Daily Papers

Recent advancements in Large Vision-Language Models built upon Large Language Models have established aligning visual features with LLM representations as the dominant paradigm. However, inherited LLM architectural designs introduce suboptimal characteristics for multimodal processing. First, LVLMs exhibit a bimodal distribution in attention allocation, leading to the progressive neglect of middle visual content as context expands. Second, conventional positional encoding schemes fail to preserve vital 2D structural relationships when processing dynamic high-resolution images. To address these limitations, we propose CoMemo - a dual-path architecture that combines a Context image path with an image Memory path for visual processing, effectively alleviating visual information neglect. Additionally, we introduce RoPE-DHR, a novel positional encoding mechanism that employs thumbnail-based positional aggregation to maintain 2D spatial awareness while mitigating remote decay in extended sequences. Evaluations across seven benchmarks,including long-context comprehension, multi-image reasoning, and visual question answering, demonstrate CoMemo's superior performance compared to conventional LVLM architectures. Project page is available at https://lalbj.github.io/projects/CoMemo/.

Adapting large-scale Vision-Language Models (VLMs) like CLIP to downstream tasks often suffers from a "one-size-fits-all" architectural approach, where visual and textual tokens are processed uniformly by wide, generic adapters. We argue that this homogeneity ignores the distinct structural nature of the modalities -- spatial locality in images versus semantic density in text. To address this, we propose HeBA (Heterogeneous Bottleneck Adapter), a unified architectural framework that introduces modality-specific structural inductive biases. HeBA departs from conventional designs through three key architectural innovations: (1) Heterogeneity: It processes visual tokens via 2D depthwise-separable convolutions to preserve spatial correlations, while distinctively processing text tokens via dense linear projections to capture semantic relationships; (2) Bottleneck Regularization: Unlike standard expanding adapters, HeBA employs a compression bottleneck (D -> D/4) that explicitly forces the model to learn compact, robust features and acts as a structural regularizer; and (3) Active Gradient Initialization: We challenge the restrictive zero-initialization paradigm, utilizing a Kaiming initialization strategy that ensures sufficient initial gradient flow to accelerate convergence without compromising the frozen backbone's pre-trained knowledge. Extensive experiments demonstrate that HeBA's architecturally specialized design achieves superior stability and accuracy, establishing a new state-of-the-art on 11 few-shot benchmarks. Code is available at https://github.com/Jahid12012021/VLM-HeBA.

Tables are ubiquitous across various domains for concisely representing structured information. Empowering large language models (LLMs) to reason over tabular data represents an actively explored direction. However, since typical LLMs only support one-dimensional~(1D) inputs, existing methods often flatten the two-dimensional~(2D) table structure into a sequence of tokens, which can severely disrupt the spatial relationships and result in an inevitable loss of vital contextual information. In this paper, we first empirically demonstrate the detrimental impact of such flattening operations on the performance of LLMs in capturing the spatial information of tables through two elaborate proxy tasks. Subsequently, we introduce a simple yet effective positional encoding method, termed ``2D-TPE'' (Two-Dimensional Table Positional Encoding), to address this challenge. 2D-TPE enables each attention head to dynamically select a permutation order of tokens within the context for attending to them, where each permutation represents a distinct traversal mode for the table, such as column-wise or row-wise traversal. 2D-TPE effectively mitigates the risk of losing essential spatial information while preserving computational efficiency, thus better preserving the table structure. Extensive experiments across five benchmarks demonstrate that 2D-TPE outperforms strong baselines, underscoring the importance of preserving the table structure for accurate table comprehension. Comprehensive analysis further reveals the substantially better scalability of 2D-TPE to large tables than baselines.

Generative models trained on internet-scale data are capable of generating novel and realistic texts, images, and videos. A natural next question is whether these models can advance science, for example by generating novel stable materials. Traditionally, models with explicit structures (e.g., graphs) have been used in modeling structural relationships in scientific data (e.g., atoms and bonds in crystals), but generating structures can be difficult to scale to large and complex systems. Another challenge in generating materials is the mismatch between standard generative modeling metrics and downstream applications. For instance, common metrics such as the reconstruction error do not correlate well with the downstream goal of discovering stable materials. In this work, we tackle the scalability challenge by developing a unified crystal representation that can represent any crystal structure (UniMat), followed by training a diffusion probabilistic model on these UniMat representations. Our empirical results suggest that despite the lack of explicit structure modeling, UniMat can generate high fidelity crystal structures from larger and more complex chemical systems, outperforming previous graph-based approaches under various generative modeling metrics. To better connect the generation quality of materials to downstream applications, such as discovering novel stable materials, we propose additional metrics for evaluating generative models of materials, including per-composition formation energy and stability with respect to convex hulls through decomposition energy from Density Function Theory (DFT). Lastly, we show that conditional generation with UniMat can scale to previously established crystal datasets with up to millions of crystals structures, outperforming random structure search (the current leading method for structure discovery) in discovering new stable materials.

Self-supervised learning has recently gained growing interest in molecular modeling for scientific tasks such as AI-assisted drug discovery. Current studies consider leveraging both 2D and 3D molecular structures for representation learning. However, relying on straightforward alignment strategies that treat each modality separately, these methods fail to exploit the intrinsic correlation between 2D and 3D representations that reflect the underlying structural characteristics of molecules, and only perform coarse-grained molecule-level alignment. To derive fine-grained alignment and promote structural molecule understanding, we introduce an atomic-relation level "blend-then-predict" self-supervised learning approach, MoleBLEND, which first blends atom relations represented by different modalities into one unified relation matrix for joint encoding, then recovers modality-specific information for 2D and 3D structures individually. By treating atom relationships as anchors, MoleBLEND organically aligns and integrates visually dissimilar 2D and 3D modalities of the same molecule at fine-grained atomic level, painting a more comprehensive depiction of each molecule. Extensive experiments show that MoleBLEND achieves state-of-the-art performance across major 2D/3D molecular benchmarks. We further provide theoretical insights from the perspective of mutual-information maximization, demonstrating that our method unifies contrastive, generative (cross-modality prediction) and mask-then-predict (single-modality prediction) objectives into one single cohesive framework.

We present a unified representation for actionable spatial perception: 3D Dynamic Scene Graphs. Scene graphs are directed graphs where nodes represent entities in the scene (e.g. objects, walls, rooms), and edges represent relations (e.g. inclusion, adjacency) among nodes. Dynamic scene graphs (DSGs) extend this notion to represent dynamic scenes with moving agents (e.g. humans, robots), and to include actionable information that supports planning and decision-making (e.g. spatio-temporal relations, topology at different levels of abstraction). Our second contribution is to provide the first fully automatic Spatial PerceptIon eNgine(SPIN) to build a DSG from visual-inertial data. We integrate state-of-the-art techniques for object and human detection and pose estimation, and we describe how to robustly infer object, robot, and human nodes in crowded scenes. To the best of our knowledge, this is the first paper that reconciles visual-inertial SLAM and dense human mesh tracking. Moreover, we provide algorithms to obtain hierarchical representations of indoor environments (e.g. places, structures, rooms) and their relations. Our third contribution is to demonstrate the proposed spatial perception engine in a photo-realistic Unity-based simulator, where we assess its robustness and expressiveness. Finally, we discuss the implications of our proposal on modern robotics applications. 3D Dynamic Scene Graphs can have a profound impact on planning and decision-making, human-robot interaction, long-term autonomy, and scene prediction. A video abstract is available at https://youtu.be/SWbofjhyPzI

Graph structure learning aims to learn connectivity in a graph from data. It is particularly important for many computer vision related tasks since no explicit graph structure is available for images for most cases. A natural way to construct a graph among images is to treat each image as a node and assign pairwise image similarities as weights to corresponding edges. It is well known that pairwise similarities between images are sensitive to the noise in feature representations, leading to unreliable graph structures. We address this problem from the viewpoint of statistical tests. By viewing the feature vector of each node as an independent sample, the decision of whether creating an edge between two nodes based on their similarity in feature representation can be thought as a {it single} statistical test. To improve the robustness in the decision of creating an edge, multiple samples are drawn and integrated by {it multiple} statistical tests to generate a more reliable similarity measure, consequentially more reliable graph structure. The corresponding elegant matrix form named B-Attention is designed for efficiency. The effectiveness of multiple tests for graph structure learning is verified both theoretically and empirically on multiple clustering and ReID benchmark datasets. Source codes are available at https://github.com/Thomas-wyh/B-Attention.

Understanding a visual scene goes beyond recognizing individual objects in isolation. Relationships between objects also constitute rich semantic information about the scene. In this work, we explicitly model the objects and their relationships using scene graphs, a visually-grounded graphical structure of an image. We propose a novel end-to-end model that generates such structured scene representation from an input image. The model solves the scene graph inference problem using standard RNNs and learns to iteratively improves its predictions via message passing. Our joint inference model can take advantage of contextual cues to make better predictions on objects and their relationships. The experiments show that our model significantly outperforms previous methods for generating scene graphs using Visual Genome dataset and inferring support relations with NYU Depth v2 dataset.

3D indoor scenes are widely used in computer graphics, with applications ranging from interior design to gaming to virtual and augmented reality. They also contain rich information, including room layout, as well as furniture type, geometry, and placement. High-quality 3D indoor scenes are highly demanded while it requires expertise and is time-consuming to design high-quality 3D indoor scenes manually. Existing research only addresses partial problems: some works learn to generate room layout, and other works focus on generating detailed structure and geometry of individual furniture objects. However, these partial steps are related and should be addressed together for optimal synthesis. We propose SCENEHGN, a hierarchical graph network for 3D indoor scenes that takes into account the full hierarchy from the room level to the object level, then finally to the object part level. Therefore for the first time, our method is able to directly generate plausible 3D room content, including furniture objects with fine-grained geometry, and their layout. To address the challenge, we introduce functional regions as intermediate proxies between the room and object levels to make learning more manageable. To ensure plausibility, our graph-based representation incorporates both vertical edges connecting child nodes with parent nodes from different levels, and horizontal edges encoding relationships between nodes at the same level. Extensive experiments demonstrate that our method produces superior generation results, even when comparing results of partial steps with alternative methods that can only achieve these. We also demonstrate that our method is effective for various applications such as part-level room editing, room interpolation, and room generation by arbitrary room boundaries.

Global dependency modeling and spatial position modeling are two core issues of the foundational architecture design in current deep learning frameworks. Recently, Vision Transformers (ViTs) have achieved remarkable success in computer vision, leveraging the powerful global dependency modeling capability of the self-attention mechanism. Furthermore, Mamba2 has demonstrated its significant potential in natural language processing tasks by explicitly modeling the spatial adjacency prior through the structured mask. In this paper, we propose Polyline Path Masked Attention (PPMA) that integrates the self-attention mechanism of ViTs with an enhanced structured mask of Mamba2, harnessing the complementary strengths of both architectures. Specifically, we first ameliorate the traditional structured mask of Mamba2 by introducing a 2D polyline path scanning strategy and derive its corresponding structured mask, polyline path mask, which better preserves the adjacency relationships among image tokens. Notably, we conduct a thorough theoretical analysis on the structural characteristics of the proposed polyline path mask and design an efficient algorithm for the computation of the polyline path mask. Next, we embed the polyline path mask into the self-attention mechanism of ViTs, enabling explicit modeling of spatial adjacency prior. Extensive experiments on standard benchmarks, including image classification, object detection, and segmentation, demonstrate that our model outperforms previous state-of-the-art approaches based on both state-space models and Transformers. For example, our proposed PPMA-T/S/B models achieve 48.7%/51.1%/52.3% mIoU on the ADE20K semantic segmentation task, surpassing RMT-T/S/B by 0.7%/1.3%/0.3%, respectively. Code is available at https://github.com/zhongchenzhao/PPMA.

The inference of topological principles is a key problem in structured reconstruction. We observe that wrongly predicted topological relationships are often incurred by the lack of holistic geometry clues in low-level features. Inspired by the fact that massive signals can be compactly described with frequency analysis, we experimentally explore the efficiency and tendency of learning structure geometry in the frequency domain. Accordingly, we propose a frequency-domain feature learning strategy (F-Learn) to fuse scattered geometric fragments holistically for topology-intact structure reasoning. Benefiting from the parsimonious design, the F-Learn strategy can be easily deployed into a deep reconstructor with a lightweight model modification. Experiments demonstrate that the F-Learn strategy can effectively introduce structure awareness into geometric primitive detection and topology inference, bringing significant performance improvement to final structured reconstruction. Code and pre-trained models are available at https://github.com/Geo-Tell/F-Learn.

Artefact descriptions are the primary carriers of engineering design knowledge that is both an outcome and a driver of the design process. While an artefact could be described in different connotations, the design process requires a description to embody engineering design knowledge, which is expressed in the text through intricate placement of entities and relationships. As large-language models learn from all kinds of text merely as a sequence of characters/tokens, these are yet to generate text that embodies explicit engineering design facts. Existing ontological design theories are less likely to guide the large-language models whose applications are currently limited to ideation and learning purposes. In this article, we explicate engineering design knowledge as knowledge graphs from a large sample of 33,881 patent documents. We examine the constituents of these knowledge graphs to understand the linguistic and structural basis of engineering design knowledge. In terms of linguistic basis, we observe that entities and relationships could be generalised to 64 and 24 linguistic syntaxes. While relationships mainly capture attributes ('of'), structure ('in', 'with'), purpose ('to', 'for'), hierarchy ('include'), exemplification ('such as'), and behaviour ('to', 'from'), the hierarchical relationships could specifically be identified using 75 unique syntaxes. To understand the structural basis, we draw inspiration from various studies on biological/ecological networks and discover motifs from patent knowledge graphs. We identify four 3-node and four 4-node patterns that could further be converged and simplified into sequence [->...->], aggregation [->...<-], and hierarchy [<-...->]. Expected to guide large-language model based design tools, we propose few regulatory precepts for concretising abstract entities and relationships within subgraphs, while explicating hierarchical structures.

