Daily Papers

In this paper, we present Reshape Dimensions Network (ReDimNet), a novel neural network architecture for extracting utterance-level speaker representations. Our approach leverages dimensionality reshaping of 2D feature maps to 1D signal representation and vice versa, enabling the joint usage of 1D and 2D blocks. We propose an original network topology that preserves the volume of channel-timestep-frequency outputs of 1D and 2D blocks, facilitating efficient residual feature maps aggregation. Moreover, ReDimNet is efficiently scalable, and we introduce a range of model sizes, varying from 1 to 15 M parameters and from 0.5 to 20 GMACs. Our experimental results demonstrate that ReDimNet achieves state-of-the-art performance in speaker recognition while reducing computational complexity and the number of model parameters.

This paper addresses a multi-echelon inventory management problem with a complex network topology where deriving optimal ordering decisions is difficult. Deep reinforcement learning (DRL) has recently shown potential in solving such problems, while designing the neural networks in DRL remains a challenge. In order to address this, a DRL model is developed whose Q-network is based on radial basis functions. The approach can be more easily constructed compared to classic DRL models based on neural networks, thus alleviating the computational burden of hyperparameter tuning. Through a series of simulation experiments, the superior performance of this approach is demonstrated compared to the simple base-stock policy, producing a better policy in the multi-echelon system and competitive performance in the serial system where the base-stock policy is optimal. In addition, the approach outperforms current DRL approaches.

We tackle the challenge of large-scale network intervention for guiding excitatory point processes, such as infectious disease spread or traffic congestion control. Our model-based reinforcement learning utilizes neural ODEs to capture how the networked excitatory point processes will evolve subject to the time-varying changes in network topology. Our approach incorporates Gradient-Descent based Model Predictive Control (GD-MPC), offering policy flexibility to accommodate prior knowledge and constraints. To address the intricacies of planning and overcome the high dimensionality inherent to such decision-making problems, we design an Amortize Network Interventions (ANI) framework, allowing for the pooling of optimal policies from history and other contexts, while ensuring a permutation equivalent property. This property enables efficient knowledge transfer and sharing across diverse contexts. Our approach has broad applications, from curbing infectious disease spread to reducing carbon emissions through traffic light optimization, and thus has the potential to address critical societal and environmental challenges.

Federated learning and gossip learning are emerging methodologies designed to mitigate data privacy concerns by retaining training data on client devices and exclusively sharing locally-trained machine learning (ML) models with others. The primary distinction between the two lies in their approach to model aggregation: federated learning employs a centralized parameter server, whereas gossip learning adopts a fully decentralized mechanism, enabling direct model exchanges among nodes. This decentralized nature often positions gossip learning as less efficient compared to federated learning. Both methodologies involve a critical step: computing a representation of received ML models and integrating this representation into the existing model. Conventionally, this representation is derived by averaging the received models, exemplified by the FedAVG algorithm. Our findings suggest that this averaging approach inherently introduces a potential delay in model convergence. We identify the underlying cause and refer to it as the "vanishing variance" problem, where averaging across uncorrelated ML models undermines the optimal variance established by the Xavier weight initialization. Unlike federated learning where the central server ensures model correlation, and unlike traditional gossip learning which circumvents this problem through model partitioning and sampling, our research introduces a variance-corrected model averaging algorithm. This novel algorithm preserves the optimal variance needed during model averaging, irrespective of network topology or non-IID data distributions. Our extensive simulation results demonstrate that our approach enables gossip learning to achieve convergence efficiency comparable to that of federated learning.

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

Decentralized learning enables distributed agents to collaboratively train a shared machine learning model without a central server, through local computation and peer-to-peer communication. Although each agent retains its dataset locally, sharing local models can still expose private information about the local training datasets to adversaries. To mitigate privacy attacks, a common strategy is to inject random artificial noise at each agent before exchanging local models between neighbors. However, this often leads to utility degradation due to the negative effects of cumulated artificial noise on the learning algorithm. In this work, we introduce CorN-DSGD, a novel covariance-based framework for generating correlated privacy noise across agents, which unifies several state-of-the-art methods as special cases. By leveraging network topology and mixing weights, CorN-DSGD optimizes the noise covariance to achieve network-wide noise cancellation. Experimental results show that CorN-DSGD cancels more noise than existing pairwise correlation schemes, improving model performance under formal privacy guarantees.

Large Language Models (LLMs) have recently made significant strides in complex reasoning tasks through the Chain-of-Thought technique. Despite this progress, their reasoning is often constrained by their intrinsic understanding, lacking external insights. To address this, we propose Exchange-of-Thought (EoT), a novel framework that enables cross-model communication during problem-solving. Drawing inspiration from network topology, EoT integrates four unique communication paradigms: Memory, Report, Relay, and Debate. This paper delves into the communication dynamics and volume associated with each paradigm. To counterbalance the risks of incorrect reasoning chains, we implement a robust confidence evaluation mechanism within these communications. Our experiments across diverse complex reasoning tasks demonstrate that EoT significantly surpasses established baselines, underscoring the value of external insights in enhancing LLM performance. Furthermore, we show that EoT achieves these superior results in a cost-effective manner, marking a promising advancement for efficient and collaborative AI problem-solving.

Training multiple tasks jointly in one deep network yields reduced latency during inference and better performance over the single-task counterpart by sharing certain layers of a network. However, over-sharing a network could erroneously enforce over-generalization, causing negative knowledge transfer across tasks. Prior works rely on human intuition or pre-computed task relatedness scores for ad hoc branching structures. They provide sub-optimal end results and often require huge efforts for the trial-and-error process. In this work, we present an automated multi-task learning algorithm that learns where to share or branch within a network, designing an effective network topology that is directly optimized for multiple objectives across tasks. Specifically, we propose a novel tree-structured design space that casts a tree branching operation as a gumbel-softmax sampling procedure. This enables differentiable network splitting that is end-to-end trainable. We validate the proposed method on controlled synthetic data, CelebA, and Taskonomy.

