# From Residuals to Reasons: LLM-Guided Mechanism Inference from Tabular Data

arXiv: https://arxiv.org/abs/2605.22897 · HTML: https://mlsanity.com/paper/2605.22897/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in Clinical and biomedical applications, one of 17 directions in LLM reasoning.
- Builds on 17 of its 39 references that are in the map.
- First posted on arXiv 21 May 2026.

## Placed in

- LLM reasoning / [Clinical and biomedical applications](https://mlsanity.com/lr/clinical-and-biomedical-applications/)

## Builds on (most cited first, 17 of 17)

- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- ["Why Should I Trust You?": Explaining the Predictions of Any Classifier](https://mlsanity.com/paper/1602.04938/) (2016)
- [Self-Refine: Iterative Refinement with Self-Feedback](https://mlsanity.com/paper/2303.17651/) (2023)
- [Improving Factuality and Reasoning in Language Models through Multiagent Debate](https://mlsanity.com/paper/2305.14325/) (2023)
- [What Makes Good In-Context Examples for GPT-3?](https://mlsanity.com/paper/2101.06804/) (2021)
- [TabPFN: A Transformer That Solves Small Tabular Classification Problems in a Second](https://mlsanity.com/paper/2207.01848/) (2022)
- [Mixture-of-Agents Enhances Large Language Model Capabilities](https://mlsanity.com/paper/2406.04692/) (2024)
- [TextGrad: Automatic "Differentiation" via Text](https://mlsanity.com/paper/2406.07496/) (2024)
- [InterpretML: A Unified Framework for Machine Learning Interpretability](https://mlsanity.com/paper/1909.09223/) (2019)
- [When Do Neural Nets Outperform Boosted Trees on Tabular Data?](https://mlsanity.com/paper/2305.02997/) (2023)
- [Diverse Demonstrations Improve In-context Compositional Generalization](https://mlsanity.com/paper/2212.06800/) (2022)
- [LLM-SR: Scientific Equation Discovery via Programming with Large Language Models](https://mlsanity.com/paper/2404.18400/) (2024)
- [Large Language Models for Automated Data Science: Introducing CAAFE for Context-Aware Automated Feature Engineering](https://mlsanity.com/paper/2305.03403/) (2023)
- [Because we have LLMs, we Can and Should Pursue Agentic Interpretability](https://mlsanity.com/paper/2506.12152/) (2025)
- [Agentic Medical Knowledge Graphs Enhance Medical Question Answering: Bridging the Gap Between LLMs and Evolving Medical Knowledge](https://mlsanity.com/paper/2502.13010/) (2025)
- [InterpreTabNet: Distilling Predictive Signals from Tabular Data by Salient Feature Interpretation](https://mlsanity.com/paper/2406.00426/) (2024)
- [Symbolic Regression with Multimodal Large Language Models and Kolmogorov Arnold Networks](https://mlsanity.com/paper/2505.07956/) (2025)

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

- [What Should a Large Language Model See? Physical Invariants as a Data Representation for PDE Discovery](https://mlsanity.com/paper/2608.25189/) (2026)

## Abstract (arXiv)

A persistent challenge in machine learning for scientific applications is jointly achieving prediction and understanding. Statistical models excel on structured data but operate as black boxes, while existing interpretability methods are largely inspective: they answer "which features matter?" but do not articulate how features interact or refine explanations iteratively alongside human understanding. Asking an LLM to predict the target directly forces it to search the entire output space; we instead anchor predictions with a base model and ask the LLM the narrower question of what that model is missing. We introduce Multi-Agent Residual In-Context Learning (MARICL), an agentic framework in which LLM agents analyze where a base-model fails, hypothesize missing structure from high-residual examples provided in context, and produce explicit correction terms refined through multi-turn textual gradient optimization. Across nine benchmarks spanning scientific, biomedical, socioeconomic, and synthetic settings, MARICL improves consistently over its base model on all datasets. To test whether these corrections reflect real structure or batch-specific noise, we freeze formulas learned on one experimental batch of the Cell-Free Protein dataset and apply them (with no retraining and no further LLM calls) to held-out batches. Within the same reagent protocol, the frozen formulas improve predictions in over 92% of cases; across a different protocol, they fail systematically. The success boundary aligns with the biochemistry, not the batch count; direct evidence of mechanistic generalization.