Sparse Interpretable Deep Learning with LIES Networks for Symbolic Regression

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Main Authors: Montazerin, Mansooreh, Aawar, Majd Al, Ortega, Antonio, Srivastava, Ajitesh
Format: Preprint
Published: 2025
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author Montazerin, Mansooreh
Aawar, Majd Al
Ortega, Antonio
Srivastava, Ajitesh
author_facet Montazerin, Mansooreh
Aawar, Majd Al
Ortega, Antonio
Srivastava, Ajitesh
contents Symbolic regression (SR) aims to discover closed-form mathematical expressions that accurately describe data, offering interpretability and analytical insight beyond standard black-box models. Existing SR methods often rely on population-based search or autoregressive modeling, which struggle with scalability and symbolic consistency. We introduce LIES (Logarithm, Identity, Exponential, Sine), a fixed neural network architecture with interpretable primitive activations that are optimized to model symbolic expressions. We develop a framework to extract compact formulae from LIES networks by training with an appropriate oversampling strategy and a tailored loss function to promote sparsity and to prevent gradient instability. After training, it applies additional pruning strategies to further simplify the learned expressions into compact formulae. Our experiments on SR benchmarks show that the LIES framework consistently produces sparse and accurate symbolic formulae outperforming all baselines. We also demonstrate the importance of each design component through ablation studies.
format Preprint
id arxiv_https___arxiv_org_abs_2506_08267
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Sparse Interpretable Deep Learning with LIES Networks for Symbolic Regression
Montazerin, Mansooreh
Aawar, Majd Al
Ortega, Antonio
Srivastava, Ajitesh
Machine Learning
Artificial Intelligence
Symbolic regression (SR) aims to discover closed-form mathematical expressions that accurately describe data, offering interpretability and analytical insight beyond standard black-box models. Existing SR methods often rely on population-based search or autoregressive modeling, which struggle with scalability and symbolic consistency. We introduce LIES (Logarithm, Identity, Exponential, Sine), a fixed neural network architecture with interpretable primitive activations that are optimized to model symbolic expressions. We develop a framework to extract compact formulae from LIES networks by training with an appropriate oversampling strategy and a tailored loss function to promote sparsity and to prevent gradient instability. After training, it applies additional pruning strategies to further simplify the learned expressions into compact formulae. Our experiments on SR benchmarks show that the LIES framework consistently produces sparse and accurate symbolic formulae outperforming all baselines. We also demonstrate the importance of each design component through ablation studies.
title Sparse Interpretable Deep Learning with LIES Networks for Symbolic Regression
topic Machine Learning
Artificial Intelligence
url https://arxiv.org/abs/2506.08267