# Precedent-Informed Reasoning: Mitigating Overthinking in Large Reasoning Models via Test-Time Precedent Learning

arXiv: https://arxiv.org/abs/2602.14451 · HTML: https://mlsanity.com/paper/2602.14451/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 15 of its 45 references that are in the map.
- First posted on arXiv 16 Feb 2026.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 15 of 15)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Stop Overthinking: A Survey on Efficient Reasoning for Large Language Models](https://mlsanity.com/paper/2503.16419/) (2025)
- [LightThinker: Thinking Step-by-Step Compression](https://mlsanity.com/paper/2502.15589/) (2025)
- [Adaptive Inference-Time Compute: LLMs Can Predict if They Can Do Better, Even Mid-Generation](https://mlsanity.com/paper/2410.02725/) (2024)
- [ThetaEvolve: Test-time Learning on Open Problems](https://mlsanity.com/paper/2511.23473/) (2025)
- [SpecReason: Fast and Accurate Inference-Time Compute via Speculative Reasoning](https://mlsanity.com/paper/2504.07891/) (2025)
- [Speculative Thinking: Enhancing Small-Model Reasoning with Large Model Guidance at Inference Time](https://mlsanity.com/paper/2504.12329/) (2025)
- [Test-Time Training on Video Streams](https://mlsanity.com/paper/2307.05014/) (2023)
- [ConCISE: Confidence-guided Compression in Step-by-step Efficient Reasoning](https://mlsanity.com/paper/2505.04881/) (2025)
- [Beyond Fast and Slow: Cognitive-Inspired Elastic Reasoning for Large Language Models](https://mlsanity.com/paper/2512.15089/) (2025)
- [Fine-Tuned In-Context Learners for Efficient Adaptation](https://mlsanity.com/paper/2512.19879/) (2025)

## Abstract (arXiv)

Reasoning in Large Language Models (LLMs) often suffers from inefficient long chain-of-thought traces with redundant self-exploration and validation, which inflate computational costs and even degrade performance. Inspired by human reasoning patterns where people solve new problems by leveraging past related cases to constrain search spaces and reduce trial-and-error, we propose Precedent Informed Reasoning (PIR) transforming LRMs'reasoning paradigm from exhaustive self-exploration to guided learning from precedents. PIR addresses two key challenges: what precedents to adopt and how to utilize them. First, Adaptive Precedent Selection (APS) constructs, for each question and LRM, a compact set of precedents that are both semantically related and informative for the model. It ranks examples by a joint score with semantic similarity and model perplexity, then adapts the amount of precedents to maximize perplexity reduction. Second, Test-time Experience Internalization (TEI) is treated as the test-time learning on precedent-informed instruction, updating lightweight adapters to internalize solution patterns and use them as a prior during subsequent reasoning. Experiments across mathematical reasoning, scientific QA, and code generation demonstrate that PIR consistently shortens reasoning traces while maintaining or improving final accuracy across LLMs, yielding outstanding accuracy-efficiency trade-offs.