We study the implications of the modeling choice to use a graph, instead of a hypergraph, to represent real-world interconnected systems whose constituent relationships are of higher order by nature. Such a modeling choice typically involves an underlying projection process that maps the original hypergraph onto a graph, and is common in graph-based analysis. While hypergraph projection can potentially lead to loss of higher-order relations, there exists very limited studies on the consequences of doing so, as well as its remediation. This work fills this gap by doing two things: (1) we develop analysis based on graph and set theory, showing two ubiquitous patterns of hyperedges that are root to structural information loss in all hypergraph projections; we also quantify the combinatorial impossibility of recovering the lost higher-order structures if no extra help is provided; (2) we still seek to recover the lost higher-order structures in hypergraph projection, and in light of (1)'s findings we propose to relax the problem into a learning-based setting. Under this setting, we develop a learning-based hypergraph reconstruction method based on an important statistic of hyperedge distributions that we find. Our reconstruction method is evaluated on 8 real-world datasets under different settings, and exhibits consistently good performance. We also demonstrate benefits of the reconstructed hypergraphs via use cases of protein rankings and link predictions.

Lattices are architected metamaterials whose properties strongly depend on their geometrical design. The analogy between lattices and graphs enables the use of graph neural networks (GNNs) as a faster surrogate model compared to traditional methods such as finite element modelling. In this work, we generate a big dataset of structure-property relationships for strut-based lattices. The dataset is made available to the community which can fuel the development of methods anchored in physical principles for the fitting of fourth-order tensors. In addition, we present a higher-order GNN model trained on this dataset. The key features of the model are (i) SE(3) equivariance, and (ii) consistency with the thermodynamic law of conservation of energy. We compare the model to non-equivariant models based on a number of error metrics and demonstrate its benefits in terms of predictive performance and reduced training requirements. Finally, we demonstrate an example application of the model to an architected material design task. The methods which we developed are applicable to fourth-order tensors beyond elasticity such as piezo-optical tensor etc.

Molecule pretraining has quickly become the go-to schema to boost the performance of AI-based drug discovery. Naturally, molecules can be represented as 2D topological graphs or 3D geometric point clouds. Although most existing pertaining methods focus on merely the single modality, recent research has shown that maximizing the mutual information (MI) between such two modalities enhances the molecule representation ability. Meanwhile, existing molecule multi-modal pretraining approaches approximate MI based on the representation space encoded from the topology and geometry, thus resulting in the loss of critical structural information of molecules. To address this issue, we propose MoleculeSDE. MoleculeSDE leverages group symmetric (e.g., SE(3)-equivariant and reflection-antisymmetric) stochastic differential equation models to generate the 3D geometries from 2D topologies, and vice versa, directly in the input space. It not only obtains tighter MI bound but also enables prosperous downstream tasks than the previous work. By comparing with 17 pretraining baselines, we empirically verify that MoleculeSDE can learn an expressive representation with state-of-the-art performance on 26 out of 32 downstream tasks.

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.

Modeling and designing urban building layouts is of significant interest in computer vision, computer graphics, and urban applications. A building layout consists of a set of buildings in city blocks defined by a network of roads. We observe that building layouts are discrete structures, consisting of multiple rows of buildings of various shapes, and are amenable to skeletonization for mapping arbitrary city block shapes to a canonical form. Hence, we propose a fully automatic approach to building layout generation using graph attention networks. Our method generates realistic urban layouts given arbitrary road networks, and enables conditional generation based on learned priors. Our results, including user study, demonstrate superior performance as compared to prior layout generation networks, support arbitrary city block and varying building shapes as demonstrated by generating layouts for 28 large cities.

Networks provide a powerful formalism for modeling complex systems by using a model of pairwise interactions. But much of the structure within these systems involves interactions that take place among more than two nodes at once; for example, communication within a group rather than person-to person, collaboration among a team rather than a pair of coauthors, or biological interaction between a set of molecules rather than just two. Such higher-order interactions are ubiquitous, but their empirical study has received limited attention, and little is known about possible organizational principles of such structures. Here we study the temporal evolution of 19 datasets with explicit accounting for higher-order interactions. We show that there is a rich variety of structure in our datasets but datasets from the same system types have consistent patterns of higher-order structure. Furthermore, we find that tie strength and edge density are competing positive indicators of higher-order organization, and these trends are consistent across interactions involving differing numbers of nodes. To systematically further the study of theories for such higher-order structures, we propose higher-order link prediction as a benchmark problem to assess models and algorithms that predict higher-order structure. We find a fundamental differences from traditional pairwise link prediction, with a greater role for local rather than long-range information in predicting the appearance of new interactions.

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.

Graphs are a fundamental data structure for representing relationships in real-world scenarios. With the success of Large Language Models (LLMs) across various natural language processing (NLP) tasks, there has been growing interest in integrating LLMs for graph learning. However, applying LLMs to graph-related tasks poses significant challenges, as these models are not inherently designed to capture the complex structural information present in graphs. Existing approaches address this challenge through two strategies: the chain of tasks approach, which uses Graph Neural Networks (GNNs) to encode the graph structure so that LLMs are relieved from understanding spatial positions; and Graph-to-Text Conversion, which translates graph structures into semantic text representations that LLMs can process. Despite their progress, these methods often struggle to fully preserve the topological information of graphs or require extensive computational resources, limiting their practical applicability. In this work, we introduce Node Tokenizer for Large Language Models (NT-LLM), a novel framework that efficiently encodes graph structures by selecting key nodes as anchors and representing each node based on its relative distance to these anchors. This position-anchored encoding effectively captures the graph topology, enabling enhanced reasoning capabilities in LLMs over graph data. Additionally, we implement a task-specific tuning procedure to further improve structural understanding within LLMs. Through extensive empirical evaluations, NT-LLM demonstrates significant performance improvements across a variety of graph-related tasks.

We address the challenge of creating 3D assets for household articulated objects from a single image. Prior work on articulated object creation either requires multi-view multi-state input, or only allows coarse control over the generation process. These limitations hinder the scalability and practicality for articulated object modeling. In this work, we propose a method to generate articulated objects from a single image. Observing the object in resting state from an arbitrary view, our method generates an articulated object that is visually consistent with the input image. To capture the ambiguity in part shape and motion posed by a single view of the object, we design a diffusion model that learns the plausible variations of objects in terms of geometry and kinematics. To tackle the complexity of generating structured data with attributes in multiple domains, we design a pipeline that produces articulated objects from high-level structure to geometric details in a coarse-to-fine manner, where we use a part connectivity graph and part abstraction as proxies. Our experiments show that our method outperforms the state-of-the-art in articulated object creation by a large margin in terms of the generated object realism, resemblance to the input image, and reconstruction quality.

Hypergraphs offer a powerful framework for modeling higher-order interactions that traditional pairwise graphs cannot fully capture. However, practical constraints often lead to their simplification into projected graphs, resulting in substantial information loss and ambiguity in representing higher-order relationships. In this work, we propose MARIOH, a supervised approach for reconstructing the original hypergraph from its projected graph by leveraging edge multiplicity. To overcome the difficulties posed by the large search space, MARIOH integrates several key ideas: (a) identifying provable size-2 hyperedges, which reduces the candidate search space, (b) predicting the likelihood of candidates being hyperedges by utilizing both structural and multiplicity-related features, and (c) not only targeting promising hyperedge candidates but also examining less confident ones to explore alternative possibilities. Together, these ideas enable MARIOH to efficiently and effectively explore the search space. In our experiments using 10 real-world datasets, MARIOH achieves up to 74.51% higher reconstruction accuracy compared to state-of-the-art methods.

Complex networks provide a means to describe cities through their street mesh, expressing characteristics that refer to the structure and organization of an urban zone. Although other studies have used complex networks to model street meshes, we observed a lack of methods to characterize the relationship between cities by using their topological features. Accordingly, this paper aims to describe interactions between cities by using vectors of topological features extracted from their street meshes represented as complex networks. The methodology of this study is based on the use of digital maps. Over the computational representation of such maps, we extract global complex-network features that embody the characteristics of the cities. These vectors allow for the use of multidimensional projection and clustering techniques, enabling a similarity-based comparison of the street meshes. We experiment with 645 cities from the Brazilian state of Sao Paulo. Our results show how the joint of global features describes urban indicators that are deep-rooted in the network's topology and how they reveal characteristics and similarities among sets of cities that are separated from each other.

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.

Graph neural networks are emerging as promising methods for modeling molecular graphs, in which nodes and edges correspond to atoms and chemical bonds, respectively. Recent studies show that when 3D molecular geometries, such as bond lengths and angles, are available, molecular property prediction tasks can be made more accurate. However, computing of 3D molecular geometries requires quantum calculations that are computationally prohibitive. For example, accurate calculation of 3D geometries of a small molecule requires hours of computing time using density functional theory (DFT). Here, we propose to predict the ground-state 3D geometries from molecular graphs using machine learning methods. To make this feasible, we develop a benchmark, known as Molecule3D, that includes a dataset with precise ground-state geometries of approximately 4 million molecules derived from DFT. We also provide a set of software tools for data processing, splitting, training, and evaluation, etc. Specifically, we propose to assess the error and validity of predicted geometries using four metrics. We implement two baseline methods that either predict the pairwise distance between atoms or atom coordinates in 3D space. Experimental results show that, compared with generating 3D geometries with RDKit, our method can achieve comparable prediction accuracy but with much smaller computational costs. Our Molecule3D is available as a module of the MoleculeX software library (https://github.com/divelab/MoleculeX).

We present a method for teaching machines to understand and model the underlying spatial common sense of diverse human-object interactions in 3D in a self-supervised way. This is a challenging task, as there exist specific manifolds of the interactions that can be considered human-like and natural, but the human pose and the geometry of objects can vary even for similar interactions. Such diversity makes the annotating task of 3D interactions difficult and hard to scale, which limits the potential to reason about that in a supervised way. One way of learning the 3D spatial relationship between humans and objects during interaction is by showing multiple 2D images captured from different viewpoints when humans interact with the same type of objects. The core idea of our method is to leverage a generative model that produces high-quality 2D images from an arbitrary text prompt input as an "unbounded" data generator with effective controllability and view diversity. Despite its imperfection of the image quality over real images, we demonstrate that the synthesized images are sufficient to learn the 3D human-object spatial relations. We present multiple strategies to leverage the synthesized images, including (1) the first method to leverage a generative image model for 3D human-object spatial relation learning; (2) a framework to reason about the 3D spatial relations from inconsistent 2D cues in a self-supervised manner via 3D occupancy reasoning with pose canonicalization; (3) semantic clustering to disambiguate different types of interactions with the same object types; and (4) a novel metric to assess the quality of 3D spatial learning of interaction.

Heterogeneous tabular data poses unique challenges in generative modelling due to its fundamentally different underlying data structure compared to homogeneous modalities, such as images and text. Although previous research has sought to adapt the successes of generative modelling in homogeneous modalities to the tabular domain, defining an effective generator for tabular data remains an open problem. One major reason is that the evaluation criteria inherited from other modalities often fail to adequately assess whether tabular generative models effectively capture or utilise the unique structural information encoded in tabular data. In this paper, we carefully examine the limitations of the prevailing evaluation framework and introduce TabStruct, a novel evaluation benchmark that positions structural fidelity as a core evaluation dimension. Specifically, TabStruct evaluates the alignment of causal structures in real and synthetic data, providing a direct measure of how effectively tabular generative models learn the structure of tabular data. Through extensive experiments using generators from eight categories on seven datasets with expert-validated causal graphical structures, we show that structural fidelity offers a task-independent, domain-agnostic evaluation dimension. Our findings highlight the importance of tabular data structure and offer practical guidance for developing more effective and robust tabular generative models. Code is available at https://github.com/SilenceX12138/TabStruct.

Spatial relationships between objects represent key scene information for humans to understand and interact with the world. To study the capability of current computer vision systems to recognize physically grounded spatial relations, we start by proposing precise relation definitions that permit consistently annotating a benchmark dataset. Despite the apparent simplicity of this task relative to others in the recognition literature, we observe that existing approaches perform poorly on this benchmark. We propose new approaches exploiting the long-range attention capabilities of transformers for this task, and evaluating key design principles. We identify a simple "RelatiViT" architecture and demonstrate that it outperforms all current approaches. To our knowledge, this is the first method to convincingly outperform naive baselines on spatial relation prediction in in-the-wild settings. The code and datasets are available in https://sites.google.com/view/spatial-relation.

Despite encouraging progress in 3D scene understanding, it remains challenging to develop an effective Large Multi-modal Model (LMM) that is capable of understanding and reasoning in complex 3D environments. Most previous methods typically encode 3D point and 2D image features separately, neglecting interactions between 2D semantics and 3D object properties, as well as the spatial relationships within the 3D environment. This limitation not only hinders comprehensive representations of 3D scene, but also compromises training and inference efficiency. To address these challenges, we propose a unified Instance-aware 3D Large Multi-modal Model (Inst3D-LMM) to deal with multiple 3D scene understanding tasks simultaneously. To obtain the fine-grained instance-level visual tokens, we first introduce a novel Multi-view Cross-Modal Fusion (MCMF) module to inject the multi-view 2D semantics into their corresponding 3D geometric features. For scene-level relation-aware tokens, we further present a 3D Instance Spatial Relation (3D-ISR) module to capture the intricate pairwise spatial relationships among objects. Additionally, we perform end-to-end multi-task instruction tuning simultaneously without the subsequent task-specific fine-tuning. Extensive experiments demonstrate that our approach outperforms the state-of-the-art methods across 3D scene understanding, reasoning and grounding tasks. Source code is available at https://github.com/hanxunyu/Inst3D-LMM

Reconstructing 3D representations from 2D inputs is a fundamental task in computer vision and graphics, serving as a cornerstone for understanding and interacting with the physical world. While traditional methods achieve high fidelity, they are limited by slow per-scene optimization or category-specific training, which hinders their practical deployment and scalability. Hence, generalizable feed-forward 3D reconstruction has witnessed rapid development in recent years. By learning a model that maps images directly to 3D representations in a single forward pass, these methods enable efficient reconstruction and robust cross-scene generalization. Our survey is motivated by a critical observation: despite the diverse geometric output representations, ranging from implicit fields to explicit primitives, existing feed-forward approaches share similar high-level architectural patterns, such as image feature extraction backbones, multi-view information fusion mechanisms, and geometry-aware design principles. Consequently, we abstract away from these representation differences and instead focus on model design, proposing a novel taxonomy centered on model design strategies that are agnostic to the output format. Our proposed taxonomy organizes the research directions into five key problems that drive recent research development: feature enhancement, geometry awareness, model efficiency, augmentation strategies and temporal-aware models. To support this taxonomy with empirical grounding and standardized evaluation, we further comprehensively review related benchmarks and datasets, and extensively discuss and categorize real-world applications based on feed-forward 3D models. Finally, we outline future directions to address open challenges such as scalability, evaluation standards, and world modeling.

