Daily Papers

We present CAGE (Continuity-Aware edGE) network, a robust framework for reconstructing vector floorplans directly from point-cloud density maps. Traditional corner-based polygon representations are highly sensitive to noise and incomplete observations, often resulting in fragmented or implausible layouts.Recent line grouping methods leverage structural cues to improve robustness but still struggle to recover fine geometric details. To address these limitations,we propose a native edge-centric formulation, modeling each wall segment as a directed, geometrically continuous edge. This representation enables inference of coherent floorplan structures, ensuring watertight, topologically valid room boundaries while improving robustness and reducing artifacts. Towards this design, we develop a dual-query transformer decoder that integrates perturbed and latent queries within a denoising framework, which not only stabilizes optimization but also accelerates convergence. Extensive experiments on Structured3D and SceneCAD show that CAGE achieves state-of-the-art performance, with F1 scores of 99.1% (rooms), 91.7% (corners), and 89.3% (angles). The method also demonstrates strong cross-dataset generalization, underscoring the efficacy of our architectural innovations. Code and pretrained models are available on our project page: https://github.com/ee-Liu/CAGE.git.

With their meaningful geometry and their omnipresence in the 3D world, edges are extremely useful primitives in computer vision. 3D edges comprise of lines and curves, and methods to reconstruct them use either multi-view images or point clouds as input. State-of-the-art image-based methods first learn a 3D edge point cloud then fit 3D edges to it. The edge point cloud is obtained by learning a 3D neural implicit edge field from which the 3D edge points are sampled on a specific level set (0 or 1). However, such methods present two important drawbacks: i) it is not realistic to sample points on exact level sets due to float imprecision and training inaccuracies. Instead, they are sampled within a range of levels so the points do not lie accurately on the 3D edges and require further processing. ii) Such implicit representations are computationally expensive and require long training times. In this paper, we address these two limitations and propose a 3D edge mapping that is simpler, more efficient, and preserves accuracy. Our method learns explicitly the 3D edge points and their edge direction hence bypassing the need for point sampling. It casts a 3D edge point as the center of a 3D Gaussian and the edge direction as the principal axis of the Gaussian. Such a representation has the advantage of being not only geometrically meaningful but also compatible with the efficient training optimization defined in Gaussian Splatting. Results show that the proposed method produces edges as accurate and complete as the state-of-the-art while being an order of magnitude faster. Code is released at https://github.com/kunalchelani/EdgeGaussians.

Given a graph, the shortest-path problem requires finding a sequence of edges with minimum cumulative length that connects a source vertex to a target vertex. We consider a variant of this classical problem in which the position of each vertex in the graph is a continuous decision variable constrained in a convex set, and the length of an edge is a convex function of the position of its endpoints. Problems of this form arise naturally in many areas, from motion planning of autonomous vehicles to optimal control of hybrid systems. The price for such a wide applicability is the complexity of this problem, which is easily seen to be NP-hard. Our main contribution is a strong and lightweight mixed-integer convex formulation based on perspective operators, that makes it possible to efficiently find globally optimal paths in large graphs and in high-dimensional spaces.

Graph generation is integral to various engineering and scientific disciplines. Nevertheless, existing methodologies tend to overlook the generation of edge attributes. However, we identify critical applications where edge attributes are essential, making prior methods potentially unsuitable in such contexts. Moreover, while trivial adaptations are available, empirical investigations reveal their limited efficacy as they do not properly model the interplay among graph components. To address this, we propose a joint score-based model of nodes and edges for graph generation that considers all graph components. Our approach offers two key novelties: (i) node and edge attributes are combined in an attention module that generates samples based on the two ingredients; and (ii) node, edge and adjacency information are mutually dependent during the graph diffusion process. We evaluate our method on challenging benchmarks involving real-world and synthetic datasets in which edge features are crucial. Additionally, we introduce a new synthetic dataset that incorporates edge values. Furthermore, we propose a novel application that greatly benefits from the method due to its nature: the generation of traffic scenes represented as graphs. Our method outperforms other graph generation methods, demonstrating a significant advantage in edge-related measures.

Point clouds provide a flexible geometric representation suitable for countless applications in computer graphics; they also comprise the raw output of most 3D data acquisition devices. While hand-designed features on point clouds have long been proposed in graphics and vision, however, the recent overwhelming success of convolutional neural networks (CNNs) for image analysis suggests the value of adapting insight from CNN to the point cloud world. Point clouds inherently lack topological information so designing a model to recover topology can enrich the representation power of point clouds. To this end, we propose a new neural network module dubbed EdgeConv suitable for CNN-based high-level tasks on point clouds including classification and segmentation. EdgeConv acts on graphs dynamically computed in each layer of the network. It is differentiable and can be plugged into existing architectures. Compared to existing modules operating in extrinsic space or treating each point independently, EdgeConv has several appealing properties: It incorporates local neighborhood information; it can be stacked applied to learn global shape properties; and in multi-layer systems affinity in feature space captures semantic characteristics over potentially long distances in the original embedding. We show the performance of our model on standard benchmarks including ModelNet40, ShapeNetPart, and S3DIS.

Edge intelligence paradigm is increasingly demanded by the emerging autonomous systems, such as robotics. Beyond ensuring privacy-preserving operation and resilience in connectivity-limited environments, edge deployment offers significant energy and cost advantages over cloud-based solutions. However, deploying large language models (LLMs) for reasoning tasks on edge GPUs faces critical challenges from strict latency constraints and limited computational resources. To navigate these constraints, developers must balance multiple design factors - choosing reasoning versus non-reasoning architectures, selecting appropriate model sizes, allocating token budgets, and applying test-time scaling strategies - to meet target latency and optimize accuracy. Yet guidance on optimal combinations of these variables remains scarce. In this work, we present EdgeReasoning, a comprehensive study characterizing the deployment of reasoning LLMs on edge GPUs. We systematically quantify latency-accuracy tradeoffs across various LLM architectures and model sizes. We systematically evaluate prompt-based and model-tuning-based techniques for reducing reasoning token length while maintaining performance quality. We further profile test-time scaling methods with varying degrees of parallelism to maximize accuracy under strict latency budgets. Through these analyses, EdgeReasoning maps the Pareto frontier of achievable accuracy-latency configurations, offering systematic guidance for optimal edge deployment of reasoning LLMs.

Deploying high-performance dense prediction models on resource-constrained edge devices remains challenging due to strict limits on computation and memory. In practice, lightweight systems for object detection, instance segmentation, and pose estimation are still dominated by CNN-based architectures such as YOLO, while compact Vision Transformers (ViTs) often struggle to achieve similarly strong accuracy efficiency tradeoff, even with large scale pretraining. We argue that this gap is largely due to insufficient task specific representation learning in small scale ViTs, rather than an inherent mismatch between ViTs and edge dense prediction. To address this issue, we introduce EdgeCrafter, a unified compact ViT framework for edge dense prediction centered on ECDet, a detection model built from a distilled compact backbone and an edge-friendly encoder decoder design. On the COCO dataset, ECDet-S achieves 51.7 AP with fewer than 10M parameters using only COCO annotations. For instance segmentation, ECInsSeg achieves performance comparable to RF-DETR while using substantially fewer parameters. For pose estimation, ECPose-X reaches 74.8 AP, significantly outperforming YOLO26Pose-X (71.6 AP) despite the latter's reliance on extensive Objects365 pretraining. These results show that compact ViTs, when paired with task-specialized distillation and edge-aware design, can be a practical and competitive option for edge dense prediction. Code is available at: https://intellindust-ai-lab.github.io/projects/EdgeCrafter/

The conventional deep learning paradigm often involves training a deep model on a server and then deploying the model or its distilled ones to resource-limited edge devices. Usually, the models shall remain fixed once deployed (at least for some period) due to the potential high cost of model adaptation for both the server and edge sides. However, in many real-world scenarios, the test environments may change dynamically (known as distribution shifts), which often results in degraded performance. Thus, one has to adapt the edge models promptly to attain promising performance. Moreover, with the increasing data collected at the edge, this paradigm also fails to further adapt the cloud model for better performance. To address these, we encounter two primary challenges: 1) the edge model has limited computation power and may only support forward propagation; 2) the data transmission budget between cloud and edge devices is limited in latency-sensitive scenarios. In this paper, we establish a Cloud-Edge Elastic Model Adaptation (CEMA) paradigm in which the edge models only need to perform forward propagation and the edge models can be adapted online. In our CEMA, to reduce the communication burden, we devise two criteria to exclude unnecessary samples from uploading to the cloud, i.e., dynamic unreliable and low-informative sample exclusion. Based on the uploaded samples, we update and distribute the affine parameters of normalization layers by distilling from the stronger foundation model to the edge model with a sample replay strategy. Extensive experimental results on ImageNet-C and ImageNet-R verify the effectiveness of our CEMA.

In recent years, Graph Neural Networks (GNNs) have made significant advances in processing structured data. However, most of them primarily adopted a model-centric approach, which simplifies graphs by converting them into undirected formats and emphasizes model designs. This approach is inherently limited in real-world applications due to the unavoidable information loss in simple undirected graphs and the model optimization challenges that arise when exceeding the upper bounds of this sub-optimal data representational capacity. As a result, there has been a shift toward data-centric methods that prioritize improving graph quality and representation. Specifically, various types of graphs can be derived from naturally structured data, including heterogeneous graphs, hypergraphs, and directed graphs. Among these, directed graphs offer distinct advantages in topological systems by modeling causal relationships, and directed GNNs have been extensively studied in recent years. However, a comprehensive survey of this emerging topic is still lacking. Therefore, we aim to provide a comprehensive review of directed graph learning, with a particular focus on a data-centric perspective. Specifically, we first introduce a novel taxonomy for existing studies. Subsequently, we re-examine these methods from the data-centric perspective, with an emphasis on understanding and improving data representation. It demonstrates that a deep understanding of directed graphs and their quality plays a crucial role in model performance. Additionally, we explore the diverse applications of directed GNNs across 10+ domains, highlighting their broad applicability. Finally, we identify key opportunities and challenges within the field, offering insights that can guide future research and development in directed graph learning.

Edge Computing (EC) has gained significant traction in recent years, promising enhanced efficiency by integrating Artificial Intelligence (AI) capabilities at the edge. While the focus has primarily been on the deployment and inference of Machine Learning (ML) models at the edge, the training aspect remains less explored. This survey delves into Edge Learning (EL), specifically the optimization of ML model training at the edge. The objective is to comprehensively explore diverse approaches and methodologies in EL, synthesize existing knowledge, identify challenges, and highlight future trends. Utilizing Scopus' advanced search, relevant literature on EL was identified, revealing a concentration of research efforts in distributed learning methods, particularly Federated Learning (FL). This survey further provides a guideline for comparing techniques used to optimize ML for edge learning, along with an exploration of different frameworks, libraries, and simulation tools available for EL. In doing so, the paper contributes to a holistic understanding of the current landscape and future directions in the intersection of edge computing and machine learning, paving the way for informed comparisons between optimization methods and techniques designed for edge learning.

Efficient adaption of large language models (LLMs) on edge devices is essential for applications requiring continuous and privacy-preserving adaptation and inference. However, existing tuning techniques fall short because of the high computation and memory overheads. To this end, we introduce a computation- and memory-efficient LLM tuning framework, called Edge-LLM, to facilitate affordable and effective LLM adaptation on edge devices. Specifically, Edge-LLM features three core components: (1) a layer-wise unified compression (LUC) technique to reduce the computation overhead by generating layer-wise pruning sparsity and quantization bit-width policies, (2) an adaptive layer tuning and voting scheme to reduce the memory overhead by reducing the backpropagation depth, and (3) a complementary hardware scheduling strategy to handle the irregular computation patterns introduced by LUC and adaptive layer tuning, thereby achieving efficient computation and data movements. Extensive experiments demonstrate that Edge-LLM achieves a 2.92x speed up and a 4x memory overhead reduction as compared to vanilla tuning methods with comparable task accuracy. Our code is available at https://github.com/GATECH-EIC/Edge-LLM

Diffusion-based generative graph models have been proven effective in generating high-quality small graphs. However, they need to be more scalable for generating large graphs containing thousands of nodes desiring graph statistics. In this work, we propose EDGE, a new diffusion-based generative graph model that addresses generative tasks with large graphs. To improve computation efficiency, we encourage graph sparsity by using a discrete diffusion process that randomly removes edges at each time step and finally obtains an empty graph. EDGE only focuses on a portion of nodes in the graph at each denoising step. It makes much fewer edge predictions than previous diffusion-based models. Moreover, EDGE admits explicitly modeling the node degrees of the graphs, further improving the model performance. The empirical study shows that EDGE is much more efficient than competing methods and can generate large graphs with thousands of nodes. It also outperforms baseline models in generation quality: graphs generated by our approach have more similar graph statistics to those of the training graphs.

<<<This is a pre-acceptance version, please, go through Pattern Recognition Journal on Sciencedirect to read the final version>>>. Edge detection is the basis of many computer vision applications. State of the art predominantly relies on deep learning with two decisive factors: dataset content and network's architecture. Most of the publicly available datasets are not curated for edge detection tasks. Here, we offer a solution to this constraint. First, we argue that edges, contours and boundaries, despite their overlaps, are three distinct visual features requiring separate benchmark datasets. To this end, we present a new dataset of edges. Second, we propose a novel architecture, termed Dense Extreme Inception Network for Edge Detection (DexiNed), that can be trained from scratch without any pre-trained weights. DexiNed outperforms other algorithms in the presented dataset. It also generalizes well to other datasets without any fine-tuning. The higher quality of DexiNed is also perceptually evident thanks to the sharper and finer edges it outputs.

Stable Diffusion Models (SDMs) have shown remarkable proficiency in image synthesis. However, their broad application is impeded by their large model sizes and intensive computational requirements, which typically require expensive cloud servers for deployment. On the flip side, while there are many compact models tailored for edge devices that can reduce these demands, they often compromise on semantic integrity and visual quality when compared to full-sized SDMs. To bridge this gap, we introduce Hybrid SD, an innovative, training-free SDMs inference framework designed for edge-cloud collaborative inference. Hybrid SD distributes the early steps of the diffusion process to the large models deployed on cloud servers, enhancing semantic planning. Furthermore, small efficient models deployed on edge devices can be integrated for refining visual details in the later stages. Acknowledging the diversity of edge devices with differing computational and storage capacities, we employ structural pruning to the SDMs U-Net and train a lightweight VAE. Empirical evaluations demonstrate that our compressed models achieve state-of-the-art parameter efficiency (225.8M) on edge devices with competitive image quality. Additionally, Hybrid SD reduces the cloud cost by 66% with edge-cloud collaborative inference.

The development of modern Artificial Intelligence (AI) models, particularly diffusion-based models employed in computer vision and image generation tasks, is undergoing a paradigmatic shift in development methodologies. Traditionally dominated by a "Model Centric" approach, in which performance gains were primarily pursued through increasingly complex model architectures and hyperparameter optimization, the field is now recognizing a more nuanced "Data-Centric" approach. This emergent framework foregrounds the quality, structure, and relevance of training data as the principal driver of model performance. To operationalize this paradigm shift, we introduce the DataSeeds.AI sample dataset (the "DSD"), initially comprised of approximately 10,610 high-quality human peer-ranked photography images accompanied by extensive multi-tier annotations. The DSD is a foundational computer vision dataset designed to usher in a new standard for commercial image datasets. Representing a small fraction of DataSeed.AI's 100 million-plus image catalog, the DSD provides a scalable foundation necessary for robust commercial and multimodal AI development. Through this in-depth exploratory analysis, we document the quantitative improvements generated by the DSD on specific models against known benchmarks and make the code and the trained models used in our evaluation publicly available.

