The underlying structures of self-attention: symmetry, directionality, and emergent dynamics in Transformer training
This provides a theoretical perspective to improve interpretability of Transformer models, but it is incremental as it builds on existing self-attention analysis without introducing a new paradigm.
The paper tackled the unclear embedding of information in self-attention matrices by developing a mathematical framework to analyze their structures, showing that bidirectional training induces symmetry and autoregressive training leads to directionality, with symmetric initialization improving encoder-only model performance on language tasks.
Self-attention is essential to Transformer architectures, yet how information is embedded in the self-attention matrices and how different objective functions impact this process remains unclear. We present a mathematical framework to analyze self-attention matrices by deriving the structures governing their weight updates. Using this framework, we demonstrate that bidirectional training induces symmetry in the weight matrices, while autoregressive training results in directionality and column dominance. Our theoretical findings are validated across multiple Transformer models - including ModernBERT, GPT, LLaMA3, and Mistral - and input modalities like text, vision, and audio. Finally, we apply these insights by showing that symmetric initialization improves the performance of encoder-only models on language tasks. This mathematical analysis offers a novel theoretical perspective on how information is embedded through self-attention, thereby improving the interpretability of Transformer models.