Equivariant neural networks and equivarification
A key difference from existing works is that our equivarification method can be applied without knowledge of the detailed functions of a layer in a neural network, and hence, can be generalized to any feedforward neural networks. Although the network size scales up, the constructed equivariant neural network does not increase the complexity of the network compared with the original one, in terms of the number of parameters. As an illustration, we build an equivariant neural network for image classification by equivarifying a convolutional neural network. Results show that our proposed method significantly reduces the design and training complexity, yet preserving the learning performance in terms of accuracy.
Motivated by group action theory, this paper proposes a method to obtain ‘equivariant’ neural nets given trained one, where ‘equivariant’ refers to a network that gives identical output if certain symmetry of the dataset is performed on the input (for example, if we rotate a sample the predicted class should not change). After reading the paper, I don’t understand the experiments section. In particular, it is not clear to me how the proposed method differs from regular data augmentation, as to my understanding, the input to conv1 is copied 4 times and performed rotation for 0, 90, 180 and 270 degrees and the 4 times increased number of parameters (in-depth) of conv1 are shared. Furthermore, the same rotations are performed to the input to the second layer-conv 2: as the augmentation is cyclic I don’t understand why the authors perform this operation second time. Could the authors elaborate on this? After reading this section, I don’t understand the proposed fine-tuning procedure (pre-train, finetune and test): (1) what is the accuracy of the pre-trained network that was started from? (2) how is the initial network fine-tuned and modified? (as the authors mention that during training the samples are not rotated). Also, I am confused with the first sentence on page 8: ‘the complexity of the constructed network does not grow in terms of the number of parameters’. It would be useful if the results in Fig. 4 are more clearly illustrated. Is the order or increased computation 4x4x4? It would be useful to compare the method (computation & performance) with a baseline where the dataset is enlarged with data augmentation. The authors mention in the introduction that this increases training overhead, whereas the proposed practical method increases the computation at inference as well as the memory footprint of the model and the forward pass. It would be useful if the authors compared empirically with baselines with (1) data augmentation (2) network with an increased number of parameters (same as the proposed one). In summary, the idea of using group action theory seems interesting. However after reading the paper, it is not clear to me how the idea is carried out, and although the authors provide theoretical justification, it is not clear how this connects with the practical proposed method and whether it outperforms standard data augmentation (see above). Moreover, I find the writing of the paper quite unclear (see discussion above and examples below). - If digits 6 or 9 are rotated the label changes, how does the proposed method handle this? - page 8, conclusion: The authors claim that the proposed approach yields a ‘significant reduction in the design and training complexity’. I don’t understand relative to what this comparison refers to, as the regular data augmentation approach is more straightforward in my opinion. Also, given that this is pointed as an important contribution, in my opinion, an empirical comparison must be done with such baselines (see above). - Page 1: it is mentioned that ‘the number of parameters can be the same as the original network’ but the experiments do not include such architecture. After reading the paper I don’t understand how such a network can be implemented and whether it works. — Minor — - Page 1 & 1par-Pg2: I don’t understand what the authors mean by ‘uniformly *across layers* of NN? - Page 2: In these existing works, … I don’t understand this sentence - Page 2: our .. method use -> uses - Page 2: map over the orbits. I don’t understand this - Page 2: the first truly equivariant NN. After reading Sec 5 I don’t understand this point. - Sec. 4: how to equivarifying -> equivarify - Page 4: ‘pick a generator’, would recommend elaborating this term or only mentioning g as an element of G for clarity for readers unfamiliar with group theory - What is the testing accuracy if rotated for different angles than trained (e.g. 45 degrees)?
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Equivariant neural networks and equivarification
A key difference from existing works is that our equivarification method can be applied without knowledge of the detailed functions of a layer in a neural network, and hence, can be generalized to any feedforward neural networks. Although the network size scales up, the constructed equivariant neural network does not increase the complexity of the network compared with the original one, in terms of the number of parameters. As an illustration, we build an equivariant neural network for image classification by equivarifying a convolutional neural network. Results show that our proposed method significantly reduces the design and training complexity, yet preserving the learning performance in terms of accuracy.
