arXiv:2608. 04460v1 Announce Type: cross Abstract: The quantitative analysis of 3D neuronal morphologies requires capturing both graph topology and spatial geometry.
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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.
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.
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.
arXiv:2608. 05336v1 Announce Type: cross Abstract: Molecular representations are essential for the evaluation of molecular similarity and the development of structure-property relationships.
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...
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...