CAPS: Cascaded Adaptive Pairwise Selection for Efficient Parallel Reasoning

2026-05-15

AI Summary

This work addresses the high computational cost of traditional pairwise verification methods in parallel inference, which require reading full solutions regardless of comparison efficacy. The authors propose a cascade-based adaptive pairwise selection framework exclusively for the inference phase, enabling, for the first time, non-uniform dynamic allocation of verifier resources across evidence depth and candidate distributions. The approach integrates a four-stage cascaded architecture, partial evidence verification, dynamic comparison scheduling, and a closed-form token cost model, augmented with an optional rescue subroutine. Evaluated across four self-verification models and five reasoning benchmarks, the method achieves superior performance to the strongest existing pairwise verification approach on 14 out of 20 test sets while using only 25.4% of the verifier’s token budget, and consistently outperforms pointwise self-verification.

Abstract

Parallel reasoning, where a generator samples many candidate solutions and an aggregator selects the best, is one of the most effective forms of test-time scaling in large language models, and pairwise self-verification has become its strongest aggregation primitive. Yet pairwise verification carries a heavy cost: each judgment reads two complete solutions in full, and existing methods perform tens of such judgments per problem regardless of whether the comparison is informative. We introduce CAPS (Cascaded Adaptive Pairwise Selection), an inference-only framework that allocates verifier compute non-uniformly along two orthogonal axes: an evidence axis that adapts how much of each candidate the judge sees, and a distribution axis that adapts how comparisons are spread across the pool. CAPS instantiates these into a four-stage cascade with an optional rescue subroutine, and admits a closed-form verifier-token cost in which the per-candidate marginal cost is roughly halved relative to uniform full-evidence schedules. On four self-verifying models (Qwen3-14B, GPT-OSS-20B, Qwen3-4B-Instruct/Thinking) and five reasoning benchmarks spanning code (LiveCodeBench-v5/v6, CodeContests) and math (AIME 2025, HMMT 2025), CAPS outperforms the leading pairwise verifier on 14 of 20 suites while using 25.4% of its verifier-token budget on code, and outperforms pointwise self-verification on all 20. The trade-off suites admit an interpretable diagnostic in terms of the verifier's accuracy at partial versus full evidence, providing a concrete pre-deployment check for cascade suitability.

Problem

• parallel reasoning
• pairwise self-verification
• verifier cost
• test-time scaling
• candidate selection

Innovation

• Cascaded Adaptive Pairwise Selection
• parallel reasoning
• pairwise self-verification
• verifier-token efficiency
• adaptive evidence allocation