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A General Theory of Equivariant CNNs on Homogeneous Spaces
Taco Cohen, Mario Geiger, Maurice Weiler
We present a general theory of Group equivariant Convolutional Neural Networks (G-CNNs) on homogeneous spaces such as Euclidean space and the sphere. Feature maps in these networks…
A jamming transition from under- to over-parametrization affects loss landscape and generalization
Stefano Spigler, Mario Geiger, Stéphane d'Ascoli +3
We argue that in fully-connected networks a phase transition delimits the over- and under-parametrized regimes where fitting can or cannot be achieved. Under some general condition…
The jamming transition as a paradigm to understand the loss landscape of deep neural networks
Mario Geiger, Stefano Spigler, Stéphane d'Ascoli +4
Deep learning has been immensely successful at a variety of tasks, ranging from classification to AI. Learning corresponds to fitting training data, which is implemented by descend…
3D Steerable CNNs: Learning Rotationally Equivariant Features in Volumetric Data
Maurice Weiler, Mario Geiger, Max Welling +2
We present a convolutional network that is equivariant to rigid body motions. The model uses scalar-, vector-, and tensor fields over 3D Euclidean space to represent data, and equi…
Intertwiners between Induced Representations (with Applications to the Theory of Equivariant Neural Networks)
Taco S. Cohen, Mario Geiger, Maurice Weiler
Group equivariant and steerable convolutional neural networks (regular and steerable G-CNNs) have recently emerged as a very effective model class for learning from signal data suc…
Comparing Dynamics: Deep Neural Networks versus Glassy Systems
M. Baity-Jesi, L. Sagun, M. Geiger +6
We analyze numerically the training dynamics of deep neural networks (DNN) by using methods developed in statistical physics of glassy systems. The two main issues we address are (…
Spherical CNNs
Taco S. Cohen, Mario Geiger, Jonas Koehler +1
Convolutional Neural Networks (CNNs) have become the method of choice for learning problems involving 2D planar images. However, a number of problems of recent interest have create…
The Strong Gravitational Lens Finding Challenge
R. Benton Metcalf, M. Meneghetti, Camille Avestruz +33
Large scale imaging surveys will increase the number of galaxy-scale strong lensing candidates by maybe three orders of magnitudes beyond the number known today. Finding these rare…