Robust Gradient-Adaptive RBF Network with Lambert-Kaniadakis Activation for High-Fidelity Stock Price Prediction

This paper proposed a robust gradient-adaptive Radial Basis Function (RBF) network architecture for high-fidelity stock price prediction, addressing the challenges posed by noisy and non-stationary financial time-series data. The proposed method integrates a novel Lambert-Kaniadakis hybrid activation framework with a distributionally robust gradient estimation module, enabling adaptive feature extraction and noise suppression. The RBF layer employs a specialized kernel combining exponential decay with Lambert-Kaniadakis deformation, which captures both local and global market patterns more effectively than conventional Gaussian RBFs. Furthermore, the system incorporates a frequency-adaptive learning rate scheduler that dynamically adjusts optimization parameters based on short-term and long-term gradient variance metrics, thereby stabilizing training in volatile regimes. A key innovation lies in the closed-loop interaction between robust gradient processing and adaptive learning rate modulation, which jointly mitigate the impact of outliers while preserving sensitivity to critical market transitions. Experimental validation demonstrates significant improvements in prediction accuracy and robustness compared to existing neural network and kernel-based approaches. The implementation leverages modern parallel computing frameworks for efficient computation of complex activation functions and real-time gradient statistics. This work advances the state-of-the-art in financial time-series modeling by providing a principled, adaptive framework that balances noise resilience with pattern recognition capabilities.