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

Test-time scaling improves the reasoning performance of large language models but often results in token-inefficient overthinking, where models continue reasoning beyond what is necessary for a correct answer. Existing dynamic early-exit methods typically rely on single-step confidence signals, which are often unreliable for detecting reasoning convergence in multi-step settings. To mitigate this limitation, we propose TRACE, a training-free framework for efficient test-time scaling that determines when to terminate reasoning based on temporal aggregation of multi-step evidence rather than instantaneous signals. TRACE detects reasoning convergence over time by aggregating two complementary signals across recent reasoning steps: answer consistency, capturing the persistence of predicted answers, and confidence trajectory, modeling the temporal evolution of model confidence. Benefiting from these two factors, TRACE can accurately determine whether the reasoning process has converged, thereby promptly halting inference and effectively avoiding redundant reasoning steps. Extensive experiments on multiple challenging benchmarks show that TRACE reduces reasoning token usage by 25-30% on average while maintaining accuracy within 1-2% of full-length reasoning, consistently outperforming existing dynamic reasoning methods.

Multi-agent systems (MAS) can substantially extend the reasoning capacity of large language models (LLMs). Most MAS frameworks aggregate agent outputs via simple majority voting, discarding the evidential structure of reasoning traces. Majority voting is brittle under confabulation consensus, where agents share correlated biases and converge on the same incorrect rationale. We introduce AgentAuditor, which moves beyond frequency-based aggregation by organizing agent traces into a Reasoning Tree that explicitly represents agreements and divergences in their reasoning. AgentAuditor resolves conflicts by comparing branch-level evidence at critical divergence points, turning global adjudication into efficient, localized verification. We further propose Anti-Consensus Preference Optimization (ACPO), which trains the adjudicator with evidence-verified preference supervision to reduce conformity to misleading majority cues. Across four MAS frameworks and multiple reasoning benchmarks, AgentAuditor consistently improves aggregation performance over majority voting, with gains of up to 5% absolute accuracy while remaining token-efficient.

Chain-of-thought (CoT) reasoning with self-consistency improves performance by aggregating multiple sampled reasoning paths. In this setting, correctness is no longer tied to a single reasoning trace but to the aggregation rule over a pool of candidate paths, making aggregation uncertainty the central challenge. This issue is critical where confidently incorrect answers are far more costly than abstentions. We introduce a conformal procedure for CoT reasoning that directly addresses aggregation uncertainty. Our approach replaces majority voting with weighted score aggregation over reasoning paths and calibrates an abstention rule using conformal risk control. This approach leads to finite-sample guarantees on the confident-error rate--the probability that the system answers and is wrong. We further identify score separability as the key condition under which abstention provably improves selective accuracy, and derive closed-form expressions that predict accuracy gains from calibration data alone. The method is fully inference-time, and requires no retraining. Across four benchmarks, four open-source models, and three score classes, realized confident-error rates are consistent with the prescribed targets up to calibration-split and test-set variability. Our method achieves $90.1\%$ selective accuracy on GSM8K by abstaining on less than $5\%$ of problems, compared with $82\%$ accuracy under majority-voting baseline.