Sparse Interpretable Deep Learning with LIES Networks for Symbolic Regression

• URL: http://arxiv.org/abs/2506.08267v2
• Date: Sat, 14 Jun 2025 21:24:10 GMT
• Title: Sparse Interpretable Deep Learning with LIES Networks for Symbolic Regression
• Authors: Mansooreh Montazerin, Majd Al Aawar, Antonio Ortega, Ajitesh Srivastava,
• Abstract summary: Symbolic regression aims to discover closed-form mathematical expressions that accurately describe data.<n>Existing SR methods often rely on population-based search or autoregressive modeling.<n>We introduce LIES (Logarithm, Identity, Exponential, Sine), a fixed neural network architecture with interpretable primitive activations that are optimized to model symbolic expressions.
• Score: 22.345828337550575
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

Related papers

• Implicit Neural Representation-Based Continuous Single Image Super Resolution: An Empirical Study [50.15623093332659]
  Implicit neural representation (INR) has become the standard approach for arbitrary-scale image super-resolution (ASSR)<n>We compare existing techniques across diverse settings and present aggregated performance results on multiple image quality metrics.<n>We examine a new loss function that penalizes intensity variations while preserving edges, textures, and finer details during training.
  arXiv  Detail & Related papers  (2026-01-25T07:09:20Z)
• Beyond Error-Based Optimization: Experience-Driven Symbolic Regression with Goal-Conditioned Reinforcement Learning [14.473539776112666]
  We propose a novel framework named EGRL-SR (Experience-driven Goal-conditioned Reinforcement Learning for Regression)<n>We formulate symbolic regression as a goal-conditioned reinforcement learning problem and incorporate hindsight experience replay.<n>We design an all-point satisfaction binary reward function that encourages the action-value network to focus on structural patterns rather than low-error expressions.
  arXiv  Detail & Related papers  (2026-01-21T06:08:37Z)
• SIGMA: Scalable Spectral Insights for LLM Collapse [51.863164847253366]
  We introduce SIGMA (Spectral Inequalities for Gram Matrix Analysis), a unified framework for model collapse.<n>By utilizing benchmarks that deriving and deterministic bounds on the matrix's spectrum, SIGMA provides a mathematically grounded metric to track the contraction of the representation space.<n>We demonstrate that SIGMA effectively captures the transition towards states, offering both theoretical insights into the mechanics of collapse.
  arXiv  Detail & Related papers  (2026-01-06T19:47:11Z)
• Current Challenges of Symbolic Regression: Optimization, Selection, Model Simplification, and Benchmarking [0.0]
  Symbolic Regression (SR) aims to discover mathematical expressions that describe the relationship between variables.<n>Current methods must be constantly re-evaluated to understand the SR landscape.<n>This thesis addresses these challenges through a sequence of studies conducted throughout the doctorate.
  arXiv  Detail & Related papers  (2025-12-01T13:48:07Z)
• Unlocking Symbol-Level Precoding Efficiency Through Tensor Equivariant Neural Network [84.22115118596741]
  We propose an end-to-end deep learning (DL) framework with low inference complexity for symbol-level precoding.<n>We show that the proposed framework captures substantial performance gains of optimal SLP, while achieving an approximately 80-times speedup over conventional methods.
  arXiv  Detail & Related papers  (2025-10-02T15:15:50Z)
• Discovering Mathematical Equations with Diffusion Language Model [6.384075523245284]
  We introduce DiffuSR, a pre-training framework for symbolic regression built upon a continuous-state diffusion language model.<n>DrouSR employs a trainable embedding layer within the diffusion process to map discrete mathematical symbols into a continuous latent space.<n>We also design an effective inference strategy to enhance the accuracy of the diffusion-based equation generator.
  arXiv  Detail & Related papers  (2025-09-16T14:53:44Z)
• ASP-Assisted Symbolic Regression: Uncovering Hidden Physics in Fluid Mechanics [0.34952465649465553]
  This study applies Symbolic Regression to model a fundamental 3D incompressible flow in a rectangular channel.<n>By employing the PySR library, compact symbolic equations were derived directly from numerical simulation data.<n>We propose an innovative approach that integrates SR with the knowledge-representation framework of Answer Set Programming.
  arXiv  Detail & Related papers  (2025-07-22T15:16:20Z)
• Identifiable Convex-Concave Regression via Sub-gradient Regularised Least Squares [1.9580473532948397]
  We propose a novel nonparametric regression method that models complex input-relationships as the sum of convex and concave components.<n>The method-ICCNLS-decomposes sub-constrained shape-constrained additive decomposition.
