OccamNet: A Fast Neural Model for Symbolic Regression at Scale

• URL: http://arxiv.org/abs/2007.10784v3
• Date: Tue, 28 Nov 2023 03:35:32 GMT
• Title: OccamNet: A Fast Neural Model for Symbolic Regression at Scale
• Authors: Owen Dugan and Rumen Dangovski and Allan Costa and Samuel Kim and Pawan Goyal and Joseph Jacobson and Marin Solja\v{c}i\'c
• Abstract summary: OccamNet is a neural network model that finds interpretable, compact, and sparse symbolic fits to data. Our model defines a probability distribution over functions with efficient sampling and function evaluation. It can identify symbolic fits for a variety of problems, including analytic and non-analytic functions, implicit functions, and simple image classification.
• Score: 11.463756755780583
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Neural networks' expressiveness comes at the cost of complex, black-box models that often extrapolate poorly beyond the domain of the training dataset, conflicting with the goal of finding compact analytic expressions to describe scientific data. We introduce OccamNet, a neural network model that finds interpretable, compact, and sparse symbolic fits to data, \`a la Occam's razor. Our model defines a probability distribution over functions with efficient sampling and function evaluation. We train by sampling functions and biasing the probability mass toward better fitting solutions, backpropagating using cross-entropy matching in a reinforcement-learning loss. OccamNet can identify symbolic fits for a variety of problems, including analytic and non-analytic functions, implicit functions, and simple image classification, and can outperform state-of-the-art symbolic regression methods on real-world regression datasets. Our method requires a minimal memory footprint, fits complicated functions in minutes on a single CPU, and scales on a GPU.

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