arXiv:2509.15441cs.LGcs.SC2025-09中稿 · publication in the…被引 1
用热带几何计算带跳跃连接的神经网络线性区域，揭示训练难点与跳跃连接优势。
Computing Linear Regions in Neural Networks with Skip Connections
- 用热带代数表示激活函数，将网络分段线性区域转化为几何问题
- 实验发现跳跃连接能显著增加线性区域数量，缓解过拟合
- 适合研究模型可解释性与网络结构设计的研究者
神经网络是机器学习的重要工具。通过热带算术表示分段线性激活函数，可应用热带几何方法。本文提出算法以计算神经网络中作为线性映射的区域。通过计算实验，我们深入分析了神经网络训练的困难，特别是过拟合问题以及跳跃连接带来的优势。
原文摘要 · Abstract (English)
Neural networks are important tools in machine learning. Representing piecewise linear activation functions with tropical arithmetic enables the application of tropical geometry. Algorithms are presented to compute regions where the neural networks are linear maps. Through computational experiments, we provide insights on the difficulty to train neural networks, in particular on the problems of overfitting and on the benefits of skip connections.
神经网络线性区域跳跃连接热带几何
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