Doina Precup

Samin Yeasar Arnob

PhD - McGill University

Sumana Basu

Collaborating Alumni - McGill University

Co-supervisor :

Adriana Romero Soriano

Collaborating Alumni - McGill University

Raymond Chua

PhD - McGill University

Co-supervisor :

PhD - McGill University

Principal supervisor :

David Meger

Jonathan Colaço Carr

Master's Research - McGill University

Principal supervisor :

Prakash Panangaden

Élodie Coté-Gauthier

Collaborating researcher - McGill University

Co-supervisor :

Isabeau Prémont-Schwarz

Franco Del Balso

Collaborating researcher - Université de Montréal

Jesse Farebrother

PhD - McGill University

Principal supervisor :

Marc Gendron-Bellemare

PhD - McGill University

Principal supervisor :

Collaborating researcher - Birla Institute of Technology

Jonathan Hu

Master's Research - McGill University

Howard Huang

PhD - McGill University

Haque Ishfaq

Collaborating Alumni - McGill University

Mohammad Sami Nur Islam Islam

Master's Research - McGill University

Hangzhan Jin

PhD - Polytechnique Montréal

Martin Klissarov

PhD - McGill University

Postdoctorate - McGill University

Jonathan Lebensold

Collaborating Alumni - McGill University

Collaborating Alumni - McGill University

Ray Luo

PhD - McGill University

Principal supervisor :

G McCracken

PhD - McGill University

Nazanin Mohammadi Sepahvand

Collaborating Alumni - McGill University

Shahrad Mohammadzadeh

Master's Research - McGill University

Principal supervisor :

Collaborating researcher - McGill University

Co-supervisor :

Irina Rish

Padideh Nouri

PhD - Université de Montréal

Co-supervisor :

PhD - McGill University

Co-supervisor :

Research Intern - McGill University

Nate Rahn

PhD - McGill University

Principal supervisor :

Marc Gendron-Bellemare

Manoosh Samiei

PhD - McGill University

Co-supervisor :

PhD - McGill University

Co-supervisor :

PhD - McGill University

Nishanth Anand Vemgal

PhD - McGill University

PhD - McGill University

Co-supervisor :

Samira Ebrahimi Kahou

Research Intern - McGill University

Zihan Wang

PhD - McGill University

Skipper: Combining Spatial and Temporal Abstraction for Better Generalization

Steve Wen

Master's Research - McGill University

Co-supervisor :

Gregory Dudek

Zijing Wu

PhD - McGill University

Principal supervisor :

PhD - McGill University

Harry Zhao

Collaborating Alumni - McGill University

Co-supervisor :

Blog Posts

Generic thumbnail for Mila Blog articles.

February 22, 2024

Mingde Harry Zhao

Safa Alver

Harm van Seijen

Romain Laroche

Doina Precup

Yoshua Bengio

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Publications

The Geometry and Topology of Circuits: the Manifolds of Modular Addition

Colin Daniels

Jonathan Love

The Clock and Pizza interpretations, associated with architectures differing in either uniform or learnable attention, were introduced to ar… (see more)gue that different architectural designs can yield distinct circuits for modular addition. In this work, we show that this is not the case, and that both the uniform and trainable attention architectures implement the same algorithm via topologically and geometrically equivalent representations. Our methodology goes beyond the interpretation of individual neurons and weights. Instead, we identify all of the neurons corresponding to each learned representation and then study the collective group of neurons as one entity. This method reveals that each learned representation is a manifold that we can study utilizing tools from topology. Based on this insight, we can statistically analyze the learned representations across hundreds of circuits to demonstrate the similarity between learned modular addition circuits that arise naturally from common deep learning paradigms.

2025-12-31

International Conference on Learning Representations (Accept (Poster))

On the geometry and topology of representations: the manifolds of modular addition

Colin Daniels

Jonathan Love

The Clock and Pizza interpretations, associated with architectures differing in either uniform or learnable attention, were introduced to ar… (see more)gue that different architectural designs can yield distinct circuits for modular addition. In this work, we show that this is not the case, and that both uniform attention and trainable attention architectures implement the same algorithm via topologically and geometrically equivalent representations. Our methodology goes beyond the interpretation of individual neurons and weights. Instead, we identify all of the neurons corresponding to each learned representation and then study the collective group of neurons as one entity. This method reveals that each learned representation is a manifold that we can study utilizing tools from topology. Based on this insight, we can statistically analyze the learned representations across hundreds of circuits to demonstrate the similarity between learned modular addition circuits that arise naturally from common deep learning paradigms.

