Spectral momentum integration: hybrid optimization of frequency and time domain gradients

We propose Spectral Momentum Integration (SMI), an optimization enhancement that processes gradients in both frequency and time domains. SMI applies the Fast Fourier Transform to selectively filter gradient frequency components before blending them with original gradients using an adaptive scheduling mechanism. Experiments on a character-level language model demonstrate that SMI can achieve inference acceleration while maintaining model performance. Our approach integrates with existing optimizers without modifying model architecture, though it introduces computational overhead and hyperparameter complexity. While our current validation is limited to small-scale experiments, SMI provides a proof-of-concept for incorporating frequency-domain processing into neural network optimization, suggesting potential for broader applications pending large-scale validation.