Monolith: Differentiable EML Trees for Symbolic Regression via Gradient Descent on a Universal Operator

Key Points

• The research aims to implement differentiable EML trees for effective symbolic regression through a new training framework.
• Developed differentiable EML trees as trainable PyTorch modules.
• Applied gradient descent on a single universal operator for optimization.
• Employed hierarchical training for trees of depth 4 and above.
• Conducted symbolic decompilation and established honest baselines for comparison with PySR and MLP.
• Successfully recovered all 7 elementary functions using 24 or fewer parameters.
• Demonstrated high performance benchmarks against existing symbolic regression methods.
• Confirmed the efficiency of training with gradient descent on a universal operator.

Abstract