A Free Probabilistic Framework for Analyzing the Transformer-based Language Models

• URL: http://arxiv.org/abs/2506.16550v2
• Date: Sun, 27 Jul 2025 20:04:17 GMT
• Title: A Free Probabilistic Framework for Analyzing the Transformer-based Language Models
• Authors: Swagatam Das,
• Abstract summary: We present a formal operator-theoretic framework for analyzing Transformer-based language models using free probability theory.<n>This work offers a principled, though theoretical, perspective on structural dynamics in large language models.
• Score: 19.78896931593813
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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