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Monitoring Dynamic Changes In Mitochondrial Calcium Levels During Apoptosis Using A Genetically Encoded Calcium Sensor

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UniSymNet: A Unified Symbolic Network with Sparse Encoding and Bi-level Optimization.

Xinxin Li¹, Juan Zhang², Da Li³

¹School of Mathematical Sciences, East China Normal University, Shang Hai, 200241, China.

Neural Networks : the Official Journal of the International Neural Network Society

|February 2, 2026

Summary

This summary is machine-generated.

This study introduces a Unified Symbolic Network (UniSymNet) to improve mathematical expression discovery. UniSymNet unifies operators for lower complexity and better performance in modeling natural phenomena.

Keywords:

Symbolic network Symbolic regression Transformer model

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Area of Science:

Artificial Intelligence
Machine Learning
Computational Mathematics

Background:

Symbolic Regression (SR) is key for discovering mathematical expressions to model natural phenomena.
Traditional SR methods struggle with complex tree structures, limiting performance.
Existing symbolic networks face challenges with multivariate operators and fixed architectures, leading to overfitting.

Purpose of the Study:

To propose a novel Unified Symbolic Network (UniSymNet) that overcomes limitations of existing symbolic networks.
To enhance the expressivity and reduce the complexity of discovered mathematical expressions.
To develop a flexible training framework adaptable to diverse datasets.

Main Methods:

Unifying nonlinear binary operators into nested unary operators to create multivariate operators.
Developing a bi-level optimization framework: Transformer pre-training for structure selection and objective-specific parameter optimization.
Rigorous theoretical proof to establish UniSymNet's capabilities.

Main Results:

UniSymNet demonstrates theoretical advantages in complexity and expressivity.
The bi-level optimization framework enables flexible structure adaptation and reduced expression complexity.
Evaluations on Standard Benchmarks and SRBench show high symbolic solution rates, fitting accuracy, and low complexity.

Conclusions:

UniSymNet offers a promising new paradigm for symbolic regression with enhanced capabilities.
The proposed training framework effectively guides structure selection and parameter optimization.
UniSymNet achieves superior performance in discovering accurate and concise mathematical expressions.