U-HNO: A U-shaped Hybrid Neural Operator with Sparse-Point Adaptive Routing for Non-stationary PDE Dynamics

Solutions to many partial differential equations (PDEs) display coexisting smooth global transport and localized sharp features within a single trajectory: shock fronts, thin interfaces, and concentrated high-frequency content sit on top of slowly varying backgrounds. This poses a challenge for neural operators: Fourier-based architectures mix nonlocal interactions efficiently but tend to under-resolve localized non-smooth features, whereas spatially local architectures recover fine detail at the cost of long-range propagation and rollout stability. Existing hybrid operators paper over this tension with a fixed, spatially uniform fusion that forces the same trade-off everywhere. We propose U-HNO, a U-shaped hybrid neural operator whose central design is Sparse-Point Adaptive Routing (SPAR): at every spatial location, a per-pixel hard mask selects whether the global Fourier branch or the local multi-scale Gaussian branch should dominate, and the sparsity ratio is a function of the local contrast of the routing signal, so smooth and shock-aligned regions receive different mixtures of global and local computation. SPAR is embedded in a hierarchical encoder-bottleneck-decoder backbone with skip connections so that the dual branches and the gate operate at every resolution. Training combines pointwise supervision with a finite-difference H^1 gradient term and a band-wise spectral consistency regularizer. Across benchmarks spanning 1D Burgers, Kuramoto-Sivashinsky, KdV, 2D advection, Allen-Cahn, Navier-Stokes, Darcy flow, and 3D transonic compressible Navier-Stokes from PDEBench, U-HNO achieves state-of-the-art rollout accuracy on the majority of tasks in both relative L^2 and H^1 metrics, with the largest gains on problems dominated by sharp localized features. Ablations show that removing any single component substantially degrades rollout error.

AdaFocus: Adaptive Relevance-Diversity Sampling with Zero-Cache Look-back for Efficient Long Video Understanding

Long video understanding is heavily bottlenecked by a rigid one-shot paradigm: existing methods either densely encode videos at prohibitive memory and latency costs, or aggressively compress them into sparse frame sets that irreversibly discard fine-grained evidence needed for downstream reasoning. Consequently, current models struggle to simultaneously balance temporal coverage, visual details, and computational efficiency. We propose AdaFocus, an efficient framework that rethinks long-video understanding as progressive evidence acquisition rather than one-pass encoding. AdaFocus relies on two tightly coupled components. First, a Query-Aware Adaptive Relevance-Diversity sampler (AdaRD) produces a compact yet informative video preview, adaptively switching to global clustering when the query lacks reliable local grounding. Second, instead of caching exhaustive frame sequences in memory, AdaFocus introduces an uncertainty-triggered refinement mechanism. It performs targeted look-back only when the model is not confident, retrieving high-resolution evidence directly from disk via a zero-cache I/O design. This turns discarded visual details from an irreversible loss into on-demand recoverable evidence without paying the cost of exhaustive preloading. Experiments on seven standard long-video benchmarks show that AdaFocus delivers a substantially better efficiency-accuracy trade-off than strong baselines. Compared with conventional dense encoding, AdaFocus achieves improved task performance (e.g., +2.59 accuracy on VideoMME, +8.39 mIoU on Charades-STA over single-pass inference) while reducing visual token consumption by ~33x and eliminating the need for in-memory frame pre-caching through its zero-cache disk retrieval design. These findings suggest that progressive preview combined with zero-cache evidence refinement is a highly effective paradigm for scalable multimedia reasoning.

Anatomy-Slot: Unsupervised Anatomical Factorization for Homologous Bilateral Reasoning in Retinal Diagnosis

Retinal diagnosis is inherently bilateral: clinicians compare homologous structures across eyes (e.g., optic disc asymmetry), yet most deep models operate on monocular representations. We investigate whether explicit structural correspondence improves diagnosis, and propose Anatomy-Slot to operationalize this hypothesis. Anatomy-Slot introduces an unsupervised anatomical bottleneck by decomposing patch tokens into slots and aligning slots across eyes via bidirectional cross-attention. On ODIR-5K with $n=10$ seeds, the method improves AUC by 4.2% over a matched ViT-L baseline (95% CIs; Wilcoxon signed-rank test, $W=0$, $p=0.002$). Pairing disruption and stress testing under Gaussian noise provide controlled tests of correspondence dependence and robustness under corruption. We further report quantitative optic disc grounding on REFUGE and cross-attention localization analysis.