While there has been progress in develo** non-vacuous generalization bounds for deep
neural networks, these bounds tend to be uninformative about why deep learning works. In …

The explicit incorporation of task-specific inductive biases through symmetry has emerged
as a general design precept in the development of high-performance machine learning …

Graph neural networks (GNNs) are commonly described as being permutation equivariant
with respect to node relabeling in the graph. This symmetry of GNNs is often compared to …

Equivariant networks capture the inductive bias about the symmetry of the learning task by
building those symmetries into the model. In this paper, we study how equivariance relates …

We prove limitations on what neural networks trained by noisy gradient descent (GD) can
efficiently learn. Our results apply whenever GD training is equivariant, which holds for many …

Transformation invariances are present in many real-world problems. For example, image
classification is usually invariant to rotation and color transformation: a rotated car in a …

We study the generalization capacity of group convolutional neural networks. We identify
precise estimates for the VC dimensions of simple sets of group convolutional neural …

We study the implicit bias of gradient flow on linear equivariant steerable networks in group-
invariant binary classification. Our findings reveal that the parameterized predictor …

Existing causal models for link prediction assume an underlying set of inherent node factors—
an innate characteristic defined at the node's birth—that governs the causal evolution of …

Learning an interpretable representation of data without supervision is an important
precursor for the development of artificial intelligence. In this work, we introduce\textit …