Léo Gagnon

Eric Elmoznino, Tom Marty, Tejas Kasetty et al.

A central goal of machine learning is generalization. While the No Free Lunch Theorem states that we cannot obtain theoretical guarantees for 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.

Tom Marty, Eric Elmoznino, Leo Gagnon et al.

Deep neural networks exhibit a simplicity bias, a well-documented tendency to favor simple functions over complex ones. In this work, we cast new light on this phenomenon through the lens of the Minimum Description Length principle, formalizing supervised learning as a problem of optimal two-part lossless compression. Our theory explains how simplicity bias governs feature selection in neural networks through a fundamental trade-off between model complexity (the cost of describing the hypothesis) and predictive power (the cost of describing the data). Our framework predicts that as the amount of available training data increases, learners transition through qualitatively different features -- from simple spurious shortcuts to complex features -- only when the reduction in data encoding cost justifies the increased model complexity. Consequently, we identify distinct data regimes where increasing data promotes robustness by ruling out trivial shortcuts, and conversely, regimes where limiting data can act as a form of complexity-based regularization, preventing the learning of unreliable complex environmental cues. We validate our theory on a semi-synthetic benchmark showing that the feature selection of neural networks follows the same trajectory of solutions as optimal two-part compressors.

Sarthak Mittal, Leo Gagnon, Guillaume Lajoie

Frontier models have demonstrated exceptional capabilities following the integration of task-reward-based reinforcement learning (RL) into their training pipelines, enabling systems to evolve from pure reasoning models into sophisticated agents. However, debate persists regarding whether RL genuinely instills new skills within a base model or merely sharpens its existing distribution to elicit latent capabilities. To address this dichotomy, we present an explicit comparison between distribution sharpening and task-reward-based learning, utilizing RL as a tool to implement both paradigms. Our analysis reveals the inherent limitations of distribution sharpening, demonstrating from first principles how and why the optima can be unfavorable and the approach fundamentally unstable. Furthermore, our experiments using Llama-3.2-3B-Instruct, Qwen2.5-3B-Instruct and Qwen3-4B-Instruct-2507 on math datasets confirm that sharpening yields limited gains, whereas incorporating task-based reward signal can greatly help achieve robust performance improvements and stable learning.

Yinhan Lu, Eric Elmoznino, Léo Gagnon et al.

Causal Transformers model sequences through an autoregressive factorization of the joint distribution, which enables efficient left-to-right decoding and conditional likelihood computation. However, they cannot tractably sample from or evaluate arbitrary conditionals -- e.g., a block of text conditioned on past and future tokens. Recent work aims to solve this problem through novel architectures, but they often lead to sub-optimal modeling of such conditionals and degraded generations. We propose Arbitrary Conditionals GPT (AC-GPT) which introduces a simple modification to standard causal Transformers to enable evaluating and sampling from arbitrary conditionals -- including past, future, and mixed contexts -- within a single forward pass. Unlike prior approaches, our method preserves the standard left-to-right ordering and next-token prediction objective essential for both strong performance and efficient training on natural language. Crucially, this compatibility allows existing LLMs to be fine-tuned for arbitrary conditioning. Our empirical results indicate that our method outperforms baselines on modeling arbitrary conditionals, without degrading standard left-to-right performance.

Léo Gagnon, Guillaume Lajoie

The Energy-Based Model (EBM) framework is a very general approach to generative modeling that tries to learn and exploit probability distributions only defined though unnormalized scores. It has risen in popularity recently thanks to the impressive results obtained in image generation by parameterizing the distribution with Convolutional Neural Networks (CNN). However, the motivation and theoretical foundations behind modern EBMs are often absent from recent papers and this sometimes results in some confusion. In particular, the theoretical justifications behind the popular MCMC-based learning algorithm Contrastive Divergence (CD) are often glossed over and we find that this leads to theoretical errors in recent influential papers (Du & Mordatch, 2019; Du et al., 2020). After offering a first-principles introduction of MCMC-based training, we argue that the learning algorithm they use can in fact not be described as CD and reinterpret theirs methods in light of a new interpretation. Finally, we discuss the implications of our new interpretation and provide some illustrative experiments.

Christian David Márton, Léo Gagnon, Guillaume Lajoie et al.

Biological agents do not have infinite resources to learn new things. For this reason, a central aspect of human learning is the ability to recycle previously acquired knowledge in a way that allows for faster, less resource-intensive acquisition of new skills. In spite of that, how neural networks in the brain leverage existing knowledge to learn new computations is not well understood. In this work, we study this question in artificial recurrent neural networks (RNNs) trained on a corpus of commonly used neuroscience tasks. Combining brain-inspired inductive biases we call functional and structural, we propose a system that learns new tasks by building on top of pre-trained latent dynamics organised into separate recurrent modules. These modules, acting as prior knowledge acquired previously through evolution or development, are pre-trained on the statistics of the full corpus of tasks so as to be independent and maximally informative. The resulting model, we call a Modular Latent Primitives (MoLaP) network, allows for learning multiple tasks while keeping parameter counts, and updates, low. We also show that the skills acquired with our approach are more robust to a broad range of perturbations compared to those acquired with other multi-task learning strategies, and that generalisation to new tasks is facilitated. This work offers a new perspective on achieving efficient multi-task learning in the brain, illustrating the benefits of leveraging pre-trained latent dynamical primitives.