Transformer spectral optimization: From gradient frequency analysis to adaptive spectral integration

Abstract

This paper explores a novel perspective on Transformer optimization by analyzing gradient characteristics in the frequency domain. First, we systematically quantify spectral differences between attention and MLP layer gradients, revealing that attention gradients consistently exhibit higher frequency content (23% higher mean frequency, 37% more prominent high-frequency components) compared to MLP gradients. Second, we demonstrate the potential of using spectral features for monitoring training dynamics, finding a strong correlation (r=-0.82) between early-stage spectral entropy and final validation loss. Third, building on these insights, we introduce Adaptive Spectral Integration (ASI), an optimization framework that selectively filters gradient spectra during training. Our experiments on GPT2-small with standard datasets (Penn Treebank and WikiText-2) show that ASI achieves notable inference speed improvements (6.3%-9.1%) and training time reductions (13.2%-18.8%) while maintaining comparable model quality. However, cross-architecture validation with BERT-style models reveals that ASI’s efficiency benefits are architecture-dependent, showing limited improvements on bidirectional models. These findings provide evidence that frequency domain analysis offers valuable insights for optimizing autoregressive Transformer models, while highlighting the need for architecture-aware spectral optimization strategies.