The paper introduces a computational tropical geometry framework for symbolically analyzing neural networks with tropical activations. It presents an algorithm that computes the network’s linear regions as explicit unions of polyhedra, proves its correctness, and connects the number of linear regions to the monomials in the tropical expression. The authors also define the Hoffman constant to bound distances to the farthest linear region and release the open‑source Julia library TropicalNN.jl to implement these tools, demonstrating their use on proof‑of‑concept examples.
By Paul Lezeau, Thomas Walker, Yueqi Cao, Shiv Bhatia, Anthea Monod
arXiv:2605. 13894v2 Announce Type: replace-cross Abstract: In this work, we introduce a Tropical Axial Attention neural reasoning architecture that replaces vanilla softmax dot-product attention with max-plus operators, inducing a piecewise-linear structure aligned with dynamic programming formulations.
By Chris Teska, Kurt Pasque, Ruriko Yoshida, Baran Hashemi
arXiv:2512. 18454v3 Announce Type: replace Abstract: Predictive machine learning models generally excel on in-distribution data, but their performance degrades on out-of-distribution (OOD) inputs.
By David Graber, Victor Armegioiu, Rebecca Buller, Siddhartha Mishra
arXiv:2608. 05336v1 Announce Type: cross Abstract: Molecular representations are essential for the evaluation of molecular similarity and the development of structure-property relationships.
By Jacob W. Toney, Ayleen Y. Farnood, Samir Darouich, Heather J. Kulik
arXiv:2507.23559v2 Announce Type: replace-cross
Abstract: Certain data are naturally modeled by networks or weighted graphs, be they biological networks or mobility networks. When there is no canonic...
By Elodie Maignant, Xavier Pennec, Alain Trouv\'e, Anna Calissano
arXiv:2507.21135v2 Announce Type: replace
Abstract: We demonstrate how Quantum Cognition Machine Learning (QCML) encodes data as quantum geometry. In QCML, features of the data are represented by lea...
By Alexander G. Abanov, Luca Candelori, Harold C. Steinacker, Martin T. Wells, Jerome R. Busemeyer, Cameron J. Hogan, Vahagn Kirakosyan, Nicola Marzari, Sunil Pinnamaneni, Dario Villani, Mengjia Xu, Kharen Musaelian
arXiv:2608. 14743v1 Announce Type: new Abstract: The identification and reconstruction of the boundaries separating basins of attraction in multistable, multidimensional dynamical systems presents a fundamental challenge in computational dynamics.
By Ellis R. Crabtree, Dimitris G. Giovanis, Anastasia Georgiou, George Datseris, Ioannis G. Kevrekidis
arXiv:2509. 22468v2 Announce Type: replace-cross Abstract: High-quality molecular representations are essential for property prediction and molecular design, yet large labeled datasets remain scarce.
By Boshra Ariguib, Mathias Niepert, Andrei Manolache
arXiv:2609.38506v1 Announce Type: new
Abstract: Tree-like branching structures are common in nature, from botanical trees to neurons, blood vessels and respiratory trees. Their branching shape often...
By Umer Gupta, Saku Peltonen, Martin Ritzert
Heat Field Signatures (HFS) lift irregular point clouds into a multiscale family of smooth ambient heat fields, enabling closed‑form computation of global and local geometric signatures directly from pairwise distances. HFS captures heat concentration, intrinsic dimension, anisotropy, and scale transitions, and introduces the Heat Dimension Spectrum (HDS) as a compact multiscale summary. The method serves as a descriptor, lightweight learned representation, or feature channel for neural point‑cloud models, outperforming strong baselines on synthetic and real‑world benchmarks while reducing end‑to‑end cost.
By Yuanqing Wang, Yapeng Tian, Baris Coskunuzer
arXiv:2608. 04257v1 Announce Type: new Abstract: Blood-brain barrier permeability (BBBP) prediction is a critical screening task in central nervous system drug discovery, where candidate molecules must be assessed for whether they can cross, or should be prevented from crossing, the blood-brain barrier.
By Marco Vieto Vega, Long D. Nguyen, Binh P. Nguyen
The paper introduces Bayesian matrix-valued graphs (BMVG), where each edge is represented by a symmetric positive-definite matrix instead of a scalar weight, allowing the capture of direction-dependent interactions in scientific graphs. Using the affine-invariant Riemannian metric, BMVG quantifies deformation magnitude and signed directions of edge changes across contexts, and demonstrates competitive performance against existing methods in precision recovery and structural change detection. Experiments on weather data and TCGA-BRCA gene networks show that BMVG can reveal context-dependent reconfigurations in spatial coupling and gene-module interactions.
By Papri Dey