# Symbolic Regression on FPGAs for Fast Machine Learning Inference

arXiv: https://arxiv.org/abs/2305.04099 · HTML: https://mlsanity.com/paper/2305.04099/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 13 references that are in the map.
- First posted on arXiv 6 May 2023.

## Builds on (most cited first, 2 of 2)

- [Automatic heterogeneous quantization of deep neural networks for low-latency inference on the edge for particle detectors](https://mlsanity.com/paper/2006.10159/) (2020)
- [Ps and Qs: Quantization-aware pruning for efficient low latency neural network inference](https://mlsanity.com/paper/2102.11289/) (2021)

## Built on by (most cited first, 9 of 9)

- [hls4ml: A Flexible, Open-Source Platform for Deep Learning Acceleration on Reconfigurable Hardware](https://mlsanity.com/paper/2512.01463/) (2025)
- [SymbolNet: Neural Symbolic Regression with Adaptive Dynamic Pruning for Compression](https://mlsanity.com/paper/2401.09949/) (2024)
- [Symbolic Regression for Beyond the Standard Model Physics](https://mlsanity.com/paper/2405.18471/) (2024)
- [SymbolFit: Automatic Parametric Modeling with Symbolic Regression](https://mlsanity.com/paper/2411.09851/) (2024)
- [Analyzing Generalization in Pre-Trained Symbolic Regression](https://mlsanity.com/paper/2509.19849/) (2025)
- [Symbolic Regression and Differentiable Fits in Beyond the Standard Model Physics](https://mlsanity.com/paper/2510.20453/) (2025)
- [Inferring Interpretable Models of Fragmentation Functions using Symbolic Regression](https://mlsanity.com/paper/2501.07123/) (2025)
- [SparsePixels: Efficient Convolution for Sparse Data on FPGAs](https://mlsanity.com/paper/2512.06208/) (2025)
- [PQuantML: A Tool for End-to-End Hardware-aware Model Compression](https://mlsanity.com/paper/2603.26595/) (2026)

## Abstract (arXiv)

The high-energy physics community is investigating the potential of deploying machine-learning-based solutions on Field-Programmable Gate Arrays (FPGAs) to enhance physics sensitivity while still meeting data processing time constraints. In this contribution, we introduce a novel end-to-end procedure that utilizes a machine learning technique called symbolic regression (SR). It searches the equation space to discover algebraic relations approximating a dataset. We use PySR (a software to uncover these expressions based on an evolutionary algorithm) and extend the functionality of hls4ml (a package for machine learning inference in FPGAs) to support PySR-generated expressions for resource-constrained production environments. Deep learning models often optimize the top metric by pinning the network size because the vast hyperparameter space prevents an extensive search for neural architecture. Conversely, SR selects a set of models on the Pareto front, which allows for optimizing the performance-resource trade-off directly. By embedding symbolic forms, our implementation can dramatically reduce the computational resources needed to perform critical tasks. We validate our method on a physics benchmark: the multiclass classification of jets produced in simulated proton-proton collisions at the CERN Large Hadron Collider. We show that our approach can approximate a 3-layer neural network using an inference model that achieves up to a 13-fold decrease in execution time, down to 5 ns, while still preserving more than 90% approximation accuracy.