# On Memorization of Large Language Models in Logical Reasoning

arXiv: https://arxiv.org/abs/2410.23123 · HTML: https://mlsanity.com/paper/2410.23123/

## Key facts

- Cited by 117 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 70 of its 88 references that are in the map.
- First posted on arXiv 30 Oct 2024.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 30 of 70)

- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Scaling Instruction-Finetuned Language Models](https://mlsanity.com/paper/2210.11416/) (2022)
- [The Pile: An 800GB Dataset of Diverse Text for Language Modeling](https://mlsanity.com/paper/2101.00027/) (2020)
- [Extracting Training Data from Large Language Models](https://mlsanity.com/paper/2012.07805/) (2020)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Calibrate Before Use: Improving Few-Shot Performance of Language Models](https://mlsanity.com/paper/2102.09690/) (2021)
- [STaR: Bootstrapping Reasoning With Reasoning](https://mlsanity.com/paper/2203.14465/) (2022)
- [Adversarial NLI: A New Benchmark for Natural Language Understanding](https://mlsanity.com/paper/1910.14599/) (2019)
- [Quantifying Memorization Across Neural Language Models](https://mlsanity.com/paper/2202.07646/) (2022)
- [Distilling Step-by-Step! Outperforming Larger Language Models with Less Training Data and Smaller Model Sizes](https://mlsanity.com/paper/2305.02301/) (2023)
- [Deduplicating Training Data Makes Language Models Better](https://mlsanity.com/paper/2107.06499/) (2021)
- [Designing and Interpreting Probes with Control Tasks](https://mlsanity.com/paper/1909.03368/) (2019)
- [Grokking: Generalization Beyond Overfitting on Small Algorithmic Datasets](https://mlsanity.com/paper/2201.02177/) (2022)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [DecodingTrust: A Comprehensive Assessment of Trustworthiness in GPT Models](https://mlsanity.com/paper/2306.11698/) (2023)
- [Faith and Fate: Limits of Transformers on Compositionality](https://mlsanity.com/paper/2305.18654/) (2023)
- [The Instruction Hierarchy: Training LLMs to Prioritize Privileged Instructions](https://mlsanity.com/paper/2404.13208/) (2024)
- [What you can cram into a single vector: Probing sentence embeddings for linguistic properties](https://mlsanity.com/paper/1805.01070/) (2018)
- [Logic-LM: Empowering Large Language Models with Symbolic Solvers for Faithful Logical Reasoning](https://mlsanity.com/paper/2305.12295/) (2023)
- [Detecting Pretraining Data from Large Language Models](https://mlsanity.com/paper/2310.16789/) (2023)
- [Language Models Are Greedy Reasoners: A Systematic Formal Analysis of Chain-of-Thought](https://mlsanity.com/paper/2210.01240/) (2022)
- [Large Language Models Are Reasoning Teachers](https://mlsanity.com/paper/2212.10071/) (2022)
- [Large Language Models are Better Reasoners with Self-Verification](https://mlsanity.com/paper/2212.09561/) (2022)
- [Analyzing Leakage of Personally Identifiable Information in Language Models](https://mlsanity.com/paper/2302.00539/) (2023)
- [Transformers as Soft Reasoners over Language](https://mlsanity.com/paper/2002.05867/) (2020)
- [Reasoning or Reciting? Exploring the Capabilities and Limitations of Language Models Through Counterfactual Tasks](https://mlsanity.com/paper/2307.02477/) (2023)
- [Deep learning: a statistical viewpoint](https://mlsanity.com/paper/2103.09177/) (2021)
- [Data Contamination: From Memorization to Exploitation](https://mlsanity.com/paper/2203.08242/) (2022)
- [From Explicit CoT to Implicit CoT: Learning to Internalize CoT Step by Step](https://mlsanity.com/paper/2405.14838/) (2024)

