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