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arXiv · 2405.06848

ISR: Invertible Symbolic Regression

Tony Tohme·Mohammad Javad Khojasteh·Mohsen Sadr·Florian Meyer·Kamal Youcef-Toumi
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Abstract

We introduce an Invertible Symbolic Regression (ISR) method. It is a machine learning technique that generates analytical relationships between inputs and outputs of a given dataset via invertible maps (or architectures). The proposed ISR method naturally combines the principles of Invertible Neural Networks (INNs) and Equation Learner (EQL), a neural network-based symbolic architecture for function learning. In particular, we transform the affine coupling blocks of INNs into a symbolic framework, resulting in an end-to-end differentiable symbolic invertible architecture that allows for efficient gradient-based learning. The proposed ISR framework also relies on sparsity promoting regularization, allowing the discovery of concise and interpretable invertible expressions. We show that ISR can serve as a (symbolic) normalizing flow for density estimation tasks. Furthermore, we highlight its practical applicability in solving inverse problems, including a benchmark inverse kinematics problem, and notably, a geoacoustic inversion problem in oceanography aimed at inferring posterior distributions of underlying seabed parameters from acoustic signals.

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Tony Tohme, Mohammad Javad Khojasteh, Mohsen Sadr, Florian Meyer, Kamal Youcef-Toumi. 2024-05-10. ISR: Invertible Symbolic Regression. https://arxiv.org/abs/2405.06848

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