# How and Why LLMs Generalize: A Fine-Grained Analysis of LLM Reasoning from Cognitive Behaviors to Low-Level Patterns

arXiv: https://arxiv.org/abs/2512.24063 · HTML: https://mlsanity.com/paper/2512.24063/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 29 of its 47 references that are in the map.
- First posted on arXiv 30 Dec 2025.

## Placed in

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

## Builds on (most cited first, 29 of 29)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Fine-Tuning Language Models from Human Preferences](https://mlsanity.com/paper/1909.08593/) (2019)
- [Beyond the Imitation Game: Quantifying and extrapolating the capabilities of language models](https://mlsanity.com/paper/2206.04615/) (2022)
- [LlamaFactory: Unified Efficient Fine-Tuning of 100+ Language Models](https://mlsanity.com/paper/2403.13372/) (2024)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Tulu 3: Pushing Frontiers in Open Language Model Post-Training](https://mlsanity.com/paper/2411.15124/) (2024)
- [SFT Memorizes, RL Generalizes: A Comparative Study of Foundation Model Post-training](https://mlsanity.com/paper/2501.17161/) (2025)
- [GSM-Symbolic: Understanding the Limitations of Mathematical Reasoning in Large Language Models](https://mlsanity.com/paper/2410.05229/) (2024)
- [Omni-MATH: A Universal Olympiad Level Mathematic Benchmark For Large Language Models](https://mlsanity.com/paper/2410.07985/) (2024)
- [DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning](https://mlsanity.com/paper/2504.11456/) (2025)
- [Can language models learn from explanations in context?](https://mlsanity.com/paper/2204.02329/) (2022)
- [GSM-Plus: A Comprehensive Benchmark for Evaluating the Robustness of LLMs as Mathematical Problem Solvers](https://mlsanity.com/paper/2402.19255/) (2024)
- [Llama-Nemotron: Efficient Reasoning Models](https://mlsanity.com/paper/2505.00949/) (2025)
- [Automatically Interpreting Millions of Features in Large Language Models](https://mlsanity.com/paper/2410.13928/) (2024)
- [Does Math Reasoning Improve General LLM Capabilities? Understanding Transferability of LLM Reasoning](https://mlsanity.com/paper/2507.00432/) (2025)
- [Revisiting Reinforcement Learning for LLM Reasoning from A Cross-Domain Perspective](https://mlsanity.com/paper/2506.14965/) (2025)
- [OMEGA: Can LLMs Reason Outside the Box in Math? Evaluating Exploratory, Compositional, and Transformative Generalization](https://mlsanity.com/paper/2506.18880/) (2025)
- [Large Language Models and Cognitive Science: A Comprehensive Review of Similarities, Differences, and Challenges](https://mlsanity.com/paper/2409.02387/) (2024)
- [RL Grokking Recipe: How Does RL Unlock and Transfer New Algorithms in LLMs?](https://mlsanity.com/paper/2509.21016/) (2025)
- [Climbing the Ladder of Reasoning: What LLMs Can-and Still Can't-Solve after SFT?](https://mlsanity.com/paper/2504.11741/) (2025)
- [From Scores to Skills: A Cognitive Diagnosis Framework for Evaluating Financial Large Language Models](https://mlsanity.com/paper/2508.13491/) (2025)

## Built on by (most cited first, 8 of 8)

- [Large Language Model Reasoning Failures](https://mlsanity.com/paper/2602.06176/) (2026)
- [Steer2Adapt: Dynamically Composing Steering Vectors Elicits Efficient Adaptation of LLMs](https://mlsanity.com/paper/2602.07276/) (2026)
- [Interactive Evaluation Requires a Design Science](https://mlsanity.com/paper/2605.17829/) (2026)
- [M2A: Synergizing Mathematical and Agentic Reasoning in Large Language Models](https://mlsanity.com/paper/2605.09879/) (2026)
- [Rethinking Psychometric Evaluation of LLMs: When and Why Self-Reports Predict Behavior](https://mlsanity.com/paper/2606.12730/) (2026)
- [Metacognitive Behavioral Tuning of Large Language Models for Multi-Hop Question Answering](https://mlsanity.com/paper/2602.22508/) (2026)
- [X-RAY: Mapping LLM Reasoning Capability via Formalized and Calibrated Probes](https://mlsanity.com/paper/2603.05290/) (2026)
- [When RL Suppresses Its Own Vocabulary: Recovering Reasoning Diversity in Puzzle-to-Math Transfer](https://mlsanity.com/paper/2605.29190/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) display strikingly different generalization behaviors: supervised fine-tuning (SFT) often narrows capability, whereas reinforcement-learning (RL) tuning tends to preserve it. The reasons behind this divergence remain unclear, as prior studies have largely relied on coarse accuracy metrics. We address this gap by introducing a novel benchmark that decomposes reasoning into atomic core skills such as calculation, fact retrieval, simulation, enumeration, and diagnostic, providing a concrete framework for addressing the fundamental question of what constitutes reasoning in LLMs. By isolating and measuring these core skills, the benchmark offers a more granular view of how specific cognitive abilities emerge, transfer, and sometimes collapse during post-training. Combined with analyses of low-level statistical patterns such as distributional divergence and parameter statistics, it enables a fine-grained study of how generalization evolves under SFT and RL across mathematical, scientific reasoning, and non-reasoning tasks. Our meta-probing framework tracks model behavior at different training stages and reveals that RL-tuned models maintain more stable behavioral profiles and resist collapse in reasoning skills, whereas SFT models exhibit sharper drift and overfit to surface patterns. This work provides new insights into the nature of reasoning in LLMs and points toward principles for designing training strategies that foster broad, robust generalization.