We introduce MPM Lite, a hybrid Lagrangian/Eulerian method that eliminates the need for particle-based quadrature at solve time. Standard Material Point Method (MPM) practices suffer from a performance bottleneck where expensive implicit solves are proportional to particle-per-cell (PPC) counts due to the the choices of particle-based quadrature and wide-stencil kernels. By contrast, MPM Lite treats particles primarily as carriers of kinematic state and material history. Conceptualizing the background Cartesian grid as a voxel hexahedral mesh, we resample particle states onto fixed-location quadrature points using efficient, compact linear kernels. This architectural shift allows force assembly and the entire time-integration process to proceed without accessing particles, thus making the solver's complexity independent of the particle count. At the core of our method is a novel stress transfer and stretch reconstruction strategy. To avoid non-physical averaging of deformation gradients, we resample the extensive Kirchhoff stress and derive a rotation-free deformation reference solution, which naturally supports an optimization-based incremental potential formulation. Consequently, MPM Lite can be implemented as modular resampling units coupled with an FEM-style integration module, enabling the direct use of off-the-shelf nonlinear solvers, preconditioners, and unambiguous boundary conditions. We demonstrate through extensive experiments that MPM Lite preserves the robustness and versatility of traditional MPM across diverse materials while delivering significant speedups in implicit settings while simultaneously improving explicit ones. Project page: https://mpmlite.github.io.
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We present an algorithm for global knit structure planning that leverages a generalization of power diagrams to triangulated surfaces. This generalization is based on modified geodesic heat kernels and is used to quantize the curl measure of a normalized knitting time function gradient. Knit singularity positions are optimized jointly in a global fashion via an iterative Lloyd-type algorithm, leading to faster and more optimal placement of singularities than prior work, allowing for practical creation of denser knit graphs. In this denser setting, we present singularity ordering constraints that more robustly achieve helix-free knit graphs. The speed and robustness of the method is demonstrated via a diverse array of knits, and a virtual gallery of helix-free knit graphs. We also provide further demonstration of user constraints for knit singularity masking, level set alignment constraints, and apparent seam placement via curl boosting.
To enable differentiation with respect to object geometries, boundary path integrals—central to physics-based differentiable rendering—must be estimated numerically. Although their mathematical formulation is well established, designing efficient and robust numerical estimators remains challenging. Most state-of-the-art boundary sampling methods rely on primary-sample-space guiding, which tends to break down on finely tessellated geometries; reparameterization-based alternatives, meanwhile, often incur high variance and/or significant computational overhead. In this paper, we introduce a simple, robust, and consistent solution to this problem. At the core of our approach is a novel formulation of the boundary integral based on kernel-density estimation. Much like photon mapping, we slightly expand the measure-zero domain of integration with a kernel, sidestepping the need to sample directly on a delta-function region in path space. To our knowledge, this is the first such application of kernel-density methods for boundary integral evaluation. We validate our method by comparing its derivative estimates against finite differences (FD), and further demonstrate its practical utility by benchmarking against several state-of-the-art baselines in synthetic inverse-rendering scenarios.
Elliptic partial differential equations are ubiquitous in graphics and engineering, but remain challenging to solve on complex or evolving geometries. Traditional discretization schemes (e.g., FEM/FDM) provide stable, globally coupled solutions but require heavy meshing or extreme refinement to accurately resolve geometric detail. In contrast, grid-free Monte Carlo methods (e.g., Walk on Spheres/Stars) adapt naturally to arbitrary geometry and offer massive parallelism, but rely on long random walks whose variance grows rapidly, particularly in the presence of Neumann boundaries, leading to slow convergence. We introduce a hybrid approach that combines the geometric flexibility of Monte Carlo estimation with deterministic global solves that do not introduce additional stochastic error. Our method decomposes the domain into simple, regular subdomains and uses Monte Carlo to estimate local first-passage solution operators (Poisson kernels), where walk lengths and variance are inherently controlled by the reduced spatial scale. These local operators are assembled into a sparse global system whose solution is obtained via a deterministic linear solve that exactly replaces simulating discrete random walks throughout the domain. This global solve trades stochastic variance for a fixed, resolution-dependent discretization bias, yielding stable and reusable solution operators. As a result, our method attains accurate, geometry-aware solutions even on coarse discretizations, and enables efficient solves and re-solves by computing and updating only the local operators affected by the geometry and its changes. We evaluate the approach on complex two-dimensional domains, benchmarking accuracy and convergence against standard grid-free and grid-based baselines, and demonstrate applications to microstructure simulation and flow-based path planning and streamline visualization.
