arXiv:2607. 28080v1 Announce Type: cross Abstract: We extend a recently introduced Entropy-Optimal Manifold Clustering (EOMC) to allow for a joint simultaneous identification of subsets and subspaces of relevant features in nonstationary and nonlinear regression problems.
By Illia Horenko
arXiv:2607. 00207v1 Announce Type: cross Abstract: We develop a framework for analyzing the learning dynamics of $\ell_2$-adversarial training of single-index models on Gaussian mixtures in the high-dimensional limit under streaming stochastic gradient descent (SGD).
By Fabrizzio Sabelli
arXiv:2604. 08625v2 Announce Type: replace-cross Abstract: We develop a theoretical framework for generalization in the interpolating regime of statistical learning.
By Gustav Olaf Yunus Laitinen-Lundstr\"om Fredriksson-Imanov
The paper analyzes training dynamics of multiclass logistic regression on high‑dimensional Gaussian mixture models with many classes. It finds that learning proceeds sequentially from the most to the least frequent classes and, when class priors follow a power‑law, the cross‑entropy risk evolves through an initial plateau, a power‑law decay phase, and a final convergence phase. The study also shows how model capacity and optimization trade‑off under a fixed compute budget, leading to a compute‑optimal scaling law that prescribes model size and training time as functions of compute.
By Konstantinos Christopher Tsiolis, Denny Wu, Christos Thrampoulidis, Murat A. Erdogdu
arXiv:2512. 22088v3 Announce Type: replace-cross Abstract: The scaling law, a cornerstone of Large Language Model (LLM) development, predicts improvements in model performance with increasing computational resources.
By Chiwun Yang
The paper introduces Dynafit, a kernel-based method for classifying trajectories produced by distinct nonlinear dynamical systems. It learns a distance metric by approximating the Koopman operator, enabling classification in a feature space without explicit dimensionality. The authors demonstrate Dynafit on logistic map chaos detection, handwritten dynamical pattern recognition, and visual dynamic texture classification.
By Dominique Martinez