Optimization problems over dynamic networks have been extensively studied and widely used in the past decades to formulate numerous real-world problems. However, (1) traditional optimization-based approaches do not scale to large networks, and (2) the design of good heuristics or approximation algorithms often requires significant manual trial-and-error. In this work, we argue that data-driven strategies can automate this process and learn efficient algorithms without compromising optimality. To do so, we present network control problems through the lens of reinforcement learning and propose a graph network-based framework to handle a broad class of problems. Instead of naively computing actions over high-dimensional graph elements, e.g., edges, we propose a bi-level formulation where we (1) specify a desired next state via RL, and (2) solve a convex program to best achieve it, leading to drastically improved scalability and performance. We further highlight a collection of desirable features to system designers, investigate design decisions, and present experiments on real-world control problems showing the utility, scalability, and flexibility of our framework.

Scientific inquiry requires systems-level reasoning that integrates heterogeneous experimental data, cross-domain knowledge, and mechanistic evidence into coherent explanations. While Large Language Models (LLMs) offer inferential capabilities, they often depend on retrieval-augmented contexts that lack structural depth. Traditional Knowledge Graphs (KGs) attempt to bridge this gap, yet their pairwise constraints fail to capture the irreducible higher-order interactions that govern emergent physical behavior. To address this, we introduce a methodology for constructing hypergraph-based knowledge representations that faithfully encode multi-entity relationships. Applied to a corpus of ~1,100 manuscripts on biocomposite scaffolds, our framework constructs a global hypergraph of 161,172 nodes and 320,201 hyperedges, revealing a scale-free topology (power law exponent ~1.23) organized around highly connected conceptual hubs. This representation prevents the combinatorial explosion typical of pairwise expansions and explicitly preserves the co-occurrence context of scientific formulations. We further demonstrate that equipping agentic systems with hypergraph traversal tools, specifically using node-intersection constraints, enables them to bridge semantically distant concepts. By exploiting these higher-order pathways, the system successfully generates grounded mechanistic hypotheses for novel composite materials, such as linking cerium oxide to PCL scaffolds via chitosan intermediates. This work establishes a "teacherless" agentic reasoning system where hypergraph topology acts as a verifiable guardrail, accelerating scientific discovery by uncovering relationships obscured by traditional graph methods.

Polygonal meshes provide an efficient representation for 3D shapes. They explicitly capture both shape surface and topology, and leverage non-uniformity to represent large flat regions as well as sharp, intricate features. This non-uniformity and irregularity, however, inhibits mesh analysis efforts using neural networks that combine convolution and pooling operations. In this paper, we utilize the unique properties of the mesh for a direct analysis of 3D shapes using MeshCNN, a convolutional neural network designed specifically for triangular meshes. Analogous to classic CNNs, MeshCNN combines specialized convolution and pooling layers that operate on the mesh edges, by leveraging their intrinsic geodesic connections. Convolutions are applied on edges and the four edges of their incident triangles, and pooling is applied via an edge collapse operation that retains surface topology, thereby, generating new mesh connectivity for the subsequent convolutions. MeshCNN learns which edges to collapse, thus forming a task-driven process where the network exposes and expands the important features while discarding the redundant ones. We demonstrate the effectiveness of our task-driven pooling on various learning tasks applied to 3D meshes.

Graph neural networks have recently achieved remarkable success in representing graph-structured data, with rapid progress in both the node embedding and graph pooling methods. Yet, they mostly focus on capturing information from the nodes considering their connectivity, and not much work has been done in representing the edges, which are essential components of a graph. However, for tasks such as graph reconstruction and generation, as well as graph classification tasks for which the edges are important for discrimination, accurately representing edges of a given graph is crucial to the success of the graph representation learning. To this end, we propose a novel edge representation learning framework based on Dual Hypergraph Transformation (DHT), which transforms the edges of a graph into the nodes of a hypergraph. This dual hypergraph construction allows us to apply message-passing techniques for node representations to edges. After obtaining edge representations from the hypergraphs, we then cluster or drop edges to obtain holistic graph-level edge representations. We validate our edge representation learning method with hypergraphs on diverse graph datasets for graph representation and generation performance, on which our method largely outperforms existing graph representation learning methods. Moreover, our edge representation learning and pooling method also largely outperforms state-of-the-art graph pooling methods on graph classification, not only because of its accurate edge representation learning, but also due to its lossless compression of the nodes and removal of irrelevant edges for effective message-passing.

Recent approaches for predicting layouts from 360 panoramas produce excellent results. These approaches build on a common framework consisting of three steps: a pre-processing step based on edge-based alignment, prediction of layout elements, and a post-processing step by fitting a 3D layout to the layout elements. Until now, it has been difficult to compare the methods due to multiple different design decisions, such as the encoding network (e.g. SegNet or ResNet), type of elements predicted (e.g. corners, wall/floor boundaries, or semantic segmentation), or method of fitting the 3D layout. To address this challenge, we summarize and describe the common framework, the variants, and the impact of the design decisions. For a complete evaluation, we also propose extended annotations for the Matterport3D dataset [3], and introduce two depth-based evaluation metrics.

We propose a graph clustering formulation based on multicut (a.k.a. weighted correlation clustering) on the complete graph. Our formulation does not need specification of the graph topology as in the original sparse formulation of multicut, making our approach simpler and potentially better performing. In contrast to unweighted correlation clustering we allow for a more expressive weighted cost structure. In dense multicut, the clustering objective is given in a factorized form as inner products of node feature vectors. This allows for an efficient formulation and inference in contrast to multicut/weighted correlation clustering, which has at least quadratic representation and computation complexity when working on the complete graph. We show how to rewrite classical greedy algorithms for multicut in our dense setting and how to modify them for greater efficiency and solution quality. In particular, our algorithms scale to graphs with tens of thousands of nodes. Empirical evidence on instance segmentation on Cityscapes and clustering of ImageNet datasets shows the merits of our approach.

The deployment and training of neural networks on edge computing devices pose many challenges. The low memory nature of edge devices is often one of the biggest limiting factors encountered in the deployment of large neural network models. Tensor rematerialization or recompute is a way to address high memory requirements for neural network training and inference. In this paper we consider the problem of execution time minimization of compute graphs subject to a memory budget. In particular, we develop a new constraint programming formulation called Moccasin with only O(n) integer variables, where n is the number of nodes in the compute graph. This is a significant improvement over the works in the recent literature that propose formulations with O(n^2) Boolean variables. We present numerical studies that show that our approach is up to an order of magnitude faster than recent work especially for large-scale graphs.

In this paper, we propose VideoLLaMA3, a more advanced multimodal foundation model for image and video understanding. The core design philosophy of VideoLLaMA3 is vision-centric. The meaning of "vision-centric" is two-fold: the vision-centric training paradigm and vision-centric framework design. The key insight of our vision-centric training paradigm is that high-quality image-text data is crucial for both image and video understanding. Instead of preparing massive video-text datasets, we focus on constructing large-scale and high-quality image-text datasets. VideoLLaMA3 has four training stages: 1) vision-centric alignment stage, which warms up the vision encoder and projector; 2) vision-language pretraining stage, which jointly tunes the vision encoder, projector, and LLM with large-scale image-text data covering multiple types (including scene images, documents, charts) as well as text-only data. 3) multi-task fine-tuning stage, which incorporates image-text SFT data for downstream tasks and video-text data to establish a foundation for video understanding. 4) video-centric fine-tuning, which further improves the model's capability in video understanding. As for the framework design, to better capture fine-grained details in images, the pretrained vision encoder is adapted to encode images of varying sizes into vision tokens with corresponding numbers, rather than a fixed number of tokens. For video inputs, we reduce the number of vision tokens according to their similarity so that the representation of videos will be more precise and compact. Benefit from vision-centric designs, VideoLLaMA3 achieves compelling performances in both image and video understanding benchmarks.

The abundance of data has given machine learning considerable momentum in natural sciences and engineering, though modeling of physical processes is often difficult. A particularly tough problem is the efficient representation of geometric boundaries. Triangularized geometric boundaries are well understood and ubiquitous in engineering applications. However, it is notoriously difficult to integrate them into machine learning approaches due to their heterogeneity with respect to size and orientation. In this work, we introduce an effective theory to model particle-boundary interactions, which leads to our new Boundary Graph Neural Networks (BGNNs) that dynamically modify graph structures to obey boundary conditions. The new BGNNs are tested on complex 3D granular flow processes of hoppers, rotating drums and mixers, which are all standard components of modern industrial machinery but still have complicated geometry. BGNNs are evaluated in terms of computational efficiency as well as prediction accuracy of particle flows and mixing entropies. BGNNs are able to accurately reproduce 3D granular flows within simulation uncertainties over hundreds of thousands of simulation timesteps. Most notably, in our experiments, particles stay within the geometric objects without using handcrafted conditions or restrictions.

Edge computing, with its low latency, dynamic scalability, and location awareness, along with the convergence of computing and communication paradigms, has been successfully applied in critical domains such as industrial IoT, smart healthcare, smart homes, and public safety. This paper provides a comprehensive survey of open-source edge computing simulators and emulators, presented in our GitHub repository (https://github.com/qijianpeng/awesome-edge-computing), emphasizing the convergence of computing and networking paradigms. By examining more than 40 tools, including CloudSim, NS-3, and others, we identify the strengths and limitations in simulating and emulating edge environments. This survey classifies these tools into three categories: packet-level, application-level, and emulators. Furthermore, we evaluate them across five dimensions, ranging from resource representation to resource utilization. The survey highlights the integration of different computing paradigms, packet processing capabilities, support for edge environments, user-defined metric interfaces, and scenario visualization. The findings aim to guide researchers in selecting appropriate tools for developing and validating advanced computing and networking technologies.

Geometric Deep Learning has recently made striking progress with the advent of continuous deep implicit fields. They allow for detailed modeling of watertight surfaces of arbitrary topology while not relying on a 3D Euclidean grid, resulting in a learnable parameterization that is unlimited in resolution. Unfortunately, these methods are often unsuitable for applications that require an explicit mesh-based surface representation because converting an implicit field to such a representation relies on the Marching Cubes algorithm, which cannot be differentiated with respect to the underlying implicit field. In this work, we remove this limitation and introduce a differentiable way to produce explicit surface mesh representations from Deep Implicit Fields. Our key insight is that by reasoning on how implicit field perturbations impact local surface geometry, one can ultimately differentiate the 3D location of surface samples with respect to the underlying deep implicit field. We exploit this to define DeepMesh - an end-to-end differentiable mesh representation that can vary its topology. We validate our theoretical insight through several applications: Single view 3D Reconstruction via Differentiable Rendering, Physically-Driven Shape Optimization, Full Scene 3D Reconstruction from Scans and End-to-End Training. In all cases our end-to-end differentiable parameterization gives us an edge over state-of-the-art algorithms.

Recent advances in large language model-powered multi-agent systems have demonstrated remarkable collective intelligence through effective communication. However, existing approaches face two primary challenges: (i) Ineffective group collaboration modeling, as they rely on pairwise edge representations in graph structures, limiting their ability to capture relationships among multiple agents; and (ii) Limited task-adaptiveness in communication topology design, leading to excessive communication cost for simple tasks and insufficient coordination for complex scenarios. These issues restrict the scalability and practical deployment of adaptive collaboration frameworks. To address these challenges, we propose HyperAgent, a hypergraph-based framework that optimizes communication topologies and effectively captures group collaboration patterns using direct hyperedge representations. Unlike edge-based approaches, HyperAgent uses hyperedges to link multiple agents within the same subtask and employs hypergraph convolutional layers to achieve one-step information aggregation in collaboration groups. Additionally, it incorporates a variational autoencoder framework with sparsity regularization to dynamically adjust hypergraph topologies based on task complexity. Experiments highlight the superiority of HyperAgent in both performance and efficiency. For instance, on GSM8K, HyperAgent achieves 95.07\% accuracy while reducing token consumption by 25.33\%, demonstrating the potential of hypergraph-based optimization for multi-agent communication.

This paper presents EdgeSAM, an accelerated variant of the Segment Anything Model (SAM), optimized for efficient execution on edge devices with minimal compromise in performance. Our approach involves distilling the original ViT-based SAM image encoder into a purely CNN-based architecture, better suited for edge devices. We carefully benchmark various distillation strategies and demonstrate that task-agnostic encoder distillation fails to capture the full knowledge embodied in SAM. To overcome this bottleneck, we include both the prompt encoder and mask decoder in the distillation process, with box and point prompts in the loop, so that the distilled model can accurately capture the intricate dynamics between user input and mask generation. To mitigate dataset bias issues stemming from point prompt distillation, we incorporate a lightweight module within the encoder. EdgeSAM achieves a 40-fold speed increase compared to the original SAM, and it also outperforms MobileSAM, being 14 times as fast when deployed on edge devices while enhancing the mIoUs on COCO and LVIS by 2.3 and 3.2 respectively. It is also the first SAM variant that can run at over 30 FPS on an iPhone 14. Code and models are available at https://github.com/chongzhou96/EdgeSAM.

Deep learning models have achieved significant success in various image related tasks. However, they often encounter challenges related to computational complexity and overfitting. In this paper, we propose an efficient approach that leverages polygonal representations of images using dominant points or contour coordinates. By transforming input images into these compact forms, our method significantly reduces computational requirements, accelerates training, and conserves resources making it suitable for real time and resource constrained applications. These representations inherently capture essential image features while filtering noise, providing a natural regularization effect that mitigates overfitting. The resulting lightweight models achieve performance comparable to state of the art methods using full resolution images while enabling deployment on edge devices. Extensive experiments on benchmark datasets validate the effectiveness of our approach in reducing complexity, improving generalization, and facilitating edge computing applications. This work demonstrates the potential of polygonal representations in advancing efficient and scalable deep learning solutions for real world scenarios. The code for the experiments of the paper is provided in https://github.com/salimkhazem/PolygoNet.

