Portrait of Guillaume Lajoie

Guillaume Lajoie

Core Academic Member
Canada CIFAR AI Chair
Associate Professor, Université de Montréal, Department of Mathematics and Statistics
Visiting Researcher, Google
Research Topics
AI for Science
AI in Health
Cognition
Computational Neuroscience
Deep Learning
Dynamical Systems
Optimization
Reasoning
Recurrent Neural Networks
Representation Learning

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

Collaborating researcher - ETH Zurich
Independent visiting researcher
Principal supervisor :
PhD - Université de Montréal
Co-supervisor :
Postdoctorate - Université de Montréal
Co-supervisor :
PhD - Université de Montréal
Postdoctorate - Université de Montréal
Co-supervisor :
PhD - Université de Montréal
Principal supervisor :
PhD - Université de Montréal
Principal supervisor :
PhD - Université de Montréal
Research Intern - McGill University
Principal supervisor :
Master's Research - Polytechnique Montréal
Principal supervisor :
Collaborating researcher - Western Washington University (faculty; assistant prof))
Principal supervisor :
PhD - Université de Montréal
Co-supervisor :
Master's Research - Université de Montréal
Co-supervisor :
Research Intern - Concordia University
Co-supervisor :
PhD - Université de Montréal
Co-supervisor :
PhD - Université de Montréal
Co-supervisor :
PhD - Université de Montréal
Co-supervisor :
PhD - Université de Montréal
Co-supervisor :
Collaborating researcher - Université de Montréal
Collaborating researcher
Principal supervisor :
Collaborating Alumni - McGill University
Principal supervisor :
Master's Research - Université de Montréal
Collaborating Alumni - Université de Montréal
Master's Research - Université de Montréal
Principal supervisor :
PhD - Université de Montréal
Co-supervisor :
Independent visiting researcher - Champalimeau Institute for the Unknown
Postdoctorate - Université de Montréal
Research Intern - Western Washington University
Co-supervisor :
PhD - Université de Montréal

Publications

Celo: Training Versatile Learned Optimizers on a Compute Diet
Abhinav Moudgil
Boris Knyazev
Learned optimization has emerged as a promising alternative to hand-crafted optimizers, with the potential to discover stronger learned upda… (see more)te rules that enable faster, hyperparameter-free training of neural networks. A critical element for practically useful learned optimizers, that can be used off-the-shelf after meta-training, is strong meta-generalization: the ability to apply the optimizers to new tasks. Recent state-of-the-art work in learned optimizers, VeLO (Metz et al., 2022), requires a large number of highly diverse meta-training tasks along with massive computational resources, 4000 TPU months, to achieve meta-generalization. This makes further improvements to such learned optimizers impractical. In this work, we identify several key elements in learned optimizer architectures and meta-training procedures that can lead to strong meta-generalization. We also propose evaluation metrics to reliably assess quantitative performance of an optimizer at scale on a set of evaluation tasks. Our proposed approach, Celo, makes a significant leap in improving the meta-generalization performance of learned optimizers and also outperforms tuned state-of-the-art optimizers on a diverse set of out-of-distribution tasks, despite being meta-trained for just 24 GPU hours.
Neuromorphic hierarchical modular reservoirs
Filip Milisav
Andrea I Luppi
Laura E Suárez
Bratislav Mišić
Next-Token Prediction Should be Ambiguity-Sensitive: A Meta-Learning Perspective
Leo Gagnon
Eric Elmoznino
Sarthak Mittal
Tom Marty
Tejas Kasetty
The rapid adaptation ability of auto-regressive foundation models is often attributed to the diversity of their pre-training data. This is b… (see more)ecause, from a Bayesian standpoint, minimizing prediction error in such settings requires integrating over all plausible latent hypotheses consistent with observations. While this behavior is desirable in principle, it often proves too ambitious in practice: under high ambiguity, the number of plausible latent alternatives makes Bayes-optimal prediction computationally intractable. Cognitive science has long recognized this limitation, suggesting that under such conditions, heuristics or information-seeking strategies are preferable to exhaustive inference. Translating this insight to next-token prediction, we hypothesize that low- and high-ambiguity predictions pose different computational demands, making ambiguity-agnostic next-token prediction a detrimental inductive bias. To test this, we introduce MetaHMM, a synthetic sequence meta-learning benchmark with rich compositional structure and a tractable Bayesian oracle. We show that Transformers indeed struggle with high-ambiguity predictions across model sizes. Motivated by cognitive theories, we propose a method to convert pre-trained models into Monte Carlo predictors that decouple task inference from token prediction. Preliminary results show substantial gains in ambiguous contexts through improved capacity allocation and test-time scalable inference, though challenges remain.
Next-Token Prediction Should be Ambiguity-Sensitive: A Meta-Learning Perspective
Leo Gagnon
Eric Elmoznino
Sarthak Mittal
Tom Marty
Tejas Kasetty
The rapid adaptation ability of auto-regressive foundation models is often attributed to the diversity of their pre-training data. This is b… (see more)ecause, from a Bayesian standpoint, minimizing prediction error in such settings requires integrating over all plausible latent hypotheses consistent with observations. While this behavior is desirable in principle, it often proves too ambitious in practice: under high ambiguity, the number of plausible latent alternatives makes Bayes-optimal prediction computationally intractable. Cognitive science has long recognized this limitation, suggesting that under such conditions, heuristics or information-seeking strategies are preferable to exhaustive inference. Translating this insight to next-token prediction, we hypothesize that low- and high-ambiguity predictions pose different computational demands, making ambiguity-agnostic next-token prediction a detrimental inductive bias. To test this, we introduce MetaHMM, a synthetic sequence meta-learning benchmark with rich compositional structure and a tractable Bayesian oracle. We show that Transformers indeed struggle with high-ambiguity predictions across model sizes. Motivated by cognitive theories, we propose a method to convert pre-trained models into Monte Carlo predictors that decouple task inference from token prediction. Preliminary results show substantial gains in ambiguous contexts through improved capacity allocation and test-time scalable inference, though challenges remain.
Tracing the representation geometry of language models from pretraining to post-training
Melody Zixuan Li
Kumar Krishna Agrawal
Arna Ghosh
Komal Kumar Teru
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.
Generalizable, real-time neural decoding with hybrid state-space models
Avery Hee-Woon Ryoo
Nanda H Krishna
Ximeng Mao
Mehdi Azabou
Eva L Dyer
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.
Generalizable, real-time neural decoding with hybrid state-space models
Avery Hee-Woon Ryoo
Nanda H Krishna
Ximeng Mao
Mehdi Azabou
Eva L Dyer
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.
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
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.
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
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.
Bidirectional Information Flow (BIF) - A Sample Efficient Hierarchical Gaussian Process for Bayesian Optimization
Juan David Guerra
Thomas Garbay
Hierarchical Gaussian Process (H-GP) models divide problems into different subtasks, allowing for different models to address each part, mak… (see more)ing them well-suited for problems with inherent hierarchical structure. However, typical H-GP models do not fully take advantage of this structure, only sending information up or down the hierarchy. This one-way coupling limits sample efficiency and slows convergence. We propose Bidirectional Information Flow (BIF), an efficient H-GP framework that establishes bidirectional information exchange between parent and child models in H-GPs for online training. BIF retains the modular structure of hierarchical models - the parent combines subtask knowledge from children GPs - while introducing top-down feedback to continually refine children models during online learning. This mutual exchange improves sample efficiency, enables robust training, and allows modular reuse of learned subtask models. BIF outperforms conventional H-GP Bayesian Optimization methods, achieving up to 85% and 5x higher
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.
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.