\n
{tabu}\n
@l @\u00a0\u00a0c @\u00a0\u00a0c @\u00a0\u00a0c @\u00a0\u00a0\u00a0|@\u00a0\u00a0\u00a0c @\u00a0\u00a0c @\u00a0\u00a0c\n& KD on the VOC Dataset
\n
EPG Teacher shi IoU Teachers
\n
EPG IoU F1 EPG IoU F1 \n
\n
Teacher 75.7 21.3 72.5 65.0 49.7 72.8 \n
Baseline 50.0 29.0 58.0 50.0 29.0 58.0 \n
KD 60.1 31.6 60.1 58.9 35.7 62.7 \n
+ e2KD 71.1 24.8 67.6 60.3 45.7 64.8\n\n\n\n{tabu}\n@l@\u00a0\u00a0c@\u00a0\u00a0c@\u00a0\u00a0\u00a0\u00a0|@\u00a0\u00a0\u00a0\u00a0c@\u00a0\u00a0c\n KD on Unrelated Images\nIMNSUN SUNIMN \n
\n Acc. Agr. Acc. Agr.\n
\n 60.5 - 75.2 -\n
57.7 67.9 68.7 75.5\n
53.5 65.0 14.9 16.7\n
54.9 67.7 19.8 22.1\n\n\n\nResults.\nAs we show in Sec.\u00a04.3.1 ###reference_.SSS1###, the explanations of an e2KD student indeed more closely mirror those of the teacher than a student trained via vanilla KD:\ne2KD students exhibit significantly higher EPG when distilled from the EPG teacher (EPG: 71.1 vs.\u00a060.3) and vice versa (IoU: 45.7 vs.\u00a024.8). In contrast, \u2018vanilla\u2019 KD students show only minor differences (EPG: 60.1 vs.\u00a058.9; IoU: 35.7 vs.\u00a031.6). These improvements also show qualitatively (Fig.\u00a03 ###reference_###), with the e2KD students reflecting the teacher\u2019s focus much more faithfully in their explanations.\n\nWhile this might be expected as e2KD explicitly optimizes for explanation similarity, we would like to highlight that this not only ensures that the desired properties of the teachers are better represented in the student model, but also significantly improves the students\u2019 performance (e.g., F1: 60.167.6 for the EPG teacher). As such, we find e2KD to be an easy-to-use and effective addition to vanilla KD for improving both interpretability as well as task performance.\n\n\nFigure 3: Maintaining focused explanations. We visualize B-cos explanations, when distilling a B-cos ResNet-50 teacher that has been trained to not focus on confounding input features (col.\u00a02), to a B-cos ResNet-18 student with KD (col.\u00a03) and e2KD (col.\u00a04).\nExplanations of\ne2KD students are significantly closer to the teacher\u2019s (and hence more human-aligned). Samples are drawn from the VOC test set, with all models correctly classifying the shown samples. For more qualitative results, see Sec.\u00a0A.2 ###reference_.SS2###.\n\n\n\n\n4.3.2 Distill to ViT.
