + 506, + 549 + ], + "score": 1.0, + "content": "Figure 18: The label of each line denotes the kernel configuration of each 1D-CNN. 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Lines of similar color are 1D-CNNs with the same receptive field", + "type": "text" + } + ], + "index": 24 + }, + { + "bbox": [ + 106, + 569, + 293, + 581 + ], + "spans": [ + { + "bbox": [ + 106, + 569, + 293, + 581 + ], + "score": 1.0, + "content": "size, and they are also of similar performance.", + "type": "text" + } + ], + "index": 25 + } + ], + "index": 23.5 + } + ], + "index": 21.75 + }, + { + "type": "image", + "bbox": [ + 106, + 591, + 503, + 671 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 106, + 591, + 503, + 671 + ], + "group_id": 3, + "lines": [ + { + "bbox": [ + 106, + 591, + 503, + 671 + ], + "spans": [ + { + "bbox": [ + 106, + 591, + 503, + 671 + ], + "score": 0.827, + "type": "image", + "image_path": "718d3534b189c896e844b279b461eda926698493e0d5cea8fef659578e7b0d02.jpg" + } + ] + } + ], + "index": 27, + "virtual_lines": [ + { + "bbox": [ + 106, + 591, + 503, + 617.6666666666666 + ], + "spans": [], + "index": 26 + }, + { + "bbox": [ + 106, + 617.6666666666666, + 503, + 644.3333333333333 + ], + "spans": [], + "index": 27 + }, + { + "bbox": [ + 106, + 644.3333333333333, + 503, + 670.9999999999999 + ], + "spans": [], + "index": 28 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 106, + 684, + 505, + 729 + ], + "group_id": 3, + "lines": [ + { + "bbox": [ + 106, + 684, + 505, + 696 + ], + "spans": [ + { + "bbox": [ + 106, + 684, + 505, + 696 + ], + "score": 1.0, + "content": "Figure 19: Purple color in those images are the zero mask and yellow denotes the location where", + "type": "text" + } + ], + "index": 29 + }, + { + "bbox": [ + 104, + 694, + 505, + 708 + ], + "spans": [ + { + "bbox": [ + 104, + 694, + 505, + 708 + ], + "score": 1.0, + "content": "has the ability to hold weight. Left: Convolution layers in of OS-block can be calculated parallelly,", + "type": "text" + } + ], + "index": 30 + }, + { + "bbox": [ + 106, + 707, + 505, + 718 + ], + "spans": [ + { + "bbox": [ + 106, + 707, + 505, + 718 + ], + "score": 1.0, + "content": "thus, each layer can be viewed as one convolutional layer with zero masks.(s) Right: layers in the", + "type": "text" + } + ], + "index": 31 + }, + { + "bbox": [ + 105, + 716, + 282, + 730 + ], + "spans": [ + { + "bbox": [ + 105, + 716, + 282, + 730 + ], + "score": 1.0, + "content": "OS-block can work with the dilation design", + "type": "text" + } + ], + "index": 32 + } + ], + "index": 30.5 + } + ], + "index": 28.75 + } + ] + }, + { + "preproc_blocks": [ + { + "type": "title", + "bbox": [ + 113, + 83, + 401, + 93 + ], + "lines": [ + { + "bbox": [ + 110, + 82, + 403, + 95 + ], + "spans": [ + { + "bbox": [ + 110, + 82, + 403, + 95 + ], + "score": 1.0, + "content": "A.6 EXPERIMENT RESULT OF OS-BLOCK WITH OTHER STRUCTURES", + "type": "text" + } + ], + "index": 0 + } + ], + "index": 0 + }, + { + "type": "text", + "bbox": [ + 107, + 102, + 505, + 147 + ], + "lines": [ + { + "bbox": [ + 106, + 102, + 506, + 115 + ], + "spans": [ + { + "bbox": [ + 106, + 102, + 506, + 115 + ], + "score": 1.0, + "content": "The Figure 20 and Figure 21 show that applied OS-block with residual connection, ensemble, and", + "type": "text" + } + ], + "index": 1 + }, + { + "bbox": [ + 106, + 114, + 505, + 126 + ], + "spans": [ + { + "bbox": [ + 106, + 114, + 505, + 126 + ], + "score": 1.0, + "content": "multi-channel architectures (individually or together) could further improve the performance. The", + "type": "text" + } + ], + "index": 