# Process In-Context Learning: Enhancing Mathematical Reasoning via Dynamic Demonstration Insertion

arXiv: https://arxiv.org/abs/2601.11979 · HTML: https://mlsanity.com/paper/2601.11979/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 9 of its 46 references that are in the map.
- First posted on arXiv 17 Jan 2026.

## Placed in

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

## Builds on (most cited first, 9 of 9)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [WebGPT: Browser-assisted question-answering with human feedback](https://mlsanity.com/paper/2112.09332/) (2021)
- [Beyond the 80/20 Rule: High-Entropy Minority Tokens Drive Effective Reinforcement Learning for LLM Reasoning](https://mlsanity.com/paper/2506.01939/) (2025)
- [WebThinker: Empowering Large Reasoning Models with Deep Research Capability](https://mlsanity.com/paper/2504.21776/) (2025)
- [In-context Example Selection with Influences](https://mlsanity.com/paper/2302.11042/) (2023)
- [The Curse of CoT: On the Limitations of Chain-of-Thought in In-Context Learning](https://mlsanity.com/paper/2504.05081/) (2025)
- [Revisiting Chain-of-Thought Prompting: Zero-shot Can Be Stronger than Few-shot](https://mlsanity.com/paper/2506.14641/) (2025)
- [RefCritic: Training Long Chain-of-Thought Critic Models with Refinement Feedback](https://mlsanity.com/paper/2507.15024/) (2025)

## Built on by (most cited first, 1 of 1)

- [LLMs with in-context learning for Algorithmic Theoretical Physics](https://mlsanity.com/paper/2605.08212/) (2026)

## Abstract (arXiv)

In-context learning (ICL) has proven highly effective across diverse large language model (LLM) tasks. However, its potential for enhancing tasks that demand step-by-step logical deduction, such as mathematical reasoning, remains underexplored. A core limitation of existing ICL approaches is their static use of demonstrations: examples are pre-selected before inference and remain fixed, failing to adapt to the dynamic confusion points that often arise during multi-step reasoning such as ambiguous calculations or logical gaps. These unresolved confusion points can lead to cascading errors that degrade final accuracy. To tackle this issue, we propose Process In-Context Learning (PICL), a dynamic demonstration integration framework designed to boost mathematical reasoning by responding to real-time inference needs. PICL operates in two stages: 1)~it identifies potential confusion points by analyzing semantics and entropy in the reasoning process and summarizes their core characteristics; 2)~upon encountering these points, it retrieves relevant demonstrations from the demonstration pool that match the confusion context and inserts them directly into the ongoing reasoning process to guide subsequent steps. Experiments show that PICL outperforms baseline methods by mitigating mid-inference confusion, highlighting the value of adaptive demonstration insertion in complex mathematical reasoning.