# Sharpness-Aware Minimization in Genetic Programming

arXiv: https://arxiv.org/abs/2405.10267 · HTML: https://mlsanity.com/paper/2405.10267/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 34 references that are in the map.
- First posted on arXiv 16 May 2024.

## Builds on (most cited first, 6 of 6)

- [Sharpness-Aware Minimization for Efficiently Improving Generalization](https://mlsanity.com/paper/2010.01412/) (2020)
- [Visualizing the Loss Landscape of Neural Nets](https://mlsanity.com/paper/1712.09913/) (2017)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [Neural Symbolic Regression that Scales](https://mlsanity.com/paper/2106.06427/) (2021)
- [On The Nature Of The Phenotype In Tree Genetic Programming](https://mlsanity.com/paper/2402.08011/) (2024)
- [Sharpness-Aware Minimization for Evolutionary Feature Construction in Regression](https://mlsanity.com/paper/2405.06869/) (2024)

## Built on by (most cited first, 2 of 2)

- [Enhancing Generalization in Evolutionary Feature Construction for Symbolic Regression through Vicinal Jensen Gap Minimization](https://mlsanity.com/paper/2602.01510/) (2026)
- [SymboLLM-FE: LLM-Accelerated Symbolic Regression for Automated Feature Engineering on Tabular Data](https://mlsanity.com/paper/2608.28408/) (2026)

## Abstract (arXiv)

Sharpness-Aware Minimization (SAM) was recently introduced as a regularization procedure for training deep neural networks. It simultaneously minimizes the fitness (or loss) function and the so-called fitness sharpness. The latter serves as a measure of the nonlinear behavior of a solution and does so by finding solutions that lie in neighborhoods having uniformly similar loss values across all fitness cases. In this contribution, we adapt SAM for tree Genetic Programming (TGP) by exploring the semantic neighborhoods of solutions using two simple approaches. By capitalizing upon perturbing input and output of program trees, sharpness can be estimated and used as a second optimization criterion during the evolution. To better understand the impact of this variant of SAM on TGP, we collect numerous indicators of the evolutionary process, including generalization ability, complexity, diversity, and a recently proposed genotype-phenotype mapping to study the amount of redundancy in trees. The experimental results demonstrate that using any of the two proposed SAM adaptations in TGP allows (i) a significant reduction of tree sizes in the population and (ii) a decrease in redundancy of the trees. When assessed on real-world benchmarks, the generalization ability of the elite solutions does not deteriorate.