TF-SNO: Time-Frequency Gated Spectral Neural Operators for Learning Non-Stationary Partial Differential Equations

Non-stationary partial differential equations (PDEs) arise throughout scientific computing, where the dominant frequency content and energy distribution can drift over time. While efficient in PDE solving, many spectral neural operators apply a shared spectral response across rollout stages, leading to mismatch with time-varying spectra in non-stationary systems. To address this issue, we propose Time-Frequency Gated Spectral Neural Operator (TF-SNO), a state-adaptive framework with learnable time-frequency gating inside spectral blocks. TF-SNO extracts compact frequency-domain and physical-space statistics from the current state to generate modulation coefficients, enabling the spectral response to evolve with the dynamics. TF-SNO learns temporal variation implicitly from the evolving state without introducing an explicit time dimension or time embedding, keeping the modeling complexity low. We further embed the adaptive operator blocks to accurately capture the multi-scale features, thereby improving long-horizon stability. Experiments on six non-stationary PDE benchmarks in 1D and 2D demonstrate that TF-SNO significantly reduces prediction errors and improves robustness compared to strong baselines, with particularly clear gains in long rollout, suggesting the effectiveness of state-dependent spectral adaptation in modeling non-stationary physical systems.

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.