# EVIL: Evolving Interpretable Algorithms for Zero-Shot Inference on Event Sequences and Time Series with LLMs

arXiv: https://arxiv.org/abs/2604.15787 · HTML: https://mlsanity.com/paper/2604.15787/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 28 of its 54 references that are in the map.
- First posted on arXiv 17 Apr 2026.

## Builds on (most cited first, 28 of 28)

- [CSDI: Conditional Score-based Diffusion Models for Probabilistic Time Series Imputation](https://mlsanity.com/paper/2107.03502/) (2021)
- [Illuminating search spaces by mapping elites](https://mlsanity.com/paper/1504.04909/) (2015)
- [Transformers Can Do Bayesian Inference](https://mlsanity.com/paper/2112.10510/) (2021)
- [BRITS: Bidirectional Recurrent Imputation for Time Series](https://mlsanity.com/paper/1805.10572/) (2018)
- [SAITS: Self-Attention-based Imputation for Time Series](https://mlsanity.com/paper/2202.08516/) (2022)
- [Intensity-Free Learning of Temporal Point Processes](https://mlsanity.com/paper/1909.12127/) (2019)
- [VAMPnets: Deep learning of molecular kinetics](https://mlsanity.com/paper/1710.06012/) (2017)
- [LLM-SR: Scientific Equation Discovery via Programming with Large Language Models](https://mlsanity.com/paper/2404.18400/) (2024)
- [Learning Tree-based Deep Model for Recommender Systems](https://mlsanity.com/paper/1801.02294/) (2018)
- [Transformer Embeddings of Irregularly Spaced Events and Their Participants](https://mlsanity.com/paper/2201.00044/) (2021)
- [Mathematical exploration and discovery at scale](https://mlsanity.com/paper/2511.02864/) (2025)
- [HYPRO: A Hybridly Normalized Probabilistic Model for Long-Horizon Prediction of Event Sequences](https://mlsanity.com/paper/2210.01753/) (2022)
- [Coarse Graining Molecular Dynamics with Graph Neural Networks](https://mlsanity.com/paper/2007.11412/) (2020)
- [Learning unknown ODE models with Gaussian processes](https://mlsanity.com/paper/1803.04303/) (2018)
- [Imputing Missing Events in Continuous-Time Event Streams](https://mlsanity.com/paper/1905.05570/) (2019)
- [TSI-Bench: Benchmarking Time Series Imputation](https://mlsanity.com/paper/2406.12747/) (2024)
- [Exploring Generative Neural Temporal Point Process](https://mlsanity.com/paper/2208.01874/) (2022)
- [Long Horizon Forecasting With Temporal Point Processes](https://mlsanity.com/paper/2101.02815/) (2021)
- [Context parroting: A simple but tough-to-beat baseline for foundation models in scientific machine learning](https://mlsanity.com/paper/2505.11349/) (2025)
- [Decomposable Transformer Point Processes](https://mlsanity.com/paper/2409.18158/) (2024)
- [Zero-shot Imputation with Foundation Inference Models for Dynamical Systems](https://mlsanity.com/paper/2402.07594/) (2024)
- [Foundation Inference Models for Markov Jump Processes](https://mlsanity.com/paper/2406.06419/) (2024)
- [Neural Markov Jump Processes](https://mlsanity.com/paper/2305.19744/) (2023)
- [BayOTIDE: Bayesian Online Multivariate Time series Imputation with functional decomposition](https://mlsanity.com/paper/2308.14906/) (2023)
- [Interacting Diffusion Processes for Event Sequence Forecasting](https://mlsanity.com/paper/2310.17800/) (2023)
- [In-Context Learning of Temporal Point Processes with Foundation Inference Models](https://mlsanity.com/paper/2509.24762/) (2025)
- [In-Context Learning of Stochastic Differential Equations with Foundation Inference Models](https://mlsanity.com/paper/2502.19049/) (2025)
- [Foundation Inference Models for Ordinary Differential Equations](https://mlsanity.com/paper/2602.08733/) (2026)

## Abstract (arXiv)

We introduce EVIL (EVolving Interpretable algorithms with LLMs), an approach that uses LLM-guided evolutionary search to discover simple, interpretable algorithms for dynamical systems inference. Rather than training neural networks on large datasets, EVIL evolves pure Python/NumPy programs that perform zero-shot, in-context inference across datasets. We apply EVIL to three distinct tasks: next-event prediction in temporal point processes, rate matrix estimation for Markov jump processes, and time series imputation. In each case, a single evolved algorithm generalizes across all evaluation datasets without per-dataset training (analogous to an amortized inference model). To the best of our knowledge, this is the first work to show that LLM-guided program evolution can discover a single compact inference function for these dynamical-systems problems. Across the three domains, the discovered algorithms are often competitive with, and even outperform, state-of-the-art deep learning models while being orders of magnitudes faster, and remaining fully interpretable.