arXiv subjects

Dongsheng Li

Publications and source records attributed to Dongsheng Li.

3 recordsLinked to original sources

arXiv2026

PAPT++: Risk-Aware Adversarial Tuning and Generation for Single Domain Generalization

Single domain generalization (SDG) aims to learn a model from one labeled source domain that generalizes to unseen target domains. A common strategy is to enrich the source distribution with augmented or generated samples, and recent text-to-image (T2I) diffusion models provide a strong generative prior for this purpose. However, diversity alone is insufficient for robust generalization, because useful generated samples should also capture variations that the current classifier finds difficult. Motivated by distributionally robust optimization (DRO), we define a semantic ambiguity set in the class-conditional generative space of a pretrained T2I model and search it for samples with high classification loss under the current classifier. To this end, we introduce PAPT++, a risk-aware adversarial generation-training framework for SDG. PAPT++ first learns diverse semantic reference images for each class through image-text alignment and intra-class diversity regularization. These references then serve as denoising targets during classifier-guided diffusion synthesis, reducing semantic drift while guiding generation toward challenging variations. The generated samples are combined with the source data to update the classifier, and the updated classifier guides the next synthesis round in return. In this way, PAPT++ progressively exposes the classifier to challenging yet semantically consistent variations. Extensive experiments on standard SDG benchmarks demonstrate the superiority of the proposed PAPT++ method and the effectiveness of its main components.

cs.CV↗

arXiv2026

Solution-space heterogeneity shapes federated learning dynamics across partial differential equations

Federated scientific machine learning enables institutions to train neural surrogates without centralizing local physical data, yet studies of partial differential equations (PDEs) lack a transferable definition of non-independent and identically distributed data. Existing protocols partition coordinates, coefficients, boundary conditions, or geometries according to equation-specific rules. Here, we introduce solution-space PDE-Dirichlet, a protocol that converts continuous supervised responses into reusable solution bins and quantifies the realized separation between clients through optimal transport over the geometry of these bins. We derive an exact inverse relation between population allocation heterogeneity and the Dirichlet concentration, and we establish conditions under which response heterogeneity induces gradient disagreement, local-update dispersion, and parameter divergence. Across seven controlled and public PDE tasks, three neural-operator families, and five random seeds, a lower concentration consistently increases the realized solution distance and optimization heterogeneity. The degradation in final error is task dependent: the largest effect occurs for low-viscosity Burgers, reaching 4.157 percentage points under the most heterogeneous setting, whereas additional communication or smoother dynamics can reduce the final gap despite persistent parameter separation. These results distinguish a reproducible geometric mechanism from task-dependent generalization outcomes and provide a common basis for evaluating non-IID federated PDE learning.

cs.LG↗

arXiv2026

Gradient-Update Mismatch: Rethinking Conflict-Free Training of Physics-Informed Neural Networks

Training Physics-Informed Neural Networks (PINNs) requires jointly optimizing physics residual and initial/boundary condition loss terms, which often induce conflicting gradients. Gradient surgery methods mitigate this issue by constructing directions from loss-specific gradients to reduce conflict before optimizer transformation. However, even when the constructed direction is conflict-free, this property may not be preserved after optimizer transformation. Let $a_t$ denote the direction constructed by gradient surgery, $u_t$ the optimizer proposal, and $\mathcal{C}_t$ the conflict-free cone induced by the loss-specific gradients. We show that modern optimizers can transform $a_t$ through mechanisms such as historical state, adaptive scaling, preconditioning, or decoupled weight decay, so $a_t \in \mathcal{C}_t$ does not generally imply $u_t \in \mathcal{C}_t$. We refer to this optimizer-induced discrepancy in conflict-freeness between $a_t$ and $u_t$ as Gradient-Update Mismatch (GUM). Accordingly, we propose Gradient-Update Alignment (GUA), which projects $u_t$ onto $\mathcal{C}_t$ to obtain the aligned update $p_t$ and applies $p_t$ to the parameters. When the optimizer maintains internal state, GUA further adjusts this state toward targets reconstructed from the applied update. We conduct extensive experiments and find that GUM is widespread across momentum, adaptive, and curvature-based optimizers, with conflict rates reaching up to 86.3%. Across all PINN settings, GUA achieves conflict-free applied updates and consistently improves various gradient surgery methods, reducing the relative $L_2$ error by up to 98.2% in individual settings. Data and code are available at https://github.com/JingXiao10/GUA.

cs.LG↗