# [RETRACTED]Evolving Form and Function: Dual-Objective Optimization in Neural Symbolic Regression Networks

arXiv: https://arxiv.org/abs/2502.17393 · HTML: https://mlsanity.com/paper/2502.17393/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 24 Feb 2025.

## Built on by (most cited first, 3 of 3)

- [Neuro-Evolutionary Approach to Physics-Aware Symbolic Regression](https://mlsanity.com/paper/2504.16503/) (2025)
- [Multi-Modal Learning meets Genetic Programming: Analyzing Alignment in Latent Space Optimization](https://mlsanity.com/paper/2604.08324/) (2026)
- [Learning Parametric Nitrogen Fertilizer Response Curves Using Neuro Symbolic Regression](https://mlsanity.com/paper/2605.31276/) (2026)

## Abstract (arXiv)

[RETRACTED]Data increasingly abounds, but distilling their underlying relationships down to something interpretable remains challenging. One approach is genetic programming, which `symbolically regresses' a data set down into an equation. However, symbolic regression (SR) faces the issue of requiring training from scratch for each new dataset. To generalize across all datasets, deep learning techniques have been applied to SR. These networks, however, are only able to be trained using a symbolic objective: NN-generated and target equations are symbolically compared. But this does not consider the predictive power of these equations, which could be measured by a behavioral objective that compares the generated equation's predictions to actual data. Here we introduce a method that combines gradient descent and evolutionary computation to yield neural networks that minimize the symbolic and behavioral errors of the equations they generate from data. As a result, these evolved networks are shown to generate more symbolically and behaviorally accurate equations than those generated by networks trained by state-of-the-art gradient based neural symbolic regression methods. We hope this method suggests that evolutionary algorithms, combined with gradient descent, can improve SR results by yielding equations with more accurate form and function.