arXiv:2503. 04263v2 Announce Type: replace Abstract: Motivated by applications to the simulation of quantum many-body systems by neural networks, researchers have suggested several models which are antisymmetric by construction, and can approximate all antisymmetric functions.
arXiv:2511. 12398v2 Announce Type: replace Abstract: Deep neural networks have been widely used as universal approximators for functions with inherent physical structures, including permutation symmetry.
arXiv:2608. 11911v1 Announce Type: cross Abstract: A central promise of useful quantum advantage is the ability to compute ground states of Hamiltonian systems beyond the reach of classical simulation methods.
arXiv:2610.17424v1 Announce Type: cross Abstract: Respecting a-priori known symmetries of underlying data is a key principle in designing efficient neural architectures. Convolutional neural networks...
arXiv:2606. 00442v1 Announce Type: new Abstract: Many machine learning techniques rely on approximating a loss function's curvature, but this is notoriously hard to do at the scale of modern deep networks.
The paper presents a theoretical analysis of symmetric autoencoders, a class of deep learning architectures frequently used in machine learning tasks. It distinguishes between different symmetric designs and shows that the reconstruction error of orthonormal symmetric autoencoders can be interpreted via the Eckart‑Young‑Schmidt theorem. Building on this insight, the authors propose an EYS‑based initialization strategy using repeated SVD, and validate its effectiveness through numerical experiments comparing it to conventional deep autoencoders.
arXiv:2608. 12010v1 Announce Type: new Abstract: Equivariant Neural Networks (ENNs) have empowered numerous applications in scientific fields.
Equivariant Neural Networks (ENNs) have empowered numerous applications in scientific fields. Despite their remarkable capacity for representing geometric structures, ENNs suffer from degraded expressivity when processing symmetric inputs: the output representations are invariant to transformations that extend beyond the input's symmetries.
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.
arXiv:2607. 23645v1 Announce Type: cross Abstract: Communication complexity provides a natural framework for quantifying the classical resources required to reproduce quantum statistics.
arXiv:2606. 15983v1 Announce Type: cross Abstract: Recent theoretical progress has established conditions under which machine learning models can efficiently predict ground-state properties of gapped local Hamiltonians when trained on quantum-generated data.
arXiv:2603. 00408v2 Announce Type: replace-cross Abstract: We present an Ising-compatible framework for formal neural-network robustness verification under bounded input perturbations.
arXiv:2606. 31536v1 Announce Type: new Abstract: As Quantum Machine Learning (QML) transitions toward practical implementation, the field faces a critical architectural bottleneck that challenges the fundamental assumptions of classical statistical learning theory.