We study the problem of visualizing large-scale and high-dimensional data in a low-dimensional (typically 2D or 3D) space. Much success has been reported recently by techniques that first compute a similarity structure of the data points and then project them into a low-dimensional space with the structure preserved. These two steps suffer from considerable computational costs, preventing the state-of-the-art methods such as the t-SNE from scaling to large-scale and high-dimensional data (e.g., millions of data points and hundreds of dimensions). We propose the LargeVis, a technique that first constructs an accurately approximated K-nearest neighbor graph from the data and then layouts the graph in the low-dimensional space. Comparing to t-SNE, LargeVis significantly reduces the computational cost of the graph construction step and employs a principled probabilistic model for the visualization step, the objective of which can be effectively optimized through asynchronous stochastic gradient descent with a linear time complexity. The whole procedure thus easily scales to millions of high-dimensional data points. Experimental results on real-world data sets demonstrate that the LargeVis outperforms the state-of-the-art methods in both efficiency and effectiveness. The hyper-parameters of LargeVis are also much more stable over different data sets.

Multi-relational graphs (MRGs) are an expressive data structure for modeling diverse interactions/relations among real objects (i.e., nodes), which pervade extensive applications and scenarios. Given an MRG G with N nodes, partitioning the node set therein into K disjoint clusters (MRGC) is a fundamental task in analyzing MRGs, which has garnered considerable attention. However, the majority of existing solutions towards MRGC either yield severely compromised result quality by ineffective fusion of heterogeneous graph structures and attributes, or struggle to cope with sizable MRGs with millions of nodes and billions of edges due to the adoption of sophisticated and costly deep learning models. In this paper, we present DEMM and DEMM+, two effective MRGC approaches to address the limitations above. Specifically, our algorithms are built on novel two-stage optimization objectives, where the former seeks to derive high-caliber node feature vectors by optimizing the multi-relational Dirichlet energy specialized for MRGs, while the latter minimizes the Dirichlet energy of clustering results over the node affinity graph. In particular, DEMM+ achieves significantly higher scalability and efficiency over our based method DEMM through a suite of well-thought-out optimizations. Key technical contributions include (i) a highly efficient approximation solver for constructing node feature vectors, and (ii) a theoretically-grounded problem transformation with carefully-crafted techniques that enable linear-time clustering without explicitly materializing the NxN dense affinity matrix. Further, we extend DEMM+ to handle attribute-less MRGs through non-trivial adaptations. Extensive experiments, comparing DEMM+ against 20 baselines over 11 real MRGs, exhibit that DEMM+ is consistently superior in terms of clustering quality measured against ground-truth labels, while often being remarkably faster.

Linear structural equation models are multivariate statistical models encoded by mixed graphs. In particular, the set of covariance matrices for distributions belonging to a linear structural equation model for a fixed mixed graph G=(V, D,B) is parameterized by a rational function with parameters for each vertex and edge in G. This rational parametrization naturally allows for the study of these models from an algebraic and combinatorial point of view. Indeed, this point of view has led to a collection of results in the literature, mainly focusing on questions related to identifiability and determining relationships between covariances (i.e., finding polynomials in the Gaussian vanishing ideal). So far, a large proportion of these results has focused on the case when D, the directed part of the mixed graph G, is acyclic. This is due to the fact that in the acyclic case, the parametrization becomes polynomial and there is a description of the entries of the covariance matrices in terms of a finite sum. We move beyond the acyclic case and give a closed form expression for the entries of the covariance matrices in terms of the one-connections in a graph obtained from D through some small operations. This closed form expression then allows us to show that if G is simple, then the parametrization map is generically finite-to-one. Finally, having a closed form expression for the covariance matrices allows for the development of an algorithm for systematically exploring possible polynomials in the Gaussian vanishing ideal.

Generation of graphs is a major challenge for real-world tasks that require understanding the complex nature of their non-Euclidean structures. Although diffusion models have achieved notable success in graph generation recently, they are ill-suited for modeling the topological properties of graphs since learning to denoise the noisy samples does not explicitly learn the graph structures to be generated. To tackle this limitation, we propose a generative framework that models the topology of graphs by explicitly learning the final graph structures of the diffusion process. Specifically, we design the generative process as a mixture of endpoint-conditioned diffusion processes which is driven toward the predicted graph that results in rapid convergence. We further introduce a simple parameterization of the mixture process and develop an objective for learning the final graph structure, which enables maximum likelihood training. Through extensive experimental validation on general graph and 2D/3D molecule generation tasks, we show that our method outperforms previous generative models, generating graphs with correct topology with both continuous (e.g. 3D coordinates) and discrete (e.g. atom types) features. Our code is available at https://github.com/harryjo97/GruM.

We introduce a new generative model that combines latent diffusion with persistent homology to create 3D shapes with high diversity, with a special emphasis on their topological characteristics. Our method involves representing 3D shapes as implicit fields, then employing persistent homology to extract topological features, including Betti numbers and persistence diagrams. The shape generation process consists of two steps. Initially, we employ a transformer-based autoencoding module to embed the implicit representation of each 3D shape into a set of latent vectors. Subsequently, we navigate through the learned latent space via a diffusion model. By strategically incorporating topological features into the diffusion process, our generative module is able to produce a richer variety of 3D shapes with different topological structures. Furthermore, our framework is flexible, supporting generation tasks constrained by a variety of inputs, including sparse and partial point clouds, as well as sketches. By modifying the persistence diagrams, we can alter the topology of the shapes generated from these input modalities.

The field of face recognition (FR) has undergone significant advancements with the rise of deep learning. Recently, the success of unsupervised learning and graph neural networks has demonstrated the effectiveness of data structure information. Considering that the FR task can leverage large-scale training data, which intrinsically contains significant structure information, we aim to investigate how to encode such critical structure information into the latent space. As revealed from our observations, directly aligning the structure information between the input and latent spaces inevitably suffers from an overfitting problem, leading to a structure collapse phenomenon in the latent space. To address this problem, we propose TopoFR, a novel FR model that leverages a topological structure alignment strategy called PTSA and a hard sample mining strategy named SDE. Concretely, PTSA uses persistent homology to align the topological structures of the input and latent spaces, effectively preserving the structure information and improving the generalization performance of FR model. To mitigate the impact of hard samples on the latent space structure, SDE accurately identifies hard samples by automatically computing structure damage score (SDS) for each sample, and directs the model to prioritize optimizing these samples. Experimental results on popular face benchmarks demonstrate the superiority of our TopoFR over the state-of-the-art methods. Code and models are available at: https://github.com/modelscope/facechain/tree/main/face_module/TopoFR.

A 3D scene graph represents a compact scene model, storing information about the objects and the semantic relationships between them, making its use promising for robotic tasks. When interacting with a user, an embodied intelligent agent should be capable of responding to various queries about the scene formulated in natural language. Large Language Models (LLMs) are beneficial solutions for user-robot interaction due to their natural language understanding and reasoning abilities. Recent methods for creating learnable representations of 3D scenes have demonstrated the potential to improve the quality of LLMs responses by adapting to the 3D world. However, the existing methods do not explicitly utilize information about the semantic relationships between objects, limiting themselves to information about their coordinates. In this work, we propose a method 3DGraphLLM for constructing a learnable representation of a 3D scene graph. The learnable representation is used as input for LLMs to perform 3D vision-language tasks. In our experiments on popular ScanRefer, RIORefer, Multi3DRefer, ScanQA, Sqa3D, and Scan2cap datasets, we demonstrate the advantage of this approach over baseline methods that do not use information about the semantic relationships between objects. The code is publicly available at https://github.com/CognitiveAISystems/3DGraphLLM.

The cascade of 2D geometric transformations were exploited to model relations between entities in a knowledge graph (KG), leading to an effective KG embedding (KGE) model, CompoundE. Furthermore, the rotation in the 3D space was proposed as a new KGE model, Rotate3D, by leveraging its non-commutative property. Inspired by CompoundE and Rotate3D, we leverage 3D compound geometric transformations, including translation, rotation, scaling, reflection, and shear and propose a family of KGE models, named CompoundE3D, in this work. CompoundE3D allows multiple design variants to match rich underlying characteristics of a KG. Since each variant has its own advantages on a subset of relations, an ensemble of multiple variants can yield superior performance. The effectiveness and flexibility of CompoundE3D are experimentally verified on four popular link prediction datasets.

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.

Relational databases (RDBs) are composed of interconnected tables, where relationships between them are defined through foreign keys. Recent research on applying machine learning to RDBs has explored graph-based representations of RDBs, where rows of tables are modeled as nodes, and foreign key relationships are modeled as edges. RDB-to-graph modeling helps capture cross-table dependencies, ultimately leading to enhanced performance across diverse tasks. However, there are numerous ways to model RDBs as graphs, and performance varies significantly depending on the chosen graph model. In our analysis, applying a common heuristic rule for graph modeling leads to up to a 10% drop in performance compared to the best-performing graph model, which remains non-trivial to identify. To foster research on intelligent RDB-to-graph modeling, we introduce RDB2G-Bench, the first benchmark framework for evaluating such methods. We construct extensive datasets covering 5 real-world RDBs and 12 predictive tasks, resulting in around 50k graph-performance pairs for efficient and reproducible evaluations. Thanks to our precomputed datasets, we were able to benchmark 9 automatic RDB-to-graph modeling methods on the 12 tasks over 600x faster than on-the-fly evaluation, which requires repeated model training. Our analysis of the datasets and benchmark results reveals key structural patterns affecting graph model effectiveness, along with practical implications for effective graph modeling.

We investigate the problem of producing structured graph representations of visual scenes. Our work analyzes the role of motifs: regularly appearing substructures in scene graphs. We present new quantitative insights on such repeated structures in the Visual Genome dataset. Our analysis shows that object labels are highly predictive of relation labels but not vice-versa. We also find that there are recurring patterns even in larger subgraphs: more than 50% of graphs contain motifs involving at least two relations. Our analysis motivates a new baseline: given object detections, predict the most frequent relation between object pairs with the given labels, as seen in the training set. This baseline improves on the previous state-of-the-art by an average of 3.6% relative improvement across evaluation settings. We then introduce Stacked Motif Networks, a new architecture designed to capture higher order motifs in scene graphs that further improves over our strong baseline by an average 7.1% relative gain. Our code is available at github.com/rowanz/neural-motifs.

For robots to perform a wide variety of tasks, they require a 3D representation of the world that is semantically rich, yet compact and efficient for task-driven perception and planning. Recent approaches have attempted to leverage features from large vision-language models to encode semantics in 3D representations. However, these approaches tend to produce maps with per-point feature vectors, which do not scale well in larger environments, nor do they contain semantic spatial relationships between entities in the environment, which are useful for downstream planning. In this work, we propose ConceptGraphs, an open-vocabulary graph-structured representation for 3D scenes. ConceptGraphs is built by leveraging 2D foundation models and fusing their output to 3D by multi-view association. The resulting representations generalize to novel semantic classes, without the need to collect large 3D datasets or finetune models. We demonstrate the utility of this representation through a number of downstream planning tasks that are specified through abstract (language) prompts and require complex reasoning over spatial and semantic concepts. (Project page: https://concept-graphs.github.io/ Explainer video: https://youtu.be/mRhNkQwRYnc )

In this paper we introduce a novel family of attributed graphs for the purpose of shape discrimination. Our graphs typically arise from variations on the Mapper graph construction, which is an approximation of the Reeb graph for point cloud data. Our attributions enrich these constructions with (persistent) homology in ways that are provably stable, thereby recording extra topological information that is typically lost in these graph constructions. We provide experiments which illustrate the use of these invariants for shape representation and classification. In particular, we obtain competitive shape classification results when using our topologically attributed graphs as inputs to a simple graph neural network classifier.

Recently, there has been growing interest in developing learning-based methods to detect and utilize salient semi-global or global structures, such as junctions, lines, planes, cuboids, smooth surfaces, and all types of symmetries, for 3D scene modeling and understanding. However, the ground truth annotations are often obtained via human labor, which is particularly challenging and inefficient for such tasks due to the large number of 3D structure instances (e.g., line segments) and other factors such as viewpoints and occlusions. In this paper, we present a new synthetic dataset, Structured3D, with the aim of providing large-scale photo-realistic images with rich 3D structure annotations for a wide spectrum of structured 3D modeling tasks. We take advantage of the availability of professional interior designs and automatically extract 3D structures from them. We generate high-quality images with an industry-leading rendering engine. We use our synthetic dataset in combination with real images to train deep networks for room layout estimation and demonstrate improved performance on benchmark datasets.

Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification. Being able to capture long range graph properties via higher-order topological features, such as cycles of arbitrary length, in combination with multi-scale topological descriptors, has improved predictive performance for data sets with prominent topological structures, such as molecules. At the same time, the theoretical properties of persistent homology have not been formally assessed in this context. This paper intends to bridge the gap between computational topology and graph machine learning by providing a brief introduction to persistent homology in the context of graphs, as well as a theoretical discussion and empirical analysis of its expressivity for graph learning tasks.

Topological data analysis (TDA) is an area of data science that focuses on using invariants from algebraic topology to provide multiscale shape descriptors for geometric data sets such as point clouds. One of the most important such descriptors is {\em persistent homology}, which encodes the change in shape as a filtration parameter changes; a typical parameter is the feature scale. For many data sets, it is useful to simultaneously vary multiple filtration parameters, for example feature scale and density. While the theoretical properties of single parameter persistent homology are well understood, less is known about the multiparameter case. In particular, a central question is the problem of representing multiparameter persistent homology by elements of a vector space for integration with standard machine learning algorithms. Existing approaches to this problem either ignore most of the multiparameter information to reduce to the one-parameter case or are heuristic and potentially unstable in the face of noise. In this article, we introduce a new general representation framework that leverages recent results on {\em decompositions} of multiparameter persistent homology. This framework is rich in information, fast to compute, and encompasses previous approaches. Moreover, we establish theoretical stability guarantees under this framework as well as efficient algorithms for practical computation, making this framework an applicable and versatile tool for analyzing geometric and point cloud data. We validate our stability results and algorithms with numerical experiments that demonstrate statistical convergence, prediction accuracy, and fast running times on several real data sets.