Neural networks (NNs) are increasingly used in always-on safety-critical applications deployed on hardware accelerators (NN-HAs) employing various memory technologies. Reliable continuous operation of NN is essential for safety-critical applications. During online operation, NNs are susceptible to single and multiple permanent and soft errors due to factors such as radiation, aging, and thermal effects. Explicit NN-HA testing methods cannot detect transient faults during inference, are unsuitable for always-on applications, and require extensive test vector generation and storage. Therefore, in this paper, we propose the uncertainty fingerprint approach representing the online fault status of NN. Furthermore, we propose a dual head NN topology specifically designed to produce uncertainty fingerprints and the primary prediction of the NN in a single shot. During the online operation, by matching the uncertainty fingerprint, we can concurrently self-test NNs with up to 100% coverage with a low false positive rate while maintaining a similar performance of the primary task. Compared to existing works, memory overhead is reduced by up to 243.7 MB, multiply and accumulate (MAC) operation is reduced by up to 10000times, and false-positive rates are reduced by up to 89%.

Key graph-based problems play a central role in understanding network topology and uncovering patterns of similarity in homogeneous and temporal data. Such patterns can be revealed by analyzing communities formed by nodes, which in turn can be effectively modeled through temporal k-cores. This paper introduces a novel decentralized and incremental algorithm for computing the core decomposition of temporal networks. Decentralized solutions leverage the ability of network nodes to communicate and coordinate locally, addressing complex problems in a scalable, adaptive, and timely manner. By leveraging previously computed coreness values, our approach significantly reduces the activation of nodes and the volume of message exchanges when the network changes over time. This enables scalability with only a minimal trade-off in precision. Experimental evaluations on large real-world networks under varying levels of dynamism demonstrate the efficiency of our solution compared to a state-of-the-art approach, particularly in terms of active nodes, communication overhead, and convergence speed.

Accurately predicting road networks from satellite images requires a global understanding of the network topology. We propose to capture such high-level information by introducing a graph-based framework that simulates the addition of sequences of graph edges using a reinforcement learning (RL) approach. In particular, given a partially generated graph associated with a satellite image, an RL agent nominates modifications that maximize a cumulative reward. As opposed to standard supervised techniques that tend to be more restricted to commonly used surrogate losses, these rewards can be based on various complex, potentially non-continuous, metrics of interest. This yields more power and flexibility to encode problem-dependent knowledge. Empirical results on several benchmark datasets demonstrate enhanced performance and increased high-level reasoning about the graph topology when using a tree-based search. We further highlight the superiority of our approach under substantial occlusions by introducing a new synthetic benchmark dataset for this task.

Neural architecture search (NAS) automatically finds the best task-specific neural network topology, outperforming many manual architecture designs. However, it can be prohibitively expensive as the search requires training thousands of different networks, while each can last for hours. In this work, we propose the Graph HyperNetwork (GHN) to amortize the search cost: given an architecture, it directly generates the weights by running inference on a graph neural network. GHNs model the topology of an architecture and therefore can predict network performance more accurately than regular hypernetworks and premature early stopping. To perform NAS, we randomly sample architectures and use the validation accuracy of networks with GHN generated weights as the surrogate search signal. GHNs are fast -- they can search nearly 10 times faster than other random search methods on CIFAR-10 and ImageNet. GHNs can be further extended to the anytime prediction setting, where they have found networks with better speed-accuracy tradeoff than the state-of-the-art manual designs.

Communication costs within Federated learning hinder the system scalability for reaching more data from more clients. The proposed FL adopts a hub-and-spoke network topology. All clients communicate through the central server. Hence, reducing communication overheads via techniques such as data compression has been proposed to mitigate this issue. Another challenge of federated learning is unbalanced data distribution, data on each client are not independent and identically distributed (non-IID) in a typical federated learning setting. In this paper, we proposed a new compression compensation scheme called Global Momentum Fusion (GMF) which reduces communication overheads between FL clients and the server and maintains comparable model accuracy in the presence of non-IID data. GitHub repository: https://github.com/tony92151/global-momentum-fusion-fl

Deep learning-based computational methods have achieved promising results in predicting protein-protein interactions (PPIs). However, existing benchmarks predominantly focus on isolated pairwise evaluations, overlooking a model's capability to reconstruct biologically meaningful PPI networks, which is crucial for biology research. To address this gap, we introduce PRING, the first comprehensive benchmark that evaluates protein-protein interaction prediction from a graph-level perspective. PRING curates a high-quality, multi-species PPI network dataset comprising 21,484 proteins and 186,818 interactions, with well-designed strategies to address both data redundancy and leakage. Building on this golden-standard dataset, we establish two complementary evaluation paradigms: (1) topology-oriented tasks, which assess intra and cross-species PPI network construction, and (2) function-oriented tasks, including protein complex pathway prediction, GO module analysis, and essential protein justification. These evaluations not only reflect the model's capability to understand the network topology but also facilitate protein function annotation, biological module detection, and even disease mechanism analysis. Extensive experiments on four representative model categories, consisting of sequence similarity-based, naive sequence-based, protein language model-based, and structure-based approaches, demonstrate that current PPI models have potential limitations in recovering both structural and functional properties of PPI networks, highlighting the gap in supporting real-world biological applications. We believe PRING provides a reliable platform to guide the development of more effective PPI prediction models for the community. The dataset and source code of PRING are available at https://github.com/SophieSarceau/PRING.

