arXiv Machine Learning By Sviatoslav V. Dzhenzher

Quantum Kolmogorov--Arnold representation theorem for continuous unitary-valued maps

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arXiv:2607. 03187v1 Announce Type: cross Abstract: The classical Kolmogorov--Arnold representation theorem states that any continuous multivariate function can be exactly decomposed into a finite composition of univariate continuous functions and addition operations.

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arXiv AI
Jul 8

Lean-Quantum: Toward AI-Assisted Formalization of Quantum Information

arXiv:2607. 05492v1 Announce Type: cross Abstract: Quantum information theory is built on entropic quantities; among them, the sandwiched R\'enyi relative entropy is a fundamental divergence with various applications, and its data processing inequality (DPI) under quantum channels is a cornerstone result.

By Kazumi Kasaura, Kei Tsukamoto, Kento Mori, Risa Mizuno, Takahiro Namatame, Yuta Oriike, Masaya Taniguchi, Sho Sonoda, Hayata Yamasaki
arXiv Machine Learning
Sep 10

Observability conditions for neural state-space models with eigenvalues and their roots of unity

The paper investigates observability in neural state‑space models, particularly the Mamba architecture, using tools from ordinary differential equations and control theory. It introduces several strategies—based on eigenvalues, roots of unity, permutations, Fourier transforms, and Vandermonde matrices—to enforce observability in high‑dimensional, learnable hidden states while maintaining computational efficiency. The authors also present a shared‑parameter construction for Mamba and a training algorithm that satisfies a Robbins‑Monro condition, contrasting it with classical procedures that fail to meet contraction requirements.

By Andrew Gracyk