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They can be used", "type": "text" } ], "index": 4 }, { "bbox": [ 105, 243, 506, 257 ], "spans": [ { "bbox": [ 105, 243, 506, 257 ], "score": 1.0, "content": "for various downstream applications, such as continual learning and membership inference defense.", "type": "text" } ], "index": 5 } ], "index": 4 } ], "index": 2.5 }, { "type": "text", "bbox": [ 107, 279, 505, 357 ], "lines": [ { "bbox": [ 105, 279, 507, 293 ], "spans": [ { "bbox": [ 105, 279, 507, 293 ], "score": 1.0, "content": "huge compute and memory requirement [14], training instability [15, 16], and truncation bias [17].", "type": "text" } ], "index": 6 }, { "bbox": [ 105, 290, 506, 303 ], "spans": [ { "bbox": [ 105, 290, 506, 303 ], "score": 1.0, "content": "To avoid unrolled optimization, surrogate objectives are used to derive the meta-gradient, such", "type": "text" } ], "index": 7 }, { "bbox": [ 105, 301, 506, 315 ], "spans": [ { "bbox": [ 105, 301, 506, 315 ], "score": 1.0, "content": "as gradient matching [5, 7, 18], feature alignment [8, 19], and training trajectory matching [20].", "type": "text" } ], "index": 8 }, { "bbox": [ 105, 312, 505, 325 ], "spans": [ { "bbox": [ 105, 312, 505, 325 ], "score": 1.0, "content": "Nevertheless, a surrogate objective may introduce its own bias [19], and thus, may not accurately", "type": "text" } ], "index": 9 }, { "bbox": [ 105, 323, 505, 336 ], "spans": [ { "bbox": [ 105, 323, 505, 336 ], "score": 1.0, "content": "reflect the true objective. 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Meanwhile,", "type": "text" } ], "index": 15 }, { "bbox": [ 106, 393, 506, 407 ], "spans": [ { "bbox": [ 106, 393, 506, 407 ], "score": 1.0, "content": "the model can also overfit the distilled data during training, which is the most common cause of", "type": "text" } ], "index": 16 }, { "bbox": [ 106, 405, 505, 416 ], "spans": [ { "bbox": [ 106, 405, 505, 416 ], "score": 1.0, "content": "overfitting when we train on a small dataset. All these kinds of overfitting impose difficulties on the", "type": "text" } ], "index": 17 }, { "bbox": [ 106, 417, 321, 428 ], "spans": [ { "bbox": [ 106, 417, 321, 428 ], "score": 1.0, "content": "training and general-purpose use of the distilled data.", "type": "text" } ], "index": 18 } ], "index": 15.5 }, { "type": "text", "bbox": [ 107, 433, 505, 564 ], "lines": [ { "bbox": [ 106, 433, 505, 444 ], "spans": [ { "bbox": [ 106, 433, 505, 444 ], "score": 1.0, "content": "We propose an efficient meta-gradient computation method and a “model pool” to address the", "type": "text" } ], "index": 19 }, { "bbox": [ 106, 443, 505, 455 ], "spans": [ { "bbox": [ 106, 443, 505, 455 ], "score": 1.0, "content": "overfitting problems. The bottleneck in meta-gradient computation arises due to the complexity of", "type": "text" } ], "index": 20 }, { "bbox": [ 106, 455, 506, 467 ], "spans": [ { "bbox": [ 106, 455, 506, 467 ], "score": 1.0, "content": "inner optimization, as we need to know how the inner parameters vary with the outer parameters [24].", "type": "text" } ], "index": 21 }, { "bbox": [ 106, 465, 506, 478 ], "spans": [ { "bbox": [ 106, 465, 506, 478 ], "score": 1.0, "content": "However, the inner optimization can be pretty simple if we only train the last layer of a neural network", "type": "text" } ], "index": 22 }, { "bbox": [ 106, 477, 505, 488 ], "spans": [ { "bbox": [ 106, 477, 505, 488 ], "score": 1.0, "content": "to convergence while keeping the feature extractor fixed. In this case, computing the prediction on the", "type": "text" } ], "index": 23 }, { "bbox": [ 105, 487, 505, 500 ], "spans": [ { "bbox": [ 105, 487, 505, 500 ], "score": 1.0, "content": "real data using the model trained on the distilled data can be expressed as a kernel ridge regression", "type": "text" } ], "index": 24 }, { "bbox": [ 105, 497, 505, 511 ], "spans": [ { "bbox": [ 105, 497, 505, 511 ], "score": 1.0, "content": "(KRR) with respect to the conjugate kernel [25]. Hence, computing the meta-gradient is simply", "type": "text" } ], "index": 25 }, { "bbox": [ 105, 508, 506, 523 ], "spans": [ { "bbox": [ 105, 508, 506, 523 ], "score": 1.0, "content": "back-propagating through the kernel and a fixed feature extractor. To alleviate overfitting, we propose", "type": "text" } ], "index": 26 }, { "bbox": [ 105, 519, 506, 533 ], "spans": [ { "bbox": [ 105, 519, 506, 533 ], "score": 1.0, "content": "to maintain a diverse pool of models instead of periodically training and resetting a single model as in", "type": "text" } ], "index": 27 }, { "bbox": [ 105, 530, 506, 543 ], "spans": [ { "bbox": [ 105, 530, 506, 543 ], "score": 1.0, "content": "prior work [7, 13, 18]. Intuitively, our algorithm targets the following question: what is the best data", "type": "text" } ], "index": 28 }, { "bbox": [ 106, 542, 505, 553 ], "spans": [ { "bbox": [ 106, 542, 505, 553 ], "score": 1.0, "content": "to train the linear classifier given the current feature extractor? 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Our method, named neural Feature", "type": "text" } ], "index": 32 }, { "bbox": [ 141, 601, 506, 614 ], "spans": [ { "bbox": [ 141, 601, 506, 614 ], "score": 1.0, "content": "Regression with Pooling (FRePo), achieves state-of-the-art results on various benchmark", "type": "text" } ], "index": 33 }, { "bbox": [ 142, 613, 506, 625 ], "spans": [ { "bbox": [ 142, 613, 202, 625 ], "score": 1.0, "content": "datasets with a", "type": "text" }, { "bbox": [ 203, 613, 223, 623 ], "score": 0.64, "content": "1 0 0 \\mathrm { x }", "type": "inline_equation" }, { "bbox": [ 224, 613, 350, 625 ], "score": 1.0, "content": "reduction in training time and a", "type": "text" }, { "bbox": [ 350, 613, 366, 623 ], "score": 0.39, "content": "1 0 \\mathrm { x }", "type": "inline_equation" }, { "bbox": [ 366, 613, 506, 625 ], "score": 1.0, "content": "reduction in GPU memory require-", "type": "text" } ], "index": 34 }, { "bbox": [ 142, 624, 499, 636 ], "spans": [ { "bbox": [ 142, 624, 499, 636 ], "score": 1.0, "content": "ment. Our distilled data looks real (Figure 1) and transfers well to different architectures.", "type": "text" } ], "index": 35 }, { "bbox": [ 140, 641, 505, 654 ], "spans": [ { "bbox": [ 140, 641, 505, 654 ], "score": 1.0, "content": "We show that FRePo scales well to datasets with high-resolution images or complex label", "type": "text" } ], "index": 36 }, { "bbox": [ 141, 652, 507, 666 ], "spans": [ { "bbox": [ 141, 652, 216, 666 ], "score": 1.0, "content": "space. We achieve", "type": "text" }, { "bbox": [ 216, 653, 238, 663 ], "score": 0.86, "content": "7 . 5 \\%", "type": "inline_equation" }, { "bbox": [ 238, 652, 507, 666 ], "score": 1.0, "content": "top1 accuracy on ImageNet-1K [26] using only one image per class.", "type": "text" } ], "index": 37 }, { "bbox": [ 141, 663, 505, 676 ], "spans": [ { "bbox": [ 141, 663, 273, 676 ], "score": 1.0, "content": "The same classifier obtains only", "type": "text" }, { "bbox": [ 274, 663, 296, 674 ], "score": 0.86, "content": "1 . 1 \\%", "type": "inline_equation" }, { "bbox": [ 296, 663, 505, 676 ], "score": 1.0, "content": "accuracy from a random subset of real images. The", "type": "text" } ], "index": 38 }, { "bbox": [ 141, 674, 492, 688 ], "spans": [ { "bbox": [ 141, 674, 492, 688 ], "score": 1.0, "content": "previous methods struggle in this task due to large memory and compute requirements.", "type": "text" } ], "index": 39 }, { "bbox": [ 136, 692, 505, 704 ], "spans": [ { "bbox": [ 136, 692, 505, 704 ], "score": 1.0, "content": "• We demonstrate that high-quality distilled data can significantly improve various downstream", "type": "text" } ], "index": 40 }, { "bbox": [ 142, 703, 446, 716 ], "spans": [ { "bbox": [ 142, 703, 446, 716 ], "score": 1.0, "content": "applications, such as continual learning and membership inference defense.", "type": "text" } ], "index": 41 } ], "index": 36.5 } ], "page_idx": 1, "page_size": [ 612, 792 ], "discarded_blocks": [ { "type": "discarded", "bbox": [ 302, 742, 308, 750 ], "lines": [ { "bbox": [ 302, 741, 310, 753 ], "spans": [ { "bbox": [ 302, 741, 310, 753 ], "score": 1.0, "content": "", "type": "text", "height": 12, "width": 8 } ] } ] } ], "para_blocks": [ { "type": "image", "bbox": [ 109, 70, 501, 216 ], "blocks": [ { "type": "image_body", "bbox": [ 109, 70, 501, 216 ], "group_id": 0, "lines": [ { "bbox": [ 109, 70, 501, 216 ], "spans": [ { "bbox": [ 109, 70, 501, 216 ], "score": 0.972, "type": "image", "image_path": "99c51e47398cb446d8e74bd29e225e4ce9dc4051310f93f7693b478569789644.jpg" } ] } ], "index": 1, "virtual_lines": [ { "bbox": [ 109, 70, 501, 118.66666666666666 ], "spans": [], "index": 0 }, { "bbox": [ 109, 118.66666666666666, 501, 167.33333333333331 ], "spans": [], "index": 1 }, { "bbox": [ 109, 167.33333333333331, 501, 215.99999999999997 ], "spans": [], "index": 2 } ] }, { "type": "image_caption", "bbox": [ 106, 222, 504, 255 ], "group_id": 0, "lines": [ { "bbox": [ 106, 221, 504, 235 ], "spans": [ { "bbox": [ 106, 221, 276, 235 ], "score": 1.0, "content": "Figure 1: Example distilled images from", "type": "text" }, { "bbox": [ 276, 222, 303, 232 ], "score": 0.67, "content": "3 2 \\mathbf { x } 3 2", "type": "inline_equation" }, { "bbox": [ 304, 221, 467, 235 ], "score": 1.0, "content": "CIFAR100, 64x64 Tiny ImageNet, and", "type": "text" }, { "bbox": [ 468, 222, 504, 232 ], "score": 0.47, "content": "1 2 8 \\mathrm { x } 1 2 8", "type": "inline_equation" } ], "index": 3 }, { "bbox": [ 106, 233, 505, 245 ], "spans": [ { "bbox": [ 106, 233, 505, 245 ], "score": 1.0, "content": "ImageNet Subset. 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They can be used", "type": "text" } ], "index": 4 }, { "bbox": [ 105, 243, 506, 257 ], "spans": [ { "bbox": [ 105, 243, 506, 257 ], "score": 1.0, "content": "for various downstream applications, such as continual learning and membership inference defense.", "type": "text" } ], "index": 5 } ], "index": 4 } ], "index": 2.5 }, { "type": "text", "bbox": [ 107, 279, 505, 357 ], "lines": [], "index": 9, "bbox_fs": [ 105, 279, 507, 358 ], "lines_deleted": true }, { "type": "text", "bbox": [ 107, 361, 505, 428 ], "lines": [ { "bbox": [ 105, 360, 507, 375 ], "spans": [ { "bbox": [ 105, 360, 507, 375 ], "score": 1.0, "content": "Even with an accurate meta-gradient, dataset distillation still suffers from various types of overfitting.", "type": "text" } ], "index": 13 }, { "bbox": [ 105, 372, 506, 385 ], "spans": [ { "bbox": [ 105, 372, 506, 385 ], "score": 1.0, "content": "For instance, the distilled data can easily overfit to a particular learning algorithm [4, 13, 20], a", "type": "text" } ], "index": 14 }, { "bbox": [ 105, 384, 506, 396 ], "spans": [ { "bbox": [ 105, 384, 506, 396 ], "score": 1.0, "content": "certain stage of optimization [13, 19], or a certain network architecture [5, 7, 20, 22, 23]. Meanwhile,", "type": "text" } ], "index": 15 }, { "bbox": [ 106, 393, 506, 407 ], "spans": [ { "bbox": [ 106, 393, 506, 407 ], "score": 1.0, "content": "the model can also overfit the distilled data during training, which is the most common cause of", "type": "text" } ], "index": 16 }, { "bbox": [ 106, 405, 505, 416 ], "spans": [ { "bbox": [ 106, 405, 505, 416 ], "score": 1.0, "content": "overfitting when we train on a small dataset. All these kinds of overfitting impose difficulties on the", "type": "text" } ], "index": 17 }, { "bbox": [ 106, 417, 321, 428 ], "spans": [ { "bbox": [ 106, 417, 321, 428 ], "score": 1.0, "content": "training and general-purpose use of the distilled data.", "type": "text" } ], "index": 18 } ], "index": 15.5, "bbox_fs": [ 105, 360, 507, 428 ] }, { "type": "text", "bbox": [ 107, 433, 505, 564 ], "lines": [ { "bbox": [ 106, 433, 505, 444 ], "spans": [ { "bbox": [ 106, 433, 505, 444 ], "score": 1.0, "content": "We propose an efficient meta-gradient computation method and a “model pool” to address the", "type": "text" } ], "index": 19 }, { "bbox": [ 106, 443, 505, 455 ], "spans": [ { "bbox": [ 106, 443, 505, 455 ], "score": 1.0, "content": "overfitting problems. The bottleneck in meta-gradient computation arises due to the complexity of", "type": "text" } ], "index": 20 }, { "bbox": [ 106, 455, 506, 467 ], "spans": [ { "bbox": [ 106, 455, 506, 467 ], "score": 1.0, "content": "inner optimization, as we need to know how the inner parameters vary with the outer parameters [24].", "type": "text" } ], "index": 21 }, { "bbox": [ 106, 465, 506, 478 ], "spans": [ { "bbox": [ 106, 465, 506, 478 ], "score": 1.0, "content": "However, the inner optimization can be pretty simple if we only train the last layer of a neural network", "type": "text" } ], "index": 22 }, { "bbox": [ 106, 477, 505, 488 ], "spans": [ { "bbox": [ 106, 477, 505, 488 ], "score": 1.0, "content": "to convergence while keeping the feature extractor fixed. 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To alleviate overfitting, we propose", "type": "text" } ], "index": 26 }, { "bbox": [ 105, 519, 506, 533 ], "spans": [ { "bbox": [ 105, 519, 506, 533 ], "score": 1.0, "content": "to maintain a diverse pool of models instead of periodically training and resetting a single model as in", "type": "text" } ], "index": 27 }, { "bbox": [ 105, 530, 506, 543 ], "spans": [ { "bbox": [ 105, 530, 506, 543 ], "score": 1.0, "content": "prior work [7, 13, 18]. Intuitively, our algorithm targets the following question: what is the best data", "type": "text" } ], "index": 28 }, { "bbox": [ 106, 542, 505, 553 ], "spans": [ { "bbox": [ 106, 542, 505, 553 ], "score": 1.0, "content": "to train the linear classifier given the current feature extractor? 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Our distilled data looks real (Figure 1) and transfers well to different architectures.", "type": "text" } ], "index": 35 }, { "bbox": [ 140, 641, 505, 654 ], "spans": [ { "bbox": [ 140, 641, 505, 654 ], "score": 1.0, "content": "We show that FRePo scales well to datasets with high-resolution images or complex label", "type": "text" } ], "index": 36 }, { "bbox": [ 141, 652, 507, 666 ], "spans": [ { "bbox": [ 141, 652, 216, 666 ], "score": 1.0, "content": "space. We achieve", "type": "text" }, { "bbox": [ 216, 653, 238, 663 ], "score": 0.86, "content": "7 . 5 \\%", "type": "inline_equation" }, { "bbox": [ 238, 652, 507, 666 ], "score": 1.0, "content": "top1 accuracy on ImageNet-1K [26] using only one image per class.", "type": "text" } ], "index": 37 }, { "bbox": [ 141, 663, 505, 676 ], "spans": [ { "bbox": [ 141, 663, 273, 676 ], "score": 1.0, "content": "The same classifier obtains only", "type": "text" }, { "bbox": [ 274, 663, 296, 674 ], "score": 0.86, "content": "1 . 1 \\%", "type": "inline_equation" }, { "bbox": [ 296, 663, 505, 676 ], "score": 1.0, "content": "accuracy from a random subset of real images. The", "type": "text" } ], "index": 38 }, { "bbox": [ 141, 674, 492, 688 ], "spans": [ { "bbox": [ 141, 674, 492, 688 ], "score": 1.0, "content": "previous methods struggle in this task due to large memory and compute requirements.", "type": "text" } ], "index": 39 }, { "bbox": [ 136, 692, 505, 704 ], "spans": [ { "bbox": [ 136, 692, 505, 704 ], "score": 1.0, "content": "• We demonstrate that high-quality distilled data can significantly improve various downstream", "type": "text" } ], "index": 40 }, { "bbox": [ 142, 703, 446, 716 ], "spans": [ { "bbox": [ 142, 703, 446, 716 ], "score": 1.0, "content": "applications, such as continual learning and membership inference defense.", "type": "text" } ], "index": 41 } ], "index": 36.5, "bbox_fs": [ 133, 590, 507, 716 ] } ] }, { "preproc_blocks": [ { "type": "image", "bbox": [ 106, 70, 506, 160 ], "blocks": [ { "type": "image_body", "bbox": [ 106, 70, 506, 160 ], "group_id": 0, "lines": [ { "bbox": [ 106, 70, 506, 160 ], "spans": [ { "bbox": [ 106, 70, 506, 160 ], "score": 0.964, "type": "image", "image_path": "bd356bac9e8a26f60ac46a3e8c2299fdbc56eeb9580bd6cdb628ffbec6e98257.jpg" } ] } ], "index": 1, "virtual_lines": [ { "bbox": [ 106, 70, 506, 100.0 ], "spans": [], "index": 0 }, { "bbox": [ 106, 100.0, 506, 130.0 ], "spans": [], "index": 1 }, { "bbox": [ 106, 130.0, 506, 160.0 ], "spans": [], "index": 2 } ] }, { "type": "image_caption", "bbox": [ 106, 167, 506, 235 ], "group_id": 0, "lines": [ { "bbox": [ 105, 166, 506, 181 ], "spans": [ { "bbox": [ 105, 166, 362, 181 ], "score": 1.0, "content": "Figure 2: Comparison of FRePo and Unrolled Optimization.", "type": "text" }, { "bbox": [ 362, 168, 370, 178 ], "score": 0.44, "content": "S", "type": "inline_equation" }, { "bbox": [ 370, 166, 374, 181 ], "score": 1.0, "content": ",", "type": "text" }, { "bbox": [ 375, 168, 388, 178 ], "score": 0.73, "content": "X _ { s }", "type": "inline_equation" }, { "bbox": [ 388, 166, 392, 181 ], "score": 1.0, "content": ",", "type": "text" }, { "bbox": [ 393, 168, 404, 178 ], "score": 0.78, "content": "Y _ { s }", "type": "inline_equation" }, { "bbox": [ 404, 166, 506, 181 ], "score": 1.0, "content": "are the distilled dataset,", "type": "text" } ], "index": 3 }, { "bbox": [ 105, 177, 506, 193 ], "spans": [ { "bbox": [ 105, 177, 184, 193 ], "score": 1.0, "content": "images and labels.", "type": "text" }, { "bbox": [ 185, 180, 193, 190 ], "score": 0.74, "content": "\\mathcal { L }", "type": "inline_equation" }, { "bbox": [ 193, 177, 311, 193 ], "score": 1.0, "content": "is the meta-training loss and", "type": "text" }, { "bbox": [ 311, 178, 328, 190 ], "score": 0.85, "content": "\\dot { \\theta } ^ { ( k ) }", "type": "inline_equation" }, { "bbox": [ 328, 177, 331, 193 ], "score": 1.0, "content": ",", "type": "text" }, { "bbox": [ 332, 178, 349, 191 ], "score": 0.87, "content": "g ^ { ( k ) }", "type": "inline_equation" }, { "bbox": [ 350, 177, 506, 193 ], "score": 1.0, "content": "are the model parameter and gradient", "type": "text" } ], "index": 4 }, { "bbox": [ 103, 185, 508, 208 ], "spans": [ { "bbox": [ 103, 185, 135, 208 ], "score": 1.0, "content": "at step", "type": "text" }, { "bbox": [ 136, 191, 142, 201 ], "score": 0.58, "content": "k", "type": "inline_equation" }, { "bbox": [ 142, 185, 146, 208 ], "score": 1.0, "content": ".", "type": "text" }, { "bbox": [ 147, 190, 171, 203 ], "score": 0.89, "content": "f ( X )", "type": "inline_equation" }, { "bbox": [ 171, 185, 265, 208 ], "score": 1.0, "content": "is the feature for input", "type": "text" }, { "bbox": [ 265, 191, 275, 201 ], "score": 0.8, "content": "X", "type": "inline_equation" }, { "bbox": [ 276, 185, 294, 208 ], "score": 1.0, "content": "and", "type": "text" }, { "bbox": [ 294, 190, 324, 204 ], "score": 0.93, "content": "K _ { X _ { t } X _ { s } } ^ { \\theta }", "type": "inline_equation" }, { "bbox": [ 324, 185, 415, 208 ], "score": 1.0, "content": "is the Gram matrix of", "type": "text" }, { "bbox": [ 416, 191, 429, 201 ], "score": 0.89, "content": "X _ { t }", "type": "inline_equation" }, { "bbox": [ 429, 185, 447, 208 ], "score": 1.0, "content": "and", "type": "text" }, { "bbox": [ 447, 191, 461, 201 ], "score": 0.88, "content": "X _ { s }", "type": "inline_equation" }, { "bbox": [ 461, 185, 508, 208 ], "score": 1.0, "content": ". FRePo is", "type": "text" } ], "index": 5 }, { "bbox": [ 106, 201, 505, 214 ], "spans": [ { "bbox": [ 106, 201, 505, 214 ], "score": 1.0, "content": "analogous to 1-step TBPTT as it computes the meta-gradient at each step while performing the online", "type": "text" } ], "index": 6 }, { "bbox": [ 105, 211, 506, 225 ], "spans": [ { "bbox": [ 105, 211, 506, 225 ], "score": 1.0, "content": "model update. However, instead of backpropagating through the inner optimization, FRePo computes", "type": "text" } ], "index": 7 }, { "bbox": [ 106, 223, 333, 236 ], "spans": [ { "bbox": [ 106, 223, 333, 236 ], "score": 1.0, "content": "the meta-gradient through a kernel and feature extractor.", "type": "text" } ], "index": 8 } ], "index": 5.5 } ], "index": 3.25 }, { "type": "title", "bbox": [ 107, 253, 166, 266 ], "lines": [ { "bbox": [ 104, 251, 168, 269 ], "spans": [ { "bbox": [ 104, 251, 168, 269 ], "score": 1.0, "content": "2 Method", "type": "text" } ], "index": 9 } ], "index": 9 }, { "type": "title", "bbox": [ 107, 277, 317, 289 ], "lines": [ { "bbox": [ 105, 275, 318, 292 ], "spans": [ { "bbox": [ 105, 275, 318, 292 ], "score": 1.0, "content": "2.1 Dataset Distillation as Bi-level Optimization", "type": "text" } ], "index": 10 } ], "index": 10 }, { "type": "text", "bbox": [ 106, 296, 506, 399 ], "lines": [ { "bbox": [ 105, 295, 506, 312 ], "spans": [ { "bbox": [ 105, 295, 266, 312 ], "score": 1.0, "content": "Suppose we have a large labeled dataset", "type": "text" }, { "bbox": [ 266, 296, 403, 311 ], "score": 0.93, "content": "\\mathcal { T } = \\left\\{ \\left( \\mathbf { x } _ { 1 } , \\mathbf { y } _ { 1 } \\right) , \\dotsc , \\left( \\mathbf { x } _ { | T | } , \\mathbf { y } _ { | T | } \\right) \\right\\}", "type": "inline_equation" }, { "bbox": [ 404, 295, 425, 312 ], "score": 1.0, "content": "with", "type": "text" }, { "bbox": [ 425, 298, 439, 309 ], "score": 0.88, "content": "| \\tau |", "type": "inline_equation" }, { "bbox": [ 440, 295, 506, 312 ], "score": 1.0, "content": "image and label` ˘(", "type": "text" } ], "index": 11 }, { "bbox": [ 104, 309, 504, 326 ], "spans": [ { "bbox": [ 104, 309, 368, 326 ], "score": 1.0, "content": "pairs. Dataset distillation aims to learn a small synthetic dataset", "type": "text" }, { "bbox": [ 368, 309, 504, 324 ], "score": 0.9, "content": "\\mathcal { S } = \\left\\{ ( \\mathbf { x } _ { 1 } , \\mathbf { y } _ { 1 } ) , \\dotsc , \\left( \\mathbf { x } _ { | S | } , \\mathbf { y } _ { | S | } \\right) \\right\\}", "type": "inline_equation" } ], "index": 12 }, { "bbox": [ 105, 322, 506, 334 ], "spans": [ { "bbox": [ 105, 322, 278, 334 ], "score": 1.0, "content": "that preserves most of the information in", "type": "text" }, { "bbox": [ 278, 322, 288, 332 ], "score": 0.8, "content": "\\tau", "type": "inline_equation" }, { "bbox": [ 288, 322, 506, 334 ], "score": 1.0, "content": ". We train several neural networks parameterized by", "type": "text" } ], "index": 13 }, { "bbox": [ 107, 332, 506, 345 ], "spans": [ { "bbox": [ 107, 333, 113, 342 ], "score": 0.78, "content": "\\theta", "type": "inline_equation" }, { "bbox": [ 113, 332, 175, 345 ], "score": 1.0, "content": "on the dataset", "type": "text" }, { "bbox": [ 175, 333, 183, 342 ], "score": 0.8, "content": "s", "type": "inline_equation" }, { "bbox": [ 184, 332, 341, 345 ], "score": 1.0, "content": "and then compute the validation loss", "type": "text" }, { "bbox": [ 341, 332, 412, 344 ], "score": 0.92, "content": "\\mathcal { L } ( \\mathcal { A } l g \\left( \\theta , \\mathcal { S } \\right) , \\mathcal { T } )", "type": "inline_equation" }, { "bbox": [ 412, 332, 493, 345 ], "score": 1.0, "content": "on the real dataset", "type": "text" }, { "bbox": [ 493, 333, 502, 343 ], "score": 0.8, "content": "\\tau", "type": "inline_equation" }, { "bbox": [ 503, 332, 506, 345 ], "score": 1.0, "content": ",", "type": "text" } ], "index": 14 }, { "bbox": [ 105, 343, 506, 356 ], "spans": [ { "bbox": [ 105, 343, 133, 356 ], "score": 1.0, "content": "where", "type": "text" }, { "bbox": [ 134, 343, 176, 355 ], "score": 0.93, "content": "{ \\mathcal { A } } l g \\left( \\theta , S \\right)", "type": "inline_equation" }, { "bbox": [ 176, 343, 451, 356 ], "score": 1.0, "content": "is the neural network parameters optimized by a learning algorithm", "type": "text" }, { "bbox": [ 452, 344, 468, 354 ], "score": 0.85, "content": "\\mathcal { A } g", "type": "inline_equation" }, { "bbox": [ 469, 343, 506, 356 ], "score": 1.0, "content": "with the", "type": "text" } ], "index": 15 }, { "bbox": [ 105, 354, 506, 367 ], "spans": [ { "bbox": [ 105, 354, 187, 367 ], "score": 1.0, "content": "model initialization", "type": "text" }, { "bbox": [ 187, 355, 193, 364 ], "score": 0.77, "content": "\\theta", "type": "inline_equation" }, { "bbox": [ 194, 354, 276, 367 ], "score": 1.0, "content": "and distilled dataset", "type": "text" }, { "bbox": [ 276, 355, 284, 364 ], "score": 0.79, "content": "s", "type": "inline_equation" }, { "bbox": [ 285, 354, 416, 367 ], "score": 1.0, "content": "as its inputs. The validation loss", "type": "text" }, { "bbox": [ 416, 355, 487, 366 ], "score": 0.91, "content": "\\mathcal { L } ( \\mathcal { A } l g \\left( \\theta , S \\right) , \\mathcal { T } )", "type": "inline_equation" }, { "bbox": [ 488, 354, 506, 367 ], "score": 1.0, "content": "is a", "type": "text" } ], "index": 16 }, { "bbox": [ 104, 363, 506, 379 ], "spans": [ { "bbox": [ 104, 363, 506, 379 ], "score": 1.0, "content": "noisy objective with the stochasticity coming from random model initialization and inner learning", "type": "text" } ], "index": 17 }, { "bbox": [ 105, 375, 506, 389 ], "spans": [ { "bbox": [ 105, 375, 506, 389 ], "score": 1.0, "content": "algorithm. Thus, we are interested in minimizing the expected value of this loss, which we denote it", "type": "text" } ], "index": 18 }, { "bbox": [ 105, 387, 482, 400 ], "spans": [ { "bbox": [ 105, 387, 117, 400 ], "score": 1.0, "content": "as", "type": "text" }, { "bbox": [ 118, 387, 140, 399 ], "score": 0.92, "content": "F ( S )", "type": "inline_equation" }, { "bbox": [ 141, 387, 482, 400 ], "score": 1.0, "content": ". We formulate the dataset distillation as the following bi-level optimization problem.", "type": "text" } ], "index": 19 } ], "index": 15 }, { "type": "interline_equation", "bbox": [ 165, 403, 445, 440 ], "lines": [ { "bbox": [ 165, 403, 445, 440 ], "spans": [ { "bbox": [ 165, 403, 445, 440 ], "score": 0.93, "content": "\\overbrace { \\mathcal { S } ^ { * } : = \\mathop { \\mathrm { a r g m i n } } _ { \\mathcal { S } } F ( \\mathcal { S } ) } ^ { o u t e r - l e v e l } , \\mathrm { w h e r e } F ( \\mathcal { S } ) = \\mathbb { E } _ { \\theta \\sim P _ { \\theta } } \\biggl [ \\mathcal { L } \\Bigl ( \\overbrace { \\mathcal { A } l g \\left( \\theta , \\mathcal { S } \\right) } ^ { i n n e r - l e v e l } , \\ T \\Bigr ) \\biggr ] .", "type": "interline_equation", "image_path": "5d90a6e2a97898bb43c032413b0dda3e03ac154d8a7d9d7a921494e9f9e4b013.jpg" } ] } ], "index": 21, "virtual_lines": [ { "bbox": [ 165, 403, 445, 415.3333333333333 ], "spans": [], "index": 20 }, { "bbox": [ 165, 415.3333333333333, 445, 427.66666666666663 ], "spans": [], "index": 21 }, { "bbox": [ 165, 427.66666666666663, 445, 439.99999999999994 ], "spans": [], "index": 22 } ] }, { "type": "text", "bbox": [ 106, 442, 505, 531 ], "lines": [ { "bbox": [ 106, 443, 506, 455 ], "spans": [ { "bbox": [ 106, 443, 415, 455 ], "score": 1.0, "content": "In this bi-level setup, the outer loop optimizes the distilled data to minimize", "type": "text" }, { "bbox": [ 415, 443, 438, 455 ], "score": 0.91, "content": "F ( S )", "type": "inline_equation" }, { "bbox": [ 438, 443, 506, 455 ], "score": 1.0, "content": ", while the inner", "type": "text" } ], "index": 23 }, { "bbox": [ 106, 453, 505, 466 ], "spans": [ { "bbox": [ 106, 453, 339, 466 ], "score": 1.0, "content": "loop trains a neural network using the learning algorithm,", "type": "text" }, { "bbox": [ 340, 454, 357, 