Wikipedia relies on an extensive review process to verify that the content of each individual page is unbiased and presents a neutral point of view. Less attention has been paid to possible biases in the hyperlink structure of Wikipedia, which has a significant influence on the user's exploration process when visiting more than one page. The evaluation of hyperlink bias is challenging because it depends on the global view rather than the text of individual pages. In this paper, we focus on the influence of the interconnect topology between articles describing complementary aspects of polarizing topics. We introduce a novel measure of exposure to diverse information to quantify users' exposure to different aspects of a topic throughout an entire surfing session, rather than just one click ahead. We apply this measure to six polarizing topics (e.g., gun control and gun right), and we identify cases in which the network topology significantly limits the exposure of users to diverse information on the topic, encouraging users to remain in a knowledge bubble. Our findings demonstrate the importance of evaluating Wikipedia's network structure in addition to the extensive review of individual articles.

Recently, nonnegative matrix factorization (NMF) has been widely adopted for community detection, because of its better interpretability. However, the existing NMF-based methods have the following three problems: 1) they directly transform the original network into community membership space, so it is difficult for them to capture the hierarchical information; 2) they often only pay attention to the topology of the network and ignore its node attributes; 3) it is hard for them to learn the global structure information necessary for community detection. Therefore, we propose a new community detection algorithm, named Contrastive Deep Nonnegative Matrix Factorization (CDNMF). Firstly, we deepen NMF to strengthen its capacity for information extraction. Subsequently, inspired by contrastive learning, our algorithm creatively constructs network topology and node attributes as two contrasting views. Furthermore, we utilize a debiased negative sampling layer and learn node similarity at the community level, thereby enhancing the suitability of our model for community detection. We conduct experiments on three public real graph datasets and the proposed model has achieved better results than state-of-the-art methods. Code available at https://github.com/6lyc/CDNMF.git.

This study examines the effects of de-globalization trends on international trade networks and their role in improving forecasts for economic growth. Using section-level trade data from nearly 200 countries from 2010 to 2022, we identify significant shifts in the network topology driven by rising trade policy uncertainty. Our analysis highlights key global players through centrality rankings, with the United States, China, and Germany maintaining consistent dominance. Using a horse race of supervised regressors, we find that network topology descriptors evaluated from section-specific trade networks substantially enhance the quality of a country's GDP growth forecast. We also find that non-linear models, such as Random Forest, XGBoost, and LightGBM, outperform traditional linear models used in the economics literature. Using SHAP values to interpret these non-linear model's predictions, we find that about half of most important features originate from the network descriptors, underscoring their vital role in refining forecasts. Moreover, this study emphasizes the significance of recent economic performance, population growth, and the primary sector's influence in shaping economic growth predictions, offering novel insights into the intricacies of economic growth forecasting.

Wireless mesh networks (WMNs) have emerged as a key technology for next generation wireless broadband networks showing rapid progress and inspiring numerous compelling applications. A WMN comprises of a set of mesh routers (MRs) and mesh clients (MCs), where MRs are connected to the Internet backbone through the Internet gateways (IGWs). The MCs are wireless devices and communicate among themselves over possibly multi-hop paths with or without the involvement of MRs. User privacy and security have been primary concerns in WMNs due to their peer-to-peer network topology, shared wireless medium, stringent resource constraints, and highly dynamic environment. Moreover, to support real-time applications, WMNs must also be equipped with robust, reliable and efficient communication protocols so as to minimize the end-to-end latency and packet drops. Design of a secure and efficient communication protocol for WMNs, therefore, is of paramount importance. In this paper, we propose a security and privacy protocol that provides security and user anonymity while maintaining communication efficiency in a WMN. The security protocol ensures secure authentication and encryption in access and the backbone networks. The user anonymity, authentication and data privacy is achieved by application of a protocol that is based on Rivest's ring signature scheme. Simulation results demonstrate that while the protocols have minimal storage and communication overhead, they are robust and provide high level of security and privacy to the users of the network services.

The rapid scaling of large language models (LLMs) has unveiled critical limitations in current hardware architectures, including constraints in memory capacity, computational efficiency, and interconnection bandwidth. DeepSeek-V3, trained on 2,048 NVIDIA H800 GPUs, demonstrates how hardware-aware model co-design can effectively address these challenges, enabling cost-efficient training and inference at scale. This paper presents an in-depth analysis of the DeepSeek-V3/R1 model architecture and its AI infrastructure, highlighting key innovations such as Multi-head Latent Attention (MLA) for enhanced memory efficiency, Mixture of Experts (MoE) architectures for optimized computation-communication trade-offs, FP8 mixed-precision training to unlock the full potential of hardware capabilities, and a Multi-Plane Network Topology to minimize cluster-level network overhead. Building on the hardware bottlenecks encountered during DeepSeek-V3's development, we engage in a broader discussion with academic and industry peers on potential future hardware directions, including precise low-precision computation units, scale-up and scale-out convergence, and innovations in low-latency communication fabrics. These insights underscore the critical role of hardware and model co-design in meeting the escalating demands of AI workloads, offering a practical blueprint for innovation in next-generation AI systems.

The existing peer-to-peer networks have several problems such as fake content distribution, free riding, white-washing and poor search scalability, lack of a robust trust model and absence of user privacy protection mechanism. Although, several trust management and semantic community-based mechanisms for combating free riding and distribution of malicious contents have been proposed by some researchers, most of these schemes lack scalability due to their high computational, communication and storage overhead. This paper presents a robust trust management scheme for P2P networks that utilizes topology adaptation by constructing an overlay of trusted peers where the neighbors are selected based on their trust ratings and content similarities. While increasing the search efficiency by intelligently exploiting the formation of semantic community structures by topology adaptation among the trustworthy peers, the scheme provides the users a very high level of privacy protection of their usage and consumption patterns of network resources. Simulation results demonstrate that the proposed scheme provides efficient searching to good peers while penalizing the malicious peers by increasing their search times as the network topology stabilizes.

