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Probing the State of the Art: A Critical Look at Visual Representation Evaluation
Cinjon Resnick, Zeping Zhan, Joan Bruna
Self-supervised research improved greatly over the past half decade, with much of the growth being driven by objectives that are hard to quantitatively compare. These techniques in…
Stability of Graph Neural Networks to Relative Perturbations
Fernando Gama, Joan Bruna, Alejandro Ribeiro
Graph neural networks (GNNs), consisting of a cascade of layers applying a graph convolution followed by a pointwise nonlinearity, have become a powerful architecture to process si…
Pure and Spurious Critical Points: a Geometric Study of Linear Networks
Matthew Trager, Kathlén Kohn, Joan Bruna
The critical locus of the loss function of a neural network is determined by the geometry of the functional space and by the parameterization of this space by the network's weights…
Gradient Dynamics of Shallow Univariate ReLU Networks
Francis Williams, Matthew Trager, Claudio Silva +3
We present a theoretical and empirical study of the gradient dynamics of overparameterized shallow ReLU networks with one-dimensional input, solving least-squares interpolation. We…
Stability of Graph Scattering Transforms
Fernando Gama, Joan Bruna, Alejandro Ribeiro
Scattering transforms are non-trainable deep convolutional architectures that exploit the multi-scale resolution of a wavelet filter bank to obtain an appropriate representation of…
Finding the Needle in the Haystack with Convolutions: on the benefits of architectural bias
Stéphane d'Ascoli, Levent Sagun, Joan Bruna +1
Despite the phenomenal success of deep neural networks in a broad range of learning tasks, there is a lack of theory to understand the way they work. In particular, Convolutional N…