arXiv subjects

Zhenpeng Wang

Publications and source records attributed to Zhenpeng Wang.

2 recordsLinked to original sources

arXiv2026

Chern flow and Chern moment algebras

We construct realizable-volume models over every field for the factorial normalizations of homogeneous Lascoux, Lascoux-atom, and positive Grothendieck packets, including their minimal homogenizations and layers. In particular, the construction realizes the factorial normalizations of all Schubert and key polynomials and of the minimal sign-corrected homogeneous Grothendieck polynomials. The normalized polynomials are Lorentzian, and the ordinary supports are the lattice points of integral generalized polymatroids. On a Bott--Samelson tower, row and co-row filtrations assemble the local factors into globally generated bundles; a creation-state graph absorbs the remaining kernel factors by Chern flow. We also construct intrinsic algebras of joint Chern moments. Positive inverse-Chern presentations give these algebras Hard Lefschetz and Hodge--Riemann relations, and supply source-level Hodge completions of the packets. For globally generated tropical toric bundles in the sense of Kaveh--Manon, finite generating witnesses and matroid duality provide the presentations required by Larson--Partida's theorem, without representability. These constructions yield joint Chern-number inequalities, nonvanishing polymatroids, and equality criteria.

math.CO↗

arXiv2026

Refining the Information Bottleneck via Adversarial Information Separation

Generalizing from limited data is particularly critical for models in domains such as material science, where task-relevant features in experimental datasets are often heavily confounded by measurement noise and experimental artifacts. Standard regularization techniques fail to precisely separate meaningful features from noise, while existing adversarial adaptation methods are limited by their reliance on explicit separation labels. To address this challenge, we propose the Adversarial Information Separation Framework (AdverISF), which isolates task-relevant features from noise without requiring explicit supervision. AdverISF introduces a self-supervised adversarial mechanism to enforce statistical independence between task-relevant features and noise representations. It further employs a multi-layer separation architecture that progressively recycles noise information across feature hierarchies to recover features inadvertently discarded as noise, thereby enabling finer-grained feature extraction. Extensive experiments demonstrate that AdverISF outperforms state-of-the-art methods in data-scarce scenarios. In addition, evaluations on real-world material design tasks show that it achieves superior generalization performance.

cs.LG↗