With the emergence of data marketplaces, the demand for methods to assess the value of data has increased significantly. While numerous techniques have been proposed for this purpose, none have specifically addressed graphs as the main data modality. Graphs are widely used across various fields, ranging from chemical molecules to social networks. In this study, we break down graphs into two main components: structural and featural, and we focus on evaluating data without relying on specific task-related metrics, making it applicable in practical scenarios where validation requirements may be lacking. We introduce a novel framework called blind message passing, which aligns the seller's and buyer's graphs using a shared node permutation based on graph matching. This allows us to utilize the graph Wasserstein distance to quantify the differences in the structural distribution of graph datasets, called the structural disparities. We then consider featural aspects of buyers' and sellers' graphs for data valuation and capture their statistical similarities and differences, referred to as relevance and diversity, respectively. Our approach ensures that buyers and sellers remain unaware of each other's datasets. Our experiments on real datasets demonstrate the effectiveness of our approach in capturing the relevance, diversity, and structural disparities of seller data for buyers, particularly in graph-based data valuation scenarios.

Controllable 3D scene generation has extensive applications in virtual reality and interior design, where the generated scenes should exhibit high levels of realism and controllability in terms of geometry. Scene graphs provide a suitable data representation that facilitates these applications. However, current graph-based methods for scene generation are constrained to text-based inputs and exhibit insufficient adaptability to flexible user inputs, hindering the ability to precisely control object geometry. To address this issue, we propose MMGDreamer, a dual-branch diffusion model for scene generation that incorporates a novel Mixed-Modality Graph, visual enhancement module, and relation predictor. The mixed-modality graph allows object nodes to integrate textual and visual modalities, with optional relationships between nodes. It enhances adaptability to flexible user inputs and enables meticulous control over the geometry of objects in the generated scenes. The visual enhancement module enriches the visual fidelity of text-only nodes by constructing visual representations using text embeddings. Furthermore, our relation predictor leverages node representations to infer absent relationships between nodes, resulting in more coherent scene layouts. Extensive experimental results demonstrate that MMGDreamer exhibits superior control of object geometry, achieving state-of-the-art scene generation performance. Project page: https://yangzhifeio.github.io/project/MMGDreamer.

Link prediction, a fundamental task on graphs, has proven indispensable in various applications, e.g., friend recommendation, protein analysis, and drug interaction prediction. However, since datasets span a multitude of domains, they could have distinct underlying mechanisms of link formation. Evidence in existing literature underscores the absence of a universally best algorithm suitable for all datasets. In this paper, we endeavor to explore principles of link prediction across diverse datasets from a data-centric perspective. We recognize three fundamental factors critical to link prediction: local structural proximity, global structural proximity, and feature proximity. We then unearth relationships among those factors where (i) global structural proximity only shows effectiveness when local structural proximity is deficient. (ii) The incompatibility can be found between feature and structural proximity. Such incompatibility leads to GNNs for Link Prediction (GNN4LP) consistently underperforming on edges where the feature proximity factor dominates. Inspired by these new insights from a data perspective, we offer practical instruction for GNN4LP model design and guidelines for selecting appropriate benchmark datasets for more comprehensive evaluations.

We introduce the task of predicting functional 3D scene graphs for real-world indoor environments from posed RGB-D images. Unlike traditional 3D scene graphs that focus on spatial relationships of objects, functional 3D scene graphs capture objects, interactive elements, and their functional relationships. Due to the lack of training data, we leverage foundation models, including visual language models (VLMs) and large language models (LLMs), to encode functional knowledge. We evaluate our approach on an extended SceneFun3D dataset and a newly collected dataset, FunGraph3D, both annotated with functional 3D scene graphs. Our method significantly outperforms adapted baselines, including Open3DSG and ConceptGraph, demonstrating its effectiveness in modeling complex scene functionalities. We also demonstrate downstream applications such as 3D question answering and robotic manipulation using functional 3D scene graphs. See our project page at https://openfungraph.github.io

Structural analyses are an integral part of computational research on nucleation and supercooled water, whose accuracy and efficiency can impact the validity and feasibility of such studies. The underlying molecular mechanisms of these often elusive and computationally expensive processes can be inferred from the evolution of ice-like structures, determined using appropriate structural analysis techniques. We present d-SEAMS, a free and open-source post-processing engine for the analysis of molecular dynamics trajectories, which is specifically able to qualitatively classify ice structures, in both strong confinement and bulk systems. For the first time, recent algorithms for confined ice structure determination have been implemented, along with topological network criteria for bulk ice structure determination. Recognizing the need for customization in structural analysis, d-SEAMS has a unique code architecture, built with `nix`, employing a `YAML`-`Lua` scripting pipeline. The software has been designed to be user-friendly and easy to extend. The engine outputs are compatible with popular graphics software suites, allowing for immediate visual insights into the systems studied. We demonstrate the features of d-SEAMS by using it to analyze nucleation in the bulk regime and for quasi-one and quasi-two-dimensional systems. Structural time evolution and quantitative metrics are determined for heterogenous ice nucleation on a silver-exposed beta-AgI surface, homogenous ice nucleation, flat monolayer square ice formation and freezing of an ice nanotube.

Topological deep learning has emerged for modeling higher-order relational structures beyond pairwise interactions that standard graph neural networks fail to capture. Although combinatorial complexes offer a unified topological framework, most existing topological deep learning methods rely on local message passing via attention mechanisms, which incur quadratic complexity and remain low-dimensional, limiting scalability and rank-aware information aggregation in higher-order complexes.We propose Combinatorial Complex Mamba (CCMamba), the first unified mamba-based neural framework for learning on combinatorial complexes. CCMamba reformulates message passing as a selective state-space modeling problem by organizing multi-rank incidence relations into structured sequences processed by rank-aware state-space models. This enables adaptive, directional, and long range information propagation in linear time without self attention. We further establish the theoretical analysis that the expressive power upper-bound of CCMamba message passing is the 1-Weisfeiler-Lehman test. Experiments on graph, hypergraph, and simplicial benchmarks demonstrate that CCMamba consistently outperforms existing methods while exhibiting improved scalability and robustness to depth.

We view the reconstruction of CAD models in the boundary representation (B-Rep) as the detection of geometric primitives of different orders, i.e. vertices, edges and surface patches, and the correspondence of primitives, which are holistically modeled as a chain complex, and show that by modeling such comprehensive structures more complete and regularized reconstructions can be achieved. We solve the complex generation problem in two steps. First, we propose a novel neural framework that consists of a sparse CNN encoder for input point cloud processing and a tri-path transformer decoder for generating geometric primitives and their mutual relationships with estimated probabilities. Second, given the probabilistic structure predicted by the neural network, we recover a definite B-Rep chain complex by solving a global optimization maximizing the likelihood under structural validness constraints and applying geometric refinements. Extensive tests on large scale CAD datasets demonstrate that the modeling of B-Rep chain complex structure enables more accurate detection for learning and more constrained reconstruction for optimization, leading to structurally more faithful and complete CAD B-Rep models than previous results.

Spider webs are incredible biological structures, comprising thin but strong silk filament and arranged into complex hierarchical architectures with striking mechanical properties (e.g., lightweight but high strength, achieving diverse mechanical responses). While simple 2D orb webs can easily be mimicked, the modeling and synthesis of 3D-based web structures remain challenging, partly due to the rich set of design features. Here we provide a detailed analysis of the heterogenous graph structures of spider webs, and use deep learning as a way to model and then synthesize artificial, bio-inspired 3D web structures. The generative AI models are conditioned based on key geometric parameters (including average edge length, number of nodes, average node degree, and others). To identify graph construction principles, we use inductive representation sampling of large experimentally determined spider web graphs, to yield a dataset that is used to train three conditional generative models: 1) An analog diffusion model inspired by nonequilibrium thermodynamics, with sparse neighbor representation, 2) a discrete diffusion model with full neighbor representation, and 3) an autoregressive transformer architecture with full neighbor representation. All three models are scalable, produce complex, de novo bio-inspired spider web mimics, and successfully construct graphs that meet the design objectives. We further propose algorithm that assembles web samples produced by the generative models into larger-scale structures based on a series of geometric design targets, including helical and parametric shapes, mimicking, and extending natural design principles towards integration with diverging engineering objectives. Several webs are manufactured using 3D printing and tested to assess mechanical properties.

Advancements in generative models have sparked significant interest in generating images while adhering to specific structural guidelines. Scene graph to image generation is one such task of generating images which are consistent with the given scene graph. However, the complexity of visual scenes poses a challenge in accurately aligning objects based on specified relations within the scene graph. Existing methods approach this task by first predicting a scene layout and generating images from these layouts using adversarial training. In this work, we introduce a novel approach to generate images from scene graphs which eliminates the need of predicting intermediate layouts. We leverage pre-trained text-to-image diffusion models and CLIP guidance to translate graph knowledge into images. Towards this, we first pre-train our graph encoder to align graph features with CLIP features of corresponding images using a GAN based training. Further, we fuse the graph features with CLIP embedding of object labels present in the given scene graph to create a graph consistent CLIP guided conditioning signal. In the conditioning input, object embeddings provide coarse structure of the image and graph features provide structural alignment based on relationships among objects. Finally, we fine tune a pre-trained diffusion model with the graph consistent conditioning signal with reconstruction and CLIP alignment loss. Elaborate experiments reveal that our method outperforms existing methods on standard benchmarks of COCO-stuff and Visual Genome dataset.

Due to the advantages of hypergraphs in modeling high-order relationships in complex systems, they have been applied to higher-order clustering, hypergraph neural networks and computer vision. These applications rely heavily on access to high-quality, large-scale real-world hypergraph data. Yet, compared to traditional pairwise graphs, real hypergraph datasets remain scarce in both scale and diversity. This shortage significantly limits the development and evaluation of advanced hypergraph learning algorithms. Therefore, how to quickly generate large-scale hypergraphs that conform to the characteristics of real networks is a crucial task that has not received sufficient attention. Motivated by recent advances in large language models (LLMs), particularly their capabilities in semantic reasoning, structured generation, and simulating human behavior, we investigate whether LLMs can facilitate hypergraph generation from a fundamentally new perspective. We introduce HyperLLM, a novel LLM-driven hypergraph generator that simulates the formation and evolution of hypergraphs through a multi-agent collaboration. The framework integrates prompts and structural feedback mechanisms to ensure that the generated hypergraphs reflect key real-world patterns. Extensive experiments across diverse datasets demonstrate that HyperLLM achieves superior fidelity to structural and temporal hypergraph patterns, while requiring minimal statistical priors. Our findings suggest that LLM-based frameworks offer a promising new direction for hypergraph modeling.

3D shape generation aims to produce innovative 3D content adhering to specific conditions and constraints. Existing methods often decompose 3D shapes into a sequence of localized components, treating each element in isolation without considering spatial consistency. As a result, these approaches exhibit limited versatility in 3D data representation and shape generation, hindering their ability to generate highly diverse 3D shapes that comply with the specified constraints. In this paper, we introduce a novel spatial-aware 3D shape generation framework that leverages 2D plane representations for enhanced 3D shape modeling. To ensure spatial coherence and reduce memory usage, we incorporate a hybrid shape representation technique that directly learns a continuous signed distance field representation of the 3D shape using orthogonal 2D planes. Additionally, we meticulously enforce spatial correspondences across distinct planes using a transformer-based autoencoder structure, promoting the preservation of spatial relationships in the generated 3D shapes. This yields an algorithm that consistently outperforms state-of-the-art 3D shape generation methods on various tasks, including unconditional shape generation, multi-modal shape completion, single-view reconstruction, and text-to-shape synthesis.

Identifying relations between objects is central to understanding the scene. While several works have been proposed for relation modeling in the image domain, there have been many constraints in the video domain due to challenging dynamics of spatio-temporal interactions (e.g., between which objects are there an interaction? when do relations start and end?). To date, two representative methods have been proposed to tackle Video Visual Relation Detection (VidVRD): segment-based and window-based. We first point out limitations of these methods and propose a novel approach named Temporal Span Proposal Network (TSPN). TSPN tells what to look: it sparsifies relation search space by scoring relationness of object pair, i.e., measuring how probable a relation exist. TSPN tells when to look: it simultaneously predicts start-end timestamps (i.e., temporal spans) and categories of the all possible relations by utilizing full video context. These two designs enable a win-win scenario: it accelerates training by 2X or more than existing methods and achieves competitive performance on two VidVRD benchmarks (ImageNet-VidVDR and VidOR). Moreover, comprehensive ablative experiments demonstrate the effectiveness of our approach. Codes are available at https://github.com/sangminwoo/Temporal-Span-Proposal-Network-VidVRD.

Partial correlations quantify linear association between two variables adjusting for the influence of the remaining variables. They form the backbone for graphical models and are readily obtained from the inverse of the covariance matrix. For compositional data, the covariance structure is specified from log ratios of variables, so unless we try to "open" the data via a normalization, this implies changes in the definition and interpretation of partial correlations. In the present work, we elucidate how results derived by Aitchison (1986) lead to a natural definition of partial correlation that has a number of advantages over current measures of association. For this, we show that the residuals of log-ratios between a variable with a reference, when adjusting for all remaining variables including the reference, are reference-independent. Since the reference itself can be controlled for, correlations between residuals are defined for the variables directly without the necessity to recur to ratios except when specifying which variables are partialled out. Thus, perhaps surprisingly, partial correlations do not have the problems commonly found with measures of pairwise association on compositional data. They are well-defined between two variables, are properly scaled, and allow for negative association. By design, they are subcompositionally incoherent, but they share this property with conventional partial correlations (where results change when adjusting for the influence of fewer variables). We discuss the equivalence with normalization-based approaches whenever the normalizing variables are controlled for. We also discuss the partial variances and correlations we obtain from a previously studied data set of Roman glass cups.

Discovering the underlying relationships among variables from temporal observations has been a longstanding challenge in numerous scientific disciplines, including biology, finance, and climate science. The dynamics of such systems are often best described using continuous-time stochastic processes. Unfortunately, most existing structure learning approaches assume that the underlying process evolves in discrete-time and/or observations occur at regular time intervals. These mismatched assumptions can often lead to incorrect learned structures and models. In this work, we introduce a novel structure learning method, SCOTCH, which combines neural stochastic differential equations (SDE) with variational inference to infer a posterior distribution over possible structures. This continuous-time approach can naturally handle both learning from and predicting observations at arbitrary time points. Theoretically, we establish sufficient conditions for an SDE and SCOTCH to be structurally identifiable, and prove its consistency under infinite data limits. Empirically, we demonstrate that our approach leads to improved structure learning performance on both synthetic and real-world datasets compared to relevant baselines under regular and irregular sampling intervals.

