| Method | | JSFA→DA→WD-→WW-→DD-→AW→AAvg |
| MCD [44] CDAN [34] MDD[69]] DMRL[59] MCC[19] | X .xxxxx | 92.2 88.6 92.9 94.1 90.4 90.4 93.4 90.8 95.6 95.4 | 98.5 98.6 100.0 98.7 99.9 99.0 100.0 98.6 100.0 | 100.0 69.5 69.7 86.5 71.0 75.0 73.0 71.2 72.6 | 69.3 87.7 73.7 88.0 87.9 |
| SRDC [50] SHOT[26] 3C-GAN [24] NRC[64] HCL [15] BNM-S [6] | | 95.8 95.7 94.0 90.1 92.7 93.7 96.0 90.8 94.7 92.5 93.0 92.9 | 99.2 98.4 98.5 99.0 98.2 98.2 | 100.0 76.7 77.1 99.9 74.7 74.3 99.8 75.3 77.8 100.0 75.3 75.0 100.0 75.9 77.7 99.9 75.4 75.0 | 73.9 89.4 90.8 88.6 89.6 89.4 89.8 89.1 |
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+| Method | | JSFA→DA→WD-→WW-→DD-→AW→AAvg |
| MCD [44] CDAN [34] MDD[69]] DMRL[59] MCC[19] | X .xxxxx | 92.2 88.6 92.9 94.1 90.4 90.4 93.4 90.8 95.6 95.4 | 98.5 98.6 100.0 98.7 99.9 99.0 100.0 98.6 100.0 | 100.0 69.5 69.7 86.5 71.0 75.0 73.0 71.2 72.6 | 69.3 87.7 73.7 88.0 87.9 |
| SRDC [50] SHOT[26] 3C-GAN [24] NRC[64] HCL [15] BNM-S [6] | | 95.8 95.7 94.0 90.1 92.7 93.7 96.0 90.8 94.7 92.5 93.0 92.9 | 99.2 98.4 98.5 99.0 98.2 98.2 | 100.0 76.7 77.1 99.9 74.7 74.3 99.8 75.3 77.8 100.0 75.3 75.0 100.0 75.9 77.7 99.9 75.4 75.0 | 73.9 89.4 90.8 88.6 89.6 89.4 89.8 89.1 |
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| MCD [44] CDAN [34] MDD[69]] DMRL[59] MCC[19] | X .xxxxx | 92.2 88.6 92.9 94.1 90.4 90.4 93.4 90.8 95.6 95.4 | 98.5 98.6 100.0 98.7 99.9 99.0 100.0 98.6 100.0 | 100.0 69.5 69.7 86.5 71.0 75.0 73.0 71.2 72.6 | 69.3 87.7 73.7 88.0 87.9 |
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| MCD [44] CDAN [34] MDD[69]] DMRL[59] MCC[19] | X .xxxxx | 92.2 88.6 92.9 94.1 90.4 90.4 93.4 90.8 95.6 95.4 | 98.5 98.6 100.0 98.7 99.9 99.0 100.0 98.6 100.0 | 100.0 69.5 69.7 86.5 71.0 75.0 73.0 71.2 72.6 | 69.3 87.7 73.7 88.0 87.9 |
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+ "html": "| Require: Domain data D1,.,Dk,number of training steps T, batch size b,step size n, smoothing parameterc∈ [0,1] (e.g.,c=1e-3 in our implementation). | |
| Initialize proxy weights 0o | |
| Initialize domain weights αo = 11 | |
| for t from 1 to T do | Sample minibatch B={xi1,,xj} of size b from Pu, where u= 1 |
| Let |x| be the token length of example x (|x|≤ L) | |
| Compute per-domain excess losses for each domain i∈ {1,2,.,k} (le.,j(x) is j-th token-level |
| loss): 1 1|x | max{lθt-1,j(x)-lref,j(x),0} |
| 入t[i]←Ω∈BnD ∑xEBnDi∑j=11 |x | Update domain weights (exp is entrywise): αt ← αt-1exp(n入t) |
| Renormalize and smooth domain weights: αt ← (1-c) | a +cu |
| |
| end for | Update proxy model weights 0t for the objective L(0t-1,αt) (using Adam, Adafactor, etc.) |
+
+Iterated DoReMi. We extend DoReMi by running it for multiple rounds, setting the reference domain weights $\alpha _ { \mathrm { r e f } }$ for the next round to be $\bar { \alpha }$ from the previous round. We call this iterated DoReMi. The entire iterated process still only uses small models for tuning domain weights. We stop iterating when the domain weights converge, which we define as when maximum change in any domain weight $\left\| \bar { \alpha } - \alpha _ { \mathrm { r e f } } \right\| _ { \infty }$ is less than 1e-3. Empirically, this takes only 3 rounds on the GLaM dataset (Section 3.2).
