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

Weida Liang, Kenji Kawaguchi

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…