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

TL;DR

This paper introduces PICL, a dynamic framework that improves mathematical reasoning in large language models by adaptively inserting relevant demonstrations during inference to address confusion points and reduce errors.

Contribution

It proposes a novel dynamic demonstration insertion method that responds to real-time reasoning challenges, enhancing LLM performance on mathematical tasks.

Findings

PICL outperforms static ICL baselines in mathematical reasoning tasks.

Adaptive demonstration insertion reduces cascading errors during inference.

PICL effectively identifies and addresses confusion points in real-time.

Abstract

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.