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Joint Consistency: A Unified Test-Time Aggregation Framework via Energy Minimization

NeurIPS 2026 · Large language models › Reasoning and chain of thought · approach: Test-time compute scaling · 0 citations (OpenAlex)

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Proposes Joint Consistency, a constrained Ising-type energy minimization over answer groups that combines independent LLM-judge scores (external field) with LLM-judge pairwise comparisons (interaction matrix) for test-time aggregation, reporting gains on MathArena, AIME 2025 and CruxEval-O.

Problem

Test-time aggregation of multiple reasoning traces into one answer is typically done via voting or isolated trace scores, ignoring comparative interactions among candidates, and naive all-pair comparison costs O(N^2).

Approach

Formulate aggregation as a constrained Ising energy minimization where independent judge scores are external fields and pairwise LLM-judge preferences form a PSD interaction matrix J = CC^T; the objective subsumes SC/WSC (J=0) and, under answer-level homogeneity, reduces to answer-level preference aggregation, enabling answer-group-level approximation.

Key results

• On MathArena-Full AIME 2025 with N=120 traces, JC reaches 96.6% vs 96.6% WSC and 94.3% SC; on HMMT 2025 (Feb) with N=120 JC reaches 99.8% vs 99.7% WSC.
• On AIME 2025 with DS-R1-8B judge, JC improves over WSC by up to 7.3 points (e.g., 84.1 vs 76.8 on Qwen3-8B traces).
• On CruxEval-O with N=24 traces, JC reaches 80.5% vs 78.1% for the strongest baseline WSC.

Surprising findings

• KT performs far worse than even Pass@1 on MathArena-Full (e.g., 23.4% on BRUMO N=24), suggesting knockout elimination discards correct candidates.
• Naive power-based variants of J (tau>1) do not consistently improve over tau=1 for larger N.

Limitations

• Focuses on final-answer aggregation for reasoning tasks; generalization to open-ended or research-level problems is unclear.
• The interaction-matrix construction is theoretically motivated but not claimed to be optimal.
• Method may inherit limitations and risks of generation and judge models.

Experimental setup

Datasets: MathArena CruxEval-O

Benchmarks: AIME 2025 HMMT 2025 (Feb) HMMT 2025 (Nov) BRUMO 2025 CruxEval-O

Metrics: accuracy

Baselines: Pass@1 Best-of-N Self-Consistency Weighted Self-Consistency Knockout Tournament Self-Certainty DeepConf

Builds on: Self-Consistency Weighted Self-Consistency Knockout Tournament Self-Certainty DeepConf

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