Guillaume Lajoie

Biography

Guillaume Lajoie is an Associate professor in the Department of Mathematics and Statistics at Université de Montréal and a Core Academic Member of Mila – Quebec Artificial Intelligence Institute. He holds a Canada-CIFAR AI Research Chair, and a Canada Research Chair (CRC) in Neural Computation and Interfacing.

His research is positioned at the intersection of AI and Neuroscience where he develops tools to better understand mechanisms of intelligence common to both biological and artificial systems. His research group's contributions range from advances in multi-scale learning paradigms for large artificial systems, to applications in neurotechnology. Dr. Lajoie is actively involved in responsible AI development efforts, seeking to identify guidelines and best practices for use of AI in research and beyond.

Current Students

Federico Arangath Joseph

Collaborating researcher - ETH Zurich

Stefan Bauer

Independent visiting researcher

Principal supervisor :

Yoshua Bengio

Sangnie Bhardwaj

PhD - Université de Montréal

Co-supervisor :

Hugo Larochelle

Colin Bredenberg

Postdoctorate - Université de Montréal

Co-supervisor :

Blake Richards

Leo Choiniere

PhD - Université de Montréal

Olivier Codol

Postdoctorate - Université de Montréal

Co-supervisor :

PhD - Université de Montréal

Principal supervisor :

PhD - Université de Montréal

Principal supervisor :

Leo Gagnon

PhD - Université de Montréal

Skylar Gu

Research Intern - McGill University

Principal supervisor :

Juan Guerra

Master's Research - Polytechnique Montréal

Principal supervisor :

Marco Bonizzato

Nanda Harishankar Krishna

PhD - Université de Montréal

Collaborating researcher - Western Washington University (faculty; assistant prof))

Principal supervisor :

PhD - Université de Montréal

Co-supervisor :

Master's Research - Université de Montréal

Co-supervisor :

tejaskasetty@gmail.com

Research Intern - Concordia University

Co-supervisor :

Matt Perich

Ximeng Mao

PhD - Université de Montréal

Co-supervisor :

Joelle Pineau

Abdel Mfougouon Njupoun

PhD - Université de Montréal

Co-supervisor :

PhD - Université de Montréal

Co-supervisor :

Amine Natik

PhD - Université de Montréal

Co-supervisor :

Guy Wolf

Alexandre Payeur

Collaborating researcher - Université de Montréal

Mohammad Pezeshki

Collaborating researcher

Principal supervisor :

Collaborating Alumni - McGill University

Principal supervisor :

Julia Price

Master's Research - Université de Montréal

Param Raval

Collaborating Alumni - Université de Montréal

Avery Ryoo

Master's Research - Université de Montréal

Principal supervisor :

PhD - Université de Montréal

Co-supervisor :

Lune Bellec

Ayesha Vermani

Independent visiting researcher - Champalimeau Institute for the Unknown

Ryan Vogt

Postdoctorate - Université de Montréal

Vivian White

Research Intern - Western Washington University

Co-supervisor :

PhD - Université de Montréal

Machine Learning for the Segmentation of Different Nerve Fibre Activations from Brain-to-body Neural Signals

Blog Posts

Représentation graphique d'un nerf vague

May 21, 2025

Param Raval

Olivier Tessier-Larivière

Pascal Fortier-Poisson

Blake Richards

Guillaume Lajoie

Read the article

June 13, 2024

What Do Synaptic Weight Distributions Tell Us About Learning in the Brain ?

Roman Pogodin

Jonathan Cornford

Arna Ghosh

Gauthier Gidel

Guillaume Lajoie

Blake Richards

Read the article

Publications

Tracing the representation geometry of language models from pretraining to post-training

Melody Zixuan Li

Kumar Krishna Agrawal

Arna Ghosh

Komal Kumar Teru

Blake Richards

The geometry of representations in a neural network can significantly impact downstream generalization. It is unknown how representation geo… (see more)metry changes in large language models (LLMs) over pretraining and post-training. Here, we characterize the evolving geometry of LLM representations using spectral methods (effective rank and eigenspectrum decay). With the OLMo and Pythia model families we uncover a consistent non-monotonic sequence of three distinct geometric phases in pretraining. An initial \warmup phase sees rapid representational compression. This is followed by an "entropy-seeking" phase, characterized by expansion of the representation manifold's effective dimensionality, which correlates with an increase in memorization. Subsequently, a "compression seeking" phase imposes anisotropic consolidation, selectively preserving variance along dominant eigendirections while contracting others, correlating with improved downstream task performance. We link the emergence of these phases to the fundamental interplay of cross-entropy optimization, information bottleneck, and skewed data distribution. Additionally, we find that in post-training the representation geometry is further transformed: Supervised Fine-Tuning (SFT) and Direct Preference Optimization (DPO) correlate with another "entropy-seeking" dynamic to integrate specific instructional or preferential data, reducing out-of-distribution robustness. Conversely, Reinforcement Learning with Verifiable Rewards (RLVR) often exhibits a "compression seeking" dynamic, consolidating reward-aligned behaviors and reducing the entropy in its output distribution. This work establishes the utility of spectral measures of representation geometry for understanding the multiphase learning dynamics within LLMs.

