We present a computational framework for numerical homogenization of origami materials—thin sheets structured with periodic crease patterns that, once folded, exhibit diverse and often unusual mechanical properties. Whereas the in-plane stiffness of conventional sheet materials is typically orders of magnitude larger than their resistance to bending, origami-based folding introduces geometric structure that can drastically reshape both bending and stretching behavior. However, predicting how a particular crease pattern gives rise to effective macroscopic properties remains challenging due to the complex coupling of crease geometry, folding kinematics, and surface deformations. In this work, we introduce a computational framework that integrates simulation-based folding and numerical homogenization to explore the relationship between crease pattern and effective material behavior. To describe the macromechanical response of origami materials, we employ a quadratic energy model based on Classical Laminate Theory, together with a simplified treatment of crease plasticity. Our unified representation accommodates both straight- and curved-crease designs, revealing a rich space of origami materials with diverse behavior. In particular, we examine how pattern symmetry governs material symmetries, demonstrating examples that span the full spectrum from perfectly isotropic to highly anisotropic membrane and bending responses. Our framework further enables controlled exploration of parameter variations, illustrating how geometric features such as crease curvature shape macroscopic mechanical behavior. We showcase the potential of this approach through a broad set of examples, ranging from canonical straight-crease patterns such as Miura-ori to complex curved-crease tessellations. While a quantitative analysis is left for future work, we validate our homogenized descriptions against native-scale simulations and qualitatively compare deformation behaviors with real-world prototypes.
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Constant mean curvature surfaces are æsthetically appealing geometric objects with applications in physics, differential geometry, and architecture. We present a straightforward discretization of constant mean curvature surfaces based on the classical observation that their Gauß maps are harmonic. Our construction is elementary—requiring only discrete Dirichlet energy minimization and a Poisson solve—yet it exactly mirrors this aspect of the smooth theory. A discrete analog of conjugation produces discrete constant Gauß curvature surfaces. Their unit offsets are discrete CMC surfaces with a conformal parameterization. Additionally, we introduce a novel Möbius-invariant discretization of the Dirichlet energy for sphere-valued maps on dual meshes that is derived from the discrete Willmore energy. It is more robust than standard formulations based on inverse cotangent weights. Our approach to the construction of constant mean curvature surfaces provides direct control over tangent planes along a boundary, if present, and naturally handles closed and periodic examples. We demonstrate the approach on a range of free-boundary, symmetric, and periodic CMC surfaces.
The theory of light transport on Gaussian process implicit surface (GPIS) provides a unified framework for rendering surfaces, participating media, and the intermediate spectrum. However, previous approaches rely on brute-force ray marching for surface intersections, requiring full noise evaluations at each marching point, whether using multivariate Gaussian sampling or sparse convolution noise approximation. This imposes a severe limitation on the rendering efficiency. In this paper, we derive bounds to significantly reduce the total number of full noise evaluations, leading to efficient ray marching for ray-surface intersections. We introduce stratified Bernoulli impulses, enabling a fast point-level bound for individual realizations to replace unnecessary full noise evaluations. To further reduce the number of point-level bound evaluations, we propose a region-level bound, leveraging a spatial acceleration structure to prune probabilistically empty regions, thereby avoiding unnecessary marching points in advance. By combining these two bounds, our bounded ray marching accelerates ray-surface intersections in GPIS, and consequently significantly improves overall GPIS rendering efficiency. Code for this paper are at https://github.com/Cchen-77/bounded-gpis.
We introduce a spatially discrete formulation of the Schrödinger bridge problem on meshes and grids that enables structure-preserving and scalable interpolation between probability distributions. Our approach builds on the duality between entropy-regularized optimal transport and the log-heat equation, deriving a discrete theory that is compatible with mesh-based finite element discretizations. The resulting Sinkhorn algorithm alternates application of the heat kernel with multiplicative updates to enforce marginal constraints. Compared to interpolation via Wasserstein barycenters, our formulation produces sharper interpolants for a given level of regularization and enforces exact endpoint marginals, in addition to enjoying faster computation. It also scales to high-resolution meshes and finer temporal discretizations, avoiding the prohibitive cost of directly discretizing dynamical transport. We demonstrate our approach across mesh- and grid-based applications, including displacement interpolation, shape interpolation, and color histogram manipulation, highlighting its ability to achieve geometric fidelity with computational efficiency.
