Information Structure in Mappings: An Approach to Learning, Representation, and Generalisation

TL;DR

This paper develops quantitative methods to analyze the structure of neural network representations, revealing how they learn, generalize, and relate to human cognition across various models and scales.

Contribution

It introduces novel techniques for identifying and quantifying structural primitives in neural mappings, enabling deeper understanding of learning and generalization.

Findings

Structural primitives correlate with model performance

Representation structures evolve during training

Language structures parallel neural network organization

Abstract

Despite the remarkable success of large large-scale neural networks, we still lack unified notation for thinking about and describing their representational spaces. We lack methods to reliably describe how their representations are structured, how that structure emerges over training, and what kinds of structures are desirable. This thesis introduces quantitative methods for identifying systematic structure in a mapping between spaces, and leverages them to understand how deep-learning models learn to represent information, what representational structures drive generalisation, and how design decisions condition the structures that emerge. To do this I identify structural primitives present in a mapping, along with information theoretic quantifications of each. These allow us to analyse learning, structure, and generalisation across multi-agent reinforcement learning models, sequence-to-sequence models trained on a single task, and Large Language Models. I also introduce a novel, performant, approach to estimating the entropy of vector space, that allows this analysis to be applied to models ranging in size from 1 million to 12 billion parameters. The experiments here work to shed light on how large-scale distributed models of cognition learn, while allowing us to draw parallels between those systems and their human analogs. They show how the structures of language and the constraints that give rise to them in many ways parallel the kinds of structures that drive performance of contemporary neural networks.