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Discovering Mathematical Expressions Through DeepSymNet: A Classification-Based Symbolic Regression Framework.

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    Symbolic regression (SR) is accelerated by treating expression structure as a classification problem. A novel DeepSymNet model enhances performance and simplifies complex problems for faster, more robust results.

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    Area of Science:

    • Computer Science
    • Artificial Intelligence
    • Machine Learning

    Background:

    • Symbolic regression (SR) aims to discover mathematical expressions from data, crucial for interpretable machine learning and knowledge discovery.
    • The primary challenge in SR is the NP-hard nature of identifying expression structures, leading to significant computational time.
    • Existing SR methods face limitations in efficiency and scalability due to the complexity of structure discovery.

    Purpose of the Study:

    • To develop a faster and more robust algorithm for symbolic regression.
    • To address the computational bottleneck in finding mathematical expression structures.
    • To improve the representation of symbolic expressions for enhanced prediction accuracy.

    Main Methods:

    • Symbolic regression problem reframed as a supervised classification task for accelerated solutions.
    • Implementation of classification techniques like equivalent label merging and sample balance for improved algorithm robustness.
    • Introduction of DeepSymNet, a novel neural network architecture for symbolic expression representation, offering superior expressiveness and reduced search space.

    Main Results:

    • DeepSymNet demonstrates strong representational capabilities with more concise labels compared to existing methods.
    • The proposed approach effectively decomposes the SR problem into manageable subproblems, simplifying the solving process.
    • Experimental validation on synthetic and public datasets confirms the algorithm's effectiveness and superiority over other SR methods.

    Conclusions:

    • The classification-based approach combined with DeepSymNet significantly enhances the speed and efficiency of symbolic regression.
    • DeepSymNet provides a powerful and compact representation for symbolic expressions, advancing the field of interpretable machine learning.
    • The proposed method offers a promising solution for complex knowledge discovery tasks requiring accurate and efficient mathematical expression inference.