Daily Papers

Due to the convenience of mobile devices, the online games have become an important part for user entertainments in reality, creating a demand for friend recommendation in online games. However, none of existing approaches can effectively incorporate the multi-modal user features (e.g., images and texts) with the structural information in the friendship graph, due to the following limitations: (1) some of them ignore the high-order structural proximity between users, (2) some fail to learn the pairwise relevance between users at modality-specific level, and (3) some cannot capture both the local and global user preferences on different modalities. By addressing these issues, in this paper, we propose an end-to-end model FROG that better models the user preferences on potential friends. Comprehensive experiments on both offline evaluation and online deployment at Tencent have demonstrated the superiority of FROG over existing approaches.

In this study, we focus on the graph representation learning (a.k.a. network embedding) in attributed graphs. Different from existing embedding methods that treat the incorporation of graph structure and semantic as the simple combination of two optimization objectives, we propose a novel semantic graph representation (SGR) method to formulate the joint optimization of the two heterogeneous sources into a common high-order proximity based framework. Concretely, we first construct an auxiliary weighted graph, where the complex homogeneous and heterogeneous relations among nodes and attributes in the original graph are comprehensively encoded. Conventional embedding methods that consider high-order topology proximities can then be easily applied to the newly constructed graph to learn the representations of both node and attribute while capturing the nonlinear high-order intrinsic correlation inside or among graph structure and semantic. The learned attribute embeddings can also effectively support some semantic-oriented inference tasks (e.g., semantic community detection), helping to reveal the graph's deep semantic. The effectiveness of SGR is further verified on a series of real graphs, where it achieves impressive performance over other baselines.

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 a new approach for the approximate K-nearest neighbor search based on navigable small world graphs with controllable hierarchy (Hierarchical NSW, HNSW). The proposed solution is fully graph-based, without any need for additional search structures, which are typically used at the coarse search stage of the most proximity graph techniques. Hierarchical NSW incrementally builds a multi-layer structure consisting from hierarchical set of proximity graphs (layers) for nested subsets of the stored elements. The maximum layer in which an element is present is selected randomly with an exponentially decaying probability distribution. This allows producing graphs similar to the previously studied Navigable Small World (NSW) structures while additionally having the links separated by their characteristic distance scales. Starting search from the upper layer together with utilizing the scale separation boosts the performance compared to NSW and allows a logarithmic complexity scaling. Additional employment of a heuristic for selecting proximity graph neighbors significantly increases performance at high recall and in case of highly clustered data. Performance evaluation has demonstrated that the proposed general metric space search index is able to strongly outperform previous opensource state-of-the-art vector-only approaches. Similarity of the algorithm to the skip list structure allows straightforward balanced distributed implementation.

Despite the recent successes of vanilla Graph Neural Networks (GNNs) on many tasks, their foundation on pairwise interaction networks inherently limits their capacity to discern latent higher-order interactions in complex systems. To bridge this capability gap, we propose a novel approach exploiting the rich mathematical theory of simplicial complexes (SCs) - a robust tool for modeling higher-order interactions. Current SC-based GNNs are burdened by high complexity and rigidity, and quantifying higher-order interaction strengths remains challenging. Innovatively, we present a higher-order Flower-Petals (FP) model, incorporating FP Laplacians into SCs. Further, we introduce a Higher-order Graph Convolutional Network (HiGCN) grounded in FP Laplacians, capable of discerning intrinsic features across varying topological scales. By employing learnable graph filters, a parameter group within each FP Laplacian domain, we can identify diverse patterns where the filters' weights serve as a quantifiable measure of higher-order interaction strengths. The theoretical underpinnings of HiGCN's advanced expressiveness are rigorously demonstrated. Additionally, our empirical investigations reveal that the proposed model accomplishes state-of-the-art (SOTA) performance on a range of graph tasks and provides a scalable and flexible solution to explore higher-order interactions in graphs.

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.

Higher-order interactions (HOIs) are ubiquitous in real-world complex systems and applications. Investigation of deep learning for HOIs, thus, has become a valuable agenda for the data mining and machine learning communities. As networks of HOIs are expressed mathematically as hypergraphs, hypergraph neural networks (HNNs) have emerged as a powerful tool for representation learning on hypergraphs. Given the emerging trend, we present the first survey dedicated to HNNs, with an in-depth and step-by-step guide. Broadly, the present survey overviews HNN architectures, training strategies, and applications. First, we break existing HNNs down into four design components: (i) input features, (ii) input structures, (iii) message-passing schemes, and (iv) training strategies. Second, we examine how HNNs address and learn HOIs with each of their components. Third, we overview the recent applications of HNNs in recommendation, bioinformatics and medical science, time series analysis, and computer vision. Lastly, we conclude with a discussion on limitations and future directions.

Node importance estimation (NIE) in heterogeneous knowledge graphs is a critical yet challenging task, essential for applications such as recommendation, knowledge reasoning, and question answering. Existing methods often rely on pairwise connections, neglecting high-order dependencies among multiple entities and relations, and they treat structural and semantic signals independently, hindering effective cross-modal integration. To address these challenges, we propose MetaHGNIE, a meta-path induced hypergraph contrastive learning framework for disentangling and aligning structural and semantic information. MetaHGNIE constructs a higher-order knowledge graph via meta-path sequences, where typed hyperedges capture multi-entity relational contexts. Structural dependencies are aggregated with local attention, while semantic representations are encoded through a hypergraph transformer equipped with sparse chunking to reduce redundancy. Finally, a multimodal fusion module integrates structural and semantic embeddings under contrastive learning with auxiliary supervision, ensuring robust cross-modal alignment. Extensive experiments on benchmark NIE datasets demonstrate that MetaHGNIE consistently outperforms state-of-the-art baselines. These results highlight the effectiveness of explicitly modeling higher-order interactions and cross-modal alignment in heterogeneous knowledge graphs. Our code is available at https://github.com/SEU-WENJIA/DualHNIE

We study the realizability of simplicial complexes with a given pair of integer sequences, representing the node degree distribution and the facet size distribution, respectively. While the s-uniform variant of the problem is NP-complete when s geq 3, we identify two populations of input sequences, most of which can be solved in polynomial time using a recursive algorithm that we contribute. Combining with a sampler for the simplicial configuration model [J.-G. Young et al., Phys. Rev. E 96, 032312 (2017)], we facilitate the efficient sampling of simplicial ensembles from arbitrary degree and size distributions. We find that, contrary to expectations based on dyadic networks, increasing the nodes' degrees reduces the number of loops in simplicial complexes. Our work unveils a fundamental constraint on the degree-size sequences and sheds light on further analysis of higher-order phenomena based on local structures.

In this paper, we study the problem of inference in high-order structured prediction tasks. In the context of Markov random fields, the goal of a high-order inference task is to maximize a score function on the space of labels, and the score function can be decomposed into sum of unary and high-order potentials. We apply a generative model approach to study the problem of high-order inference, and provide a two-stage convex optimization algorithm for exact label recovery. We also provide a new class of hypergraph structural properties related to hyperedge expansion that drives the success in general high-order inference problems. Finally, we connect the performance of our algorithm and the hyperedge expansion property using a novel hypergraph Cheeger-type inequality.

In this work, we propose a framework that constructs reduced order models for nonlinear structural mechanics in a nonintrusive fashion, and can handle large scale simulations. We identify three steps that are carried out separately in time, and possibly on different devices: (i) the production of high-fidelity solutions by a commercial software, (ii) the offline stage of the model reduction and (iii) the online stage where the reduced order model is exploited. The nonintrusivity assumes that only the displacement field solution is known, and relies on operations on simulation data during the offline phase by using an in-house code. The compatibility with a new commercial code only needs the implementation of a routine converting the mesh and result format into our in-house data format. The nonintrusive capabilities of the framework are demonstrated on numerical experiments using commercial versions of the finite element softwares Zset and Ansys Mechanical. The nonlinear constitutive equations are evaluated by using the same external plugins as for Zset or Ansys Mechanical. The large scale simulations are handled using domain decomposition and parallel computing with distributed memory. The features and performances of the framework are evaluated on two numerical applications involving elastoviscoplastic materials: the second one involves a model of high-pressure blade, where the framework is used to extrapolate cyclic loadings in 6.5 hours, whereas the reference high-fidelity computation would take 9.5 days.

Hypergraph Neural Networks (HGNNs) have recently attracted much attention and exhibited satisfactory performance due to their superiority in high-order correlation modeling. However, it is noticed that the high-order modeling capability of hypergraph also brings increased computation complexity, which hinders its practical industrial deployment. In practice, we find that one key barrier to the efficient deployment of HGNNs is the high-order structural dependencies during inference. In this paper, we propose to bridge the gap between the HGNNs and inference-efficient Multi-Layer Perceptron (MLPs) to eliminate the hypergraph dependency of HGNNs and thus reduce computational complexity as well as improve inference speed. Specifically, we introduce LightHGNN and LightHGNN^+ for fast inference with low complexity. LightHGNN directly distills the knowledge from teacher HGNNs to student MLPs via soft labels, and LightHGNN^+ further explicitly injects reliable high-order correlations into the student MLPs to achieve topology-aware distillation and resistance to over-smoothing. Experiments on eight hypergraph datasets demonstrate that even without hypergraph dependency, the proposed LightHGNNs can still achieve competitive or even better performance than HGNNs and outperform vanilla MLPs by 16.3 on average. Extensive experiments on three graph datasets further show the average best performance of our LightHGNNs compared with all other methods. Experiments on synthetic hypergraphs with 5.5w vertices indicate LightHGNNs can run 100times faster than HGNNs, showcasing their ability for latency-sensitive deployments.

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.

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.

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.

Hypergraph neural networks (HNNs) using neural networks to encode hypergraphs provide a promising way to model higher-order relations in data and further solve relevant prediction tasks built upon such higher-order relations. However, higher-order relations in practice contain complex patterns and are often highly irregular. So, it is often challenging to design an HNN that suffices to express those relations while keeping computational efficiency. Inspired by hypergraph diffusion algorithms, this work proposes a new HNN architecture named ED-HNN, which provably represents any continuous equivariant hypergraph diffusion operators that can model a wide range of higher-order relations. ED-HNN can be implemented efficiently by combining star expansions of hypergraphs with standard message passing neural networks. ED-HNN further shows great superiority in processing heterophilic hypergraphs and constructing deep models. We evaluate ED-HNN for node classification on nine real-world hypergraph datasets. ED-HNN uniformly outperforms the best baselines over these nine datasets and achieves more than 2\%uparrow in prediction accuracy over four datasets therein.

While most network embedding techniques model the relative positions of nodes in a network, recently there has been significant interest in structural embeddings that model node role equivalences, irrespective of their distances to any specific nodes. We present PhUSION, a proximity-based unified framework for computing structural and positional node embeddings, which leverages well-established methods for calculating node proximity scores. Clarifying a point of contention in the literature, we show which step of PhUSION produces the different kinds of embeddings and what steps can be used by both. Moreover, by aggregating the PhUSION node embeddings, we obtain graph-level features that model information lost by previous graph feature learning and kernel methods. In a comprehensive empirical study with over 10 datasets, 4 tasks, and 35 methods, we systematically reveal successful design choices for node and graph-level machine learning with embeddings.

We show the existence of a Locality-Sensitive Hashing (LSH) family for the angular distance that yields an approximate Near Neighbor Search algorithm with the asymptotically optimal running time exponent. Unlike earlier algorithms with this property (e.g., Spherical LSH [Andoni, Indyk, Nguyen, Razenshteyn 2014], [Andoni, Razenshteyn 2015]), our algorithm is also practical, improving upon the well-studied hyperplane LSH [Charikar, 2002] in practice. We also introduce a multiprobe version of this algorithm, and conduct experimental evaluation on real and synthetic data sets. We complement the above positive results with a fine-grained lower bound for the quality of any LSH family for angular distance. Our lower bound implies that the above LSH family exhibits a trade-off between evaluation time and quality that is close to optimal for a natural class of LSH functions.

