# Emergent Bayesian Behaviour and Optimal Cue Combination in LLMs

arXiv: https://arxiv.org/abs/2512.02719 · HTML: https://mlsanity.com/paper/2512.02719/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning.
- Builds on 7 of its 28 references that are in the map.
- First posted on arXiv 2 Dec 2025.

## Placed in

- LLM reasoning / [Reasoning benchmarks and evaluation](https://mlsanity.com/lr/reasoning-benchmarks-and-evaluation/)

## Builds on (most cited first, 7 of 7)

- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [MMBench: Is Your Multi-modal Model an All-around Player?](https://mlsanity.com/paper/2307.06281/) (2023)
- [An Explanation of In-context Learning as Implicit Bayesian Inference](https://mlsanity.com/paper/2111.02080/) (2021)
- [Are Multimodal Transformers Robust to Missing Modality?](https://mlsanity.com/paper/2204.05454/) (2022)
- [Human-inspired Episodic Memory for Infinite Context LLMs](https://mlsanity.com/paper/2407.09450/) (2024)
- [Bayesian Teaching Enables Probabilistic Reasoning in Large Language Models](https://mlsanity.com/paper/2503.17523/) (2025)
- [Bayesian sense of time in biological and artificial brains](https://mlsanity.com/paper/2201.05464/) (2022)

## Built on by (most cited first, 1 of 1)

- [Where Should Language Sit in a Multimodal Model? Lessons from What Language Does to Human Perception and Cognition](https://mlsanity.com/paper/2609.07474/) (2026)

## Abstract (arXiv)

Large language models (LLMs) excel at explicit reasoning, but their implicit computational strategies remain underexplored. Decades of psychophysics research show that humans intuitively process and integrate noisy signals using near-optimal Bayesian strategies in perceptual tasks. We ask whether LLMs exhibit similar behaviour and perform optimal multimodal integration without explicit training or instruction. Adopting the psychophysics paradigm, we infer computational principles of LLMs from systematic behavioural studies. We introduce a behavioural benchmark - BayesBench: four magnitude estimation tasks (length, location, distance, and duration) over text and image, inspired by classic psychophysics, and evaluate a diverse set of nine LLMs alongside human judgments for calibration. Through controlled ablations of noise, context, and instruction prompts, we measure performance, behaviour and efficiency in multimodal cue-combination. Beyond accuracy and efficiency metrics, we introduce a Bayesian Consistency Score that detects Bayes-consistent behavioural shifts even when accuracy saturates. Our results show that while capable models often adapt in Bayes-consistent ways, accuracy does not guarantee robustness. Notably, GPT-5 Mini achieves perfect text accuracy but fails to integrate visual cues efficiently. This reveals a critical dissociation between capability and strategy, suggesting accuracy-centric benchmarks may over-index on performance while missing brittle uncertainty handling. These findings reveal emergent principled handling of uncertainty and highlight the correlation between accuracy and Bayesian tendencies. We release our psychophysics benchmark and consistency metric (https://bayes-bench.github.io) as evaluation tools and to inform future multimodal architecture designs.