arXiv:2607. 05815v1 Announce Type: new Abstract: The Minkowski functionals of a field's excursion sets -- area, boundary measure, and Euler characteristic -- describe its level-set morphology; the Euler characteristic is the cheapest handle on topology.
arXiv:2607. 20171v1 Announce Type: cross Abstract: Learned solvers for compressible flow are usually compared to classical methods at equal mesh resolution rather than at equal computational cost, and they typically offer no guarantee that their solutions remain physically admissible.
arXiv:2609.25576v1 Announce Type: cross Abstract: We study the estimation of a $K$-dimensional simplex from $N$ i.i.d.\ points sampled uniformly from its interior; the observations are convex combina...
arXiv:2608. 08322v1 Announce Type: cross Abstract: Physics-informed neural networks applied to the level-set formulation of interface advection commonly augment the residual and initial-condition losses with an eikonal regulariser, penalising the deviation of $\|\nabla\phi\|$ from unity.
arXiv:2608.24568v1 Announce Type: cross Abstract: Deep neural networks generalize well despite their highly nonconvex, overparameterized loss landscapes, a phenomenon often associated with the geomet...
arXiv:2608. 06428v1 Announce Type: new Abstract: Deep Operator Networks (DeepONets; arXiv:1910.
arXiv:2605. 01928v2 Announce Type: replace Abstract: We optimize losses that jump: spiking thresholds, quantized layers, and discrete routing put jumps in the forward pass, where backpropagation does not apply.
arXiv:2608. 19232v1 Announce Type: cross Abstract: Spiking point cloud networks usually scan space in a fixed, input-agnostic order, which leaves the most distinctive resource of spiking computation, the temporal evolution of the membrane potential, unused as a locus of decision-making.
arXiv:2602. 17596v2 Announce Type: replace Abstract: We study pathwise connectivity of sublevel sets for one-hidden-layer ReLU networks with constrained first-layer weights and an $\ell_1$ penalty on the output layer.
arXiv:2604. 20219v2 Announce Type: replace Abstract: Depth is widely viewed as a central contributor to the success of deep neural networks, whereas standard neural network approximation theory typically provides guarantees only for the final output and leaves the role of intermediate layers largely unclear.
arXiv:2603. 15384v2 Announce Type: replace-cross Abstract: We improve and extend persistence spheres, introduced in~\cite{pegoraro2025persistence}.
arXiv:2610.02201v1 Announce Type: cross Abstract: High-resolution 3D generation increasingly relies on voxel latents and multi-stage pipelines that first predict active structure and then synthesize...
M-plicits introduces a multiscale framework for neural implicit surfaces that models a surface as a residual sum of MLPs trained on nested neighborhoods. By localizing supervision to narrow bands around previous zero-level sets, the method achieves robustness to noisy input, avoids costly mesh extraction, and enables a multiscale sphere-tracing algorithm with analytical normal computation. Experiments on Stanford and Thingi32 show superior Chamfer distance and IoU metrics compared to existing methods while using far fewer parameters.