We present ST-FLIP, a spatiotemporal extension of the Fluid-Implicit Particle (FLIP) method for incompressible free-surface and two-phase liquid simulation. ST-FLIP enables time steps up to an order of magnitude larger than those typically used in CFL-constrained solvers, while preserving detailed flow structures and visual fidelity. It addresses a common failure mode of large time steps in hybrid particle-grid liquid solvers: temporal under-sampling of particle motion produces aliasing-driven free-surface artifacts after projection. Our key idea is to interpret particles as samples in four-dimensional space-time: in addition to standard spatial jittering, we randomize particle positions along the time axis as well and perform particle-to-grid deposition using a separable 4D kernel. This yields a Monte Carlo estimator of perstep time-slab-integrated particle quantities. Although particles are treated as samples in 4D space-time, our approach works as a lightweight plugin by collapsing to slab-integrated 3D grid fields for projection. Building on recent particle-based phase-field work, we reuse the particle-to-grid weight accumulators as a conceptual space-time phase field, providing variable-coefficient projection weights and eliminating the need for per-step surface reconstruction. The method can be easily integrated into existing FLIP/PIC or APIC solvers with negligible additional computational cost per time step. The effectiveness of our approach is demonstrated through a series of comparisons with state-of-the-art solvers, yielding several-fold speedups for multi-billion-particle simulations at high effective 3D resolutions on a single workstation.
The simultaneous pursuit of high fidelity, large computational throughput, and a minimal memory footprint has long constituted the central challenge in fluid simulation research. Yet state-of-the-art methods struggle to reconcile all these objectives, and often entail navigating trade-offs among them. We present Kinetic Predicted-Moment Flux Reconstruction (KPM-FR), a high-order kinetic-based scheme for low-Mach-number weakly compressible flows that advances all three fronts within a single framework. KPM-FR is a flux-form fluid flow solver rooted in the principles of the gas-kinetic scheme (GKS), deriving numerical fluxes from the locally evolved Boltzmann-BGK equation to recover Navier-Stokes (NS) solutions. Departing from the GKS and its variants, it carries out kinetic evolution entirely in moment space within the high-order flux reconstruction (FR) framework through a concise predictor-corrector scheme. This translates to two fused GPU kernels per time step, streamlining computation and confining intermediate data to on-chip memory. This design confers several practical advantages. First, compared to conventional high-fidelity lattice Boltzmann methods (LBM), the moment-based formulation reduces the per-point memory footprint by more than fivefold. Second, at matched resolutions, its high-order spatial formulation exhibits markedly lower numerical dissipation, preserving fine-scale vortical structures with greater fidelity. Combining these advantages with a near-saturated throughput exceeding 8 billion solution-point updates per second on a single consumer GPU, KPM-FR delivers large-scale fluid simulation on commodity hardware. Quantitative benchmarks confirm highorder spatial convergence and spectral-like dissipation characteristics, while validation against reference data for flow past solid bodies verifies its practical accuracy. Ultimately, we demonstrate the versatility of KPM-FR across complex geometries and large-scale turbulent flows, capturing multiscale structures with 1.8 billion solution points on a single desktop workstation.
