arXiv subjects

Weisheng Wang

Publications and source records attributed to Weisheng Wang.

5 recordsLinked to original sources

arXiv2026

Singular Learning and Occam's Razor in Deep Monomial Networks

In the optimization of neural networks, gradient dynamics are influenced by critical points that arise from the model's architecture. These critical points occur where the Jacobian of the model's parametrization is rank-deficient, and are the most pronounced singularities studied in Singular Learning Theory. We investigate such points in deep fully-connected networks with monomial activations via tools from polynomial algebra such as Mason's Theorem. We show that, for sufficiently large activation degree, criticality occurs precisely at subnetworks, i.e., at parameter configurations where some neurons are inactive or redundant. This offers a mathematical perspective on the implicit bias in deep neural networks, explaining the tendency of these models to converge toward simpler functions.

cs.LG↗

arXiv2025

Euler characteristics of moduli of twisted sheaves on Enriques surfaces

Let $Y$ be an Enriques surface and let $\mathcal{A}$ be an Azumaya algebra corresponding to the non-trivial Brauer class. Let $M$ be the moduli space of stable twisted sheaves on Enriques surfaces with twisted Chern character $M^H_{\mathcal{A}/Y}(2,c_1,\operatorname{ch}_2)$ with virtual dimension $N$. We show that the virtual Euler characteristic $e^\mathrm{vir}(M)$ only depends on $N$, more precisely, $e^\mathrm{vir}(M)=0$ when $N$ is odd and $e^\mathrm{vir}(M)=2\cdot e(Y^{[\frac{N}{2}]})$ when $N$ is even.

math.AG↗

arXiv2024

Virasoro constraints for K3 surfaces and monodromy operators

The Virasoro constraints for moduli spaces of stable torsion free sheaves on a surface with only $(p,p)$-cohomology were recently proved by Bojko-Moreira-Lim. The rank 1 case, which is not restricted to surfaces with only $(p,p)$-cohomology, was established by Moreira. We prove Virasoro constraints for K3 surfaces using Markman monodromy operators, which allow us to reduce to the rank 1 case. We also prove new Virasoro constraints in rank 0. Finally, for K3 surfaces, we introduce new Virasoro operators in negative degree which, together with the previous Virasoro operators, give a representation of Virasoro algebra with central charge $24$.

math.AG↗

arXiv2023

InstructBLIP: Towards General-purpose Vision-Language Models with Instruction Tuning

Large-scale pre-training and instruction tuning have been successful at creating general-purpose language models with broad competence. However, building general-purpose vision-language models is challenging due to the rich input distributions and task diversity resulting from the additional visual input. Although vision-language pretraining has been widely studied, vision-language instruction tuning remains under-explored. In this paper, we conduct a systematic and comprehensive study on vision-language instruction tuning based on the pretrained BLIP-2 models. We gather 26 publicly available datasets, covering a wide variety of tasks and capabilities, and transform them into instruction tuning format. Additionally, we introduce an instruction-aware Query Transformer, which extracts informative features tailored to the given instruction. Trained on 13 held-in datasets, InstructBLIP attains state-of-the-art zero-shot performance across all 13 held-out datasets, substantially outperforming BLIP-2 and larger Flamingo models. Our models also lead to state-of-the-art performance when finetuned on individual downstream tasks (e.g., 90.7% accuracy on ScienceQA questions with image contexts). Furthermore, we qualitatively demonstrate the advantages of InstructBLIP over concurrent multimodal models. All InstructBLIP models are open-sourced at https://github.com/salesforce/LAVIS/tree/main/projects/instructblip.

cs.CV↗

arXiv2021

Robust Scheduling of Virtual Power Plant under Exogenous and Endogenous Uncertainties

Virtual power plant (VPP) provides a flexible solution to distributed energy resources integration by aggregating renewable generation units, conventional power plants, energy storages, and flexible demands. This paper proposes a novel model for determining the optimal offering strategy in the day-ahead energy-reserve market and the optimal self-scheduling plan. It considers exogenous uncertainties (or called decision-independent uncertainties, DIUs) associated with market clearing prices and available wind power generation, as well as the endogenous uncertainties (or called decision-dependent uncertainties, DDUs) pertaining to real-time reserve deployment requests. A tractable solution method based on strong duality theory, McCormick relaxation, and the Benders' decomposition to solve the proposed stochastic adaptive robust optimization with DDUs formulation is developed. Simulation results demonstrate the applicability of the proposed approach.

eess.SY↗