  arXiv  Detail & Related papers  (2025-06-22T15:53:12Z)
• A Statistical Theory of Contrastive Learning via Approximate Sufficient Statistics [19.24473530318175]
  We develop a new theoretical framework for analyzing data augmentation-based contrastive learning.<n>We show that minimizing SimCLR and other contrastive losses yields encoders that are approximately sufficient.
  arXiv  Detail & Related papers  (2025-03-21T21:07:18Z)
• Graph Structure Refinement with Energy-based Contrastive Learning [56.957793274727514]
  We introduce an unsupervised method based on a joint of generative training and discriminative training to learn graph structure and representation.<n>We propose an Energy-based Contrastive Learning (ECL) guided Graph Structure Refinement (GSR) framework, denoted as ECL-GSR.<n>ECL-GSR achieves faster training with fewer samples and memories against the leading baseline, highlighting its simplicity and efficiency in downstream tasks.
  arXiv  Detail & Related papers  (2024-12-20T04:05:09Z)
• Training Strategies for Isolated Sign Language Recognition [72.27323884094953]
  This paper introduces a comprehensive model training pipeline for Isolated Sign Language Recognition.<n>The constructed pipeline incorporates carefully selected image and video augmentations to tackle the challenges of low data quality and varying sign speeds.
  arXiv  Detail & Related papers  (2024-12-16T08:37:58Z)
• On Discriminative Probabilistic Modeling for Self-Supervised Representation Learning [85.75164588939185]
  We study the discriminative probabilistic modeling on a continuous domain for the data prediction task of (multimodal) self-supervised representation learning.<n>We conduct generalization error analysis to reveal the limitation of current InfoNCE-based contrastive loss for self-supervised representation learning.<n>We propose a novel non-parametric method for approximating the sum of conditional probability densities required by MIS.
  arXiv  Detail & Related papers  (2024-10-11T18:02:46Z)
• ISR: Invertible Symbolic Regression [7.499800486499609]
  Invertible Symbolic Regression is a machine learning technique that generates analytical relationships between inputs and outputs of a given dataset via invertible maps. We transform the affine coupling blocks of INNs into a symbolic framework, resulting in an end-to-end differentiable symbolic invertible architecture. We show that ISR can serve as a (symbolic) normalizing flow for density estimation tasks.
  arXiv  Detail & Related papers  (2024-05-10T23:20:46Z)
• The Role of Foundation Models in Neuro-Symbolic Learning and Reasoning [54.56905063752427]
  Neuro-Symbolic AI (NeSy) holds promise to ensure the safe deployment of AI systems. Existing pipelines that train the neural and symbolic components sequentially require extensive labelling. New architecture, NeSyGPT, fine-tunes a vision-language foundation model to extract symbolic features from raw data.
  arXiv  Detail & Related papers  (2024-02-02T20:33:14Z)
• SymbolNet: Neural Symbolic Regression with Adaptive Dynamic Pruning for Compression [1.0356366043809717]
  We propose $ttSymbolNet$, a neural network approach to symbolic regression specifically designed as a model compression technique.<n>This framework allows dynamic pruning of model weights, input features, and mathematical operators in a single training process.
  arXiv  Detail & Related papers  (2024-01-18T12:51:38Z)
• Deep Generative Symbolic Regression [83.04219479605801]
  Symbolic regression aims to discover concise closed-form mathematical equations from data. Existing methods, ranging from search to reinforcement learning, fail to scale with the number of input variables. We propose an instantiation of our framework, Deep Generative Symbolic Regression.
  arXiv  Detail & Related papers  (2023-12-30T17:05:31Z)
• Transformer-based Planning for Symbolic Regression [18.90700817248397]
  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.
  arXiv  Detail & Related papers  (2023-03-13T03:29:58Z)
• PredRNN: A Recurrent Neural Network for Spatiotemporal Predictive Learning [109.84770951839289]
  We present PredRNN, a new recurrent network for learning visual dynamics from historical context. We show that our approach obtains highly competitive results on three standard datasets.
  arXiv  Detail & Related papers  (2021-03-17T08:28:30Z)
• Neural BRDF Representation and Importance Sampling [79.84316447473873]
  We present a compact neural network-based representation of reflectance BRDF data. We encode BRDFs as lightweight networks, and propose a training scheme with adaptive angular sampling. We evaluate encoding results on isotropic and anisotropic BRDFs from multiple real-world datasets.
  arXiv  Detail & Related papers  (2021-02-11T12:00:24Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.