# Data-Driven Discovery of Interpretable Kalman Filter Variants through Large Language Models and Genetic Programming

arXiv: https://arxiv.org/abs/2508.11703 · HTML: https://mlsanity.com/paper/2508.11703/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 35 references that are in the map.
- First posted on arXiv 13 Aug 2025.

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

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Gemini 2.5: Pushing the Frontier with Advanced Reasoning, Multimodality, Long Context, and Next Generation Agentic Capabilities](https://mlsanity.com/paper/2507.06261/) (2025)
- [QLoRA: Efficient Finetuning of Quantized LLMs](https://mlsanity.com/paper/2305.14314/) (2023)
- [AlphaEvolve: A coding agent for scientific and algorithmic discovery](https://mlsanity.com/paper/2506.13131/) (2025)
- [StarCoder: may the source be with you!](https://mlsanity.com/paper/2305.06161/) (2023)
- [Probabilistic 3D Multi-Modal, Multi-Object Tracking for Autonomous Driving](https://mlsanity.com/paper/2012.13755/) (2020)
- [Algorithm Discovery With LLMs: Evolutionary Search Meets Reinforcement Learning](https://mlsanity.com/paper/2504.05108/) (2025)
- [Probabilistic 3D Multi-Object Cooperative Tracking for Autonomous Driving via Differentiable Multi-Sensor Kalman Filter](https://mlsanity.com/paper/2309.14655/) (2023)
- [Optimization or Architecture: How to Hack Kalman Filtering](https://mlsanity.com/paper/2310.00675/) (2023)
- [Perceptual Kalman Filters: Online State Estimation under a Perfect Perceptual-Quality Constraint](https://mlsanity.com/paper/2306.02400/) (2023)

## Abstract (arXiv)

Algorithmic discovery has traditionally relied on human ingenuity and extensive experimentation. Here we investigate whether a prominent scientific computing algorithm, the Kalman Filter, can be discovered through an automated, data-driven, evolutionary process that relies on Cartesian Genetic Programming (CGP) and Large Language Models (LLM). We evaluate the contributions of both modalities (CGP and LLM) in discovering the Kalman filter under varying conditions. Our results demonstrate that our framework of CGP and LLM-assisted evolution converges to near-optimal solutions when Kalman optimality assumptions hold. When these assumptions are violated, our framework evolves interpretable alternatives that outperform the Kalman filter. These results demonstrate that combining evolutionary algorithms and generative models for interpretable, data-driven synthesis of simple computational modules is a potent approach for algorithmic discovery in scientific computing.