Large-language models (LLMs) have demonstrated powerful problem-solving capabilities, in particular when organized in multi-agent systems. However, the advent of such systems also raises several questions on the ability of a complex network of agents to effectively self-organize and collaborate. While measuring performance on standard reasoning benchmarks indicates how well multi-agent systems can solve reasoning tasks, it is unclear whether these systems are able to leverage their topology effectively. Here, we propose AgentsNet, a new benchmark for multi-agent reasoning. By drawing inspiration from classical problems in distributed systems and graph theory, AgentsNet measures the ability of multi-agent systems to collaboratively form strategies for problem-solving, self-organization, and effective communication given a network topology. We evaluate a variety of baseline methods on AgentsNet including homogeneous networks of agents which first have to agree on basic protocols for organization and communication. We find that some frontier LLMs are already demonstrating strong performance for small networks but begin to fall off once the size of the network scales. While existing multi-agent benchmarks cover at most 2-5 agents, AgentsNet is practically unlimited in size and can scale with new generations of LLMs. As such, we also probe frontier models in a setup with up to 100 agents.

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

Sparsity in Deep Neural Networks (DNNs) has been widely studied to compress and accelerate the models on resource-constrained environments. It can be generally categorized into unstructured fine-grained sparsity that zeroes out multiple individual weights distributed across the neural network, and structured coarse-grained sparsity which prunes blocks of sub-networks of a neural network. Fine-grained sparsity can achieve a high compression ratio but is not hardware friendly and hence receives limited speed gains. On the other hand, coarse-grained sparsity cannot concurrently achieve both apparent acceleration on modern GPUs and decent performance. In this paper, we are the first to study training from scratch an N:M fine-grained structured sparse network, which can maintain the advantages of both unstructured fine-grained sparsity and structured coarse-grained sparsity simultaneously on specifically designed GPUs. Specifically, a 2:4 sparse network could achieve 2x speed-up without performance drop on Nvidia A100 GPUs. Furthermore, we propose a novel and effective ingredient, sparse-refined straight-through estimator (SR-STE), to alleviate the negative influence of the approximated gradients computed by vanilla STE during optimization. We also define a metric, Sparse Architecture Divergence (SAD), to measure the sparse network's topology change during the training process. Finally, We justify SR-STE's advantages with SAD and demonstrate the effectiveness of SR-STE by performing comprehensive experiments on various tasks. Source codes and models are available at https://github.com/NM-sparsity/NM-sparsity.

Sequence parallelism (SP), which divides the sequence dimension of input tensors across multiple computational devices, is becoming key to unlocking the long-context capabilities of generative AI models. This paper investigates the state-of-the-art SP approaches, i.e. DeepSpeed-Ulysses and Ring-Attention, and proposes a unified SP approach, which is more robust to transformer model architectures and network hardware topology. This paper compares the communication and memory cost of SP and existing parallelism, including data/tensor/zero/expert/pipeline parallelism, and discusses the best practices for designing hybrid 4D parallelism involving SP. We achieved 86% MFU on two 8xA800 nodes using SP for sequence length 208K for the LLAMA3-8B model. Our code is publicly available on https://github.com/feifeibear/long-context-attention.

This tutorial serves as a comprehensive guide for understanding graph databases, focusing on the fundamentals of graph theory while showcasing practical applications across various fields. It starts by introducing foundational concepts and delves into the structure of graphs through nodes and edges, covering different types such as undirected, directed, weighted, and unweighted graphs. Key graph properties, terminologies, and essential algorithms for network analysis are outlined, including Dijkstras shortest path algorithm and methods for calculating node centrality and graph connectivity. The tutorial highlights the advantages of graph databases over traditional relational databases, particularly in efficiently managing complex, interconnected data. It examines leading graph database systems such as Neo4j, Amazon Neptune, and ArangoDB, emphasizing their unique features for handling large datasets. Practical instructions on graph operations using NetworkX and Neo4j are provided, covering node and edge creation, attribute assignment, and advanced queries with Cypher. Additionally, the tutorial explores common graph visualization techniques using tools like Plotly and Neo4j Bloom, which enhance the interpretation and usability of graph data. It also delves into community detection algorithms, including the Louvain method, which facilitates clustering in large networks. Finally, the paper concludes with recommendations for researchers interested in exploring the vast potential of graph technologies.

The state space models, employing recursively propagated features, demonstrate strong representation capabilities comparable to Transformer models and superior efficiency. However, constrained by the inherent geometric constraints of sequences, it still falls short in modeling long-range dependencies. To address this issue, we propose the GrootVL network, which first dynamically generates a tree topology based on spatial relationships and input features. Then, feature propagation is performed based on this graph, thereby breaking the original sequence constraints to achieve stronger representation capabilities. Additionally, we introduce a linear complexity dynamic programming algorithm to enhance long-range interactions without increasing computational cost. GrootVL is a versatile multimodal framework that can be applied to both visual and textual tasks. Extensive experiments demonstrate that our method significantly outperforms existing structured state space models on image classification, object detection and segmentation. Besides, by fine-tuning large language models, our approach achieves consistent improvements in multiple textual tasks at minor training cost.

The shared topology of human skeletons motivated the recent investigation of graph convolutional network (GCN) solutions for action recognition. However, the existing GCNs rely on the binary connection of two neighbouring vertices (joints) formed by an edge (bone), overlooking the potential of constructing multi-vertex convolution structures. In this paper we address this oversight and explore the merits of a hyper-graph convolutional network (Hyper-GCN) to achieve the aggregation of rich semantic information conveyed by skeleton vertices. In particular, our Hyper-GCN adaptively optimises multi-scale hyper-graphs during training, revealing the action-driven multi-vertex relations. Besides, virtual connections are often designed to support efficient feature aggregation, implicitly extending the spectrum of dependencies within the skeleton. By injecting virtual connections into hyper-graphs, the semantic clues of diverse action categories can be highlighted. The results of experiments conducted on the NTU-60, NTU-120, and NW-UCLA datasets, demonstrate the merits of our Hyper-GCN, compared to the state-of-the-art methods. Specifically, we outperform the existing solutions on NTU-120, achieving 90.2\% and 91.4\% in terms of the top-1 recognition accuracy on X-Sub and X-Set.

