Bayesian Test-Time Inference of Task-Aligned Similarity from Weak Interactive Feedback

Abstract:Language model systems repeatedly make test-time decisions by comparing similarity: they retrieve exemplars, rank candidates, and revise responses. Yet similarity is not unique: lexical, semantic, structural, and stylistic resemblance can point to different candidates, and the task-aligned notion can change across instances. We introduce BASIS (Bayesian Axis Selection via Interactive Signals), a training-free Bayesian method that uses weak test-time feedback to infer which criterion in a supplied, task-specific library governs the current decision. It maintains a joint posterior over candidate targets and criteria, updates it from scalar scores, pairwise preferences, or verifier outputs, and selects probes by expected information gain. In a finite noisy model, we characterize when the target-criterion pair is recoverable and show why fixed-criterion and fixed-mixture rules can fail under criterion shift. Across concept recovery, reasoning exemplar selection, and response refinement, BASIS improves six-probe concept-recovery Success@1 from 56.0% to 68.1%, reasoning accuracy from 72.3% to 73.1%, and refinement win rate from 61.4% to 63.8% over tuned static mixtures. It also exceeds compute-matched best-of-N selection on reasoning (72.1%) and refinement (61.2%). Gains are largest under criterion mismatch and with larger candidate pools, and matched controls indicate that adaptive criterion weighting explains much of the benefit, with joint target-criterion inference adding further value. BASIS selects only among supplied criteria and does not discover new ones.

Accepted at NeurIPS 2026. 10 pages main text, 25 pages total including appendix; 4 figures, 15 tables

Machine Learning (cs.LG); Computation and Language (cs.CL)

arXiv:2610.18656 [cs.LG]

(or arXiv:2610.18656v1 [cs.LG] for this version)

https://doi.org/10.48550/arXiv.2610.18656 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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