## Built on by (most cited first, 30 of 117)

- [Towards Reasoning Era: A Survey of Long Chain-of-Thought for Reasoning Large Language Models](https://mlsanity.com/paper/2503.09567/) (2025)
- [ZebraLogic: On the Scaling Limits of LLMs for Logical Reasoning](https://mlsanity.com/paper/2502.01100/) (2025)
- [MATH-Perturb: Benchmarking LLMs' Math Reasoning Abilities against Hard Perturbations](https://mlsanity.com/paper/2502.06453/) (2025)
- [AceReason-Nemotron: Advancing Math and Code Reasoning through Reinforcement Learning](https://mlsanity.com/paper/2505.16400/) (2025)
- [Segment Policy Optimization: Effective Segment-Level Credit Assignment in RL for Large Language Models](https://mlsanity.com/paper/2505.23564/) (2025)
- [LLM-SRBench: A New Benchmark for Scientific Equation Discovery with Large Language Models](https://mlsanity.com/paper/2504.10415/) (2025)
- [Can Large Reasoning Models Self-Train?](https://mlsanity.com/paper/2505.21444/) (2025)
- [Blending Supervised and Reinforcement Fine-Tuning with Prefix Sampling](https://mlsanity.com/paper/2507.01679/) (2025)
- [Understanding Aha Moments: from External Observations to Internal Mechanisms](https://mlsanity.com/paper/2504.02956/) (2025)
- [SynLogic: Synthesizing Verifiable Reasoning Data at Scale for Learning Logical Reasoning and Beyond](https://mlsanity.com/paper/2505.19641/) (2025)
- [RLVE: Scaling Up Reinforcement Learning for Language Models with Adaptive Verifiable Environments](https://mlsanity.com/paper/2511.07317/) (2025)
- [DUMP: Automated Distribution-Level Curriculum Learning for RL-based LLM Post-training](https://mlsanity.com/paper/2504.09710/) (2025)
- [Do Not Let Low-Probability Tokens Over-Dominate in RL for LLMs](https://mlsanity.com/paper/2505.12929/) (2025)
- [Recent Advances in Large Langauge Model Benchmarks against Data Contamination: From Static to Dynamic Evaluation](https://mlsanity.com/paper/2502.17521/) (2025)
- [The Avengers: A Simple Recipe for Uniting Smaller Language Models to Challenge Proprietary Giants](https://mlsanity.com/paper/2505.19797/) (2025)
- [LLMRouterBench: A Massive Benchmark and Unified Framework for LLM Routing](https://mlsanity.com/paper/2601.07206/) (2026)
- [Reinforcement-aware Knowledge Distillation for LLM Reasoning](https://mlsanity.com/paper/2602.22495/) (2026)
- [One-shot Entropy Minimization](https://mlsanity.com/paper/2505.20282/) (2025)
- [Is It Thinking or Cheating? Detecting Implicit Reward Hacking by Measuring Reasoning Effort](https://mlsanity.com/paper/2510.01367/) (2025)
- [Shorten After You're Right: Lazy Length Penalties for Reasoning RL](https://mlsanity.com/paper/2505.12284/) (2025)
- [The Reasoning-Memorization Interplay in Language Models Is Mediated by a Single Direction](https://mlsanity.com/paper/2503.23084/) (2025)
- [Language Mixing in Reasoning Language Models: Patterns, Impact, and Internal Causes](https://mlsanity.com/paper/2505.14815/) (2025)
- [Interleaved Reasoning for Large Language Models via Reinforcement Learning](https://mlsanity.com/paper/2505.19640/) (2025)
- [Copyright Protection for Large Language Models: A Survey of Methods, Challenges, and Trends](https://mlsanity.com/paper/2508.11548/) (2025)
- [ABench-Physics: Benchmarking Physical Reasoning in LLMs via High-Difficulty and Dynamic Physics Problems](https://mlsanity.com/paper/2507.04766/) (2025)
- [Dissecting Logical Reasoning in LLMs: A Fine-Grained Evaluation and Supervision Study](https://mlsanity.com/paper/2506.04810/) (2025)
- [Can One Domain Help Others? A Data-Centric Study on Multi-Domain Reasoning via Reinforcement Learning](https://mlsanity.com/paper/2507.17512/) (2025)
- [Data Mixing Can Induce Phase Transitions in Knowledge Acquisition](https://mlsanity.com/paper/2505.18091/) (2025)
- [Proximal Supervised Fine-Tuning](https://mlsanity.com/paper/2508.17784/) (2025)
- [DRPO: Efficient Reasoning via Decoupled Reward Policy Optimization](https://mlsanity.com/paper/2510.04474/) (2025)

## Abstract (arXiv)

Large language models (LLMs) achieve good performance on challenging reasoning benchmarks, yet could also make basic reasoning mistakes. This contrasting behavior is puzzling when it comes to understanding the mechanisms behind LLMs' reasoning capabilities. One hypothesis is that the increasingly high and nearly saturated performance on common reasoning benchmarks could be due to the memorization of similar problems. In this paper, we systematically investigate this hypothesis with a quantitative measurement of memorization in reasoning tasks, using a dynamically generated logical reasoning benchmark based on Knights and Knaves (K&K) puzzles. We find that LLMs could interpolate and memorize the training puzzles (achieving near-perfect accuracy) after fine-tuning, yet they struggle with slight variations of these puzzles. On the other hand, we show that while fine-tuning leads to heavy memorization, it also consistently improves generalization performance. Through in-depth analyses with perturbation tests, cross difficulty-level transferability, probing model internals, and fine-tuning with wrong answers, we establish that LLMs develop reasoning skills on K&K puzzles alongside memorization. Finally, our analysis based on a per-sample memorization score sheds light on how LLMs switch between reasoning and memorization when solving logical puzzles. Our code and data are available at https://memkklogic.github.io.