Symbolic regression (SR) is a powerful technique for discovering the underlying mathematical expressions from observed data. Inspired by the success of deep learning, recent efforts have focused on two categories for SR methods. One is using a neural network or genetic programming to search the expression tree directly. Although this has shown promising results, the large search space poses difficulties in learning constant factors and processing high-dimensional problems. Another approach is leveraging a transformer-based model training on synthetic data and offers advantages in inference speed. However, this method is limited to fixed small numbers of dimensions and may encounter inference problems when given data is out-of-distribution compared to the synthetic data. In this work, we propose DySymNet, a novel neural-guided Dynamic Symbolic Network for SR. Instead of searching for expressions within a large search space, we explore DySymNet with various structures and optimize them to identify expressions that better-fitting the data. With a topology structure like neural networks, DySymNet not only tackles the challenge of high-dimensional problems but also proves effective in optimizing constants. Based on extensive numerical experiments using low-dimensional public standard benchmarks and the well-known SRBench with more variables, our method achieves state-of-the-art performance in terms of fitting accuracy and robustness to noise.

Image-based 3D reconstruction has increasingly stunning results over the past few years with the latest improvements in computer vision and graphics. Geometry and topology are two fundamental concepts when dealing with 3D mesh structures. But the latest often remains a side issue in the 3D mesh-based reconstruction literature. Indeed, performing per-vertex elementary displacements over a 3D sphere mesh only impacts its geometry and leaves the topological structure unchanged and fixed. Whereas few attempts propose to update the geometry and the topology, all need to lean on costly 3D ground-truth to determine the faces/edges to prune. We present in this work a method that aims to refine the topology of any 3D mesh through a face-pruning strategy that extensively relies upon 2D alpha masks and camera pose information. Our solution leverages a differentiable renderer that renders each face as a 2D soft map. Its pixel intensity reflects the probability of being covered during the rendering process by such a face. Based on the 2D soft-masks available, our method is thus able to quickly highlight all the incorrectly rendered faces for a given viewpoint. Because our module is agnostic to the network that produces the 3D mesh, it can be easily plugged into any self-supervised image-based (either synthetic or natural) 3D reconstruction pipeline to get complex meshes with a non-spherical topology.

Electroencephalography (EEG) offers a non-invasive lens into human brain activity, but building large-scale models is hampered by topological heterogeneity: each public EEG data defines its own electrode layout, limiting generalization. We introduce LUNA (Latent Unified Network Architecture), a self-supervised foundation model that reconciles disparate electrode geometries while scaling linearly -- not quadratically -- with channel count. LUNA compresses multi-channel EEG into a fixed-size, topology-agnostic latent space via learned queries and cross-attention. Downstream transformer blocks then operate exclusively on this latent representation using patch-wise temporal self-attention, decoupling computation from electrode count. Pre-trained on TUEG and Siena (over 21,000 hours of raw EEG across diverse montages) using a masked-patch reconstruction objective, LUNA transfers effectively to four downstream tasks: abnormality detection, artifact rejection, slowing classification, and emotion recognition. It demonstrates highly competitive performance across several benchmarks, achieving state-of-the-art results on TUAR and TUSL, e.g., 0.921 AUROC on TUAR, while reducing FLOPs by 300x and trimming GPU memory use by up to 10x. Critically, these gains are consistent across all evaluated electrode configurations. Code is available at https://github.com/pulp-bio/BioFoundation

We propose SAM-Road, an adaptation of the Segment Anything Model (SAM) for extracting large-scale, vectorized road network graphs from satellite imagery. To predict graph geometry, we formulate it as a dense semantic segmentation task, leveraging the inherent strengths of SAM. The image encoder of SAM is fine-tuned to produce probability masks for roads and intersections, from which the graph vertices are extracted via simple non-maximum suppression. To predict graph topology, we designed a lightweight transformer-based graph neural network, which leverages the SAM image embeddings to estimate the edge existence probabilities between vertices. Our approach directly predicts the graph vertices and edges for large regions without expensive and complex post-processing heuristics, and is capable of building complete road network graphs spanning multiple square kilometers in a matter of seconds. With its simple, straightforward, and minimalist design, SAM-Road achieves comparable accuracy with the state-of-the-art method RNGDet++, while being 40 times faster on the City-scale dataset. We thus demonstrate the power of a foundational vision model when applied to a graph learning task. The code is available at https://github.com/htcr/sam_road.

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

The learnability of different neural architectures can be characterized directly by computable measures of data complexity. In this paper, we reframe the problem of architecture selection as understanding how data determines the most expressive and generalizable architectures suited to that data, beyond inductive bias. After suggesting algebraic topology as a measure for data complexity, we show that the power of a network to express the topological complexity of a dataset in its decision region is a strictly limiting factor in its ability to generalize. We then provide the first empirical characterization of the topological capacity of neural networks. Our empirical analysis shows that at every level of dataset complexity, neural networks exhibit topological phase transitions. This observation allowed us to connect existing theory to empirically driven conjectures on the choice of architectures for fully-connected neural networks.