Molecular interactions often involve high-order relationships that cannot be fully captured by traditional graph-based models limited to pairwise connections. Hypergraphs naturally extend graphs by enabling multi-way interactions, making them well-suited for modeling complex molecular systems. In this work, we introduce EquiHGNN, an Equivariant HyperGraph Neural Network framework that integrates symmetry-aware representations to improve molecular modeling. By enforcing the equivariance under relevant transformation groups, our approach preserves geometric and topological properties, leading to more robust and physically meaningful representations. We examine a range of equivariant architectures and demonstrate that integrating symmetry constraints leads to notable performance gains on large-scale molecular datasets. Experiments on both small and large molecules show that high-order interactions offer limited benefits for small molecules but consistently outperform 2D graphs on larger ones. Adding geometric features to these high-order structures further improves the performance, emphasizing the value of spatial information in molecular learning. Our source code is available at https://github.com/HySonLab/EquiHGNN/

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.

There is a recently discovered and intriguing phenomenon called Neural Collapse: at the terminal phase of training a deep neural network for classification, the within-class penultimate feature means and the associated classifier vectors of all flat classes collapse to the vertices of a simplex Equiangular Tight Frame (ETF). Recent work has tried to exploit this phenomenon by fixing the related classifier weights to a pre-computed ETF to induce neural collapse and maximize the separation of the learned features when training with imbalanced data. In this work, we propose to fix the linear classifier of a deep neural network to a Hierarchy-Aware Frame (HAFrame), instead of an ETF, and use a cosine similarity-based auxiliary loss to learn hierarchy-aware penultimate features that collapse to the HAFrame. We demonstrate that our approach reduces the mistake severity of the model's predictions while maintaining its top-1 accuracy on several datasets of varying scales with hierarchies of heights ranging from 3 to 12. Code: https://github.com/ltong1130ztr/HAFrame

Cross-modal metric learning is a prominent research topic that bridges the semantic heterogeneity between vision and language. Existing methods frequently utilize simple cosine or complex distance metrics to transform the pairwise features into a similarity score, which suffers from an inadequate or inefficient capability for distance measurements. Consequently, we propose a Generalized Structural Sparse Function to dynamically capture thorough and powerful relationships across modalities for pair-wise similarity learning while remaining concise but efficient. Specifically, the distance metric delicately encapsulates two formats of diagonal and block-diagonal terms, automatically distinguishing and highlighting the cross-channel relevancy and dependency inside a structured and organized topology. Hence, it thereby empowers itself to adapt to the optimal matching patterns between the paired features and reaches a sweet spot between model complexity and capability. Extensive experiments on cross-modal and two extra uni-modal retrieval tasks (image-text retrieval, person re-identification, fine-grained image retrieval) have validated its superiority and flexibility over various popular retrieval frameworks. More importantly, we further discover that it can be seamlessly incorporated into multiple application scenarios, and demonstrates promising prospects from Attention Mechanism to Knowledge Distillation in a plug-and-play manner. Our code is publicly available at: https://github.com/Paranioar/GSSF.

Recently, many mesh-based graph neural network (GNN) models have been proposed for modeling complex high-dimensional physical systems. Remarkable achievements have been made in significantly reducing the solving time compared to traditional numerical solvers. These methods are typically designed to i) reduce the computational cost in solving physical dynamics and/or ii) propose techniques to enhance the solution accuracy in fluid and rigid body dynamics. However, it remains under-explored whether they are effective in addressing the challenges of flexible body dynamics, where instantaneous collisions occur within a very short timeframe. In this paper, we present Hierarchical Contact Mesh Transformer (HCMT), which uses hierarchical mesh structures and can learn long-range dependencies (occurred by collisions) among spatially distant positions of a body -- two close positions in a higher-level mesh correspond to two distant positions in a lower-level mesh. HCMT enables long-range interactions, and the hierarchical mesh structure quickly propagates collision effects to faraway positions. To this end, it consists of a contact mesh Transformer and a hierarchical mesh Transformer (CMT and HMT, respectively). Lastly, we propose a flexible body dynamics dataset, consisting of trajectories that reflect experimental settings frequently used in the display industry for product designs. We also compare the performance of several baselines using well-known benchmark datasets. Our results show that HCMT provides significant performance improvements over existing methods. Our code is available at https://github.com/yuyudeep/hcmt.

Nonlinear model order reduction has opened the door to parameter optimization and uncertainty quantification in complex physics problems governed by nonlinear equations. In particular, the computational cost of solving these equations can be reduced by means of local reduced-order bases. This article examines the benefits of a physics-informed cluster analysis for the construction of cluster-specific reduced-order bases. We illustrate that the choice of the dissimilarity measure for clustering is fundamental and highly affects the performances of the local reduced-order bases. It is shown that clustering with an angle-based dissimilarity on simulation data efficiently decreases the intra-cluster Kolmogorov N-width. Additionally, an a priori efficiency criterion is introduced to assess the relevance of a ROM-net, a methodology for the reduction of nonlinear physics problems introduced in our previous work in [T. Daniel, F. Casenave, N. Akkari, D. Ryckelynck, Model order reduction assisted by deep neural networks (ROM-net), Advanced Modeling and Simulation in Engineering Sciences 7 (16), 2020]. This criterion also provides engineers with a very practical method for ROM-nets' hyperparameters calibration under constrained computational costs for the training phase. On five different physics problems, our physics-informed clustering strategy significantly outperforms classic strategies for the construction of local reduced-order bases in terms of projection errors.

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.

Structural topology optimization (TO) is central to engineering design but remains computationally intensive due to complex physics and hard constraints. Existing deep-learning methods are limited to fixed square grids, a few hand-coded boundary conditions, and post-hoc optimization, preventing general deployment. We introduce Optimize Any Topology (OAT), a foundation-model framework that directly predicts minimum-compliance layouts for arbitrary aspect ratios, resolutions, volume fractions, loads, and fixtures. OAT combines a resolution- and shape-agnostic autoencoder with an implicit neural-field decoder and a conditional latent-diffusion model trained on OpenTO, a new corpus of 2.2 million optimized structures covering 2 million unique boundary-condition configurations. On four public benchmarks and two challenging unseen tests, OAT lowers mean compliance up to 90% relative to the best prior models and delivers sub-1 second inference on a single GPU across resolutions from 64 x 64 to 256 x 256 and aspect ratios as high as 10:1. These results establish OAT as a general, fast, and resolution-free framework for physics-aware topology optimization and provide a large-scale dataset to spur further research in generative modeling for inverse design. Code & data can be found at https://github.com/ahnobari/OptimizeAnyTopology.

Recently, studies exemplified by Hyper-Connections (HC) have extended the ubiquitous residual connection paradigm established over the past decade by expanding the residual stream width and diversifying connectivity patterns. While yielding substantial performance gains, this diversification fundamentally compromises the identity mapping property intrinsic to the residual connection, which causes severe training instability and restricted scalability, and additionally incurs notable memory access overhead. To address these challenges, we propose Manifold-Constrained Hyper-Connections (mHC), a general framework that projects the residual connection space of HC onto a specific manifold to restore the identity mapping property, while incorporating rigorous infrastructure optimization to ensure efficiency. Empirical experiments demonstrate that mHC is effective for training at scale, offering tangible performance improvements and superior scalability. We anticipate that mHC, as a flexible and practical extension of HC, will contribute to a deeper understanding of topological architecture design and suggest promising directions for the evolution of foundational models.

Large language models (LLMs) excel in language tasks, especially with supervised fine-tuning after pre-training. However, their substantial memory and computational requirements hinder practical applications. Structural pruning, which reduces less significant weight dimensions, is one solution. Yet, traditional post-hoc pruning often leads to significant performance loss, with limited recovery from further fine-tuning due to reduced capacity. Since the model fine-tuning refines the general and chaotic knowledge in pre-trained models, we aim to incorporate structural pruning with the fine-tuning, and propose the Pruning-Aware Tuning (PAT) paradigm to eliminate model redundancy while preserving the model performance to the maximum extend. Specifically, we insert the innovative Hybrid Sparsification Modules (HSMs) between the Attention and FFN components to accordingly sparsify the upstream and downstream linear modules. The HSM comprises a lightweight operator and a globally shared trainable mask. The lightweight operator maintains a training overhead comparable to that of LoRA, while the trainable mask unifies the channels to be sparsified, ensuring structural pruning. Additionally, we propose the Identity Loss which decouples the transformation and scaling properties of the HSMs to enhance training robustness. Extensive experiments demonstrate that PAT excels in both performance and efficiency. For example, our Llama2-7b model with a 25\% pruning ratio achieves 1.33times speedup while outperforming the LoRA-finetuned model by up to 1.26\% in accuracy with a similar training cost. Code: https://github.com/kriskrisliu/PAT_Pruning-Aware-Tuning

Automated analysis for engineering structures offers considerable potential for boosting efficiency by minimizing repetitive tasks. Although AI-driven methods are increasingly common, no systematic framework yet leverages Large Language Models (LLMs) for automatic structural analysis. To address this gap, we propose a novel framework that integrates LLMs with structural analysis software. LLMs serve as the core engine: they parse structural descriptions from text and translate them into executable Python scripts. Moreover, the framework integrates the generative capabilities of LLMs with code-based finite element (FE) tools like OpenSeesPy. It employs domain-specific prompt design and in-context learning strategies to enhance the LLM's problem-solving capabilities and generative stability, enabling fully automated structural analysis from descriptive text to model outputs. In our experiments, we introduce a well-curated small-scale benchmark dataset of 20 structural analysis word problems (SAWPs) with ground-truth solutions and evaluate the performance of different LLMs within our framework in solving these SAWPs. The role of system instructions, crafted by structural engineers, is also investigated to understand their impact on LLM-driven structural analysis. Additionally, the generative stability of our framework is examined. Through multiple validation experiments on the benchmark, our results demonstrate that the proposed framework can substantially increase the level of automation in solving SAWPs compared to traditional methods. Quantitatively, the framework, built on GPT-4o, achieved 100% accuracy, surpassing GPT-4 (85%), Gemini 1.5 Pro (80%), and Llama-3.3 (30%) on the test examples. Furthermore, integrating domain-specific instructions enhanced performance by 30% on problems with asymmetrical structural configurations.

Despite advances in indoor 3D scene layout generation, synthesizing scenes with dense object arrangements remains challenging. Existing methods primarily focus on large furniture while neglecting smaller objects, resulting in unrealistically empty scenes. Those that place small objects typically do not honor arrangement specifications, resulting in largely random placement not following the text description. We present HSM, a hierarchical framework for indoor scene generation with dense object arrangements across spatial scales. Indoor scenes are inherently hierarchical, with surfaces supporting objects at different scales, from large furniture on floors to smaller objects on tables and shelves. HSM embraces this hierarchy and exploits recurring cross-scale spatial patterns to generate complex and realistic indoor scenes in a unified manner. Our experiments show that HSM outperforms existing methods by generating scenes that are more realistic and better conform to user input across room types and spatial configurations.

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.

The quadratic cost of scaled dot-product attention is a central obstacle to scaling autoregressive language models to long contexts. Linear-time attention and State Space Models (SSMs) provide scalable alternatives but are typically restricted to first-order or kernel-based approximations, which can limit expressivity. We introduce Higher-order Linear Attention (HLA), a causal, streaming mechanism that realizes higher interactions via compact prefix sufficient statistics. In the second-order case, HLA maintains a constant-size state and computes per-token outputs in linear time without materializing any n times n matrices. We give closed-form streaming identities, a strictly causal masked variant using two additional summaries, and a chunk-parallel training scheme based on associative scans that reproduces the activations of a serial recurrence exactly. We further outline extensions to third and higher orders. Collectively, these results position HLA as a principled, scalable building block that combines attention-like, data-dependent mixing with the efficiency of modern recurrent architectures. Project Page: https://github.com/yifanzhang-pro/HLA.

Deep image inpainting has made impressive progress with recent advances in image generation and processing algorithms. We claim that the performance of inpainting algorithms can be better judged by the generated structures and textures. Structures refer to the generated object boundary or novel geometric structures within the hole, while texture refers to high-frequency details, especially man-made repeating patterns filled inside the structural regions. We believe that better structures are usually obtained from a coarse-to-fine GAN-based generator network while repeating patterns nowadays can be better modeled using state-of-the-art high-frequency fast fourier convolutional layers. In this paper, we propose a novel inpainting network combining the advantages of the two designs. Therefore, our model achieves a remarkable visual quality to match state-of-the-art performance in both structure generation and repeating texture synthesis using a single network. Extensive experiments demonstrate the effectiveness of the method, and our conclusions further highlight the two critical factors of image inpainting quality, structures, and textures, as the future design directions of inpainting networks.

