# CAPS: Cascaded Adaptive Pairwise Selection for Efficient Parallel Reasoning

arXiv: https://arxiv.org/abs/2605.15513 · HTML: https://mlsanity.com/paper/2605.15513/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning.
- Builds on 28 of its 58 references that are in the map.
- First posted on arXiv 15 May 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, 28 of 28)

- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [LiveCodeBench: Holistic and Contamination Free Evaluation of Large Language Models for Code](https://mlsanity.com/paper/2403.07974/) (2024)
- [Scaling LLM Test-Time Compute Optimally can be More Effective than Scaling Model Parameters](https://mlsanity.com/paper/2408.03314/) (2024)
- [gpt-oss-120b & gpt-oss-20b Model Card](https://mlsanity.com/paper/2508.10925/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [MathArena: Evaluating LLMs on Uncontaminated Math Competitions](https://mlsanity.com/paper/2505.23281/) (2025)
- [Universal Self-Consistency for Large Language Model Generation](https://mlsanity.com/paper/2311.17311/) (2023)
- [On the Self-Verification Limitations of Large Language Models on Reasoning and Planning Tasks](https://mlsanity.com/paper/2402.08115/) (2024)
- [Inference-Aware Fine-Tuning for Best-of-N Sampling in Large Language Models](https://mlsanity.com/paper/2412.15287/) (2024)
- [Scaling Test-Time Compute Without Verification or RL is Suboptimal](https://mlsanity.com/paper/2502.12118/) (2025)
- [Learning Adaptive Parallel Reasoning with Language Models](https://mlsanity.com/paper/2504.15466/) (2025)
- [The Majority is not always right: RL training for solution aggregation](https://mlsanity.com/paper/2509.06870/) (2025)
- [Recursive Self-Aggregation Unlocks Deep Thinking in Large Language Models](https://mlsanity.com/paper/2509.26626/) (2025)
- [Rethinking Thinking Tokens: LLMs as Improvement Operators](https://mlsanity.com/paper/2510.01123/) (2025)
- [V1: Unifying Generation and Self-Verification for Parallel Reasoners](https://mlsanity.com/paper/2603.04304/) (2026)
- [A Survey on Parallel Reasoning](https://mlsanity.com/paper/2510.12164/) (2025)
- [BibAgent: An Agentic Framework for Traceable Miscitation Detection in Scientific Literature](https://mlsanity.com/paper/2601.16993/) (2026)
- [Position: Human-Centric AI Requires a Minimum Viable Level of Human Understanding](https://mlsanity.com/paper/2602.00854/) (2026)
- [A Language Anchor-Guided Method for Robust Noisy Domain Generalization](https://mlsanity.com/paper/2503.17211/) (2025)
- [Traversal-as-Policy: Log-Distilled Gated Behavior Trees as Externalized, Verifiable Policies for Safe, Robust, and Efficient Agents](https://mlsanity.com/paper/2603.05517/) (2026)
- [KANMixer: a minimal KAN-centered mixer for long-term time series forecasting](https://mlsanity.com/paper/2508.01575/) (2025)
- [TimePre: Bridging Accuracy, Efficiency, and Stability in Probabilistic Time-Series Forecasting](https://mlsanity.com/paper/2511.18539/) (2025)
- [Let the Abyss Stare Back Adaptive Falsification for Autonomous Scientific Discovery](https://mlsanity.com/paper/2603.29045/) (2026)
- [AdaptFuse: Training-Free Sequential Preference Inference via Externalized Bayesian Computation](https://mlsanity.com/paper/2604.03925/) (2026)

## Built on by (most cited first, 2 of 2)

- [PathCal: State-Aware Reflection-Marker Calibration for Efficient Reasoning](https://mlsanity.com/paper/2605.23074/) (2026)
- [ROUTEAUDIT: Interaction-Aware Identification for Budgeted Multi-Verifier Routing](https://mlsanity.com/paper/2610.02808/) (2026)

## Abstract (arXiv)

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.