Network embedding, which maps graphs to distributed representations, is a unified framework for various graph inference tasks. According to the topology properties (e.g., structural roles and community memberships of nodes) to be preserved, it can be categorized into the identity and position embedding. However, existing methods can only capture one type of property. Some approaches can support the inductive inference that generalizes the embedding model to new nodes or graphs but relies on the availability of attributes. Due to the complicated correlations between topology and attributes, it is unclear for some inductive methods which type of property they can capture. In this study, we explore a unified framework for the joint inductive inference of identity and position embeddings without attributes. An inductive random walk embedding (IRWE) method is proposed, which combines multiple attention units to handle the random walk on graph topology and simultaneously derives identity and position embeddings that are jointly optimized. In particular, we demonstrate that some random walk statistics can be informative features to characterize node identities and positions while supporting the inductive embedding inference. Experiments validate the superior performance of IRWE beyond various baselines for the transductive and inductive inference of identity and position embeddings.

The automated extraction of complete and precise road network graphs from remote sensing imagery remains a critical challenge in geospatial computer vision. Segmentation-based approaches, while effective in pixel-level recognition, struggle to maintain topology fidelity after vectorization postprocessing. Graph-growing methods build more topologically faithful graphs but suffer from computationally prohibitive iterative ROI cropping. Graph-generating methods first predict global static candidate road network vertices, and then infer possible edges between vertices. They achieve fast topology-aware inference, but limits the dynamic insertion of vertices. To address these challenges, we propose DeH4R, a novel hybrid model that combines graph-generating efficiency and graph-growing dynamics. This is achieved by decoupling the task into candidate vertex detection, adjacent vertex prediction, initial graph contruction, and graph expansion. This architectural innovation enables dynamic vertex (edge) insertions while retaining fast inference speed and enhancing both topology fidelity and spatial consistency. Comprehensive evaluations on CityScale and SpaceNet benchmarks demonstrate state-of-the-art (SOTA) performance. DeH4R outperforms the prior SOTA graph-growing method RNGDet++ by 4.62 APLS and 10.18 IoU on CityScale, while being approximately 10 times faster. The code will be made publicly available at https://github.com/7777777FAN/DeH4R.

Generating motion for arbitrary skeletons is a longstanding challenge in computer graphics, remaining largely unexplored due to the scarcity of diverse datasets and the irregular nature of the data. In this work, we introduce AnyTop, a diffusion model that generates motions for diverse characters with distinct motion dynamics, using only their skeletal structure as input. Our work features a transformer-based denoising network, tailored for arbitrary skeleton learning, integrating topology information into the traditional attention mechanism. Additionally, by incorporating textual joint descriptions into the latent feature representation, AnyTop learns semantic correspondences between joints across diverse skeletons. Our evaluation demonstrates that AnyTop generalizes well, even with as few as three training examples per topology, and can produce motions for unseen skeletons as well. Furthermore, our model's latent space is highly informative, enabling downstream tasks such as joint correspondence, temporal segmentation and motion editing. Our webpage, https://anytop2025.github.io/Anytop-page, includes links to videos and code.

Understanding the road genome is essential to realize autonomous driving. This highly intelligent problem contains two aspects - the connection relationship of lanes, and the assignment relationship between lanes and traffic elements, where a comprehensive topology reasoning method is vacant. On one hand, previous map learning techniques struggle in deriving lane connectivity with segmentation or laneline paradigms; or prior lane topology-oriented approaches focus on centerline detection and neglect the interaction modeling. On the other hand, the traffic element to lane assignment problem is limited in the image domain, leaving how to construct the correspondence from two views an unexplored challenge. To address these issues, we present TopoNet, the first end-to-end framework capable of abstracting traffic knowledge beyond conventional perception tasks. To capture the driving scene topology, we introduce three key designs: (1) an embedding module to incorporate semantic knowledge from 2D elements into a unified feature space; (2) a curated scene graph neural network to model relationships and enable feature interaction inside the network; (3) instead of transmitting messages arbitrarily, a scene knowledge graph is devised to differentiate prior knowledge from various types of the road genome. We evaluate TopoNet on the challenging scene understanding benchmark, OpenLane-V2, where our approach outperforms all previous works by a great margin on all perceptual and topological metrics. The code is released at https://github.com/OpenDriveLab/TopoNet

A central question for neuroscience is how to characterize brain representations of perceptual and cognitive content. An ideal characterization should distinguish different functional regions with robustness to noise and idiosyncrasies of individual brains that do not correspond to computational differences. Previous studies have characterized brain representations by their representational geometry, which is defined by the representational dissimilarity matrix (RDM), a summary statistic that abstracts from the roles of individual neurons (or responses channels) and characterizes the discriminability of stimuli. Here we explore a further step of abstraction: from the geometry to the topology of brain representations. We propose topological representational similarity analysis (tRSA), an extension of representational similarity analysis (RSA) that uses a family of geo-topological summary statistics that generalizes the RDM to characterize the topology while de-emphasizing the geometry. We evaluate this new family of statistics in terms of the sensitivity and specificity for model selection using both simulations and functional MRI (fMRI) data. In the simulations, the ground truth is a data-generating layer representation in a neural network model and the models are the same and other layers in different model instances (trained from different random seeds). In fMRI, the ground truth is a visual area and the models are the same and other areas measured in different subjects. Results show that topology-sensitive characterizations of population codes are robust to noise and interindividual variability and maintain excellent sensitivity to the unique representational signatures of different neural network layers and brain regions.

Sketch-based terrain generation seeks to create realistic landscapes for virtual environments in various applications such as computer games, animation and virtual reality. Recently, deep learning based terrain generation has emerged, notably the ones based on generative adversarial networks (GAN). However, these methods often struggle to fulfill the requirements of flexible user control and maintain generative diversity for realistic terrain. Therefore, we propose a novel diffusion-based method, namely terrain diffusion network (TDN), which actively incorporates user guidance for enhanced controllability, taking into account terrain features like rivers, ridges, basins, and peaks. Instead of adhering to a conventional monolithic denoising process, which often compromises the fidelity of terrain details or the alignment with user control, a multi-level denoising scheme is proposed to generate more realistic terrains by taking into account fine-grained details, particularly those related to climatic patterns influenced by erosion and tectonic activities. Specifically, three terrain synthesisers are designed for structural, intermediate, and fine-grained level denoising purposes, which allow each synthesiser concentrate on a distinct terrain aspect. Moreover, to maximise the efficiency of our TDN, we further introduce terrain and sketch latent spaces for the synthesizers with pre-trained terrain autoencoders. Comprehensive experiments on a new dataset constructed from NASA Topology Images clearly demonstrate the effectiveness of our proposed method, achieving the state-of-the-art performance. Our code and dataset will be publicly available.