+
+# 3 DoReMi Improves LM Training Efficiency and Performance
+
+In this section, we use DoReMi domain weights optimized with a 280M-parameter proxy model to train a 8B-parameter main model $3 0 \mathrm { x }$ larger). We consider two datasets, The Pile [17] and the GLaM dataset [13]. On The Pile, DoReMi reduces perplexity significantly on every domain, improves average downstream accuracy on generative one-shot tasks by $6 . 5 \%$ , and achieves the baseline accuracy $2 . 6 \mathbf { x }$ faster. On the GLaM dataset where domain weights tuned on downstream datasets are available, DoReMi finds domain weights with comparable performance to downstream-tuned domain weights.
+
+# 3.1 Experimental setup
+
+The Pile dataset. The Pile [17] is a 800GB text dataset with 22 domains (Table 1). The default domain weights were determined heuristically. We use the default domain weights from The Pile dataset to train the baseline and as the reference domain weights $\alpha _ { \mathrm { r e f } }$ in DoReMi (see Appendix C).
+
+GLaM dataset. The GLaM dataset [13] (also used in training PaLM [10]) includes text from 8 domains (Table 2). For comparison, the GLaM domain weights (downstream-tuned) were tuned according to the downstream performance of models trained on each domain and the size of each domain [13]. We consider this an oracle comparison, since these domain weights are tuned on downstream tasks that are in our evaluation set. We use uniform domain weights both for training the baseline and the reference domain weights $\alpha _ { \mathrm { r e f } }$ for DoReMi.
+
+Training setup. We train Transformer [51] decoder-only LMs with the standard next-token language modeling loss. We conduct a controlled comparison by equalizing the amount of compute, measured by the number of tokens processed during training. For The Pile, we train each model for $2 0 0 \mathrm { k }$ steps; for the GLaM dataset, we train each model for 300k steps. All models use a batch size of 512 and maximum token length of 1024. The proxy and reference models have 280M parameters. All models are trained from scratch (other hyperparameters are in Appendix C).
+
+Evaluation. We use held-out validation data to measure the perplexity on each domain. For downstream evaluation, we use the generative one-shot tasks from the GPT-3 paper [9]: TriviaQA [21], NaturalQuestions [27], WebQuestions [5], SQuADv2 [41], and LAMBADA [36]. We use the standard exact-match accuracy metric for the these datasets. The performance on these datasets (particularly TriviaQA) has been shown to correlate well with model scale even at the 100M–1B range [9].
+
+Compute used for optimizing domain weights. We train two 280M models (the reference and proxy models) to optimize the domain weights. This is $8 \%$ of the FLOPs required to train the main 8B model. All FLOPs come from standard forward and backward passes.
+
+Notation for model sizes in DoReMi. We denote the size of the reference/proxy models (which are always the same size in our experiments) and the size of the main model trained with DoReMi domain weights as “DoReMi (size of reference/proxy size of main model)”: for example, DoReMi $( 2 8 0 \mathbf { M } \partial \mathbf { B }$ ). When we are discussing the optimized domain weights independently of the main model, we only include one number (e.g., DoReMi (280M)) which refers to the reference/proxy model size.
+
+
+Figure 3: Average one-shot downstream accuracy (exact match) on 5 tasks, with 8B parameter models trained on The Pile (left) and the GLaM dataset (right). On The Pile, DoReMi improves downstream accuracy by $6 . 5 \%$ points and achieves the baseline accuracy $2 . 6 \mathbf { x }$ faster (same plot as Figure 2). On the GLaM dataset, iterated DoReMi (round 2) attains comparable performance to oracle domain weights tuned with downstream tasks that are in our evaluation set.
+
+
+Figure 4: Per-domain log-perplexity of 8B models on The Pile. Despite downweighting some domains, DoReMi improves log-perplexity on all domains.
+
+Table 1: Domain weights on The Pile. Baseline domain weights are computed from the default Pile dataset. DoReMi (280M) uses a 280M proxy model to optimize the domain weights.