Computing the Hausdorff distance between triangle meshes with guaranteed accuracy is a computationally intensive task. Conventional Branch-and-Bound (B&B) approaches are fundamentally ill-suited for massive parallelism. Their reliance on a global priority queue (PQ) for both best-first scheduling and global termination checks creates a serial bottleneck that prevents scalable performance. We introduce PQ-Free HD, a parallel B&B framework that eliminates this dependency by decoupling the algorithm's termination logic from its scheduling order. This is achieved by relaxing the culling criterion, thereby replacing the priority queue with a contention-free ring buffer, which transforms the execution model from a state-dependent serial search into a high-throughput, asynchronous batch-processing paradigm. The framework consists of four key components: (1) a parallel priority-queue-free B&B paradigm; (2) a hierarchical GPU execution architecture combining batched depth-first scheduling with fused collaborative kernels; (3) a geometrically robust seven-stage culling pipeline featuring novel tests for challenging geometries; and (4) a compact 29-byte procedural task descriptor that achieves an 83.9% memory reduction. Evaluations demonstrate substantial speedups: a median of 71.7× over the state-of-the-art CPU algorithm on general benchmarks, and exceeding 10,000× on challenging CAD models with dense planar structures. The throughput advantage scales super-linearly with problem complexity. We showcase practical value by building a strictly Hausdorff-distance-bounded mesh simplification tool entirely on the GPU. Our work provides a new method for high-throughput, tolerance-controllable B&B-based geometric queries on GPUs. Code and data are available at https://github.com/huzhihao2001/pqfree-hd.
Deep images store a variable number of “bins” within each pixel, enabling deep compositing workflows with clean separation of overlapping objects, but Monte Carlo noise limits their practical use. Existing deep image denoisers are limited in quality, generality, and temporal processing because ragged bin neighborhoods are incompatible with fixed convolution kernels. We introduce the ragged neighborhood attention (RaNA) operator, which extends neighborhood attention to semi-structured deep images by dynamically resolving bin-to-bin relationships across spatial and temporal neighborhoods. Using RaNA, we build the first spatiotemporal neural denoiser for deep Monte Carlo renderings, termed RaNAD, with a multi-U-Net backbone, multi-scale reconstruction, and an optimized CUDA implementation. RaNAD handles both deep-Z and deep-OID variants and supports temporal windows of up to 7 frames. Compared with the previous state of the art for deep image denoising, RaNAD improves denoising quality substantially while preserving the layered structure needed for deep compositing; when its output is flattened for evaluation, it also attains quality competitive with strong flat image denoisers. As a kernel-based method, RaNAD efficiently denoises multi-AOV images, and temporal processing further improves quality and stability, making the method practical for offline production rendering and compositing workflows.
Large-kernel filtering is a fundamental operation in image post-processing and video effects. While decomposing large kernels into multiple sparse ones is a proven strategy for acceleration on parallel architectures, existing optimization-based approximation methods are constrained to fixed-resolution processing. In this paper, we propose a novel framework based on Polyphase Filtering, which enables the differentiable optimization of sparse kernels across varying resolutions. This approach achieves the fastest approximation to date for large kernels and remains highly effective even for spatially-variant dense kernels. To further enhance efficiency, we introduce Spatial-to-Depth Transformation and Asymmetric Intensity-Decoupled Transformation. Furthermore, to address scenarios with spatially varying kernel sizes, we employ a Layer-Adaptive Filtering strategy that integrates kernels from multiple levels for rapid filtering. Extensive experiments demonstrate that our method significantly outperforms existing state-of-the-art techniques in both computational performance and visual quality.