We introduce PhysGaussian, a new method that seamlessly integrates physically grounded Newtonian dynamics within 3D Gaussians to achieve high-quality novel motion synthesis. Employing a custom Material Point Method (MPM), our approach enriches 3D Gaussian kernels with physically meaningful kinematic deformation and mechanical stress attributes, all evolved in line with continuum mechanics principles. A defining characteristic of our method is the seamless integration between physical simulation and visual rendering: both components utilize the same 3D Gaussian kernels as their discrete representations. This negates the necessity for triangle/tetrahedron meshing, marching cubes, "cage meshes," or any other geometry embedding, highlighting the principle of "what you see is what you simulate (WS^2)." Our method demonstrates exceptional versatility across a wide variety of materials--including elastic entities, metals, non-Newtonian fluids, and granular materials--showcasing its strong capabilities in creating diverse visual content with novel viewpoints and movements. Our project page is at: https://xpandora.github.io/PhysGaussian/

The rapid expansion of sixth-generation (6G) wireless networks and the Internet of Things (IoT) has catalyzed the evolution from centralized cloud intelligence towards decentralized edge general intelligence. However, traditional edge intelligence methods, characterized by static models and limited cognitive autonomy, fail to address the dynamic, heterogeneous, and resource-constrained scenarios inherent to emerging edge networks. Agentic artificial intelligence (Agentic AI) emerges as a transformative solution, enabling edge systems to autonomously perceive multimodal environments, reason contextually, and adapt proactively through continuous perception-reasoning-action loops. In this context, the agentification of edge intelligence serves as a key paradigm shift, where distributed entities evolve into autonomous agents capable of collaboration and continual adaptation. This paper presents a comprehensive survey dedicated to Agentic AI and agentification frameworks tailored explicitly for edge general intelligence. First, we systematically introduce foundational concepts and clarify distinctions from traditional edge intelligence paradigms. Second, we analyze important enabling technologies, including compact model compression, energy-aware computing strategies, robust connectivity frameworks, and advanced knowledge representation and reasoning mechanisms. Third, we provide representative case studies demonstrating Agentic AI's capabilities in low-altitude economy networks, intent-driven networking, vehicular networks, and human-centric service provisioning, supported by numerical evaluations. Furthermore, we identify current research challenges, review emerging open-source platforms, and highlight promising future research directions to guide robust, scalable, and trustworthy Agentic AI deployments for next-generation edge environments.

Learning compositional representation is a key aspect of object-centric learning as it enables flexible systematic generalization and supports complex visual reasoning. However, most of the existing approaches rely on auto-encoding objective, while the compositionality is implicitly imposed by the architectural or algorithmic bias in the encoder. This misalignment between auto-encoding objective and learning compositionality often results in failure of capturing meaningful object representations. In this study, we propose a novel objective that explicitly encourages compositionality of the representations. Built upon the existing object-centric learning framework (e.g., slot attention), our method incorporates additional constraints that an arbitrary mixture of object representations from two images should be valid by maximizing the likelihood of the composite data. We demonstrate that incorporating our objective to the existing framework consistently improves the objective-centric learning and enhances the robustness to the architectural choices.

Object-centric reconstruction seeks to recover the 3D structure of a scene through composition of independent objects. While this independence can simplify modeling, it discards strong signals that could improve reconstruction, notably repetition where the same object model is seen multiple times in a scene, or across scans. We propose the Joint Reconstruction Model (JRM) to leverage repetition by framing object reconstruction as one of personalized generation: multiple observations share a common subject that should be consistent for all observations, while still adhering to the specific pose and state from each. Prior methods in this direction rely on explicit matching and rigid alignment across observations, making them sensitive to errors and difficult to extend to non-rigid transformations. In contrast, JRM is a 3D flow-matching generative model that implicitly aggregates unaligned observations in its latent space, learning to produce consistent and faithful reconstructions in a data-driven manner without explicit constraints. Evaluations on synthetic and real-world data show that JRM's implicit aggregation removes the need for explicit alignment, improves robustness to incorrect associations, and naturally handles non-rigid changes such as articulation. Overall, JRM outperforms both independent and alignment-based baselines in reconstruction quality.

While learning visuomotor skills in an end-to-end manner is appealing, deep neural networks are often uninterpretable and fail in surprising ways. For robotics tasks, such as autonomous driving, models that explicitly represent objects may be more robust to new scenes and provide intuitive visualizations. We describe a taxonomy of "object-centric" models which leverage both object instances and end-to-end learning. In the Grand Theft Auto V simulator, we show that object-centric models outperform object-agnostic methods in scenes with other vehicles and pedestrians, even with an imperfect detector. We also demonstrate that our architectures perform well on real-world environments by evaluating on the Berkeley DeepDrive Video dataset, where an object-centric model outperforms object-agnostic models in the low-data regimes.

Limited by the encoder-decoder architecture, learning-based edge detectors usually have difficulty predicting edge maps that satisfy both correctness and crispness. With the recent success of the diffusion probabilistic model (DPM), we found it is especially suitable for accurate and crisp edge detection since the denoising process is directly applied to the original image size. Therefore, we propose the first diffusion model for the task of general edge detection, which we call DiffusionEdge. To avoid expensive computational resources while retaining the final performance, we apply DPM in the latent space and enable the classic cross-entropy loss which is uncertainty-aware in pixel level to directly optimize the parameters in latent space in a distillation manner. We also adopt a decoupled architecture to speed up the denoising process and propose a corresponding adaptive Fourier filter to adjust the latent features of specific frequencies. With all the technical designs, DiffusionEdge can be stably trained with limited resources, predicting crisp and accurate edge maps with much fewer augmentation strategies. Extensive experiments on four edge detection benchmarks demonstrate the superiority of DiffusionEdge both in correctness and crispness. On the NYUDv2 dataset, compared to the second best, we increase the ODS, OIS (without post-processing) and AC by 30.2%, 28.1% and 65.1%, respectively. Code: https://github.com/GuHuangAI/DiffusionEdge.

The boundary representation (B-Rep) is the standard data structure used in Computer-Aided Design (CAD) for defining solid models. Despite recent progress, directly generating B-Reps end-to-end with precise geometry and watertight topology remains a challenge. This paper presents AutoBrep, a novel Transformer model that autoregressively generates B-Reps with high quality and validity. AutoBrep employs a unified tokenization scheme that encodes both geometric and topological characteristics of a B-Rep model as a sequence of discrete tokens. Geometric primitives (i.e., surfaces and curves) are encoded as latent geometry tokens, and their structural relationships are defined as special topological reference tokens. Sequence order in AutoBrep naturally follows a breadth first traversal of the B-Rep face adjacency graph. At inference time, neighboring faces and edges along with their topological structure are progressively generated. Extensive experiments demonstrate the advantages of our unified representation when coupled with next-token prediction for B-Rep generation. AutoBrep outperforms baselines with better quality and watertightness. It is also highly scalable to complex solids with good fidelity and inference speed. We further show that autocompleting B-Reps is natively supported through our unified tokenization, enabling user-controllable CAD generation with minimal changes. Code is available at https://github.com/AutodeskAILab/AutoBrep.

Normalizing flows are a promising tool for modeling probability distributions in physical systems. While state-of-the-art flows accurately approximate distributions and energies, applications in physics additionally require smooth energies to compute forces and higher-order derivatives. Furthermore, such densities are often defined on non-trivial topologies. A recent example are Boltzmann Generators for generating 3D-structures of peptides and small proteins. These generative models leverage the space of internal coordinates (dihedrals, angles, and bonds), which is a product of hypertori and compact intervals. In this work, we introduce a class of smooth mixture transformations working on both compact intervals and hypertori. Mixture transformations employ root-finding methods to invert them in practice, which has so far prevented bi-directional flow training. To this end, we show that parameter gradients and forces of such inverses can be computed from forward evaluations via the inverse function theorem. We demonstrate two advantages of such smooth flows: they allow training by force matching to simulation data and can be used as potentials in molecular dynamics simulations.

Hypergraphs are widely being employed to represent complex higher-order relations in real-world applications. Most existing research on hypergraph learning focuses on node-level or edge-level tasks. A practically relevant and more challenging task, edge-dependent node classification (ENC), is still under-explored. In ENC, a node can have different labels across different hyperedges, which requires the modeling of node features unique to each hyperedge. The state-of-the-art ENC solution, WHATsNet, only outputs single node and edge representations, leading to the limitations of entangled edge-specific features and non-adaptive representation sizes when applied to ENC. Additionally, WHATsNet suffers from the common oversmoothing issue in most HGNNs. To address these limitations, we propose CoNHD, a novel HGNN architecture specifically designed to model edge-specific features for ENC. Instead of learning separate representations for nodes and edges, CoNHD reformulates within-edge and within-node interactions as a hypergraph diffusion process over node-edge co-representations. We develop a neural implementation of the proposed diffusion process, leveraging equivariant networks as diffusion operators to effectively learn the diffusion dynamics from data. Extensive experiments demonstrate that CoNHD achieves the best performance across all benchmark ENC datasets and several downstream tasks without sacrificing efficiency. Our implementation is available at https://github.com/zhengyijia/CoNHD.

Estimating surface normals from 3D point clouds is critical for various applications, including surface reconstruction and rendering. While existing methods for normal estimation perform well in regions where normals change slowly, they tend to fail where normals vary rapidly. To address this issue, we propose a novel approach called MSECNet, which improves estimation in normal varying regions by treating normal variation modeling as an edge detection problem. MSECNet consists of a backbone network and a multi-scale edge conditioning (MSEC) stream. The MSEC stream achieves robust edge detection through multi-scale feature fusion and adaptive edge detection. The detected edges are then combined with the output of the backbone network using the edge conditioning module to produce edge-aware representations. Extensive experiments show that MSECNet outperforms existing methods on both synthetic (PCPNet) and real-world (SceneNN) datasets while running significantly faster. We also conduct various analyses to investigate the contribution of each component in the MSEC stream. Finally, we demonstrate the effectiveness of our approach in surface reconstruction.

Part-based 3D generation holds great potential for various applications. Previous part generators that represent parts using implicit vector-set tokens often suffer from insufficient geometric details. Another line of work adopts an explicit voxel representation but shares a global voxel grid among all parts; this often causes small parts to occupy too few voxels, leading to degraded quality. In this paper, we propose FullPart, a novel framework that combines both implicit and explicit paradigms. It first derives the bounding box layout through an implicit box vector-set diffusion process, a task that implicit diffusion handles effectively since box tokens contain little geometric detail. Then, it generates detailed parts, each within its own fixed full-resolution voxel grid. Instead of sharing a global low-resolution space, each part in our method - even small ones - is generated at full resolution, enabling the synthesis of intricate details. We further introduce a center-point encoding strategy to address the misalignment issue when exchanging information between parts of different actual sizes, thereby maintaining global coherence. Moreover, to tackle the scarcity of reliable part data, we present PartVerse-XL, the largest human-annotated 3D part dataset to date with 40K objects and 320K parts. Extensive experiments demonstrate that FullPart achieves state-of-the-art results in 3D part generation. We will release all code, data, and model to benefit future research in 3D part generation.

Object-centric learning (OCL) aspires general and compositional understanding of scenes by representing a scene as a collection of object-centric representations. OCL has also been extended to multi-view image and video datasets to apply various data-driven inductive biases by utilizing geometric or temporal information in the multi-image data. Single-view images carry less information about how to disentangle a given scene than videos or multi-view images do. Hence, owing to the difficulty of applying inductive biases, OCL for single-view images remains challenging, resulting in inconsistent learning of object-centric representation. To this end, we introduce a novel OCL framework for single-view images, SLot Attention via SHepherding (SLASH), which consists of two simple-yet-effective modules on top of Slot Attention. The new modules, Attention Refining Kernel (ARK) and Intermediate Point Predictor and Encoder (IPPE), respectively, prevent slots from being distracted by the background noise and indicate locations for slots to focus on to facilitate learning of object-centric representation. We also propose a weak semi-supervision approach for OCL, whilst our proposed framework can be used without any assistant annotation during the inference. Experiments show that our proposed method enables consistent learning of object-centric representation and achieves strong performance across four datasets. Code is available at https://github.com/object-understanding/SLASH.

Although polygon meshes have been a standard representation in geometry processing, their irregular and combinatorial nature hinders their suitability for learning-based applications. In this work, we introduce a novel learnable mesh representation through a set of local 3D sample Points and their associated Normals and Quadric error metrics (QEM) w.r.t. the underlying shape, which we denote PoNQ. A global mesh is directly derived from PoNQ by efficiently leveraging the knowledge of the local quadric errors. Besides marking the first use of QEM within a neural shape representation, our contribution guarantees both topological and geometrical properties by ensuring that a PoNQ mesh does not self-intersect and is always the boundary of a volume. Notably, our representation does not rely on a regular grid, is supervised directly by the target surface alone, and also handles open surfaces with boundaries and/or sharp features. We demonstrate the efficacy of PoNQ through a learning-based mesh prediction from SDF grids and show that our method surpasses recent state-of-the-art techniques in terms of both surface and edge-based metrics.

Neural representations of 3D data have been widely adopted across various applications, particularly in recent work leveraging coordinate-based networks to model scalar or vector fields. However, these approaches face inherent challenges, such as handling thin structures and non-watertight geometries, which limit their flexibility and accuracy. In contrast, we propose a novel geometric data representation that models geometry as distributions-a powerful representation that makes no assumptions about surface genus, connectivity, or boundary conditions. Our approach uses diffusion models with a novel network architecture to learn surface point distributions, capturing fine-grained geometric details. We evaluate our representation qualitatively and quantitatively across various object types, demonstrating its effectiveness in achieving high geometric fidelity. Additionally, we explore applications using our representation, such as textured mesh representation, neural surface compression, dynamic object modeling, and rendering, highlighting its potential to advance 3D geometric learning.

Implicit Neural Spatial Representation (INSR) has emerged as an effective representation of spatially-dependent vector fields. This work explores solving time-dependent PDEs with INSR. Classical PDE solvers introduce both temporal and spatial discretizations. Common spatial discretizations include meshes and meshless point clouds, where each degree-of-freedom corresponds to a location in space. While these explicit spatial correspondences are intuitive to model and understand, these representations are not necessarily optimal for accuracy, memory usage, or adaptivity. Keeping the classical temporal discretization unchanged (e.g., explicit/implicit Euler), we explore INSR as an alternative spatial discretization, where spatial information is implicitly stored in the neural network weights. The network weights then evolve over time via time integration. Our approach does not require any training data generated by existing solvers because our approach is the solver itself. We validate our approach on various PDEs with examples involving large elastic deformations, turbulent fluids, and multi-scale phenomena. While slower to compute than traditional representations, our approach exhibits higher accuracy and lower memory consumption. Whereas classical solvers can dynamically adapt their spatial representation only by resorting to complex remeshing algorithms, our INSR approach is intrinsically adaptive. By tapping into the rich literature of classic time integrators, e.g., operator-splitting schemes, our method enables challenging simulations in contact mechanics and turbulent flows where previous neural-physics approaches struggle. Videos and codes are available on the project page: http://www.cs.columbia.edu/cg/INSR-PDE/

Geometric Deep Learning has recently made striking progress with the advent of continuous Deep Implicit Fields. They allow for detailed modeling of watertight surfaces of arbitrary topology while not relying on a 3D Euclidean grid, resulting in a learnable parameterization that is not limited in resolution. Unfortunately, these methods are often not suitable for applications that require an explicit mesh-based surface representation because converting an implicit field to such a representation relies on the Marching Cubes algorithm, which cannot be differentiated with respect to the underlying implicit field. In this work, we remove this limitation and introduce a differentiable way to produce explicit surface mesh representations from Deep Signed Distance Functions. Our key insight is that by reasoning on how implicit field perturbations impact local surface geometry, one can ultimately differentiate the 3D location of surface samples with respect to the underlying deep implicit field. We exploit this to define MeshSDF, an end-to-end differentiable mesh representation which can vary its topology. We use two different applications to validate our theoretical insight: Single-View Reconstruction via Differentiable Rendering and Physically-Driven Shape Optimization. In both cases our differentiable parameterization gives us an edge over state-of-the-art algorithms.