+
+| Require: Domain data D1,.,Dk,number of training steps T, batch size b,step size n, smoothing parameterc∈ [0,1] (e.g.,c=1e-3 in our implementation). | |
| Initialize proxy weights 0o | |
| Initialize domain weights αo = 11 | |
| for t from 1 to T do | Sample minibatch B={xi1,,xj} of size b from Pu, where u= 1 |
| Let |x| be the token length of example x (|x|≤ L) | |
| Compute per-domain excess losses for each domain i∈ {1,2,.,k} (le.,j(x) is j-th token-level |
| loss): 1 1|x | max{lθt-1,j(x)-lref,j(x),0} |
| 入t[i]←Ω∈BnD ∑xEBnDi∑j=11 |x | Update domain weights (exp is entrywise): αt ← αt-1exp(n入t) |
| Renormalize and smooth domain weights: αt ← (1-c) | a +cu |
| |
| end for | Update proxy model weights 0t for the objective L(0t-1,αt) (using Adam, Adafactor, etc.) |
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+ "text": "Evaluation. We use held-out validation data to measure the perplexity on each domain. For downstream evaluation, we use the generative one-shot tasks from the GPT-3 paper [9]: TriviaQA [21], NaturalQuestions [27], WebQuestions [5], SQuADv2 [41], and LAMBADA [36]. We use the standard exact-match accuracy metric for the these datasets. The performance on these datasets (particularly TriviaQA) has been shown to correlate well with model scale even at the 100M–1B range [9]. ",
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+ "Figure 3: Average one-shot downstream accuracy (exact match) on 5 tasks, with 8B parameter models trained on The Pile (left) and the GLaM dataset (right). On The Pile, DoReMi improves downstream accuracy by $6 . 5 \\%$ points and achieves the baseline accuracy $2 . 6 \\mathbf { x }$ faster (same plot as Figure 2). On the GLaM dataset, iterated DoReMi (round 2) attains comparable performance to oracle domain weights tuned with downstream tasks that are in our evaluation set. "
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+ "Figure 4: Per-domain log-perplexity of 8B models on The Pile. Despite downweighting some domains, DoReMi improves log-perplexity on all domains. "
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+ "Table 1: Domain weights on The Pile. Baseline domain weights are computed from the default Pile dataset. DoReMi (280M) uses a 280M proxy model to optimize the domain weights. "
+ ],
+ "table_footnote": [],
+ "table_body": "| Require: Domain data D1,.,Dk,number of training steps T, batch size b,step size n, smoothing parameterc∈ [0,1] (e.g.,c=1e-3 in our implementation). | |
| Initialize proxy weights 0o | |
| Initialize domain weights αo = 11 | |
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| Let |x| be the token length of example x (|x|≤ L) | |
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| loss): 1 1|x | max{lθt-1,j(x)-lref,j(x),0} |
| 入t[i]←Ω∈BnD ∑xEBnDi∑j=11 |x | Update domain weights (exp is entrywise): αt ← αt-1exp(n入t) |
| Renormalize and smooth domain weights: αt ← (1-c) | a +cu |
| |
| end for | Update proxy model weights 0t for the objective L(0t-1,αt) (using Adam, Adafactor, etc.) |
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| Initialize proxy weights 0o | |
| Initialize domain weights αo = 11 | |
| for t from 1 to T do | Sample minibatch B={xi1,,xj} of size b from Pu, where u= 1 |
| Let |x| be the token length of example x (|x|≤ L) | |
| Compute per-domain excess losses for each domain i∈ {1,2,.,k} (le.,j(x) is j-th token-level |
| loss): 1 1|x | max{lθt-1,j(x)-lref,j(x),0} |
| 入t[i]←Ω∈BnD ∑xEBnDi∑j=11 |x | Update domain weights (exp is entrywise): αt ← αt-1exp(n入t) |
| Renormalize and smooth domain weights: αt ← (1-c) | a +cu |
| |
| end for | Update proxy model weights 0t for the objective L(0t-1,αt) (using Adam, Adafactor, etc.) |
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| Coreset | Herding | | 14.6±1.6 35.1±4.1 20.9±1.3 50.5±3.3 | 70.9±0.9 72.6±0.8 | 14.4±2.0 26.0±1.2 43.4±1.0 | | | 4.2±0.3 | 14.6±0.5 30.0±0.4 | |
| | | | 21.5±1.3 31.6±0.7 40.4±0.6 | | | 8.4±0.3 | 17.3±0.3 33.7±0.5 | |
| K-Center | | 21.0±1.5 14.0±1.3 20.1±1.4 | | 21.5±1.3 14.7±0.9 27.0±1.4 | | | 8.3±0.3 | 7.1±0.2 30.5±0.3 | |
| Forgetting | 12.1±1.7 | 16.8±1.2 | 227.2±1.5 | 13.5±1.2 | | 23.3±1.0 23.3±1.1 | 4.5±0.3 | 9.8±0.2 | |
| Distillation | DD+ [47] LD+ [3] | | | | | 36.8±1.2 | | | | |
| | | | 25.7±0.7 38.3±0.4 42.5±0.4 | | | 11.5±0.4 | | |
| DC [55] | | 31.2±1.4 76.1±0.6 82.3±0.3 | | 28.3±0.5 44.9±0.5 53.9±0.5 | | | 12.8±0.3 25.2±0.3 | | |
| DSA[53] | | 27.5±1.4 79.2±0.5 84.4±0.4 | | 28.8±0.7 52.1±0.5 60.6±0.5 | | | 13.9±0.3 | 32.3±0.3 42.8±0.4 | |
| DM [54] | | | | 26.0±0.8 48.9±0.6 63.0±0.4 | | | 11.4±0.3 | 29.7±0.3 43.6±0.4 | |
| CAFE[46] CAFE+DSA[46] | | 42.6±3.3 75.9±0.6 81.3±0.3 | | 30.3±1.1 46.3±0.6 55.5±0.6 | | | | 12.9±0.3 27.8±0.3 37.9±0.3 | |
| MTT[5] | 58.5±1.4 70.8±1.8 85.7±0.1 | 42.9±3.0 77.9±0.6 82.3±0.4 | | 31.6±0.8 50.9±0.5 62.3±0.4 46.3±0.8 65.3±0.7 71.6±0.2 | | | 14.0±0.3 31.5±0.2 24.3±0.3 | 39.0±0.1 | 42.9±0.2 46.1±0.2 |
| BPC | | | 49 | | 9 | | | | |
| Ratio % HaBa | 1 9 0.028 | | | 1 | | 49 | 1 | 9 | 49 |
| Factorization | 69.8±1.3 83.2±0.4 88.3±0.1 | 0.14 | 0.7 | 0.04 48.3±0.8 69.9±0.4 74.0±0.2 | 0.2 | 1 | 0.22 33.4±0.4 40.2±0.2 47.0±0.2 | 1.82 | 9.82 |
| Whole Dataset | | 95.4±0.1 | | | 84.8±0.1 | | | 56.2±0.3 | |
+
+Table 1: The performance (test accuracy $\%$ ) comparison to state-of-the-art methods. LD† and DD† use AlexNet for CIFAR10, while the rest use ConvNet for training and testing. IPC: Number of Images Per Class; BPC: Number of Bases Per Class; Ratio $( \% )$ : the ratio of distilled images to whole training set. Underline denotes results by our implementation.