user
<think>Okay, to do a decent peer review, I should start with summarizing what the work is about. This includes novelty, contributions, clarity, and impact. I might include suggestions to issues that I find critical to the usefulness of the work. Starting with novelty, there are different types of novelty. The first aspect of novelty is scope and scale. Is the work covering a broader perspective than previous works? The second aspect is methodology. Is the proposed methodology novel compared to previous methods? Do they provide any significant advantage over previous methodologies? The third aspect is results. Are the results different compared previous work? Does this lead to any novel theories or an extension of current theories? Next is clarity, I will be reading the work in depth and analyze if any sentences can be potentially ambiguous or misleading. If any sentences are ambiguous, I will state them and give a suggestion on how to rephrase such sentence or how to make more clear to the audience. Lastly, impact is important. I will attempt to predict how such work will impact the scientific community. This might include the applications of such work and how the work might transform the way we study a certain topic. Finally, I will might only mention issues that are critical. This is to keep the review as concise and helpful as possible.</think>



Motivated by group action theory, this paper proposes a method to obtain ‘equivariant’ neural nets given trained one, where ‘equivariant’ refers to a network that gives identical output if certain symmetry of the dataset is performed on the input (for example, if we rotate a sample the predicted class should not change). After reading the paper, I don’t understand the experiments section. In particular, it is not clear to me how the proposed method differs from regular data augmentation, as to my understanding, the input to conv1 is copied 4 times and performed rotation for 0, 90, 180 and 270 degrees and the 4 times increased number of parameters (in-depth) of conv1 are shared. Furthermore, the same rotations are performed to the input to the second layer-conv 2: as the augmentation is cyclic I don’t understand why the authors perform this operation second time. Could the authors elaborate on this? After reading this section, I don’t understand the proposed fine-tuning procedure (pre-train, finetune and test): (1) what is the accuracy of the pre-trained network that was started from? (2) how is the initial network fine-tuned and modified? (as the authors mention that during training the samples are not rotated). Also, I am confused with the first sentence on page 8: ‘the complexity of the constructed network does not grow in terms of the number of parameters’. It would be useful if the results in Fig. 4 are more clearly illustrated. Is the order or increased computation 4x4x4? It would be useful to compare the method (computation & performance) with a baseline where the dataset is enlarged with data augmentation. The authors mention in the introduction that this increases training overhead, whereas the proposed practical method increases the computation at inference as well as the memory footprint of the model and the forward pass. It would be useful if the authors compared empirically with baselines with (1) data augmentation (2) network with an increased number of parameters (same as the proposed one). In summary, the idea of using group action theory seems interesting. However after reading the paper, it is not clear to me how the idea is carried out, and although the authors provide theoretical justification, it is not clear how this connects with the practical proposed method and whether it outperforms standard data augmentation (see above). Moreover, I find the writing of the paper quite unclear (see discussion above and examples below). - If digits 6 or 9 are rotated the label changes, how does the proposed method handle this? - page 8, conclusion: The authors claim that the proposed approach yields a ‘significant reduction in the design and training complexity’. I don’t understand relative to what this comparison refers to, as the regular data augmentation approach is more straightforward in my opinion. Also, given that this is pointed as an important contribution, in my opinion, an empirical comparison must be done with such baselines (see above). - Page 1: it is mentioned that ‘the number of parameters can be the same as the original network’ but the experiments do not include such architecture. After reading the paper I don’t understand how such a network can be implemented and whether it works. — Minor — - Page 1 & 1par-Pg2: I don’t understand what the authors mean by ‘uniformly *across layers* of NN? - Page 2: In these existing works, … I don’t understand this sentence - Page 2: our .. method use -> uses - Page 2: map over the orbits. I don’t understand this - Page 2: the first truly equivariant NN. After reading Sec 5 I don’t understand this point. - Sec. 4: how to equivarifying -> equivarify - Page 4: ‘pick a generator’, would recommend elaborating this term or only mentioning g as an element of G for clarity for readers unfamiliar with group theory - What is the testing accuracy if rotated for different angles than trained (e.g. 45 degrees)?
assistant
Motivated by group action theory, this paper proposes a method to obtain ‘equivariant’ neural nets given trained one, where ‘equivariant’ refers to a network that gives identical output if certain symmetry of the dataset is performed on the input (for example, if we rotate a sample the predicted class should not change). After reading the paper, I don’t understand the experiments section. In particular, it is not clear to me how the proposed method differs from regular data augmentation, as to my understanding, the input to conv1 is copied 4 times and performed rotation for 0, 90, 180 and 270 degrees and the 4 times increased number of parameters (in-depth) of conv1 are shared. Furthermore, the same rotations are performed to the input to the second layer-conv 2: as the augmentation is cyclic I don’t understand why the authors perform this operation second time. Could the authors elaborate on this? After reading this section, I don’t understand the proposed fine-tuning procedure (pre-train, finetune and test): (1) what is the accuracy of the pre-trained network that was started from? (2) how is the initial network fine-tuned and modified? (as the authors mention that during training the samples are not rotated). Also, I am confused with the first sentence on page 8: ‘the complexity of the constructed network does not grow in terms of the number of parameters’. It would be useful if the results in Fig. 4 are more clearly illustrated. Is the order or increased computation 4x4x4? It would be useful to compare the method (computation & performance) with a baseline where the dataset is enlarged with data augmentation. The authors mention in the introduction that this increases training overhead, whereas the proposed practical method increases the computation at inference as well as the memory footprint of the model and the forward pass. It would be useful if the authors compared empirically with baselines with (1) data augmentation (2) network with an increased number of parameters (same as the proposed one). In summary, the idea of using group action theory seems interesting. However after reading the paper, it is not clear to me how the idea is carried out, and although the authors provide theoretical justification, it is not clear how this connects with the practical proposed method and whether it outperforms standard data augmentation (see above). Moreover, I find the writing of the paper quite unclear (see discussion above and examples below). - If digits 6 or 9 are rotated the label changes, how does the proposed method handle this? - page 8, conclusion: The authors claim that the proposed approach yields a ‘significant reduction in the design and training complexity’. I don’t understand relative to what this comparison refers to, as the regular data augmentation approach is more straightforward in my opinion. Also, given that this is pointed as an important contribution, in my opinion, an empirical comparison must be done with such baselines (see above). - Page 1: it is mentioned that ‘the number of parameters can be the same as the original network’ but the experiments do not include such architecture. After reading the paper I don’t understand how such a network can be implemented and whether it works. — Minor — - Page 1 & 1par-Pg2: I don’t understand what the authors mean by ‘uniformly *across layers* of NN? - Page 2: In these existing works, … I don’t understand this sentence - Page 2: our .. method use -> uses - Page 2: map over the orbits. I don’t understand this - Page 2: the first truly equivariant NN. After reading Sec 5 I don’t understand this point. - Sec. 4: how to equivarifying -> equivarify - Page 4: ‘pick a generator’, would recommend elaborating this term or only mentioning g as an element of G for clarity for readers unfamiliar with group theory - What is the testing accuracy if rotated for different angles than trained (e.g. 45 degrees)?