2025-06-09

ICML.cc/2025/Workshop/HiLD (poster)

openreview.net

Generalizable, real-time neural decoding with hybrid state-space models

Avery Hee-Woon Ryoo

Nanda H Krishna

Ximeng Mao

Mehdi Azabou

Eva L Dyer

Matt Perich

Real-time decoding of neural activity is central to neuroscience and neurotechnology applications, from closed-loop experiments to brain-com… (see more)puter interfaces, where models are subject to strict latency constraints. Traditional methods, including simple recurrent neural networks, are fast and lightweight but often struggle to generalize to unseen data. In contrast, recent Transformer-based approaches leverage large-scale pretraining for strong generalization performance, but typically have much larger computational requirements and are not always suitable for low-resource or real-time settings. To address these shortcomings, we present POSSM, a novel hybrid architecture that combines individual spike tokenization via a cross-attention module with a recurrent state-space model (SSM) backbone to enable (1) fast and causal online prediction on neural activity and (2) efficient generalization to new sessions, individuals, and tasks through multi-dataset pretraining. We evaluate POSSM's decoding performance and inference speed on intracortical decoding of monkey motor tasks, and show that it extends to clinical applications, namely handwriting and speech decoding in human subjects. Notably, we demonstrate that pretraining on monkey motor-cortical recordings improves decoding performance on the human handwriting task, highlighting the exciting potential for cross-species transfer. In all of these tasks, we find that POSSM achieves decoding accuracy comparable to state-of-the-art Transformers, at a fraction of the inference cost (up to 9x faster on GPU). These results suggest that hybrid SSMs are a promising approach to bridging the gap between accuracy, inference speed, and generalization when training neural decoders for real-time, closed-loop applications.

2025-06-05

ArXiv (preprint)

Generalizable, real-time neural decoding with hybrid state-space models

Avery Hee-Woon Ryoo

Nanda H Krishna

Ximeng Mao

Mehdi Azabou

Eva L Dyer

Matt Perich

2025-06-05

ArXiv (preprint)

MesaNet: Sequence Modeling by Locally Optimal Test-Time Training

Johannes Von Oswald

Nino Scherrer

Seijin Kobayashi

Luca Versari

Songlin Yang

Maximilian Schlegel

Kaitlin Maile

Yanick Schimpf

Oliver Sieberling

Alexander Meulemans

Rif A. Saurous

Charlotte Frenkel

Razvan Pascanu

Blaise Aguera y Arcas

João Sacramento

Sequence modeling is currently dominated by causal transformer architectures that use softmax self-attention. Although widely adopted, trans… (see more)formers require scaling memory and compute linearly during inference. A recent stream of work linearized the softmax operation, resulting in powerful recurrent neural network (RNN) models with constant memory and compute costs such as DeltaNet, Mamba or xLSTM. These models can be unified by noting that their recurrent layer dynamics can all be derived from an in-context regression objective, approximately optimized through an online learning rule. Here, we join this line of work and introduce a numerically stable, chunkwise parallelizable version of the recently proposed Mesa layer (von Oswald et al., 2024), and study it in language modeling at the billion-parameter scale. This layer again stems from an in-context loss, but which is now minimized to optimality at every time point using a fast conjugate gradient solver. Through an extensive suite of experiments, we show that optimal test-time training enables reaching lower language modeling perplexity and higher downstream benchmark performance than previous RNNs, especially on tasks requiring long context understanding. This performance gain comes at the cost of additional flops spent during inference time. Our results are therefore intriguingly related to recent trends of increasing test-time compute to improve performance -- here by spending compute to solve sequential optimization problems within the neural network itself.

2025-06-05

ArXiv (preprint)

MesaNet: Sequence Modeling by Locally Optimal Test-Time Training

Johannes Von Oswald

Nino Scherrer

Seijin Kobayashi

Luca Versari

Songlin Yang

Maximilian Schlegel

Kaitlin Maile

Yanick Schimpf

Oliver Sieberling

Alexander Meulemans

Rif A. Saurous

Charlotte Frenkel

Razvan Pascanu

Blaise Aguera y Arcas

João Sacramento

2025-06-05

ArXiv (preprint)

Does learning the right latent variables necessarily improve in-context learning?

Sarthak Mittal

Eric Elmoznino

Leo Gagnon

Sangnie Bhardwaj

Large autoregressive models like Transformers can solve tasks through in-context learning (ICL) without learning new weights, suggesting ave… (see more)nues for efficiently solving new tasks. For many tasks, e.g., linear regression, the data factorizes: examples are independent given a task latent that generates the data, e.g., linear coefficients. While an optimal predictor leverages this factorization by inferring task latents, it is unclear if Transformers implicitly do so or if they instead exploit heuristics and statistical shortcuts enabled by attention layers. Both scenarios have inspired active ongoing work. In this paper, we systematically investigate the effect of explicitly inferring task latents. We minimally modify the Transformer architecture with a bottleneck designed to prevent shortcuts in favor of more structured solutions, and then compare performance against standard Transformers across various ICL tasks. Contrary to intuition and some recent works, we find little discernible difference between the two; biasing towards task-relevant latent variables does not lead to better out-of-distribution performance, in general. Curiously, we find that while the bottleneck effectively learns to extract latent task variables from context, downstream processing struggles to utilize them for robust prediction. Our study highlights the intrinsic limitations of Transformers in achieving structured ICL solutions that generalize, and shows that while inferring the right latents aids interpretability, it is not sufficient to alleviate this problem.