+
+
+Figure 4: Visualization of factorized results by our HaBa $7 0 . 2 7 \%$ test acc.) and baseline MTT $( 6 5 . 9 2 \%$ test acc.). Zoom-in for better comparisons.
+
+The comparison results are shown in Tab. 1 and we can observe that HaBa achieves state-of-the-art performance in all datasets and settings. Especially when the ratio of distilled images to the whole training set is less than $1 \%$ , our method can yield significant improvement over all the candidate methods, which demonstrates that the scheme of hallucinator-basis factorization improves the data efficiency for the task of dataset distillation.
+
+Qualitative Comparisons: We visualize the factorized results by our method as well as the baseline on CIFAR10 dataset with 10 BPC in Fig. 4. Due to the space limitation, we only provide images generated by 2 hallucinators here. More results can be found in the supplement. As shown in the figure, we can find that bases mainly store some main structures and contour information. Different hallucinators would render a basis with diverse styles and details. Thanks to the dataset factorization scheme, the diversity of distilled images by our method is higher than that by the baseline.
+
+Building upon Different Baselines: To reflect the versatility of the insight, we implement HaBa on multiple state-of-the-art training pipelines of DD, including DC, DM, and MTT. We evaluate the performance of synthetic datasets on CIFAR10 and maintain the IPC of baseline methods as BPC plus 1, which makes storage costs for synthetic datasets as close as possible for fairness. As shown in Tab. 2, when training and testing on ConvNet, the strategy of HaBa can make a consistent improvement over all the baselines, which demonstrates that factorization is a general idea to improve the data efficiency in DD.
+
+Cross-Architecture Performance: For DD, a satisfactory distilled dataset should have similar training effects to the original one on downstream models with arbitrary architectures. Thus, crossarchitecture generalization performance is an important metric for DD. We use the synthetic datasets trained on ConvNet to train models with different structures including ResNet [14], VGG [41], and AlexNet [23]. The results can be found in Tab. 2. Benefiting from the increased data diversity, HaBa can improve the across-architecture accuracy significantly with a performance gain up to $\mathrm { \bar { 1 } 7 . 5 7 \% }$ . The consistent and significant improvement validates the superior ability of our method to capture the informative features and thus original datasets can be replaced by the synthetic ones better.
+
+ | |Method | DC [55] | DM [54] | MTT[5] |
| IPC BPC | 2 | 11 | 51 | 2 | 11 | 51 | 2 | 11 | 51 |
| Baseline | 1 |31.36±0.16 45.29±0.30 54.24±0.61 | 10 | 50 | 1 134.57±0.52 50.35±0.36 62.03±0.29|50.59±0.95 63.90±0.29 69.81±0.48 | 10 | 50 | 1 | 10 | 50 |
| ConvNet w.HaBa Gain Baseline | 34.11±0.47 49.88±0.52 58.91±0.23 +2.75 18.10±0.7618.36±0.3622.14±0.38| | +4.59 | +4.67 | +2.75 | 37.32±0.13 56.83±0.11 64.44±0.40 +6.48 3|22.25±1.00 40.00±1.49 53.40±0.68|35.15±0.96 45.05±1.46 54.47±0.95 | +2.41 | +6.17 | 56.76±0.38 69.48±0.26 73.25±0.21 +5.58 | +3.44 |
| ResNet | w.HaBa Gain Baseline | 24.49±0.55 24.27±0.56 31.08±0.32 +6.39 28.02±0.26 35.88±0.67 38.73±0.482 | +6.11 | +8.94 | +9.09 | 31.34±0.7247.57±0.4959.61±0.35 +7.57 | +6.21 | +12.24 322.28±1.0341.64±0.64 55.17±0.54|38.04±1.19 50.49±1.02 61.36±0.30 | 47.39±0.7157.97±0.8864.35±0.60 +12.92 | +9.88 |
| VGG | w.HaBa Gain | 29.42±0.93 37.03±0.42 41.91±0.55 +1.40 | +1.15 | +3.18 | 26.93±0.62 49.41±0.36 67.47±0.43 +4.65 | +7.77 | +12.30 | +10.22 | 48.26±0.54 60.47±0.56 67.47±0.43 +9.98 | +6.11 |
| AlexNet | w. HaBa Gain | Baseline|20.02±1.312.42±1.3529.48±0.8720.67±3.6437.04±0.9249.14±0.94|26.06±1.0135.95±1.5249.20±1.27 22.24±1.14 33.02±0.91 33.42±1.39 +2.22 | +10.60 | +3.94 | +11.47 | 32.14±0.60 44.14±0.67 53.09±0.89 +7.10 | +3.95 | 43.63±1.46 48.96±3.00 60.07±1.37 +17.57 | +13.01 | +10.87 |
+
+Table 2: Cross-architecture performance (test accuracy $\%$ ) comparison to different baseline methods of DD HaBa built upon.
