A Free Probabilistic Framework for Analyzing the Transformer-based Language Models
This work offers a theoretical perspective on structural dynamics in large language models, which is incremental as it applies existing mathematical frameworks to a known domain.
The authors tackled the problem of analyzing Transformer-based language models by developing a formal operator-theoretic framework using free probability theory, which reinterprets attention as non-commutative convolution and provides insights into spectral dynamics and generalization bounds.
We present a formal operator-theoretic framework for analyzing Transformer-based language models using free probability theory. By modeling token embeddings and attention mechanisms as self-adjoint operators in a tracial \( W^* \)-probability space, we reinterpret attention as non-commutative convolution and describe representation propagation via free additive convolution. This leads to a spectral dynamic system interpretation of deep Transformers. We derive entropy-based generalization bounds under freeness assumptions and provide insight into positional encoding, spectral evolution, and representational complexity. This work offers a principled, though theoretical, perspective on structural dynamics in large language models.