\n\nWe assess if inductive biases of CNN can be distilled to ViT.\nSetup. To test whether students learn architectural priors of the models, we evaluate whether a B-cos ViT student can learn to give explanations that are similar to those of a pretrained CNN (B-cos DenseNet-169) teacher model;\nfor this, we again use the ImageNet dataset.\n\n\n\nFigure 4: Distilling inductive biases (CNNViT). We distill a B-cos DenseNet-169 teacher to a B-cos ViT. Top-Left: e2KD yields significant gains in accuracy and agreement. Bottom-Left: Cosine similarity of explanations for shifted images w.r.t.\u00a0the unshifted image (=0). With e2KD (blue) the ViT student learns to mimic the shift periodicity of the teacher (purple), despite the inherent periodicity of 16 of the ViT architecture (seen for vanilla KD, yellow). Notably, e2KD with frozen explanations yields shift-equivariant students (red), see also Sec.\u00a04.3.2 ###reference_.SSS2### \u2018Distill to ViT\u2019. Right: e2KD significantly improves the explanations of the ViT model, thus maintaining the utility of the explanations of the CNN teacher model. While the explanations for KD change significantly under shift (subcol.\u00a03), for e2KD (subcol.\u00a04), as with the CNN teacher (subcol.\u00a02), the explanations remain consistent. See also Sec.\u00a0A.3 ###reference_.SS3###.\n\n\n\nResults.\nIn line with the results of the preceding sections, we find (Fig.\u00a04 ###reference_###, left) that e2KD significantly improves the accuracy of the ViT student model (64.866.3), as well as the agreement with the teacher (70.171.8).\n\n\nInterestingly, we find that the ViT student\u2019s explanations seem to become similarly robust to image shifts as those of the teacher (Fig.\u00a04 ###reference_###, bottom-left and right.). Specifically, note that the image tokenization of the ViT model using vanilla KD (extracting non-overlapping patches of size 1616) induces a periodicity of 16 with respect to image shifts , see, e.g., Fig.\u00a04 ###reference_### (bottom-left, yellow curve): here, we plot the cosine similarity of the explanations at various shifts with respect to the explanation given for the original, unshifted image (=0). In contrast, due to smaller strides (stride for any layer) and overlapping convolutional kernels, the CNN teacher model is inherently more robust to image shifts, see Fig.\u00a04 ###reference_### (purple curve), exhibiting a periodicity of 4.\nA ViT student trained via e2KD learns to mimic the behaviour of the teacher (see Fig.\u00a04 ###reference_###, blue curve) and exhibits the same periodicity, indicating that e2KD indeed helps the student learn a function more similar to the teacher.\n\n\nIn Fig.\u00a04 ###reference_### (right), we see that e2KD also significantly improves the explanations of the ViT model. We show explanations for original and 8-pixel diagonally shifted () images. Our ViT\u2019s explanations are more robust to shifts and more interpretable, thus maintaining the utility of the explanations of the teacher.\n\n\n\n\n4.4 e2KD with Frozen Explanations
\n\nIn the previous sections, we showed that e2KD is a robust approach that provides consistent gains even when only limited data is available (see Sec.\u00a04.1 ###reference_###) and works across different architectures (e.g., DenseNetResNet or DenseNetViT, see Secs.\u00a04.1 ###reference_### and\u00a04.3.2 ###reference_.SSS2### \u2018Distill to ViT\u2019).\nIn the following, we show that e2KD even works when only \u2018approximate\u2019 explanations for the teacher are available (cf. Sec.\u00a03.3 ###reference_###).\n\n\nSetup.\nTo test the robustness of e2KD when using frozen explanations, we distill from a B-cos DenseNet-169 teacher to a B-cos ResNet-18 student using pre-computed, frozen explanations on the ImageNet dataset. We also evaluate across varying dataset sizes, as in Sec.\u00a04.1 ###reference_###.\n\n\nResults.\nTab.\u00a03 ###reference_### (bottom) shows\nthat e2KD with frozen explanations is effective for improving both the accuracy and agreement over KD with frozen logits across dataset sizes (e.g. accuracy: 33.438.7 for 50 shots). Furthermore, e2KD with frozen explanations also outperforms vanilla KD under both metrics when using limited data (e.g. accuracy: 37.338.7 for 50 shots). As such, a frozen teacher constitutes a more cost-effective alternative for obtaining the benefits of e2KD, whilst also highlighting its robustness to using \u2018approximate\u2019 explanations.\n\n\nOur results also indicate that it might be possible to instill desired properties into a DNN model even beyond knowledge distillation. Note that the frozen explanations are by design equivariant explanations across shifts and crops. Based on our observations for the ViTs (cf. Sec.\u00a04.3.2 ###reference_.SSS2###), we thus expect a student trained on frozen explanations to become almost fully shift-equivariant, which is indeed the case for our ViT students (see Fig.\u00a04 ###reference_###, bottom-left, red curve, ViT \u2744 e2KD).\n\n\n\n\n5 Conclusion
