Real-world scientific applications frequently encounter incomplete observational data due to sensor limitations, geographic constraints, or measurement costs. Although neural operators significantly advanced PDE solving in terms of computational efficiency and accuracy, their underlying assumption of fully-observed spatial inputs severely restricts applicability in real-world application. We introduce the first systematic framework for learning neural operators from partial observation. We identify and formalize two fundamental obstacles: (i) the supervision gap in unobserved regions that prevents effective learning of physical correlations, and (ii) the dynamic spatial mismatch between incomplete inputs and complete solution fields. Specifically, our proposed LANO (Latent Autoregressive Neural Operator) introduces two novel components designed explicitly to address the core difficulties of partial observations: (i) a mask-to-predict training strategy that creates artificial supervision by strategically masking observed regions, and (ii) a Physics-Aware Latent Propagator that reconstructs solutions through boundary-first autoregressive generation in latent space. Additionally, we develop POBench-PDE, a dedicated and comprehensive benchmark designed specifically for evaluating neural operators under partial observation conditions across three PDE-governed tasks. LANO achieves state-of-the-art performance with relative error reductions ranging from eighteen to sixty-nine percent across all benchmarks under patch-wise missingness with missing rates below fifty percent, including real-world climate prediction. Our approach effectively addresses practical scenarios with missing rates of up to seventy-five percent, to some extent bridging the existing gap between idealized research settings and the complexities of real-world scientific computing.

Large language models (LLMs) have demonstrated impressive capabilities, but their enormous size poses significant challenges for deployment in real-world applications. To address this issue, researchers have sought to apply network pruning techniques to LLMs. A critical challenge in pruning is the allocation of sparsity for each layer. Recent sparsity allocation methods are often based on heuristics or search that can easily lead to suboptimal performance. In this paper, we conducted an extensive investigation into various LLMs and revealed three significant discoveries: (1) the Layerwise Pruning Sensitivity (LPS) of LLMs is highly non-uniform, (2) the choice of pruning metric affects LPS, and (3) the performance of a sparse model is related to the uniformity of its layerwise redundancy level. Based on these discoveries, we propose that the layerwise sparsity of LLMs should adhere to three principles: non-uniformity, pruning metric dependency, and uniform layerwise redundancy level in the pruned model. To this end, we proposed Maximum Redundancy Pruning (MRP), an iterative pruning algorithm that prunes in the most redundant layers (i.e., those with the highest non-outlier ratio) at each iteration. The achieved layerwise sparsity aligns with the outlined principles. We conducted extensive experiments on publicly available LLMs, including LLaMA2 and OPT, on various benchmarks. The experimental results validate the effectiveness of MRP, demonstrating its superiority over previous methods.

Most works of interpretable neural networks strive for learning the semantics concepts merely from single modal information such as images. However, humans usually learn semantic concepts from multiple modalities and the semantics is encoded by the brain from fused multi-modal information. Inspired by cognitive science and vision-language learning, we propose a Prototype-Concept Alignment Network (ProCoNet) for learning visual prototypes under the guidance of textual concepts. In the ProCoNet, we have designed a visual encoder to decompose the input image into regional features of prototypes, while also developing a prompt generation strategy that incorporates in-context learning to prompt large language models to generate textual concepts. To align visual prototypes with textual concepts, we leverage the multimodal space provided by the pre-trained CLIP as a bridge. Specifically, the regional features from the vision space and the cropped regions of prototypes encoded by CLIP reside on different but semantically highly correlated manifolds, i.e. follow a multi-manifold distribution. We transform the multi-manifold distribution alignment problem into optimizing the projection matrix by Cayley transform on the Stiefel manifold. Through the learned projection matrix, visual prototypes can be projected into the multimodal space to align with semantically similar textual concept features encoded by CLIP. We conducted two case studies on the CUB-200-2011 and Oxford Flower dataset. Our experiments show that the ProCoNet provides higher accuracy and better interpretability compared to the single-modality interpretable model. Furthermore, ProCoNet offers a level of interpretability not previously available in other interpretable methods.