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Hao Wang

Publications and source records attributed to Hao Wang.

5 recordsLinked to original sources

arXiv2026

Learning PDE Time-Stepping with Neural Cellular Automata

Classical numerical solvers for partial differential equations (PDEs) are computationally expensive to solve repeatedly across varying initial conditions, motivating the need for learned surrogates. In this paper, we propose a trainable Neural Cellular Automata (NCA) based surrogate model for learning long time PDE dynamics. Rather than mapping an entire initial field to a full trajectory in one shot, our proposed model learns a small, local, homogeneous update rule that is applied identically and repeatedly at every grid cell, mirroring the locality of differential operators. We benchmark this framework against three baselines: PDE - Net, a modified physics-informed neural network (PINN), and a Fourier Neural Operator (FNO), on five canonical PDEs (heat, advection, Burgers, Allen - Cahn, and Fisher - KPP), evaluated at temporal domain two times beyond the training temporal domain. The proposed model achieves the lowest long-horizon relative errors on the majority of the experiments.

cs.LG↗

arXiv2026

Mirror Descent Linearized Augmented Lagrangian Methods for Nonconvex Constrained Stochastic Zeroth-Order Optimization

In this paper, we study nonconvex constrained stochastic zeroth-order optimization problems with exact constraints and stochastic objective evaluations. To solve this class of problems, we propose a framework of mirror descent linearized augmented Lagrangian methods that employs two-point stochastic zeroth-order gradient estimators and exploits non-Euclidean mirror descent geometry. Under mild assumptions, we establish oracle complexity guarantees for finding an $ε$-KKT point parameterized by $p \geq 2$. Under Rademacher smoothing, our analysis reveals a trade-off between the variance of the zeroth-order gradient estimators and the smoothness of the mirror map. In the high-accuracy regime, the resulting effective oracle complexity is $\mathcal{O}(p d^{2/p}ε^{-3})$ for $p \in [2,2\ln d]$ and $\mathcal{O}(\ln d\,ε^{-3})$ for $p > 2\ln d$. These bounds reduce the dimension dependence in the leading term. When $p=2$, our method recovers the Euclidean setting with an oracle complexity of $\mathcal{O}(dε^{-3})$, improving the $ε$-dependence over existing methods. Furthermore, to eliminate initial near-feasibility requirements, we introduce a multi-stage scheme that finds an $ε$-KKT point within $\mathcal{O}(1+\log\log(e/ε))$ stages while maintaining the leading-order complexity. Numerical tests on QCQPs, black-box adversarial attacks, and fairness-constrained classification demonstrate the effectiveness of our proposed method.

math.OC↗

arXiv2026

PhysWave: Physics-Guided Latent Diffusion Models for Controllable Spatial Audio Generation

Text-to-spatial audio generation, such as text-to-First-Order Ambisonics (FOA), provides a convenient way to create spatial audio for billion-dollar gaming and film industries. However, existing text-to-FOA methods are largely data-driven and may produce audio that violates acoustic relations between source direction and distance. They also separate descriptive and parametric control, forcing users to trade usability for precision. In this paper, we present PhysWave, a physics-guided latent diffusion model for controllable text-to-FOA generation. PhysWave unifies natural-language and trajectory control through a shared waypoint-caption representation, and augments diffusion training with two differentiable acoustic priors: spherical-harmonic direction consistency and inverse-square distance consistency. To support dynamic spatial generation, we further construct a 300K-clip FOA dataset with diverse sound categories and source trajectories. Extensive results show that the proposed priors help PhysWave generate spatially consistent FOA audio while maintaining competitive audio quality. Further analyses show that these physics priors improve spatial consistency during training and can also be used as inference-time guidance for training-free spatial refinement.

cs.SD↗

arXiv2026

Diverse via bounded Agreement: Geometric Regularization for Multimodal Fusion

Multimodal fusion is often treated as an optimization-balancing problem, where training signals are adjusted to prevent one modality from dominating the others. However, balanced optimization does not fully determine the geometry of intermediate representations. Supervised multimodal models may still learn low-diversity modality-specific embeddings or allow paired cross-modal observations to drift excessively apart, weakening both unimodal robustness and multimodal fusion. We introduce \regName, a lightweight plug-and-play geometric regularization framework for multimodal representation learning. Rather than enforcing rigid cross-modal alignment, \regName follows a bounded-agreement principle: preserve modality-specific diversity while softly constraining only the portion of paired cross-modal drift that exceeds an admissible agreement band. Operationally, \regName combines a dispersion term that mitigates spectral concentration with an agreement-band anchoring term that controls excessive paired drift, requiring no architectural modification or inference-time overhead. Experiments across audio-visual, image-text, and RF-based benchmarks show that \regName consistently improves multimodal performance and often strengthens unimodal representations. These results suggest that explicitly regulating representation geometry is an effective complement to optimization balancing, and provide evidence that geometry-aware regularization can improve multimodal learning across diverse architectures and domains.

cs.CV↗

arXiv2026

SOMTab: Set-Order Mamba for Efficient Tabular In-Context Learning

Tabular foundation models based on in-context learning have recently emerged as strong alternatives to task-specific model fitting. However, the current performance frontier remains dominated by attention-heavy architectures, where attention is used throughout the modeling pipeline. This raises a natural question: is attention necessary at every stage of tabular in-context learning? We introduce SOMTab, a Set-Order Mamba architecture for efficient tabular in-context learning. SOMTab separates representation construction from query-conditioned retrieval. For row and column representations, it maps unordered table tokens into stable latent slots and applies Mamba-based state-space mixing to construct compact representations. For final prediction, it retains attention-based in-context learning to preserve query-conditioned retrieval from labeled context examples. We further introduce DCH-TailMix, a synthetic prior that combines degree-corrected graph heterogeneity with mixed heavy-tailed regimes to diversify synthetic dependency structures. Across tabular benchmarks, SOMTab approaches the performance of strong Transformer-based tabular foundation models while achieving faster inference and lower GPU memory usage, yielding a favorable efficiency--accuracy trade-off.

cs.LG↗