465 ], "score": 0.88, "content": "\\mathcal { A } g", "type": "inline_equation" }, { "bbox": [ 357, 453, 505, 466 ], "score": 1.0, "content": ", to minimize the training loss on the", "type": "text" } ], "index": 24 }, { "bbox": [ 105, 464, 506, 478 ], "spans": [ { "bbox": [ 105, 464, 160, 478 ], "score": 1.0, "content": "distilled data", "type": "text" }, { "bbox": [ 161, 465, 169, 475 ], "score": 0.77, "content": "s", "type": "inline_equation" }, { "bbox": [ 169, 464, 506, 478 ], "score": 1.0, "content": ". From the meta-learning perspective, the task is defined by the model initialization", "type": "text" } ], "index": 25 }, { "bbox": [ 107, 476, 505, 488 ], "spans": [ { "bbox": [ 107, 477, 113, 486 ], "score": 0.76, "content": "\\theta", "type": "inline_equation" }, { "bbox": [ 113, 476, 274, 488 ], "score": 1.0, "content": ", and we want to learn a meta-parameter", "type": "text" }, { "bbox": [ 275, 476, 283, 486 ], "score": 0.79, "content": "s", "type": "inline_equation" }, { "bbox": [ 283, 476, 505, 488 ], "score": 1.0, "content": "that generalizes well to different models sampled from", "type": "text" } ], "index": 26 }, { "bbox": [ 105, 486, 506, 499 ], "spans": [ { "bbox": [ 105, 486, 201, 499 ], "score": 1.0, "content": "the model distributions", "type": "text" }, { "bbox": [ 202, 487, 213, 498 ], "score": 0.88, "content": "P _ { \\theta }", "type": "inline_equation" }, { "bbox": [ 214, 486, 419, 499 ], "score": 1.0, "content": ". During learning, we optimize the meta-parameter", "type": "text" }, { "bbox": [ 420, 487, 428, 497 ], "score": 0.8, "content": "s", "type": "inline_equation" }, { "bbox": [ 428, 486, 506, 499 ], "score": 1.0, "content": "by minimizing the", "type": "text" } ], "index": 27 }, { "bbox": [ 105, 498, 505, 510 ], "spans": [ { "bbox": [ 105, 498, 180, 509 ], "score": 1.0, "content": "meta-training loss", "type": "text" }, { "bbox": [ 181, 498, 204, 510 ], "score": 0.92, "content": "F ( S )", "type": "inline_equation" }, { "bbox": [ 204, 498, 479, 509 ], "score": 1.0, "content": ". In contrast, at meta-test time, we train a new model from scratch on", "type": "text" }, { "bbox": [ 479, 498, 487, 507 ], "score": 0.8, "content": "s", "type": "inline_equation" }, { "bbox": [ 487, 498, 505, 509 ], "score": 1.0, "content": "and", "type": "text" } ], "index": 28 }, { "bbox": [ 105, 508, 505, 521 ], "spans": [ { "bbox": [ 105, 508, 505, 521 ], "score": 1.0, "content": "evaluate the trained model on a held-out real dataset. This meta-test performance reflects the quality", "type": "text" } ], "index": 29 }, { "bbox": [ 106, 519, 188, 531 ], "spans": [ { "bbox": [ 106, 519, 188, 531 ], "score": 1.0, "content": "of the distilled data.", "type": "text" } ], "index": 30 } ], "index": 26.5 }, { "type": "title", "bbox": [ 108, 542, 447, 555 ], "lines": [ { "bbox": [ 104, 541, 445, 558 ], "spans": [ { "bbox": [ 104, 541, 411, 558 ], "score": 1.0, "content": "2.2 Dataset Distillation using Neural Feature Regression with Pooling", "type": "text" }, { "bbox": [ 411, 543, 445, 554 ], "score": 0.25, "content": "\\mathbf { ( F R e P 0 ) }", "type": "inline_equation" } ], "index": 31 } ], "index": 31 }, { "type": "text", "bbox": [ 107, 563, 505, 641 ], "lines": [ { "bbox": [ 105, 563, 505, 577 ], "spans": [ { "bbox": [ 105, 563, 417, 577 ], "score": 1.0, "content": "The outer-level problem can be solved using gradient-based methods of the form", "type": "text" }, { "bbox": [ 418, 563, 501, 576 ], "score": 0.89, "content": "\\mathcal { S } \\gets \\mathcal { S } \\ – \\alpha \\nabla _ { \\mathcal { S } } F ( \\mathcal { S } )", "type": "inline_equation" }, { "bbox": [ 502, 563, 505, 577 ], "score": 1.0, "content": ",", "type": "text" } ], "index": 32 }, { "bbox": [ 105, 574, 506, 587 ], "spans": [ { "bbox": [ 105, 574, 134, 587 ], "score": 1.0, "content": "where", "type": "text" }, { "bbox": [ 134, 576, 142, 584 ], "score": 0.77, "content": "\\alpha", "type": "inline_equation" }, { "bbox": [ 142, 574, 330, 587 ], "score": 1.0, "content": "is the learning rate for the distilled data and", "type": "text" }, { "bbox": [ 330, 574, 368, 586 ], "score": 0.91, "content": "\\nabla _ { S } F ( S )", "type": "inline_equation" }, { "bbox": [ 369, 574, 506, 587 ], "score": 1.0, "content": "is the meta-gradient [27]. For a", "type": "text" } ], "index": 33 }, { "bbox": [ 105, 585, 505, 598 ], "spans": [ { "bbox": [ 105, 585, 176, 598 ], "score": 1.0, "content": "particular model", "type": "text" }, { "bbox": [ 177, 586, 183, 595 ], "score": 0.71, "content": "\\theta", "type": "inline_equation" }, { "bbox": [ 183, 585, 346, 598 ], "score": 1.0, "content": ", the meta-gradient can be expressed as", "type": "text" }, { "bbox": [ 346, 585, 433, 597 ], "score": 0.93, "content": "\\nabla _ { \\mathcal { S } } \\hat { \\mathcal { L } } \\left( \\mathcal { A } l g \\left( \\theta , \\mathcal { S } \\right) , \\mathcal { T } \\right)", "type": "inline_equation" }, { "bbox": [ 433, 585, 505, 598 ], "score": 1.0, "content": ". Computing this", "type": "text" } ], "index": 34 }, { "bbox": [ 105, 596, 505, 609 ], "spans": [ { "bbox": [ 105, 596, 387, 609 ], "score": 1.0, "content": "meta-gradient requires differentiating through inner optimization. If", "type": "text" }, { "bbox": [ 387, 597, 404, 608 ], "score": 0.83, "content": "\\mathcal { A } \\boldsymbol { { l } } _ { g }", "type": "inline_equation" }, { "bbox": [ 405, 596, 505, 609 ], "score": 1.0, "content": "is an iterative algorithm", "type": "text" } ], "index": 35 }, { "bbox": [ 105, 606, 506, 621 ], "spans": [ { "bbox": [ 105, 606, 506, 621 ], "score": 1.0, "content": "like gradient descent, then backpropagating through the unrolled computation graph [14] can be a", "type": "text" } ], "index": 36 }, { "bbox": [ 105, 617, 505, 632 ], "spans": [ { "bbox": [ 105, 617, 505, 632 ], "score": 1.0, "content": "solution. However, this type of unrolled optimization introduces significant computation and memory", "type": "text" } ], "index": 37 }, { "bbox": [ 105, 628, 451, 642 ], "spans": [ { "bbox": [ 105, 628, 451, 642 ], "score": 1.0, "content": "overhead, as the whole training trajectory needs to be stored in memory (Figure 2(b)).", "type": "text" } ], "index": 38 } ], "index": 35 }, { "type": "text", "bbox": [ 107, 645, 505, 722 ], "lines": [ { "bbox": [ 105, 644, 506, 658 ], "spans": [ { "bbox": [ 105, 644, 506, 658 ], "score": 1.0, "content": "Traditionally, these issues are alleviated with truncated backpropagation through time (TBPTT)", "type": "text" } ], "index": 39 }, { "bbox": [ 105, 655, 507, 670 ], "spans": [ { "bbox": [ 105, 655, 507, 670 ], "score": 1.0, "content": "[28–30]. Instead of backpropagating through an entire unrolled sequence, TBPTT performs backprop-", "type": "text" } ], "index": 40 }, { "bbox": [ 105, 667, 506, 680 ], "spans": [ { "bbox": [ 105, 667, 506, 680 ], "score": 1.0, "content": "agation for each subsequence separately. It is efficient because its time and memory complexity scale", "type": "text" } ], "index": 41 }, { "bbox": [ 105, 678, 505, 691 ], "spans": [ { "bbox": [ 105, 678, 505, 691 ], "score": 1.0, "content": "linearly with respect to the truncation steps. However, truncation may yield highly biased gradients", "type": "text" } ], "index": 42 }, { "bbox": [ 105, 687, 505, 703 ], "spans": [ { "bbox": [ 105, 687, 505, 703 ], "score": 1.0, "content": "that severely impact training. To mitigate this truncation bias [14], we consider training only the top", "type": "text" } ], "index": 43 }, { "bbox": [ 105, 700, 506, 712 ], "spans": [ { "bbox": [ 105, 700, 506, 712 ], "score": 1.0, "content": "layer of a network to convergence. The key insight is that the data helpful for training the output", "type": "text" } ], "index": 44 }, { "bbox": [ 105, 711, 505, 723 ], "spans": [ { "bbox": [ 105, 711, 505, 723 ], "score": 1.0, "content": "layer can also help train the whole network. Thus, we decompose the neural network into a feature", "type": "text" } ], "index": 45 } ], "index": 42 } ], "page_idx": 2, "page_size": [ 612, 792 ], "discarded_blocks": [ { "type": "discarded", "bbox": [ 302, 741, 309, 750 ], "lines": [ { "bbox": [ 301, 740, 310, 752 ], "spans": [ { "bbox": [ 301, 740, 310, 752 ], "score": 1.0, "content": "3", "type": "text" } ] } ] } ], "para_blocks": [ { "type": "image", "bbox": [ 106, 70, 506, 160 ], "blocks": [ { "type": "image_body", "bbox": [ 106, 70, 506, 160 ], "group_id": 0, "lines": [ { "bbox": [ 106, 70, 506, 160 ], "spans": [ { "bbox": [ 106, 70, 506, 160 ], "score": 0.964, "type": "image", "image_path": "bd356bac9e8a26f60ac46a3e8c2299fdbc56eeb9580bd6cdb628ffbec6e98257.jpg" } ] } ], "index": 1, "virtual_lines": [ { "bbox": [ 106, 70, 506, 100.0 ], "spans": [], "index": 0 }, { "bbox": [ 106, 100.0, 506, 130.0 ], "spans": [], "index": 1 }, { "bbox": [ 106, 130.0, 506, 160.0 ], "spans": [], "index": 2 } ] }, { "type": "image_caption", "bbox": [ 106, 167, 506, 235 ], "group_id": 0, "lines": [ { "bbox": [ 105, 166, 506, 181 ], "spans": [ { "bbox": [ 105, 166, 362, 181 ], "score": 1.0, "content": "Figure 2: Comparison of FRePo and Unrolled Optimization.", "type": "text" }, { "bbox": [ 362, 168, 370, 178 ], "score": 0.44, "content": "S", "type": "inline_equation" }, { "bbox": [ 370, 166, 374, 181 ], "score": 1.0, "content": ",", "type": "text" }, { "bbox": [ 375, 168, 388, 178 ], "score": 0.73, "content": "X _ { s }", "type": "inline_equation" }, { "bbox": [ 388, 166, 392, 181 ], "score": 1.0, "content": ",", "type": "text" }, { "bbox": [ 393, 168, 404, 178 ], "score": 0.78, "content": "Y _ { s }", "type": "inline_equation" }, { "bbox": [ 404, 166, 506, 181 ], "score": 1.0, "content": "are the distilled dataset,", "type": "text" } ], "index": 3 }, { "bbox": [ 105, 177, 506, 193 ], "spans": [ { "bbox": [ 105, 177, 184, 193 ], "score": 1.0, "content": "images and labels.", "type": "text" }, { "bbox": [ 185, 180, 193, 190 ], "score": 0.74, "content": "\\mathcal { L }", "type": "inline_equation" }, { "bbox": [ 193, 177, 311, 193 ], "score": 1.0, "content": "is the meta-training loss and", "type": "text" }, { "bbox": [ 311, 178, 328, 190 ], "score": 0.85, "content": "\\dot { \\theta } ^ { ( k ) }", "type": "inline_equation" }, { "bbox": [ 328, 177, 331, 193 ], "score": 1.0, "content": ",", "type": "text" }, { "bbox": [ 332, 178, 349, 191 ], "score": 0.87, "content": "g ^ { ( k ) }", "type": "inline_equation" }, { "bbox": [ 350, 177, 506, 193 ], "score": 1.0, "content": "are the model parameter and gradient", "type": "text" } ], "index": 4 }, { "bbox": [ 103, 185, 508, 208 ], "spans": [ { "bbox": [ 103, 185, 135, 208 ], "score": 1.0, "content": "at step", "type": "text" }, { "bbox": [ 136, 191, 142, 201 ], "score": 0.58, "content": "k", "type": "inline_equation" }, { "bbox": [ 142, 185, 146, 208 ], "score": 1.0, "content": ".", "type": "text" }, { "bbox": [ 147, 190, 171, 203 ], "score": 0.89, "content": "f ( X )", "type": "inline_equation" }, { "bbox": [ 171, 185, 265, 208 ], "score": 1.0, "content": "is the feature for input", "type": "text" }, { "bbox": [ 265, 191, 275, 201 ], "score": 0.8, "content": "X", "type": "inline_equation" }, { "bbox": [ 276, 185, 294, 208 ], "score": 1.0, "content": "and", "type": "text" }, { "bbox": [ 294, 190, 324, 204 ], "score": 0.93, "content": "K _ { X _ { t } X _ { s } } ^ { \\theta }", "type": "inline_equation" }, { "bbox": [ 324, 185, 415, 208 ], "score": 1.0, "content": "is the Gram matrix of", "type": "text" }, { "bbox": [ 416, 191, 429, 201 ], "score": 0.89, "content": "X _ { t }", "type": "inline_equation" }, { "bbox": [ 429, 185, 447, 208 ], "score": 1.0, "content": "and", "type": "text" }, { "bbox": [ 447, 191, 461, 201 ], "score": 0.88, "content": "X _ { s }", "type": "inline_equation" }, { "bbox": [ 461, 185, 508, 208 ], "score": 1.0, "content": ". FRePo is", "type": "text" } ], "index": 5 }, { "bbox": [ 106, 201, 505, 214 ], "spans": [ { "bbox": [ 106, 201, 505, 214 ], "score": 1.0, "content": "analogous to 1-step TBPTT as it computes the meta-gradient at each step while performing the online", "type": "text" } ], "index": 6 }, { "bbox": [ 105, 211, 506, 225 ], "spans": [ { "bbox": [ 105, 211, 506, 225 ], "score": 1.0, "content": "model update. However, instead of backpropagating through the inner optimization, FRePo computes", "type": "text" } ], "index": 7 }, { "bbox": [ 106, 223, 333, 236 ], "spans": [ { "bbox": [ 106, 223, 333, 236 ], "score": 1.0, "content": "the meta-gradient through a kernel and feature extractor.", "type": "text" } ], "index": 8 } ], "index": 5.5 } ], "index": 3.25 }, { "type": "title", "bbox": [ 107, 253, 166, 266 ], "lines": [ { "bbox": [ 104, 251, 168, 269 ], "spans": [ { "bbox": [ 104, 251, 168, 269 ], "score": 1.0, "content": "2 Method", "type": "text" } ], "index": 9 } ], "index": 9 }, { "type": "title", "bbox": [ 107, 277, 317, 289 ], "lines": [ { "bbox": [ 105, 275, 318, 292 ], "spans": [ { "bbox": [ 105, 275, 318, 292 ], "score": 1.0, "content": "2.1 Dataset Distillation as Bi-level Optimization", "type": "text" } ], "index": 10 } ], "index": 10 }, { "type": "text", "bbox": [ 106, 296, 506, 399 ], "lines": [ { "bbox": [ 105, 295, 506, 312 ], "spans": [ { "bbox": [ 105, 295, 266, 312 ], "score": 1.0, "content": "Suppose we have a large labeled dataset", "type": "text" }, { "bbox": [ 266, 296, 403, 311 ], "score": 0.93, "content": "\\mathcal { T } = \\left\\{ \\left( \\mathbf { x } _ { 1 } , \\mathbf { y } _ { 1 } \\right) , \\dotsc , \\left( \\mathbf { x } _ { | T | } , \\mathbf { y } _ { | T | } \\right) \\right\\}", "type": "inline_equation" }, { "bbox": [ 404, 295, 425, 312 ], "score": 1.0, "content": "with", "type": "text" }, { "bbox": [ 425, 298, 439, 309 ], "score": 0.88, "content": "| \\tau |", "type": "inline_equation" }, { "bbox": [ 440, 295, 506, 312 ], "score": 1.0, "content": "image and label` ˘(", "type": "text" } ], "index": 11 }, { "bbox": [ 104, 309, 504, 326 ], "spans": [ { "bbox": [ 104, 309, 368, 326 ], "score": 1.0, "content": "pairs. Dataset distillation aims to learn a small synthetic dataset", "type": "text" }, { "bbox": [ 368, 309, 504, 324 ], "score": 0.9, "content": "\\mathcal { S } = \\left\\{ ( \\mathbf { x } _ { 1 } , \\mathbf { y } _ { 1 } ) , \\dotsc , \\left( \\mathbf { x } _ { | S | } , \\mathbf { y } _ { | S | } \\right) \\right\\}", "type": "inline_equation" } ], "index": 12 }, { "bbox": [ 105, 322, 506, 334 ], "spans": [ { "bbox": [ 105, 322, 278, 334 ], "score": 1.0, "content": "that preserves most of the information in", "type": "text" }, { "bbox": [ 278, 322, 288, 332 ], "score": 0.8, "content": "\\tau", "type": "inline_equation" }, { "bbox": [ 288, 322, 506, 334 ], "score": 1.0, "content": ". We train several neural networks parameterized by", "type": "text" } ], "index": 13 }, { "bbox": [ 107, 332, 506, 345 ], "spans": [ { "bbox": [ 107, 333, 113, 342 ], "score": 0.78, "content": "\\theta", "type": "inline_equation" }, { "bbox": [ 113, 332, 175, 345 ], "score": 1.0, "content": "on the dataset", "type": "text" }, { "bbox": [ 175, 333, 183, 342 ], "score": 0.8, "content": "s", "type": "inline_equation" }, { "bbox": [ 184, 332, 341, 345 ], "score": 1.0, "content": "and then compute the validation loss", "type": "text" }, { "bbox": [ 341, 332, 412, 344 ], "score": 0.92, "content": "\\mathcal { L } ( \\mathcal { A } l g \\left( \\theta , \\mathcal { S } \\right) , \\mathcal { T } )", "type": "inline_equation" }, { "bbox": [ 412, 332, 493, 345 ], "score": 1.0, "content": "on the real dataset", "type": "text" }, { "bbox": [ 493, 333, 502, 343 ], "score": 0.8, "content": "\\tau", "type": "inline_equation" }, { "bbox": [ 503, 332, 506, 345 ], "score": 1.0, "content": ",", "type": "text" } ], "index": 14 }, { "bbox": [ 105, 343, 506, 356 ], "spans": [ { "bbox": [ 105, 343, 133, 356 ], "score": 1.0, "content": "where", "type": "text" }, { "bbox": [ 134, 343, 176, 355 ], "score": 0.93, "content": "{ \\mathcal { A } } l g \\left( \\theta , S \\right)", "type": "inline_equation" }, { "bbox": [ 176, 343, 451, 356 ], "score": 1.0, "content": "is the neural network parameters optimized by a learning algorithm", "type": "text" }, { "bbox": [ 452, 344, 468, 354 ], "score": 0.85, "content": "\\mathcal { A } g", "type": "inline_equation" }, { "bbox": [ 469, 343, 506, 356 ], "score": 1.0, "content": "with the", "type": "text" } ], "index": 15 }, { "bbox": [ 105, 354, 506, 367 ], "spans": [ { "bbox": [ 105, 354, 187, 367 ], "score": 1.0, "content": "model initialization", "type": "text" }, { "bbox": [ 187, 355, 193, 364 ], "score": 0.77, "content": "\\theta", "type": "inline_equation" }, { "bbox": [ 194, 354, 276, 367 ], "score": 1.0, "content": "and distilled dataset", "type": "text" }, { "bbox": [ 276, 355, 284, 364 ], "score": 0.79, "content": "s", "type": "inline_equation" }, { "bbox": [ 285, 354, 416, 367 ], "score": 1.0, "content": "as its inputs. The validation loss", "type": "text" }, { "bbox": [ 416, 355, 487, 366 ], "score": 0.91, "content": "\\mathcal { L } ( \\mathcal { A } l g \\left( \\theta , S \\right) , \\mathcal { T } )", "type": "inline_equation" }, { "bbox": [ 488, 354, 506, 367 ], "score": 1.0, "content": "is a", "type": "text" } ], "index": 16 }, { "bbox": [ 104, 363, 506, 379 ], "spans": [ { "bbox": [ 104, 363, 506, 379 ], "score": 1.0, "content": "noisy objective with the stochasticity coming from random model initialization and inner learning", "type": "text" } ], "index": 17 }, { "bbox": [ 105, 375, 506, 389 ], "spans": [ { "bbox": [ 105, 375, 506, 389 ], "score": 1.0, "content": "algorithm. Thus, we are interested in minimizing the expected value of this loss, which we denote it", "type": "text" } ], "index": 18 }, { "bbox": [ 105, 387, 482, 400 ], "spans": [ { "bbox": [ 105, 387, 117, 400 ], "score": 1.0, "content": "as", "type": "text" }, { "bbox": [ 118, 387, 140, 399 ], "score": 0.92, "content": "F ( S )", "type": "inline_equation" }, { "bbox": [ 141, 387, 482, 400 ], "score": 1.0, "content": ". We formulate the dataset distillation as the following bi-level optimization problem.", "type": "text" } ], "index": 19 } ], "index": 15, "bbox_fs": [ 104, 295, 506, 400 ] }, { "type": "interline_equation", "bbox": [ 165, 403, 445, 440 ], "lines": [ { "bbox": [ 165, 403, 445, 440 ], "spans": [ { "bbox": [ 165, 403, 445, 440 ], "score": 0.93, "content": "\\overbrace { \\mathcal { S } ^ { * } : = \\mathop { \\mathrm { a r g m i n } } _ { \\mathcal { S } } F ( \\mathcal { S } ) } ^ { o u t e r - l e v e l } , \\mathrm { w h e r e } F ( \\mathcal { S } ) = \\mathbb { E } _ { \\theta \\sim P _ { \\theta } } \\biggl [ \\mathcal { L } \\Bigl ( \\overbrace { \\mathcal { A } l g \\left( \\theta , \\mathcal { S } \\right) } ^ { i n n e r - l e v e l } , \\ T \\Bigr ) \\biggr ] .", "type": "interline_equation", "image_path": "5d90a6e2a97898bb43c032413b0dda3e03ac154d8a7d9d7a921494e9f9e4b013.jpg" } ] } ], "index": 21, "virtual_lines": [ { "bbox": [ 165, 403, 445, 415.3333333333333 ], "spans": [], "index": 20 }, { "bbox": [ 165, 415.3333333333333, 445, 427.66666666666663 ], "spans": [], "index": 21 }, { "bbox": [ 165, 427.66666666666663, 445, 439.99999999999994 ], "spans": [], "index": 22 } ] }, { "type": "text", "bbox": [ 106, 442, 505, 531 ], "lines": [ { "bbox": [ 106, 443, 506, 455 ], "spans": [ { "bbox": [ 106, 443, 415, 455 ], "score": 1.0, "content": "In this bi-level setup, the outer loop optimizes the distilled data to minimize", "type": "text" }, { "bbox": [ 415, 443, 438, 455 ], "score": 0.91, "content": "F ( S )", "type": "inline_equation" }, { "bbox": [ 438, 443, 506, 455 ], "score": 1.0, "content": ", while the inner", "type": "text" } ], "index": 23 }, { "bbox": [ 106, 453, 505, 466 ], "spans": [ { "bbox": [ 106, 453, 339, 466 ], "score": 1.0, "content": "loop trains a neural network using the learning algorithm,", "type": "text" }, { "bbox": [ 340, 454, 357, 465 ], "score": 0.88, "content": "\\mathcal { A } g", "type": "inline_equation" }, { "bbox": [ 357, 453, 505, 466 ], "score": 1.0, "content": ", to minimize the training loss on the", "type": "text" } ], "index": 24 }, { "bbox": [ 105, 464, 506, 478 ], "spans": [ { "bbox": [ 105, 464, 160, 478 ], "score": 1.0, "content": "distilled data", "type": "text" }, { "bbox": [ 161, 465, 169, 475 ], "score": 0.77, "content": "s", "type": "inline_equation" }, { "bbox": [ 169, 464, 506, 478 ], "score": 1.0, "content": ". From the meta-learning perspective, the task is defined by the model initialization", "type": "text" } ], "index": 25 }, { "bbox": [ 107, 476, 505, 488 ], "spans": [ { "bbox": [ 107, 477, 113, 486 ], "score": 0.76, "content": "\\theta", "type": "inline_equation" }, { "bbox": [ 113, 476, 274, 488 ], "score": 1.0, "content": ", and we want to learn a meta-parameter", "type": "text" }, { "bbox": [ 275, 476, 283, 486 ], "score": 0.79, "content": "s", "type": "inline_equation" }, { "bbox": [ 283, 476, 505, 488 ], "score": 1.0, "content": "that generalizes well to different models sampled from", "type": "text" } ], "index": 26 }, { "bbox": [ 105, 486, 506, 499 ], "spans": [ { "bbox": [ 105, 486, 201, 499 ], "score": 1.0, "content": "the model distributions", "type": "text" }, { "bbox": [ 202, 487, 213, 498 ], "score": 0.88, "content": "P _ { \\theta }", "type": "inline_equation" }, { "bbox": [ 214, 486, 419, 499 ], "score": 1.0, "content": ". During learning, we optimize the meta-parameter", "type": "text" }, { "bbox": [ 420, 487, 428, 497 ], "score": 0.8, "content": "s", "type": "inline_equation" }, { "bbox": [ 428, 486, 506, 499 ], "score": 1.0, "content": "by minimizing the", "type": "text" } ], "index": 27 }, { "bbox": [ 105, 498, 505, 510 ], "spans": [ { "bbox": [ 105, 498, 180, 509 ], "score": 1.0, "content": "meta-training loss", "type": "text" }, { "bbox": [ 181, 498, 204, 510 ], "score": 0.92, "content": "F ( S )", "type": "inline_equation" }, { "bbox": [ 204, 498, 479, 509 ], "score": 1.0, "content": ". In contrast, at meta-test time, we train a new model from scratch on", "type": "text" }, { "bbox": [ 479, 498, 487, 507 ], "score": 0.8, "content": "s", "type": "inline_equation" }, { "bbox": [ 487, 498, 505, 509 ], "score": 1.0, "content": "and", "type": "text" } ], "index": 28 }, { "bbox": [ 105, 508, 505, 521 ], "spans": [ { "bbox": [ 105, 508, 505, 521 ], "score": 1.0, "content": "evaluate the trained model on a held-out real dataset. This meta-test performance reflects the quality", "type": "text" } ], "index": 29 }, { "bbox": [ 106, 519, 188, 531 ], "spans": [ { "bbox": [ 106, 519, 188, 531 ], "score": 1.0, "content": "of the distilled data.", "type": "text" } ], "index": 30 } ], "index": 26.5, "bbox_fs": [ 105, 443, 506, 531 ] }, { "type": "title", "bbox": [ 108, 542, 447, 555 ], "lines": [ { "bbox": [ 104, 541, 445, 558 ], "spans": [ { "bbox": [ 104, 541, 411, 558 ], "score": 1.0, "content": "2.2 Dataset Distillation using Neural Feature Regression with Pooling", "type": "text" }, { "bbox": [ 411, 543, 445, 554 ], "score": 0.25, "content": "\\mathbf { ( F R e P 0 ) }", "type": "inline_equation" } ], "index": 31 } ], "index": 31 }, { "type": "text", "bbox": [ 107, 563, 505, 641 ], "lines": [ { "bbox": [ 105, 563, 505, 577 ], "spans": [ { "bbox": [ 105, 563, 417, 577 ], "score": 1.0, "content": "The outer-level problem can be solved using gradient-based methods of the form", "type": "text" }, { "bbox": [ 418, 563, 501, 576 ], "score": 0.89, "content": "\\mathcal { S } \\gets \\mathcal { S } \\ – \\alpha \\nabla _ { \\mathcal { S } } F ( \\mathcal { S } )", "type": "inline_equation" }, { "bbox": [ 502, 563, 505, 577 ], "score": 1.0, "content": ",", "type": "text" } ], "index": 32 }, { "bbox": [ 105, 574, 506, 587 ], "spans": [ { "bbox": [ 105, 574, 134, 587 ], "score": 1.0, "content": "where", "type": "text" }, { "bbox": [ 134, 576, 142, 584 ], "score": 0.77, "content": "\\alpha", "type": "inline_equation" }, { "bbox": [ 142, 574, 330, 587 ], "score": 1.0, "content": "is the learning rate for the distilled data and", "type": "text" }, { "bbox": [ 330, 574, 368, 586 ], "score": 0.91, "content": "\\nabla _ { S } F ( S )", "type": "inline_equation" }, { "bbox": [ 369, 574, 506, 587 ], "score": 1.0, "content": "is the meta-gradient [27]. For a", "type": "text" } ], "index": 33 }, { "bbox": [ 105, 585, 505, 598 ], "spans": [ { "bbox": [ 105, 585, 176, 598 ], "score": 1.0, "content": "particular model", "type": "text" }, { "bbox": [ 177, 586, 183, 595 ], "score": 0.71, "content": "\\theta", "type": "inline_equation" }, { "bbox": [ 183, 585, 346, 598 ], "score": 1.0, "content": ", the meta-gradient can be expressed as", "type": "text" }, { "bbox": [ 346, 585, 433, 597 ], "score": 0.93, "content": "\\nabla _ { \\mathcal { S } } \\hat { \\mathcal { L } } \\left( \\mathcal { A } l g \\left( \\theta , \\mathcal { S } \\right) , \\mathcal { T } \\right)", "type": "inline_equation" }, { "bbox": [ 433, 585, 505, 598 ], "score": 1.0, "content": ". Computing this", "type": "text" } ], "index": 34 }, { "bbox": [ 105, 596, 505, 609 ], "spans": [ { "bbox": [ 105, 596, 387, 609 ], "score": 1.0, "content": "meta-gradient requires differentiating through inner optimization. If", "type": "text" }, { "bbox": [ 387, 597, 404, 608 ], "score": 0.83, "content": "\\mathcal { A } \\boldsymbol { { l } } _ { g }", "type": "inline_equation" }, { "bbox": [ 405, 596, 505, 609 ], "score": 1.0, "content": "is an iterative algorithm", "type": "text" } ], "index": 35 }, { "bbox": [ 105, 606, 506, 621 ], "spans": [ { "bbox": [ 105, 606, 506, 621 ], "score": 1.0, "content": "like gradient descent, then backpropagating through the unrolled computation graph [14] can be a", "type": "text" } ], "index": 36 }, { "bbox": [ 105, 617, 505, 632 ], "spans": [ { "bbox": [ 105, 617, 505, 632 ], "score": 1.0, "content": "solution. However, this type of unrolled optimization introduces significant computation and memory", "type": "text" } ], "index": 37 }, { "bbox": [ 105, 628, 451, 642 ], "spans": [ { "bbox": [ 105, 628, 451, 642 ], "score": 1.0, "content": "overhead, as the whole training trajectory needs to be stored in memory (Figure 2(b)).", "type": "text" } ], "index": 38 } ], "index": 35, "bbox_fs": [ 105, 563, 506, 642 ] }, { "type": "text", "bbox": [ 107, 645, 505, 722 ], "lines": [ { "bbox": [ 105, 644, 506, 658 ], "spans": [ { "bbox": [ 105, 644, 506, 658 ], "score": 1.0, "content": "Traditionally, these issues are alleviated with truncated backpropagation through time (TBPTT)", "type": "text" } ], "index": 39 }, { "bbox": [ 105, 655, 507, 670 ], "spans": [ { "bbox": [ 105, 655, 507, 670 ], "score": 1.0, "content": "[28–30]. Instead of backpropagating through an entire unrolled sequence, TBPTT performs backprop-", "type": "text" } ], "index": 40 }, { "bbox": [ 105, 667, 506, 680 ], "spans": [ { "bbox": [ 105, 667, 506, 680 ], "score": 1.0, "content": "agation for each subsequence separately. It is efficient because its time and memory complexity scale", "type": "text" } ], "index": 41 }, { "bbox": [ 105, 678, 505, 691 ], "spans": [ { "bbox": [ 105, 678, 505, 691 ], "score": 1.0, "content": "linearly with respect to the truncation steps. However, truncation may yield highly biased gradients", "type": "text" } ], "index": 