Transformer-based Planning for Symbolic Regression

• URL: http://arxiv.org/abs/2303.06833v5
• Date: Fri, 27 Oct 2023 20:13:13 GMT
• Title: Transformer-based Planning for Symbolic Regression
• Authors: Parshin Shojaee, Kazem Meidani, Amir Barati Farimani, Chandan K. Reddy
• Abstract summary: We propose TPSR, a Transformer-based Planning strategy for Symbolic Regression. Unlike conventional decoding strategies, TPSR enables the integration of non-differentiable feedback, such as fitting accuracy and complexity. Our approach outperforms state-of-the-art methods, enhancing the model's fitting-complexity trade-off, Symbolic abilities, and robustness to noise.
• Score: 18.90700817248397
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Symbolic regression (SR) is a challenging task in machine learning that involves finding a mathematical expression for a function based on its values. Recent advancements in SR have demonstrated the effectiveness of pre-trained transformer-based models in generating equations as sequences, leveraging large-scale pre-training on synthetic datasets and offering notable advantages in terms of inference time over classical Genetic Programming (GP) methods. However, these models primarily rely on supervised pre-training goals borrowed from text generation and overlook equation discovery objectives like accuracy and complexity. To address this, we propose TPSR, a Transformer-based Planning strategy for Symbolic Regression that incorporates Monte Carlo Tree Search into the transformer decoding process. Unlike conventional decoding strategies, TPSR enables the integration of non-differentiable feedback, such as fitting accuracy and complexity, as external sources of knowledge into the transformer-based equation generation process. Extensive experiments on various datasets show that our approach outperforms state-of-the-art methods, enhancing the model's fitting-complexity trade-off, extrapolation abilities, and robustness to noise.

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