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.

Machine learning force fields (MLFFs) have revolutionized molecular simulations by providing quantum mechanical accuracy at the speed of molecular mechanical computations. However, a fundamental reliance of these models on fixed-cutoff architectures limits their applicability to macromolecular systems where long-range interactions dominate. We demonstrate that this locality constraint causes force prediction errors to scale monotonically with system size, revealing a critical architectural bottleneck. To overcome this, we establish the systematically designed MolLR25 ({Mol}ecules with {L}ong-{R}ange effect) benchmark up to 1200 atoms, generated using high-fidelity DFT, and introduce E2Former-LSR, an equivariant transformer that explicitly integrates long-range attention blocks. E2Former-LSR exhibits stable error scaling, achieves superior fidelity in capturing non-covalent decay, and maintains precision on complex protein conformations. Crucially, its efficient design provides up to 30% speedup compared to purely local models. This work validates the necessity of non-local architectures for generalizable MLFFs, enabling high-fidelity molecular dynamics for large-scale chemical and biological systems.

We present RigAnything, a novel autoregressive transformer-based model, which makes 3D assets rig-ready by probabilistically generating joints, skeleton topologies, and assigning skinning weights in a template-free manner. Unlike most existing auto-rigging methods, which rely on predefined skeleton template and are limited to specific categories like humanoid, RigAnything approaches the rigging problem in an autoregressive manner, iteratively predicting the next joint based on the global input shape and the previous prediction. While autoregressive models are typically used to generate sequential data, RigAnything extends their application to effectively learn and represent skeletons, which are inherently tree structures. To achieve this, we organize the joints in a breadth-first search (BFS) order, enabling the skeleton to be defined as a sequence of 3D locations and the parent index. Furthermore, our model improves the accuracy of position prediction by leveraging diffusion modeling, ensuring precise and consistent placement of joints within the hierarchy. This formulation allows the autoregressive model to efficiently capture both spatial and hierarchical relationships within the skeleton. Trained end-to-end on both RigNet and Objaverse datasets, RigAnything demonstrates state-of-the-art performance across diverse object types, including humanoids, quadrupeds, marine creatures, insects, and many more, surpassing prior methods in quality, robustness, generalizability, and efficiency. Please check our website for more details: https://www.liuisabella.com/RigAnything.

Building credible simulators from data is difficult because structure design, parameter calibration, and out-of-distribution (OOD) robustness are tightly coupled. We introduce SOCIA (Simulation Orchestration for Computational Intelligence with Agents), a framework that treats simulator construction as joint structure-parameter co-optimization: it elicits mechanism-rich blueprints, exposes explicit tunable parameters, and instantiates a calibration schema, producing an executable simulator with built-in calibration hooks. SOCIA couples Bayesian Optimization for sample-efficient point calibration with Simulation-Based Inference for uncertainty-aware fitting; diagnostics trigger targeted structural edits in an outer refinement loop to co-optimize design and parameters under tight budgets. Across three diverse tasks, SOCIA consistently outperforms strong baselines, excelling on both in-distribution (ID) fitting and OOD shift. Ablations that weaken structure, calibration design, or tuning yield near-monotone degradations, underscoring the necessity of unified structure-parameter optimization. We will release the code soon.

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.

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.

Vector databases typically rely on approximate nearest neighbor (ANN) search to retrieve the top-k closest vectors to a query in embedding space. While effective, this approach often yields semantically redundant results, missing the diversity and contextual richness required by applications such as retrieval-augmented generation (RAG), multi-hop QA, and memory-augmented agents. We introduce a new retrieval paradigm: semantic compression, which aims to select a compact, representative set of vectors that captures the broader semantic structure around a query. We formalize this objective using principles from submodular optimization and information geometry, and show that it generalizes traditional top-k retrieval by prioritizing coverage and diversity. To operationalize this idea, we propose graph-augmented vector retrieval, which overlays semantic graphs (e.g., kNN or knowledge-based links) atop vector spaces to enable multi-hop, context-aware search. We theoretically analyze the limitations of proximity-based retrieval under high-dimensional concentration and highlight how graph structures can improve semantic coverage. Our work outlines a foundation for meaning-centric vector search systems, emphasizing hybrid indexing, diversity-aware querying, and structured semantic retrieval. We make our implementation publicly available to foster future research in this area.

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.

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.

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.

We introduce a diffusion-based framework that performs aligned novel view image and geometry generation via a warping-and-inpainting methodology. Unlike prior methods that require dense posed images or pose-embedded generative models limited to in-domain views, our method leverages off-the-shelf geometry predictors to predict partial geometries viewed from reference images, and formulates novel-view synthesis as an inpainting task for both image and geometry. To ensure accurate alignment between generated images and geometry, we propose cross-modal attention distillation, where attention maps from the image diffusion branch are injected into a parallel geometry diffusion branch during both training and inference. This multi-task approach achieves synergistic effects, facilitating geometrically robust image synthesis as well as well-defined geometry prediction. We further introduce proximity-based mesh conditioning to integrate depth and normal cues, interpolating between point cloud and filtering erroneously predicted geometry from influencing the generation process. Empirically, our method achieves high-fidelity extrapolative view synthesis on both image and geometry across a range of unseen scenes, delivers competitive reconstruction quality under interpolation settings, and produces geometrically aligned colored point clouds for comprehensive 3D completion. Project page is available at https://cvlab-kaist.github.io/MoAI.

Many graph representation learning (GRL) problems are dynamic, with millions of edges added or removed per second. A fundamental workload in this setting is dynamic link prediction: using a history of graph updates to predict whether a given pair of vertices will become connected. Recent schemes for link prediction in such dynamic settings employ Transformers, modeling individual graph updates as single tokens. In this work, we propose HOT: a model that enhances this line of works by harnessing higher-order (HO) graph structures; specifically, k-hop neighbors and more general subgraphs containing a given pair of vertices. Harnessing such HO structures by encoding them into the attention matrix of the underlying Transformer results in higher accuracy of link prediction outcomes, but at the expense of increased memory pressure. To alleviate this, we resort to a recent class of schemes that impose hierarchy on the attention matrix, significantly reducing memory footprint. The final design offers a sweetspot between high accuracy and low memory utilization. HOT outperforms other dynamic GRL schemes, for example achieving 9%, 7%, and 15% higher accuracy than - respectively - DyGFormer, TGN, and GraphMixer, for the MOOC dataset. Our design can be seamlessly extended towards other dynamic GRL workloads.

We study the conditions under which the convex relaxation of a mixed-integer linear programming formulation for ordered optimization problems, where sorting is part of the decision process, yields integral optimal solutions. Thereby solving the problem exactly in polynomial time. Our analysis identifies structural properties of the input data that influence the integrality of the relaxation. We show that incorporating ordered components introduces additional layers of combinatorial complexity that invalidate the exactness observed in classical (non-ordered) settings. In particular, for certain ordered problems such as the min--max case, the linear relaxation never recovers the integral solution. These results clarify the intrinsic hardness introduced by sorting and reveal that the strength of the relaxation depends critically on the ``proximity'' of the ordered problem to its classical counterpart: problems closer to the non-ordered case tend to admit tighter relaxations, while those further away exhibit substantially weaker behavior. Computational experiments on benchmark instances confirm the predictive value of the integrality conditions and demonstrate the practical implications of exact relaxations for ordered location problems.

The lifting of 3D structure and camera from 2D landmarks is at the cornerstone of the entire discipline of computer vision. Traditional methods have been confined to specific rigid objects, such as those in Perspective-n-Point (PnP) problems, but deep learning has expanded our capability to reconstruct a wide range of object classes (e.g. C3PDO and PAUL) with resilience to noise, occlusions, and perspective distortions. All these techniques, however, have been limited by the fundamental need to establish correspondences across the 3D training data -- significantly limiting their utility to applications where one has an abundance of "in-correspondence" 3D data. Our approach harnesses the inherent permutation equivariance of transformers to manage varying number of points per 3D data instance, withstands occlusions, and generalizes to unseen categories. We demonstrate state of the art performance across 2D-3D lifting task benchmarks. Since our approach can be trained across such a broad class of structures we refer to it simply as a 3D Lifting Foundation Model (3D-LFM) -- the first of its kind.

Click Through Rate (CTR) prediction plays an essential role in recommender systems and online advertising. It is crucial to effectively model feature interactions to improve the prediction performance of CTR models. However, existing methods face three significant challenges. First, while most methods can automatically capture high-order feature interactions, their performance tends to diminish as the order of feature interactions increases. Second, existing methods lack the ability to provide convincing interpretations of the prediction results, especially for high-order feature interactions, which limits the trustworthiness of their predictions. Third, many methods suffer from the presence of redundant parameters, particularly in the embedding layer. This paper proposes a novel method called Gated Deep Cross Network (GDCN) and a Field-level Dimension Optimization (FDO) approach to address these challenges. As the core structure of GDCN, Gated Cross Network (GCN) captures explicit high-order feature interactions and dynamically filters important interactions with an information gate in each order. Additionally, we use the FDO approach to learn condensed dimensions for each field based on their importance. Comprehensive experiments on five datasets demonstrate the effectiveness, superiority and interpretability of GDCN. Moreover, we verify the effectiveness of FDO in learning various dimensions and reducing model parameters. The code is available on https://github.com/anonctr/GDCN.

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.

Optimizing neural networks with loss that contain high-dimensional and high-order differential operators is expensive to evaluate with back-propagation due to O(d^{k}) scaling of the derivative tensor size and the O(2^{k-1}L) scaling in the computation graph, where d is the dimension of the domain, L is the number of ops in the forward computation graph, and k is the derivative order. In previous works, the polynomial scaling in d was addressed by amortizing the computation over the optimization process via randomization. Separately, the exponential scaling in k for univariate functions (d=1) was addressed with high-order auto-differentiation (AD). In this work, we show how to efficiently perform arbitrary contraction of the derivative tensor of arbitrary order for multivariate functions, by properly constructing the input tangents to univariate high-order AD, which can be used to efficiently randomize any differential operator. When applied to Physics-Informed Neural Networks (PINNs), our method provides >1000times speed-up and >30times memory reduction over randomization with first-order AD, and we can now solve 1-million-dimensional PDEs in 8 minutes on a single NVIDIA A100 GPU. This work opens the possibility of using high-order differential operators in large-scale problems.

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.

The heterogeneous network is a robust data abstraction that can model entities of different types interacting in various ways. Such heterogeneity brings rich semantic information but presents nontrivial challenges in aggregating the heterogeneous relationships between objects - especially those of higher-order indirect relations. Recent graph neural network approaches for representation learning on heterogeneous networks typically employ the attention mechanism, which is often only optimized for predictions based on direct links. Furthermore, even though most deep learning methods can aggregate higher-order information by building deeper models, such a scheme can diminish the degree of interpretability. To overcome these challenges, we explore an architecture - Layer-stacked ATTention Embedding (LATTE) - that automatically decomposes higher-order meta relations at each layer to extract the relevant heterogeneous neighborhood structures for each node. Additionally, by successively stacking layer representations, the learned node embedding offers a more interpretable aggregation scheme for nodes of different types at different neighborhood ranges. We conducted experiments on several benchmark heterogeneous network datasets. In both transductive and inductive node classification tasks, LATTE can achieve state-of-the-art performance compared to existing approaches, all while offering a lightweight model. With extensive experimental analyses and visualizations, the framework can demonstrate the ability to extract informative insights on heterogeneous networks.