Relational databases (RDBs) underpin the majority of global data management systems, where information is structured into multiple interdependent tables. In social media platforms, for instance, massive user-generated data are organized across related tables such as users, posts, comments, and interactions, enabling large-scale analysis and predictive modeling of social behaviors. To effectively use the knowledge within RDBs for predictive tasks, recent advances leverage graph representation learning to capture complex inter-table relations as multi-hop dependencies. Despite achieving state-of-the-art performance, these methods remain hindered by the prohibitive storage overhead and excessive training time, due to the massive scale of database and the computational burden of intensive message passing across interconnected tables. To alleviate these concerns, we propose and study the problem of Relational Database Distillation (RDD). Specifically, we aim to distill large-scale RDBs into compact heterogeneous graphs while retaining the predictive power (i.e., utility) required for training graph-based models. Multi-modal column information is preserved through node features, and primary–foreign key relations are encoded via heterogeneous edges, thereby maintaining both data fidelity and relational structure. To ensure adaptability across diverse downstream tasks without engaging the traditional, inefficient bi-level distillation framework, we further design a kernel ridge regression-guided objective with pseudo-labels, which produces quality features for the distilled graph. Extensive experiments on multiple real-world RDBs demonstrate that our solution substantially reduces the data size while maintaining competitive performances on classification and regression tasks, creating an effective pathway for scalable learning with RDBs.
The multimodal Chinese idiom reading comprehension task aims to select the most appropriate idiom from a candidate list via the given text and image. This poses a significant challenge for the model to comprehend each Chinese idiom accurately. Existing multimodal Chinese idiom reading comprehension methods primarily focus on aligning contextual text and images, while overlooking two key attributes of Chinese idioms.(1) There is a discrepancy between the literal and metaphorical meanings of Chinese idioms. (2) The same Chinese idiom has different meanings in different scenarios, which requires targeted understanding by experts who specialize in different fields. To address the above challenges, we rethink the solution to the multimodal idiom reading comprehension task from a metaphorical perspective and propose a framework named MePe. Firstly, we propose a literal metaphorical semantic graph that systematically transforms the implicit discrepancy between the literal and metaphorical meanings of Chinese idioms into structured explicit relationships, thereby making metaphorical meanings more understandable. Then, we propose a mixture of idiom experts consisting of a literal idiom expert and a metaphorical idiom expert. Through division of labor and collaboration among these experts, we achieve an understanding of the dual meanings of Chinese idioms across different scenarios. Finally, we employ the maximum mean discrepancy to adjust the variance between the literal and metaphorical semantic features of Chinese idioms. By mapping these features onto a shared reproducing kernel Hilbert space, the model can better distinguish between the two based on contextual clues. Extensive experiments demonstrate that MePe achieves state-of-the-art performance on the MChIRC dataset.
Convex clustering is a well-regarded clustering method, resembling the similar centroid-based approach of Lloyd's $k$-means, without requiring a predefined cluster count. It starts with each data point as its centroid and iteratively merges them. Despite its advantages, this method can fail when dealing with data exhibiting linearly non-separable or non-convex structures. To mitigate the limitations, we propose a kernelized extension of the convex clustering method. This approach projects the data points into a Reproducing Kernel Hilbert Space (RKHS) using a feature map, enabling convex clustering in this transformed space. This kernelization not only allows for better handling of complex data distributions but also produces an embedding in a finite-dimensional vector space. We provide a comprehensive theoretical underpinning for our kernelized approach, proving algorithmic convergence and establishing finite sample bounds for our estimates. The effectiveness of our method is demonstrated through extensive experiments on both synthetic and real-world datasets, showing superior performance compared to state-of-the-art clustering techniques. This work marks a significant advancement in the field, offering an effective solution for clustering in non-linear and non-convex data scenarios.
Transformer-based architectures have demonstrated strong performance in 3D point cloud understanding, yet many existing methods generate attention weights mainly from semantic feature similarity. In deep networks, feature-centric attention may become less selective as point features are progressively smoothed, a behavior associated with feature homogenization and rank collapse, which can weaken the structural discrimination of local aggregation.We propose PointGP, a geometry-primed framework that uses rectified local geometric topology as the primary cue for attention generation. PointGP introduces a Semantic-Guided Manifold Rectifier to predict feature-conditioned local coordinate offsets, and a Dual-Stream Geometric Kernel to compute attention logits from both raw and rectified geometric cues. By reducing reliance on explicit query-key feature matching while implicitly incorporating semantic guidance through geometric rectification, PointGP provides an effective and efficient mechanism for local point aggregation.Experiments across five benchmarks covering classification, part segmentation, and indoor scene segmentation show that PointGP achieves competitive accuracy with strong parameter and computational efficiency compared with representative strong baselines.
