Mathieu Alain

Mathieu Alain, So Takao, Brooks Paige et al.

In recent years, there has been considerable interest in developing machine learning models on graphs to account for topological inductive biases. In particular, recent attention has been given to Gaussian processes on such structures since they can additionally account for uncertainty. However, graphs are limited to modelling relations between two vertices. In this paper, we go beyond this dyadic setting and consider polyadic relations that include interactions between vertices, edges and one of their generalisations, known as cells. Specifically, we propose Gaussian processes on cellular complexes, a generalisation of graphs that captures interactions between these higher-order cells. One of our key contributions is the derivation of two novel kernels, one that generalises the graph Matérn kernel and one that additionally mixes information of different cell types.

Daniele Paliotta, Mathieu Alain, Bálint Máté et al.

We present the Graph Forward-Forward (GFF) algorithm, an extension of the Forward-Forward procedure to graphs, able to handle features distributed over a graph's nodes. This allows training graph neural networks with forward passes only, without backpropagation. Our method is agnostic to the message-passing scheme, and provides a more biologically plausible learning scheme than backpropagation, while also carrying computational advantages. With GFF, graph neural networks are trained greedily layer by layer, using both positive and negative samples. We run experiments on 11 standard graph property prediction tasks, showing how GFF provides an effective alternative to backpropagation for training graph neural networks. This shows in particular that this procedure is remarkably efficient in spite of combining the per-layer training with the locality of the processing in a GNN.

Richard von Moos, Mathieu Alain, Bastian Rieck

Progress on graph foundation models is hindered by benchmark practices that conflate the contributions of node features and graph structure, making it hard to tell whether a model actually learns from connectivity, or whether it even needs to. We propose addressing this using graph invariants, i.e., permutation-invariant, task-agnostic structural descriptors that serve as a diagnostic framework for graph benchmarks. We show that (i) invariants are more expressive than standard GNNs, (ii) invariants characterize structural heterogeneity within and across benchmark datasets, (iii) invariants predict multi-task performance, and (iv) simple invariant-based models are competitive with, and sometimes exceed, transformer and message-passing baselines across 26 datasets. Our results suggest that expressivity is not the main driver of predictive performance, and that on tasks where structure matters, a non-trainable structural proxy often matches trained message-passing models. We thus posit that invariant baselines should become a standard for evaluating whether structure is required for a task and whether a model picks up on it, serving as a stepping stone towards graph foundation models.

Mathieu Alain, So Takao, Xiaowen Dong et al.

The problem of classifying graphs is ubiquitous in machine learning. While it is standard to apply graph neural networks or graph kernel methods, Gaussian processes can be employed by transforming spatial features from the graph domain into spectral features in the Euclidean domain, and using them as the input points of classical kernels. However, this approach currently only takes into account features on vertices, whereas some graph datasets also support features on edges. In this work, we present a Gaussian process-based classification algorithm that can leverage one or both vertex and edges features. Furthermore, we take advantage of the Hodge decomposition to better capture the intricate richness of vertex and edge features, which can be beneficial on diverse tasks.

Yann Pequignot, Mathieu Alain, Patrick Dallaire et al.

It is crucial to detect when an instance lies downright too far from the training samples for the machine learning model to be trusted, a challenge known as out-of-distribution (OOD) detection. For neural networks, one approach to this task consists of learning a diversity of predictors that all can explain the training data. This information can be used to estimate the epistemic uncertainty at a given newly observed instance in terms of a measure of the disagreement of the predictions. Evaluation and certification of the ability of a method to detect OOD require specifying instances which are likely to occur in deployment yet on which no prediction is available. Focusing on regression tasks, we choose a simple yet insightful model for this OOD distribution and conduct an empirical evaluation of the ability of various methods to discriminate OOD samples from the data. Moreover, we exhibit evidence that a diversity of parameters may fail to translate to a diversity of predictors. Based on the choice of an OOD distribution, we propose a new way of estimating the entropy of a distribution on predictors based on nearest neighbors in function space. This leads to a variational objective which, combined with the family of distributions given by a generative neural network, systematically produces a diversity of predictors that provides a robust way to detect OOD samples.