Structural pruning enhances hardware-agnostic inference efficiency for large language models (LLMs) yet often fails to maintain comparable performance. Local pruning performs efficient layer-by-layer compression but ignores global topology. Although global pruning aims to identify an optimal sparse model, intuitive methods typically adopt a two-stage paradigm that first evaluates substructure saliency and then applies global pruning, which ignores inter-structure dependencies and fails to achieve end-to-end optimization. To address these limitations, we propose T\'yr-the-Pruner, an efficient end-to-end search-based global structural pruning framework. This framework constructs a supernet by repeatedly applying local pruning across a range of sparsity ratios to each layer in an LLM, with the core goal of determining the optimal sparsity distribution under a target overall sparsity ratio. Concretely, we introduce an effective local pruning and an expectation error accumulation approach to improve supernet construction. Furthermore, we employ an iterative prune-and-search strategy with coarse-to-fine sparsity granularity to ensure efficient search convergence. Experimental results show that T\'yr-the-Pruner achieves state-of-the-art structural pruning, retaining 97% of the dense model's performance while removing a challenging 50% of Llama-3.1-70B's parameters. Code will be available at https://github.com/AMD-AGI/Tyr-the-Pruner.

To provide more accurate, diverse, and explainable recommendation, it is compulsory to go beyond modeling user-item interactions and take side information into account. Traditional methods like factorization machine (FM) cast it as a supervised learning problem, which assumes each interaction as an independent instance with side information encoded. Due to the overlook of the relations among instances or items (e.g., the director of a movie is also an actor of another movie), these methods are insufficient to distill the collaborative signal from the collective behaviors of users. In this work, we investigate the utility of knowledge graph (KG), which breaks down the independent interaction assumption by linking items with their attributes. We argue that in such a hybrid structure of KG and user-item graph, high-order relations --- which connect two items with one or multiple linked attributes --- are an essential factor for successful recommendation. We propose a new method named Knowledge Graph Attention Network (KGAT) which explicitly models the high-order connectivities in KG in an end-to-end fashion. It recursively propagates the embeddings from a node's neighbors (which can be users, items, or attributes) to refine the node's embedding, and employs an attention mechanism to discriminate the importance of the neighbors. Our KGAT is conceptually advantageous to existing KG-based recommendation methods, which either exploit high-order relations by extracting paths or implicitly modeling them with regularization. Empirical results on three public benchmarks show that KGAT significantly outperforms state-of-the-art methods like Neural FM and RippleNet. Further studies verify the efficacy of embedding propagation for high-order relation modeling and the interpretability benefits brought by the attention mechanism.

We introduce Image2Struct, a benchmark to evaluate vision-language models (VLMs) on extracting structure from images. Our benchmark 1) captures real-world use cases, 2) is fully automatic and does not require human judgment, and 3) is based on a renewable stream of fresh data. In Image2Struct, VLMs are prompted to generate the underlying structure (e.g., LaTeX code or HTML) from an input image (e.g., webpage screenshot). The structure is then rendered to produce an output image (e.g., rendered webpage), which is compared against the input image to produce a similarity score. This round-trip evaluation allows us to quantitatively evaluate VLMs on tasks with multiple valid structures. We create a pipeline that downloads fresh data from active online communities upon execution and evaluates the VLMs without human intervention. We introduce three domains (Webpages, LaTeX, and Musical Scores) and use five image metrics (pixel similarity, cosine similarity between the Inception vectors, learned perceptual image patch similarity, structural similarity index measure, and earth mover similarity) that allow efficient and automatic comparison between pairs of images. We evaluate Image2Struct on 14 prominent VLMs and find that scores vary widely, indicating that Image2Struct can differentiate between the performances of different VLMs. Additionally, the best score varies considerably across domains (e.g., 0.402 on sheet music vs. 0.830 on LaTeX equations), indicating that Image2Struct contains tasks of varying difficulty. For transparency, we release the full results at https://crfm.stanford.edu/helm/image2struct/v1.0.1/.

Attention operators have been applied on both 1-D data like texts and higher-order data such as images and videos. Use of attention operators on high-order data requires flattening of the spatial or spatial-temporal dimensions into a vector, which is assumed to follow a multivariate normal distribution. This not only incurs excessive requirements on computational resources, but also fails to preserve structures in data. In this work, we propose to avoid flattening by assuming the data follow matrix-variate normal distributions. Based on this new view, we develop Kronecker attention operators (KAOs) that operate on high-order tensor data directly. More importantly, the proposed KAOs lead to dramatic reductions in computational resources. Experimental results show that our methods reduce the amount of required computational resources by a factor of hundreds, with larger factors for higher-dimensional and higher-order data. Results also show that networks with KAOs outperform models without attention, while achieving competitive performance as those with original attention operators.

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.

We consider higher-order linear-chain conditional random fields (HO-LC-CRFs) for sequence modelling, and use sum-product networks (SPNs) for representing higher-order input- and output-dependent factors. SPNs are a recently introduced class of deep models for which exact and efficient inference can be performed. By combining HO-LC-CRFs with SPNs, expressive models over both the output labels and the hidden variables are instantiated while still enabling efficient exact inference. Furthermore, the use of higher-order factors allows us to capture relations of multiple input segments and multiple output labels as often present in real-world data. These relations can not be modelled by the commonly used first-order models and higher-order models with local factors including only a single output label. We demonstrate the effectiveness of our proposed models for sequence labeling. In extensive experiments, we outperform other state-of-the-art methods in optical character recognition and achieve competitive results in phone classification.

Reasoning ability is one of the most crucial capabilities of a foundation model, signifying its capacity to address complex reasoning tasks. Chain-of-Thought (CoT) technique is widely regarded as one of the effective methods for enhancing the reasoning ability of foundation models and has garnered significant attention. However, the reasoning process of CoT is linear, step-by-step, similar to personal logical reasoning, suitable for solving general and slightly complicated problems. On the contrary, the thinking pattern of an expert owns two prominent characteristics that cannot be handled appropriately in CoT, i.e., high-order multi-hop reasoning and multimodal comparative judgement. Therefore, the core motivation of this paper is transcending CoT to construct a reasoning paradigm that can think like an expert. The hyperedge of a hypergraph could connect various vertices, making it naturally suitable for modelling high-order relationships. Inspired by this, this paper innovatively proposes a multimodal Hypergraph-of-Thought (HoT) reasoning paradigm, which enables the foundation models to possess the expert-level ability of high-order multi-hop reasoning and multimodal comparative judgement. Specifically, a textual hypergraph-of-thought is constructed utilizing triple as the primary thought to model higher-order relationships, and a hyperedge-of-thought is generated through multi-hop walking paths to achieve multi-hop inference. Furthermore, we devise a visual hypergraph-of-thought to interact with the textual hypergraph-of-thought via Cross-modal Co-Attention Graph Learning for multimodal comparative verification. Experimentations on the ScienceQA benchmark demonstrate the proposed HoT-based T5 outperforms CoT-based GPT3.5 and chatGPT, which is on par with CoT-based GPT4 with a lower model size.

Foundation multi-modal models are often designed by stitching of multiple existing pretrained uni-modal models: for example, an image classifier with an text model. This stitching process is performed by training a connector module that aims to align the representation spaces of these uni-modal models towards a multi-modal objective. However, given the complexity of training such connectors on large scale web-based datasets coupled with the ever-increasing number of available pretrained uni-modal models, the task of uni-modal models selection and subsequent connector module training becomes computationally demanding. To address this under-studied critical problem, we propose Hypernetwork Model Alignment (Hyma), a novel all-in-one solution for optimal uni-modal model selection and connector training by leveraging hypernetworks. Specifically, our framework utilizes the parameter prediction capability of a hypernetwork to obtain jointly trained connector modules for N times M combinations of uni-modal models. In our experiments, Hyma reduces the cost of searching for the best performing uni-modal model pair by 10times, while matching the ranking and trained connector performance obtained via grid search across a suite of diverse multi-modal benchmarks.

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.

Text-to-3D generation represents an exciting field that has seen rapid advancements, facilitating the transformation of textual descriptions into detailed 3D models. However, current progress often neglects the intricate high-order correlation of geometry and texture within 3D objects, leading to challenges such as over-smoothness, over-saturation and the Janus problem. In this work, we propose a method named ``3D Gaussian Generation via Hypergraph (Hyper-3DG)'', designed to capture the sophisticated high-order correlations present within 3D objects. Our framework is anchored by a well-established mainflow and an essential module, named ``Geometry and Texture Hypergraph Refiner (HGRefiner)''. This module not only refines the representation of 3D Gaussians but also accelerates the update process of these 3D Gaussians by conducting the Patch-3DGS Hypergraph Learning on both explicit attributes and latent visual features. Our framework allows for the production of finely generated 3D objects within a cohesive optimization, effectively circumventing degradation. Extensive experimentation has shown that our proposed method significantly enhances the quality of 3D generation while incurring no additional computational overhead for the underlying framework. (Project code: https://github.com/yjhboy/Hyper3DG)

We address the problem of detecting human-object interactions in images using graphical neural networks. Unlike conventional methods, where nodes send scaled but otherwise identical messages to each of their neighbours, we propose to condition messages between pairs of nodes on their spatial relationships, resulting in different messages going to neighbours of the same node. To this end, we explore various ways of applying spatial conditioning under a multi-branch structure. Through extensive experimentation we demonstrate the advantages of spatial conditioning for the computation of the adjacency structure, messages and the refined graph features. In particular, we empirically show that as the quality of the bounding boxes increases, their coarse appearance features contribute relatively less to the disambiguation of interactions compared to the spatial information. Our method achieves an mAP of 31.33% on HICO-DET and 54.2% on V-COCO, significantly outperforming state-of-the-art on fine-tuned detections.

Recent advances in molecular representation learning have produced highly effective encodings of molecules for numerous cheminformatics and bioinformatics tasks. However, extracting general chemical insight while balancing predictive accuracy, interpretability, and computational efficiency remains a major challenge. In this work, we introduce a novel Graph Neural Network (GNN) architecture that combines compressed higher-order topological signals with standard molecular features. Our approach captures global geometric information while preserving computational tractability and human-interpretable structure. We evaluate our model across a range of benchmarks, from small-molecule datasets to complex material datasets, and demonstrate superior performance using a parameter-efficient architecture. We achieve the best performing results in both accuracy and robustness across almost all benchmarks. We open source all code All code and results can be found on Github https://github.com/rahulkhorana/TFC-PACT-Net.

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.

State-space models (SSMs) have recently emerged as a framework for learning long-range sequence tasks. An example is the structured state-space sequence (S4) layer, which uses the diagonal-plus-low-rank structure of the HiPPO initialization framework. However, the complicated structure of the S4 layer poses challenges; and, in an effort to address these challenges, models such as S4D and S5 have considered a purely diagonal structure. This choice simplifies the implementation, improves computational efficiency, and allows channel communication. However, diagonalizing the HiPPO framework is itself an ill-posed problem. In this paper, we propose a general solution for this and related ill-posed diagonalization problems in machine learning. We introduce a generic, backward-stable "perturb-then-diagonalize" (PTD) methodology, which is based on the pseudospectral theory of non-normal operators, and which may be interpreted as the approximate diagonalization of the non-normal matrices defining SSMs. Based on this, we introduce the S4-PTD and S5-PTD models. Through theoretical analysis of the transfer functions of different initialization schemes, we demonstrate that the S4-PTD/S5-PTD initialization strongly converges to the HiPPO framework, while the S4D/S5 initialization only achieves weak convergences. As a result, our new models show resilience to Fourier-mode noise-perturbed inputs, a crucial property not achieved by the S4D/S5 models. In addition to improved robustness, our S5-PTD model averages 87.6% accuracy on the Long-Range Arena benchmark, demonstrating that the PTD methodology helps to improve the accuracy of deep learning models.

Latent Graph Inference (LGI) relaxed the reliance of Graph Neural Networks (GNNs) on a given graph topology by dynamically learning it. However, most of LGI methods assume to have a (noisy, incomplete, improvable, ...) input graph to rewire and can solely learn regular graph topologies. In the wake of the success of Topological Deep Learning (TDL), we study Latent Topology Inference (LTI) for learning higher-order cell complexes (with sparse and not regular topology) describing multi-way interactions between data points. To this aim, we introduce the Differentiable Cell Complex Module (DCM), a novel learnable function that computes cell probabilities in the complex to improve the downstream task. We show how to integrate DCM with cell complex message passing networks layers and train it in a end-to-end fashion, thanks to a two-step inference procedure that avoids an exhaustive search across all possible cells in the input, thus maintaining scalability. Our model is tested on several homophilic and heterophilic graph datasets and it is shown to outperform other state-of-the-art techniques, offering significant improvements especially in cases where an input graph is not provided.

