CauchyNet: Compact and Data-Efficient Learning using Holomorphic Activation Functions
This provides an efficient tool for predictive modeling in resource-constrained and data-scarce environments, though it appears incremental as it builds on existing complex-valued neural network concepts.
The paper tackled function approximation tasks like time series forecasting and missing data imputation by proposing CauchyNet, a neural network using complex-valued activation functions based on Cauchy's integral formula, which achieved up to 50% lower mean absolute error with fewer parameters compared to state-of-the-art models.
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.