+
+Comparisons under the Same Number of Final Images: In the default comparison protocol, we compare our method with the baselines using the same budget of storage, where our method can store information of exponentially more images than the baselines with the same number of parameters. In this part, we also examine the performance of HaBa under the condition that the number of final images, i.e., $| { \mathcal { H } } | \times | B |$ , is equal to that used by the baseline. Intuitively, given that the objective functions of our method and the baseline are the same exactly, the performance of the baseline can be viewed as an upper bound of ours, since there are significantly less parameters in our method to carry the information of final images in this case. Therefore, we first remove the term $\mathcal { L } _ { c o s }$ . from the loss function of DD in Eq. 6 to guarantee a consistent optimization objective with the baseline. Then, we compare the performance of HaBa and the baseline using 10, 20, 30, 40, and 50 final images respectively. Here, the number of hallucinators $| \mathcal { H } |$ is 2 and the number of bases is thus half of the number of final images. As shown in the red and green curves in Fig. 7, performance of the baseline can be well approximated by ours with only half of the number of parameters, especially when the number of images is relatively large. Remarkably, with the proposed adversary contrastive constraint, our method can even outperform the baseline consistently, as shown in the blue curve, which further demonstrates the effectiveness of the proposed solution.
+
+Comparisons with Concurrent Works on Efficient Distilled Dataset Parameterization: As a concurrent work on efficient distilled dataset parameterization, IDC [21] is proposed to store $4 \times$ number of $2 \times$ down-sample synthetic images compared with the baseline. The core is to reduce the spatial size for efficient parameterization. For HaBa of this paper, instead, we do not modify the spatial size of bases in the default setting for better qualitative explainablity and more intuitive comparisons with the baselines. In this sense, IDC and HaBa are in fact two orthogonal techniques and they can readily join force to enhance the baseline performance. Here, we try using the technique of IDC and adopting $2 \times$ down-sample synthetic images on the baseline MTT, based on which we further consider adding our HaBa and involving 5 hallucinators. As shown in Tab. 3, with the efficient parameterization of IDC, the performance of baseline can be improved. With HaBa in this paper, the performance can even be further improved a lot: $5 . 1 4 \%$ , $1 . 2 9 \%$ , and $4 . 3 0 \%$ in the three settings respectively, which demonstrates that IDC and HaBa work in different ways.
+
+Applications in Continual Learning: To further demonstrate the advantage of the proposed method for improving data efficiency, following the setting of DM [54], we conduct experiments on the setting of continual learning on CIFAR-100, with 20 random classes per stage. The average number of parameters per class is $2 0 \times 3 2 \times 3 2 \times 3$ . The synthetic datasets are trained with a ConvNet with 3 blocks. We evaluate synthetic datasets by our method and the DM baseline on the same ConvNet architecture and ResNet18. The results in Fig. 5 demonstrate that the proposed method increases the informativeness of synthetic datasets and thus produce significantly better performance, especially in the cross-architecture setting.
+
+# 4.3 Ablation Studies
+
+Loss Terms: To validate the effectiveness of the proposed adversarial contrastive constraints, we design ablation studies on the CIFAR10 dataset over three loss terms: $\mathcal { L } _ { c o s }$ . in Eq. 5, $\mathcal { L } _ { c o n }$ . in Eq. 3, and the task-specific loss $\mathcal { L } _ { t a s k }$ . Through the results in Tab. 4, we can find that deleting any one of them would hurt the performance. We also experiment with involving $\mathcal { L } _ { c o n }$ . for downstream training, to enforce the similarity among images composed of different hallucinators and a common basis. Observed from the last row of Tab. 4, the performance can be further improved, since $\mathcal { L } _ { c o n }$ . helps the representation learning of related samples [20]. Note that we do not use this loss term for downstream training in other experiments for fair and standard comparison.
+
+Table 3: Comparisons with concurrent work IDC [21] on efficient synthetic parameterization.