Hypergraphs are a powerful abstraction for representing higher-order interactions between entities of interest. To exploit these relationships in making downstream predictions, a variety of hypergraph neural network architectures have recently been proposed, in large part building upon precursors from the more traditional graph neural network (GNN) literature. Somewhat differently, in this paper we begin by presenting an expressive family of parameterized, hypergraph-regularized energy functions. We then demonstrate how minimizers of these energies effectively serve as node embeddings that, when paired with a parameterized classifier, can be trained end-to-end via a supervised bilevel optimization process. Later, we draw parallels between the implicit architecture of the predictive models emerging from the proposed bilevel hypergraph optimization, and existing GNN architectures in common use. Empirically, we demonstrate state-of-the-art results on various hypergraph node classification benchmarks. Code is available at https://github.com/yxzwang/PhenomNN.

Generative models have had a profound impact on vision and language, paving the way for a new era of multimodal generative applications. While these successes have inspired researchers to explore using generative models in science and engineering to accelerate the design process and reduce the reliance on iterative optimization, challenges remain. Specifically, engineering optimization methods based on physics still outperform generative models when dealing with constrained environments where data is scarce and precision is paramount. To address these challenges, we introduce Diffusion Optimization Models (DOM) and Trajectory Alignment (TA), a learning framework that demonstrates the efficacy of aligning the sampling trajectory of diffusion models with the optimization trajectory derived from traditional physics-based methods. This alignment ensures that the sampling process remains grounded in the underlying physical principles. Our method allows for generating feasible and high-performance designs in as few as two steps without the need for expensive preprocessing, external surrogate models, or additional labeled data. We apply our framework to structural topology optimization, a fundamental problem in mechanical design, evaluating its performance on in- and out-of-distribution configurations. Our results demonstrate that TA outperforms state-of-the-art deep generative models on in-distribution configurations and halves the inference computational cost. When coupled with a few steps of optimization, it also improves manufacturability for out-of-distribution conditions. By significantly improving performance and inference efficiency, DOM enables us to generate high-quality designs in just a few steps and guide them toward regions of high performance and manufacturability, paving the way for the widespread application of generative models in large-scale data-driven design.

Fine-tuning large pre-trained LLMs generally demands extensive GPU memory. Traditional first-order optimizers like SGD encounter substantial difficulties due to increased memory requirements from storing activations and gradients during both the forward and backward phases as the model size expands. Alternatively, zeroth-order (ZO) techniques can compute gradients using just forward operations, eliminating the need to store activations. Furthermore, by leveraging CPU capabilities, it's feasible to enhance both the memory and processing power available to a single GPU. We propose a novel framework, ZO2 (Zeroth-Order Offloading), for efficient zeroth-order fine-tuning of LLMs with only limited GPU memory. Our framework dynamically shifts model parameters between the CPU and GPU as required, optimizing computation flow and maximizing GPU usage by minimizing downtime. This integration of parameter adjustments with ZO's double forward operations reduces unnecessary data movement, enhancing the fine-tuning efficacy. Additionally, our framework supports an innovative low-bit precision approach in AMP mode to streamline data exchanges between the CPU and GPU. Employing this approach allows us to fine-tune extraordinarily large models, such as the OPT-175B with more than 175 billion parameters, on a mere 18GB GPU--achievements beyond the reach of traditional methods. Moreover, our framework achieves these results with almost no additional time overhead and absolutely no accuracy loss compared to standard zeroth-order methods. ZO2's code has been open-sourced in https://github.com/liangyuwang/zo2.

Image inpainting has made significant advances in recent years. However, it is still challenging to recover corrupted images with both vivid textures and reasonable structures. Some specific methods only tackle regular textures while losing holistic structures due to the limited receptive fields of convolutional neural networks (CNNs). On the other hand, attention-based models can learn better long-range dependency for the structure recovery, but they are limited by the heavy computation for inference with large image sizes. To address these issues, we propose to leverage an additional structure restorer to facilitate the image inpainting incrementally. The proposed model restores holistic image structures with a powerful attention-based transformer model in a fixed low-resolution sketch space. Such a grayscale space is easy to be upsampled to larger scales to convey correct structural information. Our structure restorer can be integrated with other pretrained inpainting models efficiently with the zero-initialized residual addition. Furthermore, a masking positional encoding strategy is utilized to improve the performance with large irregular masks. Extensive experiments on various datasets validate the efficacy of our model compared with other competitors. Our codes are released in https://github.com/DQiaole/ZITS_inpainting.

Realistic 3D indoor scene generation is crucial for virtual reality, interior design, embodied intelligence, and scene understanding. While existing methods have made progress in coarse-scale furniture arrangement, they struggle to capture fine-grained object placements, limiting the realism and utility of generated environments. This gap hinders immersive virtual experiences and detailed scene comprehension for embodied AI applications. To address these issues, we propose Hierarchical Layout Generation (HLG), a novel method for fine-grained 3D scene generation. HLG is the first to adopt a coarse-to-fine hierarchical approach, refining scene layouts from large-scale furniture placement to intricate object arrangements. Specifically, our fine-grained layout alignment module constructs a hierarchical layout through vertical and horizontal decoupling, effectively decomposing complex 3D indoor scenes into multiple levels of granularity. Additionally, our trainable layout optimization network addresses placement issues, such as incorrect positioning, orientation errors, and object intersections, ensuring structurally coherent and physically plausible scene generation. We demonstrate the effectiveness of our approach through extensive experiments, showing superior performance in generating realistic indoor scenes compared to existing methods. This work advances the field of scene generation and opens new possibilities for applications requiring detailed 3D environments. We will release our code upon publication to encourage future research.

Universally modeling all typical information extraction tasks (UIE) with one generative language model (GLM) has revealed great potential by the latest study, where various IE predictions are unified into a linearized hierarchical expression under a GLM. Syntactic structure information, a type of effective feature which has been extensively utilized in IE community, should also be beneficial to UIE. In this work, we propose a novel structure-aware GLM, fully unleashing the power of syntactic knowledge for UIE. A heterogeneous structure inductor is explored to unsupervisedly induce rich heterogeneous structural representations by post-training an existing GLM. In particular, a structural broadcaster is devised to compact various latent trees into explicit high-order forests, helping to guide a better generation during decoding. We finally introduce a task-oriented structure fine-tuning mechanism, further adjusting the learned structures to most coincide with the end-task's need. Over 12 IE benchmarks across 7 tasks our system shows significant improvements over the baseline UIE system. Further in-depth analyses show that our GLM learns rich task-adaptive structural bias that greatly resolves the UIE crux, the long-range dependence issue and boundary identifying. Source codes are open at https://github.com/ChocoWu/LasUIE.

We define and investigate the problem of c-approximate window search: approximate nearest neighbor search where each point in the dataset has a numeric label, and the goal is to find nearest neighbors to queries within arbitrary label ranges. Many semantic search problems, such as image and document search with timestamp filters, or product search with cost filters, are natural examples of this problem. We propose and theoretically analyze a modular tree-based framework for transforming an index that solves the traditional c-approximate nearest neighbor problem into a data structure that solves window search. On standard nearest neighbor benchmark datasets equipped with random label values, adversarially constructed embeddings, and image search embeddings with real timestamps, we obtain up to a 75times speedup over existing solutions at the same level of recall.

Training deep neural networks for classification often includes minimizing the training loss beyond the zero training error point. In this phase of training, a "neural collapse" behavior has been observed: the variability of features (outputs of the penultimate layer) of within-class samples decreases and the mean features of different classes approach a certain tight frame structure. Recent works analyze this behavior via idealized unconstrained features models where all the minimizers exhibit exact collapse. However, with practical networks and datasets, the features typically do not reach exact collapse, e.g., because deep layers cannot arbitrarily modify intermediate features that are far from being collapsed. In this paper, we propose a richer model that can capture this phenomenon by forcing the features to stay in the vicinity of a predefined features matrix (e.g., intermediate features). We explore the model in the small vicinity case via perturbation analysis and establish results that cannot be obtained by the previously studied models. For example, we prove reduction in the within-class variability of the optimized features compared to the predefined input features (via analyzing gradient flow on the "central-path" with minimal assumptions), analyze the minimizers in the near-collapse regime, and provide insights on the effect of regularization hyperparameters on the closeness to collapse. We support our theory with experiments in practical deep learning settings.

Deep neural representations of 3D shapes as implicit functions have been shown to produce high fidelity models surpassing the resolution-memory trade-off faced by the explicit representations using meshes and point clouds. However, most such approaches focus on representing closed shapes. Unsigned distance function (UDF) based approaches have been proposed recently as a promising alternative to represent both open and closed shapes. However, since the gradients of UDFs vanish on the surface, it is challenging to estimate local (differential) geometric properties like the normals and tangent planes which are needed for many downstream applications in vision and graphics. There are additional challenges in computing these properties efficiently with a low-memory footprint. This paper presents a novel approach that models such surfaces using a new class of implicit representations called the closest surface-point (CSP) representation. We show that CSP allows us to represent complex surfaces of any topology (open or closed) with high fidelity. It also allows for accurate and efficient computation of local geometric properties. We further demonstrate that it leads to efficient implementation of downstream algorithms like sphere-tracing for rendering the 3D surface as well as to create explicit mesh-based representations. Extensive experimental evaluation on the ShapeNet dataset validate the above contributions with results surpassing the state-of-the-art.

Code classification is a difficult issue in program understanding and automatic coding. Due to the elusive syntax and complicated semantics in programs, most existing studies use techniques based on abstract syntax tree (AST) and graph neural network (GNN) to create code representations for code classification. These techniques utilize the structure and semantic information of the code, but they only take into account pairwise associations and neglect the high-order correlations that already exist between nodes in the AST, which may result in the loss of code structural information. On the other hand, while a general hypergraph can encode high-order data correlations, it is homogeneous and undirected which will result in a lack of semantic and structural information such as node types, edge types, and directions between child nodes and parent nodes when modeling AST. In this study, we propose to represent AST as a heterogeneous directed hypergraph (HDHG) and process the graph by heterogeneous directed hypergraph neural network (HDHGN) for code classification. Our method improves code understanding and can represent high-order data correlations beyond paired interactions. We assess heterogeneous directed hypergraph neural network (HDHGN) on public datasets of Python and Java programs. Our method outperforms previous AST-based and GNN-based methods, which demonstrates the capability of our model.

Graph contrastive learning (GCL) has become a powerful tool for learning graph data, but its scalability remains a significant challenge. In this work, we propose a simple yet effective training framework called Structural Compression (StructComp) to address this issue. Inspired by a sparse low-rank approximation on the diffusion matrix, StructComp trains the encoder with the compressed nodes. This allows the encoder not to perform any message passing during the training stage, and significantly reduces the number of sample pairs in the contrastive loss. We theoretically prove that the original GCL loss can be approximated with the contrastive loss computed by StructComp. Moreover, StructComp can be regarded as an additional regularization term for GCL models, resulting in a more robust encoder. Empirical studies on seven benchmark datasets show that StructComp greatly reduces the time and memory consumption while improving model performance compared to the vanilla GCL models and scalable training methods.

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.

Directed acyclic graphs (DAGs) encode a lot of information about a particular distribution in their structure. However, compute required to infer these structures is typically super-exponential in the number of variables, as inference requires a sweep of a combinatorially large space of potential structures. That is, until recent advances made it possible to search this space using a differentiable metric, drastically reducing search time. While this technique -- named NOTEARS -- is widely considered a seminal work in DAG-discovery, it concedes an important property in favour of differentiability: transportability. To be transportable, the structures discovered on one dataset must apply to another dataset from the same domain. We introduce D-Struct which recovers transportability in the discovered structures through a novel architecture and loss function while remaining fully differentiable. Because D-Struct remains differentiable, our method can be easily adopted in existing differentiable architectures, as was previously done with NOTEARS. In our experiments, we empirically validate D-Struct with respect to edge accuracy and structural Hamming distance in a variety of settings.

