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
The paper introduces GSF-χ, a graph transformer that incorporates global stereochemical fields to handle chiral molecules. Unlike traditional models that focus on a single atom, GSF-χ modulates all pairwise interactions using stereogenic units, producing a reflection‑even phase field and a handedness pseudoscalar that guide relative rotations in latent query–key blocks. The authors prove the operator’s even–odd decomposition and demonstrate that GSF-χ improves central‑ECD, axial Rotation, and Symbol metrics over strong baselines, while maintaining enantiomer‑pair consistency through a C₂ projection.
By Jiaqing Xie, Yuxin Wang, Xipeng Qiu
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
The paper introduces the Intersection Euler Characteristic Profile, a topological metric for measuring class overlap in neural representations, and provides exact permutation and sign‑flip tests to assess disentanglement across layers. Using this statistic, the authors analyze 111 networks and 52,650 measurements, finding that disentanglement is depth‑graded, occurs early, and is influenced by training choices such as augmentation and weight decay. The study also demonstrates that the unnormalized mass of the profile predicts test accuracy, while the dimensionless quotient does not outperform simple linear probes.
By Sushovan Majhi
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:2608.30417v1 Announce Type: new
Abstract: We give a complete characterization of equivariant multi-head self-attention (MHSA): if an MHSA layer is equivariant to a symmetry group $G$, then $G$...
By T\=ikun \^Ong
arXiv:2609.40290v1 Announce Type: cross
Abstract: In algorithmic statistics a string x is explained by a finite set containing it, and Kolmogorov's structure function records the smallest such model...
By Romie Banerjee
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