We describe a method for computing signed distance to point clouds that allows fast pointwise evaluation at arbitrary spatial resolution. As input, our method takes a point cloud with normals; as output, it provides an analytical parameterization that allows queries of signed distance to the approximate underlying surface at arbitrary points — simultaneously providing reconstruction and distance. Our key idea is to reconstruct shapes by locally fitting point clouds with tori, which have closed-form signed distance functions. Tori are fitted in a feed-forward manner, using a pre-trained network to output per-point curvature and shift parameters. Importantly, our method does not require costly global optimization or spatial discretization, and is easily parallelizable. Underlying our method is a new theory that unifies signed distance with the classic reconstruction methods of winding numbers and Poisson surface reconstruction. We use our method to compute signed distance to point clouds arising from photogrammetry, meshes, 3D Gaussians, and neural implicits. Our method allows point clouds to be used directly in applications, without explicit surface reconstruction: as examples, we take offsets of point clouds, apply morphological and Boolean operations, and directly visualize offset surfaces using sphere tracing.
Coordinate-motion assemblies can only be disassembled by the simultaneous motion of multiple parts along distinct paths, providing high structural stability and enabling efficient robotic assembly. Existing examples are largely limited to architectural structures using joint-based connections, or puzzles created through trial-and-error, as the relationship between part geometry and coordinate motion remains poorly understood. Computationally designing such assemblies is challenging because it requires jointly achieving distributed contacts across the entire assembly and a unique coordinate motion for disassembly that rules out other feasible motions. We address this challenge by establishing a theoretical connection between part geometry and unique coordinate motion, enabling us to rigorously verify whether a given assembly admits a unique coordinate motion. Building on this theory, we introduce a two-stage algorithm that optimizes contact interfaces for a target motion and constructs physically feasible part geometries that conform to a user-specified global shape. We demonstrate our approach on models with complex geometries and topologies, including assemblies with large part counts, and validate it through physical fabrication and experiments.
Multimodal Sentiment Analysis (MSA) and Emotion Recognition in Conversations (ERC) have rapidly developed into pivotal tasks in artificial intelligence. Large Language Models (LLMs) offer powerful semantic reasoning and computational capabilities, showing great potential for understanding emotional content. However, when applied to multimodal sentiment data, LLMs face significant challenges, including the inability to directly process heterogeneous data, difficulties in coping with feature misalignment and suboptimal cross-modal fusion. To address these challenges, we propose a novel multimodal sentiment inference framework named ATGFB-MFF which grounded in fiber bundle theory. This method decomposes multimodal features into an adaptive text-guided shared semantic space and fiber offset spaces to achieve structured alignment and fusion. Then the fused features are converted into structured pseudo-token sequences for effective inference via frozen LLMs. We also introduce two loss functions respectively called shared space consistency loss and fiber offset regularization loss which are used to improve representation stability. Extensive experiments on four benchmark datasets demonstrate that ATGFB-MFF consistently outperforms state-of-the-art baselines. These results highlight the efficacy of geometric structural modeling in unlocking the potential of LLMs for multimodal sentiment inference.
Human mobility prediction is crucial for applications ranging from location-based recommendations to urban planning, which aims to forecast users' next location visits based on historical trajectories. While existing mobility prediction models excel at capturing sequential patterns through diverse architectures for different scenarios, they are hindered by the long-tailed distribution of location visits, leading to biased predictions and limited applicability. This highlights the need for a solution that enhances the long-tailed prediction capabilities of these models with broad compatibility and efficiency across diverse architectures. To address this need, we propose the first architecture-agnostic plugin for long-tailed human mobility prediction, named Adaptive LO cation HierArchy learning (ALOHA). Inspired by Maslow's theory of human motivation, we exploit and explore common mobility knowledge of head and tail locations derived from human mobility trajectories to effectively mitigate long-tailed bias. Specifically, we introduce an automatic pipeline to construct city-tailored location hierarchies based on Large Language Models (LLMs) and Chain-of-Thought (CoT) prompts, capturing high-level mobility semantics with minimal human verification. We further design an Adaptive Hierarchical Loss (AHL) that rebalances learning through Gumbel disturbance and node-wise adaptive weighting, enabling both exploitation of multi-level signals and exploration within semantically related groups. Extensive experiments across multiple state-of-the-art models demonstrate that ALOHA consistently improves long-tailed mobility prediction performance by up to 16.59% while maintaining efficiency and robustness. Our code is at https://github.com/Star607/ALOHA.