2 + }, + { + "bbox": [ + 106, + 125, + 505, + 137 + ], + "spans": [ + { + "bbox": [ + 106, + 125, + 505, + 137 + ], + "score": 1.0, + "content": "evaluation was on both UCR 85 and UEA 30 archives which contain datasets from different domains", + "type": "text" + } + ], + "index": 3 + }, + { + "bbox": [ + 106, + 136, + 446, + 148 + ], + "spans": [ + { + "bbox": [ + 106, + 136, + 446, + 148 + ], + "score": 1.0, + "content": "such as electrical devices analysis, Spectrum analysis, traffic analysis, EEG analysis.", + "type": "text" + } + ], + "index": 4 + } + ], + "index": 2.5 + }, + { + "type": "image", + "bbox": [ + 108, + 166, + 504, + 223 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 108, + 166, + 504, + 223 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 108, + 166, + 504, + 223 + ], + "spans": [ + { + "bbox": [ + 108, + 166, + 504, + 223 + ], + "score": 0.947, + "type": "image", + "image_path": "6d21c94fe3f81ca4e6379dbbfbc9cf3884e458ad896c38e24586427e400e98d5.jpg" + } + ] + } + ], + "index": 6, + "virtual_lines": [ + { + "bbox": [ + 108, + 166, + 504, + 185.0 + ], + "spans": [], + "index": 5 + }, + { + "bbox": [ + 108, + 185.0, + 504, + 204.0 + ], + "spans": [], + "index": 6 + }, + { + "bbox": [ + 108, + 204.0, + 504, + 223.0 + ], + "spans": [], + "index": 7 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 107, + 237, + 505, + 260 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 105, + 236, + 505, + 251 + ], + "spans": [ + { + "bbox": [ + 105, + 236, + 505, + 251 + ], + "score": 1.0, + "content": "Figure 20: Using the OS-block with residual connection and ensemble (individually or together)", + "type": "text" + } + ], + "index": 8 + }, + { + "bbox": [ + 106, + 249, + 234, + 261 + ], + "spans": [ + { + "bbox": [ + 106, + 249, + 234, + 261 + ], + "score": 1.0, + "content": "could increase the performance", + "type": "text" + } + ], + "index": 9 + } + ], + "index": 8.5 + } + ], + "index": 7.25 + }, + { + "type": "image", + "bbox": [ + 110, + 287, + 503, + 364 + ], + "blocks": [ + { + "type": "image_body", + "bbox": [ + 110, + 287, + 503, + 364 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 110, + 287, + 503, + 364 + ], + "spans": [ + { + "bbox": [ + 110, + 287, + 503, + 364 + ], + "score": 0.949, + "type": "image", + "image_path": "d40bd168df3705d61c3518f7eedc78faa78ebabd1f046b9dde65f12a6a7b044f.jpg" + } + ] + } + ], + "index": 11, + "virtual_lines": [ + { + "bbox": [ + 110, + 287, + 503, + 312.6666666666667 + ], + "spans": [], + "index": 10 + }, + { + "bbox": [ + 110, + 312.6666666666667, + 503, + 338.33333333333337 + ], + "spans": [], + "index": 11 + }, + { + "bbox": [ + 110, + 338.33333333333337, + 503, + 364.00000000000006 + ], + "spans": [], + "index": 12 + } + ] + }, + { + "type": "image_caption", + "bbox": [ + 112, + 378, + 496, + 390 + ], + "group_id": 1, + "lines": [ + { + "bbox": [ + 113, + 376, + 497, + 393 + ], + "spans": [ + { + "bbox": [ + 113, + 376, + 497, + 393 + ], + "score": 1.0, + "content": "Figure 21: Using the multi-channel architecture with OS-block could improve the performance", + "type": "text" + } + ], + "index": 13 + } + ], + "index": 13 + } + ], + "index": 12.0 + }, + { + "type": "text", + "bbox": [ + 107, + 408, + 342, + 420 + ], + "lines": [ + { + "bbox": [ + 106, + 408, + 343, + 421 + ], + "spans": [ + { + "bbox": [ + 106, + 408, + 343, + 421 + ], + "score": 1.0, + "content": "A.7 COMPARE THE OS-BLOCK WITH OTHER DESIGNS", + "type": "text" + } + ], + "index": 14 + } + ], + "index": 14 + }, + { + "type": "text", + "bbox": [ + 107, + 446, + 505, + 491 + ], + "lines": [ + { + "bbox": [ + 105, + 446, + 505, + 459 + ], + "spans": [ + { + "bbox": [ + 105, + 446, + 505, + 459 + ], + "score": 1.0, + "content": "Mathematically, finding the optimal kernel configuration is challenging, for it is a constrained com-", + "type": "text" + } + ], + "index": 15 + }, + { + "bbox": [ + 105, + 457, + 505, + 470 + ], + "spans": [ + { + "bbox": [ + 105, + 457, + 505, + 470 + ], + "score": 1.0, + "content": "binatorial optimization searching for the best configuration among an exponential number of can-", + "type": "text" + } + ], + "index": 16 + }, + { + "bbox": [ + 105, + 468, + 505, + 481 + ], + "spans": [ + { + "bbox": [ + 105, + 468, + 505, + 481 + ], + "score": 1.0, + "content": "didates. Our contribution is a simple and effective model design that does not need to solve the", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 480, + 499, + 491 + ], + "spans": [ + { + "bbox": [ + 105, + 480, + 499, + 491 + ], + "score": 1.0, + "content": "complex optimization problems and achieves state-of-the-art performance on several benchmarks.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 16.5 + }, + { + "type": "text", + "bbox": [ + 106, + 496, + 505, + 563 + ], + "lines": [ + { + "bbox": [ + 106, + 496, + 506, + 509 + ], + "spans": [ + { + "bbox": [ + 106, + 496, + 506, + 509 + ], + "score": 1.0, + "content": "From the model size perspective, using prime numbers is more efficient than using even numbers or", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 506, + 506, + 520 + ], + "spans": [ + { + "bbox": [ + 105, + 506, + 506, + 520 + ], + "score": 1.0, + "content": "odd numbers. To be specific, to cover RF of range r, the model size complexity of using prime size", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 517, + 506, + 531 + ], + "spans": [ + { + "bbox": [ + 105, + 517, + 148, + 531 + ], + "score": 1.0, + "content": "kernels is", + "type": "text" + }, + { + "bbox": [ + 149, + 518, + 204, + 531 + ], + "score": 0.93, + "content": "O ( r ^ { 2 } / l o g ( \\dot { r } ) )", + "type": "inline_equation" + }, + { + "bbox": [ + 205, + 517, + 506, + 531 + ], + "score": 1.0, + "content": ". On the other hand, no matter we use even number pairs or odd number", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 528, + 505, + 542 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 457, + 542 + ], + "score": 1.0, + "content": "pairs, kernel sizes in each layer, the model size complexity of using the sequence is", + "type": "text" + }, + { + "bbox": [ + 458, + 529, + 483, + 541 + ], + "score": 0.92, + "content": "O ( r ^ { 2 } )", + "type": "inline_equation" + }, + { + "bbox": [ + 484, + 528, + 505, + 542 + ], + "score": 1.0, + "content": ". As", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 540, + 505, + 552 + ], + "spans": [ + { + "bbox": [ + 106, + 540, + 505, + 552 + ], + "score": 1.0, + "content": "Table 2 shows, compared with using odd number pairs or even numbers pairs prime numbers can", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 552, + 319, + 563 + ], + "spans": [ + { + "bbox": [ + 106, + 552, + 319, + 563 + ], + "score": 1.0, + "content": "achieve similar performance in a smaller model size.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 21.5 + }, + { + "type": "table", + "bbox": [ + 109, + 573, + 504, + 640 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 109, + 573, + 504, + 640 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 109, + 573, + 504, + 640 + ], + "spans": [ + { + "bbox": [ + 109, + 573, + 504, + 640 + ], + "score": 0.262, + "html": "
Number of parameters
