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

arXiv: https://arxiv.org/abs/2610.18656 · HTML: https://mlsanity.com/paper/2610.18656/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 31 references that are in the map.
- First posted on arXiv 13 Oct 2026.

## Builds on (most cited first, 22 of 22)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Retrieval-Augmented Generation for Knowledge-Intensive NLP Tasks](https://mlsanity.com/paper/2005.11401/) (2020)
- [Reflexion: Language Agents with Verbal Reinforcement Learning](https://mlsanity.com/paper/2303.11366/) (2023)
- [Training a Helpful and Harmless Assistant with Reinforcement Learning from Human Feedback](https://mlsanity.com/paper/2204.05862/) (2022)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Self-RAG: Learning to Retrieve, Generate, and Critique through Self-Reflection](https://mlsanity.com/paper/2310.11511/) (2023)
- [Challenging BIG-Bench Tasks and Whether Chain-of-Thought Can Solve Them](https://mlsanity.com/paper/2210.09261/) (2022)
- [ConceptNet 5.5: An Open Multilingual Graph of General Knowledge](https://mlsanity.com/paper/1612.03975/) (2016)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [CRITIC: Large Language Models Can Self-Correct with Tool-Interactive Critiquing](https://mlsanity.com/paper/2305.11738/) (2023)
- [Did Aristotle Use a Laptop? A Question Answering Benchmark with Implicit Reasoning Strategies](https://mlsanity.com/paper/2101.02235/) (2021)
- [OpenAssistant Conversations -- Democratizing Large Language Model Alignment](https://mlsanity.com/paper/2304.07327/) (2023)
- [Learning To Retrieve Prompts for In-Context Learning](https://mlsanity.com/paper/2112.08633/) (2021)
- [Rewarding Progress: Scaling Automated Process Verifiers for LLM Reasoning](https://mlsanity.com/paper/2410.08146/) (2024)
- [SimLex-999: Evaluating Semantic Models with (Genuine) Similarity Estimation](https://mlsanity.com/paper/1408.3456/) (2014)
- [In-Context Learning through the Bayesian Prism](https://mlsanity.com/paper/2306.04891/) (2023)
- [FollowIR: Evaluating and Teaching Information Retrieval Models to Follow Instructions](https://mlsanity.com/paper/2403.15246/) (2024)
- [RaFe: Ranking Feedback Improves Query Rewriting for RAG](https://mlsanity.com/paper/2405.14431/) (2024)
- [Interpretable by Design: Learning Predictors by Composing Interpretable Queries](https://mlsanity.com/paper/2207.00938/) (2022)
- [Bayesian Example Selection Improves In-Context Learning for Speech, Text, and Visual Modalities](https://mlsanity.com/paper/2404.14716/) (2024)
- [Reasoning Graph Enhanced Exemplars Retrieval for In-Context Learning](https://mlsanity.com/paper/2409.11147/) (2024)

## Abstract (arXiv)

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.