Bird's-eye-view (BEV) representation is crucial for the perception function in autonomous driving tasks. It is difficult to balance the accuracy, efficiency and range of BEV representation. The existing works are restricted to a limited perception range within 50 meters. Extending the BEV representation range can greatly benefit downstream tasks such as topology reasoning, scene understanding, and planning by offering more comprehensive information and reaction time. The Standard-Definition (SD) navigation maps can provide a lightweight representation of road structure topology, characterized by ease of acquisition and low maintenance costs. An intuitive idea is to combine the close-range visual information from onboard cameras with the beyond line-of-sight (BLOS) environmental priors from SD maps to realize expanded perceptual capabilities. In this paper, we propose BLOS-BEV, a novel BEV segmentation model that incorporates SD maps for accurate beyond line-of-sight perception, up to 200m. Our approach is applicable to common BEV architectures and can achieve excellent results by incorporating information derived from SD maps. We explore various feature fusion schemes to effectively integrate the visual BEV representations and semantic features from the SD map, aiming to leverage the complementary information from both sources optimally. Extensive experiments demonstrate that our approach achieves state-of-the-art performance in BEV segmentation on nuScenes and Argoverse benchmark. Through multi-modal inputs, BEV segmentation is significantly enhanced at close ranges below 50m, while also demonstrating superior performance in long-range scenarios, surpassing other methods by over 20% mIoU at distances ranging from 50-200m.

We put forward the dynamical study of a novel higher-order small network of Chialvo neurons arranged in a ring-star topology, with the neurons interacting via linear diffusive couplings. This model is perceived to imitate the nonlinear dynamical properties exhibited by a realistic nervous system where the neurons transfer information through higher-order multi-body interactions. We first analyze our model using the tools from nonlinear dynamics literature: fixed point analysis, Jacobian matrix, and bifurcation patterns. We observe the coexistence of chaotic attractors, and also an intriguing route to chaos starting from a fixed point, to period-doubling, to cyclic quasiperiodic closed invariant curves, to ultimately chaos. We numerically observe the existence of codimension-1 bifurcation patterns: saddle-node, period-doubling, and Neimark Sacker. We also qualitatively study the typical phase portraits of the system and numerically quantify chaos and complexity using the 0-1 test and sample entropy measure respectively. Finally, we study the collective behavior of the neurons in terms of two synchronization measures: the cross-correlation coefficient, and the Kuramoto order parameter.

The Circle of Willis (CoW) is an important network of arteries connecting major circulations of the brain. Its vascular architecture is believed to affect the risk, severity, and clinical outcome of serious neurovascular diseases. However, characterizing the highly variable CoW anatomy is still a manual and time-consuming expert task. The CoW is usually imaged by two non-invasive angiographic imaging modalities, magnetic resonance angiography (MRA) and computed tomography angiography (CTA), but there exist limited datasets with annotations on CoW anatomy, especially for CTA. Therefore, we organized the TopCoW challenge with the release of an annotated CoW dataset. The TopCoW dataset is the first public dataset with voxel-level annotations for 13 CoW vessel components, enabled by virtual reality technology. It is also the first large dataset using 200 pairs of MRA and CTA from the same patients. As part of the benchmark, we invited submissions worldwide and attracted over 250 registered participants from six continents. The submissions were evaluated on both internal and external test datasets of 226 scans from over five centers. The top performing teams achieved over 90% Dice scores at segmenting the CoW components, over 80% F1 scores at detecting key CoW components, and over 70% balanced accuracy at classifying CoW variants for nearly all test sets. The best algorithms also showed clinical potential in classifying fetal-type posterior cerebral artery and locating aneurysms with CoW anatomy. TopCoW demonstrated the utility and versatility of CoW segmentation algorithms for a wide range of downstream clinical applications with explainability. The annotated datasets and best performing algorithms have been released as public Zenodo records to foster further methodological development and clinical tool building.

Lane detection is a challenging task that requires predicting complex topology shapes of lane lines and distinguishing different types of lanes simultaneously. Earlier works follow a top-down roadmap to regress predefined anchors into various shapes of lane lines, which lacks enough flexibility to fit complex shapes of lanes due to the fixed anchor shapes. Lately, some works propose to formulate lane detection as a keypoint estimation problem to describe the shapes of lane lines more flexibly and gradually group adjacent keypoints belonging to the same lane line in a point-by-point manner, which is inefficient and time-consuming during postprocessing. In this paper, we propose a Global Association Network (GANet) to formulate the lane detection problem from a new perspective, where each keypoint is directly regressed to the starting point of the lane line instead of point-by-point extension. Concretely, the association of keypoints to their belonged lane line is conducted by predicting their offsets to the corresponding starting points of lanes globally without dependence on each other, which could be done in parallel to greatly improve efficiency. In addition, we further propose a Lane-aware Feature Aggregator (LFA), which adaptively captures the local correlations between adjacent keypoints to supplement local information to the global association. Extensive experiments on two popular lane detection benchmarks show that our method outperforms previous methods with F1 score of 79.63% on CULane and 97.71% on Tusimple dataset with high FPS. The code will be released at https://github.com/Wolfwjs/GANet.

