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.
arXiv:2607. 17327v1 Announce Type: cross Abstract: Quantum machine learning models define probabilistic input--output maps through coherent quantum evolution and measurement.
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.
arXiv:2609.00372v1 Announce Type: cross Abstract: With quantum sensors, simulators and networks emerging, a future of quantum technology may produce quantum states as data---that is, coherently rathe...
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.
arXiv:2510.06848v3 Announce Type: replace-cross Abstract: Bell sampling is a simple yet powerful tool based on measuring two copies of a quantum state in the Bell basis, and has found applications in...
arXiv:2609.37958v1 Announce Type: new Abstract: As the input dimension $n$ grows, rule-based machine learning, such as Learning Classifier Systems (LCSs), faces a fundamental scalability bottleneck f...
arXiv:2609.21567v1 Announce Type: cross Abstract: Quantum Signal Processing is a powerful quantum framework for generating and approximating univariate polynomials. However, QSP is often limited by c...
arXiv:2609.07240v1 Announce Type: new Abstract: Here we investigate the stability of the Kolmogorov--Arnold representation theorem (KART) under adversarial reparameterisations of the hidden layer for...
arXiv:2503. 17020v2 Announce Type: replace-cross Abstract: Kernel methods compare inputs through feature maps.
arXiv:2507.21135v2 Announce Type: replace Abstract: We demonstrate how Quantum Cognition Machine Learning (QCML) encodes data as quantum geometry. In QCML, features of the data are represented by lea...
arXiv:2502. 00037v4 Announce Type: replace-cross Abstract: We introduce Superstate Quantum Mechanics (SQM), a theory that considers states in Hilbert space subject to multiple quadratic constraints, with ``energy'' also expressed as a quadratic function of these states.
arXiv:2503. 24092v2 Announce Type: replace-cross Abstract: Motivated by the rapidly growing field of mathematics for operator approximation with neural networks, we present a novel universal operator approximation theorem for broad classes of encoder-decoder architectures and a wide range of input and output spaces.