Deciphering the Factors Influencing the Efficacy of Chain-of-Thought: Probability, Memorization, and Noisy Reasoning

TL;DR

This paper investigates how factors like output probability, memorization, and noisy reasoning influence the effectiveness of Chain-of-Thought prompting in large language models, revealing that performance depends on both learned patterns and probabilistic reasoning.

Contribution

It provides a detailed case study analyzing the impact of probability, memorization, and noise on CoT performance across multiple LLMs using a symbolic decoding task.

Findings

Performance varies with output probability, e.g., 26% to 70% accuracy in GPT-4.

CoT performance is affected by memorization and probabilistic reasoning.

Factors like task complexity and learned patterns significantly influence reasoning accuracy.

Abstract

Chain-of-Thought (CoT) prompting has been shown to enhance the multi-step reasoning capabilities of Large Language Models (LLMs). However, debates persist about whether LLMs exhibit abstract generalization or rely on shallow heuristics when given CoT prompts. To understand the factors influencing CoT reasoning we provide a detailed case study of the symbolic reasoning task of decoding shift ciphers, where letters are shifted forward some number of steps in the alphabet. We analyze the pattern of results produced by three LLMs -- GPT-4, Claude 3, and Llama 3.1 -- performing this task using CoT prompting. By focusing on a single relatively simple task, we are able to identify three factors that systematically affect CoT performance: the probability of the task's expected output (probability), what the model has implicitly learned during pre-training (memorization), and the number of intermediate operations involved in reasoning (noisy reasoning). We show that these factors can drastically influence task accuracy across all three LLMs; e.g., when tested with GPT-4, varying the output's probability of occurrence shifts accuracy from 26% to 70%. Overall, we conclude that CoT prompting performance reflects both memorization and a probabilistic version of genuine reasoning. Code and data at this https://github.com/aksh555/deciphering_cot