\n\nWe proposed a simple approach to promote the faithfulness of knowledge distillation (KD) by explicitly optimizing for the explanation similarity between the teacher and the student, and showed its effectiveness in distilling the teacher\u2019s properties under multiple settings. Specifically, e2KD helps the student (1) achieve competitive and often higher accuracy and agreement than vanilla KD, (2) learn to be \u2018right for the right reasons\u2019, and (3) learn to give similar explanations as the teacher, e.g. even when distilling from a CNN teacher to a ViT student. Finally, we showed that e2KD is robust in the presence of limited data, approximate explanations, and across model architectures. In short, we find e2KD to be a simple but versatile addition to KD that allows for a more faithful distillation of the teacher, whilst also maintaining competitive task performance.\n\n\n\n\nReferences
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\n
\n\n\nskip\nGood Teachers Explain: Explanation-Enhanced Knowledge Distillation\n
\nAppendix\n\nIn this supplement to our work on explanation-enhanced knowledge distillation (e2KD), we provide:\n\n
\n{adjustwidth}\n0.15cm0.15cm\n\n(A ###reference_###)\n\nAdditional Qualitative Results A ###reference_###\n\n{adjustwidth}0cm0cm\nIn this section, we provide additional qualitative results for each evaluation setting.\nSpecifically, we show qualitative results of the model explanations of standard models (GradCAM) and B-cos models (B-cos explanations) for KD and e2KD for the following:\n\n\u00a0\n
\n(A.1 ###reference_.SS1###)\n\u00a0\u00a0 Learning the \u2018right\u2019 features (Waterbirds-100). \n
\n(A.2 ###reference_.SS2###)\n\u00a0\u00a0 Maintaining focused explanations (PASCAL VOC). \n
\n(A.3 ###reference_.SS3###)\n\u00a0\u00a0 Distilling architectural priors (CNNViT on ImageNet). \n
\n\n(B ###reference_###)\n\nAdditional Quantitative Results B ###reference_###\n\n{adjustwidth}0cm0cm\nIn this section, we provide additional quantitative results:\n\n\u00a0\n
\n(B.1 ###reference_.SS1###)\n\u00a0\u00a0 Reproducing previously reported ImageNet results for prior work. \n
\n(B.2 ###reference_.SS2###)\n\u00a0\u00a0 In- and out-of-distribution results for B-cos models on Waterbirds.\n
\n(B.3 ###reference_.SS3###)\n\u00a0\u00a0 Detailed Comparison with respect to CAT-KD \n
\n\n(C ###reference_###)\n\nImplementation Details C ###reference_###\n\n{adjustwidth}0cm0cm\nIn this section, we provide implementation details, including the setup used in each experiment and the procedure followed to adapt prior work to B-cos models. Code will be made available on publication.\n\n\u00a0\n
\n(C.1 ###reference_.SS1###)\n\u00a0\u00a0 Training details. \n
\n(C.2 ###reference_.SS2###)\n\u00a0\u00a0 Adaptation of prior work to B-cos networks. \n
\n\n\n\n\n\nAppendix A Additional Qualitative Results
\n\n\nA.1 Learning the \u2018Right\u2019 Features
\n\nIn this section we provide qualitative results on the Waterbirds-100 dataset \\citeSwb100S,galsS. We show GradCAM explanations \\citeSgradcamS for standard models and B-cos explanations for B-cos models \\citeSbcosS,bcosv2S. In Fig.\u00a0A1 ###reference_.F1###, we show explanations for in-distribution (i.e. \u2018Landbird on Land\u2019 and \u2018Waterbird on Water\u2019) test samples, and in Fig.\u00a0A2 ###reference_.F2### we show them for out-of-distribution samples (i.e. \u2018Landbird on Water\u2019 and \u2018Waterbird on Land\u2019). Corresponding quantitative results can be found in Sec.\u00a0B.2 ###reference_.SS2###.\n\n\nFrom Fig.\u00a0A1 ###reference_.F1###, we observe that the explanations of the teacher and vanilla KD student may significantly differ (for both standard and B-cos models): while the teacher is focusing on the bird, the student may use spuriously correlated input-features (i.e. background). We observe that e2KD is successfully promoting explanation similarity and keeping the student \u2018right for right reasons\u2019.\nWhile in Fig.\u00a0A1 ###reference_.F1### (i.e. in-distribution data) all models correctly classify the samples despite the difference in their focus, in Fig.