The Path of Least Resistance: Guiding LLM Reasining Trajectories with Prefix Consensus

TL;DR

This paper addresses the high compute cost of Self-Consistency (SC) decoding in multi-step reasoning by introducing PoLR, a training-free inference-time method that exploits prefix consistency. PoLR samples short prefixes of length $L_p$, embeds and clusters them with lightweight TF–IDF features, identifies the dominant cluster $C^*$, and expands only the $K$ prefixes in that cluster to full traces for final voting, drastically reducing token usage. Theoretical justification links efficiency to structural skew and correctness alignment via mutual information, and empirical results show PoLR achieves 40–60% token savings and up to 50% wall-clock latency reductions while maintaining or improving accuracy across GSM8K, Math500, AIME, GPQA-Diamond, and StrategyQA, with robustness across models, clustering methods, and prefix lengths. PoLR also complements adaptive inference methods (AC, ESC), serving as an effective pre-filter that enhances scalability without requiring model fine-tuning, making high-quality reasoning more practical for real-world deployment.

Abstract

Large language models achieve strong reasoning performance, but inference strategies such as Self-Consistency (SC) are computationally expensive, as they fully expand all reasoning traces. We introduce PoLR (Path of Least Resistance), the first inference-time method to leverage prefix consistency for compute-efficient reasoning. PoLR clusters short prefixes of reasoning traces, identifies the dominant cluster, and expands all paths in that cluster, preserving the accuracy benefits of SC while substantially reducing token usage and latency. Our theoretical analysis, framed via mutual information and entropy, explains why early reasoning steps encode strong signals predictive of final correctness. Empirically, PoLR consistently matches or exceeds SC across GSM8K, MATH500, AIME24/25, and GPQA-DIAMOND, reducing token usage by up to 60% and wall-clock latency by up to 50%. Moreover, PoLR is fully complementary to adaptive inference methods (e.g., Adaptive Consistency, Early-Stopping SC) and can serve as a drop-in pre-filter, making SC substantially more efficient and scalable without requiring model fine-tuning.

Figures (5)

• Figure 1: (a) Comparison of Self-Consistency (SC) and PoLR. Top: SC expands all $N$ sampled traces to completion (100% expansion), then aggregates answers via majority vote. Bottom: PoLR first generates $N$ short prefixes of length $L_p$, embeds and clusters them, and selects the dominant cluster. All $K \ll N$ traces from this cluster are expanded, after which majority voting is applied. (b) PoLR exceeds SC accuracy, while reducing token cost by approx 50%.
• Figure 2: Impact of different cluster threshold selection.
• Figure 3: Efficiency gains of PoLR across three models on GSM8K as a function of prefix length. All models achieve over 50% token savings by 256-512 prefix tokens.
• Figure 4: Performance comparison of PoLR versus SC across datasets (GSM8K, Math500, AIME24, AIME25, GPQA-Diamond) and model sizes. The table shows accuracy differences (green = improvement, red = drop), token efficiency $\eta$ (%), and sample size $N$ as a function of different prefix lengths $L_p$.
• Figure 5: Cluster-wise self-consistency for (GSM8K, Math500, AIME24, AIME25, GPQA-Diamond) datasets with different model sizes.

Theorems & Definitions (2)

• Proposition 1
• proof : Sketch