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Vincent Létourneau

Collaborating Alumni - Université de Montréal
Supervisor
Guy Wolf
Research Topics
Generative Models
Graph Neural Networks

Publications

Uncovering a Universal Abstract Algorithm for Modular Addition in Neural Networks
Gavin McCracken
Gabriela Moisescu-Pareja
Vincent Létourneau
Doina Precup
Jonathan Love
We propose a testable universality hypothesis, asserting that seemingly disparate neural network solutions observed in the simple task of mo… (see more)dular addition are unified under a common abstract algorithm. While prior work interpreted variations in neuron-level representations as evidence for distinct algorithms, we demonstrate - through multi-level analyses spanning neurons, neuron clusters, and entire networks - that multilayer perceptrons and transformers universally implement the abstract algorithm we call the approximate Chinese Remainder Theorem. Crucially, we introduce approximate cosets and show that neurons activate exclusively on them. Furthermore, our theory works for deep neural networks (DNNs). It predicts that universally learned solutions in DNNs with trainable embeddings or more than one hidden layer require only O(log n) features, a result we empirically confirm. This work thus provides the first theory-backed interpretation of multilayer networks solving modular addition. It advances generalizable interpretability and opens a testable universality hypothesis for group multiplication beyond modular addition.
2025-05-23
ArXiv (preprint)
arxiv.org
arxiv.org
Uncovering a Universal Abstract Algorithm for Modular Addition in Neural Networks
Gavin McCracken
Gabriela Moisescu-Pareja
Vincent Létourneau
Doina Precup
Jonathan Love
We propose a testable universality hypothesis, asserting that seemingly disparate neural network solutions observed in the simple task of mo… (see more)dular addition are unified under a common abstract algorithm. While prior work interpreted variations in neuron-level representations as evidence for distinct algorithms, we demonstrate - through multi-level analyses spanning neurons, neuron clusters, and entire networks - that multilayer perceptrons and transformers universally implement the abstract algorithm we call the approximate Chinese Remainder Theorem. Crucially, we introduce approximate cosets and show that neurons activate exclusively on them. Furthermore, our theory works for deep neural networks (DNNs). It predicts that universally learned solutions in DNNs with trainable embeddings or more than one hidden layer require only O(log n) features, a result we empirically confirm. This work thus provides the first theory-backed interpretation of multilayer networks solving modular addition. It advances generalizable interpretability and opens a testable universality hypothesis for group multiplication beyond modular addition.
2025-05-01
arXiv (published)
doi.org
arxiv.org
Graph Positional and Structural Encoder
Renming Liu
Semih Cantürk
Olivier Lapointe-Gagné
Vincent Létourneau
Guy Wolf
Dominique Beaini
Ladislav Rampášek
Positional and structural encodings (PSE) enable better identifiability of nodes within a graph, as in general graphs lack a canonical node … (see more)ordering. This renders PSEs essential tools for empowering modern GNNs, and in particular graph Transformers. However, designing PSEs that work optimally for a variety of graph prediction tasks is a challenging and unsolved problem. Here, we present the graph positional and structural encoder (GPSE), a first-ever attempt to train a graph encoder that captures rich PSE representations for augmenting any GNN. GPSE can effectively learn a common latent representation for multiple PSEs, and is highly transferable. The encoder trained on a particular graph dataset can be used effectively on datasets drawn from significantly different distributions and even modalities. We show that across a wide range of benchmarks, GPSE-enhanced models can significantly improve the performance in certain tasks, while performing on par with those that employ explicitly computed PSEs in other cases. Our results pave the way for the development of large pre-trained models for extracting graph positional and structural information and highlight their potential as a viable alternative to explicitly computed PSEs as well as to existing self-supervised pre-training approaches.
2024-07-08
Proceedings of the 41st International Conference on Machine Learning (published)
doi.org
openreview.net
Directional Graph Networks
Dominique Beaini
Saro Passaro
Vincent Létourneau
William L. Hamilton
Gabriele Corso
Pietro Lió
The lack of anisotropic kernels in graph neural networks (GNNs) strongly limits their expressiveness, contributing to well-known issues such… (see more) as over-smoothing. To overcome this limitation, we propose the first globally consistent anisotropic kernels for GNNs, allowing for graph convolutions that are defined according to topologicaly-derived directional flows. First, by defining a vector field in the graph, we develop a method of applying directional derivatives and smoothing by projecting node-specific messages into the field. Then, we propose the use of the Laplacian eigenvectors as such vector field. We show that the method generalizes CNNs on an
2021-07-01
Proceedings of the 38th International Conference on Machine Learning (published)
proceedings.mlr.press
openreview.net
Rethinking Graph Transformers with Spectral Attention
Devin Kreuzer
Dominique Beaini
William L. Hamilton
Vincent Létourneau
Prudencio Tossou
In recent years, the Transformer architecture has proven to be very successful in sequence processing, but its application to other data str… (see more)uctures, such as graphs, has remained limited due to the difficulty of properly defining positions. Here, we present the
openreview.net