\u00a0A2 ###reference_.F2### (i.e. out-of-distribution) we observe that the student trained with e2KD is able to arrive at the correct prediction, whereas the vanilla KD student wrongly classifies the samples based on the background.\n\n\n\nFigure A1: In-distribution samples for distillation on biased data using the Waterbirds-100 dataset. We show explanations for both standard models (cols.\u00a02-4) and B-cos models (cols.\u00a05-7), given both in-distribution groups: \u2018Landbird on Land\u2019 (top half) and \u2018Waterbird on Water\u2019 (bottom half). We find that e2KD approach (col.\u00a04 and 7) is effective in preserving the teacher\u2019s focus (col.\u00a02 and 5) to the bird instead of the background as opposed to vanilla KD (col.\u00a03 and 6). Correct and incorrect predictions marked by \u2713 and \u2717 respectively.\n\n\n\n\nFigure A2: Out-of-distribution samples for distillation on biased data using the Waterbirds-100 dataset. We show explanations for standard (cols.\u00a02-4) and B-cos models (cols.\u00a05-7), for the out-of-distribution groups \u2018Landbird on Water\u2019 (top half) and \u2018Waterbird on Land\u2019 (bottom half). e2KD (col.\u00a04 and 7) is effective in preserving the teacher\u2019s focus (col.\u00a02 and 5), leading to higher robustness to distribution shifts than when training students via vanilla KD. Correct and incorrect predictions marked by \u2713 and \u2717 respectively.\n\n\n\n\n\nA.2 Maintaining Focused Explanations
\n\nIn this section we provide additional qualitative examples for experiments on PASCAL VOC (see Sec.\u00a04.3.1 ###reference_.SSS1###). We provide samples for all of the 20 classes in the PASCAL VOC dataset (every row in Figs.\u00a0A3 ###reference_.F3### and\u00a0A4 ###reference_.F4###). Across all classes we ovserve that the student trained with e2KD maintains focused explanations on the class-specific input-features, whereas the student trained with vanilla KD may often focus on the background.\n\n![\"Refer](\"x15.png\")
\nFigure A3: Maintaining focused explanations (classes 1-10): Similar to Fig.\u00a03 ###reference_### in the main paper, here we show qualitative difference of explanations. Each row shows two samples per class (for classes 11-20 see Fig.\u00a0A4 ###reference_.F4###). We find that explanations of the student trained with e2KD (subcol.\u00a04 on both sides) is significantly closer to the teacher\u2019s (subcol.\u00a02), whereas vanilla KD students also focus on the background (subcol.\u00a03). Samples were drawn from the test set with all models having correct predictions.\n\n![\"Refer](\"x16.png\")
\nFigure A4: Maintaining focused explanations (classes 11-20): Similar to Fig.\u00a03 ###reference_### in the main paper, here we show qualitative difference of explanations. Each row shows two samples per class (for classes 1-10 see Fig.\u00a0A3 ###reference_.F3###). We find that explanations of the student trained with e2KD (subcol.\u00a04 on both sides) is significantly closer to the teacher\u2019s (subcol.\u00a02), whereas vanilla KD students also focus on the background (subcol.\u00a03). Samples were drawn from test set with all models having correct predictions.\n\n\n\n\n\nA.3 Distilling Architectural Priors
\n\nWe provide additional qualitative samples for Sec.\u00a04.3.2 ###reference_.SSS2### in the main paper, where we distill a B-cos CNN to a B-cos ViT. Looking at Fig.\u00a0A5 ###reference_.F5###, one can immediately observe the difference in interpretability of the B-cos ViT explanations when trained with e2KD vs.\u00a0vanilla KD. Following the discussion in Fig.\u00a04 ###reference_###, one can see that the ViT trained with e2KD, similar to its CNN Teacher, gives consistent explanations under shift, despite its inherent tokenization, whereas the explanations from vanilla KD significantly differ (compare odd rows to the one below).\n\n![\"Refer](\"x17.png\")
\nFigure A5: Qualitative results on distilling B-cos DenseNet-169 to B-cos ViT. The explanations of the e2KD ViT student (subcols.\u00a04) are significantly more interpretable than vanilla KD student (subcols.\u00a03), and very close to the teacher\u2019s explanations (subcols.\u00a02). We also shift images diagonally to the bottom right by 8 pixels and show the explanations for the same class (rows indicated by ).\nThe explanations of the ViT student trained with e2KD are shift-equivariant, whereas the ViT student from vanilla KD is sensitive to such shifts and the explanations change significantly.\n\n\n\n\n\n\nAppendix B Additional Quantitative Results
\n\n\nB.1 Reproducing previously reported results for prior work.
