The paper introduces FHEAT, a fractional diffusion operator derived from the discrete cosine transform, to learn how much spectral mixing each stage of a 3D medical segmentation network should perform. By reparameterizing the operator with a semigroup time, the authors enable the optimizer to decide whether global mixing is needed, resulting in a lightweight U‑shaped architecture (Light‑UNETR) paired with a Kolmogorov‑Arnold mixer (KAN3D). In semi‑supervised experiments, FHEAT‑Seg achieves state‑of‑the‑art Dice scores while dramatically reducing FLOPs through learned spectral sparsification.
By Yi-Hui Shen, Tie-Qiang Li
The paper investigates the relationship between discrete gradient descent (GD) and its continuous-time gradient-flow counterpart in the context of ReLU neural networks. It shows that while GD states converge over a finite horizon, the exact discrete derivatives obtained via automatic differentiation do not necessarily match the derivative of the limiting flow, due to singular curvature at activation events. The authors provide a Stieltjes representation that separates continuous regional Hessians from atomic interface curvature, revealing rank-one discrepancies at activation jumps and demonstrating that even globally strongly convex residual-ReLU losses can exhibit large sensitivity ratios on certain initialization sets.
By Xiaoyang Li, Runni Zhou
arXiv:2607. 15773v1 Announce Type: new Abstract: Higher-order couplings enhance the expressive power of hypergraph neural networks (HGNNs), but they also intensify representation collapse in deep propagation due to strong multi-way feature mixing.
By Zhiheng Zhou, Mengyao Zhou, Yancheng Chen, Dengyi Zhao, Xingqin Qi, Guiying Yan
arXiv:2602. 08542v3 Announce Type: replace-cross Abstract: Given a weighted undirected graph, a number of clusters $k$, and an exponent $z$, the goal in the $(k, z)$-clustering problem on graphs is to select $k$ vertices as centers that minimize the sum of the distances raised to the power $z$ of each vertex to its closest center.
By Emilio Cruciani, Sebastian Forster, Antonis Skarlatos
The paper investigates how exact automatic differentiation behaves under hard‑ReLU gradient descent. It shows that while gradient‑descent states converge to the piecewise‑smooth gradient flow, the derivative of the training map does not, due to missing event‑time sensitivities captured by saltation matrices. The study demonstrates that for convex objectives, activation events can create large sensitivity gaps, and provides empirical evidence that event‑aware corrections are necessary for accurate flow derivatives.
By Xiaoyang Li, Runni Zhou
arXiv:2607. 22906v1 Announce Type: new Abstract: We study adaptive gradient descent for continuously differentiable, possibly nonconvex objectives under one-sided H\"older regularity.
By Arzu Ahmadova, Ismail Huseynov
arXiv:2607. 16568v1 Announce Type: new Abstract: Function-preserving network growth techniques such as Net2Net and progressive stacking expand a model's capacity without destroying its learned function, but existing formulations either tolerate numerical perturbations or require a full rebuild of the training program.
By Abdallah Khemais (ISITCOM, University of Sousse)
arXiv:2608.21466v1 Announce Type: new
Abstract: We develop spectral algorithms for selecting state-space partitions that define averaging kernels for finite, ergodic and reversible Markov chains. For...
By Michael C. H. Choi, Youjia Wang
arXiv:2609. 30477v1 Announce Type: cross Abstract: Exact Euclidean \(K\)-means partitions \(n\) observations into \(K\) unlabelled clusters, but the unrestricted search is generally exponential.
By Yordan P. Raykov, Max A. Little
Spectral-Guided Diffusion introduces a method to accelerate diffusion inference by identifying and reusing residual branches that need not be recomputed during the trajectory. The approach uses a Spectral Concentration Ratio (SCR) combined with Frobenius magnitude to create an offline sensitivity proxy and deterministic lifetime for each scheduled unit, eliminating the need for routers or input-dependent searches. Experiments on models such as LLaDA-8B, DiT-XL/2, U-ViT-L, and SDXL show that this scheduling preserves quality better than several baselines and achieves up to a 3.0× wall‑clock speedup over eager inference.
By Ibne Farabi Shihab, Abu Sa-Adat Mohamed Moon-Im Al Ahsan, Anuj Sharma
arXiv:2606. 00366v1 Announce Type: new Abstract: We consider the problem of generating a large collection of initial guesses for local minima of multimodal non-convex continuous optimization problems.
By Anjian Li, Bartolomeo Stellato, Ryne Beeson
arXiv:2606. 21253v2 Announce Type: replace Abstract: Continual learning that is gradient-free, local, online, and append-only is attractive for edge and streaming deployment, but its value is usually argued informally.
By Jianwei Lou (RailMind Systems, Neuss, Germany)