Graphs are ubiquitous structures found in numerous real-world applications, such as drug discovery, recommender systems, and social network analysis. To model graph-structured data, graph neural networks (GNNs) have become a popular tool. However, existing GNN architectures encounter challenges in cross-graph learning where multiple graphs have different feature spaces. To address this, recent approaches introduce text-attributed graphs (TAGs), where each node is associated with a textual description, which can be projected into a unified feature space using textual encoders. While promising, this method relies heavily on the availability of text-attributed graph data, which is difficult to obtain in practice. To bridge this gap, we propose a novel method named Topology-Aware Node description Synthesis (TANS), leveraging large language models (LLMs) to convert existing graphs into text-attributed graphs. The key idea is to integrate topological information into LLMs to explain how graph topology influences node semantics. We evaluate our TANS on text-rich, text-limited, and text-free graphs, demonstrating its applicability. Notably, on text-free graphs, our method significantly outperforms existing approaches that manually design node features, showcasing the potential of LLMs for preprocessing graph-structured data in the absence of textual information. The code and data are available at https://github.com/Zehong-Wang/TANS.

We consider the problem of graph matching, or learning vertex correspondence, between two correlated stochastic block models (SBMs). The graph matching problem arises in various fields, including computer vision, natural language processing and bioinformatics, and in particular, matching graphs with inherent community structure has significance related to de-anonymization of correlated social networks. Compared to the correlated Erdos-Renyi (ER) model, where various efficient algorithms have been developed, among which a few algorithms have been proven to achieve the exact matching with constant edge correlation, no low-order polynomial algorithm has been known to achieve exact matching for the correlated SBMs with constant correlation. In this work, we propose an efficient algorithm for matching graphs with community structure, based on the comparison between partition trees rooted from each vertex, by extending the idea of Mao et al. (2021) to graphs with communities. The partition tree divides the large neighborhoods of each vertex into disjoint subsets using their edge statistics to different communities. Our algorithm is the first low-order polynomial-time algorithm achieving exact matching between two correlated SBMs with high probability in dense graphs.

Evaluating tabular generators remains a challenging problem, as the unique causal structural prior of heterogeneous tabular data does not lend itself to intuitive human inspection. Recent work has introduced structural fidelity as a tabular-specific evaluation dimension to assess whether synthetic data complies with the causal structures of real data. However, existing benchmarks often neglect the interplay between structural fidelity and conventional evaluation dimensions, thus failing to provide a holistic understanding of model performance. Moreover, they are typically limited to toy datasets, as quantifying existing structural fidelity metrics requires access to ground-truth causal structures, which are rarely available for real-world datasets. In this paper, we propose a novel evaluation framework that jointly considers structural fidelity and conventional evaluation dimensions. We introduce a new evaluation metric, global utility, which enables the assessment of structural fidelity even in the absence of ground-truth causal structures. In addition, we present TabStruct, a comprehensive evaluation benchmark offering large-scale quantitative analysis on 13 tabular generators from nine distinct categories, across 29 datasets. Our results demonstrate that global utility provides a task-independent, domain-agnostic lens for tabular generator performance. We release the TabStruct benchmark suite, including all datasets, evaluation pipelines, and raw results. Code is available at https://github.com/SilenceX12138/TabStruct.

Networks have become indispensable and ubiquitous structures in many fields to model the interactions among different entities, such as friendship in social networks or protein interactions in biological graphs. A major challenge is to understand the structure and dynamics of these systems. Although networks evolve through time, most existing graph representation learning methods target only static networks. Whereas approaches have been developed for the modeling of dynamic networks, there is a lack of efficient continuous time dynamic graph representation learning methods that can provide accurate network characterization and visualization in low dimensions while explicitly accounting for prominent network characteristics such as homophily and transitivity. In this paper, we propose the Piecewise-Velocity Model (PiVeM) for the representation of continuous-time dynamic networks. It learns dynamic embeddings in which the temporal evolution of nodes is approximated by piecewise linear interpolations based on a latent distance model with piecewise constant node-specific velocities. The model allows for analytically tractable expressions of the associated Poisson process likelihood with scalable inference invariant to the number of events. We further impose a scalable Kronecker structured Gaussian Process prior to the dynamics accounting for community structure, temporal smoothness, and disentangled (uncorrelated) latent embedding dimensions optimally learned to characterize the network dynamics. We show that PiVeM can successfully represent network structure and dynamics in ultra-low two-dimensional spaces. It outperforms relevant state-of-art methods in downstream tasks such as link prediction. In summary, PiVeM enables easily interpretable dynamic network visualizations and characterizations that can further improve our understanding of the intrinsic dynamics of time-evolving networks.

Leveraging generative Artificial Intelligence (AI), we have transformed a dataset comprising 1,000 scientific papers into an ontological knowledge graph. Through an in-depth structural analysis, we have calculated node degrees, identified communities and connectivities, and evaluated clustering coefficients and betweenness centrality of pivotal nodes, uncovering fascinating knowledge architectures. The graph has an inherently scale-free nature, is highly connected, and can be used for graph reasoning by taking advantage of transitive and isomorphic properties that reveal unprecedented interdisciplinary relationships that can be used to answer queries, identify gaps in knowledge, propose never-before-seen material designs, and predict material behaviors. We compute deep node embeddings for combinatorial node similarity ranking for use in a path sampling strategy links dissimilar concepts that have previously not been related. One comparison revealed structural parallels between biological materials and Beethoven's 9th Symphony, highlighting shared patterns of complexity through isomorphic mapping. In another example, the algorithm proposed a hierarchical mycelium-based composite based on integrating path sampling with principles extracted from Kandinsky's 'Composition VII' painting. The resulting material integrates an innovative set of concepts that include a balance of chaos/order, adjustable porosity, mechanical strength, and complex patterned chemical functionalization. We uncover other isomorphisms across science, technology and art, revealing a nuanced ontology of immanence that reveal a context-dependent heterarchical interplay of constituents. Graph-based generative AI achieves a far higher degree of novelty, explorative capacity, and technical detail, than conventional approaches and establishes a widely useful framework for innovation by revealing hidden connections.

The activations of Facial Action Units (AUs) mutually influence one another. While the relationship between a pair of AUs can be complex and unique, existing approaches fail to specifically and explicitly represent such cues for each pair of AUs in each facial display. This paper proposes an AU relationship modelling approach that deep learns a unique graph to explicitly describe the relationship between each pair of AUs of the target facial display. Our approach first encodes each AU's activation status and its association with other AUs into a node feature. Then, it learns a pair of multi-dimensional edge features to describe multiple task-specific relationship cues between each pair of AUs. During both node and edge feature learning, our approach also considers the influence of the unique facial display on AUs' relationship by taking the full face representation as an input. Experimental results on BP4D and DISFA datasets show that both node and edge feature learning modules provide large performance improvements for CNN and transformer-based backbones, with our best systems achieving the state-of-the-art AU recognition results. Our approach not only has a strong capability in modelling relationship cues for AU recognition but also can be easily incorporated into various backbones. Our PyTorch code is made available.

Spatial understanding is a fundamental aspect of computer vision and integral for human-level reasoning about images, making it an important component for grounded language understanding. While recent text-to-image synthesis (T2I) models have shown unprecedented improvements in photorealism, it is unclear whether they have reliable spatial understanding capabilities. We investigate the ability of T2I models to generate correct spatial relationships among objects and present VISOR, an evaluation metric that captures how accurately the spatial relationship described in text is generated in the image. To benchmark existing models, we introduce a dataset, SR_{2D}, that contains sentences describing two or more objects and the spatial relationships between them. We construct an automated evaluation pipeline to recognize objects and their spatial relationships, and employ it in a large-scale evaluation of T2I models. Our experiments reveal a surprising finding that, although state-of-the-art T2I models exhibit high image quality, they are severely limited in their ability to generate multiple objects or the specified spatial relations between them. Our analyses demonstrate several biases and artifacts of T2I models such as the difficulty with generating multiple objects, a bias towards generating the first object mentioned, spatially inconsistent outputs for equivalent relationships, and a correlation between object co-occurrence and spatial understanding capabilities. We conduct a human study that shows the alignment between VISOR and human judgement about spatial understanding. We offer the SR_{2D} dataset and the VISOR metric to the community in support of T2I reasoning research.

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.

We introduce a novel dataset designed to benchmark the physical and spatial reasoning capabilities of Large Language Models (LLM) based on topology optimization, a method for computing optimal material distributions within a design space under prescribed loads and supports. In this dataset, LLMs are provided with conditions such as 2D boundary, applied forces and supports, and must reason about the resulting optimal material distribution. The dataset includes a variety of tasks, ranging from filling in masked regions within partial structures to predicting complete material distributions. Solving these tasks requires understanding the flow of forces and the required material distribution under given constraints, without access to simulation tools or explicit physical models, challenging models to reason about structural stability and spatial organization. Our dataset targets the evaluation of spatial and physical reasoning abilities in 2D settings, offering a complementary perspective to traditional language and logic benchmarks.

Despite the widespread application of latent factor analysis, existing methods suffer from the following weaknesses: requiring the number of factors to be known, lack of theoretical guarantees for learning the model structure, and nonidentifiability of the parameters due to rotation invariance properties of the likelihood. We address these concerns by proposing a fast correlation thresholding (CT) algorithm that simultaneously learns the number of latent factors and a rotationally identifiable model structure. Our novel approach translates this structure learning problem into the search for so-called independent maximal cliques in a thresholded correlation graph that can be easily constructed from the observed data. Our clique analysis technique scales well up to thousands of variables, while competing methods are not applicable in a reasonable amount of running time. We establish a finite-sample error bound and high-dimensional consistency for the structure learning of our method. Through a series of simulation studies and a real data example, we show that the CT algorithm is an accurate method for learning the structure of factor analysis models and is robust to violations of its assumptions.

Recent advancements in large language models and their multi-modal extensions have demonstrated the effectiveness of unifying generation and understanding through autoregressive next-token prediction. However, despite the critical role of 3D structural generation and understanding ({3D GU}) in AI for science, these tasks have largely evolved independently, with autoregressive methods remaining underexplored. To bridge this gap, we introduce Uni-3DAR, a unified framework that seamlessly integrates {3D GU} tasks via autoregressive prediction. At its core, Uni-3DAR employs a novel hierarchical tokenization that compresses 3D space using an octree, leveraging the inherent sparsity of 3D structures. It then applies an additional tokenization for fine-grained structural details, capturing key attributes such as atom types and precise spatial coordinates in microscopic 3D structures. We further propose two optimizations to enhance efficiency and effectiveness. The first is a two-level subtree compression strategy, which reduces the octree token sequence by up to 8x. The second is a masked next-token prediction mechanism tailored for dynamically varying token positions, significantly boosting model performance. By combining these strategies, Uni-3DAR successfully unifies diverse {3D GU} tasks within a single autoregressive framework. Extensive experiments across multiple microscopic {3D GU} tasks, including molecules, proteins, polymers, and crystals, validate its effectiveness and versatility. Notably, Uni-3DAR surpasses previous state-of-the-art diffusion models by a substantial margin, achieving up to 256\% relative improvement while delivering inference speeds up to 21.8x faster. The code is publicly available at https://github.com/dptech-corp/Uni-3DAR.

Generative models are now used to create a variety of high-quality digital artifacts. Yet their use in designing physical objects has received far less attention. In this paper, we advocate for the construction toy, LEGO, as a platform for developing generative models of sequential assembly. We develop a generative model based on graph-structured neural networks that can learn from human-built structures and produce visually compelling designs. Our code is released at: https://github.com/uoguelph-mlrg/GenerativeLEGO.

Molecular structure recognition is the task of translating a molecular image into its graph structure. Significant variation in drawing styles and conventions exhibited in chemical literature poses a significant challenge for automating this task. In this paper, we propose MolScribe, a novel image-to-graph generation model that explicitly predicts atoms and bonds, along with their geometric layouts, to construct the molecular structure. Our model flexibly incorporates symbolic chemistry constraints to recognize chirality and expand abbreviated structures. We further develop data augmentation strategies to enhance the model robustness against domain shifts. In experiments on both synthetic and realistic molecular images, MolScribe significantly outperforms previous models, achieving 76-93% accuracy on public benchmarks. Chemists can also easily verify MolScribe's prediction, informed by its confidence estimation and atom-level alignment with the input image. MolScribe is publicly available through Python and web interfaces: https://github.com/thomas0809/MolScribe.

3D scene graphs have recently emerged as a powerful high-level representation of 3D environments. A 3D scene graph describes the environment as a layered graph where nodes represent spatial concepts at multiple levels of abstraction and edges represent relations between concepts. While 3D scene graphs can serve as an advanced "mental model" for robots, how to build such a rich representation in real-time is still uncharted territory. This paper describes a real-time Spatial Perception System, a suite of algorithms to build a 3D scene graph from sensor data in real-time. Our first contribution is to develop real-time algorithms to incrementally construct the layers of a scene graph as the robot explores the environment; these algorithms build a local Euclidean Signed Distance Function (ESDF) around the current robot location, extract a topological map of places from the ESDF, and then segment the places into rooms using an approach inspired by community-detection techniques. Our second contribution is to investigate loop closure detection and optimization in 3D scene graphs. We show that 3D scene graphs allow defining hierarchical descriptors for loop closure detection; our descriptors capture statistics across layers in the scene graph, ranging from low-level visual appearance to summary statistics about objects and places. We then propose the first algorithm to optimize a 3D scene graph in response to loop closures; our approach relies on embedded deformation graphs to simultaneously correct all layers of the scene graph. We implement the proposed Spatial Perception System into a architecture named Hydra, that combines fast early and mid-level perception processes with slower high-level perception. We evaluate Hydra on simulated and real data and show it is able to reconstruct 3D scene graphs with an accuracy comparable with batch offline methods despite running online.

Finding meaningful representations and distances of hierarchical data is important in many fields. This paper presents a new method for hierarchical data embedding and distance. Our method relies on combining diffusion geometry, a central approach to manifold learning, and hyperbolic geometry. Specifically, using diffusion geometry, we build multi-scale densities on the data, aimed to reveal their hierarchical structure, and then embed them into a product of hyperbolic spaces. We show theoretically that our embedding and distance recover the underlying hierarchical structure. In addition, we demonstrate the efficacy of the proposed method and its advantages compared to existing methods on graph embedding benchmarks and hierarchical datasets.