\n\nSince we use prior work on new settings, namely ImageNet with limited data, Waterbirds-100, and B-cos models, we reproduce the performance reported in the original works in the following. In particular, in Tab.\u00a0B1 ###reference_.T1###, we report the results obtained by the training \u2018recipes\u2019 from by prior work to validate our implementation and enable better comparability with previously reported results.\n\n\nFor this section, we distilled the standard ResNet-34 teacher to a ResNet-18 on ImageNet for 100 epochs, with an initial learning rate of 0.1, decayed by 10% every 30 epochs. We used SGD with momentum of 0.9 and a weight-decay factor of 1e-4. For AT, ReviewKD, and CRD, we followed the respective original works and employed weighting coefficients of respectively. For CAT-KD, we used after identifying this as a reasonable range in preliminary experiments. Here we also, similar to Sec.\u00a0C.1 ###reference_.SS1###, used a held-out validation set from the training samples.\n\n\nFollowing \\citeSkdS, we also report the results for KD in which the cross-entropy loss with respect to the ground truth labels is used in the loss function. We were able to reproduce the reported numbers by a close margin. Our numbers are also comparable to the torchdistill\u2019s reproduced numbers \\citeStorchdistillS, see Tab.\u00a0B1 ###reference_.T1###. We see that e2KD again improves both accuracy and agreement of vanilla KD (agreement 80.280.5). Similar gains are also observed for CRD (agreement 78.479.2). Also note that the vanilla KD baseline significantly improves once we used the longer training recipe from \\citeSconsistencyS in Tab.\u00a01 ###reference_### in the main paper (accuracy 70.671.8; agreement 80.281.2).\n\n\nTable B1: Distilling Standard ResNet-34 to ResNet-18 for reproducing prior work. We verify our implementation of prior work by distilling them in the 100 epoch setting used in \\citeSattentionS,reviewkdS,catkdS,tian2019crdS. We observe that our accuracy is very close to the reported one and the reproduced numbers by torchdistill \\citeStorchdistillS. We also see that e2KD, similar to Tab.\u00a01 ###reference_###, improves accuracy and agreement of vanilla KD and CRD.\n\n\n\n\nStandard Models\nTeacher ResNet-34\nAccuracy 73.3%\n\n\n\nAccuracy\n\n\n\nAgreement\n\n\n\nReported\nAccuracy\n\n\n\ntorchdistillp\nAccuracy\n\n\nKD \\citeSkdS (with cross-entropy)\n71.0\n79.7\n70.7\n71.4\n\nAT \\citeSattentionS\n70.2\n78.3\n70.7\n70.9\n\nReviewKD \\citeSreviewkdS\n71.6\n80.1\n71.6\n71.6\n\nCAT-KD \\citeScatkdS\n71.0\n80.1\n71.3\n-\n\nKD\n70.6\n80.2\n-\n-\n\n+ e2KD (GradCAM)\n70.7\n80.5\n-\n-\n\n\n+ 0.1 \n+ 0.3 \n\n\n\nCRD \\citeStian2019crdS\n70.6\n78.4\n71.2\n70.9\n\n+ e2KD (GradCAM)\n71.0\n79.2\n-\n-\n\n\n+ 0.4 \n+ 0.8 \n\n\n\n\n\n\n\n\nB.2 Full results on Waterbirds\u00a0\u2014 B-cos models
\n\nIn this section we provide complete quantitative results on Waterbirds-100 \\citeSwb100S,galsS for B-cos models. In Fig.\u00a0B1 ###reference_.F1###, we report in-distribution and out-of-distribution accuracy and agreement. Similar to what was observed for standard models in Fig.\u00a01 ###reference_### of the main paper, here we again observe that all models are performing well on in-distribution data (lowest test-accuracy is 94.9% for B-cos models). Nevertheless, e2KD (with B-cos explanations) is again consistently providing gains over vanilla KD. More importantly however, for the out-of-distribution samples, we observe that e2KD offers even larger accuracy and agreement gains over vanilla KD for both B-cos (Fig.\u00a0B1 ###reference_.F1###) and standard (Fig.\u00a01 ###reference_###, main paper) models.\nCorresponding qualitative results, for the 700 epoch experiments, can be found in Fig.\u00a0A1 ###reference_.F1###, for in-distribution, and Fig.\u00a0A2 ###reference_.F2### for out-of-distribution samples.\n\n\n\nFigure B1: \nResults for B-cos models on Waterbirds-100. We show accuracy and agreement on both in-distribution (top) and out-of-distribution (bottom) test samples when distilling from B-cos ResNet-50 teachers to B-cos ResNet-18 students with various KD approaches. As for out-of-distribution data, we find significant and consistent gains in accuracy and agreement (similar to Fig.\u00a01 ###reference_### for standard models).\n\n\n\n\n\n\nB.3 Detailed Comparison with respect to CAT-KD