42 }, { "bbox": [ 105, 687, 505, 703 ], "spans": [ { "bbox": [ 105, 687, 505, 703 ], "score": 1.0, "content": "that severely impact training. To mitigate this truncation bias [14], we consider training only the top", "type": "text" } ], "index": 43 }, { "bbox": [ 105, 700, 506, 712 ], "spans": [ { "bbox": [ 105, 700, 506, 712 ], "score": 1.0, "content": "layer of a network to convergence. The key insight is that the data helpful for training the output", "type": "text" } ], "index": 44 }, { "bbox": [ 105, 711, 505, 723 ], "spans": [ { "bbox": [ 105, 711, 505, 723 ], "score": 1.0, "content": "layer can also help train the whole network. Thus, we decompose the neural network into a feature", "type": "text" } ], "index": 45 } ], "index": 42, "bbox_fs": [ 105, 644, 507, 723 ] } ] }, { "preproc_blocks": [ { "type": "text", "bbox": [ 113, 88, 404, 99 ], "lines": [ { "bbox": [ 116, 87, 404, 100 ], "spans": [ { "bbox": [ 116, 87, 156, 100 ], "score": 1.0, "content": "Require:", "type": "text" }, { "bbox": [ 157, 88, 166, 99 ], "score": 0.57, "content": "\\tau", "type": "inline_equation" }, { "bbox": [ 167, 87, 241, 100 ], "score": 1.0, "content": ": a labeled dataset;", "type": "text" }, { "bbox": [ 242, 90, 250, 98 ], "score": 0.61, "content": "\\alpha", "type": "inline_equation" }, { "bbox": [ 250, 87, 404, 100 ], "score": 1.0, "content": ": the learning rate for the distilled data", "type": "text" } ], "index": 0 } ], "index": 0 }, { "type": "text", "bbox": [ 124, 99, 381, 109 ], "lines": [ { "bbox": [ 122, 97, 378, 111 ], "spans": [ { "bbox": [ 122, 97, 318, 111 ], "score": 1.0, "content": "nitialization: Initialize a labeled distilled dataset", "type": "text" }, { "bbox": [ 319, 99, 374, 110 ], "score": 0.91, "content": "\\boldsymbol { \\mathcal { S } } = \\left( \\boldsymbol { X _ { s } } , \\boldsymbol { Y _ { s } } \\right)", "type": "inline_equation" }, { "bbox": [ 375, 97, 378, 111 ], "score": 1.0, "content": ".", "type": "text" } ], "index": 1 } ], "index": 1 }, { "type": "text", "bbox": [ 114, 110, 500, 122 ], "lines": [ { "bbox": [ 115, 105, 497, 124 ], "spans": [ { "bbox": [ 115, 105, 270, 124 ], "score": 1.0, "content": "Initialization: Initialize a model pool", "type": "text" }, { "bbox": [ 270, 110, 284, 120 ], "score": 0.79, "content": "\\mathcal { M }", "type": "inline_equation" }, { "bbox": [ 284, 105, 304, 124 ], "score": 1.0, "content": "with", "type": "text" }, { "bbox": [ 305, 111, 315, 119 ], "score": 0.74, "content": "m", "type": "inline_equation" }, { "bbox": [ 315, 105, 347, 124 ], "score": 1.0, "content": "models", "type": "text" }, { "bbox": [ 348, 110, 379, 122 ], "score": 0.89, "content": "\\left\\{ \\boldsymbol { \\theta } _ { i } \\right\\} _ { i = 1 } ^ { m }", "type": "inline_equation" }, { "bbox": [ 379, 105, 484, 124 ], "score": 1.0, "content": "randomly initialized from", "type": "text" }, { "bbox": [ 485, 110, 497, 120 ], "score": 0.86, "content": "P _ { \\theta }", "type": "inline_equation" } ], "index": 2 } ], "index": 2 }, { "type": "text", "bbox": [ 111, 123, 440, 199 ], "lines": [ { "bbox": [ 110, 123, 220, 134 ], "spans": [ { "bbox": [ 110, 123, 220, 134 ], "score": 1.0, "content": "1: while not converged do", "type": "text" } ], "index": 3 }, { "bbox": [ 111, 133, 375, 145 ], "spans": [ { "bbox": [ 111, 133, 121, 145 ], "score": 1.0, "content": "2:", "type": "text" }, { "bbox": [ 133, 133, 337, 145 ], "score": 1.0, "content": "Ż Sample a model uniformly from the model pool:", "type": "text" }, { "bbox": [ 337, 133, 372, 144 ], "score": 0.91, "content": "\\theta _ { i } \\sim \\mathcal { M }", "type": "inline_equation" }, { "bbox": [ 372, 133, 375, 145 ], "score": 1.0, "content": ".", "type": "text" } ], "index": 4 }, { "bbox": [ 110, 144, 432, 157 ], "spans": [ { "bbox": [ 110, 145, 121, 156 ], "score": 1.0, "content": "3:", "type": "text" }, { "bbox": [ 132, 144, 373, 157 ], "score": 1.0, "content": "Ż Sample a target batch uniformly from the labeled dataset:", "type": "text" }, { "bbox": [ 374, 144, 428, 156 ], "score": 0.9, "content": "( X _ { t } , Y _ { t } ) \\sim \\tau", "type": "inline_equation" }, { "bbox": [ 429, 144, 432, 157 ], "score": 1.0, "content": ".", "type": "text" } ], "index": 5 }, { "bbox": [ 110, 155, 326, 167 ], "spans": [ { "bbox": [ 110, 155, 121, 167 ], "score": 1.0, "content": "4:", "type": "text" }, { "bbox": [ 133, 157, 140, 165 ], "score": 0.27, "content": "\\triangleright", "type": "inline_equation" }, { "bbox": [ 141, 155, 268, 167 ], "score": 1.0, "content": "Compute the meta-training loss", "type": "text" }, { "bbox": [ 269, 156, 277, 165 ], "score": 0.79, "content": "\\mathcal { L }", "type": "inline_equation" }, { "bbox": [ 277, 155, 326, 167 ], "score": 1.0, "content": "using Eq. 2", "type": "text" } ], "index": 6 }, { "bbox": [ 110, 165, 440, 179 ], "spans": [ { "bbox": [ 110, 167, 121, 178 ], "score": 1.0, "content": "5:", "type": "text" }, { "bbox": [ 133, 165, 240, 179 ], "score": 1.0, "content": "Ż Update the distilled data", "type": "text" }, { "bbox": [ 241, 166, 249, 176 ], "score": 0.37, "content": "s", "type": "inline_equation" }, { "bbox": [ 250, 166, 340, 178 ], "score": 0.86, "content": "\\mathrm { : } ~ X _ { s } \\gets X _ { s } - \\alpha \\nabla _ { X _ { s } } \\mathcal { L }", "type": "inline_equation" }, { "bbox": [ 340, 165, 360, 179 ], "score": 1.0, "content": ", and", "type": "text" }, { "bbox": [ 360, 166, 440, 178 ], "score": 0.9, "content": "Y _ { s } \\gets Y _ { s } - \\alpha \\nabla _ { Y _ { s } } \\mathcal { L }", "type": "inline_equation" } ], "index": 7 }, { "bbox": [ 110, 175, 390, 191 ], "spans": [ { "bbox": [ 110, 177, 121, 189 ], "score": 1.0, "content": "6:", "type": "text" }, { "bbox": [ 133, 179, 140, 187 ], "score": 0.35, "content": "\\triangleright", "type": "inline_equation" }, { "bbox": [ 141, 175, 206, 191 ], "score": 1.0, "content": "Train the model", "type": "text" }, { "bbox": [ 207, 177, 216, 188 ], "score": 0.88, "content": "\\theta _ { i }", "type": "inline_equation" }, { "bbox": [ 216, 175, 329, 191 ], "score": 1.0, "content": "on the current distilled data", "type": "text" }, { "bbox": [ 329, 178, 337, 187 ], "score": 0.8, "content": "s", "type": "inline_equation" }, { "bbox": [ 337, 175, 390, 191 ], "score": 1.0, "content": "for one step.", "type": "text" } ], "index": 8 }, { "bbox": [ 111, 187, 435, 201 ], "spans": [ { "bbox": [ 111, 188, 121, 199 ], "score": 1.0, "content": "7:", "type": "text" }, { "bbox": [ 133, 190, 141, 198 ], "score": 0.27, "content": "\\triangleright", "type": "inline_equation" }, { "bbox": [ 141, 187, 231, 201 ], "score": 1.0, "content": "Reinitialize the model", "type": "text" }, { "bbox": [ 231, 188, 264, 199 ], "score": 0.92, "content": "\\theta _ { i } \\sim P _ { \\theta }", "type": "inline_equation" }, { "bbox": [ 265, 187, 274, 201 ], "score": 1.0, "content": "if", "type": "text" }, { "bbox": [ 275, 188, 284, 199 ], "score": 0.88, "content": "\\theta _ { i }", "type": "inline_equation" }, { "bbox": [ 284, 187, 398, 201 ], "score": 1.0, "content": "has been updated more than", "type": "text" }, { "bbox": [ 399, 189, 410, 198 ], "score": 0.81, "content": "K", "type": "inline_equation" }, { "bbox": [ 410, 187, 435, 201 ], "score": 1.0, "content": "steps.", "type": "text" } ], "index": 9 } ], "index": 6 }, { "type": "text", "bbox": [ 111, 199, 166, 209 ], "lines": [ { "bbox": [ 110, 198, 167, 211 ], "spans": [ { "bbox": [ 110, 198, 167, 211 ], "score": 1.0, "content": "8: end while", "type": "text" } ], "index": 10 } ], "index": 10 }, { "type": "text", "bbox": [ 115, 212, 310, 223 ], "lines": [ { "bbox": [ 116, 210, 309, 226 ], "spans": [ { "bbox": [ 116, 210, 254, 226 ], "score": 1.0, "content": "Output: Learned distilled dataset", "type": "text" }, { "bbox": [ 254, 212, 309, 224 ], "score": 0.93, "content": "\\boldsymbol { \\mathcal { S } } = \\left( \\boldsymbol { X _ { s } } , \\boldsymbol { Y _ { s } } \\right)", "type": "inline_equation" } ], "index": 11 } ], "index": 11 }, { "type": "text", "bbox": [ 107, 249, 505, 294 ], "lines": [ { "bbox": [ 105, 250, 505, 262 ], "spans": [ { "bbox": [ 105, 250, 505, 262 ], "score": 1.0, "content": "extractor and a linear classifier. We fix the feature extractor at each meta-gradient computation and", "type": "text" } ], "index": 12 }, { "bbox": [ 105, 261, 505, 273 ], "spans": [ { "bbox": [ 105, 261, 329, 273 ], "score": 1.0, "content": "train the linear classifier to convergence before updating", "type": "text" }, { "bbox": [ 329, 261, 337, 271 ], "score": 0.67, "content": "s", "type": "inline_equation" }, { "bbox": [ 338, 261, 505, 273 ], "score": 1.0, "content": ". After that, we adjust the feature extractor", "type": "text" } ], "index": 13 }, { "bbox": [ 106, 272, 504, 284 ], "spans": [ { "bbox": [ 106, 272, 504, 284 ], "score": 1.0, "content": "by training the whole network on the updated distilled data. We note that similar two-phase procedure", "type": "text" } ], "index": 14 }, { "bbox": [ 105, 281, 358, 295 ], "spans": [ { "bbox": [ 105, 281, 358, 295 ], "score": 1.0, "content": "has been studied in the context of representation learning [31].", "type": "text" } ], "index": 15 } ], "index": 13.5 }, { "type": "text", "bbox": [ 106, 298, 505, 354 ], "lines": [ { "bbox": [ 106, 298, 505, 312 ], "spans": [ { "bbox": [ 106, 298, 505, 312 ], "score": 1.0, "content": "Meta-Gradient Computation: If we consider the mean square error loss, then the optimal weights", "type": "text" } ], "index": 16 }, { "bbox": [ 106, 308, 504, 323 ], "spans": [ { "bbox": [ 106, 308, 504, 323 ], "score": 1.0, "content": "for the linear classifier have a closed-form solution. Moreover, since the feature dimension is typically", "type": "text" } ], "index": 17 }, { "bbox": [ 105, 319, 506, 334 ], "spans": [ { "bbox": [ 105, 319, 506, 334 ], "score": 1.0, "content": "larger than the number of distilled data, we can use kernel ridge regression (KRR) with a conjugate", "type": "text" } ], "index": 18 }, { "bbox": [ 105, 331, 506, 345 ], "spans": [ { "bbox": [ 105, 331, 506, 345 ], "score": 1.0, "content": "kernel [25] rather than solving the weights explicitly [12]. The resulting meta-training loss (Eq. 2) is", "type": "text" } ], "index": 19 }, { "bbox": [ 105, 341, 455, 354 ], "spans": [ { "bbox": [ 105, 341, 455, 354 ], "score": 1.0, "content": "similar to that used in KIP [22, 23], but we use a more flexible kernel rather than NTK.", "type": "text" } ], "index": 20 } ], "index": 18 }, { "type": "interline_equation", "bbox": [ 182, 359, 427, 383 ], "lines": [ { "bbox": [ 182, 359, 427, 383 ], "spans": [ { "bbox": [ 182, 359, 427, 383 ], "score": 0.93, "content": "\\mathcal { L } \\left( \\mathcal { A } l g \\left( \\theta , \\mathcal { S } \\right) , \\mathcal { T } \\right) = \\frac { 1 } { 2 } | | Y _ { t } - K _ { X _ { t } X _ { s } } ^ { \\theta } ( K _ { X _ { s } X _ { s } } ^ { \\theta } + \\lambda I ) ^ { - 1 } Y _ { s } | | _ { 2 } ^ { 2 } ,", "type": "interline_equation", "image_path": "0cd9f2dca22b293f4e069930dff443abaa6142b03906a3c62fda7f6203ea2b36.jpg" } ] } ], "index": 21, "virtual_lines": [ { "bbox": [ 182, 359, 427, 383 ], "spans": [], "index": 21 } ] }, { "type": "text", "bbox": [ 106, 389, 506, 471 ], "lines": [ { "bbox": [ 105, 388, 507, 402 ], "spans": [ { "bbox": [ 105, 388, 133, 402 ], "score": 1.0, "content": "where", "type": "text" }, { "bbox": [ 134, 389, 167, 402 ], "score": 0.92, "content": "( X _ { t } , Y _ { t } )", "type": "inline_equation" }, { "bbox": [ 168, 388, 186, 402 ], "score": 1.0, "content": "and", "type": "text" }, { "bbox": [ 186, 389, 221, 402 ], "score": 0.92, "content": "( X _ { s } , Y _ { s } )", "type": "inline_equation" }, { "bbox": [ 222, 388, 384, 402 ], "score": 1.0, "content": "are the inputs and labels of the real data", "type": "text" }, { "bbox": [ 385, 390, 394, 400 ], "score": 0.82, "content": "\\tau", "type": "inline_equation" }, { "bbox": [ 394, 388, 466, 402 ], "score": 1.0, "content": "and distilled data", "type": "text" }, { "bbox": [ 466, 390, 474, 399 ], "score": 0.84, "content": "s", "type": "inline_equation" }, { "bbox": [ 474, 388, 507, 402 ], "score": 1.0, "content": "respec-", "type": "text" } ], "index": 22 }, { "bbox": [ 101, 397, 502, 420 ], "spans": [ { "bbox": [ 101, 397, 426, 420 ], "score": 1.0, "content": "tively. The Gram matrix between real inputs and distilled inputs is denoted as", "type": "text" }, { "bbox": [ 426, 401, 502, 415 ], "score": 0.92, "content": "K _ { X _ { t } X _ { s } } ^ { \\theta } \\in \\mathbb { R } ^ { | T | \\times | S | }", "type": "inline_equation" } ], "index": 23 }, { "bbox": [ 102, 409, 510, 433 ], "spans": [ { "bbox": [ 102, 409, 347, 433 ], "score": 1.0, "content": "while the Gram matrix between distilled inputs is denoted as", "type": "text" }, { "bbox": [ 348, 414, 422, 429 ], "score": 0.9, "content": "K _ { X _ { s } X _ { s } } ^ { \\theta } \\in \\mathbb { R } ^ { | S | \\times | S | }", "type": "inline_equation" }, { "bbox": [ 423, 409, 426, 433 ], "score": 1.0, "content": ".", "type": "text" }, { "bbox": [ 427, 416, 434, 425 ], "score": 0.66, "content": "\\lambda", "type": "inline_equation" }, { "bbox": [ 434, 409, 510, 433 ], "score": 1.0, "content": "t scontrols the regu-", "type": "text" } ], "index": 24 }, { "bbox": [ 105, 426, 506, 439 ], "spans": [ { "bbox": [ 105, 426, 450, 439 ], "score": 1.0, "content": "larization strength for KRR. Let us denote the neural network feature for a given input", "type": "text" }, { "bbox": [ 450, 427, 460, 437 ], "score": 0.83, "content": "X", "type": "inline_equation" }, { "bbox": [ 460, 426, 506, 439 ], "score": 1.0, "content": "and model", "type": "text" } ], "index": 25 }, { "bbox": [ 104, 434, 507, 451 ], "spans": [ { "bbox": [ 104, 434, 150, 451 ], "score": 1.0, "content": "parameter", "type": "text" }, { "bbox": [ 150, 438, 156, 447 ], "score": 0.81, "content": "\\theta", "type": "inline_equation" }, { "bbox": [ 156, 434, 168, 451 ], "score": 1.0, "content": "as", "type": "text" }, { "bbox": [ 169, 437, 237, 449 ], "score": 0.92, "content": "\\mathbf { \\bar { \\chi } } _ { f ( X , \\theta ) } \\in \\mathbb { R } ^ { N \\times d }", "type": "inline_equation" }, { "bbox": [ 237, 434, 268, 451 ], "score": 1.0, "content": ", where", "type": "text" }, { "bbox": [ 269, 439, 279, 447 ], "score": 0.83, "content": "N", "type": "inline_equation" }, { "bbox": [ 279, 434, 390, 451 ], "score": 1.0, "content": "is the number of input and", "type": "text" }, { "bbox": [ 390, 438, 397, 447 ], "score": 0.82, "content": "d", "type": "inline_equation" }, { "bbox": [ 397, 434, 507, 451 ], "score": 1.0, "content": "is the feature dimension 1.", "type": "text" } ], "index": 26 }, { "bbox": [ 106, 448, 506, 461 ], "spans": [ { "bbox": [ 106, 448, 506, 461 ], "score": 1.0, "content": "The conjugate kernel is defined by the inner product of the neural network features. Thus, the two", "type": "text" } ], "index": 27 }, { "bbox": [ 106, 460, 270, 471 ], "spans": [ { "bbox": [ 106, 460, 270, 471 ], "score": 1.0, "content": "Gram matrices are computed as follows:", "type": "text" } ], "index": 28 } ], "index": 25 }, { "type": "interline_equation", "bbox": [ 174, 477, 434, 493 ], "lines": [ { "bbox": [ 174, 477, 434, 493 ], "spans": [ { "bbox": [ 174, 477, 434, 493 ], "score": 0.91, "content": "K _ { X _ { t } X _ { s } } ^ { \\theta } = f ( X _ { t } , \\theta ) f ( X _ { s } , \\theta ) ^ { \\top } , \\quad K _ { X _ { s } X _ { s } } ^ { \\theta } = f ( X _ { s } , \\theta ) f ( X _ { s } , \\theta ) ^ { \\top } ,", "type": "interline_equation", "image_path": "87a4499ed59b016b53bcda7f7527fcb6ea8d32afd3493c3f5288d6937be23d26.jpg" } ] } ], "index": 29, "virtual_lines": [ { "bbox": [ 174, 477, 434, 493 ], "spans": [], "index": 29 } ] }, { "type": "text", "bbox": [ 106, 498, 505, 587 ], "lines": [ { "bbox": [ 105, 499, 506, 512 ], "spans": [ { "bbox": [ 105, 499, 249, 512 ], "score": 1.0, "content": "Now, computing the meta-gradient", "type": "text" }, { "bbox": [ 250, 499, 336, 511 ], "score": 0.93, "content": "\\nabla _ { \\mathcal { S } } \\mathcal { L } \\left( \\mathcal { A } l g \\left( \\theta , \\mathcal { S } \\right) , \\mathcal { T } \\right)", "type": "inline_equation" }, { "bbox": [ 337, 499, 506, 512 ], "score": 1.0, "content": "is just back-propagating through the con-", "type": "text" } ], "index": 30 }, { "bbox": [ 104, 511, 506, 523 ], "spans": [ { "bbox": [ 104, 511, 506, 523 ], "score": 1.0, "content": "jugate kernel and a fixed feature extractor, which is very efficient and takes even fewer operations", "type": "text" } ], "index": 31 }, { "bbox": [ 105, 522, 505, 534 ], "spans": [ { "bbox": [ 105, 522, 505, 534 ], "score": 1.0, "content": "than computing the gradient for the network’s weights. Moreover, we decouple the meta-gradient", "type": "text" } ], "index": 32 }, { "bbox": [ 105, 532, 506, 545 ], "spans": [ { "bbox": [ 105, 532, 506, 545 ], "score": 1.0, "content": "computation from the model online update. Hence, we can train the online model using any optimizer,", "type": "text" } ], "index": 33 }, { "bbox": [ 106, 543, 506, 556 ], "spans": [ { "bbox": [ 106, 543, 506, 556 ], "score": 1.0, "content": "and the distilled data will be agnostic to the specific learning algorithm choice. Our proposed method", "type": "text" } ], "index": 34 }, { "bbox": [ 105, 555, 505, 567 ], "spans": [ { "bbox": [ 105, 555, 505, 567 ], "score": 1.0, "content": "is similar to 1-step TBPTT in that we compute the meta-gradient at each step while performing the", "type": "text" } ], "index": 35 }, { "bbox": [ 104, 564, 506, 578 ], "spans": [ { "bbox": [ 104, 564, 506, 578 ], "score": 1.0, "content": "online model update. Unlike the conventional 1-step TBPTT, we compute the meta-gradient using a", "type": "text" } ], "index": 36 }, { "bbox": [ 106, 576, 391, 588 ], "spans": [ { "bbox": [ 106, 576, 391, 588 ], "score": 1.0, "content": "KRR output layer to mitigate truncation bias, illustrated in Figure 2(a).", "type": "text" } ], "index": 37 } ], "index": 33.5 }, { "type": "text", "bbox": [ 106, 591, 506, 691 ], "lines": [ { "bbox": [ 105, 591, 507, 605 ], "spans": [ { "bbox": [ 105, 591, 507, 605 ], "score": 1.0, "content": "Model Pool: As discussed in Section 1, there are various types of overfitting in dataset distillation.", "type": "text" } ], "index": 38 }, { "bbox": [ 105, 602, 506, 616 ], "spans": [ { "bbox": [ 105, 602, 506, 616 ], "score": 1.0, "content": "Several techniques have been proposed to alleviate such problem, such as random initialization [4],", "type": "text" } ], "index": 39 }, { "bbox": [ 104, 613, 507, 627 ], "spans": [ { "bbox": [ 104, 613, 507, 627 ], "score": 1.0, "content": "periodic reset [13, 5, 7], and dynamic bi-level optimization [19]. These techniques share the same", "type": "text" } ], "index": 40 }, { "bbox": [ 105, 624, 507, 637 ], "spans": [ { "bbox": [ 105, 624, 507, 637 ], "score": 1.0, "content": "underlying principle: the model diversity matters. Thus, we propose to maintain a “model pool”", "type": "text" } ], "index": 41 }, { "bbox": [ 105, 636, 506, 648 ], "spans": [ { "bbox": [ 105, 636, 506, 648 ], "score": 1.0, "content": "filled with diverse set of parameters obtained from different number of training steps and different", "type": "text" } ], "index": 42 }, { "bbox": [ 104, 646, 506, 660 ], "spans": [ { "bbox": [ 104, 646, 506, 660 ], "score": 1.0, "content": "random initializations. Unlike the previous methods that periodically training and resetting a single", "type": "text" } ], "index": 43 }, { "bbox": [ 105, 658, 505, 670 ], "spans": [ { "bbox": [ 105, 658, 505, 670 ], "score": 1.0, "content": "model, FRePo randomly sample a model from the pool at each meta-gradient computation and update", "type": "text" } ], "index": 44 }, { "bbox": [ 104, 667, 506, 682 ], "spans": [ { "bbox": [ 104, 667, 452, 682 ], "score": 1.0, "content": "it using the current distilled data. However, if a model has been updated more than", "type": "text" }, { "bbox": [ 453, 669, 463, 678 ], "score": 0.81, "content": "K", "type": "inline_equation" }, { "bbox": [ 464, 667, 506, 682 ], "score": 1.0, "content": "steps, we", "type": "text" } ], "index": 45 }, { "bbox": [ 105, 679, 505, 692 ], "spans": [ { "bbox": [ 105, 679, 505, 692 ], "score": 1.0, "content": "reinitialize it with a new random seed. From the meta-learning perspective, we maintain a diverse", "type": "text" } ], "index": 46 } ], "index": 42 } ], "page_idx": 3, "page_size": [ 612, 792 ], "discarded_blocks": [ { "type": "discarded", "bbox": [ 107, 701, 505, 722 ], "lines": [ { "bbox": [ 120, 700, 505, 712 ], "spans": [ { "bbox": [ 120, 700, 505, 712 ], "score": 1.0, "content": "1In practice, we use all the synthetic data and sample a minibatch from the real dataset to compute the", "type": "text" } ] }, { "bbox": [ 106, 712, 213, 722 ], "spans": [ { "bbox": [ 106, 712, 213, 722 ], "score": 1.0, "content": "meta-gradient (Algorithm 1).", "type": "text" } ] } ] }, { "type": "discarded", "bbox": [ 302, 742, 308, 750 ], "lines": [ { "bbox": [ 301, 741, 310, 752 ], "spans": [ { "bbox": [ 301, 741, 310, 752 ], "score": 1.0, "content": "", "type": "text", "height": 11, "width": 9 } ] } ] }, { "type": "discarded", "bbox": [ 107, 72, 463, 84 ], "lines": [ { "bbox": [ 105, 70, 463, 86 ], "spans": [ { "bbox": [ 105, 70, 463, 86 ], "score": 1.0, "content": "Algorithm 1 Dataset Distillation using Neural Feature Regression with Pooling (FRePo)", "type": "text" } ] } ] } ], "para_blocks": [ { "type": "text", "bbox": [ 113, 88, 404, 99 ], "lines": [ { "bbox": [ 116, 87, 404, 100 ], "spans": [ { "bbox": [ 116, 87, 156, 100 ], "score": 1.0, "content": "Require:", "type": "text" }, { "bbox": [ 157, 88, 166, 99 ], "score": 0.57, "content": "\\tau", "type": "inline_equation" }, { "bbox": [ 167, 87, 241, 100 ], "score": 1.0, "content": ": a labeled dataset;", "type": "text" }, { "bbox": [ 242, 90, 250, 98 ], "score": 0.61, "content": "\\alpha", "type": "inline_equation" }, { "bbox": [ 250, 87, 404, 100 ], "score": 1.0, "content": ": the learning rate for the distilled data", "type": "text" } ], "index": 0 }, { "bbox": [ 122, 97, 378, 111 ], "spans": [ { "bbox": [ 122, 97, 318, 111 ], "score": 1.0, "content": "nitialization: Initialize a labeled distilled dataset", "type": "text" }, { "bbox": [ 319, 99, 374, 110 ], "score": 0.91, "content": "\\boldsymbol { \\mathcal { S } } = \\left( \\boldsymbol { X _ { s } } , \\boldsymbol { Y _ { s } } \\right)", "type": "inline_equation" }, { "bbox": [ 375, 97, 378, 111 ], "score": 1.0, "content": ".", "type": "text" } ], "index": 1 } ], "index": 0, "bbox_fs": [ 116, 87, 404, 100 ] }, { "type": "text", "bbox": [ 124, 99, 381, 109 ], "lines": [], "index": 1, "bbox_fs": [ 122, 97, 378, 111 ], "lines_deleted": true }, { "type": "text", "bbox": [ 114, 110, 500, 122 ], "lines": [ { "bbox": [ 115, 105, 497, 124 ], "spans": [ { "bbox": [ 115, 105, 270, 124 ], "score": 1.0, "content": "Initialization: Initialize a model pool", "type": "text" }, { "bbox": [ 270, 110, 284, 120 ], "score": 0.79, "content": "\\mathcal { M }", "type": "inline_equation" }, { "bbox": [ 284, 105, 304, 124 ], "score": 1.0, "content": "with", "type": "text" }, { "bbox": [ 305, 111, 315, 119 ], "score": 0.74, "content": "m", "type": "inline_equation" }, { "bbox": [ 315, 105, 347, 124 ], 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"\\triangleright", "type": "inline_equation" }, { "bbox": [ 141, 155, 268, 167 ], "score": 1.0, "content": "Compute the meta-training loss", "type": "text" }, { "bbox": [ 269, 156, 277, 165 ], "score": 0.79, "content": "\\mathcal { L }", "type": "inline_equation" }, { "bbox": [ 277, 155, 326, 167 ], "score": 1.0, "content": "using Eq. 2", "type": "text" } ], "index": 6, "is_list_start_line": true }, { "bbox": [ 110, 165, 440, 179 ], "spans": [ { "bbox": [ 110, 167, 121, 178 ], "score": 1.0, "content": "5:", "type": "text" }, { "bbox": [ 133, 165, 240, 179 ], "score": 1.0, "content": "Ż Update the distilled data", "type": "text" }, { "bbox": [ 241, 166, 249, 176 ], "score": 0.37, "content": "s", "type": "inline_equation" }, { "bbox": [ 250, 166, 340, 178 ], "score": 0.86, "content": "\\mathrm { : } ~ X _ { s } \\gets X _ { s } - \\alpha \\nabla _ { X _ { s } } \\mathcal { L }", "type": "inline_equation" }, { "bbox": [ 340, 165, 360, 179 ], "score": 1.0, "content": ", and", "type": 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classifier. We fix the feature extractor at each meta-gradient computation and", "type": "text" } ], "index": 12 }, { "bbox": [ 105, 261, 505, 273 ], "spans": [ { "bbox": [ 105, 261, 329, 273 ], "score": 1.0, "content": "train the linear classifier to convergence before updating", "type": "text" }, { "bbox": [ 329, 261, 337, 271 ], "score": 0.67, "content": "s", "type": "inline_equation" }, { "bbox": [ 338, 261, 505, 273 ], "score": 1.0, "content": ". After that, we adjust the feature extractor", "type": "text" } ], "index": 13 }, { "bbox": [ 106, 272, 504, 284 ], "spans": [ { "bbox": [ 106, 272, 504, 284 ], "score": 1.0, "content": "by training the whole network on the updated distilled data. We note that similar two-phase procedure", "type": "text" } ], "index": 14 }, { "bbox": [ 105, 281, 358, 295 ], "spans": [ { "bbox": [ 105, 281, 358, 295 ], "score": 1.0, "content": "has been studied in the context of representation learning [31].", "type": "text" } ], "index": 15 } ], "index": 13.5, "bbox_fs": [ 105, 250, 505, 295 ] }, { "type": "text", "bbox": [ 106, 298, 505, 354 ], "lines": [ { "bbox": [ 106, 298, 505, 312 ], "spans": [ { "bbox": [ 106, 298, 505, 312 ], "score": 1.0, "content": "Meta-Gradient Computation: If we consider the mean square error loss, then the optimal weights", "type": "text" } ], "index": 16 }, { "bbox": [ 106, 308, 504, 323 ], "spans": [ { "bbox": [ 106, 308, 504, 323 ], "score": 1.0, "content": "for the linear classifier have a closed-form solution. Moreover, since the feature dimension is typically", "type": "text" } ], "index": 17 }, { "bbox": [ 105, 319, 506, 334 ], "spans": [ { "bbox": [ 105, 319, 506, 334 ], "score": 1.0, "content": "larger than the number of distilled data, we can use kernel ridge regression (KRR) with a conjugate", "type": "text" } ], "index": 18 }, { "bbox": [ 105, 331, 506, 345 ], "spans": [ { "bbox": [ 105, 331, 506, 345 ], "score": 1.0, "content": "kernel [25] rather than solving the weights explicitly [12]. The resulting meta-training loss (Eq. 2) is", "type": "text" } ], "index": 19 }, { "bbox": [ 105, 341, 455, 354 ], "spans": [ { "bbox": [ 105, 341, 455, 354 ], "score": 1.0, "content": "similar to that used in KIP [22, 23], but we use a more flexible kernel rather than NTK.", "type": "text" } ], "index": 20 } ], "index": 18, "bbox_fs": [ 105, 298, 506, 354 ] }, { "type": "interline_equation", "bbox": [ 182, 359, 427, 383 ], "lines": [ { "bbox": [ 182, 359, 427, 383 ], "spans": [ { "bbox": [ 182, 359, 427, 383 ], "score": 0.93, "content": "\\mathcal { L } \\left( \\mathcal { A } l g \\left( \\theta , \\mathcal { S } \\right) , \\mathcal { T } \\right) = \\frac { 1 } { 2 } | | Y _ { t } - K _ { X _ { t } X _ { s } } ^ { \\theta } ( K _ { X _ { s } X _ { s } } ^ { \\theta } + \\lambda I ) ^ { - 1 } Y _ { s } | | _ { 2 } ^ { 2 } ,", "type": "interline_equation", "image_path": "0cd9f2dca22b293f4e069930dff443abaa6142b03906a3c62fda7f6203ea2b36.jpg" } ] } ], "index": 21, "virtual_lines": [ { "bbox": [ 182, 359, 427, 383 ], "spans": [], "index": 21 } ] }, { "type": "text", "bbox": [ 106, 389, 506, 471 ], "lines": [ { "bbox": [ 105, 388, 507, 402 ], "spans": [ { "bbox": [ 105, 388, 133, 402 ], "score": 1.0, "content": "where", "type": "text" }, { "bbox": [ 134, 389, 167, 402 ], "score": 0.92, "content": "( X _ { t } , Y _ { t } )", "type": "inline_equation" }, { "bbox": [ 168, 388, 186, 402 ], "score": 1.0, "content": "and", "type": "text" }, { "bbox": [ 186, 389, 221, 402 ], "score": 0.92, "content": "( X _ { s } , Y _ { s } )", "type": "inline_equation" }, { "bbox": [ 222, 388, 384, 402 ], "score": 1.0, "content": "are the inputs and labels of the real data", "type": "text" }, { "bbox": [ 385, 390, 394, 400 ], "score": 0.82, "content": "\\tau", "type": "inline_equation" }, { "bbox": [ 394, 388, 466, 402 ], "score": 1.0, "content": "and distilled data", "type": "text" }, { "bbox": [ 466, 390, 474, 399 ], "score": 0.84, "content": "s", "type": "inline_equation" }, { "bbox": [ 474, 388, 507, 402 ], "score": 1.0, "content": "respec-", "type": "text" } ], "index": 22 }, { "bbox": [ 101, 397, 502, 420 ], "spans": [ { "bbox": [ 101, 397, 426, 420 ], "score": 1.0, "content": "tively. The Gram matrix between real inputs and distilled inputs is denoted as", "type": "text" }, { "bbox": [ 426, 401, 502, 415 ], "score": 0.92, "content": "K _ { X _ { t } X _ { s } } ^ { \\theta } \\in \\mathbb { R } ^ { | T | \\times | S | }", "type": "inline_equation" } ], "index": 23 }, { "bbox": [ 102, 409, 510, 433 ], "spans": [ { "bbox": [ 102, 409, 347, 433 ], "score": 1.0, "content": "while the Gram matrix between distilled inputs is denoted as", "type": "text" }, { "bbox": [ 348, 414, 422, 429 ], "score": 0.9, "content": "K _ { X _ { s } X _ { s } } ^ { \\theta } \\in \\mathbb { R } ^ { | S | \\times | S | }", "type": "inline_equation" }, { "bbox": [ 423, 409, 426, 433 ], "score": 1.0, "content": ".", "type": "text" }, { "bbox": [ 427, 416, 434, 425 ], "score": 0.66, "content": "\\lambda", "type": "inline_equation" }, { "bbox": [ 434, 409, 510, 433 ], "score": 1.0, "content": "t scontrols the regu-", "type": "text" } ], "index": 24 }, { "bbox": [ 105, 426, 506, 439 ], "spans": [ { "bbox": [ 105, 426, 450, 439 ], "score": 1.0, "content": "larization strength for KRR. Let us denote the neural network feature for a given input", "type": "text" }, { "bbox": [ 450, 427, 460, 437 ], "score": 0.83, "content": "X", "type": "inline_equation" }, { "bbox": [ 460, 426, 506, 439 ], "score": 1.0, "content": "and model", "type": "text" } ], "index": 25 }, { "bbox": [ 104, 434, 507, 451 ], "spans": [ { "bbox": [ 104, 434, 150, 451 ], "score": 1.0, "content": "parameter", "type": "text" }, { "bbox": [ 150, 438, 156, 447 ], "score": 0.81, "content": "\\theta", "type": "inline_equation" }, { "bbox": [ 156, 434, 168, 451 ], "score": 1.0, "content": "as", "type": "text" }, { "bbox": [ 169, 437, 237, 449 ], "score": 0.92, "content": "\\mathbf { \\bar { \\chi } } _ { f ( X , \\theta ) } \\in \\mathbb { R } ^ { N \\times d }", "type": "inline_equation" }, { "bbox": [ 237, 434, 268, 451 ], "score": 1.0, "content": ", where", "type": "text" }, { "bbox": [ 269, 439, 279, 447 ], "score": 0.83, "content": "N", "type": "inline_equation" }, { "bbox": [ 279, 434, 390, 451 ], "score": 1.0, "content": "is the number of input and", "type": "text" }, { "bbox": [ 390, 438, 397, 447 ], "score": 0.82, "content": "d", "type": "inline_equation" }, { "bbox": [ 397, 434, 507, 451 ], "score": 1.0, "content": "is the feature dimension 1.", "type": "text" } ], "index": 26 }, { "bbox": [ 106, 448, 506, 461 ], "spans": [ { "bbox": [ 106, 448, 506, 461 ], "score": 1.0, "content": "The conjugate kernel is defined by the inner product of the neural network features. Thus, the two", "type": "text" } ], "index": 27 }, { "bbox": [ 106, 460, 270, 471 ], "spans": [ { "bbox": [ 106, 460, 270, 471 ], "score": 1.0, "content": "Gram matrices are computed as follows:", "type": "text" } ], "index": 28 } ], "index": 25, "bbox_fs": [ 101, 388, 510, 471 ] }, { "type": "interline_equation", "bbox": [ 174, 477, 434, 493 ], "lines": [ { "bbox": [ 174, 477, 434, 493 ], "spans": [ { "bbox": [ 174, 477, 434, 493 ], "score": 0.91, "content": "K _ { X _ { t } X _ { s } } ^ { \\theta } = f ( X _ { t } , \\theta ) f ( X _ { s } , \\theta ) ^ { \\top } , \\quad K _ { X _ { s } X _ { s } } ^ { \\theta } = f ( X _ { s } , \\theta ) f ( X _ { s } , \\theta ) ^ { \\top } ,", "type": "interline_equation", "image_path": "87a4499ed59b016b53bcda7f7527fcb6ea8d32afd3493c3f5288d6937be23d26.jpg" } ] } ], "index": 29, "virtual_lines": [ { "bbox": [ 174, 477, 434, 493 ], "spans": [], "index": 29 } ] }, { "type": "text", "bbox": [ 106, 498, 505, 587 ], "lines": [ { "bbox": [ 105, 499, 506, 512 ], "spans": [ { "bbox": [ 105, 499, 249, 512 ], "score": 1.0, "content": "Now, computing the meta-gradient", "type": "text" }, { "bbox": [ 250, 499, 336, 511 ], "score": 0.93, "content": "\\nabla _ { \\mathcal { S } } \\mathcal { L } \\left( \\mathcal { A } l g \\left( \\theta , \\mathcal { S } \\right) , \\mathcal { T } \\right)", "type": "inline_equation" }, { "bbox": [ 337, 499, 506, 512 ], "score": 1.0, "content": "is just back-propagating through the con-", "type": "text" } ], "index": 30 }, { "bbox": [ 104, 511, 506, 523 ], "spans": [ { "bbox": [ 104, 511, 506, 523 ], "score": 1.0, "content": "jugate kernel and a fixed feature extractor, which is very efficient and takes even fewer operations", "type": "text" } ], "index": 31 }, { "bbox": [ 105, 522, 505, 534 ], "spans": [ { "bbox": [ 105, 522, 505, 534 ], "score": 1.0, "content": "than computing the gradient for the network’s weights. Moreover, we decouple the meta-gradient", "type": "text" } ], "index": 32 }, { "bbox": [ 105, 532, 506, 545 ], "spans": [ { "bbox": [ 105, 532, 506, 545 ], "score": 1.0, "content": "computation from the model online update. Hence, we can train the online model using any optimizer,", "type": "text" } ], "index": 33 }, { "bbox": [ 106, 543, 506, 556 ], "spans": [ { "bbox": [ 106, 543, 506, 556 ], "score": 1.0, "content": "and the distilled data will be agnostic to the specific learning algorithm choice. Our proposed method", "type": "text" } ], "index": 34 }, { "bbox": [ 105, 555, 505, 567 ], "spans": [ { "bbox": [ 105, 555, 505, 567 ], "score": 1.0, "content": "is similar to 1-step TBPTT in that we compute the meta-gradient at each step while performing the", "type": "text" } ], "index": 35 }, { "bbox": [ 104, 564, 506, 578 ], "spans": [ { "bbox": [ 104, 564, 506, 578 ], "score": 1.0, "content": "online model update. Unlike the conventional 1-step TBPTT, we compute the meta-gradient using a", "type": "text" } ], "index": 36 }, { "bbox": [ 106, 576, 391, 588 ], "spans": [ { "bbox": [ 106, 576, 391, 588 ], "score": 1.0, "content": "KRR output layer to mitigate truncation bias, illustrated in Figure 2(a).", "type": "text" } ], "index": 37 } ], "index": 33.5, "bbox_fs": [ 104, 499, 506, 588 ] }, { "type": "text", "bbox": [ 106, 591, 506, 691 ], "lines": [ { "bbox": [ 105, 591, 507, 605 ], "spans": [ { "bbox": [ 105, 591, 507, 605 ], "score": 1.0, "content": "Model Pool: As discussed in Section 1, there are various types of overfitting in dataset distillation.", "type": "text" } ], "index": 38 }, { "bbox": [ 105, 602, 506, 616 ], "spans": [ { "bbox": [ 105, 602, 506, 616 ], "score": 1.0, "content": "Several techniques have been proposed to alleviate such problem, such as random initialization [4],", "type": "text" } ], "index": 39 }, { "bbox": [ 104, 613, 507, 627 ], "spans": [ { "bbox": [ 104, 613, 507, 627 ], "score": 1.0, "content": "periodic reset [13, 5, 7], and dynamic bi-level optimization [19]. These techniques share the same", "type": "text" } ], "index": 40 }, { "bbox": [ 105, 624, 507, 637 ], "spans": [ { "bbox": [ 105, 624, 507, 637 ], "score": 1.0, "content": "underlying principle: the model diversity matters. Thus, we propose to maintain a “model pool”", "type": "text" } ], "index": 41 }, { "bbox": [ 105, 636, 506, 648 ], "spans": [ { "bbox": [ 105, 636, 506, 648 ], "score": 1.0, "content": "filled with diverse set of parameters obtained from different number of training steps and different", "type": "text" } ], "index": 42 }, { "bbox": [ 104, 646, 506, 660 ], "spans": [ { "bbox": [ 104, 646, 506, 660 ], "score": 1.0, "content": "random initializations. Unlike the previous methods that periodically training and resetting a single", "type": "text" } ], "index": 43 }, { "bbox": [ 105, 658, 505, 670 ], "spans": [ { "bbox": [ 105, 658, 505, 670 ], "score": 1.0, "content": "model, FRePo randomly sample a model from the pool at each meta-gradient computation and update", "type": "text" } ], "index": 44 }, { "bbox": [ 104, 667, 506, 682 ], "spans": [ { "bbox": [ 104, 667, 452, 682 ], "score": 1.0, "content": "it using the current distilled data. However, if a model has been updated more than", "type": "text" }, { "bbox": [ 453, 669, 463, 678 ], "score": 0.81, "content": "K", "type": "inline_equation" }, { "bbox": [ 464, 667, 506, 682 ], "score": 1.0, "content": "steps, we", "type": "text" } ], "index": 45 }, { "bbox": [ 105, 679, 505, 692 ], "spans": [ { "bbox": [ 105, 679, 505, 692 ], "score": 1.0, "content": "reinitialize it with a new random seed. From the meta-learning perspective, we maintain a diverse", "type": "text" } ], "index": 46 }, { "bbox": [ 106, 72, 505, 85 ], "spans": [ { "bbox": [ 106, 72, 505, 85 ], "score": 1.0, "content": "set of meta-tasks to sample from and avoid sampling very similar tasks at each consecutive gradient", "type": "text", "cross_page": true } ], "index": 0 }, { "bbox": [ 105, 83, 320, 96 ], "spans": [ { "bbox": [ 105, 83, 320, 96 ], "score": 1.0, "content": "computation to avoid overfitting to a particular setup.", "type": "text", "cross_page": true } ], "index": 1 } ], "index": 42, "bbox_fs": [ 104, 591, 507, 692 ] } ] }, { "preproc_blocks": [ { "type": "text", "bbox": [ 106, 73, 504, 95 ], "lines": [ { "bbox": [ 106, 72, 505, 85 ], "spans": [ { "bbox": [ 106, 72, 505, 85 ], "score": 1.0, "content": "set of meta-tasks to sample from and avoid sampling very similar tasks at each consecutive gradient", "type": "text" } ], "index": 0 }, { "bbox": [ 105, 83, 320, 96 ], "spans": [ { "bbox": [ 105, 83, 320, 96 ], "score": 1.0, "content": "computation to avoid overfitting to a particular setup.", "type": "text" } ], "index": 1 } ], "index": 0.5 }, { "type": "text", "bbox": [ 107, 100, 505, 166 ], "lines": [ { "bbox": [ 105, 100, 505, 113 ], "spans": [ { "bbox": [ 105, 100, 505, 113 ], "score": 1.0, "content": "Pool Diversity: We can increase the regularization strength by increasing the diversity of the model", "type": "text" } ], "index": 2 }, { "bbox": [ 105, 111, 506, 124 ], "spans": [ { "bbox": [ 105, 111, 200, 124 ], "score": 1.0, "content": "pool by setting a larger", "type": "text" }, { "bbox": [ 200, 111, 210, 121 ], "score": 0.78, "content": "K", "type": "inline_equation" }, { "bbox": [ 210, 111, 506, 124 ], "score": 1.0, "content": ", using data augmentation when training the model on the distilled data, or", "type": "text" } ], "index": 3 }, { "bbox": [ 105, 122, 505, 134 ], "spans": [ { "bbox": [ 105, 122, 505, 134 ], "score": 1.0, "content": "using models with different architectures. To keep our method simple, we use the same architecture", "type": "text" } ], "index": 4 }, { "bbox": [ 105, 132, 505, 145 ], "spans": [ { "bbox": [ 105, 132, 505, 145 ], "score": 1.0, "content": "for all models in the pool and do not use any data augmentation when training the model on the", "type": "text" } ], "index": 5 }, { "bbox": [ 105, 143, 505, 156 ], "spans": [ { "bbox": [ 105, 143, 505, 156 ], "score": 1.0, "content": "distilled data. Thus, our model pool only contains models with different initialization, at different", "type": "text" } ], "index": 6 }, { "bbox": [ 105, 154, 403, 167 ], "spans": [ { "bbox": [ 105, 154, 403, 167 ], "score": 1.0, "content": "optimization stages, and trained at different time-step of the distilled data.", "type": "text" } ], "index": 7 } ], "index": 4.5 }, { "type": "title", "bbox": [ 107, 184, 197, 198 ], "lines": [ { "bbox": [ 104, 183, 198, 200 ], "spans": [ { "bbox": [ 104, 183, 198, 200 ], "score": 1.0, "content": "3 Related Work", "type": "text" } ], "index": 8 } ], "index": 8 }, { "type": "text", "bbox": [ 107, 212, 505, 278 ], "lines": [ { "bbox": [ 106, 210, 505, 225 ], "spans": [ { "bbox": [ 106, 210, 505, 225 ], "score": 1.0, "content": "Unrolling in Bi-Level Optimization: One way to compute the meta-gradient is to differentiate", "type": "text" } ], "index": 9 }, { "bbox": [ 106, 223, 505, 236 ], "spans": [ { "bbox": [ 106, 223, 505, 236 ], "score": 1.0, "content": "through the unrolled inner optimization [4, 11–13]. However, this approach inherits several difficulties", "type": "text" } ], "index": 10 }, { "bbox": [ 106, 234, 504, 246 ], "spans": [ { "bbox": [ 106, 234, 504, 246 ], "score": 1.0, "content": "of the unrolled optimization, such as: 1) large computation and memory cost [14]; 2) truncation", "type": "text" } ], "index": 11 }, { "bbox": [ 105, 243, 505, 258 ], "spans": [ { "bbox": [ 105, 243, 505, 258 ], "score": 1.0, "content": "bias with short unrolls [17]; 3) exploding or vanishing gradients with long unrolls [15]; 4) chaotic", "type": "text" } ], "index": 12 }, { "bbox": [ 105, 255, 505, 268 ], "spans": [ { "bbox": [ 105, 255, 505, 268 ], "score": 1.0, "content": "and poorly conditioned loss landscapes with long unrolls [16]. In contrast, our method considers", "type": "text" } ], "index": 13 }, { "bbox": [ 105, 267, 503, 279 ], "spans": [ { "bbox": [ 105, 267, 503, 279 ], "score": 1.0, "content": "approximating the inner optimization with kernel ridge regression instead of unrolled optimization.", "type": "text" } ], "index": 14 } ], "index": 11.5 }, { "type": "text", "bbox": [ 107, 282, 505, 382 ], "lines": [ { "bbox": [ 105, 282, 507, 295 ], "spans": [ { "bbox": [ 105, 282, 507, 295 ], "score": 1.0, "content": "Surrogate Objective: To avoid unrolled optimization, several works turn to surrogate objectives.", "type": "text" } ], "index": 15 }, { "bbox": [ 106, 294, 505, 306 ], "spans": [ { "bbox": [ 106, 294, 505, 306 ], "score": 1.0, "content": "DC [5], DSA [7], and DCC [18] formulate the dataset distillation as a gradient matching problem", "type": "text" } ], "index": 16 }, { "bbox": [ 105, 304, 507, 318 ], "spans": [ { "bbox": [ 105, 304, 507, 318 ], "score": 1.0, "content": "between the gradients of neural network weights computed on the real and distilled data. In contrast,", "type": "text" } ], "index": 17 }, { "bbox": [ 105, 315, 506, 328 ], "spans": [ { "bbox": [ 105, 315, 506, 328 ], "score": 1.0, "content": "DM [8] and CAFE [19] consider the feature distribution alignment between the real and distilled data.", "type": "text" } ], "index": 18 }, { "bbox": [ 105, 326, 505, 339 ], "spans": [ { "bbox": [ 105, 326, 505, 339 ], "score": 1.0, "content": "Moreover, MTT [20] shows that knowledge from many expert training trajectories can be distilled to", "type": "text" } ], "index": 19 }, { "bbox": [ 105, 337, 505, 351 ], "spans": [ { "bbox": [ 105, 337, 505, 351 ], "score": 1.0, "content": "a dataset by using a training trajectory matching objective. Nevertheless, surrogate objectives may", "type": "text" } ], "index": 20 }, { "bbox": [ 106, 348, 505, 361 ], "spans": [ { "bbox": [ 106, 348, 505, 361 ], "score": 1.0, "content": "introduce new biases and thus, may not accurately reflect the true objective. For example, gradient", "type": "text" } ], "index": 21 }, { "bbox": [ 105, 358, 506, 371 ], "spans": [ { "bbox": [ 105, 358, 506, 371 ], "score": 1.0, "content": "matching approaches [5, 7, 18] only focus on short-range behavior and may easily overfit to a biased", "type": "text" } ], "index": 22 }, { "bbox": [ 106, 371, 333, 383 ], "spans": [ { "bbox": [ 106, 371, 333, 383 ], "score": 1.0, "content": "set of samples that produce dominant gradients [19, 20].", "type": "text" } ], "index": 23 } ], "index": 19 }, { "type": "text", "bbox": [ 107, 386, 505, 485 ], "lines": [ { "bbox": [ 106, 387, 506, 399 ], "spans": [ { "bbox": [ 106, 387, 506, 399 ], "score": 1.0, "content": "Closed-form Approximation: An alternative way to circumvent unrolled optimization is to find a", "type": "text" } ], "index": 24 }, { "bbox": [ 106, 398, 506, 410 ], "spans": [ { "bbox": [ 106, 398, 506, 410 ], "score": 1.0, "content": "closed-form approximation to the inner optimization. Based on the correspondence between infinitely-", "type": "text" } ], "index": 25 }, { "bbox": [ 106, 409, 505, 421 ], "spans": [ { "bbox": [ 106, 409, 505, 421 ], "score": 1.0, "content": "wide neural networks and kernel methods, KIP [22, 23] approximates the inner optimization with", "type": "text" } ], "index": 26 }, { "bbox": [ 105, 419, 506, 432 ], "spans": [ { "bbox": [ 105, 419, 506, 432 ], "score": 1.0, "content": "NTK [21]. In this case, the meta-gradient can be computed by back-propagating through the NTK.", "type": "text" } ], "index": 27 }, { "bbox": [ 105, 430, 506, 444 ], "spans": [ { "bbox": [ 105, 430, 506, 444 ], "score": 1.0, "content": "However, computing NTK for modern neural networks is extremely expensive. Thus, using NTK", "type": "text" } ], "index": 28 }, { "bbox": [ 106, 441, 506, 454 ], "spans": [ { "bbox": [ 106, 441, 506, 454 ], "score": 1.0, "content": "for dataset distillation requires thousands of GPU hours and sophisticated implementation of the", "type": "text" } ], "index": 29 }, { "bbox": [ 106, 452, 505, 465 ], "spans": [ { "bbox": [ 106, 452, 505, 465 ], "score": 1.0, "content": "distributed kernel computation framework [23]. Similar to ours, Bohdal et al. [12] also decomposes", "type": "text" } ], "index": 30 }, { "bbox": [ 106, 462, 506, 475 ], "spans": [ { "bbox": [ 106, 462, 506, 475 ], "score": 1.0, "content": "the neural network as a feature extractor and a linear classifier. However, they only learn the label", "type": "text" } ], "index": 31 }, { "bbox": [ 106, 474, 425, 487 ], "spans": [ { "bbox": [ 106, 474, 425, 487 ], "score": 1.0, "content": "and explicitly solve for the optimal classifier weights rather than perform KRR.", "type": "text" } ], "index": 32 } ], "index": 28 }, { "type": "title", "bbox": [ 108, 504, 223, 517 ], "lines": [ { "bbox": [ 105, 503, 225, 519 ], "spans": [ { "bbox": [ 105, 503, 225, 519 ], "score": 1.0, "content": "4 Dataset Distillation", "type": "text" } ], "index": 33 } ], "index": 33 }, { "type": "title", "bbox": [ 107, 531, 231, 542 ], "lines": [ { "bbox": [ 105, 530, 231, 544 ], "spans": [ { "bbox": [ 105, 530, 231, 544 ], "score": 1.0, "content": "4.1 Implementation Details", "type": "text" } ], "index": 34 } ], "index": 34 }, { "type": "text", "bbox": [ 107, 552, 505, 662 ], "lines": [ { "bbox": [ 106, 553, 505, 564 ], "spans": [ { "bbox": [ 106, 553, 505, 564 ], "score": 1.0, "content": "We compare our method to four state-of-the-art dataset distillation methods [7, 8, 20, 23] on various", "type": "text" } ], "index": 35 }, { "bbox": [ 105, 563, 506, 576 ], "spans": [ { "bbox": [ 105, 563, 506, 576 ], "score": 1.0, "content": "benchmark datasets [26, 32–37]. We train the distilled data using Algorithm 1 with the same set of", "type": "text" } ], "index": 36 }, { "bbox": [ 105, 574, 506, 587 ], "spans": [ { "bbox": [ 105, 574, 506, 587 ], "score": 1.0, "content": "hyperparameters for all experiments except stated otherwise. Unlike prior work [7, 8, 20], we do not", "type": "text" } ], "index": 37 }, { "bbox": [ 105, 585, 506, 598 ], "spans": [ { "bbox": [ 105, 585, 506, 598 ], "score": 1.0, "content": "apply data augmentation during training. However, we apply the same data augmentation [7, 20]", "type": "text" } ], "index": 38 }, { "bbox": [ 105, 596, 506, 609 ], "spans": [ { "bbox": [ 105, 596, 506, 609 ], "score": 1.0, "content": "during evaluation for a fair comparison. We preprocess the data in a similar way as in previous works", "type": "text" } ], "index": 39 }, { "bbox": [ 105, 606, 506, 620 ], "spans": [ { "bbox": [ 105, 606, 506, 620 ], "score": 1.0, "content": "[20, 23] but use a wider architecture than previous works [7, 8, 20] because the KRR component does", "type": "text" } ], "index": 40 }, { "bbox": [ 105, 618, 506, 630 ], "spans": [ { "bbox": [ 105, 618, 506, 630 ], "score": 1.0, "content": "not behave well when the feature dimension is low, resulting in a significant performance drop for our", "type": "text" } ], "index": 41 }, { "bbox": [ 105, 628, 506, 641 ], "spans": [ { "bbox": [ 105, 628, 506, 641 ], "score": 1.0, "content": "method. Results on the original architecture are included in Appendix ??. We evaluate each distilled", "type": "text" } ], "index": 42 }, { "bbox": [ 106, 640, 505, 652 ], "spans": [ { "bbox": [ 106, 640, 505, 652 ], "score": 1.0, "content": "data using five random neural networks and report the mean and standard deviation. For the baseline", "type": "text" } ], "index": 43 }, { "bbox": [ 105, 650, 497, 663 ], "spans": [ { "bbox": [ 105, 650, 497, 663 ], "score": 1.0, "content": "method, we report the best of the reported value in the original paper and our reproducing results.", "type": "text" } ], "index": 44 } ], "index": 39.5 }, { "type": "text", "bbox": [ 107, 667, 504, 722 ], "lines": [ { "bbox": [ 105, 666, 506, 680 ], "spans": [ { "bbox": [ 105, 666, 506, 680 ], "score": 1.0, "content": "For the sake of brevity, we provide implementation details about data preprocessing, distilled data", "type": "text" } ], "index": 45 }, { "bbox": [ 105, 677, 505, 691 ], "spans": [ { "bbox": [ 105, 677, 505, 691 ], "score": 1.0, "content": "initialization, and hyperparameters in Appendix ?? and various ablation studies regarding the model", "type": "text" } ], "index": 46 }, { "bbox": [ 105, 688, 506, 702 ], "spans": [ { "bbox": [ 105, 688, 506, 702 ], "score": 1.0, "content": "pool, batch size, distilled data initialization, label learning, and model architectures in Appendix", "type": "text" } ], "index": 47 }, { "bbox": [ 105, 698, 506, 713 ], "spans": [ { "bbox": [ 105, 698, 506, 713 ], "score": 1.0, "content": "??. More distilled image visualizations can be found in Appendix ??. Our code is available at", "type": "text" } ], "index": 48 }, { "bbox": [ 105, 710, 294, 724 ], "spans": [ { "bbox": [ 105, 710, 294, 724 ], "score": 1.0, "content": "https://github.com/yongchao97/FRePo.", "type": "text" } ], "index": 49 } ], "index": 47 } ], "page_idx": 4, "page_size": [ 612, 792 ], "discarded_blocks": [ { "type": "discarded", "bbox": [ 302, 741, 309, 750 ], "lines": [ { "bbox": [ 301, 740, 310, 753 ], "spans": [ { "bbox": [ 301, 740, 310, 753 ], "score": 1.0, "content": "5", "type": "text" } ] } ] } ], "para_blocks": [ { "type": "text", "bbox": [ 106, 73, 504, 95 ], "lines": [], "index": 0.5, "bbox_fs": [ 105, 72, 505, 96 ], "lines_deleted": true }, { "type": "text", "bbox": [ 107, 100, 505, 166 ], "lines": [ { "bbox": [ 105, 100, 505, 113 ], "spans": [ { "bbox": [ 105, 100, 505, 113 ], "score": 1.0, "content": "Pool Diversity: We can increase the regularization strength by increasing the diversity of the model", "type": "text" } ], "index": 2 }, { "bbox": [ 105, 111, 506, 124 ], "spans": [ { "bbox": [ 105, 111, 200, 124 ], "score": 1.0, "content": "pool by setting a larger", "type": "text" }, { "bbox": [ 200, 111, 210, 121 ], "score": 0.78, "content": "K", "type": "inline_equation" }, { "bbox": [ 210, 111, 506, 124 ], "score": 1.0, "content": ", using data augmentation when training the model on the distilled data, or", "type": "text" } ], "index": 3 }, { "bbox": [ 105, 122, 505, 134 ], "spans": [ { "bbox": [ 105, 122, 505, 134 ], "score": 1.0, "content": "using models with different architectures. To keep our method simple, we use the same architecture", "type": "text" } ], "index": 4 }, { "bbox": [ 105, 132, 505, 145 ], "spans": [ { "bbox": [ 105, 132, 505, 145 ], "score": 1.0, "content": "for all models in the pool and do not use any data augmentation when training the model on the", "type": "text" } ], "index": 5 }, { "bbox": [ 105, 143, 505, 156 ], "spans": [ { "bbox": [ 105, 143, 505, 156 ], "score": 1.0, "content": "distilled data. Thus, our model pool only contains models with different initialization, at different", "type": "text" } ], "index": 6 }, { "bbox": [ 105, 154, 403, 167 ], "spans": [ { "bbox": [ 105, 154, 403, 167 ], "score": 1.0, "content": "optimization stages, and trained at different time-step of the distilled data.", "type": "text" } ], "index": 7 } ], "index": 4.5, "bbox_fs": [ 105, 100, 506, 167 ] }, { "type": "title", "bbox": [ 107, 184, 197, 198 ], "lines": [ { "bbox": [ 104, 183, 198, 200 ], "spans": [ { "bbox": [ 104, 183, 198, 200 ], "score": 1.0, "content": "3 Related Work", "type": "text" } ], "index": 8 } ], "index": 8 }, { "type": "text", "bbox": [ 107, 212, 505, 278 ], "lines": [ { "bbox": [ 106, 210, 505, 225 ], "spans": [ { "bbox": [ 106, 210, 505, 225 ], "score": 1.0, "content": "Unrolling in Bi-Level Optimization: One way to compute the meta-gradient is to differentiate", "type": "text" } ], "index": 9 }, { "bbox": [ 106, 223, 505, 236 ], "spans": [ { "bbox": [ 106, 223, 505, 236 ], "score": 1.0, "content": "through the unrolled inner optimization [4, 11–13]. However, this approach inherits several difficulties", "type": "text" } ], "index": 10 }, { "bbox": [ 106, 234, 504, 246 ], "spans": [ { "bbox": [ 106, 234, 504, 246 ], "score": 1.0, "content": "of the unrolled optimization, such as: 1) large computation and memory cost [14]; 2) truncation", "type": "text" } ], "index": 11 }, { "bbox": [ 105, 243, 505, 258 ], "spans": [ { "bbox": [ 105, 243, 505, 258 ], "score": 1.0, "content": "bias with short unrolls [17]; 3) exploding or vanishing gradients with long unrolls [15]; 4) chaotic", "type": "text" } ], "index": 12 }, { "bbox": [ 105, 255, 505, 268 ], "spans": [ { "bbox": [ 105, 255, 505, 268 ], "score": 1.0, "content": "and poorly conditioned loss landscapes with long unrolls [16]. In contrast, our method considers", "type": "text" } ], "index": 13 }, { "bbox": [ 105, 267, 503, 279 ], "spans": [ { "bbox": [ 105, 267, 503, 279 ], "score": 1.0, "content": "approximating the inner optimization with kernel ridge regression instead of unrolled optimization.", "type": "text" } ], "index": 14 } ], "index": 11.5, "bbox_fs": [ 105, 210, 505, 279 ] }, { "type": "text", "bbox": [ 107, 282, 505, 382 ], "lines": [ { "bbox": [ 105, 282, 507, 295 ], "spans": [ { "bbox": [ 105, 282, 507, 295 ], "score": 1.0, "content": "Surrogate Objective: To avoid unrolled optimization, several works turn to surrogate objectives.", "type": "text" } ], "index": 15 }, { "bbox": [ 106, 294, 505, 306 ], "spans": [ { "bbox": [ 106, 294, 505, 306 ], "score": 1.0, "content": "DC [5], DSA [7], and