17 accepted papers
The inclusion of symmetries as an inductive bias, known as *equivariance*, often improves generalization on geometric data (e.g. grids, sets, and graphs). However, equivariant architectures are usually highly constrained, designed for symmetries chosen *a priori*, and not applicable to datasets with…
The automated detection of hallucinations and training data contamination is pivotal to the safe deployment of Large Language Models (LLMs). These tasks are particularly challenging in settings where no access to model internals is available. Current approaches in this setup typically leverage only
In many applications, we desire neural networks to exhibit invariance or equivariance to certain groups due to symmetries inherent in the data. Recently, frame-averaging methods emerged to be a unified framework for attaining symmetries efficiently by averaging over input-dependent subsets of the gr…
Neural networks efficiently encode learned information within their parameters. Consequently, many tasks can be unified by treating neural networks themselves as input data. When doing so, recent studies demonstrated the importance of accounting for the symmetries and geometry of parameter spaces. H…
Machine learning on graphs, especially using graph neural networks (GNNs), has seen a surge in interest due to the wide availability of graph data across a broad spectrum of disciplines, from life to social and engineering sciences. Despite their practical success, our theoretical understanding of t…
Self-supervised learning converts raw perceptual data such as images to a compact space where simple Euclidean distances measure meaningful variations in data. In this paper, we extend this formulation by adding additional geometric structure to the embedding space by enforcing transformations of in…
Many algorithms and observed phenomena in deep learning appear to be affected by parameter symmetries --- transformations of neural network parameters that do not change the underlying neural network function. These include linear mode connectivity, model merging, Bayesian neural network inference,…
Graph Neural Networks (GNN) are inherently limited in their expressive power. Recent seminal works (Xu et al., 2019; Morris et al., 2019b) introduced the Weisfeiler-Lehman (WL) hierarchy as a measure of expressive power. Although this hierarchy has propelled significant advances in GNN analysis and…
Recent work has shown the utility of developing machine learning models that respect the structure and symmetries of eigenvectors. These works promote sign invariance, since for any eigenvector v the negation -v is also an eigenvector. However, we show that sign invariance is theoretically limited f…
Transformers for graph data are increasingly widely studied and successful in numerous learning tasks. Graph inductive biases are crucial for Graph Transformers, and previous works incorporate them using message-passing modules and/or positional encodings. However, Graph Transformers that use messag…
We introduce SignNet and BasisNet---new neural architectures that are invariant to two key symmetries displayed by eigenvectors: (i) sign flips, since if v is an eigenvector then so is -v; and (ii) more general basis symmetries, which occur in higher dimensional eigenspaces with infinitely many choi…
To achieve a graph representation, most Graph Neural Networks (GNNs) follow two steps: first, each graph is decomposed into a number of subgraphs (which we call the recursion step), and then the collection of subgraphs is encoded by several iterative pooling steps. While recently proposed higher-ord…
Message-passing neural networks (MPNNs) are the leading architecture for deep learning on graph-structured data, in large part due to their simplicity and scalability. Unfortunately, it was shown that these architectures are limited in their expressive power. This paper proposes a novel framework ca…
The problem of projecting a matrix onto the space of
Tractably modelling distributions over manifolds has long been an important goal in the natural sciences. Recent work has focused on developing general machine learning models to learn such distributions. However, for many applications these distributions must respect manifold symmetries—a trait whi…
Many widely used datasets for graph machine learning tasks have generally been homophilous, where nodes with similar labels connect to each other. Recently, new Graph Neural Networks (GNNs) have been developed that move beyond the homophily regime; however, their evaluation has often been conducted…
To better conform to data geometry, recent deep generative modelling techniques adapt Euclidean constructions to non-Euclidean spaces. In this paper, we study normalizing flows on manifolds. Previous work has developed flow models for specific cases; however, these advancements hand craft layers on…