\n\nAs mentioned in Sec.\u00a02 ###reference_### in the main paper, works such as CAT-KD\u00a0\\citeScatkdS have explored using an explanation method (e.g. Class Activation Maps (CAM)\u00a0\\citeScamS) in the context of knowledge distillation, though without having faithfulness of the distillation as the primary focus. This has resulted in design choices such as down-sampling the explanations to . On the contrary, e2KD is designed towards promoting faithful distillation, by simply matching the explanations. While in this work we explored the benefits of e2KD under both GradCAM\u00a0\\citeSgradcamS explanations for standard models and B-cos\u00a0\\citeSbcosS explanations for B-cos models\u00a0\\citeSbcosS,bcosv2S, since GradCAM and CAM are very similar explanation methods, yet in Tab.\u00a01 ###reference_### e2KD significantly outperforms CAT-KD, in this section we ablate over all of our differences with respect to CAT-KD.\n\n\nSpecifically, we evaluate the impact of design choices over the limited-data setting for ImageNet dataset (similar to 50- and 200-Shot columns in Tab.\u00a01 ###reference_### in the main paper). In Tab.\u00a0B2 ###reference_.T2### we ablate over resolution of explanation maps (whether to have down-sampling operation from \\citeScatkdS), choice of explanation method (CAM vs. GradCAM), and other differences such as taking explanations for all or only teacher\u2019s prediction and using cross-entropy w.r.t. labels instead of Eq.\u00a01 ###reference_###. Here we use a coefficient of 10 for the explanation loss. As per the implementation of CAT-KD\u00a0\\citeScatkdS, the CAM explanations between teacher student are normalized and regularized to be similar with Mean Squared Error loss. This is equivalent to cosine similarity that we use in e2KD, except for a constant factor, with being the resolution of explanation maps, that is applied to the gradient from the explanation loss in CAT-KD. Therefore, we also re-scale the loss coefficient after changing the resolution of the maps (3rd row in Tab.\u00a0B2 ###reference_.T2###).\n\n\nIn Tab.\u00a0B2 ###reference_.T2###, we observe that not reducing the resolution of CAMs to , results in consistent (accuracy | agreement) gains in both 50-Shot (32.235.0 | 34.537.3) and 200-Shot (55.757.4 | 60.763.0) cases on ImageNet. As one would expect, both CAM and GradCAM explanations result in similar numbers, since they are essentially the same explanation, up to a ReLU operation in GradCAM.\n\n\nTable B2: Ablation with respect to CAT-KD. Here we disentangle the differences between e2KD and CAT-KD, with every row bringing it closer to e2KD\u2019s setting. We distill a standard ResNet-34 to standard ResNet-18 on a subset of ImageNet and evaluate on the complete test set.\n\n\n\n\nStandard Models\nTeacher ResNet-34:\nAccuracy 73.3%\n50 Shotsssss\n200 Shot s\n\nCAT-KD\n32.2\n34.5\n55.7\n60.7\n\n+ Remove down-sampling (use maps)\n24.4\n25.9\n46.1\n49.5\n\n+ Re-scale the explanation loss coefficient ()\n35.0\n37.3\n57.4\n63.0\n\n+ Replace CE with KL-Div., use Top-1 Explanation\n53.1\n59.3\n63.7\n72.6\n\n+ Replace CAM with GradCAM\n52.9\n59.2\n64.1\n73.2\n\n\n\n\n\n\nAppendix C Implementation Details
\n\nIn this section, we provide additional implementation details. In Sec.\u00a0C.1 ###reference_.SS1###, we provide a detailed description of our training setup, including hyperparameters used in each setting. In Sec.\u00a0C.2 ###reference_.SS2###, we describe how we adapt prior approaches that were proposed for conventional deep neural networks to B-cos models. Code for all the experiments will be made available.\n\n\n\nC.1 Training Details