We present As-Plausible-as-Possible (APAP) mesh deformation technique that leverages 2D diffusion priors to preserve the plausibility of a mesh under user-controlled deformation. Our framework uses per-face Jacobians to represent mesh deformations, where mesh vertex coordinates are computed via a differentiable Poisson Solve. The deformed mesh is rendered, and the resulting 2D image is used in the Score Distillation Sampling (SDS) process, which enables extracting meaningful plausibility priors from a pretrained 2D diffusion model. To better preserve the identity of the edited mesh, we fine-tune our 2D diffusion model with LoRA. Gradients extracted by SDS and a user-prescribed handle displacement are then backpropagated to the per-face Jacobians, and we use iterative gradient descent to compute the final deformation that balances between the user edit and the output plausibility. We evaluate our method with 2D and 3D meshes and demonstrate qualitative and quantitative improvements when using plausibility priors over geometry-preservation or distortion-minimization priors used by previous techniques. Our project page is at: https://as-plausible-aspossible.github.io/

We present two new classes of algorithms for efficient field integration on graphs encoding point clouds. The first class, SeparatorFactorization(SF), leverages the bounded genus of point cloud mesh graphs, while the second class, RFDiffusion(RFD), uses popular epsilon-nearest-neighbor graph representations for point clouds. Both can be viewed as providing the functionality of Fast Multipole Methods (FMMs), which have had a tremendous impact on efficient integration, but for non-Euclidean spaces. We focus on geometries induced by distributions of walk lengths between points (e.g., shortest-path distance). We provide an extensive theoretical analysis of our algorithms, obtaining new results in structural graph theory as a byproduct. We also perform exhaustive empirical evaluation, including on-surface interpolation for rigid and deformable objects (particularly for mesh-dynamics modeling), Wasserstein distance computations for point clouds, and the Gromov-Wasserstein variant.

The edge computing paradigm places compute-capable devices - edge servers - at the network edge to assist mobile devices in executing data analysis tasks. Intuitively, offloading compute-intense tasks to edge servers can reduce their execution time. However, poor conditions of the wireless channel connecting the mobile devices to the edge servers may degrade the overall capture-to-output delay achieved by edge offloading. Herein, we focus on edge computing supporting remote object detection by means of Deep Neural Networks (DNNs), and develop a framework to reduce the amount of data transmitted over the wireless link. The core idea we propose builds on recent approaches splitting DNNs into sections - namely head and tail models - executed by the mobile device and edge server, respectively. The wireless link, then, is used to transport the output of the last layer of the head model to the edge server, instead of the DNN input. Most prior work focuses on classification tasks and leaves the DNN structure unaltered. Herein, our focus is on DNNs for three different object detection tasks, which present a much more convoluted structure, and modify the architecture of the network to: (i) achieve in-network compression by introducing a bottleneck layer in the early layers on the head model, and (ii) prefilter pictures that do not contain objects of interest using a convolutional neural network. Results show that the proposed technique represents an effective intermediate option between local and edge computing in a parameter region where these extreme point solutions fail to provide satisfactory performance. The code and trained models are available at https://github.com/yoshitomo-matsubara/hnd-ghnd-object-detectors .

Pre-trained vision models (PVMs) are fundamental to modern robotics, yet their optimal configuration remains unclear. Through systematic evaluation, we find that while DINO and iBOT outperform MAE across visuomotor control and perception tasks, they struggle when trained on non-(single-)object-centric (NOC) data--a limitation strongly correlated with their diminished ability to learn object-centric representations. This investigation indicates that the ability to form object-centric representations from the non-object-centric robotics dataset is the key to success for PVMs. Motivated by this discovery, we designed SlotMIM, a method that induces object-centric representations by introducing a semantic bottleneck to reduce the number of prototypes to encourage the emergence of objectness as well as cross-view consistency regularization for encouraging multiview invariance. Our experiments encompass pre-training on object-centric, scene-centric, web-crawled, and ego-centric data. Across all settings, our approach learns transferrable representations and achieves significant improvements over prior work in image recognition, scene understanding, and robot learning evaluations. When scaled up with million-scale datasets, our method also demonstrates superior data efficiency and scalability. Our code and models are publicly available at https://github.com/CVMI-Lab/SlotMIM.

Graph neural networks that model 3D data, such as point clouds or atoms, are typically desired to be SO(3) equivariant, i.e., equivariant to 3D rotations. Unfortunately equivariant convolutions, which are a fundamental operation for equivariant networks, increase significantly in computational complexity as higher-order tensors are used. In this paper, we address this issue by reducing the SO(3) convolutions or tensor products to mathematically equivalent convolutions in SO(2) . This is accomplished by aligning the node embeddings' primary axis with the edge vectors, which sparsifies the tensor product and reduces the computational complexity from O(L^6) to O(L^3), where L is the degree of the representation. We demonstrate the potential implications of this improvement by proposing the Equivariant Spherical Channel Network (eSCN), a graph neural network utilizing our novel approach to equivariant convolutions, which achieves state-of-the-art results on the large-scale OC-20 and OC-22 datasets.

We propose a novel and flexible roof modeling approach that can be used for constructing planar 3D polygon roof meshes. Our method uses a graph structure to encode roof topology and enforces the roof validity by optimizing a simple but effective planarity metric we propose. This approach is significantly more efficient than using general purpose 3D modeling tools such as 3ds Max or SketchUp, and more powerful and expressive than specialized tools such as the straight skeleton. Our optimization-based formulation is also flexible and can accommodate different styles and user preferences for roof modeling. We showcase two applications. The first application is an interactive roof editing framework that can be used for roof design or roof reconstruction from aerial images. We highlight the efficiency and generality of our approach by constructing a mesh-image paired dataset consisting of 2539 roofs. Our second application is a generative model to synthesize new roof meshes from scratch. We use our novel dataset to combine machine learning and our roof optimization techniques, by using transformers and graph convolutional networks to model roof topology, and our roof optimization methods to enforce the planarity constraint.

The Boundary representation (B-rep) format is the de-facto shape representation in computer-aided design (CAD) to model solid and sheet objects. Recent approaches to generating CAD models have focused on learning sketch-and-extrude modeling sequences that are executed by a solid modeling kernel in postprocess to recover a B-rep. In this paper we present a new approach that enables learning from and synthesizing B-reps without the need for supervision through CAD modeling sequence data. Our method SolidGen, is an autoregressive neural network that models the B-rep directly by predicting the vertices, edges, and faces using Transformer-based and pointer neural networks. Key to achieving this is our Indexed Boundary Representation that references B-rep vertices, edges and faces in a well-defined hierarchy to capture the geometric and topological relations suitable for use with machine learning. SolidGen can be easily conditioned on contexts e.g., class labels, images, and voxels thanks to its probabilistic modeling of the B-rep distribution. We demonstrate qualitatively, quantitatively, and through perceptual evaluation by human subjects that SolidGen can produce high quality, realistic CAD models.

The ability to distill object-centric abstractions from intricate visual scenes underpins human-level generalization. Despite the significant progress in object-centric learning methods, learning object-centric representations in the 3D physical world remains a crucial challenge. In this work, we propose SlotLifter, a novel object-centric radiance model addressing scene reconstruction and decomposition jointly via slot-guided feature lifting. Such a design unites object-centric learning representations and image-based rendering methods, offering state-of-the-art performance in scene decomposition and novel-view synthesis on four challenging synthetic and four complex real-world datasets, outperforming existing 3D object-centric learning methods by a large margin. Through extensive ablative studies, we showcase the efficacy of designs in SlotLifter, revealing key insights for potential future directions.

This paper presents a methodology to learn surrogate models of steady state fluid dynamics simulations on meshed domains, based on Implicit Neural Representations (INRs). The proposed models can be applied directly to unstructured domains for different flow conditions, handle non-parametric 3D geometric variations, and generalize to unseen shapes at test time. The coordinate-based formulation naturally leads to robustness with respect to discretization, allowing an excellent trade-off between computational cost (memory footprint and training time) and accuracy. The method is demonstrated on two industrially relevant applications: a RANS dataset of the two-dimensional compressible flow over a transonic airfoil and a dataset of the surface pressure distribution over 3D wings, including shape, inflow condition, and control surface deflection variations. On the considered test cases, our approach achieves a more than three times lower test error and significantly improves generalization error on unseen geometries compared to state-of-the-art Graph Neural Network architectures. Remarkably, the method can perform inference five order of magnitude faster than the high fidelity solver on the RANS transonic airfoil dataset. Code is available at https://gitlab.isae-supaero.fr/gi.catalani/aero-nepf

Recent advances in 3D generation have transitioned from multi-view 2D rendering approaches to 3D-native latent diffusion frameworks that exploit geometric priors in ground truth data. Despite progress, three key limitations persist: (1) Single-latent representations fail to capture complex multi-part geometries, causing detail degradation; (2) Holistic latent coding neglects part independence and interrelationships critical for compositional design; (3) Global conditioning mechanisms lack fine-grained controllability. Inspired by human 3D design workflows, we propose CoPart - a part-aware diffusion framework that decomposes 3D objects into contextual part latents for coherent multi-part generation. This paradigm offers three advantages: i) Reduces encoding complexity through part decomposition; ii) Enables explicit part relationship modeling; iii) Supports part-level conditioning. We further develop a mutual guidance strategy to fine-tune pre-trained diffusion models for joint part latent denoising, ensuring both geometric coherence and foundation model priors. To enable large-scale training, we construct Partverse - a novel 3D part dataset derived from Objaverse through automated mesh segmentation and human-verified annotations. Extensive experiments demonstrate CoPart's superior capabilities in part-level editing, articulated object generation, and scene composition with unprecedented controllability.

Currently, prominent Transformer architectures applied on graphs and meshes for shape analysis tasks employ traditional attention layers that heavily utilize spectral features requiring costly eigenvalue decomposition-based methods. To encode the mesh structure, these methods derive positional embeddings, that heavily rely on eigenvalue decomposition based operations, e.g. on the Laplacian matrix, or on heat-kernel signatures, which are then concatenated to the input features. This paper proposes a novel approach inspired by the explicit construction of the Hodge Laplacian operator in Discrete Exterior Calculus as a product of discrete Hodge operators and exterior derivatives, i.e. (L := star_0^{-1} d_0^T star_1 d_0). We adjust the Transformer architecture in a novel deep learning layer that utilizes the multi-head attention mechanism to approximate Hodge matrices star_0, star_1 and star_2 and learn families of discrete operators L that act on mesh vertices, edges and faces. Our approach results in a computationally-efficient architecture that achieves comparable performance in mesh segmentation and classification tasks, through a direct learning framework, while eliminating the need for costly eigenvalue decomposition operations or complex preprocessing operations.

We tackle the problem of generating a complete vector map representation from aerial imagery in a single run: producing polygons for all land-cover classes with shared boundaries and without gaps or overlaps. Existing polygonization methods are typically class-specific; extending them to multiple classes via per-class runs commonly leads to topological inconsistencies, such as duplicated edges, gaps, and overlaps. We formalize this new task as All-Class Polygonal Vectorization (ACPV) and release the first public benchmark, Deventer-512, with standardized metrics jointly evaluating semantic fidelity, geometric accuracy, vertex efficiency, per-class topological fidelity and global topological consistency. To realize ACPV, we propose ACPV-Net, a unified framework introducing a novel Semantically Supervised Conditioning (SSC) mechanism coupling semantic perception with geometric primitive generation, along with a topological reconstruction that enforces shared-edge consistency by design. While enforcing such strict topological constraints, ACPV-Net surpasses all class-specific baselines in polygon quality across classes on Deventer-512. It also applies to single-class polygonal vectorization without any architectural modification, achieving the best-reported results on WHU-Building. Data, code, and models will be released at: https://github.com/HeinzJiao/ACPV-Net.

The increasing demand for virtual reality applications has highlighted the significance of crafting immersive 3D assets. We present a text-to-3D 360^{circ} scene generation pipeline that facilitates the creation of comprehensive 360^{circ} scenes for in-the-wild environments in a matter of minutes. Our approach utilizes the generative power of a 2D diffusion model and prompt self-refinement to create a high-quality and globally coherent panoramic image. This image acts as a preliminary "flat" (2D) scene representation. Subsequently, it is lifted into 3D Gaussians, employing splatting techniques to enable real-time exploration. To produce consistent 3D geometry, our pipeline constructs a spatially coherent structure by aligning the 2D monocular depth into a globally optimized point cloud. This point cloud serves as the initial state for the centroids of 3D Gaussians. In order to address invisible issues inherent in single-view inputs, we impose semantic and geometric constraints on both synthesized and input camera views as regularizations. These guide the optimization of Gaussians, aiding in the reconstruction of unseen regions. In summary, our method offers a globally consistent 3D scene within a 360^{circ} perspective, providing an enhanced immersive experience over existing techniques. Project website at: http://dreamscene360.github.io/

Recent works in geometric deep learning have introduced neural networks that allow performing inference tasks on three-dimensional geometric data by defining convolution, and sometimes pooling, operations on triangle meshes. These methods, however, either consider the input mesh as a graph, and do not exploit specific geometric properties of meshes for feature aggregation and downsampling, or are specialized for meshes, but rely on a rigid definition of convolution that does not properly capture the local topology of the mesh. We propose a method that combines the advantages of both types of approaches, while addressing their limitations: we extend a primal-dual framework drawn from the graph-neural-network literature to triangle meshes, and define convolutions on two types of graphs constructed from an input mesh. Our method takes features for both edges and faces of a 3D mesh as input and dynamically aggregates them using an attention mechanism. At the same time, we introduce a pooling operation with a precise geometric interpretation, that allows handling variations in the mesh connectivity by clustering mesh faces in a task-driven fashion. We provide theoretical insights of our approach using tools from the mesh-simplification literature. In addition, we validate experimentally our method in the tasks of shape classification and shape segmentation, where we obtain comparable or superior performance to the state of the art.

Accurate and fast 3D object detection from point clouds is a key task in autonomous driving. Existing one-stage 3D object detection methods can achieve real-time performance, however, they are dominated by anchor-based detectors which are inefficient and require additional post-processing. In this paper, we eliminate anchors and model an object as a single point--the center point of its bounding box. Based on the center point, we propose an anchor-free CenterNet3D network that performs 3D object detection without anchors. Our CenterNet3D uses keypoint estimation to find center points and directly regresses 3D bounding boxes. However, because inherent sparsity of point clouds, 3D object center points are likely to be in empty space which makes it difficult to estimate accurate boundaries. To solve this issue, we propose an extra corner attention module to enforce the CNN backbone to pay more attention to object boundaries. Besides, considering that one-stage detectors suffer from the discordance between the predicted bounding boxes and corresponding classification confidences, we develop an efficient keypoint-sensitive warping operation to align the confidences to the predicted bounding boxes. Our proposed CenterNet3D is non-maximum suppression free which makes it more efficient and simpler. We evaluate CenterNet3D on the widely used KITTI dataset and more challenging nuScenes dataset. Our method outperforms all state-of-the-art anchor-based one-stage methods and has comparable performance to two-stage methods as well. It has an inference speed of 20 FPS and achieves the best speed and accuracy trade-off. Our source code will be released at https://github.com/wangguojun2018/CenterNet3d.

