# Correlation versus RMSE Loss Functions in Symbolic Regression Tasks

arXiv: https://arxiv.org/abs/2205.15990 · HTML: https://mlsanity.com/paper/2205.15990/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 May 2022.

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

- [Active Learning in Genetic Programming: Guiding Efficient Data Collection for Symbolic Regression](https://mlsanity.com/paper/2308.00672/) (2023)
- [Node Preservation and its Effect on Crossover in Cartesian Genetic Programming](https://mlsanity.com/paper/2511.00634/) (2025)

## Abstract (arXiv)

The use of correlation as a fitness function is explored in symbolic regression tasks and the performance is compared against the typical RMSE fitness function. Using correlation with an alignment step to conclude the evolution led to significant performance gains over RMSE as a fitness function. Using correlation as a fitness function led to solutions being found in fewer generations compared to RMSE, as well it was found that fewer data points were needed in the training set to discover the correct equations. The Feynman Symbolic Regression Benchmark as well as several other old and recent GP benchmark problems were used to evaluate performance.