In this paper, we propose the MultiLevel Variational MultiScale (ML-VMS) method, a novel approach that seamlessly integrates a multilevel mesh strategy into the Variational Multiscale (VMS) framework. A key feature of the ML-VMS method is the use of the Convolutional Hierarchical Deep Neural Network (C-HiDeNN) as the approximation basis. The framework employs a coarse mesh throughout the domain, with localized fine meshes placed only in subdomains of high interest, such as those surrounding a source. Solutions at different resolutions are robustly coupled through the variational weak form and interface conditions. Compared to existing multilevel methods, ML-VMS (1) can couple an arbitrary number of mesh levels across different scales using variational multiscale framework; (2) allows approximating functions with arbitrary orders with linear finite element mesh due to the C-HiDeNN basis; (3) is supported by a rigorous theoretical error analysis; (4) features several tunable hyperparameters (e.g., order p, patch size s) with a systematic guide for their selection. We first show the theoretical error estimates of ML-VMS. Then through numerical examples, we demonstrate that ML-VMS with the C-HiDeNN takes less computational time than the FEM basis given comparable accuracy. Furthermore, we incorporate a space-time reduced-order model (ROM) based on C-HiDeNN-Tensor Decomposition (TD) into the ML-VMS framework. For a large-scale single-track laser powder bed fusion (LPBF) transient heat transfer problem that is equivalent to a full-order finite element model with 10^{10} spatial degrees of freedom (DoFs), our 3-level ML-VMS C-HiDeNN-TD achieves an approximately 5,000x speedup on a single CPU over a single-level linear FEM-TD ROM.

Standard clothing asset generation involves creating forward-facing flat-lay garment images displayed on a clear background by extracting clothing information from diverse real-world contexts, which presents significant challenges due to highly standardized sampling distributions and precise structural requirements in the generated images. Existing models have limited spatial perception and often exhibit structural hallucinations in this high-specification generative task. To address this issue, we propose a novel Retrieval-Augmented Generation (RAG) framework, termed RAGDiffusion, to enhance structure determinacy and mitigate hallucinations by assimilating external knowledge from LLM and databases. RAGDiffusion consists of two core processes: (1) Retrieval-based structure aggregation, which employs contrastive learning and a Structure Locally Linear Embedding (SLLE) to derive global structure and spatial landmarks, providing both soft and hard guidance to counteract structural ambiguities; and (2) Omni-level faithful garment generation, which introduces a three-level alignment that ensures fidelity in structural, pattern, and decoding components within the diffusing. Extensive experiments on challenging real-world datasets demonstrate that RAGDiffusion synthesizes structurally and detail-faithful clothing assets with significant performance improvements, representing a pioneering effort in high-specification faithful generation with RAG to confront intrinsic hallucinations and enhance fidelity.

Structure reasoning is a fundamental capability of large language models (LLMs), enabling them to reason about structured commonsense and answer multi-hop questions. However, existing benchmarks for structure reasoning mainly focus on horizontal and coordinate structures (e.g. graphs), overlooking the hierarchical relationships within them. Hierarchical structure reasoning is crucial for human cognition, particularly in memory organization and problem-solving. It also plays a key role in various real-world tasks, such as information extraction and decision-making. To address this gap, we propose HiBench, the first framework spanning from initial structure generation to final proficiency assessment, designed to benchmark the hierarchical reasoning capabilities of LLMs systematically. HiBench encompasses six representative scenarios, covering both fundamental and practical aspects, and consists of 30 tasks with varying hierarchical complexity, totaling 39,519 queries. To evaluate LLMs comprehensively, we develop five capability dimensions that depict different facets of hierarchical structure understanding. Through extensive evaluation of 20 LLMs from 10 model families, we reveal key insights into their capabilities and limitations: 1) existing LLMs show proficiency in basic hierarchical reasoning tasks; 2) they still struggle with more complex structures and implicit hierarchical representations, especially in structural modification and textual reasoning. Based on these findings, we create a small yet well-designed instruction dataset, which enhances LLMs' performance on HiBench by an average of 88.84\% (Llama-3.1-8B) and 31.38\% (Qwen2.5-7B) across all tasks. The HiBench dataset and toolkit are available here, https://github.com/jzzzzh/HiBench, to encourage evaluation.

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

Recently similarity graphs became the leading paradigm for efficient nearest neighbor search, outperforming traditional tree-based and LSH-based methods. Similarity graphs perform the search via greedy routing: a query traverses the graph and in each vertex moves to the adjacent vertex that is the closest to this query. In practice, similarity graphs are often susceptible to local minima, when queries do not reach its nearest neighbors, getting stuck in suboptimal vertices. In this paper we propose to learn the routing function that overcomes local minima via incorporating information about the graph global structure. In particular, we augment the vertices of a given graph with additional representations that are learned to provide the optimal routing from the start vertex to the query nearest neighbor. By thorough experiments, we demonstrate that the proposed learnable routing successfully diminishes the local minima problem and significantly improves the overall search performance.

The task of layout-to-image generation involves synthesizing images based on the captions of objects and their spatial positions. Existing methods still struggle in complex layout generation, where common bad cases include object missing, inconsistent lighting, conflicting view angles, etc. To effectively address these issues, we propose a Hierarchical Controllable (HiCo) diffusion model for layout-to-image generation, featuring object seperable conditioning branch structure. Our key insight is to achieve spatial disentanglement through hierarchical modeling of layouts. We use a multi branch structure to represent hierarchy and aggregate them in fusion module. To evaluate the performance of multi-objective controllable layout generation in natural scenes, we introduce the HiCo-7K benchmark, derived from the GRIT-20M dataset and manually cleaned. https://github.com/360CVGroup/HiCo_T2I.

Structural pruning enables model acceleration by removing structurally-grouped parameters from neural networks. However, the parameter-grouping patterns vary widely across different models, making architecture-specific pruners, which rely on manually-designed grouping schemes, non-generalizable to new architectures. In this work, we study a highly-challenging yet barely-explored task, any structural pruning, to tackle general structural pruning of arbitrary architecture like CNNs, RNNs, GNNs and Transformers. The most prominent obstacle towards this goal lies in the structural coupling, which not only forces different layers to be pruned simultaneously, but also expects all removed parameters to be consistently unimportant, thereby avoiding structural issues and significant performance degradation after pruning. To address this problem, we propose a general and {fully automatic} method, Dependency Graph (DepGraph), to explicitly model the dependency between layers and comprehensively group coupled parameters for pruning. In this work, we extensively evaluate our method on several architectures and tasks, including ResNe(X)t, DenseNet, MobileNet and Vision transformer for images, GAT for graph, DGCNN for 3D point cloud, alongside LSTM for language, and demonstrate that, even with a simple norm-based criterion, the proposed method consistently yields gratifying performances.

Complex networks have become essential tools for understanding diverse phenomena in social systems, traffic systems, biomolecular systems, and financial systems. Identifying critical nodes is a central theme in contemporary research, serving as a vital bridge between theoretical foundations and practical applications. Nevertheless, the intrinsic complexity and structural heterogeneity characterizing real-world networks, with particular emphasis on dynamic and higher-order networks, present substantial obstacles to the development of universal frameworks for critical node identification. This paper provides a comprehensive review of critical node identification techniques, categorizing them into seven main classes: centrality, critical nodes deletion problem, influence maximization, network control, artificial intelligence, higher-order and dynamic methods. Our review bridges the gaps in existing surveys by systematically classifying methods based on their methodological foundations and practical implications, and by highlighting their strengths, limitations, and applicability across different network types. Our work enhances the understanding of critical node research by identifying key challenges, such as algorithmic universality, real-time evaluation in dynamic networks, analysis of higher-order structures, and computational efficiency in large-scale networks. The structured synthesis consolidates current progress and highlights open questions, particularly in modeling temporal dynamics, advancing efficient algorithms, integrating machine learning approaches, and developing scalable and interpretable metrics for complex systems.

In this paper, we present a hypergraph neural networks (HGNN) framework for data representation learning, which can encode high-order data correlation in a hypergraph structure. Confronting the challenges of learning representation for complex data in real practice, we propose to incorporate such data structure in a hypergraph, which is more flexible on data modeling, especially when dealing with complex data. In this method, a hyperedge convolution operation is designed to handle the data correlation during representation learning. In this way, traditional hypergraph learning procedure can be conducted using hyperedge convolution operations efficiently. HGNN is able to learn the hidden layer representation considering the high-order data structure, which is a general framework considering the complex data correlations. We have conducted experiments on citation network classification and visual object recognition tasks and compared HGNN with graph convolutional networks and other traditional methods. Experimental results demonstrate that the proposed HGNN method outperforms recent state-of-the-art methods. We can also reveal from the results that the proposed HGNN is superior when dealing with multi-modal data compared with existing methods.

Large language models have been extensively studied as neural knowledge bases for their knowledge access, editability, reasoning, and explainability. However, few works focus on the structural patterns of their knowledge. Motivated by this gap, we investigate these structural patterns from a graph perspective. We quantify the knowledge of LLMs at both the triplet and entity levels, and analyze how it relates to graph structural properties such as node degree. Furthermore, we uncover the knowledge homophily, where topologically close entities exhibit similar levels of knowledgeability, which further motivates us to develop graph machine learning models to estimate entity knowledge based on its local neighbors. This model further enables valuable knowledge checking by selecting triplets less known to LLMs. Empirical results show that using selected triplets for fine-tuning leads to superior performance.

Structure-from-motion (SfM) is a long-standing problem in the computer vision community, which aims to reconstruct the camera poses and 3D structure of a scene from a set of unconstrained 2D images. Classical frameworks solve this problem in an incremental manner by detecting and matching keypoints, registering images, triangulating 3D points, and conducting bundle adjustment. Recent research efforts have predominantly revolved around harnessing the power of deep learning techniques to enhance specific elements (e.g., keypoint matching), but are still based on the original, non-differentiable pipeline. Instead, we propose a new deep pipeline VGGSfM, where each component is fully differentiable and thus can be trained in an end-to-end manner. To this end, we introduce new mechanisms and simplifications. First, we build on recent advances in deep 2D point tracking to extract reliable pixel-accurate tracks, which eliminates the need for chaining pairwise matches. Furthermore, we recover all cameras simultaneously based on the image and track features instead of gradually registering cameras. Finally, we optimise the cameras and triangulate 3D points via a differentiable bundle adjustment layer. We attain state-of-the-art performance on three popular datasets, CO3D, IMC Phototourism, and ETH3D.

Clustering aims to group unlabelled samples based on their similarities. It has become a significant tool for the analysis of high-dimensional data. However, most of the clustering methods merely generate pseudo labels and thus are unable to simultaneously present the similarities between different clusters and outliers. This paper proposes a new framework called High-dimensional Clustering onto Hamiltonian Cycle (HCHC) to solve the above problems. First, HCHC combines global structure with local structure in one objective function for deep clustering, improving the labels as relative probabilities, to mine the similarities between different clusters while keeping the local structure in each cluster. Then, the anchors of different clusters are sorted on the optimal Hamiltonian cycle generated by the cluster similarities and mapped on the circumference of a circle. Finally, a sample with a higher probability of a cluster will be mapped closer to the corresponding anchor. In this way, our framework allows us to appreciate three aspects visually and simultaneously - clusters (formed by samples with high probabilities), cluster similarities (represented as circular distances), and outliers (recognized as dots far away from all clusters). The experiments illustrate the superiority of HCHC.

Accurate reconstruction of both the geometric and topological details of a 3D object from a single 2D image embodies a fundamental challenge in computer vision. Existing explicit/implicit solutions to this problem struggle to recover self-occluded geometry and/or faithfully reconstruct topological shape structures. To resolve this dilemma, we introduce LIST, a novel neural architecture that leverages local and global image features to accurately reconstruct the geometric and topological structure of a 3D object from a single image. We utilize global 2D features to predict a coarse shape of the target object and then use it as a base for higher-resolution reconstruction. By leveraging both local 2D features from the image and 3D features from the coarse prediction, we can predict the signed distance between an arbitrary point and the target surface via an implicit predictor with great accuracy. Furthermore, our model does not require camera estimation or pixel alignment. It provides an uninfluenced reconstruction from the input-view direction. Through qualitative and quantitative analysis, we show the superiority of our model in reconstructing 3D objects from both synthetic and real-world images against the state of the art.

