Linear Time Complexity Deep Fourier Scattering Network and Extension to Nonlinear Invariants
In this paper we propose a scalable version of a state-of-the-art deterministic time- invariant feature extraction approach based on consecutive changes of basis and nonlinearities, namely, the scattering network. The first focus of the paper is to extend the scattering network to allow the use of higher order nonlinearities as well as extracting nonlinear and Fourier based statistics leading to the required in- variants of any inherently structured input. In order to reach fast convolutions and to leverage the intrinsic structure of wavelets, we derive our complete model in the Fourier domain. In addition of providing fast computations, we are now able to exploit sparse matrices due to extremely high sparsity well localized in the Fourier domain. As a result, we are able to reach a true linear time complexity with in- puts in the Fourier domain allowing fast and energy efficient solutions to machine learning tasks. Validation of the features and computational results will be pre- sented through the use of these invariant coefficients to perform classification on audio recordings of bird songs captured in multiple different soundscapes. In the end, the applicability of the presented solutions to deep artificial neural networks is discussed.
I find the general direction of the work is promising but, in my opinion, the paper has three main drawback. While the motivation and overall idea seem very reasonable, the derivation is not convincing mathematically. The experiments are limited and the presentation needs significant improvement. The writing and wording are in general poorly structured to the point that it is sometimes difficult to follow the proposed ideas. The overall organization needs improvement and the connection between sections is not properly established. The paper could be significantly improved by simply re-writing it. I*m not fully convinced by the motivation for the proposed non-linearity (|c|^2), as described on page 5. The authors argue that (Waldspurger, 2016) suggests that higher order nonlinearities might be beneficial for sparsity. But unless I*m missing something, that work seems to suggest that in the general case higher order nonlinearities can be neglected. Could you please comment on this? On the other hand, adding a second order term to the descriptor seems an interesting direction, as long as stability to small variations is preserved (which should be shown experimentally) The experimental section is rather limited. The paper would be stronger with a thorough numerical evaluation. The presented results, in my opinion, do not show convincingly a clear advantage of the proposed method over a standard implementation of the scattering transform. In order to show the merits of the proposed approach, it would be really helpful to directly compare running times and compression rates. Questions: - Can you show empirically that the proposed higher order nonlinearity produces sparser representations than the complex modulus? Other minor issues: - The proof of Section 2.1, should be preceded by a clear statement in the form of a proposition - *Hadamart* -> Hadamard - *Valid set* -> Validation set - *nonzeros coefficients* -> nonzero coefficients - Figure 3 is difficult to understand. Please provide more details. - Figure 5 is supposed to show a comparison to a standard implementation of the Scattering network, but it doesn*t seem to be such comparison in that figure. Please explain. - Please verify the references. The first reference states *MALLAT*.
You are a member of the scientific community tasked with peer review. Review the following paper title and abstract.
### Title + Abstract
Linear Time Complexity Deep Fourier Scattering Network and Extension to Nonlinear Invariants
In this paper we propose a scalable version of a state-of-the-art deterministic time- invariant feature extraction approach based on consecutive changes of basis and nonlinearities, namely, the scattering network. The first focus of the paper is to extend the scattering network to allow the use of higher order nonlinearities as well as extracting nonlinear and Fourier based statistics leading to the required in- variants of any inherently structured input. In order to reach fast convolutions and to leverage the intrinsic structure of wavelets, we derive our complete model in the Fourier domain. In addition of providing fast computations, we are now able to exploit sparse matrices due to extremely high sparsity well localized in the Fourier domain. As a result, we are able to reach a true linear time complexity with in- puts in the Fourier domain allowing fast and energy efficient solutions to machine learning tasks. Validation of the features and computational results will be pre- sented through the use of these invariant coefficients to perform classification on audio recordings of bird songs captured in multiple different soundscapes. In the end, the applicability of the presented solutions to deep artificial neural networks is discussed.
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>



I find the general direction of the work is promising but, in my opinion, the paper has three main drawback. While the motivation and overall idea seem very reasonable, the derivation is not convincing mathematically. The experiments are limited and the presentation needs significant improvement. The writing and wording are in general poorly structured to the point that it is sometimes difficult to follow the proposed ideas. The overall organization needs improvement and the connection between sections is not properly established. The paper could be significantly improved by simply re-writing it. I*m not fully convinced by the motivation for the proposed non-linearity (|c|^2), as described on page 5. The authors argue that (Waldspurger, 2016) suggests that higher order nonlinearities might be beneficial for sparsity. But unless I*m missing something, that work seems to suggest that in the general case higher order nonlinearities can be neglected. Could you please comment on this? On the other hand, adding a second order term to the descriptor seems an interesting direction, as long as stability to small variations is preserved (which should be shown experimentally) The experimental section is rather limited. The paper would be stronger with a thorough numerical evaluation. The presented results, in my opinion, do not show convincingly a clear advantage of the proposed method over a standard implementation of the scattering transform. In order to show the merits of the proposed approach, it would be really helpful to directly compare running times and compression rates. Questions: - Can you show empirically that the proposed higher order nonlinearity produces sparser representations than the complex modulus? Other minor issues: - The proof of Section 2.1, should be preceded by a clear statement in the form of a proposition - *Hadamart* -> Hadamard - *Valid set* -> Validation set - *nonzeros coefficients* -> nonzero coefficients - Figure 3 is difficult to understand. Please provide more details. - Figure 5 is supposed to show a comparison to a standard implementation of the Scattering network, but it doesn*t seem to be such comparison in that figure. Please explain. - Please verify the references. The first reference states *MALLAT*.
assistant
I find the general direction of the work is promising but, in my opinion, the paper has three main drawback. While the motivation and overall idea seem very reasonable, the derivation is not convincing mathematically. The experiments are limited and the presentation needs significant improvement. The writing and wording are in general poorly structured to the point that it is sometimes difficult to follow the proposed ideas. The overall organization needs improvement and the connection between sections is not properly established. The paper could be significantly improved by simply re-writing it. I*m not fully convinced by the motivation for the proposed non-linearity (|c|^2), as described on page 5. The authors argue that (Waldspurger, 2016) suggests that higher order nonlinearities might be beneficial for sparsity. But unless I*m missing something, that work seems to suggest that in the general case higher order nonlinearities can be neglected. Could you please comment on this? On the other hand, adding a second order term to the descriptor seems an interesting direction, as long as stability to small variations is preserved (which should be shown experimentally) The experimental section is rather limited. The paper would be stronger with a thorough numerical evaluation. The presented results, in my opinion, do not show convincingly a clear advantage of the proposed method over a standard implementation of the scattering transform. In order to show the merits of the proposed approach, it would be really helpful to directly compare running times and compression rates. Questions: - Can you show empirically that the proposed higher order nonlinearity produces sparser representations than the complex modulus? Other minor issues: - The proof of Section 2.1, should be preceded by a clear statement in the form of a proposition - *Hadamart* -> Hadamard - *Valid set* -> Validation set - *nonzeros coefficients* -> nonzero coefficients - Figure 3 is difficult to understand. Please provide more details. - Figure 5 is supposed to show a comparison to a standard implementation of the Scattering network, but it doesn*t seem to be such comparison in that figure. Please explain. - Please verify the references. The first reference states *MALLAT*.