mlsanityData to 14 Oct 2026

Gaussian Universality and Its Breakdown in Tensor-Network Machine Learning

arXiv 2610.06080 ↗First posted 5 Oct 2026quant-ph cs.LGcited by 0

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Abstract (arXiv)

Gaussian-process limits are powerful in describing overparameterized machine learning models, yet their validity in structured tensor-network architectures remains unclear. Here we analytically present a moment-based approach that identifies precise conditions for the emergence and breakdown of Gaussian universality in tensor-network learning models, with a focus on matrix product states. We prove that in the large bond dimension limit, the learning models with both local and global observables converge to Gaussian processes, with explicit finite-size bounds on higher-order moment deviations. Whereas in the large physical dimension limit, the Gaussian universality no longer persists: while the models with local observables retain Gaussian-process behavior, those global cases exhibit persistent non-Gaussian corrections. Our results reveal that Gaussian-process behavior in tensor-network learning is controlled not only by parameter number, but also by architectural scaling, observable locality, and the spectral properties.

Key facts. No citing papers in the map yet (data through 14 Oct 2026). Builds on 49 of its 109 references that are in the map. First posted on arXiv 5 Oct 2026.

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References · 49

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37 more
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