DCC [18] formulate the dataset distillation as a gradient matching problem", "type": "text" } ], "index": 16 }, { "bbox": [ 105, 304, 507, 318 ], "spans": [ { "bbox": [ 105, 304, 507, 318 ], "score": 1.0, "content": "between the gradients of neural network weights computed on the real and distilled data. In contrast,", "type": "text" } ], "index": 17 }, { "bbox": [ 105, 315, 506, 328 ], "spans": [ { "bbox": [ 105, 315, 506, 328 ], "score": 1.0, "content": "DM [8] and CAFE [19] consider the feature distribution alignment between the real and distilled data.", "type": "text" } ], "index": 18 }, { "bbox": [ 105, 326, 505, 339 ], "spans": [ { "bbox": [ 105, 326, 505, 339 ], "score": 1.0, "content": "Moreover, MTT [20] shows that knowledge from many expert training trajectories can be distilled to", "type": "text" } ], "index": 19 }, { "bbox": [ 105, 337, 505, 351 ], "spans": [ { "bbox": [ 105, 337, 505, 351 ], "score": 1.0, "content": "a dataset by using a training trajectory matching objective. Nevertheless, surrogate objectives may", "type": "text" } ], "index": 20 }, { "bbox": [ 106, 348, 505, 361 ], "spans": [ { "bbox": [ 106, 348, 505, 361 ], "score": 1.0, "content": "introduce new biases and thus, may not accurately reflect the true objective. For example, gradient", "type": "text" } ], "index": 21 }, { "bbox": [ 105, 358, 506, 371 ], "spans": [ { "bbox": [ 105, 358, 506, 371 ], "score": 1.0, "content": "matching approaches [5, 7, 18] only focus on short-range behavior and may easily overfit to a biased", "type": "text" } ], "index": 22 }, { "bbox": [ 106, 371, 333, 383 ], "spans": [ { "bbox": [ 106, 371, 333, 383 ], "score": 1.0, "content": "set of samples that produce dominant gradients [19, 20].", "type": "text" } ], "index": 23 } ], "index": 19, "bbox_fs": [ 105, 282, 507, 383 ] }, { "type": "text", "bbox": [ 107, 386, 505, 485 ], "lines": [ { "bbox": [ 106, 387, 506, 399 ], "spans": [ { "bbox": [ 106, 387, 506, 399 ], "score": 1.0, "content": "Closed-form Approximation: An alternative way to circumvent unrolled optimization is to find a", "type": "text" } ], "index": 24 }, { "bbox": [ 106, 398, 506, 410 ], "spans": [ { "bbox": [ 106, 398, 506, 410 ], "score": 1.0, "content": "closed-form approximation to the inner optimization. Based on the correspondence between infinitely-", "type": "text" } ], "index": 25 }, { "bbox": [ 106, 409, 505, 421 ], "spans": [ { "bbox": [ 106, 409, 505, 421 ], "score": 1.0, "content": "wide neural networks and kernel methods, KIP [22, 23] approximates the inner optimization with", "type": "text" } ], "index": 26 }, { "bbox": [ 105, 419, 506, 432 ], "spans": [ { "bbox": [ 105, 419, 506, 432 ], "score": 1.0, "content": "NTK [21]. In this case, the meta-gradient can be computed by back-propagating through the NTK.", "type": "text" } ], "index": 27 }, { "bbox": [ 105, 430, 506, 444 ], "spans": [ { "bbox": [ 105, 430, 506, 444 ], "score": 1.0, "content": "However, computing NTK for modern neural networks is extremely expensive. Thus, using NTK", "type": "text" } ], "index": 28 }, { "bbox": [ 106, 441, 506, 454 ], "spans": [ { "bbox": [ 106, 441, 506, 454 ], "score": 1.0, "content": "for dataset distillation requires thousands of GPU hours and sophisticated implementation of the", "type": "text" } ], "index": 29 }, { "bbox": [ 106, 452, 505, 465 ], "spans": [ { "bbox": [ 106, 452, 505, 465 ], "score": 1.0, "content": "distributed kernel computation framework [23]. Similar to ours, Bohdal et al. [12] also decomposes", "type": "text" } ], "index": 30 }, { "bbox": [ 106, 462, 506, 475 ], "spans": [ { "bbox": [ 106, 462, 506, 475 ], "score": 1.0, "content": "the neural network as a feature extractor and a linear classifier. However, they only learn the label", "type": "text" } ], "index": 31 }, { "bbox": [ 106, 474, 425, 487 ], "spans": [ { "bbox": [ 106, 474, 425, 487 ], "score": 1.0, "content": "and explicitly solve for the optimal classifier weights rather than perform KRR.", "type": "text" } ], "index": 32 } ], "index": 28, "bbox_fs": [ 105, 387, 506, 487 ] }, { "type": "title", "bbox": [ 108, 504, 223, 517 ], "lines": [ { "bbox": [ 105, 503, 225, 519 ], "spans": [ { "bbox": [ 105, 503, 225, 519 ], "score": 1.0, "content": "4 Dataset Distillation", "type": "text" } ], "index": 33 } ], "index": 33 }, { "type": "title", "bbox": [ 107, 531, 231, 542 ], "lines": [ { "bbox": [ 105, 530, 231, 544 ], "spans": [ { "bbox": [ 105, 530, 231, 544 ], "score": 1.0, "content": "4.1 Implementation Details", "type": "text" } ], "index": 34 } ], "index": 34 }, { "type": "text", "bbox": [ 107, 552, 505, 662 ], "lines": [ { "bbox": [ 106, 553, 505, 564 ], "spans": [ { "bbox": [ 106, 553, 505, 564 ], "score": 1.0, "content": "We compare our method to four state-of-the-art dataset distillation methods [7, 8, 20, 23] on various", "type": "text" } ], "index": 35 }, { "bbox": [ 105, 563, 506, 576 ], "spans": [ { "bbox": [ 105, 563, 506, 576 ], "score": 1.0, "content": "benchmark datasets [26, 32–37]. We train the distilled data using Algorithm 1 with the same set of", "type": "text" } ], "index": 36 }, { "bbox": [ 105, 574, 506, 587 ], "spans": [ { "bbox": [ 105, 574, 506, 587 ], "score": 1.0, "content": "hyperparameters for all experiments except stated otherwise. Unlike prior work [7, 8, 20], we do not", "type": "text" } ], "index": 37 }, { "bbox": [ 105, 585, 506, 598 ], "spans": [ { "bbox": [ 105, 585, 506, 598 ], "score": 1.0, "content": "apply data augmentation during training. However, we apply the same data augmentation [7, 20]", "type": "text" } ], "index": 38 }, { "bbox": [ 105, 596, 506, 609 ], "spans": [ { "bbox": [ 105, 596, 506, 609 ], "score": 1.0, "content": "during evaluation for a fair comparison. We preprocess the data in a similar way as in previous works", "type": "text" } ], "index": 39 }, { "bbox": [ 105, 606, 506, 620 ], "spans": [ { "bbox": [ 105, 606, 506, 620 ], "score": 1.0, "content": "[20, 23] but use a wider architecture than previous works [7, 8, 20] because the KRR component does", "type": "text" } ], "index": 40 }, { "bbox": [ 105, 618, 506, 630 ], "spans": [ { "bbox": [ 105, 618, 506, 630 ], "score": 1.0, "content": "not behave well when the feature dimension is low, resulting in a significant performance drop for our", "type": "text" } ], "index": 41 }, { "bbox": [ 105, 628, 506, 641 ], "spans": [ { "bbox": [ 105, 628, 506, 641 ], "score": 1.0, "content": "method. Results on the original architecture are included in Appendix ??. We evaluate each distilled", "type": "text" } ], "index": 42 }, { "bbox": [ 106, 640, 505, 652 ], "spans": [ { "bbox": [ 106, 640, 505, 652 ], "score": 1.0, "content": "data using five random neural networks and report the mean and standard deviation. For the baseline", "type": "text" } ], "index": 43 }, { "bbox": [ 105, 650, 497, 663 ], "spans": [ { "bbox": [ 105, 650, 497, 663 ], "score": 1.0, "content": "method, we report the best of the reported value in the original paper and our reproducing results.", "type": "text" } ], "index": 44 } ], "index": 39.5, "bbox_fs": [ 105, 553, 506, 663 ] }, { "type": "text", "bbox": [ 107, 667, 504, 722 ], "lines": [ { "bbox": [ 105, 666, 506, 680 ], "spans": [ { "bbox": [ 105, 666, 506, 680 ], "score": 1.0, "content": "For the sake of brevity, we provide implementation details about data preprocessing, distilled data", "type": "text" } ], "index": 45 }, { "bbox": [ 105, 677, 505, 691 ], "spans": [ { "bbox": [ 105, 677, 505, 691 ], "score": 1.0, "content": "initialization, and hyperparameters in Appendix ?? and various ablation studies regarding the model", "type": "text" } ], "index": 46 }, { "bbox": [ 105, 688, 506, 702 ], "spans": [ { "bbox": [ 105, 688, 506, 702 ], "score": 1.0, "content": "pool, batch size, distilled data initialization, label learning, and model architectures in Appendix", "type": "text" } ], "index": 47 }, { "bbox": [ 105, 698, 506, 713 ], "spans": [ { "bbox": [ 105, 698, 506, 713 ], "score": 1.0, "content": "??. More distilled image visualizations can be found in Appendix ??. Our code is available at", "type": "text" } ], "index": 48 }, { "bbox": [ 105, 710, 294, 724 ], "spans": [ { "bbox": [ 105, 710, 294, 724 ], "score": 1.0, "content": "https://github.com/yongchao97/FRePo.", "type": "text" } ], "index": 49 } ], "index": 47, "bbox_fs": [ 105, 666, 506, 724 ] } ] }, { "preproc_blocks": [ { "type": "table", "bbox": [ 106, 111, 512, 333 ], "blocks": [ { "type": "table_caption", "bbox": [ 106, 78, 506, 111 ], "group_id": 0, "lines": [ { "bbox": [ 105, 77, 506, 91 ], "spans": [ { "bbox": [ 105, 77, 506, 91 ], "score": 1.0, "content": "Table 1: Test accuracies of models trained on the distilled data from scratch. : denotes performance", "type": "text" } ], "index": 0 }, { "bbox": [ 106, 88, 504, 101 ], "spans": [ { "bbox": [ 106, 88, 504, 101 ], "score": 1.0, "content": "better than the original reported performance. KRR preformance is shown in bracket. FRePo performs", "type": "text" } ], "index": 1 }, { "bbox": [ 106, 100, 476, 112 ], "spans": [ { "bbox": [ 106, 100, 476, 112 ], "score": 1.0, "content": "extremely well for one image per class setting on CIFAR100, Tiny ImageNet and CUB-200.", "type": "text" } ], "index": 2 } ], "index": 1 }, { "type": "table_body", "bbox": [ 106, 111, 512, 333 ], "group_id": 0, "lines": [ { "bbox": [ 106, 111, 512, 333 ], "spans": [ { "bbox": [ 106, 111, 512, 333 ], "score": 0.983, "html": "
Img/ClsDSA [7]DM[8]KIP [23]MTT [20]FRePo
MNIST188.7±0.689.9 ± 0.8†90.1± 0.191.4 ± 0.9†93.0 ± 0.4 (92.6 ± 0.4)
1097.9 ±0.1†97.6 ± 0.1†97.5 ± 0.097.3 ± 0.1+98.6 ± 0.1 (98.6 ± 0.1)
5099.2 ± 0.198.6 ± 0.198.3 ± 0.198.5±0.1+99.2 ± 0.0 (99.2± 0.1)
F-MNIST170.6 ± 0.671.5 ± 0.5†73.5± 0.575.1 ± 0.9†75.6 ± 0.3 (77.1 ± 0.2)
1084.8±0.3t83.6±0.2t86.8±0.187.2± 0.3+86.2 ± 0.2 (86.8 ± 0.1)
5088.8±0.2t88.2±0.1†88.0±0.188.3± 0.1+89.6 ± 0.1 (89.9 ± 0.1)
CIFAR10136.7± 0.8†31.0 ± 0.6†49.9 ± 0.246.3 ± 0.846.8 ± 0.7 (47.9 ± 0.6)
1053.2 ± 0.8†49.2 ± 0.8†62.7± 0.365.3 ± 0.765.5 ± 0.4 (68.0 ± 0.2)
5066.8± 0.4†63.7±0.5t68.6± 0.271.6 ± 0.271.7 ± 0.2 (74.4 ± 0.1)
CIFAR100116.8± 0.2†12.2 ± 0.4†15.7 ± 0.224.3 ± 0.328.7 ± 0.1 (32.3 ± 0.1)
1032.3 ±0.329.7 ±0.328.3 ± 0.140.1 ± 0.442.5 ± 0.2 (44.9 ± 0.2)
5042.8± 0.443.6 ± 0.4147.7 ± 0.244.3 ± 0.2 (43.0 ± 0.3)
T-ImageNet16.6± 0.2t3.9± 0.28.8 ±0.315.4 ± 0.3 (19.1 ± 0.3)
1012.9 ± 0.423.2 ± 0.225.4 ± 0.2 (26.5± 0.1)
CUB-20011.3 ± 0.1†1.6 ± 0.1†2.2± 0.1†12.4 ± 0.2 (13.7 ± 0.2)
104.5 ± 0.3†4.4 ± 0.2†116.8 ± 0.1 (16.1 ± 0.3)
", "type": "table", "image_path": "a5d293177e310c0c210335bf5ab5229cfb17e497a341c9da5f6d75598dd1f5dd.jpg" } ] } ], "index": 4, "virtual_lines": [ { "bbox": [ 106, 111, 512, 185.0 ], "spans": [], "index": 3 }, { "bbox": [ 106, 185.0, 512, 259.0 ], "spans": [], "index": 4 }, { "bbox": [ 106, 259.0, 512, 333.0 ], "spans": [], "index": 5 } ] } ], "index": 2.5 }, { "type": "image", "bbox": [ 106, 351, 504, 439 ], "blocks": [ { "type": "image_body", "bbox": [ 106, 351, 504, 439 ], "group_id": 0, "lines": [ { "bbox": [ 106, 351, 504, 439 ], "spans": [ { "bbox": [ 106, 351, 504, 439 ], "score": 0.96, "type": "image", "image_path": "f1494e6fda90eb5674ceeec703ad75133081347b4f6471179e08a6c207b5ecd8.jpg" } ] } ], "index": 7, "virtual_lines": [ { "bbox": [ 106, 351, 504, 380.3333333333333 ], "spans": [], "index": 6 }, { "bbox": [ 106, 380.3333333333333, 504, 409.66666666666663 ], "spans": [], "index": 7 }, { "bbox": [ 106, 409.66666666666663, 504, 438.99999999999994 ], "spans": [], "index": 8 } ] }, { "type": "image_caption", "bbox": [ 106, 445, 506, 490 ], "group_id": 0, "lines": [ { "bbox": [ 105, 444, 506, 459 ], "spans": [ { "bbox": [ 105, 444, 347, 459 ], "score": 1.0, "content": "Figure 3: (a,b) Training efficiency comparison when learning", "type": "text" }, { "bbox": [ 347, 446, 387, 456 ], "score": 0.45, "content": "1 \\mathrm { I m g / C l s }", "type": "inline_equation" }, { "bbox": [ 387, 444, 506, 459 ], "score": 1.0, "content": "on CIFAR100. (c,d) Time per", "type": "text" } ], "index": 9 }, { "bbox": [ 105, 456, 506, 469 ], "spans": [ { "bbox": [ 105, 456, 506, 469 ], "score": 1.0, "content": "iteration and peak memory usage as we increase the model size. FRePo is significantly more efficient", "type": "text" } ], "index": 10 }, { "bbox": [ 105, 467, 506, 480 ], "spans": [ { "bbox": [ 105, 467, 506, 480 ], "score": 1.0, "content": "than the previous methods, almost two orders of magnitude faster than the second-best method (i.e.,", "type": "text" } ], "index": 11 }, { "bbox": [ 105, 478, 334, 491 ], "spans": [ { "bbox": [ 105, 478, 334, 491 ], "score": 1.0, "content": "MTT), with only 1/10 of the GPU memory requirement.", "type": "text" } ], "index": 12 } ], "index": 10.5 } ], "index": 8.75 }, { "type": "title", "bbox": [ 108, 514, 226, 526 ], "lines": [ { "bbox": [ 106, 514, 227, 527 ], "spans": [ { "bbox": [ 106, 514, 227, 527 ], "score": 1.0, "content": "4.2 Standard Benchmarks", "type": "text" } ], "index": 13 } ], "index": 13 }, { "type": "text", "bbox": [ 106, 536, 505, 722 ], "lines": [ { "bbox": [ 106, 536, 505, 547 ], "spans": [ { "bbox": [ 106, 536, 505, 547 ], "score": 1.0, "content": "Distillation Performance: We first evaluate our method on six standard benchmark datasets. We", "type": "text" } ], "index": 14 }, { "bbox": [ 105, 547, 506, 560 ], "spans": [ { "bbox": [ 105, 547, 506, 560 ], "score": 1.0, "content": "learn 1, 10, and 50 images per class for datasets with only ten classes, while we learn 1 and 10", "type": "text" } ], "index": 15 }, { "bbox": [ 104, 557, 506, 571 ], "spans": [ { "bbox": [ 104, 557, 506, 571 ], "score": 1.0, "content": "images per class for CIFAR100 [34] with 100 classes, Tiny ImageNet [35] with 200 classes, and", "type": "text" } ], "index": 16 }, { "bbox": [ 106, 568, 506, 581 ], "spans": [ { "bbox": [ 106, 568, 506, 581 ], "score": 1.0, "content": "CUB-200 [37] with 200 fine-grained classes. As shown in Table in 1, we achieve the state-of-the-art", "type": "text" } ], "index": 17 }, { "bbox": [ 105, 579, 505, 592 ], "spans": [ { "bbox": [ 105, 579, 505, 592 ], "score": 1.0, "content": "performance in most settings despite the hyperparameter may be suboptimal. Our method performs", "type": "text" } ], "index": 18 }, { "bbox": [ 105, 591, 505, 604 ], "spans": [ { "bbox": [ 105, 591, 505, 604 ], "score": 1.0, "content": "exceptionally well on datasets with a complex label space when learning few images per class. For", "type": "text" } ], "index": 19 }, { "bbox": [ 105, 600, 506, 616 ], "spans": [ { "bbox": [ 105, 600, 506, 616 ], "score": 1.0, "content": "example, we improve the CIFAR100, Tiny ImageNet, and CUB-200 in one image per class setting", "type": "text" } ], "index": 20 }, { "bbox": [ 105, 610, 506, 626 ], "spans": [ { "bbox": [ 105, 610, 129, 626 ], "score": 1.0, "content": "from", "type": "text" }, { "bbox": [ 129, 613, 156, 623 ], "score": 0.84, "content": "2 4 . 3 \\%", "type": "inline_equation" }, { "bbox": [ 157, 610, 160, 626 ], "score": 1.0, "content": ",", "type": "text" }, { "bbox": [ 160, 613, 183, 623 ], "score": 0.85, "content": "8 . 8 \\%", "type": "inline_equation" }, { "bbox": [ 183, 610, 204, 626 ], "score": 1.0, "content": ", and", "type": "text" }, { "bbox": [ 204, 613, 227, 623 ], "score": 0.87, "content": "2 . 2 \\%", "type": "inline_equation" }, { "bbox": [ 228, 610, 239, 626 ], "score": 1.0, "content": "to", "type": "text" }, { "bbox": [ 239, 613, 266, 623 ], "score": 0.84, "content": "2 8 . 7 \\%", "type": "inline_equation" }, { "bbox": [ 267, 610, 271, 626 ], "score": 1.0, "content": ",", "type": "text" }, { "bbox": [ 271, 613, 298, 623 ], "score": 0.85, "content": "1 5 . 4 \\%", "type": "inline_equation" }, { "bbox": [ 298, 610, 320, 626 ], "score": 1.0, "content": ", and", "type": "text" }, { "bbox": [ 321, 613, 347, 623 ], "score": 0.87, "content": "1 2 . 4 \\%", "type": "inline_equation" }, { "bbox": [ 348, 610, 506, 626 ], "score": 1.0, "content": ", respectively. Figure 4 shows that our", "type": "text" } ], "index": 21 }, { "bbox": [ 105, 622, 506, 637 ], "spans": [ { "bbox": [ 105, 622, 506, 637 ], "score": 1.0, "content": "distilled images look real and natural though we do not directly optimize for this objective. We", "type": "text" } ], "index": 22 }, { "bbox": [ 105, 634, 506, 648 ], "spans": [ { "bbox": [ 105, 634, 506, 648 ], "score": 1.0, "content": "observe a strong correlation between the test accuracy and image quality: the better the image quality,", "type": "text" } ], "index": 23 }, { "bbox": [ 106, 646, 505, 658 ], "spans": [ { "bbox": [ 106, 646, 505, 658 ], "score": 1.0, "content": "the higher the test accuracy. Our results suggest that a highly condensed dataset does not need to be", "type": "text" } ], "index": 24 }, { "bbox": [ 105, 655, 506, 669 ], "spans": [ { "bbox": [ 105, 655, 506, 669 ], "score": 1.0, "content": "very different from the real dataset as it may just reflect the most common pattern in a dataset. We", "type": "text" } ], "index": 25 }, { "bbox": [ 105, 667, 507, 681 ], "spans": [ { "bbox": [ 105, 667, 507, 681 ], "score": 1.0, "content": "also report the KRR predictor’s test accuracy using the feature extractor trained on the distilled data.", "type": "text" } ], "index": 26 }, { "bbox": [ 105, 677, 506, 691 ], "spans": [ { "bbox": [ 105, 677, 506, 691 ], "score": 1.0, "content": "When the dataset is as simple as MNIST [32], the KRR predictor achieves similar performance as", "type": "text" } ], "index": 27 }, { "bbox": [ 106, 689, 505, 702 ], "spans": [ { "bbox": [ 106, 689, 505, 702 ], "score": 1.0, "content": "the neural network predictor. In contrast, for more complex datasets, the KRR predictor consistently", "type": "text" } ], "index": 28 }, { "bbox": [ 106, 700, 506, 713 ], "spans": [ { "bbox": [ 106, 700, 408, 713 ], "score": 1.0, "content": "outperforms the neural network predictor, with the most significant gap being", "type": "text" }, { "bbox": [ 408, 700, 430, 711 ], "score": 0.84, "content": "3 . 7 \\%", "type": "inline_equation" }, { "bbox": [ 430, 700, 506, 713 ], "score": 1.0, "content": "for Tiny ImageNet", "type": "text" } ], "index": 29 }, { "bbox": [ 105, 710, 243, 724 ], "spans": [ { "bbox": [ 105, 710, 243, 724 ], "score": 1.0, "content": "in the one image per class setting.", "type": "text" } ], "index": 30 } ], "index": 22 } ], "page_idx": 5, "page_size": [ 612, 792 ], "discarded_blocks": [ { "type": "discarded", "bbox": [ 302, 742, 309, 750 ], "lines": [ { "bbox": [ 302, 741, 310, 752 ], "spans": [ { "bbox": [ 302, 741, 310, 752 ], "score": 1.0, "content": "6", "type": "text" } ] } ] } ], "para_blocks": [ { "type": "table", "bbox": [ 106, 111, 512, 333 ], "blocks": [ { "type": "table_caption", "bbox": [ 106, 78, 506, 111 ], "group_id": 0, "lines": [ { "bbox": [ 105, 77, 506, 91 ], "spans": [ { "bbox": [ 105, 77, 506, 91 ], "score": 1.0, "content": "Table 1: Test accuracies of models trained on the distilled data from scratch. : denotes performance", "type": "text" } ], "index": 0 }, { "bbox": [ 106, 88, 504, 101 ], "spans": [ { "bbox": [ 106, 88, 504, 101 ], "score": 1.0, "content": "better than the original reported performance. KRR preformance is shown in bracket. FRePo performs", "type": "text" } ], "index": 1 }, { "bbox": [ 106, 100, 476, 112 ], "spans": [ { "bbox": [ 106, 100, 476, 112 ], "score": 1.0, "content": "extremely well for one image per class setting on CIFAR100, Tiny ImageNet and CUB-200.", "type": "text" } ], "index": 2 } ], "index": 1 }, { "type": "table_body", "bbox": [ 106, 111, 512, 333 ], "group_id": 0, "lines": [ { "bbox": [ 106, 111, 512, 333 ], "spans": [ { "bbox": [ 106, 111, 512, 333 ], "score": 0.983, "html": "
Img/ClsDSA [7]DM[8]KIP [23]MTT [20]FRePo
MNIST188.7±0.689.9 ± 0.8†90.1± 0.191.4 ± 0.9†93.0 ± 0.4 (92.6 ± 0.4)
1097.9 ±0.1†97.6 ± 0.1†97.5 ± 0.097.3 ± 0.1+98.6 ± 0.1 (98.6 ± 0.1)
5099.2 ± 0.198.6 ± 0.198.3 ± 0.198.5±0.1+99.2 ± 0.0 (99.2± 0.1)
F-MNIST170.6 ± 0.671.5 ± 0.5†73.5± 0.575.1 ± 0.9†75.6 ± 0.3 (77.1 ± 0.2)
1084.8±0.3t83.6±0.2t86.8±0.187.2± 0.3+86.2 ± 0.2 (86.8 ± 0.1)
5088.8±0.2t88.2±0.1†88.0±0.188.3± 0.1+89.6 ± 0.1 (89.9 ± 0.1)
CIFAR10136.7± 0.8†31.0 ± 0.6†49.9 ± 0.246.3 ± 0.846.8 ± 0.7 (47.9 ± 0.6)
1053.2 ± 0.8†49.2 ± 0.8†62.7± 0.365.3 ± 0.765.5 ± 0.4 (68.0 ± 0.2)
5066.8± 0.4†63.7±0.5t68.6± 0.271.6 ± 0.271.7 ± 0.2 (74.4 ± 0.1)
CIFAR100116.8± 0.2†12.2 ± 0.4†15.7 ± 0.224.3 ± 0.328.7 ± 0.1 (32.3 ± 0.1)
1032.3 ±0.329.7 ±0.328.3 ± 0.140.1 ± 0.442.5 ± 0.2 (44.9 ± 0.2)
5042.8± 0.443.6 ± 0.4147.7 ± 0.244.3 ± 0.2 (43.0 ± 0.3)
T-ImageNet16.6± 0.2t3.9± 0.28.8 ±0.315.4 ± 0.3 (19.1 ± 0.3)
1012.9 ± 0.423.2 ± 0.225.4 ± 0.2 (26.5± 0.1)
CUB-20011.3 ± 0.1†1.6 ± 0.1†2.2± 0.1†12.4 ± 0.2 (13.7 ± 0.2)
104.5 ± 0.3†4.4 ± 0.2†116.8 ± 0.1 (16.1 ± 0.3)
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(c,d) Time per", "type": "text" } ], "index": 9 }, { "bbox": [ 105, 456, 506, 469 ], "spans": [ { "bbox": [ 105, 456, 506, 469 ], "score": 1.0, "content": "iteration and peak memory usage as we increase the model size. FRePo is significantly more efficient", "type": "text" } ], "index": 10 }, { "bbox": [ 105, 467, 506, 480 ], "spans": [ { "bbox": [ 105, 467, 506, 480 ], "score": 1.0, "content": "than the previous methods, almost two orders of magnitude faster than the second-best method (i.e.,", "type": "text" } ], "index": 11 }, { "bbox": [ 105, 478, 334, 491 ], "spans": [ { "bbox": [ 105, 478, 334, 491 ], "score": 1.0, "content": "MTT), with only 1/10 of the GPU memory requirement.", "type": "text" } ], "index": 12 } ], "index": 10.5 } ], "index": 8.75 }, { "type": "title", "bbox": [ 108, 514, 226, 526 ], "lines": [ { "bbox": [ 106, 514, 227, 527 ], "spans": [ { "bbox": [ 106, 514, 227, 527 ], "score": 1.0, "content": "4.2 Standard Benchmarks", "type": "text" } ], "index": 13 } ], "index": 13 }, { "type": "text", "bbox": [ 106, 536, 505, 722 ], "lines": [ { "bbox": [ 106, 536, 505, 547 ], "spans": [ { "bbox": [ 106, 536, 505, 547 ], "score": 1.0, "content": "Distillation Performance: We first evaluate our method on six standard benchmark datasets. We", "type": "text" } ], "index": 14 }, { "bbox": [ 105, 547, 506, 560 ], "spans": [ { "bbox": [ 105, 547, 506, 560 ], "score": 1.0, "content": "learn 1, 10, and 50 images per class for datasets with only ten classes, while we learn 1 and 10", "type": "text" } ], "index": 15 }, { "bbox": [ 104, 557, 506, 571 ], "spans": [ { "bbox": [ 104, 557, 506, 571 ], "score": 1.0, "content": "images per class for CIFAR100 [34] with 100 classes, Tiny ImageNet [35] with 200 classes, and", "type": "text" } ], "index": 16 }, { "bbox": [ 106, 568, 506, 581 ], "spans": [ { "bbox": [ 106, 568, 506, 581 ], "score": 1.0, "content": "CUB-200 [37] with 200 fine-grained classes. As shown in Table in 1, we achieve the state-of-the-art", "type": "text" } ], "index": 17 }, { "bbox": [ 105, 579, 505, 592 ], "spans": [ { "bbox": [ 105, 579, 505, 592 ], "score": 1.0, "content": "performance in most settings despite the hyperparameter may be suboptimal. Our method performs", "type": "text" } ], "index": 18 }, { "bbox": [ 105, 591, 505, 604 ], "spans": [ { "bbox": [ 105, 591, 505, 604 ], "score": 1.0, "content": "exceptionally well on datasets with a complex label space when learning few images per class. For", "type": "text" } ], "index": 19 }, { "bbox": [ 105, 600, 506, 616 ], "spans": [ { "bbox": [ 105, 600, 506, 616 ], "score": 1.0, "content": "example, we improve the CIFAR100, Tiny ImageNet, and CUB-200 in one image per class setting", "type": "text" } ], "index": 20 }, { "bbox": [ 105, 610, 506, 626 ], "spans": [ { "bbox": [ 105, 610, 129, 626 ], "score": 1.0, "content": "from", "type": "text" }, { "bbox": [ 129, 613, 156, 623 ], "score": 0.84, "content": "2 4 . 3 \\%", "type": "inline_equation" }, { "bbox": [ 157, 610, 160, 626 ], "score": 1.0, "content": ",", "type": "text" }, { "bbox": [ 160, 613, 183, 623 ], "score": 0.85, "content": "8 . 8 \\%", "type": "inline_equation" }, { "bbox": [ 183, 610, 204, 626 ], "score": 1.0, "content": ", and", "type": "text" }, { "bbox": [ 204, 613, 227, 623 ], "score": 0.87, "content": "2 . 2 \\%", "type": "inline_equation" }, { "bbox": [ 228, 610, 239, 626 ], "score": 1.0, "content": "to", "type": "text" }, { "bbox": [ 239, 613, 266, 623 ], "score": 0.84, "content": "2 8 . 7 \\%", "type": "inline_equation" }, { "bbox": [ 267, 610, 271, 626 ], "score": 1.0, "content": ",", "type": "text" }, { "bbox": [ 271, 613, 298, 623 ], "score": 0.85, "content": "1 5 . 4 \\%", "type": "inline_equation" }, { "bbox": [ 298, 610, 320, 626 ], "score": 1.0, "content": ", and", "type": "text" }, { "bbox": [ 321, 613, 347, 623 ], "score": 0.87, "content": "1 2 . 4 \\%", "type": "inline_equation" }, { "bbox": [ 348, 610, 506, 626 ], "score": 1.0, "content": ", respectively. Figure 4 shows that our", "type": "text" } ], "index": 21 }, { "bbox": [ 105, 622, 506, 637 ], "spans": [ { "bbox": [ 105, 622, 506, 637 ], "score": 1.0, "content": "distilled images look real and natural though we do not directly optimize for this objective. We", "type": "text" } ], "index": 22 }, { "bbox": [ 105, 634, 506, 648 ], "spans": [ { "bbox": [ 105, 634, 506, 648 ], "score": 1.0, "content": "observe a strong correlation between the test accuracy and image quality: the better the image quality,", "type": "text" } ], "index": 23 }, { "bbox": [ 106, 646, 505, 658 ], "spans": [ { "bbox": [ 106, 646, 505, 658 ], "score": 1.0, "content": "the higher the test accuracy. Our results suggest that a highly condensed dataset does not need to be", "type": "text" } ], "index": 24 }, { "bbox": [ 105, 655, 506, 669 ], "spans": [ { "bbox": [ 105, 655, 506, 669 ], "score": 1.0, "content": "very different from the real dataset as it may just reflect the most common pattern in a dataset. We", "type": "text" } ], "index": 25 }, { "bbox": [ 105, 667, 507, 681 ], "spans": [ { "bbox": [ 105, 667, 507, 681 ], "score": 1.0, "content": "also report the KRR predictor’s test accuracy using the feature extractor trained on the distilled data.", "type": "text" } ], "index": 26 }, { "bbox": [ 105, 677, 506, 691 ], "spans": [ { "bbox": [ 105, 677, 506, 691 ], "score": 1.0, "content": "When the dataset is as simple as MNIST [32], the KRR predictor achieves similar performance as", "type": "text" } ], "index": 27 }, { "bbox": [ 106, 689, 505, 702 ], "spans": [ { "bbox": [ 106, 689, 505, 702 ], "score": 1.0, "content": "the neural network predictor. In contrast, for more complex datasets, the KRR predictor consistently", "type": "text" } ], "index": 28 }, { "bbox": [ 106, 700, 506, 713 ], "spans": [ { "bbox": [ 106, 700, 408, 713 ], "score": 1.0, "content": "outperforms the neural network predictor, with the most significant gap being", "type": "text" }, { "bbox": [ 408, 700, 430, 711 ], "score": 0.84, "content": "3 . 7 \\%", "type": "inline_equation" }, { "bbox": [ 430, 700, 506, 713 ], "score": 1.0, "content": "for Tiny ImageNet", "type": "text" } ], "index": 29 }, { "bbox": [ 105, 710, 243, 724 ], "spans": [ { "bbox": [ 105, 710, 243, 724 ], "score": 1.0, "content": "in the one image per class setting.", "type": "text" } ], "index": 30 } ], "index": 22, "bbox_fs": [ 104, 536, 507, 724 ] } ] }, { "preproc_blocks": [ { "type": "table", "bbox": [ 106, 122, 522, 209 ], "blocks": [ { "type": "table_caption", "bbox": [ 106, 77, 506, 121 ], "group_id": 0, "lines": [ { "bbox": [ 105, 77, 505, 90 ], "spans": [ { "bbox": [ 105, 77, 370, 90 ], "score": 1.0, "content": "Table 2: Cross-architecture transfer performance on CIFAR10 with", "type": "text" }, { "bbox": [ 370, 77, 415, 89 ], "score": 0.56, "content": "1 0 \\mathrm { I m g / C l s }", "type": "inline_equation" }, { "bbox": [ 416, 77, 505, 90 ], "score": 1.0, "content": ". Despite being trained", "type": "text" } ], "index": 0 }, { "bbox": [ 105, 87, 506, 102 ], "spans": [ { "bbox": [ 105, 87, 506, 102 ], "score": 1.0, "content": "for a specific architecture, our distilled data transfer well to various architectures unseen during", "type": "text" } ], "index": 1 }, { "bbox": [ 106, 100, 506, 111 ], "spans": [ { "bbox": [ 106, 100, 506, 111 ], "score": 1.0, "content": "training. Conv is the default evaluation model used for each method. NN, DN, IN, and BN stand for", "type": "text" } ], "index": 2 }, { "bbox": [ 105, 110, 505, 123 ], "spans": [ { "bbox": [ 105, 110, 505, 123 ], "score": 1.0, "content": "no normalization, default normalization, Instance Normalization, Batch Normalization respectively.", "type": "text" } ], "index": 3 } ], "index": 1.5 }, { "type": "table_body", "bbox": [ 106, 122, 522, 209 ], "group_id": 0, "lines": [ { "bbox": [ 106, 122, 522, 209 ], "spans": [ { "bbox": [ 106, 122, 522, 209 ], "score": 0.97, "html": "
