Arna Ghosh

Tracing the Representation Geometry of Language Models from Pretraining to Post-training

Melody Zixuan Li

Komal K. Teru

Adam Santoro

Guillaume Lajoie

Blake A. Richards

Standard training metrics like loss fail to explain the emergence of complex capabilities in large language models. We take a spectral appro… (see more)ach to investigate the geometry of learned representations across pretraining and post-training, measuring effective rank (RankMe) and eigenspectrum decay (

2025-09-27

ArXiv (preprint)

Why all roads don't lead to Rome: Representation geometry varies across the human visual cortical hierarchy

Z. Chorghay

Shahab Bakhtiari

Biological and artificial intelligence systems navigate the fundamental efficiency-robustness tradeoff for optimal encoding, i.e., they must… (see more) efficiently encode numerous attributes of the input space while also being robust to noise. This challenge is particularly evident in hierarchical processing systems like the human brain. With a view towards understanding how systems navigate the efficiency-robustness tradeoff, we turned to a population geometry framework for analyzing representations in the human visual cortex alongside artificial neural networks (ANNs). In the ventral visual stream, we found general-purpose, scale-free representations characterized by a power law-decaying eigenspectrum in most areas. However, in certain higher-order visual areas did not have scale-free representations, indicating that scale-free geometry is not a universal property of the brain. In parallel, ANNs trained with a self-supervised learning objective also exhibited free-free geometry, but not after fine-tune on a specific task. Based on these empirical results and our analytical insights, we posit that a system's representation geometry is not a universal property and instead depends upon the computational objective.

2025-09-16

ArXiv (preprint)

Why all roads don't lead to Rome: Representation geometry varies across the human visual cortical hierarchy

Z. Chorghay

Shahab Bakhtiari

2025-09-16

ArXiv (preprint)

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

Melody Zixuan Li

Adam Santoro

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)

Brain-like learning with exponentiated gradients

Jonathan Cornford

Roman Pogodin

Kaiwen Sheng

Brendan A. Bicknell

Olivier Codol

Beverley A. Clark

Guillaume Lajoie

2024-10-26

bioRxiv (preprint)

Harnessing small projectors and multiple views for efficient vision pretraining

2024-09-25

NeurIPS.cc/2024/Conference (poster)

Learning Successor Features the Simple Way

Christos Kaplanis

In Deep Reinforcement Learning (RL), it is a challenge to learn representations that do not exhibit catastrophic forgetting or interference … (see more)in non-stationary environments. Successor Features (SFs) offer a potential solution to this challenge. However, canonical techniques for learning SFs from pixel-level observations often lead to representation collapse, wherein representations degenerate and fail to capture meaningful variations in the data. More recent methods for learning SFs can avoid representation collapse, but they often involve complex losses and multiple learning phases, reducing their efficiency. We introduce a novel, simple method for learning SFs directly from pixels. Our approach uses a combination of a Temporal-difference (TD) loss and a reward prediction loss, which together capture the basic mathematical definition of SFs. We show that our approach matches or outperforms existing SF learning techniques in both 2D (Minigrid), 3D (Miniworld) mazes and Mujoco, for both single and continual learning scenarios. As well, our technique is efficient, and can reach higher levels of performance in less time than other approaches. Our work provides a new, streamlined technique for learning SFs directly from pixel observations, with no pretraining required.

2024-09-25

NeurIPS.cc/2024/Conference (poster)

Stochastic Wiring of Cell Types Enhances Fitness by Generating Phenotypic Variability

Divyansha Lachi

Ann Huang

Augustine N. Mavor-Parker

Anthony Zador

The development of neural connectivity is a crucial biological process that gives rise to diverse brain circuits and behaviors. Neural devel… (see more)opment is a stochastic process, but this stochasticity is often treated as a nuisance to overcome rather than as a functional advantage. Here we use a computational model, in which connection probabilities between discrete cell types are genetically specified, to investigate the benefits of stochasticity in the development of neural wiring. We show that this model can be viewed as a generalization of a powerful class of artificial neural networks—Bayesian neural networks—where each network parameter is a sample from a distribution. Our results reveal that stochasticity confers a greater benefit in large networks and variable environments, which may explain its role in organisms with larger brains. Surprisingly, we find that the average fitness over a population of agents is higher than a single agent defined by the average connection probability. Our model reveals how developmental stochasticity, by inducing a form of non-heritable phenotypic variability, can increase the probability that at least some individuals will survive in rapidly changing, unpredictable environments. Our results suggest how stochasticity may be an important feature rather than a bug in neural development.

2024-08-08

bioRxiv (preprint)

Synaptic Weight Distributions Depend on the Geometry of Plasticity

A growing literature in computational neuroscience leverages gradient descent and learning algorithms that approximate it to study synaptic … (see more)plasticity in the brain. However, the vast majority of this work ignores a critical underlying assumption: the choice of distance for synaptic changes - i.e. the geometry of synaptic plasticity. Gradient descent assumes that the distance is Euclidean, but many other distances are possible, and there is no reason that biology necessarily uses Euclidean geometry. Here, using the theoretical tools provided by mirror descent, we show that the distribution of synaptic weights will depend on the geometry of synaptic plasticity. We use these results to show that experimentally-observed log-normal weight distributions found in several brain areas are not consistent with standard gradient descent (i.e. a Euclidean geometry), but rather with non-Euclidean distances. Finally, we show that it should be possible to experimentally test for different synaptic geometries by comparing synaptic weight distributions before and after learning. Overall, our work shows that the current paradigm in theoretical work on synaptic plasticity that assumes Euclidean synaptic geometry may be misguided and that it should be possible to experimentally determine the true geometry of synaptic plasticity in the brain.

2024-01-16

ICLR.cc/2024/Conference (spotlight)

Addressing Sample Inefficiency in Multi-View Representation Learning

Shagun Sodhani

Adam M. Oberman

2024-01-01

NeurIPS (published)

Harnessing small projectors and multiple views for efficient vision pretraining

Recent progress in self-supervised (SSL) visual representation learning has led to the development of several different proposed frameworks … (see more)that rely on augmentations of images but use different loss functions. However, there are few theoretically grounded principles to guide practice, so practical implementation of each SSL framework requires several heuristics to achieve competitive performance. In this work, we build on recent analytical results to design practical recommendations for competitive and efficient SSL that are grounded in theory. Specifically, recent theory tells us that existing SSL frameworks are minimizing the same idealized loss, which is to learn features that best match the data similarity kernel defined by the augmentations used. We show how this idealized loss can be reformulated to a functionally equivalent loss that is more efficient to compute. We study the implicit bias of using gradient descent to minimize our reformulated loss function and find that using a stronger orthogonalization constraint with a reduced projector dimensionality should yield good representations. Furthermore, the theory tells us that approximating the reformulated loss should be improved by increasing the number of augmentations, and as such using multiple augmentations should lead to improved convergence. We empirically verify our findings on CIFAR, STL and Imagenet datasets, wherein we demonstrate an improved linear readout performance when training a ResNet-backbone using our theoretically grounded recommendations. Remarkably, we also demonstrate that by leveraging these insights, we can reduce the pretraining dataset size by up to 2

2023-12-17

ArXiv (preprint)