\n\nIn this section, we first provide the general setup which, unless specified otherwise, is shared across all of our experiments. Afterwards, we describe dataset-specific details in Secs.\u00a0C.1.1 ###reference_.SS1.SSS1###, C.1.2 ###reference_.SS1.SSS2### and\u00a0C.1.3 ###reference_.SS1.SSS3###, for each dataset and experiment.\n\n\nStandard Networks.\nAs mentioned in Sec.\u00a04 ###reference_### in the main paper, we follow the recipe from \\citeSconsistencyS. For standard models, we use the AdamW optimizer \\citeSkingma2014adamS with a weight-decay factor of and a cosine-annealing learning-rate scheduler \\citeSloshchilov2017sgdrS with an initial learning-rate of 0.01, reached with an initial warmup for 5 epochs. We clip gradients by norm at 1.0.\n\n\nB-cos Networks. We use the latest implementations for B-cos models\u00a0\\citeSbcosv2S. Following \\citeSbcosS, bcosv2S, we use the Adam optimizer \\citeSkingma2014adamS and do not apply weight-decay. We use a cosine-annealing learning-rate scheduler \\citeSloshchilov2017sgdrS with an initial learning-rate of , reached with an initial warmup for 5 epochs. Following \\citeSbcosv2S, we clip gradients using adaptive gradient clipping (AGC) \\citeSagc-pmlr-v139-brock21aS. Unless specified otherwise, across all models and datasets we use random crops and random horizontal flips as data augmentation during training, and at test time we resize the images to 256 (along the smaller dimension) and apply center crop of (224, 224). We use PyTorch \\citeSpaszke2019pytorchS and PyTorch Lightning \\citeSFalcon_PyTorch_Lightning_2019S for all of our implementations.\n\n\n\nC.1.1 ImageNet Experiments.
\n\nFor experiments on the full ImageNet dataset\u00a0\\citeSimagenetS, we use a batch size of 256 and train for 200 epochs. For limited-data experiments we keep the number of steps same across both settings (roughly 40% total steps compared to full-data): when using 50 shots per class, we set the batch size to 32 and train for 250 epochs, and when having 200 shots, we use a batch size of 64 and train for 125 epochs. We use the same randomly selected shots for all limited-data experiments. For experiments on unrelated data (Sec.\u00a04.3.1 ###reference_.SSS1### (right) in the main paper), following \\citeSconsistencyS, we used equal number of training steps for both SUNIMN (125 epochs with a batch size of 128) and IMNSUN (21 epochs with a batch size of 256).\n\n\nFor the pre-trained teachers, we use the Torchvision checkpoints \\citeStorchvision2016S for standard models and available checkpoints for B-cos models \\citeSbcosv2S. For all ImageNet experiments, we pick the best checkpoint and loss coefficients based on a held-out subset of the standard train set, which has 50 random samples per class. The results are then reported on the entire official validation set. We use the following parameters for each method:\n
\n\n\nsomething\n\n\nStandard Networks (Tab.\u00a01 ###reference_###)\n\nKD\n\n\ne2KD\n, \n\nAT\n\n\nReviewKD\n\n\nCAT-KD\n\n\nCRD\n\n\ne2KD\n, \n\nsomething\n\n\nB-cos ResNet-34 Teacher (Tab.\u00a02 ###reference_###)\n\nKD\n\n\ne2KD\n, \n\nAT\n\n\nReviewKD\n\n\nCAT-KD\n\n\n
\n\n\n\n\n\nB-cos DenseNet-169 Teacher\n\n(Tab.\u00a03 ###reference_###)\n\n\nKD\n\n\ne2KD\n, \n\n\u2744 KD\n\n\n\u2744 e2KD\n, \n\n\n\n\n\nUnrelated Data (Sec.\u00a04.3.1 ###reference_.SSS1###, Right)\n\nB-cos DenseNet-169 Teacher\n\nKD\n\n\ne2KD\n, \n\n\n\n\nFor ViT students we trained for 150 epochs, and following \\citeSbcosv2S, we used 10k warmup steps, and additionally used RandAugment\\citeSNEURIPS2020_d85b63efS with magnitude of 10.\n\n\n\n\nB-cos DenseNet-169 to ViT Student (Fig.\u00a04 ###reference_###)\n\nKD\n\n\ne2KD\n, \n\n\n\n\n\n\n\nC.1.2 Waterbirds Experiments.