Deep learning algorithms are increasingly employed at the edge. However, edge devices are resource constrained and thus require efficient deployment of deep neural networks. Pruning methods are a key tool for edge deployment as they can improve storage, compute, memory bandwidth, and energy usage. In this paper we propose a novel accurate pruning technique that allows precise control over the output network size. Our method uses an efficient optimal transportation scheme which we make end-to-end differentiable and which automatically tunes the exploration-exploitation behavior of the algorithm to find accurate sparse sub-networks. We show that our method achieves state-of-the-art performance compared to previous pruning methods on 3 different datasets, using 5 different models, across a wide range of pruning ratios, and with two types of sparsity budgets and pruning granularities.

Large Language Models (LLMs) such as GPTs and LLaMa have ushered in a revolution in machine intelligence, owing to their exceptional capabilities in a wide range of machine learning tasks. However, the transition of LLMs from data centers to edge devices presents a set of challenges and opportunities. While this shift can enhance privacy and availability, it is hampered by the enormous parameter sizes of these models, leading to impractical runtime costs. In light of these considerations, we introduce EdgeMoE, the first on-device inference engine tailored for mixture-of-expert (MoE) LLMs, a popular variant of sparse LLMs that exhibit nearly constant computational complexity as their parameter size scales. EdgeMoE achieves both memory and computational efficiency by strategically partitioning the model across the storage hierarchy. Specifically, non-expert weights are stored in the device's memory, while expert weights are kept in external storage and are fetched into memory only when they are activated. This design is underpinned by a crucial insight that expert weights, though voluminous, are infrequently accessed due to sparse activation patterns. To further mitigate the overhead associated with expert I/O swapping, EdgeMoE incorporates two innovative techniques: (1) Expert-wise bitwidth adaptation: This method reduces the size of expert weights with an acceptable level of accuracy loss. (2) Expert management: It predicts the experts that will be activated in advance and preloads them into the compute-I/O pipeline, thus further optimizing the process. In empirical evaluations conducted on well-established MoE LLMs and various edge devices, EdgeMoE demonstrates substantial memory savings and performance improvements when compared to competitive baseline solutions.

Pioneered by the foundational information theory by Claude Shannon and the visionary framework of machine intelligence by Alan Turing, the convergent evolution of information and communication technologies (IT/CT) has created an unbroken wave of connectivity and computation. This synergy has sparked a technological revolution, now reaching its peak with large artificial intelligence (AI) models that are reshaping industries and redefining human-machine collaboration. However, the realization of ubiquitous intelligence faces considerable challenges due to substantial resource consumption in large models and high communication bandwidth demands. To address these challenges, AI Flow has been introduced as a multidisciplinary framework that integrates cutting-edge IT and CT advancements, with a particular emphasis on the following three key points. First, device-edge-cloud framework serves as the foundation, which integrates end devices, edge servers, and cloud clusters to optimize scalability and efficiency for low-latency model inference. Second, we introduce the concept of familial models, which refers to a series of different-sized models with aligned hidden features, enabling effective collaboration and the flexibility to adapt to varying resource constraints and dynamic scenarios. Third, connectivity- and interaction-based intelligence emergence is a novel paradigm of AI Flow. By leveraging communication networks to enhance connectivity, the collaboration among AI models across heterogeneous nodes achieves emergent intelligence that surpasses the capability of any single model. The innovations of AI Flow provide enhanced intelligence, timely responsiveness, and ubiquitous accessibility to AI services, paving the way for the tighter fusion of AI techniques and communication systems.

Computational materials discovery is limited by the high cost of first-principles calculations. Machine learning (ML) potentials that predict energies from crystal structures are promising, but existing methods face computational bottlenecks. Steerable graph neural networks (GNNs) encode geometry with spherical harmonics, respecting atomic symmetries -- permutation, rotation, and translation -- for physically realistic predictions. Yet maintaining equivariance is difficult: activation functions must be modified, and each layer must handle multiple data types for different harmonic orders. We present Facet, a GNN architecture for efficient ML potentials, developed through systematic analysis of steerable GNNs. Our innovations include replacing expensive multi-layer perceptrons (MLPs) for interatomic distances with splines, which match performance while cutting computational and memory demands. We also introduce a general-purpose equivariant layer that mixes node information via spherical grid projection followed by standard MLPs -- faster than tensor products and more expressive than linear or gate layers. On the MPTrj dataset, Facet matches leading models with far fewer parameters and under 10% of their training compute. On a crystal relaxation task, it runs twice as fast as MACE models. We further show SevenNet-0's parameters can be reduced by over 25% with no accuracy loss. These techniques enable more than 10x faster training of large-scale foundation models for ML potentials, potentially reshaping computational materials discovery.

Object-centric architectures usually apply a differentiable module to the entire feature map to decompose it into sets of entity representations called slots. Some of these methods structurally resemble clustering algorithms, where the cluster's center in latent space serves as a slot representation. Slot Attention is an example of such a method, acting as a learnable analog of the soft k-means algorithm. Our work employs a learnable clustering method based on the Gaussian Mixture Model. Unlike other approaches, we represent slots not only as centers of clusters but also incorporate information about the distance between clusters and assigned vectors, leading to more expressive slot representations. Our experiments demonstrate that using this approach instead of Slot Attention improves performance in object-centric scenarios, achieving state-of-the-art results in the set property prediction task.

Accurate weather forecasts are important for disaster prevention, agricultural planning, etc. Traditional numerical weather prediction (NWP) methods offer physically interpretable high-accuracy predictions but are computationally expensive and fail to fully leverage rapidly growing historical data. In recent years, deep learning models have made significant progress in weather forecasting, but challenges remain, such as balancing global and regional high-resolution forecasts, excessive smoothing in extreme event predictions, and insufficient dynamic system modeling. To address these issues, this paper proposes a global-regional nested weather forecasting framework (OneForecast) based on graph neural networks. By combining a dynamic system perspective with multi-grid theory, we construct a multi-scale graph structure and densify the target region to capture local high-frequency features. We introduce an adaptive messaging mechanism, using dynamic gating units to deeply integrate node and edge features for more accurate extreme event forecasting. For high-resolution regional forecasts, we propose a neural nested grid method to mitigate boundary information loss. Experimental results show that OneForecast performs excellently across global to regional scales and short-term to long-term forecasts, especially in extreme event predictions. Codes link https://github.com/YuanGao-YG/OneForecast.

Based on the theory of homogeneous spaces we derive geometrically optimal edge attributes to be used within the flexible message-passing framework. We formalize the notion of weight sharing in convolutional networks as the sharing of message functions over point-pairs that should be treated equally. We define equivalence classes of point-pairs that are identical up to a transformation in the group and derive attributes that uniquely identify these classes. Weight sharing is then obtained by conditioning message functions on these attributes. As an application of the theory, we develop an efficient equivariant group convolutional network for processing 3D point clouds. The theory of homogeneous spaces tells us how to do group convolutions with feature maps over the homogeneous space of positions R^3, position and orientations R^3 {times} S^2, and the group SE(3) itself. Among these, R^3 {times} S^2 is an optimal choice due to the ability to represent directional information, which R^3 methods cannot, and it significantly enhances computational efficiency compared to indexing features on the full SE(3) group. We support this claim with state-of-the-art results -- in accuracy and speed -- on five different benchmarks in 2D and 3D, including interatomic potential energy prediction, trajectory forecasting in N-body systems, and generating molecules via equivariant diffusion models.

Ever since the original algorithm by Nesterov (1983), the true nature of the acceleration phenomenon has remained elusive, with various interpretations of why the method is actually faster. The diagnosis of the algorithm through the lens of Ordinary Differential Equations (ODEs) and the corresponding dynamical system formulation to explain the underlying dynamics has a rich history. In the literature, the ODEs that explain algorithms are typically derived by considering the limiting case of the algorithm maps themselves, that is, an ODE formulation follows the development of an algorithm. This obfuscates the underlying higher order principles and thus provides little evidence of the working of the algorithm. Such has been the case with Nesterov algorithm and the various analogies used to describe the acceleration phenomena, viz, momentum associated with the rolling of a Heavy-Ball down a slope, Hessian damping etc. The main focus of our work is to ideate the genesis of the Nesterov algorithm from the viewpoint of dynamical systems leading to demystifying the mathematical rigour behind the algorithm. Instead of reverse engineering ODEs from discrete algorithms, this work explores tools from the recently developed control paradigm titled Passivity and Immersion approach and the Geometric Singular Perturbation theory which are applied to arrive at the formulation of a dynamical system that explains and models the acceleration phenomena. This perspective helps to gain insights into the various terms present and the sequence of steps used in Nesterovs accelerated algorithm for the smooth strongly convex and the convex case. The framework can also be extended to derive the acceleration achieved using the triple momentum method and provides justifications for the non-convergence to the optimal solution in the Heavy-Ball method.

Large Language Models (LLMs) have achieved remarkable success in serving end-users with human-like intelligence. However, LLMs demand high computational resources, making it challenging to deploy them to satisfy various performance objectives, such as meeting the resource constraints on edge devices close to end-users or achieving high accuracy with ample resources. In this paper, we introduce CE-CoLLM, a novel cloud-edge collaboration framework that supports efficient and adaptive LLM inference for end-users at the edge with two modes, (1) low-latency edge standalone inference and (2) highly accurate cloud-edge collaborative inference. First, we show that the inherent high communication costs for transmitting LLM contextual information between the edge and cloud dominate the overall latency, making it inefficient and costly to deploy LLMs using cloud-edge collaboration. Second, we propose several critical techniques to address this challenge, including early-exit mechanism, cloud context manager, and quantization in cloud-edge collaboration to enable not only low-latency standalone edge inference but also efficient and adaptive cloud-edge collaborative inference for LLMs. Third, we perform comprehensive experimental analysis, which demonstrates that CE-CoLLM significantly reduces inference time by up to 13.81% and cloud computation costs by up to 84.55% compared to the popular cloud-based LLM deployment, while maintaining comparable model accuracy. The proposed approach effectively shifts the computational load to the edge, reduces the communication overhead, scales efficiently with multiple edge clients, and provides reliable LLM deployment using cloud-edge collaboration.

The goal of object-centric representation learning is to decompose visual scenes into a structured representation that isolates the entities. Recent successes have shown that object-centric representation learning can be scaled to real-world scenes by utilizing pre-trained self-supervised features. However, so far, object-centric methods have mostly been applied in-distribution, with models trained and evaluated on the same dataset. This is in contrast to the wider trend in machine learning towards general-purpose models directly applicable to unseen data and tasks. Thus, in this work, we study current object-centric methods through the lens of zero-shot generalization by introducing a benchmark comprising eight different synthetic and real-world datasets. We analyze the factors influencing zero-shot performance and find that training on diverse real-world images improves transferability to unseen scenarios. Furthermore, inspired by the success of task-specific fine-tuning in foundation models, we introduce a novel fine-tuning strategy to adapt pre-trained vision encoders for the task of object discovery. We find that the proposed approach results in state-of-the-art performance for unsupervised object discovery, exhibiting strong zero-shot transfer to unseen datasets.

Triangle centrality is introduced for finding important vertices in a graph based on the concentration of triangles surrounding each vertex. It has the distinct feature of allowing a vertex to be central if it is in many triangles or none at all. We show experimentally that triangle centrality is broadly applicable to many different types of networks. Our empirical results demonstrate that 30% of the time triangle centrality identified central vertices that differed with those found by five well-known centrality measures, which suggests novelty without being overly specialized. It is also asymptotically faster to compute on sparse graphs than all but the most trivial of these other measures. We introduce optimal algorithms that compute triangle centrality in O(mbarδ) time and O(m+n) space, where barδle O(m) is the average degeneracy introduced by Burkhardt, Faber, and Harris (2020). In practical applications, barδ is much smaller than m so triangle centrality can be computed in nearly linear time. On a Concurrent Read Exclusive Write (CREW) Parallel Random Access Machine (PRAM), we give a near work-optimal parallel algorithm that takes O(log n) time using O(mm) CREW PRAM processors. In MapReduce, we show it takes four rounds using O(mm) communication bits and is therefore optimal. We also derive a linear algebraic formulation of triangle centrality which can be computed in O(mbarδ) time on sparse graphs.

Graphs or networks are a very convenient way to represent data with lots of interaction. Recently, Machine Learning on Graph data has gained a lot of traction. In particular, vertex classification and missing edge detection have very interesting applications, ranging from drug discovery to recommender systems. To achieve such tasks, tremendous work has been accomplished to learn embedding of nodes and edges into finite-dimension vector spaces. This task is called Graph Representation Learning. However, Graph Representation Learning techniques often display prohibitive time and memory complexities, preventing their use in real-time with business size graphs. In this paper, we address this issue by leveraging a degeneracy property of Graphs - the K-Core Decomposition. We present two techniques taking advantage of this decomposition to reduce the time and memory consumption of walk-based Graph Representation Learning algorithms. We evaluate the performances, expressed in terms of quality of embedding and computational resources, of the proposed techniques on several academic datasets. Our code is available at https://github.com/SBrandeis/kcore-embedding

We propose a minimal path method to simultaneously compute segmentation masks and extract centerlines of tubular structures with line-topology. Minimal path methods are commonly used for the segmentation of tubular structures in a wide variety of applications. Recent methods use features extracted by CNNs, and often outperform methods using hand-tuned features. However, for CNN-based methods, the samples used for training may be generated inappropriately, so that they can be very different from samples encountered during inference. We approach this discrepancy by introducing a novel iterative training scheme, which enables generating better training samples specifically tailored for the minimal path methods without changing existing annotations. In our method, segmentation masks and centerlines are not determined after one another by post-processing, but obtained using the same steps. Our method requires only very few annotated training images. Comparison with seven previous approaches on three public datasets, including satellite images and medical images, shows that our method achieves state-of-the-art results both for segmentation masks and centerlines.

The total variation (TV)-seminorm is considered for piecewise polynomial, globally discontinuous (DG) and continuous (CG) finite element functions on simplicial meshes. A novel, discrete variant (DTV) based on a nodal quadrature formula is defined. DTV has favorable properties, compared to the original TV-seminorm for finite element functions. These include a convenient dual representation in terms of the supremum over the space of Raviart--Thomas finite element functions, subject to a set of simple constraints. It can therefore be shown that a variety of algorithms for classical image reconstruction problems, including TV-L^2 and TV-L^1, can be implemented in low and higher-order finite element spaces with the same efficiency as their counterparts originally developed for images on Cartesian grids.

