# Large Language Models as Discounted Bayesian Filters

arXiv: https://arxiv.org/abs/2512.18489 · HTML: https://mlsanity.com/paper/2512.18489/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 22 references that are in the map.
- First posted on arXiv 20 Dec 2025.

## Builds on (most cited first, 15 of 15)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Mistral 7B](https://mlsanity.com/paper/2310.06825/) (2023)
- [Gemma 2: Improving Open Language Models at a Practical Size](https://mlsanity.com/paper/2408.00118/) (2024)
- [In-context Learning and Induction Heads](https://mlsanity.com/paper/2209.11895/) (2022)
- [An Explanation of In-context Learning as Implicit Bayesian Inference](https://mlsanity.com/paper/2111.02080/) (2021)
- [Data Distributional Properties Drive Emergent In-Context Learning in Transformers](https://mlsanity.com/paper/2205.05055/) (2022)
- [Mitigating Catastrophic Forgetting in Large Language Models with Self-Synthesized Rehearsal](https://mlsanity.com/paper/2403.01244/) (2024)
- [CF-VLM:CounterFactual Vision-Language Fine-tuning](https://mlsanity.com/paper/2506.17267/) (2025)
- [GAM-Agent: Game-Theoretic and Uncertainty-Aware Collaboration for Complex Visual Reasoning](https://mlsanity.com/paper/2505.23399/) (2025)
- [KABB: Knowledge-Aware Bayesian Bandits for Dynamic Expert Coordination in Multi-Agent Systems](https://mlsanity.com/paper/2502.07350/) (2025)
- [MAT-Agent: Adaptive Multi-Agent Training Optimization](https://mlsanity.com/paper/2510.17845/) (2025)
- [MM-CoT:A Benchmark for Probing Visual Chain-of-Thought Reasoning in Multimodal Models](https://mlsanity.com/paper/2512.08228/) (2025)
- [Hybrid Token Compression for Vision-Language Models](https://mlsanity.com/paper/2512.08240/) (2025)

## Built on by (most cited first, 2 of 2)

- [BayesBench: Evaluating LLM Belief Trajectories Under Multi-Turn Evidence Accumulation](https://mlsanity.com/paper/2606.30850/) (2026)
- [Belief Engine: Configurable and Inspectable Stance Dynamics in Multi-Agent LLM Deliberation](https://mlsanity.com/paper/2605.15343/) (2026)

## Abstract (arXiv)

Large Language Models (LLMs) demonstrate strong few-shot generalization through in-context learning, yet their reasoning in dynamic and stochastic environments remains opaque. Prior studies mainly focus on static tasks and overlook the online adaptation required when beliefs must be continuously updated, which is a key capability for LLMs acting as world models or agents. We introduce a Bayesian filtering framework to evaluate online inference in LLMs. Our probabilistic probe suite spans both multivariate discrete distributions, such as dice rolls, and continuous distributions, such as Gaussian processes, where ground-truth parameters shift over time. We find that while LLM belief updates resemble Bayesian posteriors, they are more accurately characterized by an exponential forgetting filter with a model-specific discount factor smaller than one. This reveals systematic discounting of older evidence that varies significantly across model architectures. Although inherent priors are often miscalibrated, the updating mechanism itself remains structured and principled. We further validate these findings in a simulated agent task and propose prompting strategies that effectively recalibrate priors with minimal computational cost.