High-quality molecular representations are essential for property prediction and molecular design, yet large labeled datasets remain scarce. While self-supervised pretraining on molecular graphs has shown promise, many existing approaches either depend on hand-crafted augmentations or complex generative objectives, and often rely solely on 2D topology, leaving valuable 3D structural information underutilized. To address this gap, we introduce C-FREE (Contrast-Free Representation learning on Ego-nets), a simple framework that integrates 2D graphs with ensembles of 3D conformers. C-FREE learns molecular representations by predicting subgraph embeddings from their complementary neighborhoods in the latent space, using fixed-radius ego-nets as modeling units across different conformers. This design allows us to integrate both geometric and topological information within a hybrid Graph Neural Network (GNN)-Transformer backbone, without negatives, positional encodings, or expensive pre-processing. Pretraining on the GEOM dataset, which provides rich 3D conformational diversity, C-FREE achieves state-of-the-art results on MoleculeNet, surpassing contrastive, generative, and other multimodal self-supervised methods. Fine-tuning across datasets with diverse sizes and molecule types further demonstrates that pretraining transfers effectively to new chemical domains, highlighting the importance of 3D-informed molecular representations.

A comprehensive semantic understanding of a scene is important for many applications - but in what space should diverse semantic information (e.g., objects, scene categories, material types, texture, etc.) be grounded and what should be its structure? Aspiring to have one unified structure that hosts diverse types of semantics, we follow the Scene Graph paradigm in 3D, generating a 3D Scene Graph. Given a 3D mesh and registered panoramic images, we construct a graph that spans the entire building and includes semantics on objects (e.g., class, material, and other attributes), rooms (e.g., scene category, volume, etc.) and cameras (e.g., location, etc.), as well as the relationships among these entities. However, this process is prohibitively labor heavy if done manually. To alleviate this we devise a semi-automatic framework that employs existing detection methods and enhances them using two main constraints: I. framing of query images sampled on panoramas to maximize the performance of 2D detectors, and II. multi-view consistency enforcement across 2D detections that originate in different camera locations.

With the increasing prevalence of graph-structured data, multi-view graph clustering has been widely used in various downstream applications. Existing approaches primarily rely on a unified message passing mechanism, which significantly enhances clustering performance. Nevertheless, this mechanism limits its applicability to heterophilous situations, as it is fundamentally predicated on the assumption of homophily, i.e., the connected nodes often belong to the same class. In reality, this assumption does not always hold; a moderately or even mildly homophilous graph is more common than a fully homophilous one due to inevitable heterophilous information in the graph. To address this issue, in this paper, we propose a novel SiMilarity-enhanced Homophily for Multi-view Heterophilous Graph Clustering (SMHGC) approach. By analyzing the relationship between similarity and graph homophily, we propose to enhance the homophily by introducing three similarity terms, i.e., neighbor pattern similarity, node feature similarity, and multi-view global similarity, in a label-free manner. Then, a consensus-based inter- and intra-view fusion paradigm is proposed to fuse the improved homophilous graph from different views and utilize them for clustering. The state-of-the-art experimental results on both multi-view heterophilous and homophilous datasets collectively demonstrate the strong capacity of similarity for unsupervised multi-view heterophilous graph learning. Additionally, the consistent performance across semi-synthetic datasets with varying levels of homophily serves as further evidence of SMHGC's resilience to heterophily.

Large language models (LLMs) have demonstrated remarkable success across a wide range of tasks; however, they still encounter challenges in reasoning tasks that require understanding and inferring relationships between distinct pieces of information within text sequences. This challenge is particularly pronounced in tasks involving multi-step processes, such as logical reasoning and multi-hop question answering, where understanding implicit relationships between entities and leveraging multi-hop connections in the given context are crucial. Graphs, as fundamental data structures, explicitly represent pairwise relationships between entities, thereby offering the potential to enhance LLMs' reasoning capabilities. External graphs have proven effective in supporting LLMs across multiple tasks. However, in many reasoning tasks, no pre-existing graph structure is provided. Can we structure implicit knowledge derived from context into graphs to assist LLMs in reasoning? In this paper, we propose Reasoning with Graphs (RwG) by first constructing explicit graphs from the context and then leveraging these graphs to enhance LLM reasoning performance on reasoning tasks. Extensive experiments demonstrate the effectiveness of the proposed method in improving both logical reasoning and multi-hop question answering tasks.

Random walks are widely used for mining networks due to the computational efficiency of computing them. For instance, graph representation learning learns a d-dimensional embedding space, so that the nodes that tend to co-occur on random walks (a proxy of being in the same network neighborhood) are close in the embedding space. Specific local network topology (i.e., structure) influences the co-occurrence of nodes on random walks, so random walks of limited length capture only partial topological information, hence diminishing the performance of downstream methods. We explicitly capture all topological neighborhood information and improve performance by introducing orbit adjacencies that quantify the adjacencies of two nodes as co-occurring on a given pair of graphlet orbits, which are symmetric positions on graphlets (small, connected, non-isomorphic, induced subgraphs of a large network). Importantly, we mathematically prove that random walks on up to k nodes capture only a subset of all the possible orbit adjacencies for up to k-node graphlets. Furthermore, we enable orbit adjacency-based analysis of networks by developing an efficient GRaphlet-orbit ADjacency COunter (GRADCO), which exhaustively computes all 28 orbit adjacency matrices for up to four-node graphlets. Note that four-node graphlets suffice, because real networks are usually small-world. In large networks on around 20,000 nodes, GRADCOcomputesthe28matricesinminutes. Onsixrealnetworksfromvarious domains, we compare the performance of node-label predictors obtained by using the network embeddings based on our orbit adjacencies to those based on random walks. We find that orbit adjacencies, which include those unseen by random walks, outperform random walk-based adjacencies, demonstrating the importance of the inclusion of the topological neighborhood information that is unseen by random walks.

Graph generation is a critical task in numerous domains, including molecular design and social network analysis, due to its ability to model complex relationships and structured data. While most modern graph generative models utilize adjacency matrix representations, this work revisits an alternative approach that represents graphs as sequences of node set and edge set. We advocate for this approach due to its efficient encoding of graphs and propose a novel representation. Based on this representation, we introduce the Graph Generative Pre-trained Transformer (G2PT), an auto-regressive model that learns graph structures via next-token prediction. To further exploit G2PT's capabilities as a general-purpose foundation model, we explore fine-tuning strategies for two downstream applications: goal-oriented generation and graph property prediction. We conduct extensive experiments across multiple datasets. Results indicate that G2PT achieves superior generative performance on both generic graph and molecule datasets. Furthermore, G2PT exhibits strong adaptability and versatility in downstream tasks from molecular design to property prediction.

Tangles were originally introduced as a concept to formalize regions of high connectivity in graphs. In recent years, they have also been discovered as a link between structural graph theory and data science: when interpreting similarity in data sets as connectivity between points, finding clusters in the data essentially amounts to finding tangles in the underlying graphs. This paper further explores the potential of tangles in data sets as a means for a formal study of clusters. Real-world data often follow a normal distribution. Accounting for this, we develop a quantitative theory of tangles in data sets drawn from Gaussian mixtures. To this end, we equip the data with a graph structure that models similarity between the points and allows us to apply tangle theory to the data. We provide explicit conditions under which tangles associated with the marginal Gaussian distributions exist asymptotically almost surely. This can be considered as a sufficient formal criterion for the separabability of clusters in the data.

Articulated 3D object generation is fundamental for creating realistic, functional, and interactable virtual assets which are not simply static. We introduce MeshArt, a hierarchical transformer-based approach to generate articulated 3D meshes with clean, compact geometry, reminiscent of human-crafted 3D models. We approach articulated mesh generation in a part-by-part fashion across two stages. First, we generate a high-level articulation-aware object structure; then, based on this structural information, we synthesize each part's mesh faces. Key to our approach is modeling both articulation structures and part meshes as sequences of quantized triangle embeddings, leading to a unified hierarchical framework with transformers for autoregressive generation. Object part structures are first generated as their bounding primitives and articulation modes; a second transformer, guided by these articulation structures, then generates each part's mesh triangles. To ensure coherency among generated parts, we introduce structure-guided conditioning that also incorporates local part mesh connectivity. MeshArt shows significant improvements over state of the art, with 57.1% improvement in structure coverage and a 209-point improvement in mesh generation FID.

Deep generative models have recently achieved superior performance in 3D molecule generation. Most of them first generate atoms and then add chemical bonds based on the generated atoms in a post-processing manner. However, there might be no corresponding bond solution for the temporally generated atoms as their locations are generated without considering potential bonds. We define this problem as the atom-bond inconsistency problem and claim it is the main reason for current approaches to generating unrealistic 3D molecules. To overcome this problem, we propose a new diffusion model called MolDiff which can generate atoms and bonds simultaneously while still maintaining their consistency by explicitly modeling the dependence between their relationships. We evaluated the generation ability of our proposed model and the quality of the generated molecules using criteria related to both geometry and chemical properties. The empirical studies showed that our model outperforms previous approaches, achieving a three-fold improvement in success rate and generating molecules with significantly better quality.

Generating 3D models lies at the core of computer graphics and has been the focus of decades of research. With the emergence of advanced neural representations and generative models, the field of 3D content generation is developing rapidly, enabling the creation of increasingly high-quality and diverse 3D models. The rapid growth of this field makes it difficult to stay abreast of all recent developments. In this survey, we aim to introduce the fundamental methodologies of 3D generation methods and establish a structured roadmap, encompassing 3D representation, generation methods, datasets, and corresponding applications. Specifically, we introduce the 3D representations that serve as the backbone for 3D generation. Furthermore, we provide a comprehensive overview of the rapidly growing literature on generation methods, categorized by the type of algorithmic paradigms, including feedforward generation, optimization-based generation, procedural generation, and generative novel view synthesis. Lastly, we discuss available datasets, applications, and open challenges. We hope this survey will help readers explore this exciting topic and foster further advancements in the field of 3D content generation.

Representational analysis explores how input data of a neural system are encoded in high dimensional spaces of its distributed neural activations, and how we can compare different systems, for instance, artificial neural networks and brains, on those grounds. While existing methods offer important insights, they typically do not account for local intrinsic geometrical properties within the high-dimensional representation spaces. To go beyond these limitations, we explore Ollivier-Ricci curvature and Ricci flow as tools to study the alignment of representations between humans and artificial neural systems on a geometric level. As a proof-of-principle study, we compared the representations of face stimuli between VGG-Face, a human-aligned version of VGG-Face, and corresponding human similarity judgments from a large online study. Using this discrete geometric framework, we were able to identify local structural similarities and differences by examining the distributions of node and edge curvature and higher-level properties by detecting and comparing community structure in the representational graphs.

Text-attributed graphs are widely used across domains, offering rich opportunities for zero-shot learning via graph-text alignment. However, existing methods struggle with tasks requiring fine-grained pattern recognition, particularly on heterophilic graphs. Through empirical and theoretical analysis, we identify an over-abstraction problem: current approaches operate at excessively large hyperbolic radii, compressing multi-scale structural information into uniform high-level abstractions. This abstraction-induced information loss obscures critical local patterns essential for accurate predictions. By analyzing embeddings in hyperbolic space, we demonstrate that optimal graph learning requires faithful preservation of fine-grained structural details, better retained by representations positioned closer to the origin. To address this, we propose H4G, a framework that systematically reduces embedding radii using learnable block-diagonal scaling matrices and M\"obius matrix multiplication. This approach restores access to fine-grained patterns while maintaining global receptive ability with minimal computational overhead. Experiments show H4G achieves state-of-the-art zero-shot performance with 12.8\% improvement on heterophilic graphs and 8.4\% on homophilic graphs, confirming that radius reduction enables faithful multi-scale representation for advancing zero-shot graph learning.

Recent research has evidenced the significant potentials of Large Language Models (LLMs) in handling challenging tasks within 3D scenes. However, current models are constrained to addressing object-centric tasks, where each question-answer pair focuses solely on an individual object. In real-world applications, users may pose queries involving multiple objects or expect for answers that precisely reference various objects. We introduce the use of object identifiers to freely reference objects during a conversation. While this solution appears straightforward, it presents two main challenges: 1) How to establish a reliable one-to-one correspondence between each object and its identifier? 2) How to incorporate complex spatial relationships among dozens of objects into the embedding space of the LLM? To address these challenges, we propose a two-stage alignment method, which involves learning an attribute-aware token and a relation-aware token for each object. These tokens capture the object's attributes and spatial relationships with surrounding objects in the 3D scene. Once the alignment is established, we can fine-tune our model on various downstream tasks using instruction tuning. Experiments conducted on traditional datasets like ScanQA, ScanRefer, and Nr3D/Sr3D showcase the effectiveness of our proposed method. Additionally, we create a 3D scene captioning dataset annotated with rich object identifiers, with the assistant of GPT-4. This dataset aims to further explore the capability of object identifiers in effective object referencing and precise scene understanding.

Computational methods that operate on three-dimensional molecular structure have the potential to solve important questions in biology and chemistry. In particular, deep neural networks have gained significant attention, but their widespread adoption in the biomolecular domain has been limited by a lack of either systematic performance benchmarks or a unified toolkit for interacting with molecular data. To address this, we present ATOM3D, a collection of both novel and existing benchmark datasets spanning several key classes of biomolecules. We implement several classes of three-dimensional molecular learning methods for each of these tasks and show that they consistently improve performance relative to methods based on one- and two-dimensional representations. The specific choice of architecture proves to be critical for performance, with three-dimensional convolutional networks excelling at tasks involving complex geometries, graph networks performing well on systems requiring detailed positional information, and the more recently developed equivariant networks showing significant promise. Our results indicate that many molecular problems stand to gain from three-dimensional molecular learning, and that there is potential for improvement on many tasks which remain underexplored. To lower the barrier to entry and facilitate further developments in the field, we also provide a comprehensive suite of tools for dataset processing, model training, and evaluation in our open-source atom3d Python package. All datasets are available for download from https://www.atom3d.ai .

Machine learning (ML) is increasingly used in structural engineering and design, yet its broader adoption is hampered by the lack of openly accessible datasets of structural systems. We introduce BridgeNet, a publicly available graph-based dataset of 20,000 form-found bridge structures aimed at enabling Graph ML and multi-modal learning in the context of conceptual structural design. Each datapoint consists of (i) a pin-jointed equilibrium wireframe model generated with the Combinatorial Equilibrium Modeling (CEM) form-finding method, (ii) a volumetric 3D mesh obtained through force-informed materialization, and (iii) rendered images from two canonical camera angles. The resulting dataset is modality-rich and application-agnostic, supporting tasks such as CEM-specific edge classification and parameter inference, surrogate modeling of form-finding, cross-modal reconstruction between graphs, meshes and images, and generative structural design. BridgeNet addresses a key bottleneck in data-driven applications for structural engineering and design by providing a dataset that facilitates the development of new ML-based approaches for equilibrium bridge structures.

