ISR: Invertible Symbolic Regression
This work addresses the need for interpretable and invertible symbolic models in machine learning, particularly for inverse problems in domains like oceanography, though it appears incremental as it builds on existing techniques like INNs and EQL.
The authors tackled the problem of generating analytical relationships between inputs and outputs using invertible maps by introducing an Invertible Symbolic Regression (ISR) method, which combines Invertible Neural Networks and Equation Learner to create a differentiable symbolic architecture with sparsity regularization for interpretability, and demonstrated its applicability in density estimation and inverse problems like geoacoustic inversion in oceanography.
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.