# Solomonoff-Inspired Hypothesis Ranking with LLMs for Prediction Under Uncertainty

arXiv: https://arxiv.org/abs/2512.17145 · HTML: https://mlsanity.com/paper/2512.17145/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 28 references that are in the map.
- First posted on arXiv 19 Dec 2025.

## Builds on (most cited first, 14 of 14)

- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [What Uncertainties Do We Need in Bayesian Deep Learning for Computer Vision?](https://mlsanity.com/paper/1703.04977/) (2017)
- [A Survey of Uncertainty in Deep Neural Networks](https://mlsanity.com/paper/2107.03342/) (2021)
- [Predictive Uncertainty Estimation via Prior Networks](https://mlsanity.com/paper/1802.10501/) (2018)
- [Weight Uncertainty in Neural Networks](https://mlsanity.com/paper/1505.05424/) (2015)
- [Hands-on Bayesian Neural Networks -- a Tutorial for Deep Learning Users](https://mlsanity.com/paper/2007.06823/) (2020)
- [Hypothesis Search: Inductive Reasoning with Language Models](https://mlsanity.com/paper/2309.05660/) (2023)
- [How Well do LLMs Compress Their Own Chain-of-Thought? A Token Complexity Approach](https://mlsanity.com/paper/2503.01141/) (2025)
- [Large Language Model (LLM) as a System of Multiple Expert Agents: An Approach to solve the Abstraction and Reasoning Corpus (ARC) Challenge](https://mlsanity.com/paper/2310.05146/) (2023)
- [ConceptSearch: Towards Efficient Program Search Using LLMs for Abstraction and Reasoning Corpus (ARC)](https://mlsanity.com/paper/2412.07322/) (2024)
- [Neural Mechanisms of Human Decision-Making](https://mlsanity.com/paper/1912.07660/) (2019)
- [ChatGPT Prompting Cannot Estimate Predictive Uncertainty in High-Resource Languages](https://mlsanity.com/paper/2311.06427/) (2023)
- [Multiple-Hypothesis Path Planning with Uncertain Object Detections](https://mlsanity.com/paper/2308.07420/) (2023)

## Abstract (arXiv)

Reasoning under uncertainty is a key challenge in AI, especially for real-world tasks, where problems with sparse data demands systematic generalisation. Existing approaches struggle to balance accuracy and simplicity when evaluating multiple candidate solutions. We propose a Solomonoff-inspired method that weights LLM-generated hypotheses by simplicity and predictive fit. Applied to benchmark (Mini-ARC) tasks, our method produces Solomonoff-weighted mixtures for per-cell predictions, yielding conservative, uncertainty-aware outputs even when hypotheses are noisy or partially incorrect. Compared to Bayesian Model Averaging (BMA), Solomonoff scoring spreads probability more evenly across competing hypotheses, while BMA concentrates weight on the most likely but potentially flawed candidates. Across tasks, this highlights the value of algorithmic information-theoretic priors for interpretable, reliable multi-hypothesis reasoning under uncertainty.