End-to-end symbolic regression with transformers
This addresses the problem of inefficient symbolic regression for researchers and practitioners by offering a faster, competitive alternative to genetic programming, though it is incremental as it builds on existing neural network and optimization techniques.
The paper tackles symbolic regression by proposing an end-to-end Transformer model that directly predicts full mathematical expressions including constants, challenging the traditional two-step approach. It shows that this method yields better results, approaching state-of-the-art genetic programming performance with orders of magnitude faster inference on SRBench benchmarks.
Symbolic regression, the task of predicting the mathematical expression of a function from the observation of its values, is a difficult task which usually involves a two-step procedure: predicting the "skeleton" of the expression up to the choice of numerical constants, then fitting the constants by optimizing a non-convex loss function. The dominant approach is genetic programming, which evolves candidates by iterating this subroutine a large number of times. Neural networks have recently been tasked to predict the correct skeleton in a single try, but remain much less powerful. In this paper, we challenge this two-step procedure, and task a Transformer to directly predict the full mathematical expression, constants included. One can subsequently refine the predicted constants by feeding them to the non-convex optimizer as an informed initialization. We present ablations to show that this end-to-end approach yields better results, sometimes even without the refinement step. We evaluate our model on problems from the SRBench benchmark and show that our model approaches the performance of state-of-the-art genetic programming with several orders of magnitude faster inference.