2025-12-30

arXiv (preprint)

A Message from AI Research Leaders: Join Us in Supporting OpenReview

Andrew Y. Ng

Ruslan Salakhutdinov

Fernando Pereira

2025-12-17

OpenReview (unknown)

On Mobile Ad Hoc Networks for Coverage of Partially Observable Worlds

Edwin Meriaux

Shuo Wen

Louis-Roy Langevin

Antonio Lor'ia

Gregory Dudek

2025-12-09

ArXiv (preprint)

arxiv.org

Large Language Model Applications in the Algebra Domain: A Systematic Review

Yajie Song

Yimei Zhang

Reihaneh Rabbany

Maria Cutumisu

2025-12-05

Technology, Knowledge and Learning (published)

Excitatory-Inhibitory Dynamics in Adaptive Decision-Making

Veronica Chelu

2025-11-15

Lecture Notes in Computer Science (published)

The Geometry and Topology of Modular Addition Representations

Colin Daniels

Jonathan Love

The Clock and Pizza interpretations, associated with neural architectures differing in either uniform or learnable attention, were introduce… (see more)d to argue that different architectural designs can yield distinct circuits for modular addition. Applying geometric and topological analyses to learned representations, we show that this is not the case: Clock and Pizza circuits are topologically and geometrically equivalent and are thus equivalent representations.

2025-11-12

TAG-DS/2025/Conference (poster)

Reward the Reward Designer: Making Reinforcement Learning Useful for Clinical Decision Making

Sumana Basu

Adriana Romero

2025-09-21

NeurIPS.cc/2025/Workshop/WiML (published)

Unifying Mechanistic Interpretations of Neural Networks Trained on Modular Addition

Gavin McCracken

Vincent Létourneau

Jonathan Love

2025-09-21

NeurIPS.cc/2025/Workshop/WiML (published)

Capturing Individual Human Preferences with Reward Features

Andre Barreto

Vincent Dumoulin

Yiran Mao

Nicolas Perez-Nieves

Mark Rowland

Bobak Shahriari

Yann Dauphin

Hugo Larochelle

Reinforcement learning from human feedback usually models preferences using a reward model that does not distinguish between people. We argu… (see more)e that this is unlikely to be a good design choice in contexts with high potential for disagreement, like in the training of large language models. We propose a method to specialise a reward model to a person or group of people. Our approach builds on the observation that individual preferences can be captured as a linear combination of a set of general reward features. We show how to learn such features and subsequently use them to quickly adapt the reward model to a specific individual, even if their preferences are not reflected in the training data. We present experiments with large language models comparing the proposed architecture with a non-adaptive reward model and also adaptive counterparts, including models that do in-context personalisation. Depending on how much disagreement there is in the training data, our model either significantly outperforms the baselines or matches their performance with a simpler architecture and more stable training.

2025-09-17

NeurIPS.cc/2025/Conference (poster)

Plasticity as the Mirror of Empowerment

David Abel

Michael Bowling

Andre Barreto

Will Dabney

Shi Dong

Steven Hansen

Anna Harutyunyan

Khimya Khetarpal

Clare Lyle

Razvan Pascanu

Georgios Piliouras

Jonathan Richens

Mark Rowland

Tom Schaul

Satinder Singh

Agents are minimally entities that are influenced by their past observations and act to influence future observations. This latter capacity … (see more)is captured by empowerment, which has served as a vital framing concept across artificial intelligence and cognitive science. This former capacity, however, is equally foundational: In what ways, and to what extent, can an agent be influenced by what it observes? In this paper, we ground this concept in a universal agent-centric measure that we refer to as plasticity, and reveal a fundamental connection to empowerment. Following a set of desiderata on a suitable definition, we define plasticity using a new information-theoretic quantity we call the generalized directed information. We show that this new quantity strictly generalizes the directed information introduced by Massey (1990) while preserving all of its desirable properties. Under this definition, we find that plasticity is well thought of as the mirror of empowerment: The two concepts are defined using the same measure, with only the direction of influence reversed. Our main result establishes a tension between the plasticity and empowerment of an agent, suggesting that agent design needs to be mindful of both characteristics. We explore the implications of these findings, and suggest that plasticity, empowerment, and their relationship are essential to understanding agency

2025-09-17

NeurIPS.cc/2025/Conference (spotlight)

Uncovering a Universal Abstract Algorithm for Modular Addition in Neural Networks

Gavin McCracken

Vincent Létourneau

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.

2025-09-17

Conference on Neural Information Processing Systems (poster)