Channel numberRF rangePrime numbers (Ours)odd numberseven numbers
161 to 45304k507k491k
321 to 451,203 k2,009k1,948k
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Our contribution is a simple and effective model design that does not need to solve the", + "type": "text" + } + ], + "index": 17 + }, + { + "bbox": [ + 105, + 480, + 499, + 491 + ], + "spans": [ + { + "bbox": [ + 105, + 480, + 499, + 491 + ], + "score": 1.0, + "content": "complex optimization problems and achieves state-of-the-art performance on several benchmarks.", + "type": "text" + } + ], + "index": 18 + } + ], + "index": 16.5, + "bbox_fs": [ + 105, + 446, + 505, + 491 + ] + }, + { + "type": "text", + "bbox": [ + 106, + 496, + 505, + 563 + ], + "lines": [ + { + "bbox": [ + 106, + 496, + 506, + 509 + ], + "spans": [ + { + "bbox": [ + 106, + 496, + 506, + 509 + ], + "score": 1.0, + "content": "From the model size perspective, using prime numbers is more efficient than using even numbers or", + "type": "text" + } + ], + "index": 19 + }, + { + "bbox": [ + 105, + 506, + 506, + 520 + ], + "spans": [ + { + "bbox": [ + 105, + 506, + 506, + 520 + ], + "score": 1.0, + "content": "odd numbers. To be specific, to cover RF of range r, the model size complexity of using prime size", + "type": "text" + } + ], + "index": 20 + }, + { + "bbox": [ + 105, + 517, + 506, + 531 + ], + "spans": [ + { + "bbox": [ + 105, + 517, + 148, + 531 + ], + "score": 1.0, + "content": "kernels is", + "type": "text" + }, + { + "bbox": [ + 149, + 518, + 204, + 531 + ], + "score": 0.93, + "content": "O ( r ^ { 2 } / l o g ( \\dot { r } ) )", + "type": "inline_equation" + }, + { + "bbox": [ + 205, + 517, + 506, + 531 + ], + "score": 1.0, + "content": ". On the other hand, no matter we use even number pairs or odd number", + "type": "text" + } + ], + "index": 21 + }, + { + "bbox": [ + 105, + 528, + 505, + 542 + ], + "spans": [ + { + "bbox": [ + 105, + 528, + 457, + 542 + ], + "score": 1.0, + "content": "pairs, kernel sizes in each layer, the model size complexity of using the sequence is", + "type": "text" + }, + { + "bbox": [ + 458, + 529, + 483, + 541 + ], + "score": 0.92, + "content": "O ( r ^ { 2 } )", + "type": "inline_equation" + }, + { + "bbox": [ + 484, + 528, + 505, + 542 + ], + "score": 1.0, + "content": ". As", + "type": "text" + } + ], + "index": 22 + }, + { + "bbox": [ + 106, + 540, + 505, + 552 + ], + "spans": [ + { + "bbox": [ + 106, + 540, + 505, + 552 + ], + "score": 1.0, + "content": "Table 2 shows, compared with using odd number pairs or even numbers pairs prime numbers can", + "type": "text" + } + ], + "index": 23 + }, + { + "bbox": [ + 106, + 552, + 319, + 563 + ], + "spans": [ + { + "bbox": [ + 106, + 552, + 319, + 563 + ], + "score": 1.0, + "content": "achieve similar performance in a smaller model size.", + "type": "text" + } + ], + "index": 24 + } + ], + "index": 21.5, + "bbox_fs": [ + 105, + 496, + 506, + 563 + ] + }, + { + "type": "table", + "bbox": [ + 109, + 573, + 504, + 640 + ], + "blocks": [ + { + "type": "table_body", + "bbox": [ + 109, + 573, + 504, + 640 + ], + "group_id": 0, + "lines": [ + { + "bbox": [ + 109, + 573, + 504, + 640 + ], + "spans": [ + { + "bbox": [ + 109, + 573, + 504, + 640 + ], + "score": 0.262, + "html": "
Number of parameters
Channel numberRF rangePrime numbers (Ours)odd numberseven numbers
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Channel numberRF rangePrime numbers (Ours)odd numberseven numbers
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321 to 450.78450.77830.7725
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