摘要
针对神经网络内部决策流程与运算机制难以被直观阐释这一问题,采用拓扑数据分析方法对多层感知器在特定合成数据集上的二元分类任务的流程及机制展开研究。基于持续同调算法,通过调整距离阈值,构建不同尺度的VR(Vietoris-rips)复形并形成过滤,进而计算持久性图,以此呈现持续同调信息。在此基础上,通过持久性景观将持久性图的离散特征转化为连续函数,并提取各函数值的第k个最大值,构建k阶景观。各阶景观形成激活景观后,其可视化平均激活景观曲线的变化趋势结果清晰展现了不同网络深度和训练精度阈值对数据拓扑结构演变的动态影响机理。由此综合形成了一套神经网络决策机制的拓扑分析方法,用该方法可以实现神经网络特征提取过程的优化。
To address the challenge of intuitively interpreting the internal decision-making processes and operational mechanisms of neural networks,this study employs topological data analysis to investigate the workflow and mechanisms of a multi-layer perceptron(MLP)in binary classification tasks on a specific synthetic dataset.Based on the persistent homology algorithm,Vietoris-rips(VR)complexes at different scales are constructed by adjusting distance thresholds,forming a filtration,and subsequently computing persistence diagrams to visualize persistent homology information.Building on this,the discrete features of persistence diagrams are converted into continuous functions via persistence landscapes,and the k-th maximum value of each function is extracted to construct k-th order landscapes.By integrating these k-th order landscapes to form activation landscapes,the visualized trends of the average activation landscape curves clearly illustrate the dynamic influence of network depth and training accuracy thresholds on the evolution of the data’s topological structure.This integrated approach develops a topological analysis method for the decision-making mechanisms of neural network,which can be used to optimize the feature extraction process in neural networks.
作者
孙海蓉
鹿奂芃
霍新爽
SUN Hairong;LU Huanpeng;HUO Xinshuang(Department of Automation,North China Electric Power University,Baoding 071003,China;Hebei Power Generation Process Simulation and Optimization Control Technology Innovation Center(North China Electric Power University),Baoding 071003,China)
出处
《电力科学与工程》
2025年第12期65-72,共8页
Electric Power Science and Engineering
基金
河北省科技计划资助项目(22567643H)。
关键词
多层感知器
拓扑数据分析
持续同调
持久性景观
multi-layer perceptron
topological data analysis
persistent homology
persistence landscape