Attention mechanisms are critical to the success of large language models (LLMs), driving significant advancements in multiple fields. However, for graph-structured data, which requires emphasis on topological connections, they fall short compared to message-passing mechanisms on fixed links, such as those employed by Graph Neural Networks (GNNs). This raises a question: ``Does attention fail for graphs in natural language settings?'' Motivated by these observations, we embarked on an empirical study from the perspective of attention mechanisms to explore how LLMs process graph-structured data. The goal is to gain deeper insights into the attention behavior of LLMs over graph structures. We uncovered unique phenomena regarding how LLMs apply attention to graph-structured data and analyzed these findings to improve the modeling of such data by LLMs. The primary findings of our research are: 1) While LLMs can recognize graph data and capture text-node interactions, they struggle to model inter-node relationships within graph structures due to inherent architectural constraints. 2) The attention distribution of LLMs across graph nodes does not align with ideal structural patterns, indicating a failure to adapt to graph topology nuances. 3) Neither fully connected attention nor fixed connectivity is optimal; each has specific limitations in its application scenarios. Instead, intermediate-state attention windows improve LLM training performance and seamlessly transition to fully connected windows during inference. Source code: https://github.com/millioniron/LLM_exploration{LLM4Exploration}

In recent years, 3D scene graphs have emerged as a powerful world representation, offering both geometric accuracy and semantic richness. Combining 3D scene graphs with large language models enables robots to reason, plan, and navigate in complex human-centered environments. However, current approaches for constructing 3D scene graphs are semantically limited to a predefined set of relationships, and their serialization in large environments can easily exceed an LLM's context window. We introduce KeySG, a framework that represents 3D scenes as a hierarchical graph consisting of floors, rooms, objects, and functional elements, where nodes are augmented with multi-modal information extracted from keyframes selected to optimize geometric and visual coverage. The keyframes allow us to efficiently leverage VLM to extract scene information, alleviating the need to explicitly model relationship edges between objects, enabling more general, task-agnostic reasoning and planning. Our approach can process complex and ambiguous queries while mitigating the scalability issues associated with large scene graphs by utilizing a hierarchical retrieval-augmented generation (RAG) pipeline to extract relevant context from the graph. Evaluated across four distinct benchmarks -- including 3D object segmentation and complex query retrieval -- KeySG outperforms prior approaches on most metrics, demonstrating its superior semantic richness and efficiency.

Despite their exceptional generative abilities, large text-to-image diffusion models, much like skilled but careless artists, often struggle with accurately depicting visual relationships between objects. This issue, as we uncover through careful analysis, arises from a misaligned text encoder that struggles to interpret specific relationships and differentiate the logical order of associated objects. To resolve this, we introduce a novel task termed Relation Rectification, aiming to refine the model to accurately represent a given relationship it initially fails to generate. To address this, we propose an innovative solution utilizing a Heterogeneous Graph Convolutional Network (HGCN). It models the directional relationships between relation terms and corresponding objects within the input prompts. Specifically, we optimize the HGCN on a pair of prompts with identical relational words but reversed object orders, supplemented by a few reference images. The lightweight HGCN adjusts the text embeddings generated by the text encoder, ensuring the accurate reflection of the textual relation in the embedding space. Crucially, our method retains the parameters of the text encoder and diffusion model, preserving the model's robust performance on unrelated descriptions. We validated our approach on a newly curated dataset of diverse relational data, demonstrating both quantitative and qualitative enhancements in generating images with precise visual relations. Project page: https://wuyinwei-hah.github.io/rrnet.github.io/.

Molecular pretrained representations (MPR) has emerged as a powerful approach for addressing the challenge of limited supervised data in applications such as drug discovery and material design. While early MPR methods relied on 1D sequences and 2D graphs, recent advancements have incorporated 3D conformational information to capture rich atomic interactions. However, these prior models treat molecules merely as discrete atom sets, overlooking the space surrounding them. We argue from a physical perspective that only modeling these discrete points is insufficient. We first present a simple yet insightful observation: naively adding randomly sampled virtual points beyond atoms can surprisingly enhance MPR performance. In light of this, we propose a principled framework that incorporates the entire 3D space spanned by molecules. We implement the framework via a novel Transformer-based architecture, dubbed SpaceFormer, with three key components: (1) grid-based space discretization; (2) grid sampling/merging; and (3) efficient 3D positional encoding. Extensive experiments show that SpaceFormer significantly outperforms previous 3D MPR models across various downstream tasks with limited data, validating the benefit of leveraging the additional 3D space beyond atoms in MPR models.

Recent studies on AMR-to-text generation often formalize the task as a sequence-to-sequence (seq2seq) learning problem by converting an Abstract Meaning Representation (AMR) graph into a word sequence. Graph structures are further modeled into the seq2seq framework in order to utilize the structural information in the AMR graphs. However, previous approaches only consider the relations between directly connected concepts while ignoring the rich structure in AMR graphs. In this paper we eliminate such a strong limitation and propose a novel structure-aware self-attention approach to better modeling the relations between indirectly connected concepts in the state-of-the-art seq2seq model, i.e., the Transformer. In particular, a few different methods are explored to learn structural representations between two concepts. Experimental results on English AMR benchmark datasets show that our approach significantly outperforms the state of the art with 29.66 and 31.82 BLEU scores on LDC2015E86 and LDC2017T10, respectively. To the best of our knowledge, these are the best results achieved so far by supervised models on the benchmarks.

Structural and Positional Encodings can significantly improve the performance of Graph Neural Networks in downstream tasks. Recent literature has begun to systematically investigate differences in the structural properties that these approaches encode, as well as performance trade-offs between them. However, the question of which structural properties yield the most effective encoding remains open. In this paper, we investigate this question from a geometric perspective. We propose a novel structural encoding based on discrete Ricci curvature (Local Curvature Profiles, short LCP) and show that it significantly outperforms existing encoding approaches. We further show that combining local structural encodings, such as LCP, with global positional encodings improves downstream performance, suggesting that they capture complementary geometric information. Finally, we compare different encoding types with (curvature-based) rewiring techniques. Rewiring has recently received a surge of interest due to its ability to improve the performance of Graph Neural Networks by mitigating over-smoothing and over-squashing effects. Our results suggest that utilizing curvature information for structural encodings delivers significantly larger performance increases than rewiring.

The capability to learn latent representations plays a key role in the effectiveness of recent machine learning methods. An active frontier in representation learning is understanding representations for combinatorial structures which may not admit well-behaved local neighborhoods or distance functions. For example, for polygons, slightly perturbing vertex locations might lead to significant changes in their combinatorial structure and may even lead to invalid polygons. In this paper, we investigate representations to capture the underlying combinatorial structures of polygons. Specifically, we study the open problem of Visibility Reconstruction: Given a visibility graph G, construct a polygon P whose visibility graph is G. We introduce VisDiff, a novel diffusion-based approach to reconstruct a polygon from its given visibility graph G. Our method first estimates the signed distance function (SDF) of P from G. Afterwards, it extracts ordered vertex locations that have the pairwise visibility relationship given by the edges of G. Our main insight is that going through the SDF significantly improves learning for reconstruction. In order to train VisDiff, we make two main contributions: (1) We design novel loss components for computing the visibility in a differentiable manner and (2) create a carefully curated dataset. We use this dataset to benchmark our method and achieve 21% improvement in F1-Score over standard methods. We also demonstrate effective generalization to out-of-distribution polygon types and show that learning a generative model allows us to sample the set of polygons with a given visibility graph. Finally, we extend our method to the related combinatorial problem of reconstruction from a triangulation. We achieve 95% classification accuracy of triangulation edges and a 4% improvement in Chamfer distance compared to current architectures.

The manifold hypothesis, which assumes that data lies on or close to an unknown manifold of low intrinsic dimension, is a staple of modern machine learning research. However, recent work has shown that real-world data exhibits distinct non-manifold structures, i.e. singularities, that can lead to erroneous findings. Detecting such singularities is therefore crucial as a precursor to interpolation and inference tasks. We address this issue by developing a topological framework that (i) quantifies the local intrinsic dimension, and (ii) yields a Euclidicity score for assessing the 'manifoldness' of a point along multiple scales. Our approach identifies singularities of complex spaces, while also capturing singular structures and local geometric complexity in image data.

The structure of topology underpins much of the research on performance and robustness, yet available topology data are typically scarce, necessitating the generation of synthetic graphs with desired properties for testing or release. Prior diffusion-based approaches either embed conditions into the diffusion model, requiring retraining for each attribute and hindering real-time applicability, or use classifier-based guidance post-training, which does not account for topology scale and practical constraints. In this paper, we show from a discrete perspective that gradients from a pre-trained graph-level classifier can be incorporated into the discrete reverse diffusion posterior to steer generation toward specified structural properties. Based on this insight, we propose Classifier-guided Conditional Topology Generation with Persistent Homology (CoPHo), which builds a persistent homology filtration over intermediate graphs and interprets features as guidance signals that steer generation toward the desired properties at each denoising step. Experiments on four generic/network datasets demonstrate that CoPHo outperforms existing methods at matching target metrics, and we further validate its transferability on the QM9 molecular dataset.

Graph Neural Networks operate through bottom-up message-passing, fundamentally differing from human visual perception, which intuitively captures global structures first. We investigate the underappreciated potential of vision models for graph understanding, finding they achieve performance comparable to GNNs on established benchmarks while exhibiting distinctly different learning patterns. These divergent behaviors, combined with limitations of existing benchmarks that conflate domain features with topological understanding, motivate our introduction of GraphAbstract. This benchmark evaluates models' ability to perceive global graph properties as humans do: recognizing organizational archetypes, detecting symmetry, sensing connectivity strength, and identifying critical elements. Our results reveal that vision models significantly outperform GNNs on tasks requiring holistic structural understanding and maintain generalizability across varying graph scales, while GNNs struggle with global pattern abstraction and degrade with increasing graph size. This work demonstrates that vision models possess remarkable yet underutilized capabilities for graph structural understanding, particularly for problems requiring global topological awareness and scale-invariant reasoning. These findings open new avenues to leverage this underappreciated potential for developing more effective graph foundation models for tasks dominated by holistic pattern recognition.

Real-world databases are predominantly relational, comprising multiple interlinked tables that contain complex structural and statistical dependencies. Learning generative models on relational data has shown great promise in generating synthetic data and imputing missing values. However, existing methods often struggle to capture this complexity, typically reducing relational data to conditionally generated flat tables and imposing limiting structural assumptions. To address these limitations, we introduce RelDiff, a novel diffusion generative model that synthesizes complete relational databases by explicitly modeling their foreign key graph structure. RelDiff combines a joint graph-conditioned diffusion process across all tables for attribute synthesis, and a 2K+SBM graph generator based on the Stochastic Block Model for structure generation. The decomposition of graph structure and relational attributes ensures both high fidelity and referential integrity, both of which are crucial aspects of synthetic relational database generation. Experiments on 11 benchmark datasets demonstrate that RelDiff consistently outperforms prior methods in producing realistic and coherent synthetic relational databases. Code is available at https://github.com/ValterH/RelDiff.

Aiming at better representing multivariate relationships, this paper investigates a motif dimensional framework for higher-order graph learning. The graph learning effectiveness can be improved through OFFER. The proposed framework mainly aims at accelerating and improving higher-order graph learning results. We apply the acceleration procedure from the dimensional of network motifs. Specifically, the refined degree for nodes and edges are conducted in two stages: (1) employ motif degree of nodes to refine the adjacency matrix of the network; and (2) employ motif degree of edges to refine the transition probability matrix in the learning process. In order to assess the efficiency of the proposed framework, four popular network representation algorithms are modified and examined. By evaluating the performance of OFFER, both link prediction results and clustering results demonstrate that the graph representation learning algorithms enhanced with OFFER consistently outperform the original algorithms with higher efficiency.

In this report, we introduce UltraShape 1.0, a scalable 3D diffusion framework for high-fidelity 3D geometry generation. The proposed approach adopts a two-stage generation pipeline: a coarse global structure is first synthesized and then refined to produce detailed, high-quality geometry. To support reliable 3D generation, we develop a comprehensive data processing pipeline that includes a novel watertight processing method and high-quality data filtering. This pipeline improves the geometric quality of publicly available 3D datasets by removing low-quality samples, filling holes, and thickening thin structures, while preserving fine-grained geometric details. To enable fine-grained geometry refinement, we decouple spatial localization from geometric detail synthesis in the diffusion process. We achieve this by performing voxel-based refinement at fixed spatial locations, where voxel queries derived from coarse geometry provide explicit positional anchors encoded via RoPE, allowing the diffusion model to focus on synthesizing local geometric details within a reduced, structured solution space. Our model is trained exclusively on publicly available 3D datasets, achieving strong geometric quality despite limited training resources. Extensive evaluations demonstrate that UltraShape 1.0 performs competitively with existing open-source methods in both data processing quality and geometry generation. All code and trained models will be released to support future research.

Visual spatial description (VSD) aims to generate texts that describe the spatial relations of the given objects within images. Existing VSD work merely models the 2D geometrical vision features, thus inevitably falling prey to the problem of skewed spatial understanding of target objects. In this work, we investigate the incorporation of 3D scene features for VSD. With an external 3D scene extractor, we obtain the 3D objects and scene features for input images, based on which we construct a target object-centered 3D spatial scene graph (Go3D-S2G), such that we model the spatial semantics of target objects within the holistic 3D scenes. Besides, we propose a scene subgraph selecting mechanism, sampling topologically-diverse subgraphs from Go3D-S2G, where the diverse local structure features are navigated to yield spatially-diversified text generation. Experimental results on two VSD datasets demonstrate that our framework outperforms the baselines significantly, especially improving on the cases with complex visual spatial relations. Meanwhile, our method can produce more spatially-diversified generation. Code is available at https://github.com/zhaoyucs/VSD.