\n\nFor the Waterbirds \\citeSwb100S experiments, we use the 100% correlated data generated by \\citeSgalsS (i.e. Waterbirds-100). We use the provided train, validation and test splits. Since the data is imbalanced (number of samples per class significantly differ), within each sweep we pick the last-epoch checkpoint with best overall validation accuracy (including both in-distribution and out-of-distribution samples). We use batch size of 64. For experiments with MixUp, we use =1. For applying AT and ReviewKD between the ResNet-50 teacher and ResNet-18 student, we used the same configuration from a ResNet-34 teacher, since they have the same number of blocks.\n\n\nThe pre-trained guided teachers were obtained from \\citeSmodelguidanceS. The standard ResNet-50 teacher had 99.0% and 61.2% in-distribution and out-of-distribution accuracy, and the B-cos ResNet-50 teacher had 98.8% and 55.1% respectively.\n\n\nWe tested the following parameters for each method:\n\n\n\n\n\nStandard models (Fig.\u00a01 ###reference_###)\n\nKD\n\n\ne2KD\n, \n\nAT\n\n\nReviewKD\n\n\nCAT-KD\n\n\n\n\nB-cos models (Sec.\u00a0B.2 ###reference_.SS2### )\n\nKD\n\n\ne2KD\n, \n\nAT\n\n\nReviewKD\n\n\nCAT-KD\n\n\n\n\n\nFor the results in Tab.\u00a04 ###reference_### in the main paper, we trained ConvNeXt\u00a0\\citeSliu2022convnetS, EfficientNetV2\u00a0\\citeSpmlr-v97-tan19aS, MobileNetV2\u00a0\\citeSSandler_2018_CVPRS, and ShuffleNetV2\u00d70.5\u00a0\\citeSMa_2018_ECCVS under the 700-Epoch recipe.\n\n\n\n\nC.1.3 PASCAL VOC Experiments.
\n\nWe use the 2012 release of PASCAL VOC dataset \\citeSpascal-voc-2012S. We randomly select 10% of the train samples as validation set and report results on the official test set. We use batch size of 64 and train for 150 epochs. The pre-trained guided teachers were obtained from \\citeSmodelguidanceS. Since we are using VOC as a multi-label classification setting, we replace the logit loss from Eq.\u00a01 ###reference_### in the main paper with the logit loss recently introduced by \\citeSyang2023multiS:\n\n\n\n\n\n(C.1)\n\nHere, is the sigmoid function and concatenates values into a vector. Note that the original loss from \\citeSyang2023multiS does not have a temperature parameter (i.e. ). For consistency with other experiments, here we also included a temperature factor.\nWhen reporting the final results on the test set, we resize images to (224, 224) and do not apply center crop.\nFor the EPG and IoU metrics, we use the implementation from \\citeSmodelguidanceS. For the IoU metric, we use threshold of 0.05. We tested the following parameters for each method:\n\n\n\n\nB-cos models (Sec.\u00a04.3.1 ###reference_.SSS1###, Left)\n\nKD\n,\n\ne2KD\n, \n\n\n\n\n\n\nC.2 Adapting Prior Feature-based Methods for B-cos Models
\n\nWhile prior feature-based KD methods have been mainly introduced for conventional networks, in Tab.\u00a02 ###reference_### we additionally tested them on B-cos networks. We applied them with the same configuration that they were originally introduced as for ResNet-34 \\citeShe2016deepS teacher and ResNet-18 student, with minor adjustments. Specifically, since B-cos networks also operate on negative subspace, we did not apply ReLU on the intermediate tensors in AT. For ReviewKD, since the additional convlution and norm layers between the teacher and student are only needed to convert intermediate representations, we used standard convolution and BatchNorm and not B-cos specific layers. For AT, ReviewKD, and CAT-KD we replaced the cross-entropy loss, with the modified binary cross entropy from \\citeSbcosv2S.\n\n\n\n\n\\bibliographystyleSsplncs04\n\\bibliographySsupp_bib\n\n\n\n\n\n\n
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\n