Computer-aided design (CAD) is vital to modern manufacturing, yet model creation remains labor-intensive and expertise-heavy. To enable non-experts to translate intuitive design intent into manufacturable artifacts, recent large language models-based text-to-CAD efforts focus on command sequences or script-based formats like CadQuery. However, these formats are kernel-dependent and lack universality for manufacturing. In contrast, the Standard for the Exchange of Product Data (STEP, ISO 10303) file is a widely adopted, neutral boundary representation (B-rep) format directly compatible with manufacturing, but its graph-structured, cross-referenced nature poses unique challenges for auto-regressive LLMs. To address this, we curate a dataset of ~40K STEP-caption pairs and introduce novel preprocessing tailored for the graph-structured format of STEP, including a depth-first search-based reserialization that linearizes cross-references while preserving locality and chain-of-thought(CoT)-style structural annotations that guide global coherence. We integrate retrieval-augmented generation to ground predictions in relevant examples for supervised fine-tuning, and refine generation quality through reinforcement learning with a specific Chamfer Distance-based geometric reward. Experiments demonstrate consistent gains of our STEP-LLM in geometric fidelity over the Text2CAD baseline, with improvements arising from multiple stages of our framework: the RAG module substantially enhances completeness and renderability, the DFS-based reserialization strengthens overall accuracy, and the RL further reduces geometric discrepancy. Both metrics and visual comparisons confirm that STEP-LLM generates shapes with higher fidelity than Text2CAD. These results show the feasibility of LLM-driven STEP model generation from natural language, showing its potential to democratize CAD design for manufacturing.

Due to high utility in many applications, from social networks to blockchain to power grids, deep learning on non-Euclidean objects such as graphs and manifolds, coined Geometric Deep Learning (GDL), continues to gain an ever increasing interest. We propose a new L\'evy Flights Graph Convolutional Networks (LFGCN) method for semi-supervised learning, which casts the L\'evy Flights into random walks on graphs and, as a result, allows both to accurately account for the intrinsic graph topology and to substantially improve classification performance, especially for heterogeneous graphs. Furthermore, we propose a new preferential P-DropEdge method based on the Girvan-Newman argument. That is, in contrast to uniform removing of edges as in DropEdge, following the Girvan-Newman algorithm, we detect network periphery structures using information on edge betweenness and then remove edges according to their betweenness centrality. Our experimental results on semi-supervised node classification tasks demonstrate that the LFGCN coupled with P-DropEdge accelerates the training task, increases stability and further improves predictive accuracy of learned graph topology structure. Finally, in our case studies we bring the machinery of LFGCN and other deep networks tools to analysis of power grid networks - the area where the utility of GDL remains untapped.

Structured adaptive mesh refinement (AMR), commonly implemented via quadtrees and octrees, underpins a wide range of applications including databases, computer graphics, physics simulations, and machine learning. However, octrees enforce isotropic refinement in regions of interest, which can be especially inefficient for problems that are intrinsically anisotropic--much resolution is spent where little information is gained. This paper presents omnitrees as an anisotropic generalization of octrees and related data structures. Omnitrees allow to refine only the locally most important dimensions, providing tree structures that are less deep than bintrees and less wide than octrees. As a result, the convergence of the AMR schemes can be increased by up to a factor of the dimensionality d for very anisotropic problems, quickly offsetting their modest increase in storage overhead. We validate this finding on the problem of binary shape representation across 4,166 three-dimensional objects: Omnitrees increase the mean convergence rate by 1.5x, require less storage to achieve equivalent error bounds, and maximize the information density of the stored function faster than octrees. These advantages are projected to be even stronger for higher-dimensional problems. We provide a first validation by introducing a time-dependent rotation to create four-dimensional representations, and discuss the properties of their 4-d octree and omnitree approximations. Overall, omnitree discretizations can make existing AMR approaches more efficient, and open up new possibilities for high-dimensional applications.

Generating 3D shapes at part level is pivotal for downstream applications such as mesh retopology, UV mapping, and 3D printing. However, existing part-based generation methods often lack sufficient controllability and suffer from poor semantically meaningful decomposition. To this end, we introduce X-Part, a controllable generative model designed to decompose a holistic 3D object into semantically meaningful and structurally coherent parts with high geometric fidelity. X-Part exploits the bounding box as prompts for the part generation and injects point-wise semantic features for meaningful decomposition. Furthermore, we design an editable pipeline for interactive part generation. Extensive experimental results show that X-Part achieves state-of-the-art performance in part-level shape generation. This work establishes a new paradigm for creating production-ready, editable, and structurally sound 3D assets. Codes will be released for public research.

Triangle meshes are fundamental to 3D applications, enabling efficient modification and rasterization while maintaining compatibility with standard rendering pipelines. However, current automatic mesh generation methods typically rely on intermediate representations that lack the continuous surface quality inherent to meshes. Converting these representations into meshes produces dense, suboptimal outputs. Although recent autoregressive approaches demonstrate promise in directly modeling mesh vertices and faces, they are constrained by the limitation in face count, scalability, and structural fidelity. To address these challenges, we propose Nautilus, a locality-aware autoencoder for artist-like mesh generation that leverages the local properties of manifold meshes to achieve structural fidelity and efficient representation. Our approach introduces a novel tokenization algorithm that preserves face proximity relationships and compresses sequence length through locally shared vertices and edges, enabling the generation of meshes with an unprecedented scale of up to 5,000 faces. Furthermore, we develop a Dual-stream Point Conditioner that provides multi-scale geometric guidance, ensuring global consistency and local structural fidelity by capturing fine-grained geometric features. Extensive experiments demonstrate that Nautilus significantly outperforms state-of-the-art methods in both fidelity and scalability. The project page is at https://nautilusmeshgen.github.io.

Diffusion-based 3D generation has made remarkable progress in recent years. However, existing 3D generative models often produce overly dense and unstructured meshes, which stand in stark contrast to the compact, structured, and sharply-edged Computer-Aided Design (CAD) models crafted by human designers. To address this gap, we introduce CADDreamer, a novel approach for generating boundary representations (B-rep) of CAD objects from a single image. CADDreamer employs a primitive-aware multi-view diffusion model that captures both local geometric details and high-level structural semantics during the generation process. By encoding primitive semantics into the color domain, the method leverages the strong priors of pre-trained diffusion models to align with well-defined primitives. This enables the inference of multi-view normal maps and semantic maps from a single image, facilitating the reconstruction of a mesh with primitive labels. Furthermore, we introduce geometric optimization techniques and topology-preserving extraction methods to mitigate noise and distortion in the generated primitives. These enhancements result in a complete and seamless B-rep of the CAD model. Experimental results demonstrate that our method effectively recovers high-quality CAD objects from single-view images. Compared to existing 3D generation techniques, the B-rep models produced by CADDreamer are compact in representation, clear in structure, sharp in edges, and watertight in topology.

We introduce featom, an open source code that implements a high-order finite element solver for the radial Schr\"odinger, Dirac, and Kohn-Sham equations. The formulation accommodates various mesh types, such as uniform or exponential, and the convergence can be systematically controlled by increasing the number and/or polynomial order of the finite element basis functions. The Dirac equation is solved using a squared Hamiltonian approach to eliminate spurious states. To address the slow convergence of the kappa=pm1 states due to divergent derivatives at the origin, we incorporate known asymptotic forms into the solutions. We achieve a high level of accuracy (10^{-8} Hartree) for total energies and eigenvalues of heavy atoms such as uranium in both Schr\"odinger and Dirac Kohn-Sham solutions. We provide detailed convergence studies and computational parameters required to attain commonly required accuracies. Finally, we compare our results with known analytic results as well as the results of other methods. In particular, we calculate benchmark results for atomic numbers (Z) from 1 to 92, verifying current benchmarks. We demonstrate significant speedup compared to the state-of-the-art shooting solver dftatom. An efficient, modular Fortran 2008 implementation, is provided under an open source, permissive license, including examples and tests, wherein particular emphasis is placed on the independence (no global variables), reusability, and generality of the individual routines.

In aerodynamics, accurately modeling subsonic compressible flow over airfoils is critical for aircraft design. However, solving the governing nonlinear perturbation velocity potential equation presents computational challenges. Traditional approaches often rely on linearized equations or finite, truncated domains, which introduce non-negligible errors and limit applicability in real-world scenarios. In this study, we propose a novel framework utilizing Physics-Informed Neural Networks (PINNs) to solve the full nonlinear compressible potential equation in an unbounded (infinite) domain. We address the unbounded-domain and convergence challenges inherent in standard PINNs by incorporating a coordinate transformation and embedding physical asymptotic constraints directly into the network architecture. Furthermore, we employ a Multi-Stage PINN (MS-PINN) approach to iteratively minimize residuals, achieving solution accuracy approaching machine precision. We validate this framework by simulating flow over circular and elliptical geometries, comparing our results against traditional finite-domain and linearized solutions. Our findings quantify the noticeable discrepancies introduced by domain truncation and linearization, particularly at higher Mach numbers, and demonstrate that this new framework is a robust, high-fidelity tool for computational fluid dynamics.

Graph foundation models represent a transformative paradigm for learning transferable representations across diverse graph domains. Recent methods leverage large language models to unify graph and text modalities into a shared representation space using contrastive learning. However, systematic evaluations reveal significant performance degradation at structural boundaries where distinct topological patterns converge, with accuracy losses exceeding 20 percentage points. This issue arises from a key limitation: current methods assume all graph structures can be encoded within a single Euclidean space. In reality, tree structures require hyperbolic geometry to preserve hierarchical branching, while cyclic patterns depend on spherical geometry for closure properties. At structural boundaries, nodes experience conflicting geometric constraints that uniform encoding spaces cannot resolve. This raises a crucial challenge: Can alignment frameworks be designed to respect the intrinsic geometric diversity of graph structures? We introduce GraphShaper, a geometry-aware framework that enhances graph encoding through multi-geometric specialization. Our approach employs expert networks tailored to different geometric spaces, dynamically computing fusion weights to adaptively integrate geometric properties based on local structural characteristics. This adaptive fusion preserves structural integrity before alignment with text embeddings. Extensive experiments demonstrate that GraphShaper achieves 9.47\% accuracy improvements on citation networks and 7.63\% on social networks in zero-shot settings.

Edge Intelligence (EI) has been instrumental in delivering real-time, localized services by leveraging the computational capabilities of edge networks. The integration of Large Language Models (LLMs) empowers EI to evolve into the next stage: Edge General Intelligence (EGI), enabling more adaptive and versatile applications that require advanced understanding and reasoning capabilities. However, systematic exploration in this area remains insufficient. This survey delineates the distinctions between EGI and traditional EI, categorizing LLM-empowered EGI into three conceptual systems: centralized, hybrid, and decentralized. For each system, we detail the framework designs and review existing implementations. Furthermore, we evaluate the performance and throughput of various Small Language Models (SLMs) that are more suitable for development on edge devices. This survey provides researchers with a comprehensive vision of EGI, offering insights into its vast potential and establishing a foundation for future advancements in this rapidly evolving field.

This work puts forth a new optimal design formulation for planar elastic membranes. The goal is to minimize the membrane's compliance through choosing the material distribution described by a positive Radon measure. The deformation of the membrane itself is governed by the convexified F\"{o}ppl's model. The uniqueness of this model lies in the convexity of its variational formulation despite the inherent nonlinearity of the strain-displacement relation. It makes it possible to rewrite the optimization problem as a pair of mutually dual convex variational problems. In the primal problem a linear functional is maximized with respect to displacement functions while enforcing that point-wisely the strain lies in an unbounded closed convex set. The dual problem consists in finding equilibrated stresses that are to minimize a convex integral functional of linear growth defined on the space of Radon measures. The pair of problems is analysed: existence and regularity results are provided, together with the system of optimality criteria. To demonstrate the computational potential of the pair, a finite element scheme is developed around it. Upon reformulation to a conic-quadratic & semi-definite programming problem, the method is employed to produce numerical simulations for several load case scenarios.

This paper introduces PDEformer, a neural solver for partial differential equations (PDEs) capable of simultaneously addressing various types of PDEs. We advocate representing the PDE in the form of a computational graph, facilitating the seamless integration of both symbolic and numerical information inherent in a PDE. A graph Transformer and an implicit neural representation (INR) are employed to generate mesh-free predicted solutions. Following pretraining on data exhibiting a certain level of diversity, our model achieves zero-shot accuracies on benchmark datasets that surpass those of adequately trained expert models. Additionally, PDEformer demonstrates promising results in the inverse problem of PDE coefficient recovery.

Machine learning (ML) and deep learning (DL) techniques have gained significant attention as reduced order models (ROMs) to computationally expensive structural analysis methods, such as finite element analysis (FEA). Graph neural network (GNN) is a particular type of neural network which processes data that can be represented as graphs. This allows for efficient representation of complex geometries that can change during conceptual design of a structure or a product. In this study, we propose a novel graph embedding technique for efficient representation of 3D stiffened panels by considering separate plate domains as vertices. This approach is considered using Graph Sampling and Aggregation (GraphSAGE) to predict stress distributions in stiffened panels with varying geometries. A comparison between a finite-element-vertex graph representation is conducted to demonstrate the effectiveness of the proposed approach. A comprehensive parametric study is performed to examine the effect of structural geometry on the prediction performance. Our results demonstrate the immense potential of graph neural networks with the proposed graph embedding method as robust reduced-order models for 3D structures.

Real-time multimodal inference on resource-constrained edge devices is essential for applications such as autonomous driving, human-computer interaction, and mobile health. However, prior work often overlooks the tight coupling between sensing dynamics and model execution, as well as the complex inter-modality dependencies. In this paper, we propose MMEdge, an new on-device multi-modal inference framework based on pipelined sensing and encoding. Instead of waiting for complete sensor inputs, MMEdge decomposes the entire inference process into a sequence of fine-grained sensing and encoding units, allowing computation to proceed incrementally as data arrive. MMEdge also introduces a lightweight but effective temporal aggregation module that captures rich temporal dynamics across different pipelined units to maintain accuracy performance. Such pipelined design also opens up opportunities for fine-grained cross-modal optimization and early decision-making during inference. To further enhance system performance under resource variability and input data complexity, MMEdge incorporates an adaptive multimodal configuration optimizer that dynamically selects optimal sensing and model configurations for each modality under latency constraints, and a cross-modal speculative skipping mechanism that bypasses future units of slower modalities when early predictions reach sufficient confidence. We evaluate MMEdge using two public multimodal datasets and deploy it on a real-world unmanned aerial vehicle (UAV)-based multimodal testbed. The results show that MMEdge significantly reduces end-to-end latency while maintaining high task accuracy across various system and data dynamics.

Constructing an adaptive hexahedral tessellation to fit an input triangle boundary is a key challenge in grid-based methods. The conventional method first removes outside elements (RO) and then projects the axis-aligned boundary onto the input triangle boundary, which has no guarantee on improving the initial Intersection over Union (IoU) and Hausdorff distance ratio (HR, w.r.t bounding box diagonal). The proposed MCHex approach replaces RO with a Marching Cubes method MCHex. Given the same computational budget (benchmarked using an identical precomputed Signed Distance Field, which dominates the runtime), MCHex provides better boundary approximation (higher IoU and lower HR) while guaranteeing a lower, yet still positive, minimum scaled Jacobian (>0 vs. RO's >0.48).

This paper proposes a Deep Learning based edge detector, which is inspired on both HED (Holistically-Nested Edge Detection) and Xception networks. The proposed approach generates thin edge-maps that are plausible for human eyes; it can be used in any edge detection task without previous training or fine tuning process. As a second contribution, a large dataset with carefully annotated edges has been generated. This dataset has been used for training the proposed approach as well the state-of-the-art algorithms for comparisons. Quantitative and qualitative evaluations have been performed on different benchmarks showing improvements with the proposed method when F-measure of ODS and OIS are considered.

