arXiv Machine Learning By Akram Aldroubi

Partition of Unity Neural Networks for Interpretable Classification with Explicit Class Regions

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arXiv:2602. 00511v3 Announce Type: replace Abstract: We introduce \emph{Partition of Unity Neural Networks} (PUNNs), a neural-network architecture for multiclass classification based on the classical mathematical notion of a partition of unity.

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arXiv Machine Learning
Oct 22

Tractable Inference with Kolmogorov-Arnold Networks

The paper introduces TOUCKANs, a variant of Kolmogorov–Arnold networks that use finite‑degree polynomial outer functions to create a decomposable sum–product structure. This design allows expectations, variances, and higher moments to be computed via deterministic recursions over one‑dimensional integrals, eliminating the need for costly Monte Carlo sampling even in high dimensions. Experiments on uniform and Gaussian benchmarks up to 50 dimensions show deterministic mean and variance errors below those of fixed‑budget Monte Carlo, and the method successfully enforces conservation laws and normalization constraints in physical simulations such as Cahn–Hilliard mass conservation and Schrödinger eigenpair computation.

By Juan Diego Toscano, Sascha Ranft, Zhiwei Gao, Li-Lian Wang, George Em Karniadakis