Accurate long-term forecasting in complex systems is frequently compromised by dataset-level distribution shifts, where diverse underlying behavioral modes and evolving system states drive the dynamic multivariate time-series. While existing methods predominantly focus on local temporal shifts, they fail to explicitly model the global structural challenge where datasets are composites of distinct operational regimes. In this paper, we propose NEST, a specialized framework designed to model and recompose these evolving structures through a two-phase dense MoE architecture. NEST first facilitates structural specialization by partitioning the dataset into distinct operational regimes through unsupervised clustering in a principled moment-entropy space. We introduce a regime-oriented router mechanism that generates initial expert weights based on temporal content, subsequently refined through geometric modulation to regime centroids. Crucially, rather than acting as monolithic predictors, individual experts function as specialized kernels that capture regime-specific dynamics by evolving unique variate-attention patterns. Extensive evaluations on diverse benchmarks, including heterogeneous network traffic and physical phenomena, demonstrate that NEST consistently achieves state-of-the-art performance. Our code and datasets are available at \url{https://github.com/Aaralshin/NEST}.
Detecting hidden confounding is crucial for reliable causal analysis from observational data, directly determining which downstream causal inference method to be deployed. Inspired by the theory of higher-order regression, recent sample-efficient hypothesis testing strategies overcome the restrictive requirement of multiple heterogeneous data environment. Despite their progress on single-environment confounder detection, such methods suffer from intrinsic flaws that the structural functions of the causal models should be specified in prior (linear or specific kernel functions). By contrast, real-world data acquisition exhibits diverse, unknown forms of structural functions, imposing an important but challenging gap between theories of higher-order regressions to practical confounder detection. In this paper, we contribute a Bi-level Kernel Confounder Detection (BiKCD) framework by learning adaptive kernelized structural space of structural functions. Subsequently, our BiKCD constructs hypothesis testing by comparing coefficients from the higher-order regression and the classical ordinary least squares in learned kernelized space. Finally, the hypothesis is calibrated to ensure valid inference under adaptivity. Theoretically, we establish an oracle-type risk bound for the selected structural space over a candidate kernel family, with the Type-I error control for the downstream test. Extensive experiments on synthetic and real-world datasets demonstrate the effectiveness of the proposed BiKCD.
Attributed graph clustering has achieved remarkable success by synergistically integrating topological structures and node attributes. While subspace learning has emerged as a dominant paradigm for node partitioning, most existing methods rely on implicit low-rank constraints, which often fail to capture complex nonlinear manifolds and suffer from prohibitive computational overhead on large-scale graphs. In this paper, we propose ELSS (Explicit Low-rank Structured Subspace learning), a scalable and robust framework that transcends implicit formulations. Specifically, ELSS learns an explicit and nonlinear low-rank subspace within a graph-structured embedding space, effectively uncovering latent cluster structures. To effectively mitigate the pervasive oversmoothing issue, we introduce a homophily-aware adaptive graph filter, which dynamically calibrates smoothing intensity to preserve discriminative ego-information. Furthermore, to ensure linear scalability, we develop a PageRank-guided structural sampling strategy for anchor-based approximation, which identifies pivotal landmarks based on their global topological prestige. Theoretical analysis guarantees that ELSS effectively mitigates spectral collapse while maintaining a linear complexity. Extensive experiments on diverse benchmarks demonstrate that ELSS consistently delivers superior clustering accuracy over state-of-the-art methods.
