arXiv:2605. 20440v2 Announce Type: replace Abstract: Symmetry is central to the physical sciences, yet machine learning usually captures it only approximately, leaving a residual per-step equivariance error $\varepsilon$ that compounds with depth $M$ as $M\varepsilon$, whereas exact equivariance holds at unbounded depth; we demonstrate this divergence at fourteen orders of magnitude.
By Paulina Hoyos, Shashanka Ubaru, Dongsung Huh, Vasileios Kalantzis, Kenneth L. Clarkson, Misha Kilmer, Haim Avron, Lior Horesh
arXiv:2606. 17851v1 Announce Type: new Abstract: A wide range of neurosymbolic (NeSy) systems compute one functional: a belief-weighted sum of a logical quantity over a space of $\sigma$-structures, of which weighted model counting, fuzzy logic, and probabilistic logic are special cases.
By Fernando Zhapa-Camacho, Robert Hoehndorf
arXiv:2607. 03108v1 Announce Type: new Abstract: Post-hoc analysis of trained neural network weights often seeks to recover geometric structure directly from the parameters.
By Naoya Chiba, Satoshi Sugiyama, Yuki Uranishi
arXiv:2607. 26344v1 Announce Type: new Abstract: A gradient-based GNN explainer given a molecule with two chemically equivalent nitro groups assigns them attribution scores that are equal to the last bit.
By Xin Xu, Siru Tao, Kaizhen Tan
arXiv:2608. 10420v1 Announce Type: new Abstract: Reasoning shortcuts are solutions of a neurosymbolic system's rules that produce correct predictions through unintended concepts.
By Xin Xu
arXiv:2606. 07627v1 Announce Type: new Abstract: Transfer learning presumes that a representation learned on source tasks carries structure that remains usable on related target tasks.
By Luciano Melodia
arXiv:2607. 07032v2 Announce Type: replace Abstract: Spectral positional encodings (PEs) for \emph{directed} graphs face two obstacles: magnetic Laplacians require an $O(n^3)$ Hermitian eigendecomposition per potential, and their complex eigenvectors are defined only up to unitary gauge, which prior work handles with basis-invariant architectures.
By Jiaqing Xie, Yuxin Wang
arXiv:2607. 07032v1 Announce Type: new Abstract: Spectral positional encodings (PEs) for \emph{directed} graphs face two obstacles: magnetic Laplacians require an $O(n^3)$ Hermitian eigendecomposition per potential, and their complex eigenvectors are defined only up to unitary gauge, which prior work handles with basis-invariant architectures.
By Jiaqing Xie, Yuxin Wang
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.
By Ning Lin, Jiacheng Cen, Anyi Li, Wenbing Huang, Hao Sun
arXiv:2607. 15536v1 Announce Type: cross Abstract: 3D Gaussian Splatting (3DGS) captures scenes by coupling explicit geometry (position, covariance) with view-dependent photometry (Spherical Harmonics).
By Chankyo Kim, Maani Ghaffari
arXiv:2607. 23182v1 Announce Type: cross Abstract: We prove the identifiability of deep generative models (DGMs) with piecewise-affine (PWA) decoders and Gaussian mixture model (GMM) priors, in a purely unsupervised setting.
By Pengzhou Wu