+
+ | Dataset | | SVHN | | | CIFAR10 | | | CIFAR100 | |
| IPC Ratio % | 1 0.014 | 10 0.14 | 50 0.7 | 1 0.02 | 10 | 50 | 1 | 10 | 50 |
| Random | | | | | 0.2 | 1 | 0.2 | 2 | 10 |
| Coreset | Herding | | 14.6±1.6 35.1±4.1 20.9±1.3 50.5±3.3 | 70.9±0.9 72.6±0.8 | 14.4±2.0 26.0±1.2 43.4±1.0 | | | 4.2±0.3 | 14.6±0.5 30.0±0.4 | |
| | | | 21.5±1.3 31.6±0.7 40.4±0.6 | | | 8.4±0.3 | 17.3±0.3 33.7±0.5 | |
| K-Center | | 21.0±1.5 14.0±1.3 20.1±1.4 | | 21.5±1.3 14.7±0.9 27.0±1.4 | | | 8.3±0.3 | 7.1±0.2 30.5±0.3 | |
| Forgetting | 12.1±1.7 | 16.8±1.2 | 227.2±1.5 | 13.5±1.2 | | 23.3±1.0 23.3±1.1 | 4.5±0.3 | 9.8±0.2 | |
| Distillation | DD+ [47] LD+ [3] | | | | | 36.8±1.2 | | | | |
| | | | 25.7±0.7 38.3±0.4 42.5±0.4 | | | 11.5±0.4 | | |
| DC [55] | | 31.2±1.4 76.1±0.6 82.3±0.3 | | 28.3±0.5 44.9±0.5 53.9±0.5 | | | 12.8±0.3 25.2±0.3 | | |
| DSA[53] | | 27.5±1.4 79.2±0.5 84.4±0.4 | | 28.8±0.7 52.1±0.5 60.6±0.5 | | | 13.9±0.3 | 32.3±0.3 42.8±0.4 | |
| DM [54] | | | | 26.0±0.8 48.9±0.6 63.0±0.4 | | | 11.4±0.3 | 29.7±0.3 43.6±0.4 | |
| CAFE[46] CAFE+DSA[46] | | 42.6±3.3 75.9±0.6 81.3±0.3 | | 30.3±1.1 46.3±0.6 55.5±0.6 | | | | 12.9±0.3 27.8±0.3 37.9±0.3 | |
| MTT[5] | 58.5±1.4 70.8±1.8 85.7±0.1 | 42.9±3.0 77.9±0.6 82.3±0.4 | | 31.6±0.8 50.9±0.5 62.3±0.4 46.3±0.8 65.3±0.7 71.6±0.2 | | | 14.0±0.3 31.5±0.2 24.3±0.3 | 39.0±0.1 | 42.9±0.2 46.1±0.2 |
| BPC | | | 49 | | 9 | | | | |
| Ratio % HaBa | 1 9 0.028 | | | 1 | | 49 | 1 | 9 | 49 |
| Factorization | 69.8±1.3 83.2±0.4 88.3±0.1 | 0.14 | 0.7 | 0.04 48.3±0.8 69.9±0.4 74.0±0.2 | 0.2 | 1 | 0.22 33.4±0.4 40.2±0.2 47.0±0.2 | 1.82 | 9.82 |
| Whole Dataset | | 95.4±0.1 | | | 84.8±0.1 | | | 56.2±0.3 | |
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+ "text": "Building upon Different Baselines: To reflect the versatility of the insight, we implement HaBa on multiple state-of-the-art training pipelines of DD, including DC, DM, and MTT. We evaluate the performance of synthetic datasets on CIFAR10 and maintain the IPC of baseline methods as BPC plus 1, which makes storage costs for synthetic datasets as close as possible for fairness. As shown in Tab. 2, when training and testing on ConvNet, the strategy of HaBa can make a consistent improvement over all the baselines, which demonstrates that factorization is a general idea to improve the data efficiency in DD. ",
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+ "text": "Cross-Architecture Performance: For DD, a satisfactory distilled dataset should have similar training effects to the original one on downstream models with arbitrary architectures. Thus, crossarchitecture generalization performance is an important metric for DD. We use the synthetic datasets trained on ConvNet to train models with different structures including ResNet [14], VGG [41], and AlexNet [23]. The results can be found in Tab. 2. Benefiting from the increased data diversity, HaBa can improve the across-architecture accuracy significantly with a performance gain up to $\\mathrm { \\bar { 1 } 7 . 5 7 \\% }$ . The consistent and significant improvement validates the superior ability of our method to capture the informative features and thus original datasets can be replaced by the synthetic ones better. ",
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+ "Table 2: Cross-architecture performance (test accuracy $\\%$ ) comparison to different baseline methods of DD HaBa built upon. "
+ ],
+ "table_body": " | |Method | DC [55] | DM [54] | MTT[5] |
| IPC BPC | 2 | 11 | 51 | 2 | 11 | 51 | 2 | 11 | 51 |
| Baseline | 1 |31.36±0.16 45.29±0.30 54.24±0.61 | 10 | 50 | 1 134.57±0.52 50.35±0.36 62.03±0.29|50.59±0.95 63.90±0.29 69.81±0.48 | 10 | 50 | 1 | 10 | 50 |
| ConvNet w.HaBa Gain Baseline | 34.11±0.47 49.88±0.52 58.91±0.23 +2.75 18.10±0.7618.36±0.3622.14±0.38| | +4.59 | +4.67 | +2.75 | 37.32±0.13 56.83±0.11 64.44±0.40 +6.48 3|22.25±1.00 40.00±1.49 53.40±0.68|35.15±0.96 45.05±1.46 54.47±0.95 | +2.41 | +6.17 | 56.76±0.38 69.48±0.26 73.25±0.21 +5.58 | +3.44 |