Recent advances have discussed cell complexes as ideal learning representations. However, there is a lack of available machine learning methods suitable for learning on CW complexes. In this paper, we derive an explicit expression for the Wasserstein distance between cell complex signal distributions in terms of a Hodge-Laplacian matrix. This leads to a structurally meaningful measure to compare CW complexes and define the optimal transportation map. In order to simultaneously include both feature and structure information, we extend the Fused Gromov-Wasserstein distance to CW complexes. Finally, we introduce novel kernels over the space of probability measures on CW complexes based on the dual formulation of optimal transport.

Recent advances in large-scale pretraining have yielded visual foundation models with strong capabilities. Not only can recent models generalize to arbitrary images for their training task, their intermediate representations are useful for other visual tasks such as detection and segmentation. Given that such models can classify, delineate, and localize objects in 2D, we ask whether they also represent their 3D structure? In this work, we analyze the 3D awareness of visual foundation models. We posit that 3D awareness implies that representations (1) encode the 3D structure of the scene and (2) consistently represent the surface across views. We conduct a series of experiments using task-specific probes and zero-shot inference procedures on frozen features. Our experiments reveal several limitations of the current models. Our code and analysis can be found at https://github.com/mbanani/probe3d.

Neural surrogates and operator networks for solving partial differential equation (PDE) problems have attracted significant research interest in recent years. However, most existing approaches are limited in their ability to generalize solutions across varying non-parametric geometric domains. In this work, we address this challenge in the context of Polyethylene Terephthalate (PET) bottle buckling analysis, a representative packaging design problem conventionally solved using computationally expensive finite element analysis (FEA). We introduce a hybrid DeepONet-Transolver framework that simultaneously predicts nodal displacement fields and the time evolution of reaction forces during top load compression. Our methodology is evaluated on two families of bottle geometries parameterized by two and four design variables. Training data is generated using nonlinear FEA simulations in Abaqus for 254 unique designs per family. The proposed framework achieves mean relative L^{2} errors of 2.5-13% for displacement fields and approximately 2.4% for time-dependent reaction forces for the four-parameter bottle family. Point-wise error analyses further show absolute displacement errors on the order of 10^{-4}-10^{-3}, with the largest discrepancies confined to localized geometric regions. Importantly, the model accurately captures key physical phenomena, such as buckling behavior, across diverse bottle geometries. These results highlight the potential of our framework as a scalable and computationally efficient surrogate, particularly for multi-task predictions in computational mechanics and applications requiring rapid design evaluation.

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

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.

Recently, Large Language Models (LLMs) have achieved significant success, prompting increased interest in expanding their generative capabilities beyond general text into domain-specific areas. This study investigates the generation of parametric sequences for computer-aided design (CAD) models using LLMs. This endeavor represents an initial step towards creating parametric 3D shapes with LLMs, as CAD model parameters directly correlate with shapes in three-dimensional space. Despite the formidable generative capacities of LLMs, this task remains challenging, as these models neither encounter parametric sequences during their pretraining phase nor possess direct awareness of 3D structures. To address this, we present CAD-Llama, a framework designed to enhance pretrained LLMs for generating parametric 3D CAD models. Specifically, we develop a hierarchical annotation pipeline and a code-like format to translate parametric 3D CAD command sequences into Structured Parametric CAD Code (SPCC), incorporating hierarchical semantic descriptions. Furthermore, we propose an adaptive pretraining approach utilizing SPCC, followed by an instruction tuning process aligned with CAD-specific guidelines. This methodology aims to equip LLMs with the spatial knowledge inherent in parametric sequences. Experimental results demonstrate that our framework significantly outperforms prior autoregressive methods and existing LLM baselines.

We present a neural operator architecture to simulate Lagrangian dynamics, such as fluid flow, granular flows, and elastoplasticity. Traditional numerical methods, such as the finite element method (FEM), suffer from long run times and large memory consumption. On the other hand, approaches based on graph neural networks are faster but still suffer from long computation times on dense graphs, which are often required for high-fidelity simulations. Our model, GIOROM or Graph Interaction Operator for Reduced-Order Modeling, learns temporal dynamics within a reduced-order setting, capturing spatial features from a highly sparse graph representation of the input and generalizing to arbitrary spatial locations during inference. The model is geometry-aware and discretization-agnostic and can generalize to different initial conditions, velocities, and geometries after training. We show that point clouds of the order of 100,000 points can be inferred from sparse graphs with sim1000 points, with negligible change in computation time. We empirically evaluate our model on elastic solids, Newtonian fluids, Non-Newtonian fluids, Drucker-Prager granular flows, and von Mises elastoplasticity. On these benchmarks, our approach results in a 25times speedup compared to other neural network-based physics simulators while delivering high-fidelity predictions of complex physical systems and showing better performance on most benchmarks. The code and the demos are provided at https://github.com/HrishikeshVish/GIOROM.

We introduce Orb-v3, the next generation of the Orb family of universal interatomic potentials. Models in this family expand the performance-speed-memory Pareto frontier, offering near SoTA performance across a range of evaluations with a >10x reduction in latency and > 8x reduction in memory. Our experiments systematically traverse this frontier, charting the trade-off induced by roto-equivariance, conservatism and graph sparsity. Contrary to recent literature, we find that non-equivariant, non-conservative architectures can accurately model physical properties, including those which require higher-order derivatives of the potential energy surface. This model release is guided by the principle that the most valuable foundation models for atomic simulation will excel on all fronts: accuracy, latency and system size scalability. The reward for doing so is a new era of computational chemistry driven by high-throughput and mesoscale all-atom simulations.

Generative models such as denoising diffusion models are quickly advancing their ability to approximate highly complex data distributions. They are also increasingly leveraged in scientific machine learning, where samples from the implied data distribution are expected to adhere to specific governing equations. We present a framework that unifies generative modeling and partial differential equation fulfillment by introducing a first-principle-based loss term that enforces generated samples to fulfill the underlying physical constraints. Our approach reduces the residual error by up to two orders of magnitude compared to previous work in a fluid flow case study and outperforms task-specific frameworks in relevant metrics for structural topology optimization. We also present numerical evidence that our extended training objective acts as a natural regularization mechanism against overfitting. Our framework is simple to implement and versatile in its applicability for imposing equality and inequality constraints as well as auxiliary optimization objectives.

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.

Attention has become more attractive in person reidentification (ReID) as it is capable of biasing the allocation of available resources towards the most informative parts of an input signal. However, state-of-the-art works concentrate only on coarse or first-order attention design, e.g. spatial and channels attention, while rarely exploring higher-order attention mechanism. We take a step towards addressing this problem. In this paper, we first propose the High-Order Attention (HOA) module to model and utilize the complex and high-order statistics information in attention mechanism, so as to capture the subtle differences among pedestrians and to produce the discriminative attention proposals. Then, rethinking person ReID as a zero-shot learning problem, we propose the Mixed High-Order Attention Network (MHN) to further enhance the discrimination and richness of attention knowledge in an explicit manner. Extensive experiments have been conducted to validate the superiority of our MHN for person ReID over a wide variety of state-of-the-art methods on three large-scale datasets, including Market-1501, DukeMTMC-ReID and CUHK03-NP. Code is available at http://www.bhchen.cn/.

Novel view synthesis (NVS) enables to generate new images of a scene or convert a set of 2D images into a comprehensive 3D model. In the context of Space Domain Awareness, since space is becoming increasingly congested, NVS can accurately map space objects and debris, improving the safety and efficiency of space operations. Similarly, in Rendezvous and Proximity Operations missions, 3D models can provide details about a target object's shape, size, and orientation, allowing for better planning and prediction of the target's behavior. In this work, we explore the generalization abilities of these reconstruction techniques, aiming to avoid the necessity of retraining for each new scene, by presenting a novel approach to 3D spacecraft reconstruction from single-view images, DreamSat, by fine-tuning the Zero123 XL, a state-of-the-art single-view reconstruction model, on a high-quality dataset of 190 high-quality spacecraft models and integrating it into the DreamGaussian framework. We demonstrate consistent improvements in reconstruction quality across multiple metrics, including Contrastive Language-Image Pretraining (CLIP) score (+0.33%), Peak Signal-to-Noise Ratio (PSNR) (+2.53%), Structural Similarity Index (SSIM) (+2.38%), and Learned Perceptual Image Patch Similarity (LPIPS) (+0.16%) on a test set of 30 previously unseen spacecraft images. Our method addresses the lack of domain-specific 3D reconstruction tools in the space industry by leveraging state-of-the-art diffusion models and 3D Gaussian splatting techniques. This approach maintains the efficiency of the DreamGaussian framework while enhancing the accuracy and detail of spacecraft reconstructions. The code for this work can be accessed on GitHub (https://github.com/ARCLab-MIT/space-nvs).

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

This paper addresses a novel task of anticipating 3D human-object interactions (HOIs). Most existing research on HOI synthesis lacks comprehensive whole-body interactions with dynamic objects, e.g., often limited to manipulating small or static objects. Our task is significantly more challenging, as it requires modeling dynamic objects with various shapes, capturing whole-body motion, and ensuring physically valid interactions. To this end, we propose InterDiff, a framework comprising two key steps: (i) interaction diffusion, where we leverage a diffusion model to encode the distribution of future human-object interactions; (ii) interaction correction, where we introduce a physics-informed predictor to correct denoised HOIs in a diffusion step. Our key insight is to inject prior knowledge that the interactions under reference with respect to contact points follow a simple pattern and are easily predictable. Experiments on multiple human-object interaction datasets demonstrate the effectiveness of our method for this task, capable of producing realistic, vivid, and remarkably long-term 3D HOI predictions.

Ultra-high-resolution text-to-image generation demands both fine-grained texture synthesis and globally coherent structure, yet current diffusion models remain constrained to sub-1K times 1K resolutions due to the prohibitive quadratic complexity of attention and the scarcity of native 4K training data. We present Scale-DiT, a new diffusion framework that introduces hierarchical local attention with low-resolution global guidance, enabling efficient, scalable, and semantically coherent image synthesis at ultra-high resolutions. Specifically, high-resolution latents are divided into fixed-size local windows to reduce attention complexity from quadratic to near-linear, while a low-resolution latent equipped with scaled positional anchors injects global semantics. A lightweight LoRA adaptation bridges global and local pathways during denoising, ensuring consistency across structure and detail. To maximize inference efficiency, we repermute token sequence in Hilbert curve order and implement a fused-kernel for skipping masked operations, resulting in a GPU-friendly design. Extensive experiments demonstrate that Scale-DiT achieves more than 2times faster inference and lower memory usage compared to dense attention baselines, while reliably scaling to 4K times 4K resolution without requiring additional high-resolution training data. On both quantitative benchmarks (FID, IS, CLIP Score) and qualitative comparisons, Scale-DiT delivers superior global coherence and sharper local detail, matching or outperforming state-of-the-art methods that rely on native 4K training. Taken together, these results highlight hierarchical local attention with guided low-resolution anchors as a promising and effective approach for advancing ultra-high-resolution image generation.

Deep learning-based point cloud modeling has been widely investigated as an indispensable component of general shape analysis. Recently, transformer and state space model (SSM) have shown promising capacities in point cloud learning. However, limited research has been conducted on medical point clouds, which have great potential in disease diagnosis and treatment. This paper presents an SSM-based hierarchical feature learning framework for medical point cloud understanding. Specifically, we down-sample input into multiple levels through the farthest point sampling. At each level, we perform a series of k-nearest neighbor (KNN) queries to aggregate multi-scale structural information. To assist SSM in processing point clouds, we introduce coordinate-order and inside-out scanning strategies for efficient serialization of irregular points. Point features are calculated progressively from short neighbor sequences and long point sequences through vanilla and group Point SSM blocks, to capture both local patterns and long-range dependencies. To evaluate the proposed method, we build a large-scale medical point cloud dataset named MedPointS for anatomy classification, completion, and segmentation. Extensive experiments conducted on MedPointS demonstrate that our method achieves superior performance across all tasks. The dataset is available at https://flemme-docs.readthedocs.io/en/latest/medpoints.html. Code is merged to a public medical imaging platform: https://github.com/wlsdzyzl/flemme.

