Chain and Causal Attention for Efficient Entity Tracking

TL;DR

This paper introduces a novel attention mechanism that enables efficient entity tracking in large language models, reducing the number of layers needed while maintaining performance and revealing structured internal representations.

Contribution

We propose a new attention mechanism that allows entity tracking with a single layer, addressing the theoretical limitations of transformers and improving efficiency.

Findings

Significant improvements on entity tracking datasets

Achieves comparable performance with fewer layers

Reveals structured internal attention representations

Abstract

This paper investigates the limitations of transformers for entity-tracking tasks in large language models. We identify a theoretical constraint, showing that transformers require at least $\log_2 (n+1)$ layers to handle entity tracking with $n$ state changes. To address this issue, we propose an efficient and frugal enhancement to the standard attention mechanism, enabling it to manage long-term dependencies more efficiently. By considering attention as an adjacency matrix, our model can track entity states with a single layer. Empirical results demonstrate significant improvements in entity tracking datasets while keeping competitive performance on standard natural language modeling. Our modified attention allows us to achieve the same performance with drastically fewer layers. Additionally, our enhanced mechanism reveals structured internal representations of attention. Extensive experiments on both toy and complex datasets validate our approach. Our contributions include theoretical insights, an improved attention mechanism, and empirical validation.