| ResNet | w.HaBa Gain Baseline | 24.49±0.55 24.27±0.56 31.08±0.32 +6.39 28.02±0.26 35.88±0.67 38.73±0.482 | +6.11 | +8.94 | +9.09 | 31.34±0.7247.57±0.4959.61±0.35 +7.57 | +6.21 | +12.24 322.28±1.0341.64±0.64 55.17±0.54|38.04±1.19 50.49±1.02 61.36±0.30 | 47.39±0.7157.97±0.8864.35±0.60 +12.92 | +9.88 |
| VGG | w.HaBa Gain | 29.42±0.93 37.03±0.42 41.91±0.55 +1.40 | +1.15 | +3.18 | 26.93±0.62 49.41±0.36 67.47±0.43 +4.65 | +7.77 | +12.30 | +10.22 | 48.26±0.54 60.47±0.56 67.47±0.43 +9.98 | +6.11 |
| AlexNet | w. HaBa Gain | Baseline|20.02±1.312.42±1.3529.48±0.8720.67±3.6437.04±0.9249.14±0.94|26.06±1.0135.95±1.5249.20±1.27 22.24±1.14 33.02±0.91 33.42±1.39 +2.22 | +10.60 | +3.94 | +11.47 | 32.14±0.60 44.14±0.67 53.09±0.89 +7.10 | +3.95 | 43.63±1.46 48.96±3.00 60.07±1.37 +17.57 | +13.01 | +10.87 |
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+ "text": "Comparisons under the Same Number of Final Images: In the default comparison protocol, we compare our method with the baselines using the same budget of storage, where our method can store information of exponentially more images than the baselines with the same number of parameters. In this part, we also examine the performance of HaBa under the condition that the number of final images, i.e., $| { \\mathcal { H } } | \\times | B |$ , is equal to that used by the baseline. Intuitively, given that the objective functions of our method and the baseline are the same exactly, the performance of the baseline can be viewed as an upper bound of ours, since there are significantly less parameters in our method to carry the information of final images in this case. Therefore, we first remove the term $\\mathcal { L } _ { c o s }$ . from the loss function of DD in Eq. 6 to guarantee a consistent optimization objective with the baseline. Then, we compare the performance of HaBa and the baseline using 10, 20, 30, 40, and 50 final images respectively. Here, the number of hallucinators $| \\mathcal { H } |$ is 2 and the number of bases is thus half of the number of final images. As shown in the red and green curves in Fig. 7, performance of the baseline can be well approximated by ours with only half of the number of parameters, especially when the number of images is relatively large. Remarkably, with the proposed adversary contrastive constraint, our method can even outperform the baseline consistently, as shown in the blue curve, which further demonstrates the effectiveness of the proposed solution. ",
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+ "text": "Applications in Continual Learning: To further demonstrate the advantage of the proposed method for improving data efficiency, following the setting of DM [54], we conduct experiments on the setting of continual learning on CIFAR-100, with 20 random classes per stage. The average number of parameters per class is $2 0 \\times 3 2 \\times 3 2 \\times 3$ . The synthetic datasets are trained with a ConvNet with 3 blocks. We evaluate synthetic datasets by our method and the DM baseline on the same ConvNet architecture and ResNet18. The results in Fig. 5 demonstrate that the proposed method increases the informativeness of synthetic datasets and thus produce significantly better performance, especially in the cross-architecture setting. ",
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+ "text": "4.3 Ablation Studies ",