Triggered by limitations of graph-based deep learning methods in terms of computational expressivity and model flexibility, recent years have seen a surge of interest in computational models that operate on higher-order topological domains such as hypergraphs and simplicial complexes. While the increased expressivity of these models can indeed lead to a better classification performance and a more faithful representation of the underlying system, the computational cost of these higher-order models can increase dramatically. To this end, we here explore a simplicial complex neural network learning architecture based on random walks and fast 1D convolutions (SCRaWl), in which we can adjust the increase in computational cost by varying the length and number of random walks considered while accounting for higher-order relationships. Importantly, due to the random walk-based design, the expressivity of the proposed architecture is provably incomparable to that of existing message-passing simplicial neural networks. We empirically evaluate SCRaWl on real-world datasets and show that it outperforms other simplicial neural networks.

The structure learning problem consists of fitting data generated by a Directed Acyclic Graph (DAG) to correctly reconstruct its arcs. In this context, differentiable approaches constrain or regularize the optimization problem using a continuous relaxation of the acyclicity property. The computational cost of evaluating graph acyclicity is cubic on the number of nodes and significantly affects scalability. In this paper we introduce COSMO, a constraint-free continuous optimization scheme for acyclic structure learning. At the core of our method, we define a differentiable approximation of an orientation matrix parameterized by a single priority vector. Differently from previous work, our parameterization fits a smooth orientation matrix and the resulting acyclic adjacency matrix without evaluating acyclicity at any step. Despite the absence of explicit constraints, we prove that COSMO always converges to an acyclic solution. In addition to being asymptotically faster, our empirical analysis highlights how COSMO performance on graph reconstruction compares favorably with competing structure learning methods.

Slot attention is a powerful method for object-centric modeling in images and videos. However, its set-equivariance limits its ability to handle videos with a dynamic number of objects because it cannot break ties. To overcome this limitation, we first establish a connection between slot attention and optimal transport. Based on this new perspective we propose MESH (Minimize Entropy of Sinkhorn): a cross-attention module that combines the tiebreaking properties of unregularized optimal transport with the speed of regularized optimal transport. We evaluate slot attention using MESH on multiple object-centric learning benchmarks and find significant improvements over slot attention in every setting.

Neural rendering techniques have made substantial progress in generating photo-realistic 3D scenes. The latest 3D Gaussian Splatting technique has achieved high quality novel view synthesis as well as fast rendering speed. However, 3D Gaussians lack proficiency in defining accurate 3D geometric structures despite their explicit primitive representations. This is due to the fact that Gaussian's attributes are primarily tailored and fine-tuned for rendering diverse 2D images by their anisotropic nature. To pave the way for efficient 3D reconstruction, we present Spherical Gaussians, a simple and effective representation for 3D geometric boundaries, from which we can directly reconstruct 3D feature curves from a set of calibrated multi-view images. Spherical Gaussians is optimized from grid initialization with a view-based rendering loss, where a 2D edge map is rendered at a specific view and then compared to the ground-truth edge map extracted from the corresponding image, without the need for any 3D guidance or supervision. Given Spherical Gaussians serve as intermedia for the robust edge representation, we further introduce a novel optimization-based algorithm called SGCR to directly extract accurate parametric curves from aligned Spherical Gaussians. We demonstrate that SGCR outperforms existing state-of-the-art methods in 3D edge reconstruction while enjoying great efficiency.

The aerodynamic coefficients of aircrafts are significantly impacted by its geometry, especially when the angle of attack (AoA) is large. In the field of aerodynamics, traditional polynomial-based parameterization uses as few parameters as possible to describe the geometry of an airfoil. However, because the 3D geometry of a wing is more complicated than the 2D airfoil, polynomial-based parameterizations have difficulty in accurately representing the entire shape of a wing in 3D space. Existing deep learning-based methods can extract massive latent neural representations for the shape of 2D airfoils or 2D slices of wings. Recent studies highlight that directly taking geometric features as inputs to the neural networks can improve the accuracy of predicted aerodynamic coefficients. Motivated by geometry theory, we propose to incorporate Riemannian geometric features for learning Coefficient of Pressure (CP) distributions on wing surfaces. Our method calculates geometric features (Riemannian metric, connection, and curvature) and further inputs the geometric features, coordinates and flight conditions into a deep learning model to predict the CP distribution. Experimental results show that our method, compared to state-of-the-art Deep Attention Network (DAN), reduces the predicted mean square error (MSE) of CP by an average of 8.41% for the DLR-F11 aircraft test set.

The non-convexity of the artificial neural network (ANN) training landscape brings inherent optimization difficulties. While the traditional back-propagation stochastic gradient descent (SGD) algorithm and its variants are effective in certain cases, they can become stuck at spurious local minima and are sensitive to initializations and hyperparameters. Recent work has shown that the training of an ANN with ReLU activations can be reformulated as a convex program, bringing hope to globally optimizing interpretable ANNs. However, naively solving the convex training formulation has an exponential complexity, and even an approximation heuristic requires cubic time. In this work, we characterize the quality of this approximation and develop two efficient algorithms that train ANNs with global convergence guarantees. The first algorithm is based on the alternating direction method of multiplier (ADMM). It solves both the exact convex formulation and the approximate counterpart. Linear global convergence is achieved, and the initial several iterations often yield a solution with high prediction accuracy. When solving the approximate formulation, the per-iteration time complexity is quadratic. The second algorithm, based on the "sampled convex programs" theory, is simpler to implement. It solves unconstrained convex formulations and converges to an approximately globally optimal classifier. The non-convexity of the ANN training landscape exacerbates when adversarial training is considered. We apply the robust convex optimization theory to convex training and develop convex formulations that train ANNs robust to adversarial inputs. Our analysis explicitly focuses on one-hidden-layer fully connected ANNs, but can extend to more sophisticated architectures.

We look at the eigenvalues of the Hessian of a loss function before and after training. The eigenvalue distribution is seen to be composed of two parts, the bulk which is concentrated around zero, and the edges which are scattered away from zero. We present empirical evidence for the bulk indicating how over-parametrized the system is, and for the edges that depend on the input data.

We introduce CLR-Wire, a novel framework for 3D curve-based wireframe generation that integrates geometry and topology into a unified Continuous Latent Representation. Unlike conventional methods that decouple vertices, edges, and faces, CLR-Wire encodes curves as Neural Parametric Curves along with their topological connectivity into a continuous and fixed-length latent space using an attention-driven variational autoencoder (VAE). This unified approach facilitates joint learning and generation of both geometry and topology. To generate wireframes, we employ a flow matching model to progressively map Gaussian noise to these latents, which are subsequently decoded into complete 3D wireframes. Our method provides fine-grained modeling of complex shapes and irregular topologies, and supports both unconditional generation and generation conditioned on point cloud or image inputs. Experimental results demonstrate that, compared with state-of-the-art generative approaches, our method achieves substantial improvements in accuracy, novelty, and diversity, offering an efficient and comprehensive solution for CAD design, geometric reconstruction, and 3D content creation.

When learning simulations for modeling physical phenomena in industrial designs, geometrical variabilities are of prime interest. While classical regression techniques prove effective for parameterized geometries, practical scenarios often involve the absence of shape parametrization during the inference stage, leaving us with only mesh discretizations as available data. Learning simulations from such mesh-based representations poses significant challenges, with recent advances relying heavily on deep graph neural networks to overcome the limitations of conventional machine learning approaches. Despite their promising results, graph neural networks exhibit certain drawbacks, including their dependency on extensive datasets and limitations in providing built-in predictive uncertainties or handling large meshes. In this work, we propose a machine learning method that do not rely on graph neural networks. Complex geometrical shapes and variations with fixed topology are dealt with using well-known mesh morphing onto a common support, combined with classical dimensionality reduction techniques and Gaussian processes. The proposed methodology can easily deal with large meshes without the need for explicit shape parameterization and provides crucial predictive uncertainties, which are essential for informed decision-making. In the considered numerical experiments, the proposed method is competitive with respect to existing graph neural networks, regarding training efficiency and accuracy of the predictions.

Unsupervised object-centric learning methods allow the partitioning of scenes into entities without additional localization information and are excellent candidates for reducing the annotation burden of multiple-object tracking (MOT) pipelines. Unfortunately, they lack two key properties: objects are often split into parts and are not consistently tracked over time. In fact, state-of-the-art models achieve pixel-level accuracy and temporal consistency by relying on supervised object detection with additional ID labels for the association through time. This paper proposes a video object-centric model for MOT. It consists of an index-merge module that adapts the object-centric slots into detection outputs and an object memory module that builds complete object prototypes to handle occlusions. Benefited from object-centric learning, we only require sparse detection labels (0%-6.25%) for object localization and feature binding. Relying on our self-supervised Expectation-Maximization-inspired loss for object association, our approach requires no ID labels. Our experiments significantly narrow the gap between the existing object-centric model and the fully supervised state-of-the-art and outperform several unsupervised trackers.

We consider a family of linear systems A_mu alpha=C with system matrix A_mu depending on a parameter mu and for simplicity parameter-independent right-hand side C. These linear systems typically result from the finite-dimensional approximation of a parameter-dependent boundary-value problem. We derive a procedure based on the Empirical Interpolation Method to obtain a separated representation of the system matrix in the form A_muapproxsum_{m}beta_m(mu)A_{mu_m} for some selected values of the parameter. Such a separated representation is in particular useful in the Reduced Basis Method. The procedure is called nonintrusive since it only requires to access the matrices A_{mu_m}. As such, it offers a crucial advantage over existing approaches that instead derive separated representations requiring to enter the code at the level of assembly. Numerical examples illustrate the performance of our new procedure on a simple one-dimensional boundary-value problem and on three-dimensional acoustic scattering problems solved by a boundary element method.

While generative artificial intelligence has advanced significantly across text, image, audio, and video domains, 3D generation remains comparatively underdeveloped due to fundamental challenges such as data scarcity, algorithmic limitations, and ecosystem fragmentation. To this end, we present Step1X-3D, an open framework addressing these challenges through: (1) a rigorous data curation pipeline processing >5M assets to create a 2M high-quality dataset with standardized geometric and textural properties; (2) a two-stage 3D-native architecture combining a hybrid VAE-DiT geometry generator with an diffusion-based texture synthesis module; and (3) the full open-source release of models, training code, and adaptation modules. For geometry generation, the hybrid VAE-DiT component produces TSDF representations by employing perceiver-based latent encoding with sharp edge sampling for detail preservation. The diffusion-based texture synthesis module then ensures cross-view consistency through geometric conditioning and latent-space synchronization. Benchmark results demonstrate state-of-the-art performance that exceeds existing open-source methods, while also achieving competitive quality with proprietary solutions. Notably, the framework uniquely bridges the 2D and 3D generation paradigms by supporting direct transfer of 2D control techniques~(e.g., LoRA) to 3D synthesis. By simultaneously advancing data quality, algorithmic fidelity, and reproducibility, Step1X-3D aims to establish new standards for open research in controllable 3D asset generation.

Constructing computer-aided design (CAD) models is labor-intensive but essential for engineering and manufacturing. Recent advances in Large Language Models (LLMs) have inspired the LLM-based CAD generation by representing CAD as command sequences. But these methods struggle in practical scenarios because command sequence representation does not support entity selection (e.g. faces or edges), limiting its ability to support complex editing operations such as chamfer or fillet. Further, the discretization of a continuous variable during sketch and extrude operations may result in topological errors. To address these limitations, we present Pointer-CAD, a novel LLM-based CAD generation framework that leverages a pointer-based command sequence representation to explicitly incorporate the geometric information of B-rep models into sequential modeling. In particular, Pointer-CAD decomposes CAD model generation into steps, conditioning the generation of each subsequent step on both the textual description and the B-rep generated from previous steps. Whenever an operation requires the selection of a specific geometric entity, the LLM predicts a Pointer that selects the most feature-consistent candidate from the available set. Such a selection operation also reduces the quantization error in the command sequence-based representation. To support the training of Pointer-CAD, we develop a data annotation pipeline that produces expert-level natural language descriptions and apply it to build a dataset of approximately 575K CAD models. Extensive experimental results demonstrate that Pointer-CAD effectively supports the generation of complex geometric structures and reduces segmentation error to an extremely low level, achieving a significant improvement over prior command sequence methods, thereby significantly mitigating the topological inaccuracies introduced by quantization error.

Object-centric learning (OCL) seeks to learn representations that only encode an object, isolated from other objects or background cues in a scene. This approach underpins various aims, including out-of-distribution (OOD) generalization, sample-efficient composition, and modeling of structured environments. Most research has focused on developing unsupervised mechanisms that separate objects into discrete slots in the representation space, evaluated using unsupervised object discovery. However, with recent sample-efficient segmentation models, we can separate objects in the pixel space and encode them independently. This achieves remarkable zero-shot performance on OOD object discovery benchmarks, is scalable to foundation models, and can handle a variable number of slots out-of-the-box. Hence, the goal of OCL methods to obtain object-centric representations has been largely achieved. Despite this progress, a key question remains: How does the ability to separate objects within a scene contribute to broader OCL objectives, such as OOD generalization? We address this by investigating the OOD generalization challenge caused by spurious background cues through the lens of OCL. We propose a novel, training-free probe called Object-Centric Classification with Applied Masks (OCCAM), demonstrating that segmentation-based encoding of individual objects significantly outperforms slot-based OCL methods. However, challenges in real-world applications remain. We provide the toolbox for the OCL community to use scalable object-centric representations, and focus on practical applications and fundamental questions, such as understanding object perception in human cognition. Our code is available https://github.com/AlexanderRubinstein/OCCAM{here}.

While complex simulations of physical systems have been widely used in engineering and scientific computing, lowering their often prohibitive computational requirements has only recently been tackled by deep learning approaches. In this paper, we present GraphSplineNets, a novel deep-learning method to speed up the forecasting of physical systems by reducing the grid size and number of iteration steps of deep surrogate models. Our method uses two differentiable orthogonal spline collocation methods to efficiently predict response at any location in time and space. Additionally, we introduce an adaptive collocation strategy in space to prioritize sampling from the most important regions. GraphSplineNets improve the accuracy-speedup tradeoff in forecasting various dynamical systems with increasing complexity, including the heat equation, damped wave propagation, Navier-Stokes equations, and real-world ocean currents in both regular and irregular domains.

While scaling laws have been continuously validated in large language models (LLMs) with increasing model parameters, the inherent tension between the inference demands of LLMs and the limited resources of edge devices poses a critical challenge to the development of edge intelligence. Recently, numerous small language models have emerged, aiming to distill the capabilities of LLMs into smaller footprints. However, these models often retain the fundamental architectural principles of their larger counterparts, still imposing considerable strain on the storage and bandwidth capacities of edge devices. In this paper, we introduce the PLM, a Peripheral Language Model, developed through a co-design process that jointly optimizes model architecture and edge system constraints. The PLM utilizes a Multi-head Latent Attention mechanism and employs the squared ReLU activation function to encourage sparsity, thereby reducing peak memory footprint during inference. During training, we collect and reorganize open-source datasets, implement a multi-phase training strategy, and empirically investigate the Warmup-Stable-Decay-Constant (WSDC) learning rate scheduler. Additionally, we incorporate Reinforcement Learning from Human Feedback (RLHF) by adopting the ARIES preference learning approach. Following a two-phase SFT process, this method yields performance gains of 2% in general tasks, 9% in the GSM8K task, and 11% in coding tasks. In addition to its novel architecture, evaluation results demonstrate that PLM outperforms existing small language models trained on publicly available data while maintaining the lowest number of activated parameters. Furthermore, deployment across various edge devices, including consumer-grade GPUs, mobile phones, and Raspberry Pis, validates PLM's suitability for peripheral applications. The PLM series models are publicly available at https://github.com/plm-team/PLM.