Train ArchEvaluation Architecture
ConvConv-NNResNet-DNResNet-BNVGG-BNAlexNet
DSA [7]Conv-IN53.2 ± 0.836.4 ± 1.542.1 ± 0.734.1 ± 1.446.3 ± 1.334.0 ± 2.3
DM[8]Conv-IN49.2 ± 0.835.2 ± 0.536.8 ± 1.235.5 ± 1.341.2 ± 1.834.9 ± 1.1
MTT[20]Conv-IN64.4 ± 0.941.6 ± 1.349.2 ± 1.142.9 ± 1.546.6 ± 2.034.2 ± 2.6
KIP [23]Conv-NTK62.7 ± 0.358.2 ±0.449.0 ± 1.245.8 ± 1.430.1 ± 1.557.2 ± 0.4
FRePoConv-BN65.5 ± 0.465.5 ± 0.458.1 ± 0.657.7 ± 0.759.4 ± 0.761.9 ± 0.7
", "type": "table", "image_path": "4e44b3dde3c2a554e1627b4447e7df3e28b023aaff4e028f17f27dce37cbd8da.jpg" } ] } ], "index": 5, "virtual_lines": [ { "bbox": [ 106, 122, 522, 151.0 ], "spans": [], "index": 4 }, { "bbox": [ 106, 151.0, 522, 180.0 ], "spans": [], "index": 5 }, { "bbox": [ 106, 180.0, 522, 209.0 ], "spans": [], "index": 6 } ] } ], "index": 3.25 }, { "type": "image", "bbox": [ 108, 226, 502, 336 ], "blocks": [ { "type": "image_body", "bbox": [ 108, 226, 502, 336 ], "group_id": 0, "lines": [ { "bbox": [ 108, 226, 502, 336 ], "spans": [ { "bbox": [ 108, 226, 502, 336 ], "score": 0.967, "type": "image", "image_path": "06d156480cb24f7de4d97dc51031b5fb9e76281f33da496484aeb238e841000d.jpg" } ] } ], "index": 8, "virtual_lines": [ { "bbox": [ 108, 226, 502, 262.6666666666667 ], "spans": [], "index": 7 }, { "bbox": [ 108, 262.6666666666667, 502, 299.33333333333337 ], "spans": [], "index": 8 }, { "bbox": [ 108, 299.33333333333337, 502, 336.00000000000006 ], "spans": [], "index": 9 } ] }, { "type": "image_caption", "bbox": [ 106, 345, 506, 379 ], "group_id": 0, "lines": [ { "bbox": [ 105, 344, 505, 360 ], "spans": [ { "bbox": [ 105, 344, 505, 360 ], "score": 1.0, "content": "Figure 4: (a,b,c) Distilled 1 img/cls from CIFAR100 using FRePo, MTT, and DSA. High quality", "type": "text" } ], "index": 10 }, { "bbox": [ 105, 356, 507, 370 ], "spans": [ { "bbox": [ 105, 356, 507, 370 ], "score": 1.0, "content": "images also produce high test accuracy. (d) Three categories of learned labels. (Top) High confidence,", "type": "text" } ], "index": 11 }, { "bbox": [ 106, 368, 491, 380 ], "spans": [ { "bbox": [ 106, 368, 491, 380 ], "score": 1.0, "content": "large margin; (Middle) High confidence, small margin; (Bottom) Low confidence, small margin.", "type": "text" } ], "index": 12 } ], "index": 11 } ], "index": 9.5 }, { "type": "text", "bbox": [ 106, 405, 505, 547 ], "lines": [ { "bbox": [ 105, 404, 505, 418 ], "spans": [ { "bbox": [ 105, 404, 505, 418 ], "score": 1.0, "content": "Label Learning: A similar trend can also be observed for label learning. When the dataset is simple", "type": "text" } ], "index": 13 }, { "bbox": [ 106, 416, 506, 429 ], "spans": [ { "bbox": [ 106, 416, 506, 429 ], "score": 1.0, "content": "and has only a few classes, label learning may not be necessary. However, it becomes crucial for", "type": "text" } ], "index": 14 }, { "bbox": [ 105, 427, 506, 440 ], "spans": [ { "bbox": [ 105, 427, 506, 440 ], "score": 1.0, "content": "complex datasets with many labels, such as CIFAR100 and Tiny-ImageNet (See more details in", "type": "text" } ], "index": 15 }, { "bbox": [ 105, 437, 505, 450 ], "spans": [ { "bbox": [ 105, 437, 505, 450 ], "score": 1.0, "content": "Appendix ??). Similar to the teacher label in the knowledge distillation [1], we observe that the", "type": "text" } ], "index": 16 }, { "bbox": [ 105, 448, 506, 461 ], "spans": [ { "bbox": [ 105, 448, 506, 461 ], "score": 1.0, "content": "distilled label also encodes the class similarity. We identify three typical cases in Figure 4d. The", "type": "text" } ], "index": 17 }, { "bbox": [ 106, 460, 505, 472 ], "spans": [ { "bbox": [ 106, 460, 505, 472 ], "score": 1.0, "content": "first group consists of highly confident labels with a much higher value for one class than other", "type": "text" } ], "index": 18 }, { "bbox": [ 106, 470, 506, 483 ], "spans": [ { "bbox": [ 106, 470, 506, 483 ], "score": 1.0, "content": "classes (large margin), such as sunflower, bicycle, and chair. In contrast, the distilled labels in the", "type": "text" } ], "index": 19 }, { "bbox": [ 105, 481, 506, 494 ], "spans": [ { "bbox": [ 105, 481, 506, 494 ], "score": 1.0, "content": "second group are confident but may get confused with some closely-related classes (small margin).", "type": "text" } ], "index": 20 }, { "bbox": [ 105, 492, 507, 505 ], "spans": [ { "bbox": [ 105, 492, 507, 505 ], "score": 1.0, "content": "For instance, the learned label for \"girl\" has almost equally high values for the girl, woman, man,", "type": "text" } ], "index": 21 }, { "bbox": [ 105, 502, 506, 517 ], "spans": [ { "bbox": [ 105, 502, 506, 517 ], "score": 1.0, "content": "boy, and baby, suggesting that these classes are very similar and may be difficult for the model to", "type": "text" } ], "index": 22 }, { "bbox": [ 105, 514, 506, 527 ], "spans": [ { "bbox": [ 105, 514, 506, 527 ], "score": 1.0, "content": "distinguish them apart. The last group contains distilled labels with low values for all classes, such", "type": "text" } ], "index": 23 }, { "bbox": [ 106, 525, 505, 537 ], "spans": [ { "bbox": [ 106, 525, 505, 537 ], "score": 1.0, "content": "as bear, beaver, and squirrel. It is often hard for humans to recognize the distilled images in such a", "type": "text" } ], "index": 24 }, { "bbox": [ 105, 537, 392, 549 ], "spans": [ { "bbox": [ 105, 537, 392, 549 ], "score": 1.0, "content": "group, suggesting that they may be the challenging classes in a dataset.", "type": "text" } ], "index": 25 } ], "index": 19 }, { "type": "text", "bbox": [ 106, 552, 505, 651 ], "lines": [ { "bbox": [ 105, 552, 506, 565 ], "spans": [ { "bbox": [ 105, 552, 506, 565 ], "score": 1.0, "content": "Training Cost Analysis: Figure 3a, 3b shows that our method is significantly more time-efficient", "type": "text" } ], "index": 26 }, { "bbox": [ 106, 563, 506, 576 ], "spans": [ { "bbox": [ 106, 563, 506, 576 ], "score": 1.0, "content": "than the previous methods. When learning one image per class on CIFAR100, FRePo reaches a", "type": "text" } ], "index": 27 }, { "bbox": [ 106, 574, 505, 587 ], "spans": [ { "bbox": [ 106, 574, 192, 587 ], "score": 1.0, "content": "similar test accuracy", "type": "text" }, { "bbox": [ 192, 574, 226, 586 ], "score": 0.87, "content": "( 2 3 . 4 \\% )", "type": "inline_equation" }, { "bbox": [ 226, 574, 335, 587 ], "score": 1.0, "content": "to the second-best method", "type": "text" }, { "bbox": [ 335, 574, 369, 586 ], "score": 0.86, "content": "( 2 4 . 0 \\% )", "type": "inline_equation" }, { "bbox": [ 369, 574, 505, 587 ], "score": 1.0, "content": "in 38 seconds, compared to 3805", "type": "text" } ], "index": 28 }, { "bbox": [ 105, 584, 505, 599 ], "spans": [ { "bbox": [ 105, 584, 484, 599 ], "score": 1.0, "content": "seconds for MTT, which is roughly two orders of magnitude faster. Moreover, FRePo achieves", "type": "text" }, { "bbox": [ 485, 585, 505, 596 ], "score": 0.87, "content": "92 \\%", "type": "inline_equation" } ], "index": 29 }, { "bbox": [ 105, 596, 506, 609 ], "spans": [ { "bbox": [ 105, 596, 211, 609 ], "score": 1.0, "content": "of its final test accuracy (", "type": "text" }, { "bbox": [ 211, 596, 239, 607 ], "score": 0.84, "content": "2 6 . 4 \\%", "type": "inline_equation" }, { "bbox": [ 239, 596, 267, 609 ], "score": 1.0, "content": "out of", "type": "text" }, { "bbox": [ 268, 596, 296, 607 ], "score": 0.84, "content": "2 8 . 7 \\%", "type": "inline_equation" }, { "bbox": [ 297, 596, 506, 609 ], "score": 1.0, "content": ") in only 385 seconds. As shown in Figure 3c, our", "type": "text" } ], "index": 30 }, { "bbox": [ 106, 607, 505, 620 ], "spans": [ { "bbox": [ 106, 607, 505, 620 ], "score": 1.0, "content": "algorithm takes much less time to perform one gradient step on the distilled data. Thus, we can", "type": "text" } ], "index": 31 }, { "bbox": [ 105, 618, 505, 631 ], "spans": [ { "bbox": [ 105, 618, 505, 631 ], "score": 1.0, "content": "perform more gradient steps in a fixed time. Furthermore, Figure 3d suggests that our algorithm has", "type": "text" } ], "index": 32 }, { "bbox": [ 105, 627, 506, 642 ], "spans": [ { "bbox": [ 105, 627, 506, 642 ], "score": 1.0, "content": "much less GPU memory requirement. Therefore, we can potentially use a much larger and more", "type": "text" } ], "index": 33 }, { "bbox": [ 106, 640, 447, 653 ], "spans": [ { "bbox": [ 106, 640, 447, 653 ], "score": 1.0, "content": "complex model to take advantage of the advancement in neural network architecture.", "type": "text" } ], "index": 34 } ], "index": 30 }, { "type": "text", "bbox": [ 107, 656, 505, 722 ], "lines": [ { "bbox": [ 106, 655, 505, 668 ], "spans": [ { "bbox": [ 106, 655, 505, 668 ], "score": 1.0, "content": "Cross-Architecture Generalization: One desired property of our distilled data is that it generalizes", "type": "text" } ], "index": 35 }, { "bbox": [ 105, 666, 505, 680 ], "spans": [ { "bbox": [ 105, 666, 505, 680 ], "score": 1.0, "content": "well to architecture it has not seen during the training. Similar to previous works [5, 20], we evaluate", "type": "text" } ], "index": 36 }, { "bbox": [ 105, 676, 506, 692 ], "spans": [ { "bbox": [ 105, 676, 506, 692 ], "score": 1.0, "content": "the distilled data from CIFAR10 on a wide range of architectures which it has not seen during training,", "type": "text" } ], "index": 37 }, { "bbox": [ 106, 689, 506, 701 ], "spans": [ { "bbox": [ 106, 689, 506, 701 ], "score": 1.0, "content": "including AlexNet [38], VGG [39], and ResNet [40]. Table 2 shows that our method outperforms", "type": "text" } ], "index": 38 }, { "bbox": [ 105, 699, 506, 713 ], "spans": [ { "bbox": [ 105, 699, 506, 713 ], "score": 1.0, "content": "previous methods on all unseen architectures. Instance Normalization (IN) [41], as the vital ingredient", "type": "text" } ], "index": 39 }, { "bbox": [ 105, 711, 505, 723 ], "spans": [ { "bbox": [ 105, 711, 505, 723 ], "score": 1.0, "content": "in several methods (DSA, DM, MTT), seems to hurt the cross-architecture transfer. The performance", "type": "text" } ], "index": 40 } ], "index": 37.5 } ], "page_idx": 6, "page_size": [ 612, 792 ], "discarded_blocks": [ { "type": "discarded", "bbox": [ 302, 741, 309, 750 ], "lines": [ { "bbox": [ 302, 741, 309, 752 ], "spans": [ { "bbox": [ 302, 741, 309, 752 ], "score": 1.0, "content": "7", "type": "text" } ] } ] } ], "para_blocks": [ { "type": "table", "bbox": [ 106, 122, 522, 209 ], "blocks": [ { "type": "table_caption", "bbox": [ 106, 77, 506, 121 ], "group_id": 0, "lines": [ { "bbox": [ 105, 77, 505, 90 ], "spans": [ { "bbox": [ 105, 77, 370, 90 ], "score": 1.0, "content": "Table 2: Cross-architecture transfer performance on CIFAR10 with", "type": "text" }, { "bbox": [ 370, 77, 415, 89 ], "score": 0.56, "content": "1 0 \\mathrm { I m g / C l s }", "type": "inline_equation" }, { "bbox": [ 416, 77, 505, 90 ], "score": 1.0, "content": ". Despite being trained", "type": "text" } ], "index": 0 }, { "bbox": [ 105, 87, 506, 102 ], "spans": [ { "bbox": [ 105, 87, 506, 102 ], "score": 1.0, "content": "for a specific architecture, our distilled data transfer well to various architectures unseen during", "type": "text" } ], "index": 1 }, { "bbox": [ 106, 100, 506, 111 ], "spans": [ { "bbox": [ 106, 100, 506, 111 ], "score": 1.0, "content": "training. Conv is the default evaluation model used for each method. NN, DN, IN, and BN stand for", "type": "text" } ], "index": 2 }, { "bbox": [ 105, 110, 505, 123 ], "spans": [ { "bbox": [ 105, 110, 505, 123 ], "score": 1.0, "content": "no normalization, default normalization, Instance Normalization, Batch Normalization respectively.", "type": "text" } ], "index": 3 } ], "index": 1.5 }, { "type": "table_body", "bbox": [ 106, 122, 522, 209 ], "group_id": 0, "lines": [ { "bbox": [ 106, 122, 522, 209 ], "spans": [ { "bbox": [ 106, 122, 522, 209 ], "score": 0.97, "html": "
Train ArchEvaluation Architecture
ConvConv-NNResNet-DNResNet-BNVGG-BNAlexNet
DSA [7]Conv-IN53.2 ± 0.836.4 ± 1.542.1 ± 0.734.1 ± 1.446.3 ± 1.334.0 ± 2.3
DM[8]Conv-IN49.2 ± 0.835.2 ± 0.536.8 ± 1.235.5 ± 1.341.2 ± 1.834.9 ± 1.1
MTT[20]Conv-IN64.4 ± 0.941.6 ± 1.349.2 ± 1.142.9 ± 1.546.6 ± 2.034.2 ± 2.6
KIP [23]Conv-NTK62.7 ± 0.358.2 ±0.449.0 ± 1.245.8 ± 1.430.1 ± 1.557.2 ± 0.4
FRePoConv-BN65.5 ± 0.465.5 ± 0.458.1 ± 0.657.7 ± 0.759.4 ± 0.761.9 ± 0.7
", "type": "table", "image_path": "4e44b3dde3c2a554e1627b4447e7df3e28b023aaff4e028f17f27dce37cbd8da.jpg" } ] } ], "index": 5, "virtual_lines": [ { "bbox": [ 106, 122, 522, 151.0 ], "spans": [], "index": 4 }, { "bbox": [ 106, 151.0, 522, 180.0 ], "spans": [], "index": 5 }, { "bbox": [ 106, 180.0, 522, 209.0 ], "spans": [], "index": 6 } ] } ], "index": 3.25 }, { "type": "image", "bbox": [ 108, 226, 502, 336 ], "blocks": [ { "type": "image_body", "bbox": [ 108, 226, 502, 336 ], "group_id": 0, "lines": [ { "bbox": [ 108, 226, 502, 336 ], "spans": [ { "bbox": [ 108, 226, 502, 336 ], "score": 0.967, "type": "image", "image_path": "06d156480cb24f7de4d97dc51031b5fb9e76281f33da496484aeb238e841000d.jpg" } ] } ], "index": 8, "virtual_lines": [ { "bbox": [ 108, 226, 502, 262.6666666666667 ], "spans": [], "index": 7 }, { "bbox": [ 108, 262.6666666666667, 502, 299.33333333333337 ], "spans": [], "index": 8 }, { "bbox": [ 108, 299.33333333333337, 502, 336.00000000000006 ], "spans": [], "index": 9 } ] }, { "type": "image_caption", "bbox": [ 106, 345, 506, 379 ], "group_id": 0, "lines": [ { "bbox": [ 105, 344, 505, 360 ], "spans": [ { "bbox": [ 105, 344, 505, 360 ], "score": 1.0, "content": "Figure 4: (a,b,c) Distilled 1 img/cls from CIFAR100 using FRePo, MTT, and DSA. High quality", "type": "text" } ], "index": 10 }, { "bbox": [ 105, 356, 507, 370 ], "spans": [ { "bbox": [ 105, 356, 507, 370 ], "score": 1.0, "content": "images also produce high test accuracy. (d) Three categories of learned labels. (Top) High confidence,", "type": "text" } ], "index": 11 }, { "bbox": [ 106, 368, 491, 380 ], "spans": [ { "bbox": [ 106, 368, 491, 380 ], "score": 1.0, "content": "large margin; (Middle) High confidence, small margin; (Bottom) Low confidence, small margin.", "type": "text" } ], "index": 12 } ], "index": 11 } ], "index": 9.5 }, { "type": "text", "bbox": [ 106, 405, 505, 547 ], "lines": [ { "bbox": [ 105, 404, 505, 418 ], "spans": [ { "bbox": [ 105, 404, 505, 418 ], "score": 1.0, "content": "Label Learning: A similar trend can also be observed for label learning. When the dataset is simple", "type": "text" } ], "index": 13 }, { "bbox": [ 106, 416, 506, 429 ], "spans": [ { "bbox": [ 106, 416, 506, 429 ], "score": 1.0, "content": "and has only a few classes, label learning may not be necessary. However, it becomes crucial for", "type": "text" } ], "index": 14 }, { "bbox": [ 105, 427, 506, 440 ], "spans": [ { "bbox": [ 105, 427, 506, 440 ], "score": 1.0, "content": "complex datasets with many labels, such as CIFAR100 and Tiny-ImageNet (See more details in", "type": "text" } ], "index": 15 }, { "bbox": [ 105, 437, 505, 450 ], "spans": [ { "bbox": [ 105, 437, 505, 450 ], "score": 1.0, "content": "Appendix ??). Similar to the teacher label in the knowledge distillation [1], we observe that the", "type": "text" } ], "index": 16 }, { "bbox": [ 105, 448, 506, 461 ], "spans": [ { "bbox": [ 105, 448, 506, 461 ], "score": 1.0, "content": "distilled label also encodes the class similarity. We identify three typical cases in Figure 4d. The", "type": "text" } ], "index": 17 }, { "bbox": [ 106, 460, 505, 472 ], "spans": [ { "bbox": [ 106, 460, 505, 472 ], "score": 1.0, "content": "first group consists of highly confident labels with a much higher value for one class than other", "type": "text" } ], "index": 18 }, { "bbox": [ 106, 470, 506, 483 ], "spans": [ { "bbox": [ 106, 470, 506, 483 ], "score": 1.0, "content": "classes (large margin), such as sunflower, bicycle, and chair. In contrast, the distilled labels in the", "type": "text" } ], "index": 19 }, { "bbox": [ 105, 481, 506, 494 ], "spans": [ { "bbox": [ 105, 481, 506, 494 ], "score": 1.0, "content": "second group are confident but may get confused with some closely-related classes (small margin).", "type": "text" } ], "index": 20 }, { "bbox": [ 105, 492, 507, 505 ], "spans": [ { "bbox": [ 105, 492, 507, 505 ], "score": 1.0, "content": "For instance, the learned label for \"girl\" has almost equally high values for the girl, woman, man,", "type": "text" } ], "index": 21 }, { "bbox": [ 105, 502, 506, 517 ], "spans": [ { "bbox": [ 105, 502, 506, 517 ], "score": 1.0, "content": "boy, and baby, suggesting that these classes are very similar and may be difficult for the model to", "type": "text" } ], "index": 22 }, { "bbox": [ 105, 514, 506, 527 ], "spans": [ { "bbox": [ 105, 514, 506, 527 ], "score": 1.0, "content": "distinguish them apart. The last group contains distilled labels with low values for all classes, such", "type": "text" } ], "index": 23 }, { "bbox": [ 106, 525, 505, 537 ], "spans": [ { "bbox": [ 106, 525, 505, 537 ], "score": 1.0, "content": "as bear, beaver, and squirrel. It is often hard for humans to recognize the distilled images in such a", "type": "text" } ], "index": 24 }, { "bbox": [ 105, 537, 392, 549 ], "spans": [ { "bbox": [ 105, 537, 392, 549 ], "score": 1.0, "content": "group, suggesting that they may be the challenging classes in a dataset.", "type": "text" } ], "index": 25 } ], "index": 19, "bbox_fs": [ 105, 404, 507, 549 ] }, { "type": "text", "bbox": [ 106, 552, 505, 651 ], "lines": [ { "bbox": [ 105, 552, 506, 565 ], "spans": [ { "bbox": [ 105, 552, 506, 565 ], "score": 1.0, "content": "Training Cost Analysis: Figure 3a, 3b shows that our method is significantly more time-efficient", "type": "text" } ], "index": 26 }, { "bbox": [ 106, 563, 506, 576 ], "spans": [ { "bbox": [ 106, 563, 506, 576 ], "score": 1.0, "content": "than the previous methods. When learning one image per class on CIFAR100, FRePo reaches a", "type": "text" } ], "index": 27 }, { "bbox": [ 106, 574, 505, 587 ], "spans": [ { "bbox": [ 106, 574, 192, 587 ], "score": 1.0, "content": "similar test accuracy", "type": "text" }, { "bbox": [ 192, 574, 226, 586 ], "score": 0.87, "content": "( 2 3 . 4 \\% )", "type": "inline_equation" }, { "bbox": [ 226, 574, 335, 587 ], "score": 1.0, "content": "to the second-best method", "type": "text" }, { "bbox": [ 335, 574, 369, 586 ], "score": 0.86, "content": "( 2 4 . 0 \\% )", "type": "inline_equation" }, { "bbox": [ 369, 574, 505, 587 ], "score": 1.0, "content": "in 38 seconds, compared to 3805", "type": "text" } ], "index": 28 }, { "bbox": [ 105, 584, 505, 599 ], "spans": [ { "bbox": [ 105, 584, 484, 599 ], "score": 1.0, "content": "seconds for MTT, which is roughly two orders of magnitude faster. Moreover, FRePo achieves", "type": "text" }, { "bbox": [ 485, 585, 505, 596 ], "score": 0.87, "content": "92 \\%", "type": "inline_equation" } ], "index": 29 }, { "bbox": [ 105, 596, 506, 609 ], "spans": [ { "bbox": [ 105, 596, 211, 609 ], "score": 1.0, "content": "of its final test accuracy (", "type": "text" }, { "bbox": [ 211, 596, 239, 607 ], "score": 0.84, "content": "2 6 . 4 \\%", "type": "inline_equation" }, { "bbox": [ 239, 596, 267, 609 ], "score": 1.0, "content": "out of", "type": "text" }, { "bbox": [ 268, 596, 296, 607 ], "score": 0.84, "content": "2 8 . 7 \\%", "type": "inline_equation" }, { "bbox": [ 297, 596, 506, 609 ], "score": 1.0, "content": ") in only 385 seconds. As shown in Figure 3c, our", "type": "text" } ], "index": 30 }, { "bbox": [ 106, 607, 505, 620 ], "spans": [ { "bbox": [ 106, 607, 505, 620 ], "score": 1.0, "content": "algorithm takes much less time to perform one gradient step on the distilled data. Thus, we can", "type": "text" } ], "index": 31 }, { "bbox": [ 105, 618, 505, 631 ], "spans": [ { "bbox": [ 105, 618, 505, 631 ], "score": 1.0, "content": "perform more gradient steps in a fixed time. Furthermore, Figure 3d suggests that our algorithm has", "type": "text" } ], "index": 32 }, { "bbox": [ 105, 627, 506, 642 ], "spans": [ { "bbox": [ 105, 627, 506, 642 ], "score": 1.0, "content": "much less GPU memory requirement. Therefore, we can potentially use a much larger and more", "type": "text" } ], "index": 33 }, { "bbox": [ 106, 640, 447, 653 ], "spans": [ { "bbox": [ 106, 640, 447, 653 ], "score": 1.0, "content": "complex model to take advantage of the advancement in neural network architecture.", "type": "text" } ], "index": 34 } ], "index": 30, "bbox_fs": [ 105, 552, 506, 653 ] }, { "type": "text", "bbox": [ 107, 656, 505, 722 ], "lines": [ { "bbox": [ 106, 655, 505, 668 ], "spans": [ { "bbox": [ 106, 655, 505, 668 ], "score": 1.0, "content": "Cross-Architecture Generalization: One desired property of our distilled data is that it generalizes", "type": "text" } ], "index": 35 }, { "bbox": [ 105, 666, 505, 680 ], "spans": [ { "bbox": [ 105, 666, 505, 680 ], "score": 1.0, "content": "well to architecture it has not seen during the training. Similar to previous works [5, 20], we evaluate", "type": "text" } ], "index": 36 }, { "bbox": [ 105, 676, 506, 692 ], "spans": [ { "bbox": [ 105, 676, 506, 692 ], "score": 1.0, "content": "the distilled data from CIFAR10 on a wide range of architectures which it has not seen during training,", "type": "text" } ], "index": 37 }, { "bbox": [ 106, 689, 506, 701 ], "spans": [ { "bbox": [ 106, 689, 506, 701 ], "score": 1.0, "content": "including AlexNet [38], VGG [39], and ResNet [40]. Table 2 shows that our method outperforms", "type": "text" } ], "index": 38 }, { "bbox": [ 105, 699, 506, 713 ], "spans": [ { "bbox": [ 105, 699, 506, 713 ], "score": 1.0, "content": "previous methods on all unseen architectures. Instance Normalization (IN) [41], as the vital ingredient", "type": "text" } ], "index": 39 }, { "bbox": [ 105, 711, 505, 723 ], "spans": [ { "bbox": [ 105, 711, 505, 723 ], "score": 1.0, "content": "in several methods (DSA, DM, MTT), seems to hurt the cross-architecture transfer. The performance", "type": "text" } ], "index": 40 }, { "bbox": [ 106, 194, 506, 206 ], "spans": [ { "bbox": [ 106, 194, 506, 206 ], "score": 1.0, "content": "degrades a lot when no normalization (NN) is applied (Conv-NN, AlexNet) or using a different", "type": "text", "cross_page": true } ], "index": 6 }, { "bbox": [ 105, 205, 505, 218 ], "spans": [ { "bbox": [ 105, 205, 505, 218 ], "score": 1.0, "content": "normalization, like Batch Normalization (BN) [42]. It suggests that the distilled data generated by", "type": "text", "cross_page": true } ], "index": 7 }, { "bbox": [ 105, 216, 506, 228 ], "spans": [ { "bbox": [ 105, 216, 506, 228 ], "score": 1.0, "content": "those methods encode the inductive bias of a particular training architecture. In contrast, our distilled", "type": "text", "cross_page": true } ], "index": 8 }, { "bbox": [ 106, 227, 506, 239 ], "spans": [ { "bbox": [ 106, 227, 506, 239 ], "score": 1.0, "content": "data generalize well to various architectures, including those without normalization (Conv-NN,", "type": "text", "cross_page": true } ], "index": 9 }, { "bbox": [ 105, 237, 506, 250 ], "spans": [ { "bbox": [ 105, 237, 506, 250 ], "score": 1.0, "content": "AlexNet). Note that Figure 1, 4 also indicate that our distilled data encode less architectural bias as", "type": "text", "cross_page": true } ], "index": 10 }, { "bbox": [ 105, 249, 506, 261 ], "spans": [ { "bbox": [ 105, 249, 506, 261 ], "score": 1.0, "content": "the distilled images look natural and authentic. A simple idea to further alleviate the overfitting of a", "type": "text", "cross_page": true } ], "index": 11 }, { "bbox": [ 105, 259, 506, 273 ], "spans": [ { "bbox": [ 105, 259, 506, 273 ], "score": 1.0, "content": "particular architecture is to include more architectures in the model pool. However, the training may", "type": "text", "cross_page": true } ], "index": 12 }, { "bbox": [ 105, 271, 474, 283 ], "spans": [ { "bbox": [ 105, 271, 474, 283 ], "score": 1.0, "content": "not be stable as the meta-gradient computed by different architectures can be very different.", "type": "text", "cross_page": true } ], "index": 13 } ], "index": 37.5, "bbox_fs": [ 105, 655, 506, 723 ] } ] }, { "preproc_blocks": [ { "type": "table", "bbox": [ 119, 111, 492, 183 ], "blocks": [ { "type": "table_caption", "bbox": [ 107, 77, 505, 110 ], "group_id": 0, "lines": [ { "bbox": [ 105, 75, 506, 91 ], "spans": [ { "bbox": [ 105, 75, 506, 91 ], "score": 1.0, "content": "Table 3: Distillation performance on higher resolution (128x128) dataset (i.e. ImageNette, Image-", "type": "text" } ], "index": 0 }, { "bbox": [ 105, 88, 505, 101 ], "spans": [ { "bbox": [ 105, 88, 505, 101 ], "score": 1.0, "content": "Woof) and medium resolution (64x64) dataset with a complex label space (i.e. ImageNet-1K). FRePo", "type": "text" } ], "index": 1 }, { "bbox": [ 106, 99, 461, 111 ], "spans": [ { "bbox": [ 106, 99, 461, 111 ], "score": 1.0, "content": "scales to high-resolution images and learns the discriminate feature of complex datasets.", "type": "text" } ], "index": 2 } ], "index": 1 }, { "type": "table_body", "bbox": [ 119, 111, 492, 183 ], "group_id": 0, "lines": [ { "bbox": [ 119, 111, 492, 183 ], "spans": [ { "bbox": [ 119, 111, 492, 183 ], "score": 0.977, "html": "
ImageNette (128x128)ImageWoof (128x128)ImageNet (64x64)
Img/Cls11011012
Random Subset23.5± 4.847.7 ± 2.414.2 ± 0.927.0± 1.91.1 ± 0.11.4 ± 0.1
MTT[20]47.7± 0.963.0 ± 1.328.6 ± 0.835.8 ± 1.811
FRePo48.1 ± 0.766.5 ± 0.829.7 ± 0.642.2 ± 0.97.5 ± 0.39.7 ± 0.2