Most real-world graphs exhibit a hierarchical structure, which is often overlooked by existing graph generation methods. To address this limitation, we propose a novel graph generative network that captures the hierarchical nature of graphs and successively generates the graph sub-structures in a coarse-to-fine fashion. At each level of hierarchy, this model generates communities in parallel, followed by the prediction of cross-edges between communities using separate neural networks. This modular approach enables scalable graph generation for large and complex graphs. Moreover, we model the output distribution of edges in the hierarchical graph with a multinomial distribution and derive a recursive factorization for this distribution. This enables us to generate community graphs with integer-valued edge weights in an autoregressive manner. Empirical studies demonstrate the effectiveness and scalability of our proposed generative model, achieving state-of-the-art performance in terms of graph quality across various benchmark datasets. The code is available at https://github.com/Karami-m/HiGen_main.

As pretrained text-to-image diffusion models become increasingly powerful, recent efforts have been made to distill knowledge from these text-to-image pretrained models for optimizing a text-guided 3D model. Most of the existing methods generate a holistic 3D model from a plain text input. This can be problematic when the text describes a complex scene with multiple objects, because the vectorized text embeddings are inherently unable to capture a complex description with multiple entities and relationships. Holistic 3D modeling of the entire scene further prevents accurate grounding of text entities and concepts. To address this limitation, we propose GraphDreamer, a novel framework to generate compositional 3D scenes from scene graphs, where objects are represented as nodes and their interactions as edges. By exploiting node and edge information in scene graphs, our method makes better use of the pretrained text-to-image diffusion model and is able to fully disentangle different objects without image-level supervision. To facilitate modeling of object-wise relationships, we use signed distance fields as representation and impose a constraint to avoid inter-penetration of objects. To avoid manual scene graph creation, we design a text prompt for ChatGPT to generate scene graphs based on text inputs. We conduct both qualitative and quantitative experiments to validate the effectiveness of GraphDreamer in generating high-fidelity compositional 3D scenes with disentangled object entities.

Mapping is crucial for spatial reasoning, planning and robot navigation. Existing approaches range from metric, which require precise geometry-based optimization, to purely topological, where image-as-node based graphs lack explicit object-level reasoning and interconnectivity. In this paper, we propose a novel topological representation of an environment based on "image segments", which are semantically meaningful and open-vocabulary queryable, conferring several advantages over previous works based on pixel-level features. Unlike 3D scene graphs, we create a purely topological graph with segments as nodes, where edges are formed by a) associating segment-level descriptors between pairs of consecutive images and b) connecting neighboring segments within an image using their pixel centroids. This unveils a "continuous sense of a place", defined by inter-image persistence of segments along with their intra-image neighbours. It further enables us to represent and update segment-level descriptors through neighborhood aggregation using graph convolution layers, which improves robot localization based on segment-level retrieval. Using real-world data, we show how our proposed map representation can be used to i) generate navigation plans in the form of "hops over segments" and ii) search for target objects using natural language queries describing spatial relations of objects. Furthermore, we quantitatively analyze data association at the segment level, which underpins inter-image connectivity during mapping and segment-level localization when revisiting the same place. Finally, we show preliminary trials on segment-level `hopping' based zero-shot real-world navigation. Project page with supplementary details: oravus.github.io/RoboHop/

Generating graph-structured data requires learning the underlying distribution of graphs. Yet, this is a challenging problem, and the previous graph generative methods either fail to capture the permutation-invariance property of graphs or cannot sufficiently model the complex dependency between nodes and edges, which is crucial for generating real-world graphs such as molecules. To overcome such limitations, we propose a novel score-based generative model for graphs with a continuous-time framework. Specifically, we propose a new graph diffusion process that models the joint distribution of the nodes and edges through a system of stochastic differential equations (SDEs). Then, we derive novel score matching objectives tailored for the proposed diffusion process to estimate the gradient of the joint log-density with respect to each component, and introduce a new solver for the system of SDEs to efficiently sample from the reverse diffusion process. We validate our graph generation method on diverse datasets, on which it either achieves significantly superior or competitive performance to the baselines. Further analysis shows that our method is able to generate molecules that lie close to the training distribution yet do not violate the chemical valency rule, demonstrating the effectiveness of the system of SDEs in modeling the node-edge relationships. Our code is available at https://github.com/harryjo97/GDSS.

When humans and robotic agents coexist in an environment, scene understanding becomes crucial for the agents to carry out various downstream tasks like navigation and planning. Hence, an agent must be capable of localizing and identifying actions performed by the human. Current research lacks reliable datasets for performing scene understanding within indoor environments where humans are also a part of the scene. Scene Graphs enable us to generate a structured representation of a scene or an image to perform visual scene understanding. To tackle this, we present HOIverse a synthetic dataset at the intersection of scene graph and human-object interaction, consisting of accurate and dense relationship ground truths between humans and surrounding objects along with corresponding RGB images, segmentation masks, depth images and human keypoints. We compute parametric relations between various pairs of objects and human-object pairs, resulting in an accurate and unambiguous relation definitions. In addition, we benchmark our dataset on state-of-the-art scene graph generation models to predict parametric relations and human-object interactions. Through this dataset, we aim to accelerate research in the field of scene understanding involving people.

Knowledge Graphs, such as Wikidata, comprise structural and textual knowledge in order to represent knowledge. For each of the two modalities dedicated approaches for graph embedding and language models learn patterns that allow for predicting novel structural knowledge. Few approaches have integrated learning and inference with both modalities and these existing ones could only partially exploit the interaction of structural and textual knowledge. In our approach, we build on existing strong representations of single modalities and we use hypercomplex algebra to represent both, (i), single-modality embedding as well as, (ii), the interaction between different modalities and their complementary means of knowledge representation. More specifically, we suggest Dihedron and Quaternion representations of 4D hypercomplex numbers to integrate four modalities namely structural knowledge graph embedding, word-level representations (e.g.\ Word2vec, Fasttext), sentence-level representations (Sentence transformer), and document-level representations (sentence transformer, Doc2vec). Our unified vector representation scores the plausibility of labelled edges via Hamilton and Dihedron products, thus modeling pairwise interactions between different modalities. Extensive experimental evaluation on standard benchmark datasets shows the superiority of our two new models using abundant textual information besides sparse structural knowledge to enhance performance in link prediction tasks.

The integration of molecule and language has garnered increasing attention in molecular science. Recent advancements in Language Models (LMs) have demonstrated potential for the comprehensive modeling of molecule and language. However, existing works exhibit notable limitations. Most existing works overlook the modeling of 3D information, which is crucial for understanding molecular structures and also functions. While some attempts have been made to leverage external structure encoding modules to inject the 3D molecular information into LMs, there exist obvious difficulties that hinder the integration of molecular structure and language text, such as modality alignment and separate tuning. To bridge this gap, we propose 3D-MolT5, a unified framework designed to model both 1D molecular sequence and 3D molecular structure. The key innovation lies in our methodology for mapping fine-grained 3D substructure representations (based on 3D molecular fingerprints) to a specialized 3D token vocabulary for 3D-MolT5. This 3D structure token vocabulary enables the seamless combination of 1D sequence and 3D structure representations in a tokenized format, allowing 3D-MolT5 to encode molecular sequence (SELFIES), molecular structure, and text sequences within a unified architecture. Alongside, we further introduce 1D and 3D joint pre-training to enhance the model's comprehension of these diverse modalities in a joint representation space and better generalize to various tasks for our foundation model. Through instruction tuning on multiple downstream datasets, our proposed 3D-MolT5 shows superior performance than existing methods in molecular property prediction, molecule captioning, and text-based molecule generation tasks. Our code will be available on GitHub soon.

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.

Graphic design is essential for visual communication with layouts being fundamental to composing attractive designs. Layout generation differs from pixel-level image synthesis and is unique in terms of the requirement of mutual relations among the desired components. We propose a method for design layout generation that can satisfy user-specified constraints. The proposed neural design network (NDN) consists of three modules. The first module predicts a graph with complete relations from a graph with user-specified relations. The second module generates a layout from the predicted graph. Finally, the third module fine-tunes the predicted layout. Quantitative and qualitative experiments demonstrate that the generated layouts are visually similar to real design layouts. We also construct real designs based on predicted layouts for a better understanding of the visual quality. Finally, we demonstrate a practical application on layout recommendation.

We address 2D floorplan reconstruction from 3D scans. Existing approaches typically employ heuristically designed multi-stage pipelines. Instead, we formulate floorplan reconstruction as a single-stage structured prediction task: find a variable-size set of polygons, which in turn are variable-length sequences of ordered vertices. To solve it we develop a novel Transformer architecture that generates polygons of multiple rooms in parallel, in a holistic manner without hand-crafted intermediate stages. The model features two-level queries for polygons and corners, and includes polygon matching to make the network end-to-end trainable. Our method achieves a new state-of-the-art for two challenging datasets, Structured3D and SceneCAD, along with significantly faster inference than previous methods. Moreover, it can readily be extended to predict additional information, i.e., semantic room types and architectural elements like doors and windows. Our code and models are available at: https://github.com/ywyue/RoomFormer.

Text-Attributed Graphs (TAGs) enhance graph structures with natural language descriptions, enabling detailed representation of data and their relationships across a broad spectrum of real-world scenarios. Despite the potential for deeper insights, existing TAG representation learning primarily relies on supervised methods, necessitating extensive labeled data and limiting applicability across diverse contexts. This paper introduces a new self-supervised learning framework, Text-And-Graph Multi-View Alignment (TAGA), which overcomes these constraints by integrating TAGs' structural and semantic dimensions. TAGA constructs two complementary views: Text-of-Graph view, which organizes node texts into structured documents based on graph topology, and the Graph-of-Text view, which converts textual nodes and connections into graph data. By aligning representations from both views, TAGA captures joint textual and structural information. In addition, a novel structure-preserving random walk algorithm is proposed for efficient training on large-sized TAGs. Our framework demonstrates strong performance in zero-shot and few-shot scenarios across eight real-world datasets.

Deep learning has revolutionized many machine learning tasks in recent years, ranging from image classification and video processing to speech recognition and natural language understanding. The data in these tasks are typically represented in the Euclidean space. However, there is an increasing number of applications where data are generated from non-Euclidean domains and are represented as graphs with complex relationships and interdependency between objects. The complexity of graph data has imposed significant challenges on existing machine learning algorithms. Recently, many studies on extending deep learning approaches for graph data have emerged. In this survey, we provide a comprehensive overview of graph neural networks (GNNs) in data mining and machine learning fields. We propose a new taxonomy to divide the state-of-the-art graph neural networks into four categories, namely recurrent graph neural networks, convolutional graph neural networks, graph autoencoders, and spatial-temporal graph neural networks. We further discuss the applications of graph neural networks across various domains and summarize the open source codes, benchmark data sets, and model evaluation of graph neural networks. Finally, we propose potential research directions in this rapidly growing field.

Multi-modal recommender system focuses on utilizing rich modal information ( i.e., images and textual descriptions) of items to improve recommendation performance. The current methods have achieved remarkable success with the powerful structure modeling capability of graph neural networks. However, these methods are often hindered by sparse data in real-world scenarios. Although contrastive learning and homography ( i.e., homogeneous graphs) are employed to address the data sparsity challenge, existing methods still suffer two main limitations: 1) Simple multi-modal feature contrasts fail to produce effective representations, causing noisy modal-shared features and loss of valuable information in modal-unique features; 2) The lack of exploration of the homograph relations between user interests and item co-occurrence results in incomplete mining of user-item interplay. To address the above limitations, we propose a novel framework for REfining multi-modAl contRastive learning and hoMography relations (REARM). Specifically, we complement multi-modal contrastive learning by employing meta-network and orthogonal constraint strategies, which filter out noise in modal-shared features and retain recommendation-relevant information in modal-unique features. To mine homogeneous relationships effectively, we integrate a newly constructed user interest graph and an item co-occurrence graph with the existing user co-occurrence and item semantic graphs for graph learning. The extensive experiments on three real-world datasets demonstrate the superiority of REARM to various state-of-the-art baselines. Our visualization further shows an improvement made by REARM in distinguishing between modal-shared and modal-unique features. Code is available https://github.com/MrShouxingMa/REARM{here}.

Large language models (LLMs) have achieved remarkable success and demonstrated superior performance across various tasks, including natural language processing (NLP), weather forecasting, biological protein folding, text generation, and solving mathematical problems. However, many real-world data exhibit highly non-Euclidean latent hierarchical anatomy, such as protein networks, transportation networks, financial networks, brain networks, and linguistic structures or syntactic trees in natural languages. Effectively learning intrinsic semantic entailment and hierarchical relationships from these raw, unstructured input data using LLMs remains an underexplored area. Due to its effectiveness in modeling tree-like hierarchical structures, hyperbolic geometry -- a non-Euclidean space -- has rapidly gained popularity as an expressive latent representation space for complex data modeling across domains such as graphs, images, languages, and multi-modal data. Here, we provide a comprehensive and contextual exposition of recent advancements in LLMs that leverage hyperbolic geometry as a representation space to enhance semantic representation learning and multi-scale reasoning. Specifically, the paper presents a taxonomy of the principal techniques of Hyperbolic LLMs (HypLLMs) in terms of four main categories: (1) hyperbolic LLMs through exp/log maps; (2) hyperbolic fine-tuned models; (3) fully hyperbolic LLMs, and (4) hyperbolic state-space models. We also explore crucial potential applications and outline future research directions. A repository of key papers, models, datasets, and code implementations is available at https://github.com/sarangp2402/Hyperbolic-LLM-Models/tree/main.

Video-based visual relation detection tasks, such as video scene graph generation, play important roles in fine-grained video understanding. However, current video visual relation detection datasets have two main limitations that hinder the progress of research in this area. First, they do not explore complex human-human interactions in multi-person scenarios. Second, the relation types of existing datasets have relatively low-level semantics and can be often recognized by appearance or simple prior information, without the need for detailed spatio-temporal context reasoning. Nevertheless, comprehending high-level interactions between humans is crucial for understanding complex multi-person videos, such as sports and surveillance videos. To address this issue, we propose a new video visual relation detection task: video human-human interaction detection, and build a dataset named SportsHHI for it. SportsHHI contains 34 high-level interaction classes from basketball and volleyball sports. 118,075 human bounding boxes and 50,649 interaction instances are annotated on 11,398 keyframes. To benchmark this, we propose a two-stage baseline method and conduct extensive experiments to reveal the key factors for a successful human-human interaction detector. We hope that SportsHHI can stimulate research on human interaction understanding in videos and promote the development of spatio-temporal context modeling techniques in video visual relation detection.

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.