We revisit the geometric theory of defects. In the differential-geometric models of defects that have been adopted since the 1950s, dislocations have been associated with torsion, disclinations with the full curvature, and point defects with the first kind trace of non-metricity. The mainstream formulation exhibits several conceptual and technical shortcomings, most notably a hierarchy inconsistency, the non-exictence of a genuine metric formulation, and the potential emergence of Ostrogradsky-type instabilities. These issues have motivated us to develop a new framework, namely a generalized teleparallel geometric theory of defects. In our model, dislocations are identified with the trace of torsion, disclinations with the second kind trace of the non-metricity, and point defects with the first kind trace of the non-metricity. In addition, we retain the scalar part torsion as a free parameter for describing some possible unknown degrees of freedom in the theory of defects. The proposed geometric theory of defects is free from all of the aforementioned drawbacks and is therefore worthy of further investigation. To ensure the coherence and completeness of the discussion, we begin our analysis with elastic deformations, then summarize the existing metric-affine geometric theory of defects, and finally proceed to our original contribution, namely the new theory introduced here. We formulate the entire theory in Eulerian coordinates. Naturally, all results can be reformulated in Lagrangian coordinates as well. All analyses and formulae are expressed in the language of exterior algebra and are carried out in coordinate-independent orthonormal frames.

With the growing volume of CT examinations, there is an increasing demand for automated tools such as organ segmentation, abnormality detection, and report generation to support radiologists in managing their clinical workload. Multi-label classification of 3D Chest CT scans remains a critical yet challenging problem due to the complex spatial relationships inherent in volumetric data and the wide variability of abnormalities. Existing methods based on 3D convolutional neural networks struggle to capture long-range dependencies, while Vision Transformers often require extensive pre-training on large-scale, domain-specific datasets to perform competitively. In this work of academic research, we propose a 2.5D alternative by introducing a new graph-based framework that represents 3D CT volumes as structured graphs, where axial slice triplets serve as nodes processed through spectral graph convolution, enabling the model to reason over inter-slice dependencies while maintaining complexity compatible with clinical deployment. Our method, trained and evaluated on 3 datasets from independent institutions, achieves strong cross-dataset generalization, and shows competitive performance compared to state-of-the-art visual encoders. We further conduct comprehensive ablation studies to evaluate the impact of various aggregation strategies, edge-weighting schemes, and graph connectivity patterns. Additionally, we demonstrate the broader applicability of our approach through transfer experiments on automated radiology report generation and abdominal CT data.

We study the properties of common loss surfaces through their Hessian matrix. In particular, in the context of deep learning, we empirically show that the spectrum of the Hessian is composed of two parts: (1) the bulk centered near zero, (2) and outliers away from the bulk. We present numerical evidence and mathematical justifications to the following conjectures laid out by Sagun et al. (2016): Fixing data, increasing the number of parameters merely scales the bulk of the spectrum; fixing the dimension and changing the data (for instance adding more clusters or making the data less separable) only affects the outliers. We believe that our observations have striking implications for non-convex optimization in high dimensions. First, the flatness of such landscapes (which can be measured by the singularity of the Hessian) implies that classical notions of basins of attraction may be quite misleading. And that the discussion of wide/narrow basins may be in need of a new perspective around over-parametrization and redundancy that are able to create large connected components at the bottom of the landscape. Second, the dependence of small number of large eigenvalues to the data distribution can be linked to the spectrum of the covariance matrix of gradients of model outputs. With this in mind, we may reevaluate the connections within the data-architecture-algorithm framework of a model, hoping that it would shed light into the geometry of high-dimensional and non-convex spaces in modern applications. In particular, we present a case that links the two observations: small and large batch gradient descent appear to converge to different basins of attraction but we show that they are in fact connected through their flat region and so belong to the same basin.

This paper presents a novel end-to-end framework for closed-form computation and visualization of critical point uncertainty in 2D uncertain scalar fields. Critical points are fundamental topological descriptors used in the visualization and analysis of scalar fields. The uncertainty inherent in data (e.g., observational and experimental data, approximations in simulations, and compression), however, creates uncertainty regarding critical point positions. Uncertainty in critical point positions, therefore, cannot be ignored, given their impact on downstream data analysis tasks. In this work, we study uncertainty in critical points as a function of uncertainty in data modeled with probability distributions. Although Monte Carlo (MC) sampling techniques have been used in prior studies to quantify critical point uncertainty, they are often expensive and are infrequently used in production-quality visualization software. We, therefore, propose a new end-to-end framework to address these challenges that comprises a threefold contribution. First, we derive the critical point uncertainty in closed form, which is more accurate and efficient than the conventional MC sampling methods. Specifically, we provide the closed-form and semianalytical (a mix of closed-form and MC methods) solutions for parametric (e.g., uniform, Epanechnikov) and nonparametric models (e.g., histograms) with finite support. Second, we accelerate critical point probability computations using a parallel implementation with the VTK-m library, which is platform portable. Finally, we demonstrate the integration of our implementation with the ParaView software system to demonstrate near-real-time results for real datasets.

Sparse matrices, more specifically SpGEMM kernels, are commonly found in a wide range of applications, spanning graph-based path-finding to machine learning algorithms (e.g., neural networks). A particular challenge in implementing SpGEMM kernels has been the pressure placed on DRAM memory. One approach to tackle this problem is to use an inner product method for the SpGEMM kernel implementation. While the inner product produces fewer intermediate results, it can end up saturating the memory bandwidth, given the high number of redundant fetches of the input matrix elements. Using an outer product-based SpGEMM kernel can reduce redundant fetches, but at the cost of increased overhead due to extra computation and memory accesses for producing/managing partial products. In this thesis, we introduce a novel SpGEMM kernel implementation based on the row-wise product approach. We leverage atomic instructions to merge intermediate partial products as they are generated. The use of atomic instructions eliminates the need to create partial product matrices. To evaluate our row-wise product approach, we map an optimized SpGEMM kernel to a custom accelerator designed to accelerate graph-based applications. The targeted accelerator is an experimental system named PIUMA, being developed by Intel. PIUMA provides several attractive features, including fast context switching, user-configurable caches, globally addressable memory, non-coherent caches, and asynchronous pipelines. We tailor our SpGEMM kernel to exploit many of the features of the PIUMA fabric. This thesis compares our SpGEMM implementation against prior solutions, all mapped to the PIUMA framework. We briefly describe some of the PIUMA architecture features and then delve into the details of our optimized SpGEMM kernel. Our SpGEMM kernel can achieve 9.4x speedup as compared to competing approaches.

Developing deep learning models that effectively learn object-centric representations, akin to human cognition, remains a challenging task. Existing approaches facilitate object discovery by representing objects as fixed-size vectors, called ``slots'' or ``object files''. While these approaches have shown promise in certain scenarios, they still exhibit certain limitations. First, they rely on architectural priors which can be unreliable and usually require meticulous engineering to identify the correct objects. Second, there has been a notable gap in investigating the practical utility of these representations in downstream tasks. To address the first limitation, we introduce a method that explicitly optimizes the constraint that each object in a scene should be associated with a distinct slot. We formalize this constraint by introducing consistency objectives which are cyclic in nature. By integrating these consistency objectives into various existing slot-based object-centric methods, we showcase substantial improvements in object-discovery performance. These enhancements consistently hold true across both synthetic and real-world scenes, underscoring the effectiveness and adaptability of the proposed approach. To tackle the second limitation, we apply the learned object-centric representations from the proposed method to two downstream reinforcement learning tasks, demonstrating considerable performance enhancements compared to conventional slot-based and monolithic representation learning methods. Our results suggest that the proposed approach not only improves object discovery, but also provides richer features for downstream tasks.

This work proposes a novel representation of injective deformations of 3D space, which overcomes existing limitations of injective methods: inaccuracy, lack of robustness, and incompatibility with general learning and optimization frameworks. The core idea is to reduce the problem to a deep composition of multiple 2D mesh-based piecewise-linear maps. Namely, we build differentiable layers that produce mesh deformations through Tutte's embedding (guaranteed to be injective in 2D), and compose these layers over different planes to create complex 3D injective deformations of the 3D volume. We show our method provides the ability to efficiently and accurately optimize and learn complex deformations, outperforming other injective approaches. As a main application, we produce complex and artifact-free NeRF and SDF deformations.

We formulate a hierarchical rectified flow to model data distributions. It hierarchically couples multiple ordinary differential equations (ODEs) and defines a time-differentiable stochastic process that generates a data distribution from a known source distribution. Each ODE resembles the ODE that is solved in a classic rectified flow, but differs in its domain, i.e., location, velocity, acceleration, etc. Unlike the classic rectified flow formulation, which formulates a single ODE in the location domain and only captures the expected velocity field (sufficient to capture a multi-modal data distribution), the hierarchical rectified flow formulation models the multi-modal random velocity field, acceleration field, etc., in their entirety. This more faithful modeling of the random velocity field enables integration paths to intersect when the underlying ODE is solved during data generation. Intersecting paths in turn lead to integration trajectories that are more straight than those obtained in the classic rectified flow formulation, where integration paths cannot intersect. This leads to modeling of data distributions with fewer neural function evaluations. We empirically verify this on synthetic 1D and 2D data as well as MNIST, CIFAR-10, and ImageNet-32 data. Our code is available at: https://riccizz.github.io/HRF/.

Scaling has been critical in improving model performance and generalization in machine learning. It involves how a model's performance changes with increases in model size or input data, as well as how efficiently computational resources are utilized to support this growth. Despite successes in other areas, the study of scaling in Neural Network Interatomic Potentials (NNIPs) remains limited. NNIPs act as surrogate models for ab initio quantum mechanical calculations. The dominant paradigm here is to incorporate many physical domain constraints into the model, such as rotational equivariance. We contend that these complex constraints inhibit the scaling ability of NNIPs, and are likely to lead to performance plateaus in the long run. In this work, we take an alternative approach and start by systematically studying NNIP scaling strategies. Our findings indicate that scaling the model through attention mechanisms is efficient and improves model expressivity. These insights motivate us to develop an NNIP architecture designed for scalability: the Efficiently Scaled Attention Interatomic Potential (EScAIP). EScAIP leverages a multi-head self-attention formulation within graph neural networks, applying attention at the neighbor-level representations. Implemented with highly-optimized attention GPU kernels, EScAIP achieves substantial gains in efficiency--at least 10x faster inference, 5x less memory usage--compared to existing NNIPs. EScAIP also achieves state-of-the-art performance on a wide range of datasets including catalysts (OC20 and OC22), molecules (SPICE), and materials (MPTrj). We emphasize that our approach should be thought of as a philosophy rather than a specific model, representing a proof-of-concept for developing general-purpose NNIPs that achieve better expressivity through scaling, and continue to scale efficiently with increased computational resources and training data.

Object-centric (OC) representations, which represent the state of a visual scene by modeling it as a composition of objects, have the potential to be used in various downstream tasks to achieve systematic compositional generalization and facilitate reasoning. However, these claims have not been thoroughly analyzed yet. Recently, foundation models have demonstrated unparalleled capabilities across diverse domains from language to computer vision, marking them as a potential cornerstone of future research for a multitude of computational tasks. In this paper, we conduct an extensive empirical study on representation learning for downstream Visual Question Answering (VQA), which requires an accurate compositional understanding of the scene. We thoroughly investigate the benefits and trade-offs of OC models and alternative approaches including large pre-trained foundation models on both synthetic and real-world data, and demonstrate a viable way to achieve the best of both worlds. The extensiveness of our study, encompassing over 600 downstream VQA models and 15 different types of upstream representations, also provides several additional insights that we believe will be of interest to the community at large.

This note describes the development of an exact solver for Minimal Directed Feedback Vertex Set as part of the PACE 2022 competition. The solver is powered largely by aggressively trying to reduce the DFVS problem to a Minimal Cover problem, and applying reduction rules adapted from Vertex Cover literature. The resulting problem is solved as an Integer Linear Program (ILP) using SCIP. The resulting solver performed the second-best in the competition, although a bug at submission time disqualified it. As an additional note, we describe a new vertex cover reduction generalizing the Desk reduction rule.

Diffusion models have made significant contributions to computer vision, sparking a growing interest in the community recently regarding the application of them to graph generation. Existing discrete graph diffusion models exhibit heightened computational complexity and diminished training efficiency. A preferable and natural way is to directly diffuse the graph within the latent space. However, due to the non-Euclidean structure of graphs is not isotropic in the latent space, the existing latent diffusion models effectively make it difficult to capture and preserve the topological information of graphs. To address the above challenges, we propose a novel geometrically latent diffusion framework HypDiff. Specifically, we first establish a geometrically latent space with interpretability measures based on hyperbolic geometry, to define anisotropic latent diffusion processes for graphs. Then, we propose a geometrically latent diffusion process that is constrained by both radial and angular geometric properties, thereby ensuring the preservation of the original topological properties in the generative graphs. Extensive experimental results demonstrate the superior effectiveness of HypDiff for graph generation with various topologies.

Mesh generation has become a critical topic in recent years, forming the foundation of all 3D objects used across various applications, such as virtual reality, gaming, and 3D printing. With advancements in computational resources and machine learning, neural networks have emerged as powerful tools for generating high-quality 3D object representations, enabling accurate scene and object reconstructions. Despite these advancements, many methods produce meshes that lack realism or exhibit geometric and textural flaws, necessitating additional processing to improve their quality. This research introduces a convex optimization programming called disciplined convex programming to enhance existing meshes by refining their texture and geometry with a conic solver. By focusing on a sparse set of point clouds from both the original and target meshes, this method demonstrates significant improvements in mesh quality with minimal data requirements. To evaluate the approach, the classical dolphin mesh dataset from Facebook AI was used as a case study, with optimization performed using the CVXPY library. The results reveal promising potential for streamlined and effective mesh refinement.

We present a high-performance system for automatic differentiation (AD) of functions defined on triangle meshes that exploits the inherent sparsity and locality of mesh-based energy functions to achieve fast gradient and Hessian computation on the GPU. Our system is designed around per-element forward-mode differentiation, enabling all local computations to remain in GPU registers or shared memory. Unlike reverse-mode approaches that construct and traverse global computation graphs, our method performs differentiation on the fly, minimizing memory traffic and avoiding global synchronization. Our programming model allows users to define local energy terms while the system handles parallel evaluation, derivative computation, and sparse Hessian assembly. We benchmark our system on a range of applications--cloth simulation, surface parameterization, mesh smoothing, and spherical manifold optimization. We achieve a geometric mean speedup of 6.2x over optimized PyTorch implementations for second-order derivatives, and 2.76x speedup for Hessian-vector products. For first-order derivatives, our system is 6.38x, 2.89x, and 1.98x faster than Warp, JAX, and Dr.JIT, respectively, while remaining on par with hand-written derivatives.