Context Collapse: In-Context Learning and Model Collapse

TL;DR

This thesis explores in-context learning and model collapse in large language models, revealing phase transitions, the role of skew-symmetric components, and the impact of data growth on model stability.

Contribution

It provides theoretical analysis of ICL phase transitions and introduces the concept of context collapse, linking model dynamics with long-term stability issues.

Findings

Phase transition in in-context learning parameters at critical context length

Skew-symmetric components induce gradient rotation during ICL

Model collapse occurs unless data grows sufficiently fast or is retained

Abstract

This thesis investigates two key phenomena in large language models (LLMs): in-context learning (ICL) and model collapse. We study ICL in a linear transformer with tied weights trained on linear regression tasks, and show that minimising the in-context loss leads to a phase transition in the learned parameters. Above a critical context length, the solution develops a skew-symmetric component. We prove this by reducing the forward pass of the linear transformer under weight tying to preconditioned gradient descent, and then analysing the optimal preconditioner. This preconditioner includes a skew-symmetric component, which induces a rotation of the gradient direction. For model collapse, we use martingale and random walk theory to analyse simplified settings - linear regression and Gaussian fitting - under both replacing and cumulative data regimes. We strengthen existing results by proving almost sure convergence, showing that collapse occurs unless the data grows sufficiently fast or is retained over time. Finally, we introduce the notion of context collapse: a degradation of context during long generations, especially in chain-of-thought reasoning. This concept links the dynamics of ICL with long-term stability challenges in generative models.