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Autore principale: Das, Swagatam
Natura: Preprint
Pubblicazione: 2025
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Accesso online:https://arxiv.org/abs/2506.16550
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author Das, Swagatam
author_facet Das, Swagatam
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2506_16550
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A Free Probabilistic Framework for Analyzing the Transformer-based Language Models
Das, Swagatam
Machine Learning
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.
title A Free Probabilistic Framework for Analyzing the Transformer-based Language Models
topic Machine Learning
url https://arxiv.org/abs/2506.16550