用复数激活函数提升小数据预测效率，性能优于传统模型
CauchyNet: Compact and Data-Efficient Learning using Holomorphic Activation Functions
- 将实数数据映射到复平面，利用柯西积分公式设计复数激活函数
- 在交通、能源等多领域测试中，误差比顶尖模型低50%，参数更少
- 适合资源受限或数据稀缺场景，理论基础强且计算开销小
受柯西积分公式启发，提出一种新型神经网络CauchyNet，用于函数逼近任务，如时间序列预测和缺失数据补全。通过将实值数据嵌入复平面，CauchyNet高效捕捉复杂时序依赖关系，在预测性能与计算效率上均优于传统实值模型。该架构基于柯西积分公式并由通用逼近定理支持，具备坚实的函数逼近理论保证。其采用复数激活函数，能在不完整数据下实现稳健学习，同时保持紧凑的参数规模并降低计算开销。在交通、能源消耗及流行病学数据等多元领域广泛实验表明，CauchyNet在预测精度上持续领先当前最优模型，常实现50%更低的平均绝对误差，且参数量更少。这些结果凸显了CauchyNet在资源受限与数据稀疏环境下的有效性和高效性。
原文摘要 · Abstract (English)
A novel neural network inspired by Cauchy's integral formula, is proposed for function approximation tasks that include time series forecasting, missing data imputation, etc. Hence, the novel neural network is named CauchyNet. By embedding real-valued data into the complex plane, CauchyNet efficiently captures complex temporal dependencies, surpassing traditional real-valued models in both predictive performance and computational efficiency. Grounded in Cauchy's integral formula and supported by the universal approximation theorem, CauchyNet offers strong theoretical guarantees for function approximation. The architecture incorporates complex-valued activation functions, enabling robust learning from incomplete data while maintaining a compact parameter footprint and reducing computational overhead. Through extensive experiments in diverse domains, including transportation, energy consumption, and epidemiological data, CauchyNet consistently outperforms state-of-the-art models in predictive accuracy, often achieving a 50% lower mean absolute error with fewer parameters. These findings highlight CauchyNet's potential as an effective and efficient tool for data-driven predictive modeling, particularly in resource-constrained and data-scarce environments.
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