Symbolic Regression Discovers Superior Neural Network Optimizers.

Charles Brum, Edward Finkelstein· July 27, 2026 View original

Summary

Researchers used fixed-depth symbolic regression to discover explicit neural network weight-update rules that outperform standard hand-designed optimizers. The discovered rules, often combining adaptive normalization and momentum, significantly reduced mean squared error on small symbolic regression benchmarks.

This research investigates the potential of symbolic regression to automatically discover novel and more effective weight-update rules for feed-forward neural networks. Instead of relying on human-designed optimizers, the study used a fixed-depth symbolic regression procedure to search for explicit update rules. These candidate rules were constructed from operands commonly found in established optimizers, such as gradient, momentum, and adaptive-gradient quantities. Across 30 combinations of benchmarks and neural networks, the symbolic regression approach successfully identified update rules that surpassed the performance of the best hyperparameter-tuned established optimizers in 25 cases. This led to an impressive aggregate Mean Squared Error (MSE) reduction of 44.47% in the improved scenarios. The discovered rules were diverse but frequently incorporated elements like adaptive normalization, momentum-like terms, non-linear transformations, and rational expressions, suggesting that symbolic regression is a lightweight yet powerful mechanism for finding compact and superior optimizer variants.

Why it matters

Improving optimizer performance can lead to faster training, better model convergence, and enhanced accuracy for machine learning models, directly impacting the efficiency and effectiveness of AI development.

How to implement this in your domain

  1. 1Explore symbolic regression techniques to customize optimizers for specific neural network architectures or tasks.
  2. 2Integrate newly discovered optimizer variants into internal ML frameworks for performance testing.
  3. 3Benchmark custom optimizers against standard ones on relevant datasets to identify potential gains.
  4. 4Investigate the interpretability of discovered rules to gain insights into effective optimization strategies.

Who benefits

AI/ML DevelopmentSoftware EngineeringResearch & DevelopmentData ScienceCloud Computing

Key takeaways

  • Symbolic regression can automatically discover novel and superior neural network weight-update rules.
  • Discovered optimizers outperformed hand-designed ones on small benchmarks, significantly reducing MSE.
  • The effective rules often combine adaptive normalization, momentum, and non-linear transformations.
  • This approach offers a lightweight mechanism for finding compact and effective optimizer variants.

Original post by Charles Brum, Edward Finkelstein

"arXiv:2607.21855v1 Announce Type: new Abstract: We investigate whether symbolic regression can discover explicit neural network weight-update rules that outperform standard hand-designed optimizers on small symbolic regression benchmarks. Candidate update rules are represented as…"

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