The persistent challenges of data sparsity and class imbalance have long limited the development of recommender systems. Fortunately, line graph theory offers a novel perspective to overcome these issues. By transforming the user-item interaction bipartite graph into a line graph, the problems of data sparsity and class imbalance are elegantly reformulated as those of insufficient labeled nodes and imbalanced label distribution in the line graph domain. This reformulation allows us to directly apply mature techniques from node classification and imbalanced graph learning to address these core challenges. Inspired by this insight, we propose a Line Graph Data Augmentation (LGDA) strategy, which features two distinct characteristics. Firstly, it is a plug-and-play module that resolves data sparsity and imbalance without modifying the underlying recommendation framework. Secondly, it employs a targeted augmentation and confidence filtering mechanism to generate high-quality, balanced augmented data. Extensive experiments on four real-world datasets validate that LGDA effectively alleviates data sparsity and class imbalance, leading to significant improvements in both recommendation performance and system robustness.
Short-video applications have attracted substantial user traffic. However, these platforms also foster problematic usage patterns, commonly referred to as short-video addiction, which pose risks to both user health and the sustainable development of platforms. Prior studies on this issue have primarily relied on questionnaires or volunteer-based data collection, which are often limited by small sample sizes and population biases. In contrast, short-video platforms have large-scale behavioral data, offering a valuable foundation for analyzing addictive behaviors. To examine addiction-aware behavior patterns, we combine economic addiction theory with users' implicit behavior captured by recommendation systems. Our analysis shows that short-video addiction follows functional patterns similar to traditional forms of addictive behavior (e.g., substance abuse) and that its intensity is consistent with findings from previous social science studies. To develop a simulator that can learn and model these patterns, we introduce a novel training framework, AddictSim. To consider the personalized addiction patterns, AddictSim uses a mean-to-adapted strategy with group relative policy optimization training. Experiments on two large-scale datasets show that AddictSim consistently outperforms existing training strategies. Our simulation results show that integrating diversity-aware algorithms can mitigate addictive behaviors well.
By allowing each client to refer to the knowledge from other clients while retaining their specific characteristics, partial knowledge sharing has become one of the main approaches to realizing personalized federated learning (pFL). Representative techniques of partial knowledge sharing propose sharing the feature extractor while customizing the classifier head of the neural network. Although such methods achieve great success, the underlying principle behind them remains yet to be comprehensively understood. A fundamental problem is whether it is really appropriate to fully share the feature extractor. Based on the theory of neural collapse, in this paper, we demonstrate both theoretically and empirically that the feature extractor should be partially shared rather than fully shared. More specifically, we identify a substantial inconsistency between the fused global feature representations and expected local feature representations, and thus it is necessary to preserve partially customized layers of the feature extractor for enhancing personalized representations. Based on this discovery, we further propose a novel method called pFedDKS which detaches the shared global knowledge and customized local knowledge by providing detached feature prototypes. Extensive experiments on various datasets and models show that pFedDKS outperforms state-of-the-arts.
User cold-start problem is a long-standing challenge in recommendation systems. Fortunately, cross-domain recommendation (CDR) has emerged as a highly effective remedy for the user cold-start challenge, with recently developed diffusion models (DMs) demonstrating exceptional performance. However, these DMs-based CDR methods focus on dealing with user-item interactions, overlooking correlations between items across the source and target domains. Meanwhile, the Gaussian noise added in the forward process of diffusion models would hurt user's personalized preference, leading to the difficulty in transferring user preference across domains. To this end, we propose a novel paradigm of Smoothing-Sharpening Process Model for CDR to cold-start users, termed as S2CDR which features a corruption-recovery architecture and is solved with respect to ordinary differential equations (ODEs). Specifically, the smoothing process gradually corrupts the original user-item/item-item interaction matrices derived from both domains into smoothed preference signals in a noise-free manner, and the sharpening process iteratively sharpens the preference signals to recover the unknown interactions for cold-start users. Wherein, for the smoothing process, we introduce the heat equation on the item-item similarity graph to better capture the correlations between items across domains, and further build the tailor-designed low-pass filter to filter out the high-frequency noise information for capturing user's intrinsic preference, in accordance with the graph signal processing (GSP) theory. Extensive experiments on three real-world CDR scenarios confirm that our S2CDR significantly outperforms previous SOTA methods in a training-free manner.
