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End-to-end Symbolic Regression with Transformers
Pierre-alexandre Kamienny · Stéphane d'Ascoli · Guillaume Lample · Francois Charton

Wed Nov 30 09:00 AM -- 11:00 AM (PST) @ Hall J #507

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.

Author Information

Pierre-alexandre Kamienny (Meta)
Stéphane d'Ascoli (ENS Paris / Meta AI)

Currently a joint Ph.D. student between ENS (supervised by Giulio Biroli) and FAIR (supervised by Levent Sagun). Working on theory of deep learning.

Guillaume Lample (Facebook AI Research)
Francois Charton (Meta AI)

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