Understanding the Language Model to Solve the Symbolic Multi-Step Reasoning Problem from the Perspective of Buffer Mechanism

TL;DR

This paper investigates how Transformer-based language models perform multi-step symbolic reasoning by analyzing their internal buffer mechanisms and introduces a simple algorithm that significantly improves reasoning performance across multiple datasets.

Contribution

The study introduces the buffer mechanism concept and a novel random matrix-based algorithm that enhances reasoning ability with minimal additional parameters.

Findings

Significant performance improvements on 7 reasoning datasets

Buffer mechanism provides insights into internal reasoning processes

A simple 132-parameter algorithm boosts reasoning capabilities

Abstract

Large language models have consistently struggled with complex reasoning tasks, such as mathematical problem-solving. Investigating the internal reasoning mechanisms of these models can help us design better model architectures and training strategies, ultimately enhancing their reasoning capability. In this study, we constructed a symbolic multi-step reasoning task to investigate the information propagation mechanisms in Transformer models when solving the task through direct answering and Chain-of-Thought (CoT) reasoning. We introduced the concept of buffer mechanism: the model stores various information in distinct buffers and selectively extracts it through the query-key matrix. We proposed a random matrix-based algorithm to enhance the model's reasoning ability. This algorithm introduces only 132 trainable parameters, yet leads to significant performance improvements on 7 multi-step reasoning datasets, including PrOntoQA, LogicAsker, and LogicInference. These findings provide new insights into understanding the large language models.