", "type": "table", "image_path": "9e5f726c177726a5d4ac70778034da91123ecdb9239c20f47687477b0608342a.jpg" } ] } ], "index": 4, "virtual_lines": [ { "bbox": [ 119, 111, 492, 135.0 ], "spans": [], "index": 3 }, { "bbox": [ 119, 135.0, 492, 159.0 ], "spans": [], "index": 4 }, { "bbox": [ 119, 159.0, 492, 183.0 ], "spans": [], "index": 5 } ] } ], "index": 2.5 }, { "type": "text", "bbox": [ 106, 194, 506, 282 ], "lines": [ { "bbox": [ 106, 194, 506, 206 ], "spans": [ { "bbox": [ 106, 194, 506, 206 ], "score": 1.0, "content": "degrades a lot when no normalization (NN) is applied (Conv-NN, AlexNet) or using a different", "type": "text" } ], "index": 6 }, { "bbox": [ 105, 205, 505, 218 ], "spans": [ { "bbox": [ 105, 205, 505, 218 ], "score": 1.0, "content": "normalization, like Batch Normalization (BN) [42]. It suggests that the distilled data generated by", "type": "text" } ], "index": 7 }, { "bbox": [ 105, 216, 506, 228 ], "spans": [ { "bbox": [ 105, 216, 506, 228 ], "score": 1.0, "content": "those methods encode the inductive bias of a particular training architecture. In contrast, our distilled", "type": "text" } ], "index": 8 }, { "bbox": [ 106, 227, 506, 239 ], "spans": [ { "bbox": [ 106, 227, 506, 239 ], "score": 1.0, "content": "data generalize well to various architectures, including those without normalization (Conv-NN,", "type": "text" } ], "index": 9 }, { "bbox": [ 105, 237, 506, 250 ], "spans": [ { "bbox": [ 105, 237, 506, 250 ], "score": 1.0, "content": "AlexNet). Note that Figure 1, 4 also indicate that our distilled data encode less architectural bias as", "type": "text" } ], "index": 10 }, { "bbox": [ 105, 249, 506, 261 ], "spans": [ { "bbox": [ 105, 249, 506, 261 ], "score": 1.0, "content": "the distilled images look natural and authentic. A simple idea to further alleviate the overfitting of a", "type": "text" } ], "index": 11 }, { "bbox": [ 105, 259, 506, 273 ], "spans": [ { "bbox": [ 105, 259, 506, 273 ], "score": 1.0, "content": "particular architecture is to include more architectures in the model pool. However, the training may", "type": "text" } ], "index": 12 }, { "bbox": [ 105, 271, 474, 283 ], "spans": [ { "bbox": [ 105, 271, 474, 283 ], "score": 1.0, "content": "not be stable as the meta-gradient computed by different architectures can be very different.", "type": "text" } ], "index": 13 } ], "index": 9.5 }, { "type": "title", "bbox": [ 107, 297, 172, 309 ], "lines": [ { "bbox": [ 105, 295, 174, 312 ], "spans": [ { "bbox": [ 105, 295, 174, 312 ], "score": 1.0, "content": "4.3 ImageNet", "type": "text" } ], "index": 14 } ], "index": 14 }, { "type": "text", "bbox": [ 107, 318, 505, 417 ], "lines": [ { "bbox": [ 106, 318, 505, 330 ], "spans": [ { "bbox": [ 106, 318, 505, 330 ], "score": 1.0, "content": "High Resolution ImageNet Subset To understand how well our method performs on high-resolution", "type": "text" } ], "index": 15 }, { "bbox": [ 105, 329, 506, 342 ], "spans": [ { "bbox": [ 105, 329, 506, 342 ], "score": 1.0, "content": "images, we evaluate it on ImageNette and ImageWoof datasets [36] with a resolution of 128x128. We", "type": "text" } ], "index": 16 }, { "bbox": [ 106, 340, 505, 352 ], "spans": [ { "bbox": [ 106, 340, 505, 352 ], "score": 1.0, "content": "learn 1 and 10 images per class on both datasets and report the performance in Table 3 and visualize", "type": "text" } ], "index": 17 }, { "bbox": [ 105, 351, 505, 364 ], "spans": [ { "bbox": [ 105, 351, 505, 364 ], "score": 1.0, "content": "some distilled images in Figure 1. As shown in Table 3, we outperform MTT on all settings and", "type": "text" } ], "index": 18 }, { "bbox": [ 104, 361, 507, 376 ], "spans": [ { "bbox": [ 104, 361, 507, 376 ], "score": 1.0, "content": "achieve much better performance when we distill ten images per class on a more difficult dataset", "type": "text" } ], "index": 19 }, { "bbox": [ 106, 372, 505, 385 ], "spans": [ { "bbox": [ 106, 372, 505, 385 ], "score": 1.0, "content": "ImageWoof. It suggests that our distilled data is better at capturing the discriminative features for", "type": "text" } ], "index": 20 }, { "bbox": [ 105, 383, 506, 397 ], "spans": [ { "bbox": [ 105, 383, 506, 397 ], "score": 1.0, "content": "each class. Figure 1 shows that our distilled images look real and capture the distinguishable feature", "type": "text" } ], "index": 21 }, { "bbox": [ 105, 393, 507, 408 ], "spans": [ { "bbox": [ 105, 393, 507, 408 ], "score": 1.0, "content": "of different classes. For the easy dataset (i.e., ImageNette), all images have clear different structures,", "type": "text" } ], "index": 22 }, { "bbox": [ 105, 405, 371, 418 ], "spans": [ { "bbox": [ 105, 405, 371, 418 ], "score": 1.0, "content": "while for ImageWoof, the texture of each dog seems to be crucial.", "type": "text" } ], "index": 23 } ], "index": 19 }, { "type": "text", "bbox": [ 107, 422, 505, 466 ], "lines": [ { "bbox": [ 106, 422, 505, 434 ], "spans": [ { "bbox": [ 106, 422, 505, 434 ], "score": 1.0, "content": "Resized ImageNet-1K: We also evaluate our method on a resized version of ILSVRC2012 [26] with", "type": "text" } ], "index": 24 }, { "bbox": [ 105, 433, 505, 445 ], "spans": [ { "bbox": [ 105, 433, 505, 445 ], "score": 1.0, "content": "a resolution of 64x64 to see how it performs on a complex label space. Surprisingly, we can achieve", "type": "text" } ], "index": 25 }, { "bbox": [ 106, 443, 505, 457 ], "spans": [ { "bbox": [ 106, 444, 128, 455 ], "score": 0.86, "content": "7 . 5 \\%", "type": "inline_equation" }, { "bbox": [ 129, 443, 146, 457 ], "score": 1.0, "content": "and", "type": "text" }, { "bbox": [ 146, 444, 168, 455 ], "score": 0.84, "content": "9 . 7 \\%", "type": "inline_equation" }, { "bbox": [ 169, 443, 302, 457 ], "score": 1.0, "content": "Top1 accuracy using only 1k and", "type": "text" }, { "bbox": [ 303, 444, 315, 454 ], "score": 0.38, "content": "2 \\mathrm { k }", "type": "inline_equation" }, { "bbox": [ 315, 443, 443, 457 ], "score": 1.0, "content": "training examples, compared to", "type": "text" }, { "bbox": [ 443, 444, 465, 454 ], "score": 0.85, "content": "1 . 1 \\%", "type": "inline_equation" }, { "bbox": [ 465, 443, 483, 457 ], "score": 1.0, "content": "and", "type": "text" }, { "bbox": [ 483, 444, 505, 454 ], "score": 0.84, "content": "1 . 4 \\%", "type": "inline_equation" } ], "index": 26 }, { "bbox": [ 105, 455, 245, 467 ], "spans": [ { "bbox": [ 105, 455, 245, 467 ], "score": 1.0, "content": "using an equally-sized real subset.", "type": "text" } ], "index": 27 } ], "index": 25.5 }, { "type": "title", "bbox": [ 107, 483, 185, 497 ], "lines": [ { "bbox": [ 104, 481, 187, 501 ], "spans": [ { "bbox": [ 104, 481, 187, 501 ], "score": 1.0, "content": "5 Application", "type": "text" } ], "index": 28 } ], "index": 28 }, { "type": "title", "bbox": [ 107, 509, 215, 522 ], "lines": [ { "bbox": [ 105, 507, 216, 524 ], "spans": [ { "bbox": [ 105, 507, 216, 524 ], "score": 1.0, "content": "5.1 Continual Learning", "type": "text" } ], "index": 29 } ], "index": 29 }, { "type": "text", "bbox": [ 107, 530, 505, 618 ], "lines": [ { "bbox": [ 106, 531, 506, 543 ], "spans": [ { "bbox": [ 106, 531, 506, 543 ], "score": 1.0, "content": "Continual learning (CL) [43] aims to address the catastrophic forgetting problem [43–45] when a", "type": "text" } ], "index": 30 }, { "bbox": [ 105, 542, 505, 554 ], "spans": [ { "bbox": [ 105, 542, 505, 554 ], "score": 1.0, "content": "model learns sequentially from a stream of tasks. A commonly used strategy to recall past knowledge", "type": "text" } ], "index": 31 }, { "bbox": [ 105, 553, 504, 565 ], "spans": [ { "bbox": [ 105, 553, 504, 565 ], "score": 1.0, "content": "is based on a replay buffer, which stores representative samples from previous tasks [46–49]. Since", "type": "text" } ], "index": 32 }, { "bbox": [ 105, 564, 505, 576 ], "spans": [ { "bbox": [ 105, 564, 505, 576 ], "score": 1.0, "content": "sample selection is an important component of constructing an effective buffer [48–51], we believe", "type": "text" } ], "index": 33 }, { "bbox": [ 105, 573, 506, 587 ], "spans": [ { "bbox": [ 105, 573, 506, 587 ], "score": 1.0, "content": "distilled data can be a key ingredient for a continual learning algorithm due to its highly condensed", "type": "text" } ], "index": 34 }, { "bbox": [ 105, 585, 505, 597 ], "spans": [ { "bbox": [ 105, 585, 505, 597 ], "score": 1.0, "content": "nature. Several works [6–8, 52] have successfully applied the dataset distillation to the continual", "type": "text" } ], "index": 35 }, { "bbox": [ 105, 597, 506, 609 ], "spans": [ { "bbox": [ 105, 597, 506, 609 ], "score": 1.0, "content": "learning scenario. Our work shows that we can achieve much better results by using a better dataset", "type": "text" } ], "index": 36 }, { "bbox": [ 105, 606, 195, 620 ], "spans": [ { "bbox": [ 105, 606, 195, 620 ], "score": 1.0, "content": "distillation technique.", "type": "text" } ], "index": 37 } ], "index": 33.5 }, { "type": "text", "bbox": [ 107, 623, 505, 722 ], "lines": [ { "bbox": [ 105, 623, 506, 636 ], "spans": [ { "bbox": [ 105, 623, 506, 636 ], "score": 1.0, "content": "We follow Zhao and Bilen [8] that sets up the baseline based on GDumb [49] which greedily stores", "type": "text" } ], "index": 38 }, { "bbox": [ 105, 633, 507, 647 ], "spans": [ { "bbox": [ 105, 633, 507, 647 ], "score": 1.0, "content": "class-balanced training examples in memory and train model from scratch on the latest memory only.", "type": "text" } ], "index": 39 }, { "bbox": [ 105, 646, 505, 658 ], "spans": [ { "bbox": [ 105, 646, 505, 658 ], "score": 1.0, "content": "In that case, the continual learning performance only depends on the quality of the replay buffer. We", "type": "text" } ], "index": 40 }, { "bbox": [ 105, 655, 506, 670 ], "spans": [ { "bbox": [ 105, 655, 506, 670 ], "score": 1.0, "content": "perform 5 and 10 step class-incremental learning [53] on CIFAR100 with an increasing buffer size", "type": "text" } ], "index": 41 }, { "bbox": [ 105, 667, 506, 681 ], "spans": [ { "bbox": [ 105, 667, 506, 681 ], "score": 1.0, "content": "of 20 images per class. Specifically, we distill 400 and 200 images at each step and put them into", "type": "text" } ], "index": 42 }, { "bbox": [ 105, 677, 506, 691 ], "spans": [ { "bbox": [ 105, 677, 506, 691 ], "score": 1.0, "content": "the replay buffer. We follow the same class split as Zhao and Bilen [8] and compare our method to", "type": "text" } ], "index": 43 }, { "bbox": [ 105, 687, 505, 702 ], "spans": [ { "bbox": [ 105, 687, 505, 702 ], "score": 1.0, "content": "random [49], herding [54, 55], DSA [7], and DM [8]. We use the default data preprocessing and", "type": "text" } ], "index": 44 }, { "bbox": [ 105, 699, 505, 712 ], "spans": [ { "bbox": [ 105, 699, 505, 712 ], "score": 1.0, "content": "default model for each method in this experiment as we find it gives the best performance for each", "type": "text" } ], "index": 45 }, { "bbox": [ 105, 710, 481, 723 ], "spans": [ { "bbox": [ 105, 710, 481, 723 ], "score": 1.0, "content": "method. We use the test accuracy on all observed classes as the performance measure [8, 48].", "type": "text" } ], "index": 46 } ], "index": 42 } ], "page_idx": 7, "page_size": [ 612, 792 ], "discarded_blocks": [ { "type": "discarded", "bbox": [ 302, 742, 308, 750 ], "lines": [ { "bbox": [ 301, 740, 310, 752 ], "spans": [ { "bbox": [ 301, 740, 310, 752 ], "score": 1.0, "content": "", "type": "text", "height": 12, "width": 9 } ] } ] } ], "para_blocks": [ { "type": "table", "bbox": [ 119, 111, 492, 183 ], "blocks": [ { "type": "table_caption", "bbox": [ 107, 77, 505, 110 ], "group_id": 0, "lines": [ { "bbox": [ 105, 75, 506, 91 ], "spans": [ { "bbox": [ 105, 75, 506, 91 ], "score": 1.0, "content": "Table 3: Distillation performance on higher resolution (128x128) dataset (i.e. ImageNette, Image-", "type": "text" } ], "index": 0 }, { "bbox": [ 105, 88, 505, 101 ], "spans": [ { "bbox": [ 105, 88, 505, 101 ], "score": 1.0, "content": "Woof) and medium resolution (64x64) dataset with a complex label space (i.e. ImageNet-1K). FRePo", "type": "text" } ], "index": 1 }, { "bbox": [ 106, 99, 461, 111 ], "spans": [ { "bbox": [ 106, 99, 461, 111 ], "score": 1.0, "content": "scales to high-resolution images and learns the discriminate feature of complex datasets.", "type": "text" } ], "index": 2 } ], "index": 1 }, { "type": "table_body", "bbox": [ 119, 111, 492, 183 ], "group_id": 0, "lines": [ { "bbox": [ 119, 111, 492, 183 ], "spans": [ { "bbox": [ 119, 111, 492, 183 ], "score": 0.977, "html": "
ImageNette (128x128)ImageWoof (128x128)ImageNet (64x64)
Img/Cls11011012
Random Subset23.5± 4.847.7 ± 2.414.2 ± 0.927.0± 1.91.1 ± 0.11.4 ± 0.1
MTT[20]47.7± 0.963.0 ± 1.328.6 ± 0.835.8 ± 1.811
FRePo48.1 ± 0.766.5 ± 0.829.7 ± 0.642.2 ± 0.97.5 ± 0.39.7 ± 0.2
", "type": "table", "image_path": "9e5f726c177726a5d4ac70778034da91123ecdb9239c20f47687477b0608342a.jpg" } ] } ], "index": 4, "virtual_lines": [ { "bbox": [ 119, 111, 492, 135.0 ], "spans": [], "index": 3 }, { "bbox": [ 119, 135.0, 492, 159.0 ], "spans": [], "index": 4 }, { "bbox": [ 119, 159.0, 492, 183.0 ], "spans": [], "index": 5 } ] } ], "index": 2.5 }, { "type": "text", "bbox": [ 106, 194, 506, 282 ], "lines": [], "index": 9.5, "bbox_fs": [ 105, 194, 506, 283 ], "lines_deleted": true }, { "type": "title", "bbox": [ 107, 297, 172, 309 ], "lines": [ { "bbox": [ 105, 295, 174, 312 ], "spans": [ { "bbox": [ 105, 295, 174, 312 ], "score": 1.0, "content": "4.3 ImageNet", "type": "text" } ], "index": 14 } ], "index": 14 }, { "type": "text", "bbox": [ 107, 318, 505, 417 ], "lines": [ { "bbox": [ 106, 318, 505, 330 ], "spans": [ { "bbox": [ 106, 318, 505, 330 ], "score": 1.0, "content": "High Resolution ImageNet Subset To understand how well our method performs on high-resolution", "type": "text" } ], "index": 15 }, { "bbox": [ 105, 329, 506, 342 ], "spans": [ { "bbox": [ 105, 329, 506, 342 ], "score": 1.0, "content": "images, we evaluate it on ImageNette and ImageWoof datasets [36] with a resolution of 128x128. We", "type": "text" } ], "index": 16 }, { "bbox": [ 106, 340, 505, 352 ], "spans": [ { "bbox": [ 106, 340, 505, 352 ], "score": 1.0, "content": "learn 1 and 10 images per class on both datasets and report the performance in Table 3 and visualize", "type": "text" } ], "index": 17 }, { "bbox": [ 105, 351, 505, 364 ], "spans": [ { "bbox": [ 105, 351, 505, 364 ], "score": 1.0, "content": "some distilled images in Figure 1. As shown in Table 3, we outperform MTT on all settings and", "type": "text" } ], "index": 18 }, { "bbox": [ 104, 361, 507, 376 ], "spans": [ { "bbox": [ 104, 361, 507, 376 ], "score": 1.0, "content": "achieve much better performance when we distill ten images per class on a more difficult dataset", "type": "text" } ], "index": 19 }, { "bbox": [ 106, 372, 505, 385 ], "spans": [ { "bbox": [ 106, 372, 505, 385 ], "score": 1.0, "content": "ImageWoof. It suggests that our distilled data is better at capturing the discriminative features for", "type": "text" } ], "index": 20 }, { "bbox": [ 105, 383, 506, 397 ], "spans": [ { "bbox": [ 105, 383, 506, 397 ], "score": 1.0, "content": "each class. Figure 1 shows that our distilled images look real and capture the distinguishable feature", "type": "text" } ], "index": 21 }, { "bbox": [ 105, 393, 507, 408 ], "spans": [ { "bbox": [ 105, 393, 507, 408 ], "score": 1.0, "content": "of different classes. For the easy dataset (i.e., ImageNette), all images have clear different structures,", "type": "text" } ], "index": 22 }, { "bbox": [ 105, 405, 371, 418 ], "spans": [ { "bbox": [ 105, 405, 371, 418 ], "score": 1.0, "content": "while for ImageWoof, the texture of each dog seems to be crucial.", "type": "text" } ], "index": 23 } ], "index": 19, "bbox_fs": [ 104, 318, 507, 418 ] }, { "type": "text", "bbox": [ 107, 422, 505, 466 ], "lines": [ { "bbox": [ 106, 422, 505, 434 ], "spans": [ { "bbox": [ 106, 422, 505, 434 ], "score": 1.0, "content": "Resized ImageNet-1K: We also evaluate our method on a resized version of ILSVRC2012 [26] with", "type": "text" } ], "index": 24 }, { "bbox": [ 105, 433, 505, 445 ], "spans": [ { "bbox": [ 105, 433, 505, 445 ], "score": 1.0, "content": "a resolution of 64x64 to see how it performs on a complex label space. Surprisingly, we can achieve", "type": "text" } ], "index": 25 }, { "bbox": [ 106, 443, 505, 457 ], "spans": [ { "bbox": [ 106, 444, 128, 455 ], "score": 0.86, "content": "7 . 5 \\%", "type": "inline_equation" }, { "bbox": [ 129, 443, 146, 457 ], "score": 1.0, "content": "and", "type": "text" }, { "bbox": [ 146, 444, 168, 455 ], "score": 0.84, "content": "9 . 7 \\%", "type": "inline_equation" }, { "bbox": [ 169, 443, 302, 457 ], "score": 1.0, "content": "Top1 accuracy using only 1k and", "type": "text" }, { "bbox": [ 303, 444, 315, 454 ], "score": 0.38, "content": "2 \\mathrm { k }", "type": "inline_equation" }, { "bbox": [ 315, 443, 443, 457 ], "score": 1.0, "content": "training examples, compared to", "type": "text" }, { "bbox": [ 443, 444, 465, 454 ], "score": 0.85, "content": "1 . 1 \\%", "type": "inline_equation" }, { "bbox": [ 465, 443, 483, 457 ], "score": 1.0, "content": "and", "type": "text" }, { "bbox": [ 483, 444, 505, 454 ], "score": 0.84, "content": "1 . 4 \\%", "type": "inline_equation" } ], "index": 26 }, { "bbox": [ 105, 455, 245, 467 ], "spans": [ { "bbox": [ 105, 455, 245, 467 ], "score": 1.0, "content": "using an equally-sized real subset.", "type": "text" } ], "index": 27 } ], "index": 25.5, "bbox_fs": [ 105, 422, 505, 467 ] }, { "type": "title", "bbox": [ 107, 483, 185, 497 ], "lines": [ { "bbox": [ 104, 481, 187, 501 ], "spans": [ { "bbox": [ 104, 481, 187, 501 ], "score": 1.0, "content": "5 Application", "type": "text" } ], "index": 28 } ], "index": 28 }, { "type": "title", "bbox": [ 107, 509, 215, 522 ], "lines": [ { "bbox": [ 105, 507, 216, 524 ], "spans": [ { "bbox": [ 105, 507, 216, 524 ], "score": 1.0, "content": "5.1 Continual Learning", "type": "text" } ], "index": 29 } ], "index": 29 }, { "type": "text", "bbox": [ 107, 530, 505, 618 ], "lines": [ { "bbox": [ 106, 531, 506, 543 ], "spans": [ { "bbox": [ 106, 531, 506, 543 ], "score": 1.0, "content": "Continual learning (CL) [43] aims to address the catastrophic forgetting problem [43–45] when a", "type": "text" } ], "index": 30 }, { "bbox": [ 105, 542, 505, 554 ], "spans": [ { "bbox": [ 105, 542, 505, 554 ], "score": 1.0, "content": "model learns sequentially from a stream of tasks. A commonly used strategy to recall past knowledge", "type": "text" } ], "index": 31 }, { "bbox": [ 105, 553, 504, 565 ], "spans": [ { "bbox": [ 105, 553, 504, 565 ], "score": 1.0, "content": "is based on a replay buffer, which stores representative samples from previous tasks [46–49]. Since", "type": "text" } ], "index": 32 }, { "bbox": [ 105, 564, 505, 576 ], "spans": [ { "bbox": [ 105, 564, 505, 576 ], "score": 1.0, "content": "sample selection is an important component of constructing an effective buffer [48–51], we believe", "type": "text" } ], "index": 33 }, { "bbox": [ 105, 573, 506, 587 ], "spans": [ { "bbox": [ 105, 573, 506, 587 ], "score": 1.0, "content": "distilled data can be a key ingredient for a continual learning algorithm due to its highly condensed", "type": "text" } ], "index": 34 }, { "bbox": [ 105, 585, 505, 597 ], "spans": [ { "bbox": [ 105, 585, 505, 597 ], "score": 1.0, "content": "nature. Several works [6–8, 52] have successfully applied the dataset distillation to the continual", "type": "text" } ], "index": 35 }, { "bbox": [ 105, 597, 506, 609 ], "spans": [ { "bbox": [ 105, 597, 506, 609 ], "score": 1.0, "content": "learning scenario. Our work shows that we can achieve much better results by using a better dataset", "type": "text" } ], "index": 36 }, { "bbox": [ 105, 606, 195, 620 ], "spans": [ { "bbox": [ 105, 606, 195, 620 ], "score": 1.0, "content": "distillation technique.", "type": "text" } ], "index": 37 } ], "index": 33.5, "bbox_fs": [ 105, 531, 506, 620 ] }, { "type": "text", "bbox": [ 107, 623, 505, 722 ], "lines": [ { "bbox": [ 105, 623, 506, 636 ], "spans": [ { "bbox": [ 105, 623, 506, 636 ], "score": 1.0, "content": "We follow Zhao and Bilen [8] that sets up the baseline based on GDumb [49] which greedily stores", "type": "text" } ], "index": 38 }, { "bbox": [ 105, 633, 507, 647 ], "spans": [ { "bbox": [ 105, 633, 507, 647 ], "score": 1.0, "content": "class-balanced training examples in memory and train model from scratch on the latest memory only.", "type": "text" } ], "index": 39 }, { "bbox": [ 105, 646, 505, 658 ], "spans": [ { "bbox": [ 105, 646, 505, 658 ], "score": 1.0, "content": "In that case, the continual learning performance only depends on the quality of the replay buffer. We", "type": "text" } ], "index": 40 }, { "bbox": [ 105, 655, 506, 670 ], "spans": [ { "bbox": [ 105, 655, 506, 670 ], "score": 1.0, "content": "perform 5 and 10 step class-incremental learning [53] on CIFAR100 with an increasing buffer size", "type": "text" } ], "index": 41 }, { "bbox": [ 105, 667, 506, 681 ], "spans": [ { "bbox": [ 105, 667, 506, 681 ], "score": 1.0, "content": "of 20 images per class. Specifically, we distill 400 and 200 images at each step and put them into", "type": "text" } ], "index": 42 }, { "bbox": [ 105, 677, 506, 691 ], "spans": [ { "bbox": [ 105, 677, 506, 691 ], "score": 1.0, "content": "the replay buffer. We follow the same class split as Zhao and Bilen [8] and compare our method to", "type": "text" } ], "index": 43 }, { "bbox": [ 105, 687, 505, 702 ], "spans": [ { "bbox": [ 105, 687, 505, 702 ], "score": 1.0, "content": "random [49], herding [54, 55], DSA [7], and DM [8]. We use the default data preprocessing and", "type": "text" } ], "index": 44 }, { "bbox": [ 105, 699, 505, 712 ], "spans": [ { "bbox": [ 105, 699, 505, 712 ], "score": 1.0, "content": "default model for each method in this experiment as we find it gives the best performance for each", "type": "text" } ], "index": 45 }, { "bbox": [ 105, 710, 481, 723 ], "spans": [ { "bbox": [ 105, 710, 481, 723 ], "score": 1.0, "content": "method. We use the test accuracy on all observed classes as the performance measure [8, 48].", "type": "text" } ], "index": 46 } ], "index": 42, "bbox_fs": [ 105, 623, 507, 723 ] } ] }, { "preproc_blocks": [ { "type": "table", "bbox": [ 115, 111, 495, 198 ], "blocks": [ { "type": "table_caption", "bbox": [ 107, 77, 505, 110 ], "group_id": 0, "lines": [ { "bbox": [ 105, 77, 505, 89 ], "spans": [ { "bbox": [ 105, 77, 505, 89 ], "score": 1.0, "content": "Table 4: AUC of five attackers on models trained on the real and distilled MNIST data. The model", "type": "text" } ], "index": 0 }, { "bbox": [ 106, 89, 505, 100 ], "spans": [ { "bbox": [ 106, 89, 505, 100 ], "score": 1.0, "content": "trained on the real data is vulnerable to MIAs, while the model trained on the distilled data is robust", "type": "text" } ], "index": 1 }, { "bbox": [ 105, 98, 505, 113 ], "spans": [ { "bbox": [ 105, 98, 505, 113 ], "score": 1.0, "content": "to MIAs. Training on distilled data allows privacy preservation while retaining model performance.", "type": "text" } ], "index": 2 } ], "index": 1 }, { "type": "table_body", "bbox": [ 115, 111, 495, 198 ], "group_id": 0, "lines": [ { "bbox": [ 115, 111, 495, 198 ], "spans": [ { "bbox": [ 115, 111, 495, 198 ], "score": 0.944, "html": "
Test Acc (%)Attack AUC
ThresholdLRMLPRFKNN
Real99.2 ± 0.10.99 ± 0.010.99 ± 0.001.00 ±0.001.00 ± 0.000.97 ±0.00
Subset96.8± 0.20.52 ±0.000.50 ± 0.010.53 ± 0.010.55 ± 0.000.54 ±0.00
DSA98.5 ± 0.10.50 ± 0.000.51 ± 0.000.54 ± 0.000.54 ± 0.010.54 ± 0.01
DM98.3 ± 0.00.50 ± 0.000.51 ± 0.010.54 ± 0.010.54 ± 0.010.53 ± 0.01
FRePo98.5± 0.10.52 ±0.000.51 ± 0.000.53 ± 0.010.52 ± 0.010.51 ± 0.01