Motor imagery (MI) electroencephalography (EEG) decoding has benefited from deep learning, yet methods operate in Euclidean space and behave as opaque black boxes, neglecting the intrinsic geometry of functional brain connectivity. EEG connectivity descriptors, such as phase synchrony and covariance matrices, naturally reside on the manifold of symmetric positive definite (SPD) matrices, where Euclidean operations are geometrically inconsistent and hinder interpretability. This work proposes the Multi-frequency and Multi-scale Riemannian Network (MFMSRNet), an interpretable end-to-end geometry-aware framework for MI EEG decoding on the SPD manifold. The method constructs kernelized phase-locking value (KPLV) functional connectivity (FC) matrices to capture nonlinear phase synchrony while ensuring positive definiteness. An attention-based Riemannian fusion mechanism adaptively integrates information across multiple frequency bands in the tangent space. Furthermore, a multi-scale Riemannian network extracts global, hemispheric, and local connectivity patterns via manifold-preserving bilinear mappings and smooth eigenvalue rectification. Extensive experiments indicate that MFMSRNet yields more expressive and interpretable representations for robust MI decoding, offering a promising solution for reliable brain–computer interface applications. The code is available at https://github.com/Raeno-Rao/MFMSRNet.
Accurate estimation of time-varying treatment effects is crucial for optimizing interventions in personalized medicine. However, observational data often contains complex confounding bias and temporal complexities, making counterfactual estimation challenging. We propose Counterfactual Estimation via Temporal-Aware Intervention Networks (TAIN), a novel model that introduces an Intervention-aware Functional Convolution kernel to emphasize the role of treatments and capture complex temporal treatment interactions. TAIN addresses confounding bias from a domain generalization perspective, approximating the unknown target domain using adversarial examples and incorporating Sharpness-Aware Minimization to derive a generalization bound. This approach is more suitable for longitudinal settings compared to existing methods inspired by domain adaptation techniques due to inherent differences between static and longitudinal contexts. Experiments on simulated datasets demonstrate TAIN's superior performance compared to state-of-the-art models for counterfactual estimation over time.
Temporal embeddings play a crucial role in dynamic graph neural networks (DGNNs) by capturing the temporal dynamics of interactions. However, existing Random Fourier Feature (RFF)-based methods in DGNNs directly sample Fourier frequencies from a fixed, data-independent distribution, neglecting the temporal characteristics of dynamic graphs and thereby limiting representational capacity. We propose DeepSTE, a deep spectral temporal embedding framework for dynamic graphs. DeepSTE learns RFF representations via Monte Carlo importance sampling with a tractable proposal distribution (e.g., Gaussian) to approximate the feature map of a shift-invariant or positive-definite kernel whose latent spectral density is analytically intractable. DeepSTE adopts a data-dependent scale parameter, estimated from interaction intervals, to construct the frequency proposal distribution reflecting time–frequency uncertainty. The frequency DNN and the importance-weighting DNN, initialized from the proposal distribution, are jointly optimized to model the importance-sampled spectral representation and learn adaptive temporal features. Experiments demonstrate the effectiveness of DeepSTE on dynamic link prediction and node classification tasks, while also revealing insights such as temporal embedding decay and accelerated convergence.
Capturing global context through attention is essential for reasoning over knowledge graphs, especially when relevant entities are distant or disconnected. To scale attention to large graphs, recent methods replace Softmax with kernel feature mappings, reducing computational complexity to linear in the number of nodes. While efficient, these approximations tend to produce overly smooth attention scores, which can reduce discrimination between correct triplets and hard negative samples. Moreover, they exhibit scale-dependent shifts in attention entropy, making them sensitive to changes in graph size during inductive inference. In this paper, we introduce LaGR, a novel approach for integrating global information in knowledge graph reasoning. Rather than approximating interactions among all nodes, LaGR compresses the graph into a fixed, compact set of latent summaries and applies exact self-attention within this latent space. This change yields scale-invariant attention and stable performance across diverse data settings. In addition, we propose a node-adaptive residual fusion mechanism that dynamically balances local and global information at the node level, leading to more expressive representations. Extensive experiments on both transductive and inductive benchmarks show that LaGR substantially outperforms state-of-the-art baselines, demonstrating that exact attention over latent summaries is an efficient and effective way to capture global context in knowledge graph reasoning. Our implementation is available at https://github.com/XMU-KG/LaGR.