arXiv:2607. 06634v1 Announce Type: new Abstract: Compact networks built from Clifford algebra Cl(3,0) primitives are exactly SO(3)-equivariant and learn synthetic 3D vector laws from few samples.
arXiv:2607. 01449v1 Announce Type: new Abstract: We propose a novel hybrid neural architecture, the Geometry-aware R-Structured Kolmogorov-Arnold Network (GRS-KAN), which integrates V.
arXiv:2608.28853v1 Announce Type: cross Abstract: Equivariant graph neural networks provide a principled way to model geometric systems, but efficient first-order architectures remain limited in how...
The paper introduces Product Interactions, an algebraic framework that unifies modern neural architectures by treating data as algebraic elements and multiplication as a core operation. It shows how convolutional, equivariant, state‑space, and attention models arise from different orders of product interactions and symmetry constraints, and demonstrates that a simplified algebraic dynamical layer can outperform Mamba on CIFAR‑10. The framework positions architecture design as a systematic algebraic construction problem, enabling both analysis of existing models and generation of new ones.
arXiv:2607. 28755v1 Announce Type: new Abstract: Over the last decade, neural networks have been applied to an increasingly diverse range of applications, including data with rich geometric, topological, or symmetry-related structure.
arXiv:2602. 22895v2 Announce Type: replace-cross Abstract: Implementations of symmetric positive definite (SPD) matrix-based neural networks for neural decoding remain fragmented across research codebases and Python packages.
arXiv:2605. 18106v3 Announce Type: replace-cross Abstract: A striking geometric disparity has long persisted in the practice of deep learning.
arXiv:2609.21039v1 Announce Type: new Abstract: A pervasive structural pattern in modern deep learning is the linear factorization block: a submodule of the form $W = BA$ in which two parameter matri...
The paper investigates how parameter symmetries in overparameterized nonlinear neural networks affect representational geometry. It shows that these symmetries can be described by three basic feature transformations—addition, duplication, and scaling—allowing a closed‑form decomposition of representations into essential and auxiliary parts. The study further demonstrates that implementation‑level selection rules can resolve the resulting degeneracy, producing identifiable geometries that reflect feature contributions to the network’s function.
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:2608. 12010v1 Announce Type: new Abstract: Equivariant Neural Networks (ENNs) have empowered numerous applications in scientific fields.
arXiv:2607. 03798v1 Announce Type: cross Abstract: Symmetry is everywhere in nature and society.