", "type": "table", "image_path": "8d5bbd95209fde91ac8ff75261cfe03055c38b7bc922e6db2fdbfc338122aed9.jpg" } ] } ], "index": 4, "virtual_lines": [ { "bbox": [ 115, 111, 495, 140.0 ], "spans": [], "index": 3 }, { "bbox": [ 115, 140.0, 495, 169.0 ], "spans": [], "index": 4 }, { "bbox": [ 115, 169.0, 495, 198.0 ], "spans": [], "index": 5 } ] } ], "index": 2.5 }, { "type": "image", "bbox": [ 111, 215, 500, 302 ], "blocks": [ { "type": "image_body", "bbox": [ 111, 215, 500, 302 ], "group_id": 0, "lines": [ { "bbox": [ 111, 215, 500, 302 ], "spans": [ { "bbox": [ 111, 215, 500, 302 ], "score": 0.953, "type": "image", "image_path": "3425d57f4bfa2229b9a55a067323e25dd62e8fcc52fb803fdd882c3fcc7566d9.jpg" } ] } ], "index": 7, "virtual_lines": [ { "bbox": [ 111, 215, 500, 244.0 ], "spans": [], "index": 6 }, { "bbox": [ 111, 244.0, 500, 273.0 ], "spans": [], "index": 7 }, { "bbox": [ 111, 273.0, 500, 302.0 ], "spans": [], "index": 8 } ] }, { "type": "image_caption", "bbox": [ 106, 308, 505, 363 ], "group_id": 0, "lines": [ { "bbox": [ 106, 308, 505, 320 ], "spans": [ { "bbox": [ 106, 308, 505, 320 ], "score": 1.0, "content": "Figure 5: (a,b) Multi-class accuracies across all classes observed up to a certain time point. We", "type": "text" } ], "index": 9 }, { "bbox": [ 105, 318, 505, 331 ], "spans": [ { "bbox": [ 105, 318, 505, 331 ], "score": 1.0, "content": "perform significantly better than other methods in both 5 and 10 step class-incremental continual", "type": "text" } ], "index": 10 }, { "bbox": [ 105, 329, 506, 344 ], "spans": [ { "bbox": [ 105, 329, 506, 344 ], "score": 1.0, "content": "learning. (c,d) Test accuracy and attack AUC as we increase the number of training steps. AUC keeps", "type": "text" } ], "index": 11 }, { "bbox": [ 105, 340, 505, 353 ], "spans": [ { "bbox": [ 105, 340, 505, 353 ], "score": 1.0, "content": "increasing when training a model on the real data for more steps. In contrast, AUC keeps low when", "type": "text" } ], "index": 12 }, { "bbox": [ 106, 352, 209, 365 ], "spans": [ { "bbox": [ 106, 352, 209, 365 ], "score": 1.0, "content": "training on distilled data.", "type": "text" } ], "index": 13 } ], "index": 11 } ], "index": 9.0 }, { "type": "text", "bbox": [ 106, 387, 505, 475 ], "lines": [ { "bbox": [ 106, 388, 505, 399 ], "spans": [ { "bbox": [ 106, 388, 505, 399 ], "score": 1.0, "content": "Figure 5 shows that our method performs significantly better than all previous methods. The final", "type": "text" } ], "index": 14 }, { "bbox": [ 105, 398, 506, 410 ], "spans": [ { "bbox": [ 105, 398, 474, 410 ], "score": 1.0, "content": "test accuracy for all classes for our method (FRePo) and the second-best method (DM) are", "type": "text" }, { "bbox": [ 475, 398, 502, 409 ], "score": 0.86, "content": "4 1 . 6 \\%", "type": "inline_equation" }, { "bbox": [ 502, 398, 506, 410 ], "score": 1.0, "content": ",", "type": "text" } ], "index": 15 }, { "bbox": [ 106, 409, 506, 423 ], "spans": [ { "bbox": [ 106, 409, 133, 420 ], "score": 0.87, "content": "3 3 . 9 \\%", "type": "inline_equation" }, { "bbox": [ 134, 409, 225, 423 ], "score": 1.0, "content": "in 5-step learning, and", "type": "text" }, { "bbox": [ 225, 410, 252, 420 ], "score": 0.83, "content": "3 8 . 0 \\%", "type": "inline_equation" }, { "bbox": [ 252, 409, 255, 423 ], "score": 1.0, "content": ",", "type": "text" }, { "bbox": [ 255, 410, 282, 420 ], "score": 0.82, "content": "3 4 . 0 \\%", "type": "inline_equation" }, { "bbox": [ 282, 409, 506, 423 ], "score": 1.0, "content": "in 10-step learning. However, we notice that for FRePo,", "type": "text" } ], "index": 16 }, { "bbox": [ 105, 419, 506, 433 ], "spans": [ { "bbox": [ 105, 419, 458, 433 ], "score": 1.0, "content": "distilling 2000 images in a continual learning setup achieves a similar test accuracy", "type": "text" }, { "bbox": [ 458, 420, 492, 432 ], "score": 0.87, "content": "( 4 1 . 6 \\% )", "type": "inline_equation" }, { "bbox": [ 492, 419, 506, 433 ], "score": 1.0, "content": "as", "type": "text" } ], "index": 17 }, { "bbox": [ 105, 430, 506, 444 ], "spans": [ { "bbox": [ 105, 430, 314, 444 ], "score": 1.0, "content": "distilling only 1000 images from the whole dataset", "type": "text" }, { "bbox": [ 314, 431, 342, 442 ], "score": 0.83, "content": "( 4 1 . 3 \\%", "type": "inline_equation" }, { "bbox": [ 343, 430, 506, 444 ], "score": 1.0, "content": "from Table 1). In addition, performance", "type": "text" } ], "index": 18 }, { "bbox": [ 105, 442, 506, 455 ], "spans": [ { "bbox": [ 105, 442, 506, 455 ], "score": 1.0, "content": "drops as we perform more steps. It suggests that FRePo considers all available classes to derive", "type": "text" } ], "index": 19 }, { "bbox": [ 105, 452, 506, 465 ], "spans": [ { "bbox": [ 105, 452, 506, 465 ], "score": 1.0, "content": "the most condensed dataset. Splitting the data into multiple groups and performing independent", "type": "text" } ], "index": 20 }, { "bbox": [ 106, 464, 482, 476 ], "spans": [ { "bbox": [ 106, 464, 482, 476 ], "score": 1.0, "content": "distillation may generate redundant information or fail to capture the distinguishable features.", "type": "text" } ], "index": 21 } ], "index": 17.5 }, { "type": "title", "bbox": [ 108, 491, 263, 503 ], "lines": [ { "bbox": [ 105, 490, 264, 505 ], "spans": [ { "bbox": [ 105, 490, 264, 505 ], "score": 1.0, "content": "5.2 Membership Inference Defense", "type": "text" } ], "index": 22 } ], "index": 22 }, { "type": "text", "bbox": [ 106, 508, 505, 597 ], "lines": [ { "bbox": [ 106, 509, 505, 521 ], "spans": [ { "bbox": [ 106, 509, 505, 521 ], "score": 1.0, "content": "Membership inference attacks (MIA) aim to infer whether a given data point has been used to train", "type": "text" } ], "index": 23 }, { "bbox": [ 106, 520, 506, 532 ], "spans": [ { "bbox": [ 106, 520, 506, 532 ], "score": 1.0, "content": "the model or not [56–58]. Ideally, we want a model to learn from the data but not memorize it to", "type": "text" } ], "index": 24 }, { "bbox": [ 105, 531, 505, 542 ], "spans": [ { "bbox": [ 105, 531, 505, 542 ], "score": 1.0, "content": "preserve privacy. However, deep neural networks are well-known for their ability to memorize all", "type": "text" } ], "index": 25 }, { "bbox": [ 105, 542, 505, 553 ], "spans": [ { "bbox": [ 105, 542, 505, 553 ], "score": 1.0, "content": "the training examples, even on large and randomly labeled datasets [59]. Several methods have been", "type": "text" } ], "index": 26 }, { "bbox": [ 105, 552, 506, 567 ], "spans": [ { "bbox": [ 105, 552, 506, 567 ], "score": 1.0, "content": "proposed to defend against such attacks by either modifying the training procedure [60] or changing", "type": "text" } ], "index": 27 }, { "bbox": [ 106, 563, 505, 576 ], "spans": [ { "bbox": [ 106, 563, 505, 576 ], "score": 1.0, "content": "the inference workflow [61]. This section shows that the distilled data contain little information", "type": "text" } ], "index": 28 }, { "bbox": [ 105, 574, 507, 587 ], "spans": [ { "bbox": [ 105, 574, 507, 587 ], "score": 1.0, "content": "regarding sample presence in the original dataset. Thus, instead of training on the original datasets,", "type": "text" } ], "index": 29 }, { "bbox": [ 106, 586, 463, 598 ], "spans": [ { "bbox": [ 106, 586, 463, 598 ], "score": 1.0, "content": "training on distilled data allows privacy preservation while retaining model performance.", "type": "text" } ], "index": 30 } ], "index": 26.5 }, { "type": "text", "bbox": [ 106, 601, 505, 722 ], "lines": [ { "bbox": [ 105, 601, 505, 614 ], "spans": [ { "bbox": [ 105, 601, 505, 614 ], "score": 1.0, "content": "We consider three distilled data generated by DSA [7], DM [8] and FRePo. We perform five popular", "type": "text" } ], "index": 31 }, { "bbox": [ 106, 612, 505, 625 ], "spans": [ { "bbox": [ 106, 612, 505, 625 ], "score": 1.0, "content": "\"black box\" MIA provided by Tensorflow Privacy [62] on models trained on the real data or the data", "type": "text" } ], "index": 32 }, { "bbox": [ 105, 622, 506, 637 ], "spans": [ { "bbox": [ 105, 622, 506, 637 ], "score": 1.0, "content": "distilled from it. The attack methods include a threshold attack and four model-based attacks using", "type": "text" } ], "index": 33 }, { "bbox": [ 105, 635, 505, 647 ], "spans": [ { "bbox": [ 105, 635, 505, 647 ], "score": 1.0, "content": "logistic regression (LR), multi-layer perceptron (MLP), random forest (RF) and K-nearest neighbor", "type": "text" } ], "index": 34 }, { "bbox": [ 105, 644, 506, 658 ], "spans": [ { "bbox": [ 105, 644, 506, 658 ], "score": 1.0, "content": "(KNN). The inputs to those attack methods are ground-truth labels, model predictions, and losses. To", "type": "text" } ], "index": 35 }, { "bbox": [ 105, 657, 506, 669 ], "spans": [ { "bbox": [ 105, 657, 506, 669 ], "score": 1.0, "content": "measure the privacy vulnerability of the trained model, we compute the area under the ROC curve", "type": "text" } ], "index": 36 }, { "bbox": [ 105, 667, 505, 680 ], "spans": [ { "bbox": [ 105, 667, 505, 680 ], "score": 1.0, "content": "(AUC) of an attack classifier. Following prior work, [56, 63], we keep a balanced set of training", "type": "text" } ], "index": 37 }, { "bbox": [ 105, 678, 505, 691 ], "spans": [ { "bbox": [ 105, 678, 505, 691 ], "score": 1.0, "content": "examples (member) and test examples (non-member) with 10K each to maximize the uncertainty of", "type": "text" } ], "index": 38 }, { "bbox": [ 105, 689, 505, 701 ], "spans": [ { "bbox": [ 105, 689, 321, 701 ], "score": 1.0, "content": "MIA. Thus, the random guessing strategy results in a", "type": "text" }, { "bbox": [ 321, 689, 340, 699 ], "score": 0.87, "content": "50 \\%", "type": "inline_equation" }, { "bbox": [ 341, 689, 505, 701 ], "score": 1.0, "content": "MIA accuracy. We conduct experiments", "type": "text" } ], "index": 39 }, { "bbox": [ 105, 699, 505, 713 ], "spans": [ { "bbox": [ 105, 699, 505, 713 ], "score": 1.0, "content": "on MNIST and FashionMNIST with a distillation size of 500. For space reasons, we provide more", "type": "text" } ], "index": 40 }, { "bbox": [ 106, 711, 297, 723 ], "spans": [ { "bbox": [ 106, 711, 297, 723 ], "score": 1.0, "content": "implementation details and results in appendix.", "type": "text" } ], "index": 41 } ], "index": 36 } ], "page_idx": 8, "page_size": [ 612, 792 ], "discarded_blocks": [ { "type": "discarded", "bbox": [ 302, 741, 309, 750 ], "lines": [ { "bbox": [ 302, 741, 309, 752 ], "spans": [ { "bbox": [ 302, 741, 309, 752 ], "score": 1.0, "content": "9", "type": "text" } ] } ] } ], "para_blocks": [ { "type": "table", "bbox": [ 115, 111, 495, 198 ], "blocks": [ { "type": "table_caption", "bbox": [ 107, 77, 505, 110 ], "group_id": 0, "lines": [ { "bbox": [ 105, 77, 505, 89 ], "spans": [ { "bbox": [ 105, 77, 505, 89 ], "score": 1.0, "content": "Table 4: AUC of five attackers on models trained on the real and distilled MNIST data. The model", "type": "text" } ], "index": 0 }, { "bbox": [ 106, 89, 505, 100 ], "spans": [ { "bbox": [ 106, 89, 505, 100 ], "score": 1.0, "content": "trained on the real data is vulnerable to MIAs, while the model trained on the distilled data is robust", "type": "text" } ], "index": 1 }, { "bbox": [ 105, 98, 505, 113 ], "spans": [ { "bbox": [ 105, 98, 505, 113 ], "score": 1.0, "content": "to MIAs. Training on distilled data allows privacy preservation while retaining model performance.", "type": "text" } ], "index": 2 } ], "index": 1 }, { "type": "table_body", "bbox": [ 115, 111, 495, 198 ], "group_id": 0, "lines": [ { "bbox": [ 115, 111, 495, 198 ], "spans": [ { "bbox": [ 115, 111, 495, 198 ], "score": 0.944, "html": "
Test Acc (%)Attack AUC
ThresholdLRMLPRFKNN
Real99.2 ± 0.10.99 ± 0.010.99 ± 0.001.00 ±0.001.00 ± 0.000.97 ±0.00
Subset96.8± 0.20.52 ±0.000.50 ± 0.010.53 ± 0.010.55 ± 0.000.54 ±0.00
DSA98.5 ± 0.10.50 ± 0.000.51 ± 0.000.54 ± 0.000.54 ± 0.010.54 ± 0.01
DM98.3 ± 0.00.50 ± 0.000.51 ± 0.010.54 ± 0.010.54 ± 0.010.53 ± 0.01
FRePo98.5± 0.10.52 ±0.000.51 ± 0.000.53 ± 0.010.52 ± 0.010.51 ± 0.01
", "type": "table", "image_path": "8d5bbd95209fde91ac8ff75261cfe03055c38b7bc922e6db2fdbfc338122aed9.jpg" } ] } ], "index": 4, "virtual_lines": [ { "bbox": [ 115, 111, 495, 140.0 ], "spans": [], "index": 3 }, { "bbox": [ 115, 140.0, 495, 169.0 ], "spans": [], "index": 4 }, { "bbox": [ 115, 169.0, 495, 198.0 ], "spans": [], "index": 5 } ] } ], "index": 2.5 }, { "type": "image", "bbox": [ 111, 215, 500, 302 ], "blocks": [ { "type": "image_body", "bbox": [ 111, 215, 500, 302 ], "group_id": 0, "lines": [ { "bbox": [ 111, 215, 500, 302 ], "spans": [ { "bbox": [ 111, 215, 500, 302 ], "score": 0.953, "type": "image", "image_path": "3425d57f4bfa2229b9a55a067323e25dd62e8fcc52fb803fdd882c3fcc7566d9.jpg" } ] } ], "index": 7, "virtual_lines": [ { "bbox": [ 111, 215, 500, 244.0 ], "spans": [], "index": 6 }, { "bbox": [ 111, 244.0, 500, 273.0 ], "spans": [], "index": 7 }, { "bbox": [ 111, 273.0, 500, 302.0 ], "spans": [], "index": 8 } ] }, { "type": "image_caption", "bbox": [ 106, 308, 505, 363 ], "group_id": 0, "lines": [ { "bbox": [ 106, 308, 505, 320 ], "spans": [ { "bbox": [ 106, 308, 505, 320 ], "score": 1.0, "content": "Figure 5: (a,b) Multi-class accuracies across all classes observed up to a certain time point. We", "type": "text" } ], "index": 9 }, { "bbox": [ 105, 318, 505, 331 ], "spans": [ { "bbox": [ 105, 318, 505, 331 ], "score": 1.0, "content": "perform significantly better than other methods in both 5 and 10 step class-incremental continual", "type": "text" } ], "index": 10 }, { "bbox": [ 105, 329, 506, 344 ], "spans": [ { "bbox": [ 105, 329, 506, 344 ], "score": 1.0, "content": "learning. (c,d) Test accuracy and attack AUC as we increase the number of training steps. AUC keeps", "type": "text" } ], "index": 11 }, { "bbox": [ 105, 340, 505, 353 ], "spans": [ { "bbox": [ 105, 340, 505, 353 ], "score": 1.0, "content": "increasing when training a model on the real data for more steps. In contrast, AUC keeps low when", "type": "text" } ], "index": 12 }, { "bbox": [ 106, 352, 209, 365 ], "spans": [ { "bbox": [ 106, 352, 209, 365 ], "score": 1.0, "content": "training on distilled data.", "type": "text" } ], "index": 13 } ], "index": 11 } ], "index": 9.0 }, { "type": "text", "bbox": [ 106, 387, 505, 475 ], "lines": [ { "bbox": [ 106, 388, 505, 399 ], "spans": [ { "bbox": [ 106, 388, 505, 399 ], "score": 1.0, "content": "Figure 5 shows that our method performs significantly better than all previous methods. The final", "type": "text" } ], "index": 14 }, { "bbox": [ 105, 398, 506, 410 ], "spans": [ { "bbox": [ 105, 398, 474, 410 ], "score": 1.0, "content": "test accuracy for all classes for our method (FRePo) and the second-best method (DM) are", "type": "text" }, { "bbox": [ 475, 398, 502, 409 ], "score": 0.86, "content": "4 1 . 6 \\%", "type": "inline_equation" }, { "bbox": [ 502, 398, 506, 410 ], "score": 1.0, "content": ",", "type": "text" } ], "index": 15 }, { "bbox": [ 106, 409, 506, 423 ], "spans": [ { "bbox": [ 106, 409, 133, 420 ], "score": 0.87, "content": "3 3 . 9 \\%", "type": "inline_equation" }, { "bbox": [ 134, 409, 225, 423 ], "score": 1.0, "content": "in 5-step learning, and", "type": "text" }, { "bbox": [ 225, 410, 252, 420 ], "score": 0.83, "content": "3 8 . 0 \\%", "type": "inline_equation" }, { "bbox": [ 252, 409, 255, 423 ], "score": 1.0, "content": ",", "type": "text" }, { "bbox": [ 255, 410, 282, 420 ], "score": 0.82, "content": "3 4 . 0 \\%", "type": "inline_equation" }, { "bbox": [ 282, 409, 506, 423 ], "score": 1.0, "content": "in 10-step learning. However, we notice that for FRePo,", "type": "text" } ], "index": 16 }, { "bbox": [ 105, 419, 506, 433 ], "spans": [ { "bbox": [ 105, 419, 458, 433 ], "score": 1.0, "content": "distilling 2000 images in a continual learning setup achieves a similar test accuracy", "type": "text" }, { "bbox": [ 458, 420, 492, 432 ], "score": 0.87, "content": "( 4 1 . 6 \\% )", "type": "inline_equation" }, { "bbox": [ 492, 419, 506, 433 ], "score": 1.0, "content": "as", "type": "text" } ], "index": 17 }, { "bbox": [ 105, 430, 506, 444 ], "spans": [ { "bbox": [ 105, 430, 314, 444 ], "score": 1.0, "content": "distilling only 1000 images from the whole dataset", "type": "text" }, { "bbox": [ 314, 431, 342, 442 ], "score": 0.83, "content": "( 4 1 . 3 \\%", "type": "inline_equation" }, { "bbox": [ 343, 430, 506, 444 ], "score": 1.0, "content": "from Table 1). In addition, performance", "type": "text" } ], "index": 18 }, { "bbox": [ 105, 442, 506, 455 ], "spans": [ { "bbox": [ 105, 442, 506, 455 ], "score": 1.0, "content": "drops as we perform more steps. It suggests that FRePo considers all available classes to derive", "type": "text" } ], "index": 19 }, { "bbox": [ 105, 452, 506, 465 ], "spans": [ { "bbox": [ 105, 452, 506, 465 ], "score": 1.0, "content": "the most condensed dataset. Splitting the data into multiple groups and performing independent", "type": "text" } ], "index": 20 }, { "bbox": [ 106, 464, 482, 476 ], "spans": [ { "bbox": [ 106, 464, 482, 476 ], "score": 1.0, "content": "distillation may generate redundant information or fail to capture the distinguishable features.", "type": "text" } ], "index": 21 } ], "index": 17.5, "bbox_fs": [ 105, 388, 506, 476 ] }, { "type": "title", "bbox": [ 108, 491, 263, 503 ], "lines": [ { "bbox": [ 105, 490, 264, 505 ], "spans": [ { "bbox": [ 105, 490, 264, 505 ], "score": 1.0, "content": "5.2 Membership Inference Defense", "type": "text" } ], "index": 22 } ], "index": 22 }, { "type": "text", "bbox": [ 106, 508, 505, 597 ], "lines": [ { "bbox": [ 106, 509, 505, 521 ], "spans": [ { "bbox": [ 106, 509, 505, 521 ], "score": 1.0, "content": "Membership inference attacks (MIA) aim to infer whether a given data point has been used to train", "type": "text" } ], "index": 23 }, { "bbox": [ 106, 520, 506, 532 ], "spans": [ { "bbox": [ 106, 520, 506, 532 ], "score": 1.0, "content": "the model or not [56–58]. Ideally, we want a model to learn from the data but not memorize it to", "type": "text" } ], "index": 24 }, { "bbox": [ 105, 531, 505, 542 ], "spans": [ { "bbox": [ 105, 531, 505, 542 ], "score": 1.0, "content": "preserve privacy. However, deep neural networks are well-known for their ability to memorize all", "type": "text" } ], "index": 25 }, { "bbox": [ 105, 542, 505, 553 ], "spans": [ { "bbox": [ 105, 542, 505, 553 ], "score": 1.0, "content": "the training examples, even on large and randomly labeled datasets [59]. Several methods have been", "type": "text" } ], "index": 26 }, { "bbox": [ 105, 552, 506, 567 ], "spans": [ { "bbox": [ 105, 552, 506, 567 ], "score": 1.0, "content": "proposed to defend against such attacks by either modifying the training procedure [60] or changing", "type": "text" } ], "index": 27 }, { "bbox": [ 106, 563, 505, 576 ], "spans": [ { "bbox": [ 106, 563, 505, 576 ], "score": 1.0, "content": "the inference workflow [61]. This section shows that the distilled data contain little information", "type": "text" } ], "index": 28 }, { "bbox": [ 105, 574, 507, 587 ], "spans": [ { "bbox": [ 105, 574, 507, 587 ], "score": 1.0, "content": "regarding sample presence in the original dataset. Thus, instead of training on the original datasets,", "type": "text" } ], "index": 29 }, { "bbox": [ 106, 586, 463, 598 ], "spans": [ { "bbox": [ 106, 586, 463, 598 ], "score": 1.0, "content": "training on distilled data allows privacy preservation while retaining model performance.", "type": "text" } ], "index": 30 } ], "index": 26.5, "bbox_fs": [ 105, 509, 507, 598 ] }, { "type": "text", "bbox": [ 106, 601, 505, 722 ], "lines": [ { "bbox": [ 105, 601, 505, 614 ], "spans": [ { "bbox": [ 105, 601, 505, 614 ], "score": 1.0, "content": "We consider three distilled data generated by DSA [7], DM [8] and FRePo. We perform five popular", "type": "text" } ], "index": 31 }, { "bbox": [ 106, 612, 505, 625 ], "spans": [ { "bbox": [ 106, 612, 505, 625 ], "score": 1.0, "content": "\"black box\" MIA provided by Tensorflow Privacy [62] on models trained on the real data or the data", "type": "text" } ], "index": 32 }, { "bbox": [ 105, 622, 506, 637 ], "spans": [ { "bbox": [ 105, 622, 506, 637 ], "score": 1.0, "content": "distilled from it. The attack methods include a threshold attack and four model-based attacks using", "type": "text" } ], "index": 33 }, { "bbox": [ 105, 635, 505, 647 ], "spans": [ { "bbox": [ 105, 635, 505, 647 ], "score": 1.0, "content": "logistic regression (LR), multi-layer perceptron (MLP), random forest (RF) and K-nearest neighbor", "type": "text" } ], "index": 34 }, { "bbox": [ 105, 644, 506, 658 ], "spans": [ { "bbox": [ 105, 644, 506, 658 ], "score": 1.0, "content": "(KNN). The inputs to those attack methods are ground-truth labels, model predictions, and losses. To", "type": "text" } ], "index": 35 }, { "bbox": [ 105, 657, 506, 669 ], "spans": [ { "bbox": [ 105, 657, 506, 669 ], "score": 1.0, "content": "measure the privacy vulnerability of the trained model, we compute the area under the ROC curve", "type": "text" } ], "index": 36 }, { "bbox": [ 105, 667, 505, 680 ], "spans": [ { "bbox": [ 105, 667, 505, 680 ], "score": 1.0, "content": "(AUC) of an attack classifier. Following prior work, [56, 63], we keep a balanced set of training", "type": "text" } ], "index": 37 }, { "bbox": [ 105, 678, 505, 691 ], "spans": [ { "bbox": [ 105, 678, 505, 691 ], "score": 1.0, "content": "examples (member) and test examples (non-member) with 10K each to maximize the uncertainty of", "type": "text" } ], "index": 38 }, { "bbox": [ 105, 689, 505, 701 ], "spans": [ { "bbox": [ 105, 689, 321, 701 ], "score": 1.0, "content": "MIA. Thus, the random guessing strategy results in a", "type": "text" }, { "bbox": [ 321, 689, 340, 699 ], "score": 0.87, "content": "50 \\%", "type": "inline_equation" }, { "bbox": [ 341, 689, 505, 701 ], "score": 1.0, "content": "MIA accuracy. We conduct experiments", "type": "text" } ], "index": 39 }, { "bbox": [ 105, 699, 505, 713 ], "spans": [ { "bbox": [ 105, 699, 505, 713 ], "score": 1.0, "content": "on MNIST and FashionMNIST with a distillation size of 500. For space reasons, we provide more", "type": "text" } ], "index": 40 }, { "bbox": [ 106, 711, 297, 723 ], "spans": [ { "bbox": [ 106, 711, 297, 723 ], "score": 1.0, "content": "implementation details and results in appendix.", "type": "text" } ], "index": 41 } ], "index": 36, "bbox_fs": [ 105, 601, 506, 723 ] } ] }, { "preproc_blocks": [ { "type": "text", "bbox": [ 106, 72, 505, 182 ], "lines": [ { "bbox": [ 105, 73, 505, 85 ], "spans": [ { "bbox": [ 105, 73, 505, 85 ], "score": 1.0, "content": "As shown in Table 4, all models trained on the distilled data preserve privacy as their attack AUCs", "type": "text" } ], "index": 0 }, { "bbox": [ 105, 83, 506, 96 ], "spans": [ { "bbox": [ 105, 83, 506, 96 ], "score": 1.0, "content": "are closed to random guessing. However, we observe a small drop in test accuracy compared to", "type": "text" } ], "index": 1 }, { "bbox": [ 105, 93, 506, 107 ], "spans": [ { "bbox": [ 105, 93, 506, 107 ], "score": 1.0, "content": "the model trained on the full dataset, which is expected as we only distill 500 examples instead of", "type": "text" } ], "index": 2 }, { "bbox": [ 105, 105, 506, 118 ], "spans": [ { "bbox": [ 105, 105, 506, 118 ], "score": 1.0, "content": "10,000 examples. Compared to the model trained on an equally sized subset of the original data, the", "type": "text" } ], "index": 3 }, { "bbox": [ 105, 116, 506, 129 ], "spans": [ { "bbox": [ 105, 116, 506, 129 ], "score": 1.0, "content": "model trained on distilled data results in much better test performance. Figure 5c, 5d demonstrate the", "type": "text" } ], "index": 4 }, { "bbox": [ 106, 128, 505, 139 ], "spans": [ { "bbox": [ 106, 128, 505, 139 ], "score": 1.0, "content": "trade-off between test accuracy and attack effectiveness as measured by ROC AUC. It shows that", "type": "text" } ], "index": 5 }, { "bbox": [ 106, 138, 505, 150 ], "spans": [ { "bbox": [ 106, 138, 505, 150 ], "score": 1.0, "content": "early stopping can be an effective technique to preserve privacy. However, we will still be under high", "type": "text" } ], "index": 6 }, { "bbox": [ 104, 147, 506, 162 ], "spans": [ { "bbox": [ 104, 147, 506, 162 ], "score": 1.0, "content": "MIA risk if we perform early stopping by monitoring the validation loss. In contrast, training a model", "type": "text" } ], "index": 7 }, { "bbox": [ 105, 159, 505, 173 ], "spans": [ { "bbox": [ 105, 159, 505, 173 ], "score": 1.0, "content": "on the distilled data does not have this problem as the attack AUCs keep at a very low level regardless", "type": "text" } ], "index": 8 }, { "bbox": [ 105, 171, 176, 184 ], "spans": [ { "bbox": [ 105, 171, 176, 184 ], "score": 1.0, "content": "of training steps.", "type": "text" } ], "index": 9 } ], "index": 4.5 }, { "type": "title", "bbox": [ 107, 198, 183, 211 ], "lines": [ { "bbox": [ 105, 196, 185, 214 ], "spans": [ { "bbox": [ 105, 196, 185, 214 ], "score": 1.0, "content": "6 Conclusion", "type": "text" } ], "index": 10 } ], "index": 10 }, { "type": "text", "bbox": [ 107, 223, 505, 299 ], "lines": [ { "bbox": [ 106, 222, 506, 236 ], "spans": [ { "bbox": [ 106, 222, 506, 236 ], "score": 1.0, "content": "We propose neural Feature Regression with Pooling (FRePo) to overcome two challenges in dataset", "type": "text" } ], "index": 11 }, { "bbox": [ 105, 233, 506, 247 ], "spans": [ { "bbox": [ 105, 233, 506, 247 ], "score": 1.0, "content": "distillation: meta-gradient computation and various types of overfitting in dataset distillation. We", "type": "text" } ], "index": 12 }, { "bbox": [ 105, 245, 505, 257 ], "spans": [ { "bbox": [ 105, 245, 358, 257 ], "score": 1.0, "content": "obtain state-of-the-art performance on various datasets with a", "type": "text" }, { "bbox": [ 359, 245, 381, 255 ], "score": 0.32, "content": "1 0 0 \\mathrm { x }", "type": "inline_equation" }, { "bbox": [ 381, 245, 505, 257 ], "score": 1.0, "content": "reduction in training time and", "type": "text" } ], "index": 13 }, { "bbox": [ 105, 256, 505, 268 ], "spans": [ { "bbox": [ 105, 256, 505, 268 ], "score": 1.0, "content": "a 10x reduction in GPU memory requirement. The distilled data generated by FRePo looks real", "type": "text" } ], "index": 14 }, { "bbox": [ 105, 266, 505, 279 ], "spans": [ { "bbox": [ 105, 266, 505, 279 ], "score": 1.0, "content": "and natural and generalizes well to a wide range of architectures. Furthermore, we demonstrate two", "type": "text" } ], "index": 15 }, { "bbox": [ 105, 277, 506, 291 ], "spans": [ { "bbox": [ 105, 277, 506, 291 ], "score": 1.0, "content": "applications that take advantage of the high-quality distilled data, namely, continual learning and", "type": "text" } ], "index": 16 }, { "bbox": [ 105, 288, 234, 301 ], "spans": [ { "bbox": [ 105, 288, 234, 301 ], "score": 1.0, "content": "membership inference defense.", "type": "text" } ], "index": 17 } ], "index": 14 }, { "type": "text", "bbox": [ 107, 304, 505, 371 ], "lines": [ { "bbox": [ 105, 304, 506, 317 ], "spans": [ { "bbox": [ 105, 304, 506, 317 ], "score": 1.0, "content": "Broader Impact “Synthetic data”, in the broader sense of artificial data created by generative models,", "type": "text" } ], "index": 18 }, { "bbox": [ 105, 316, 505, 329 ], "spans": [ { "bbox": [ 105, 316, 505, 329 ], "score": 1.0, "content": "can help researchers understand how an otherwise opaque learning machine “sees” the world. There", "type": "text" } ], "index": 19 }, { "bbox": [ 105, 326, 505, 339 ], "spans": [ { "bbox": [ 105, 326, 505, 339 ], "score": 1.0, "content": "have been concerns regarding the risk of fake data. This paper explores a new research direction", "type": "text" } ], "index": 20 }, { "bbox": [ 105, 338, 505, 349 ], "spans": [ { "bbox": [ 105, 338, 505, 349 ], "score": 1.0, "content": "in generating synthetic data only for downstream classification tasks. 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However, we observe a small drop in test accuracy compared to", "type": "text" } ], "index": 1 }, { "bbox": [ 105, 93, 506, 107 ], "spans": [ { "bbox": [ 105, 93, 506, 107 ], "score": 1.0, "content": "the model trained on the full dataset, which is expected as we only distill 500 examples instead of", "type": "text" } ], "index": 2 }, { "bbox": [ 105, 105, 506, 118 ], "spans": [ { "bbox": [ 105, 105, 506, 118 ], "score": 1.0, "content": "10,000 examples. Compared to the model trained on an equally sized subset of the original data, the", "type": "text" } ], "index": 3 }, { "bbox": [ 105, 116, 506, 129 ], "spans": [ { "bbox": [ 105, 116, 506, 129 ], "score": 1.0, "content": "model trained on distilled data results in much better test performance. Figure 5c, 5d demonstrate the", "type": "text" } ], "index": 4 }, { "bbox": [ 106, 128, 505, 139 ], "spans": [ { "bbox": [ 106, 128, 505, 139 ], "score": 1.0, "content": "trade-off between test accuracy and attack effectiveness as measured by ROC AUC. It shows that", "type": "text" } ], "index": 5 }, { "bbox": [ 106, 138, 505, 150 ], "spans": [ { "bbox": [ 106, 138, 505, 150 ], "score": 1.0, "content": "early stopping can be an effective technique to preserve privacy. However, we will still be under high", "type": "text" } ], "index": 6 }, { "bbox": [ 104, 147, 506, 162 ], "spans": [ { "bbox": [ 104, 147, 506, 162 ], "score": 1.0, "content": "MIA risk if we perform early stopping by monitoring the validation loss. 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We", "type": "text" } ], "index": 12 }, { "bbox": [ 105, 245, 505, 257 ], "spans": [ { "bbox": [ 105, 245, 358, 257 ], "score": 1.0, "content": "obtain state-of-the-art performance on various datasets with a", "type": "text" }, { "bbox": [ 359, 245, 381, 255 ], "score": 0.32, "content": "1 0 0 \\mathrm { x }", "type": "inline_equation" }, { "bbox": [ 381, 245, 505, 257 ], "score": 1.0, "content": "reduction in training time and", "type": "text" } ], "index": 13 }, { "bbox": [ 105, 256, 505, 268 ], "spans": [ { "bbox": [ 105, 256, 505, 268 ], "score": 1.0, "content": "a 10x reduction in GPU memory requirement. The distilled data generated by FRePo looks real", "type": "text" } ], "index": 14 }, { "bbox": [ 105, 266, 505, 279 ], "spans": [ { "bbox": [ 105, 266, 505, 279 ], "score": 1.0, "content": "and natural and generalizes well to a wide range of architectures. 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There", "type": "text" } ], "index": 19 }, { "bbox": [ 105, 326, 505, 339 ], "spans": [ { "bbox": [ 105, 326, 505, 339 ], "score": 1.0, "content": "have been concerns regarding the risk of fake data. This paper explores a new research direction", "type": "text" } ], "index": 20 }, { "bbox": [ 105, 338, 505, 349 ], "spans": [ { "bbox": [ 105, 338, 505, 349 ], "score": 1.0, "content": "in generating synthetic data only for downstream classification tasks. 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