Sequence modeling has produced diverse architectures -- from classical recurrent neural networks to modern Transformers and state space models (SSMs) -- yet a unified theoretical understanding of expressivity and trainability trade-offs remains limited. We introduce a unified framework that represents a broad class of sequence maps via an input-dependent effective interaction operator W_{ij}(X), making explicit two recurring construction patterns: (i) the Unified Factorized Framework (Explicit) (attention-style mixing), in which W_{ij}(X) varies through scalar coefficients applied to shared value maps, and (ii) Structured Dynamics (Implicit) (state-space recurrences), in which W_{ij} is induced by a latent dynamical system. Using this framework, we derive three theoretical results. First, we establish the Interaction Rank Gap: models in the Unified Factorized Framework, such as single-head attention, are constrained to a low-dimensional operator span and cannot represent certain structured dynamical maps. Second, we prove an Equivalence (Head-Count) Theorem showing that, within our multi-head factorized class, representing a linear SSM whose lag operators span a k-dimensional subspace on length-n sequences requires and is achievable with H=k heads. Third, we prove a Gradient Highway Result, showing that attention layers admit inputs with distance-independent gradient paths, whereas stable linear dynamics exhibit distance-dependent gradient attenuation. Together, these results formalize a fundamental trade-off between algebraic expressivity (interaction/operator span) and long-range gradient propagation, providing theoretical grounding for modern sequence architecture design.

Unified visual grounding pursues a simple and generic technical route to leverage multi-task data with less task-specific design. The most advanced methods typically present boxes and masks as vertex sequences to model referring detection and segmentation as an autoregressive sequential vertex generation paradigm. However, generating high-dimensional vertex sequences sequentially is error-prone because the upstream of the sequence remains static and cannot be refined based on downstream vertex information, even if there is a significant location gap. Besides, with limited vertexes, the inferior fitting of objects with complex contours restricts the performance upper bound. To deal with this dilemma, we propose a parallel vertex generation paradigm for superior high-dimension scalability with a diffusion model by simply modifying the noise dimension. An intuitive materialization of our paradigm is Parallel Vertex Diffusion (PVD) to directly set vertex coordinates as the generation target and use a diffusion model to train and infer. We claim that it has two flaws: (1) unnormalized coordinate caused a high variance of loss value; (2) the original training objective of PVD only considers point consistency but ignores geometry consistency. To solve the first flaw, Center Anchor Mechanism (CAM) is designed to convert coordinates as normalized offset values to stabilize the training loss value. For the second flaw, Angle summation loss (ASL) is designed to constrain the geometry difference of prediction and ground truth vertexes for geometry-level consistency. Empirical results show that our PVD achieves state-of-the-art in both referring detection and segmentation, and our paradigm is more scalable and efficient than sequential vertex generation with high-dimension data.

Measuring geometric similarity between high-dimensional network representations is a topic of longstanding interest to neuroscience and deep learning. Although many methods have been proposed, only a few works have rigorously analyzed their statistical efficiency or quantified estimator uncertainty in data-limited regimes. Here, we derive upper and lower bounds on the worst-case convergence of standard estimators of shape distancex2014a measure of representational dissimilarity proposed by Williams et al. (2021).These bounds reveal the challenging nature of the problem in high-dimensional feature spaces. To overcome these challenges, we introduce a new method-of-moments estimator with a tunable bias-variance tradeoff. We show that this estimator achieves substantially lower bias than standard estimators in simulation and on neural data, particularly in high-dimensional settings. Thus, we lay the foundation for a rigorous statistical theory for high-dimensional shape analysis, and we contribute a new estimation method that is well-suited to practical scientific settings.

Current 3D representations like meshes, voxels, point clouds, and NeRF-based neural implicit fields exhibit significant limitations: they are often task-specific, lacking universal applicability across reconstruction, generation, editing, and driving. While meshes offer high precision, their dense vertex data complicates editing; NeRFs deliver excellent rendering but suffer from structural ambiguity, hindering animation and manipulation; all representations inherently struggle with the trade-off between data complexity and fidelity. To overcome these issues, we introduce a novel 3D Hierarchical Proxy Node representation. Its core innovation lies in representing an object's shape and texture via a sparse set of hierarchically organized (tree-structured) proxy nodes distributed on its surface and interior. Each node stores local shape and texture information (implicitly encoded by a small MLP) within its neighborhood. Querying any 3D coordinate's properties involves efficient neural interpolation and lightweight decoding from relevant nearby and parent nodes. This framework yields a highly compact representation where nodes align with local semantics, enabling direct drag-and-edit manipulation, and offers scalable quality-complexity control. Extensive experiments across 3D reconstruction and editing demonstrate our method's expressive efficiency, high-fidelity rendering quality, and superior editability.

We present a new approach for generating 3D house wireframes with semantic enrichment using an autoregressive model. Unlike conventional generative models that independently process vertices, edges, and faces, our approach employs a unified wire-based representation for improved coherence in learning 3D wireframe structures. By re-ordering wire sequences based on semantic meanings, we facilitate seamless semantic integration during sequence generation. Our two-phase technique merges a graph-based autoencoder with a transformer-based decoder to learn latent geometric tokens and generate semantic-aware wireframes. Through iterative prediction and decoding during inference, our model produces detailed wireframes that can be easily segmented into distinct components, such as walls, roofs, and rooms, reflecting the semantic essence of the shape. Empirical results on a comprehensive house dataset validate the superior accuracy, novelty, and semantic fidelity of our model compared to existing generative models. More results and details can be found on https://vcc.tech/research/2024/3DWire.

We present a Morphology-Informed Heterogeneous Graph Neural Network (MI-HGNN) for learning-based contact perception. The architecture and connectivity of the MI-HGNN are constructed from the robot morphology, in which nodes and edges are robot joints and links, respectively. By incorporating the morphology-informed constraints into a neural network, we improve a learning-based approach using model-based knowledge. We apply the proposed MI-HGNN to two contact perception problems, and conduct extensive experiments using both real-world and simulated data collected using two quadruped robots. Our experiments demonstrate the superiority of our method in terms of effectiveness, generalization ability, model efficiency, and sample efficiency. Our MI-HGNN improved the performance of a state-of-the-art model that leverages robot morphological symmetry by 8.4% with only 0.21% of its parameters. Although MI-HGNN is applied to contact perception problems for legged robots in this work, it can be seamlessly applied to other types of multi-body dynamical systems and has the potential to improve other robot learning frameworks. Our code is made publicly available at https://github.com/lunarlab-gatech/Morphology-Informed-HGNN.

Dense linear layers are the dominant computational bottleneck in foundation models. Identifying more efficient alternatives to dense matrices has enormous potential for building more compute-efficient models, as exemplified by the success of convolutional networks in the image domain. In this work, we systematically explore structured matrices as replacements for dense matrices. We show that different structures often require drastically different initialization scales and learning rates, which are crucial to performance, especially as models scale. Using insights from the Maximal Update Parameterization, we determine the optimal scaling for initialization and learning rates of these unconventional layers. Finally, we measure the scaling laws of different structures to compare how quickly their performance improves with compute. We propose a novel matrix family containing Monarch matrices, the Block Tensor-Train (BTT), which we show performs better than dense matrices for the same compute on multiple tasks. On CIFAR-10/100 with augmentation, BTT achieves exponentially lower training loss than dense when training MLPs and ViTs. BTT matches dense ViT-S/32 performance on ImageNet-1k with 3.8 times less compute and is more efficient than dense for training small GPT-2 language models.

Different from the flow semantics of natural languages, programming languages are inherently rigid in structure and grammar. Existing fine-tuning methodologies for code vulnerability detection generally treat code as long text sequences, stripping away structural elements such as newlines ('/n') and whitespace. However, this approach inadvertently results in the loss of crucial structural information, diminishing the distinct characteristics of code and impairing the accuracy of vulnerability detection. To address these challenges, we propose a novel network architecture method based on pre-trained code models, which incorporates structural information awareness. We propose an enhanced code text processing workflow that retains structural elements prior to modeling. This refinement allows the model to retain and exploit line-level structural information and semantic information during the modeling process. Furthermore, we introduce a new network architecture, the Code Structure-Aware Network through Line-level Semantic Learning (CSLS), which integrates three key components: global vulnerability awareness, line-structural awareness, and sensitive-line awareness. We have conducted comprehensive experiments using vulnerability detection datasets from real-world projects. Extensive experiments were conducted on vulnerability detection datasets derived from real-world projects. The results demonstrate that our new code pre-processing flow significantly improves existing baselines (e.g., a 3\% accuracy improvement on the Devign dataset when applied to popular models such as CoderBert and UniXcoder). The proposed network architecture also demonstrates superior accuracy in detecting vulnerabilities, surpassing newly established benchmarks. These findings underscore the importance of structural information in enhancing the efficacy of code vulnerability detection models.

Topological Neural Networks (TNNs) incorporate higher-order relational information beyond pairwise interactions, enabling richer representations than Graph Neural Networks (GNNs). Concurrently, topological descriptors based on persistent homology (PH) are being increasingly employed to augment the GNNs. We investigate the benefits of integrating these two paradigms. Specifically, we introduce TopNets as a broad framework that subsumes and unifies various methods in the intersection of GNNs/TNNs and PH such as (generalizations of) RePHINE and TOGL. TopNets can also be readily adapted to handle (symmetries in) geometric complexes, extending the scope of TNNs and PH to spatial settings. Theoretically, we show that PH descriptors can provably enhance the expressivity of simplicial message-passing networks. Empirically, (continuous and E(n)-equivariant extensions of) TopNets achieve strong performance across diverse tasks, including antibody design, molecular dynamics simulation, and drug property prediction.

Linear time-invariant state space models (SSM) are a classical model from engineering and statistics, that have recently been shown to be very promising in machine learning through the Structured State Space sequence model (S4). A core component of S4 involves initializing the SSM state matrix to a particular matrix called a HiPPO matrix, which was empirically important for S4's ability to handle long sequences. However, the specific matrix that S4 uses was actually derived in previous work for a particular time-varying dynamical system, and the use of this matrix as a time-invariant SSM had no known mathematical interpretation. Consequently, the theoretical mechanism by which S4 models long-range dependencies actually remains unexplained. We derive a more general and intuitive formulation of the HiPPO framework, which provides a simple mathematical interpretation of S4 as a decomposition onto exponentially-warped Legendre polynomials, explaining its ability to capture long dependencies. Our generalization introduces a theoretically rich class of SSMs that also lets us derive more intuitive S4 variants for other bases such as the Fourier basis, and explains other aspects of training S4, such as how to initialize the important timescale parameter. These insights improve S4's performance to 86% on the Long Range Arena benchmark, with 96% on the most difficult Path-X task.

Fine-tuning large language models (LLMs) remains resource-intensive due to their sheer scale. While zeroth-order (ZO) optimization provides a memory-efficient alternative by eliminating backward passes, its application to multi-hundred-billion-parameter models is constrained by GPU memory and compute throughput. The ZO2 framework addresses the memory bottleneck by offloading model parameters to CPU memory and overlapping transformer block transfer with dual forward computation on a single GPU. However, ZO2 remains limited by its single-device execution and achieves modest throughput. In this work, we present DistZO2, a high-throughput, memory-efficient framework for distributed zeroth-order fine-tuning of LLMs. DistZO2 introduces three parallel strategies: (1) Perturbation Parallelism (PertP), which parallelizes the two perturbed forward passes across devices; (2) Distributed Data Parallelism (DDP), adapted to the scalar-gradient nature of ZO training; and (3) a unified 2D Parallelism design that combines PertP and DDP. To further mitigate communication bottlenecks introduced by parameter offloading, we propose a hardware-aware communication strategy that slices parameter blocks and redistributes them across GPUs via high-speed interconnects such as NVLink. DistZO2 scales zeroth-order fine-tuning to modern multi-GPU systems, preserving ZO2's memory efficiency while substantially improving training throughput. In our experiments on OPT-175B, DistZO2 achieves a 3x speedup over ZO2 with distributed computing. DistZO2's code has been open-sourced in https://github.com/liangyuwang/zo2.