Conversational recommender systems (CRSs) aim to provide real-time recommendations through dynamic interactions between users and the system. Recent studies have revealed the value of personalized information derived from users' historical dialogue records in refining user preferences. However, existing methods often utilize the entire historical dialogue of a user indiscriminately, leading to the issue of cognitive negative transfer, wherein historical dialogue sessions impede rather than facilitate current decision-making. This ultimately degrades the performance of conversational recommendations. To address this issue, inspired by the behavioral decision theory, this paper proposes a novel model, Personalization-Driven Agent Debate for Conversational Recommendation, named EyeCRS. EyeCRS is comprised of two core components: (i) The Multi-Agent Debate Module employs supporting and opposing agents to simulate a human-like debate process, thereby enabling a rigorous evaluation of whether historical dialogue sessions may introduce cognitive negative transfer into the recommender. (ii) The Parametric Injection Module, subsequently, parameterizes the historical dialogues that are validated as positive and injects them into the intrinsic parameter space of the downstream recommender, thereby effectively enhancing the model's ability to internalize and utilize personalized knowledge. Experimental results on two real-world datasets show that EyeCRS effectively mitigates cognitive negative transfer and achieves superior performance in conversational recommendation.
Recommendation systems aim to learn user interests from historical behaviors and deliver relevant items. Recent methods leverage large language models (LLMs) to construct and integrate semantic representations of users and items for capturing user interests. However, user behavior theories suggest that truly understanding user interests requires not only semantic integration but also semantic reasoning from explicit individual interests to implicit group interests. To this end, we propose an Iterative Semantic Reasoning Framework (ISRF) for generative recommendation. ISRF leverages LLMs to bridge explicit individual interests and implicit group interests in three steps. First, we perform multi-step bidirectional reasoning over item attributes to infer semantic item features and build a semantic interaction graph capturing users' explicit interests. Second, we generate semantic user features based on the semantic item features and construct a similarity-based user graph to infer the implicit interests of similar user groups. Third, we adopt an iterative batch optimization strategy, where individual explicit interests directly guide the refinement of group implicit interests, while group implicit interests indirectly enhance individual modeling. This iterative process ensures consistent and progressive interest reasoning, enabling more accurate and comprehensive user interest learning. Extensive experiments on the Sports, Beauty, and Toys datasets demonstrate that ISRF outperforms state-of-the-art baselines. The code is available at https://github.com/htired/ISRF.
Social media engagement prediction is a central challenge in computational social science, particularly for understanding how users interact with misinformation. Existing approaches often treat engagement as a homogeneous time-series signal, overlooking the heterogeneous social mechanisms and platform designs that shape how misinformation spreads. In this work, we ask: ''Can neural architectures discover social exchange principles from behavioral data alone?'' We introduce Dreams (Disentangled Representations and Episodic Adaptive Modeling for Social media misinformation engagements), a social exchange theory-guided framework that models misinformation engagement as a dynamic process of social exchange. Rather than treating engagement as a static outcome, Dreams models it as a sequence-to-sequence adaptation problem, where each action reflects an evolving negotiation between user effort and social reward conditioned by platform context. It integrates adaptive mechanisms to learn how emotional and contextual signals propagate through time and across platforms. On a cross-platform dataset spanning 7 platforms and 2.37M posts collected between 2021 and 2025, Dreams achieves state-of-the-art performance in predicting misinformation engagements, reaching a mean absolute percentage error of 19.25%. This is a 43.6% improvement over the strongest baseline. Beyond predictive gains, the model reveals consistent cross-platform patterns that align with social exchange principles, suggesting that integrating behavioral theory can enhance empirical modeling of online misinformation engagement. The source code is available at: https://github.com/ltian678/DREAMS.