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+ "text": "Loss Terms: To validate the effectiveness of the proposed adversarial contrastive constraints, we design ablation studies on the CIFAR10 dataset over three loss terms: $\\mathcal { L } _ { c o s }$ . in Eq. 5, $\\mathcal { L } _ { c o n }$ . in Eq. 3, and the task-specific loss $\\mathcal { L } _ { t a s k }$ . Through the results in Tab. 4, we can find that deleting any one of them would hurt the performance. We also experiment with involving $\\mathcal { L } _ { c o n }$ . for downstream training, to enforce the similarity among images composed of different hallucinators and a common basis. Observed from the last row of Tab. 4, the performance can be further improved, since $\\mathcal { L } _ { c o n }$ . helps the representation learning of related samples [20]. Note that we do not use this loss term for downstream training in other experiments for fair and standard comparison. ",
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+ "Table 3: Comparisons with concurrent work IDC [21] on efficient synthetic parameterization. "
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+ "table_body": " | Dataset | | SVHN | | | CIFAR10 | | | CIFAR100 | |
| IPC Ratio % | 1 0.014 | 10 0.14 | 50 0.7 | 1 0.02 | 10 | 50 | 1 | 10 | 50 |
| Random | | | | | 0.2 | 1 | 0.2 | 2 | 10 |
| Coreset | Herding | | 14.6±1.6 35.1±4.1 20.9±1.3 50.5±3.3 | 70.9±0.9 72.6±0.8 | 14.4±2.0 26.0±1.2 43.4±1.0 | | | 4.2±0.3 | 14.6±0.5 30.0±0.4 | |
| | | | 21.5±1.3 31.6±0.7 40.4±0.6 | | | 8.4±0.3 | 17.3±0.3 33.7±0.5 | |
| K-Center | | 21.0±1.5 14.0±1.3 20.1±1.4 | | 21.5±1.3 14.7±0.9 27.0±1.4 | | | 8.3±0.3 | 7.1±0.2 30.5±0.3 | |
| Forgetting | 12.1±1.7 | 16.8±1.2 | 227.2±1.5 | 13.5±1.2 | | 23.3±1.0 23.3±1.1 | 4.5±0.3 | 9.8±0.2 | |
| Distillation | DD+ [47] LD+ [3] | | | | | 36.8±1.2 | | | | |
| | | | 25.7±0.7 38.3±0.4 42.5±0.4 | | | 11.5±0.4 | | |
| DC [55] | | 31.2±1.4 76.1±0.6 82.3±0.3 | | 28.3±0.5 44.9±0.5 53.9±0.5 | | | 12.8±0.3 25.2±0.3 | | |
| DSA[53] | | 27.5±1.4 79.2±0.5 84.4±0.4 | | 28.8±0.7 52.1±0.5 60.6±0.5 | | | 13.9±0.3 | 32.3±0.3 42.8±0.4 | |
| DM [54] | | | | 26.0±0.8 48.9±0.6 63.0±0.4 | | | 11.4±0.3 | 29.7±0.3 43.6±0.4 | |
| CAFE[46] CAFE+DSA[46] | | 42.6±3.3 75.9±0.6 81.3±0.3 | | 30.3±1.1 46.3±0.6 55.5±0.6 | | | | 12.9±0.3 27.8±0.3 37.9±0.3 | |
| MTT[5] | 58.5±1.4 70.8±1.8 85.7±0.1 | 42.9±3.0 77.9±0.6 82.3±0.4 | | 31.6±0.8 50.9±0.5 62.3±0.4 46.3±0.8 65.3±0.7 71.6±0.2 | | | 14.0±0.3 31.5±0.2 24.3±0.3 | 39.0±0.1 | 42.9±0.2 46.1±0.2 |
| BPC | | | 49 | | 9 | | | | |
| Ratio % HaBa | 1 9 0.028 | | | 1 | | 49 | 1 | 9 | 49 |
| Factorization | 69.8±1.3 83.2±0.4 88.3±0.1 | 0.14 | 0.7 | 0.04 48.3±0.8 69.9±0.4 74.0±0.2 | 0.2 | 1 | 0.22 33.4±0.4 40.2±0.2 47.0±0.2 | 1.82 | 9.82 |
| Whole Dataset | | 95.4±0.1 | | | 84.8±0.1 | | | 56.2±0.3 | |
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| IPC BPC | 2 | 11 | 51 | 2 | 11 | 51 | 2 | 11 | 51 |
| Baseline | 1 |31.36±0.16 45.29±0.30 54.24±0.61 | 10 | 50 | 1 134.57±0.52 50.35±0.36 62.03±0.29|50.59±0.95 63.90±0.29 69.81±0.48 | 10 | 50 | 1 | 10 | 50 |
| ConvNet w.HaBa Gain Baseline | 34.11±0.47 49.88±0.52 58.91±0.23 +2.75 18.10±0.7618.36±0.3622.14±0.38| | +4.59 | +4.67 | +2.75 | 37.32±0.13 56.83±0.11 64.44±0.40 +6.48 3|22.25±1.00 40.00±1.49 53.40±0.68|35.15±0.96 45.05±1.46 54.47±0.95 | +2.41 | +6.17 | 56.76±0.38 69.48±0.26 73.25±0.21 +5.58 | +3.44 |
| ResNet | w.HaBa Gain Baseline | 24.49±0.55 24.27±0.56 31.08±0.32 +6.39 28.02±0.26 35.88±0.67 38.73±0.482 | +6.11 | +8.94 | +9.09 | 31.34±0.7247.57±0.4959.61±0.35 +7.57 | +6.21 | +12.24 322.28±1.0341.64±0.64 55.17±0.54|38.04±1.19 50.49±1.02 61.36±0.30 | 47.39±0.7157.97±0.8864.35±0.60 +12.92 | +9.88 |
| VGG | w.HaBa Gain | 29.42±0.93 37.03±0.42 41.91±0.55 +1.40 | +1.15 | +3.18 | 26.93±0.62 49.41±0.36 67.47±0.43 +4.65 | +7.77 | +12.30 | +10.22 | 48.26±0.54 60.47±0.56 67.47±0.43 +9.98 | +6.11 |
| AlexNet | w. HaBa Gain | Baseline|20.02±1.312.42±1.3529.48±0.8720.67±3.6437.04±0.9249.14±0.94|26.06±1.0135.95±1.5249.20±1.27 22.24±1.14 33.02±0.91 33.42±1.39 +2.22 | +10.60 | +3.94 | +11.47 | 32.14±0.60 44.14±0.67 53.09±0.89 +7.10 | +3.95 | 43.63±1.46 48.96±3.00 60.07±1.37 +17.57 | +13.01 | +10.87 |
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