Machine learning approaches for solving partial differential equations require learning mappings between function spaces. While convolutional or graph neural networks are constrained to discretized functions, neural operators present a promising milestone toward mapping functions directly. Despite impressive results they still face challenges with respect to the domain geometry and typically rely on some form of discretization. In order to alleviate such limitations, we present CORAL, a new method that leverages coordinate-based networks for solving PDEs on general geometries. CORAL is designed to remove constraints on the input mesh, making it applicable to any spatial sampling and geometry. Its ability extends to diverse problem domains, including PDE solving, spatio-temporal forecasting, and geometry-aware inference. CORAL demonstrates robust performance across multiple resolutions and performs well in both convex and non-convex domains, surpassing or performing on par with state-of-the-art models.

In this paper, we propose the Masked Space-Time Hash encoding (MSTH), a novel method for efficiently reconstructing dynamic 3D scenes from multi-view or monocular videos. Based on the observation that dynamic scenes often contain substantial static areas that result in redundancy in storage and computations, MSTH represents a dynamic scene as a weighted combination of a 3D hash encodingOurs and a 4DPlenoptic Dataset 30 hash encoding.

One of the most common problems studied in the context of differential privacy for graph data is counting the number of non-induced embeddings of a subgraph in a given graph. These counts have very high global sensitivity. Therefore, adding noise based on powerful alternative techniques, such as smooth sensitivity and higher-order local sensitivity have been shown to give significantly better accuracy. However, all these alternatives to global sensitivity become computationally very expensive, and to date efficient polynomial time algorithms are known only for few selected subgraphs, such as triangles, k-triangles, and k-stars. In this paper, we show that good approximations to these sensitivity metrics can be still used to get private algorithms. Using this approach, we much faster algorithms for privately counting the number of triangles in real-world social networks, which can be easily parallelized. We also give a private polynomial time algorithm for counting any constant size subgraph using less noise than the global sensitivity; we show this can be improved significantly for counting paths in special classes of graphs.

Traditional cameras produce desirable vision results but struggle with motion blur in high-speed scenes due to long exposure windows. Existing frame-based deblurring algorithms face challenges in extracting useful motion cues from severely blurred images. Recently, an emerging bio-inspired vision sensor known as the spike camera has achieved an extremely high frame rate while preserving rich spatial details, owing to its novel sampling mechanism. However, typical binary spike streams are relatively low-resolution, degraded image signals devoid of color information, making them unfriendly to human vision. In this paper, we propose a novel approach that integrates the two modalities from two branches, leveraging spike streams as auxiliary visual cues for guiding deblurring in high-speed motion scenes. We propose the first spike-based motion deblurring model with bidirectional information complementarity. We introduce a content-aware motion magnitude attention module that utilizes learnable mask to extract relevant information from blurry images effectively, and we incorporate a transposed cross-attention fusion module to efficiently combine features from both spike data and blurry RGB images. Furthermore, we build two extensive synthesized datasets for training and validation purposes, encompassing high-temporal-resolution spikes, blurry images, and corresponding sharp images. The experimental results demonstrate that our method effectively recovers clear RGB images from highly blurry scenes and outperforms state-of-the-art deblurring algorithms in multiple settings.

In this paper, we critically examine the prevalent practice of using additive mixtures of Matérn kernels in single-output Gaussian process (GP) models and explore the properties of multiplicative mixtures of Matérn kernels for multi-output GP models. For the single-output case, we derive a series of theoretical results showing that the smoothness of a mixture of Matérn kernels is determined by the least smooth component and that a GP with such a kernel is effectively equivalent to the least smooth kernel component. Furthermore, we demonstrate that none of the mixing weights or parameters within individual kernel components are identifiable. We then turn our attention to multi-output GP models and analyze the identifiability of the covariance matrix A in the multiplicative kernel K(x,y) = AK0(x,y), where K0 is a standard single output kernel such as Matérn. We show that A is identifiable up to a multiplicative constant, suggesting that multiplicative mixtures are well suited for multi-output tasks. Our findings are supported by extensive simulations and real applications for both single-and multi-output settings. This work provides insight into kernel selection and interpretation for GP models, emphasizing the importance of choosing appropriate kernel structures for different tasks.