Online hate on social media ranges from overt slurs and threats (hard hate speech ) to soft hate speech: discourse that appears reasonable on the surface but uses framing and value-based arguments to steer audiences toward blaming or excluding a target group. We hypothesize that current moderation systems, largely optimized for surface toxicity cues, are not robust to this reasoning-driven hostility, yet existing benchmarks do not measure this gap systematically. We introduce SoftHateBench, a generative benchmark that produces soft-hate variants while preserving the underlying hostile standpoint. To generate soft hate, we integrate the Argumentum Model of Topics (AMT) and Relevance Theory (RT) in a unified framework: AMT provides the backbone argument structure for rewriting an explicit hateful standpoint into a seemingly neutral discussion while preserving the stance, and RT guides generation to keep the AMT chain logically coherent. The benchmark spans 7 sociocultural domains and 28 target groups, comprising 4,745 soft-hate instances. Evaluations across encoder-based detectors, general-purpose LLMs, and safety models show a consistent drop from hard to soft tiers: systems that detect explicit hostility often fail when the same stance is conveyed through subtle, reasoning-based language. Disclaimer. Contains offensive examples used solely for research.
Restaurants, as small hospitality businesses, are inherently vulnerable, making accurate survival prediction crucial. Previous studies have demonstrated the significance of user reviews and incorporated diverse review?derived factors, yet they have largely overlooked the large?scale network formed by user–restaurant interactions. How restaurant survival is influenced by the review network remains insufficiently explored. To fill this gap, leveraging network embeddedness theory, we statistically analyze the impact of two dimensions of embeddedness, structural and positional, on each restaurant's survival. Utilizing two real-world review datasets, the newly curated OpenRice and the well-established Yelp, our results reveal that a restaurant's network embeddedness and its temporal evolution positively correlate with its survival. Building on this insight, we propose a Dynamic Embeddedness-aware Graph Neural Network, DyE-GNN, for restaurant survival prediction. DyE-GNN not only explicitly integrates network embeddedness theory to guide the model design but also leverages domain knowledge to enable robust adaptability. Extensive experiments on both datasets confirm the superiority of DyE-GNN, underscoring the importance of network embeddedness attention, temporal dynamics, and survival knowledge of peer restaurants. Visualizations further demonstrate that network embeddedness facilitates the identification of at-risk restaurants at the network margin.
Large Language Models are rapidly emerging as web-native interfaces to social platforms. On the social web, users frequently have ambiguous and dynamic goals, making complex intent understanding—rather than single-turn execution—the cornerstone of effective human-LLM collaboration. Existing approaches attempt to clarify user intents through sequential or parallel questioning, yet they fall short of addressing the core challenge: modeling the logical dependencies among clarification questions. Inspired by the Cognitive Load Theory, we propose Prism, a novel framework for complex intent understanding that enables logically coherent and efficient intent clarification. Prism comprises four tailored modules: a complex intent decomposition module, which decomposes user intents into smaller, well-structured elements and identifies logical dependencies among them; a logical clarification generation module, which organizes clarification questions based on these dependencies to ensure coherent, low-friction interactions; an intent-aware reward module, which evaluates the quality of clarification trajectories via an intent-aware reward function and leverages Monte Carlo Sample to simulate user-LLM interactions for large-scale, high-quality training data generation; and a self-evolved intent tuning module, which iteratively refines the LLM's logical clarification capability through data-driven feedback and optimization. Prism consistently outperforms existing approaches across clarification interactions, intent execution, and cognitive load benchmarks. It achieves state-of-the-art logical consistency, reduces logical conflicts to 11.5%, increases user satisfaction by 14.4%, and decreases task completion time by 34.8%. All data and code are released.
Graph Transformers (GTs) are increasingly applied to social network analysis, yet their deployment is often constrained by fairness concerns. This issue is particularly critical in incomplete social networks, where sensitive attributes are frequently missing due to privacy and ethical restrictions. Existing solutions commonly generate these incomplete attributes, which may introduce additional biases and further compromise user privacy. To address this challenge, FairGE (Fair Graph Encoding) is introduced as a fairness-aware framework for GTs in incomplete social networks. Instead of generating sensitive attributes, FairGE encodes fairness directly through spectral graph theory. By leveraging the principal eigenvector to represent structural information and padding incomplete sensitive attributes with zeros to maintain independence, FairGE ensures fairness without data reconstruction. Theoretical analysis demonstrates that the method suppresses the influence of non-principal spectral components, thereby enhancing fairness. Extensive experiments on seven real-world social network datasets confirm that FairGE achieves at least a 16% improvement in both statistical parity and equality of opportunity compared with state-of-the-art baselines.