2025-05-01

ICML.cc/2025/Conference (poster)

openreview.net

In-context learning and Occam's razor

Eric Elmoznino

Tom Marty

Tejas Kasetty

Leo Gagnon

Sarthak Mittal

Mahan Fathi

A central goal of machine learning is generalization. While the No Free Lunch Theorem states that we cannot obtain theoretical guarantees fo… (see more)r generalization without further assumptions, in practice we observe that simple models which explain the training data generalize best: a principle called Occam's razor. Despite the need for simple models, most current approaches in machine learning only minimize the training error, and at best indirectly promote simplicity through regularization or architecture design. Here, we draw a connection between Occam's razor and in-context learning: an emergent ability of certain sequence models like Transformers to learn at inference time from past observations in a sequence. In particular, we show that the next-token prediction loss used to train in-context learners is directly equivalent to a data compression technique called prequential coding, and that minimizing this loss amounts to jointly minimizing both the training error and the complexity of the model that was implicitly learned from context. Our theory and the empirical experiments we use to support it not only provide a normative account of in-context learning, but also elucidate the shortcomings of current in-context learning methods, suggesting ways in which they can be improved. We make our code available at https://github.com/3rdCore/PrequentialCode.

2025-05-01

ICML.cc/2025/Conference (poster)

openreview.net

Accelerated learning of a noninvasive human brain-computer interface via manifold geometry

Erica Lindsey Busch

E. Chandra Fincke

Smita Krishnaswamy

Nicholas B Turk-Browne

2025-04-03

bioRxiv (preprint)

In-Context Parametric Inference: Point or Distribution Estimators?

Sarthak Mittal

Yoshua Bengio

Nikolay Malkin

Bayesian and frequentist inference are two fundamental paradigms in statistical estimation. Bayesian methods treat hypotheses as random vari… (see more)ables, incorporating priors and updating beliefs via Bayes' theorem, whereas frequentist methods assume fixed but unknown hypotheses, relying on estimators like maximum likelihood. While extensive research has compared these approaches, the frequentist paradigm of obtaining point estimates has become predominant in deep learning, as Bayesian inference is challenging due to the computational complexity and the approximation gap of posterior estimation methods. However, a good understanding of trade-offs between the two approaches is lacking in the regime of amortized estimators, where in-context learners are trained to estimate either point values via maximum likelihood or maximum a posteriori estimation, or full posteriors using normalizing flows, score-based diffusion samplers, or diagonal Gaussian approximations, conditioned on observations. To help resolve this, we conduct a rigorous comparative analysis spanning diverse problem settings, from linear models to shallow neural networks, with a robust evaluation framework assessing both in-distribution and out-of-distribution generalization on tractable tasks. Our experiments indicate that amortized point estimators generally outperform posterior inference, though the latter remain competitive in some low-dimensional problems, and we further discuss why this might be the case.

2025-02-17

ArXiv (preprint)

In-Context Parametric Inference: Point or Distribution Estimators?

Sarthak Mittal

Yoshua Bengio

Nikolay Malkin

2025-02-17

ArXiv (preprint)

Amortized In-Context Bayesian Posterior Estimation

Sarthak Mittal

N. L. Bracher

Priyank Jaini

Marcus Brubaker

Bayesian inference provides a natural way of incorporating prior beliefs and assigning a probability measure to the space of hypotheses. Cur… (see more)rent solutions rely on iterative routines like Markov Chain Monte Carlo (MCMC) sampling and Variational Inference (VI), which need to be re-run whenever new observations are available. Amortization, through conditional estimation, is a viable strategy to alleviate such difficulties and has been the guiding principle behind simulation-based inference, neural processes and in-context methods using pre-trained models. In this work, we conduct a thorough comparative analysis of amortized in-context Bayesian posterior estimation methods from the lens of different optimization objectives and architectural choices. Such methods train an amortized estimator to perform posterior parameter inference by conditioning on a set of data examples passed as context to a sequence model such as a transformer. In contrast to language models, we leverage permutation invariant architectures as the true posterior is invariant to the ordering of context examples. Our empirical study includes generalization to out-of-distribution tasks, cases where the assumed underlying model is misspecified, and transfer from simulated to real problems. Subsequently, it highlights the superiority of the reverse KL estimator for predictive problems, especially when combined with the transformer architecture and normalizing flows.

2025-02-10

ArXiv (preprint)

Amortized In-Context Bayesian Posterior Estimation

Sarthak Mittal

N. L. Bracher

Priyank Jaini

Marcus Brubaker

2025-02-10

ArXiv (preprint)