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

arXiv: https://arxiv.org/abs/2407.01687 · HTML: https://mlsanity.com/paper/2407.01687/

## Key facts

- Cited by 27 papers in the map (data through 14 Oct 2026).
- Placed in Prompting and chain-of-thought reasoning, one of 17 directions in LLM reasoning.
- Builds on 10 of its 52 references that are in the map.
- First posted on arXiv 1 Jul 2024.

## Placed in

- LLM reasoning / [Prompting and chain-of-thought reasoning](https://mlsanity.com/lr/prompting-and-chain-of-thought-reasoning/)

## Builds on (most cited first, 10 of 10)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Measuring Faithfulness in Chain-of-Thought Reasoning](https://mlsanity.com/paper/2307.13702/) (2023)
- [FOLIO: Natural Language Reasoning with First-Order Logic](https://mlsanity.com/paper/2209.00840/) (2022)
- [Embers of Autoregression: Understanding Large Language Models Through the Problem They are Trained to Solve](https://mlsanity.com/paper/2309.13638/) (2023)
- [Text and Patterns: For Effective Chain of Thought, It Takes Two to Tango](https://mlsanity.com/paper/2209.07686/) (2022)
- [What and How does In-Context Learning Learn? Bayesian Model Averaging, Parameterization, and Generalization](https://mlsanity.com/paper/2305.19420/) (2023)
- [Chain of Thoughtlessness? An Analysis of CoT in Planning](https://mlsanity.com/paper/2405.04776/) (2024)
- [Functional Benchmarks for Robust Evaluation of Reasoning Performance, and the Reasoning Gap](https://mlsanity.com/paper/2402.19450/) (2024)
- [Analyzing Chain-of-Thought Prompting in Large Language Models via Gradient-based Feature Attributions](https://mlsanity.com/paper/2307.13339/) (2023)
- [Pelican Soup Framework: A Theoretical Framework for Language Model Capabilities](https://mlsanity.com/paper/2402.10424/) (2024)

## Built on by (most cited first, 27 of 27)

- [On Memorization of Large Language Models in Logical Reasoning](https://mlsanity.com/paper/2410.23123/) (2024)
- [Unveiling the Key Factors for Distilling Chain-of-Thought Reasoning](https://mlsanity.com/paper/2502.18001/) (2025)
- [Evaluating the Robustness of Analogical Reasoning in Large Language Models](https://mlsanity.com/paper/2411.14215/) (2024)
- [When a language model is optimized for reasoning, does it still show embers of autoregression? An analysis of OpenAI o1](https://mlsanity.com/paper/2410.01792/) (2024)
- [Large Language Models and Mathematical Reasoning Failures](https://mlsanity.com/paper/2502.11574/) (2025)
- [The Reasoning-Memorization Interplay in Language Models Is Mediated by a Single Direction](https://mlsanity.com/paper/2503.23084/) (2025)
- [Chain-of-Thought Prompting Obscures Hallucination Cues in Large Language Models: An Empirical Evaluation](https://mlsanity.com/paper/2506.17088/) (2025)
- [MathGAP: Out-of-Distribution Evaluation on Problems with Arbitrarily Complex Proofs](https://mlsanity.com/paper/2410.13502/) (2024)
- [Beyond Math: Stories as a Testbed for Memorization-Constrained Reasoning in LLMs](https://mlsanity.com/paper/2412.14368/) (2024)
- [Compositional Generalization from Learned Skills via CoT Training: A Theoretical and Structural Analysis for Reasoning](https://mlsanity.com/paper/2502.04667/) (2025)
- [ProRefine: Inference-Time Prompt Refinement with Textual Feedback](https://mlsanity.com/paper/2506.05305/) (2025)
- [Can Textual Reasoning Improve the Performance of MLLMs on Fine-grained Visual Classification?](https://mlsanity.com/paper/2601.06993/) (2026)
- [Chain-of-Thought in Large Language Models: Decoding, Projection, and Activation](https://mlsanity.com/paper/2412.03944/) (2024)
- [None of the Others: a General Technique to Distinguish Reasoning from Memorization in Multiple-Choice LLM Evaluation Benchmarks](https://mlsanity.com/paper/2502.12896/) (2025)
- [Ask-Before-Detection: Identifying and Mitigating Conformity Bias in LLM-Powered Error Detector for Math Word Problem Solutions](https://mlsanity.com/paper/2412.16838/) (2024)
- [CoT-ICL Lab: A Synthetic Framework for Studying Chain-of-Thought Learning from In-Context Demonstrations](https://mlsanity.com/paper/2502.15132/) (2025)
- [The Hitchhiker's Guide to Program Analysis, Part II: Deep Thoughts by LLMs](https://mlsanity.com/paper/2504.11711/) (2025)
- [Identifying and Mitigating the Influence of the Prior Distribution in Large Language Models](https://mlsanity.com/paper/2504.12585/) (2025)
- [Active Prompt Tuning Enables Gpt-40 To Do Efficient Classification Of Microscopy Images](https://mlsanity.com/paper/2411.02639/) (2024)
- [Function Induction and Task Generalization: An Interpretability Study with Off-by-One Addition](https://mlsanity.com/paper/2507.09875/) (2025)
- [Task Complexity Matters: An Empirical Study of Reasoning in LLMs for Sentiment Analysis](https://mlsanity.com/paper/2602.24060/) (2026)
- [Semantic Deception: When Reasoning Models Can't Compute an Addition](https://mlsanity.com/paper/2512.20812/) (2025)
- [On the Thinking-Language Modeling Gap in Large Language Models](https://mlsanity.com/paper/2505.12896/) (2025)
- [Engineering Sentience](https://mlsanity.com/paper/2506.20504/) (2025)
- [Chart-RL: Policy Optimization Reinforcement Learning for Enhanced Visual Reasoning in Chart Question Answering with Vision Language Models](https://mlsanity.com/paper/2604.03157/) (2026)
- [Strategy-Induct: Task-Level Strategy Induction for Instruction Generation](https://mlsanity.com/paper/2605.20924/) (2026)
- [Anthropomorphism in the age of Large Language Models: An overview of potential risks and mitigations](https://mlsanity.com/paper/2609.38486/) (2026)

## Abstract (arXiv)

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