Spectral Networks and Locally Connected Networks on Graphs
Authors: Joan Bruna, Wojciech Zaremba, Arthur Szlam, Yann LeCun
ICLR 2014

Abstract: Convolutional Neural Networks are extremely efficient architectures in image and audio recognition tasks, thanks to their ability to exploit the local translational invariance of signal classes over their domain. In this paper we consider possible generalizations of CNNs to signals defined on more general domains without the action of a translation group. In particular, we propose two constructions, one based upon a hierarchical clustering of the domain, and another based on the spectrum of the graph Laplacian. We show through experiments that for low-dimensional graphs it is possible to learn convolutional layers with $O(1)$ parameters, resulting in efficient deep architectures.


Peer review:
[Review]:
Spectral networks

This paper aims at applying convolutional neural networks to data which do not fit into the standard convolutional framework. They do so by considering that the coordinates lie on a graph and using the Laplacian of that graph.

The topic is of utmost interest as CNNs consistently achieve very high performance while keeping the number of parameters in the network. I am glad to see advances in that direction. This excitement is moderated by the extreme difficulty with which I read the paper. In fact, most of the paper assumes advanced notions of harmonic analysis which I do not possess. I fully understand that such notions are necessary to fully apprehend this work but I would have appreciated if the authors had provided pointers or tried to give intuition on the concepts. As it is, only people familiar with the field will capture the full gist of the method.

Additionally, I find the experimental section a bit weak, in great part because of the sole use of the ubiquitous MNIST dataset (albeit distorted versions of it).

That being said, I want this work to be disseminated so that CNN can be used in wider contexts.

Pros:
- Great extension of CNNs
- Results are based on profound understanding of harmonic analysis and not just trial and error

Cons:
- Extremely difficult to read for an audience not familiar with harmonic analysis
- Experimental section a bit weak.