We introduce a new function-preserving transformation for efficient neural architecture search. This network transformation allows reusing previously trained networks and existing successful architectures that improves sample efficiency. We aim to address the limitation of current network transformation operations that can only perform layer-level architecture modifications, such as adding (pruning) filters or inserting (removing) a layer, which fails to change the topology of connection paths. Our proposed path-level transformation operations enable the meta-controller to modify the path topology of the given network while keeping the merits of reusing weights, and thus allow efficiently designing effective structures with complex path topologies like Inception models. We further propose a bidirectional tree-structured reinforcement learning meta-controller to explore a simple yet highly expressive tree-structured architecture space that can be viewed as a generalization of multi-branch architectures. We experimented on the image classification datasets with limited computational resources (about 200 GPU-hours), where we observed improved parameter efficiency and better test results (97.70% test accuracy on CIFAR-10 with 14.3M parameters and 74.6% top-1 accuracy on ImageNet in the mobile setting), demonstrating the effectiveness and transferability of our designed architectures.

Topology optimization by optimally distributing materials in a given domain requires non-gradient optimizers to solve highly complicated problems. However, with hundreds of design variables or more involved, solving such problems would require millions of Finite Element Method (FEM) calculations whose computational cost is huge and impractical. Here we report Self-directed Online Learning Optimization (SOLO) which integrates Deep Neural Network (DNN) with FEM calculations. A DNN learns and substitutes the objective as a function of design variables. A small number of training data is generated dynamically based on the DNN's prediction of the optimum. The DNN adapts to the new training data and gives better prediction in the region of interest until convergence. The optimum predicted by the DNN is proved to converge to the true global optimum through iterations. Our algorithm was tested by four types of problems including compliance minimization, fluid-structure optimization, heat transfer enhancement and truss optimization. It reduced the computational time by 2 ~ 5 orders of magnitude compared with directly using heuristic methods, and outperformed all state-of-the-art algorithms tested in our experiments. This approach enables solving large multi-dimensional optimization problems.

Tensor Networks (TN) offer a powerful framework to efficiently represent very high-dimensional objects. TN have recently shown their potential for machine learning applications and offer a unifying view of common tensor decomposition models such as Tucker, tensor train (TT) and tensor ring (TR). However, identifying the best tensor network structure from data for a given task is challenging. In this work, we leverage the TN formalism to develop a generic and efficient adaptive algorithm to jointly learn the structure and the parameters of a TN from data. Our method is based on a simple greedy approach starting from a rank one tensor and successively identifying the most promising tensor network edges for small rank increments. Our algorithm can adaptively identify TN structures with small number of parameters that effectively optimize any differentiable objective function. Experiments on tensor decomposition, tensor completion and model compression tasks demonstrate the effectiveness of the proposed algorithm. In particular, our method outperforms the state-of-the-art evolutionary topology search [Li and Sun, 2020] for tensor decomposition of images (while being orders of magnitude faster) and finds efficient tensor network structures to compress neural networks outperforming popular TT based approaches [Novikov et al., 2015].

The precise knowledge regarding the state of the power grid is important in order to ensure optimal and reliable grid operation. Specifically, knowing the state of the distribution grid becomes increasingly important as more renewable energy sources are connected directly into the distribution network, increasing the fluctuations of the injected power. In this paper, we consider the case when the distribution grid becomes partially observable, and the state estimation problem is under-determined. We present a new methodology that leverages a deep neural network (DNN) to estimate the grid state. The standard DNN training method is modified to explicitly incorporate the physical information of the grid topology and line/shunt admittance. We show that our method leads to a superior accuracy of the estimation when compared to the case when no physical information is provided. Finally, we compare the performance of our method to the standard state estimation approach, which is based on the weighted least squares with pseudo-measurements, and show that our method performs significantly better with respect to the estimation accuracy.

Although deep learning models have demonstrated remarkable potential in weather prediction, most of them overlook either the physics of the underlying weather evolution or the topology of the Earth's surface. In light of these disadvantages, we develop PASSAT, a novel Physics-ASSisted And Topology-informed deep learning model for weather prediction. PASSAT attributes the weather evolution to two key factors: (i) the advection process that can be characterized by the advection equation and the Navier-Stokes equation; (ii) the Earth-atmosphere interaction that is difficult to both model and calculate. PASSAT also takes the topology of the Earth's surface into consideration, other than simply treating it as a plane. With these considerations, PASSAT numerically solves the advection equation and the Navier-Stokes equation on the spherical manifold, utilizes a spherical graph neural network to capture the Earth-atmosphere interaction, and generates the initial velocity fields that are critical to solving the advection equation from the same spherical graph neural network. In the 5.625^circ-resolution ERA5 data set, PASSAT outperforms both the state-of-the-art deep learning-based weather prediction models and the operational numerical weather prediction model IFS T42. Code and checkpoint are available at https://github.com/Yumenomae/PASSAT_5p625.

Using a set of LambdaCDM simulations of cosmic structure formation, we study the evolving connectivity and changing topological structure of the cosmic web using state-of-the-art tools of multiscale topological data analysis (TDA). We follow the development of the cosmic web topology in terms of the evolution of Betti number curves and feature persistence diagrams of the three (topological) classes of structural features: matter concentrations, filaments and tunnels, and voids. The Betti curves specify the prominence of features as a function of density level, and their evolution with cosmic epoch reflects the changing network connections between these structural features. The persistence diagrams quantify the longevity and stability of topological features. In this study we establish, for the first time, the link between persistence diagrams, the features they show, and the gravitationally driven cosmic structure formation process. By following the diagrams' development over cosmic time, the link between the multiscale topology of the cosmic web and the hierarchical buildup of cosmic structure is established. The sharp apexes in the diagrams are intimately related to key transitions in the structure formation process. The apex in the matter concentration diagrams coincides with the density level at which, typically, they detach from the Hubble expansion and begin to collapse. At that level many individual islands merge to form the network of the cosmic web and a large number of filaments and tunnels emerge to establish its connecting bridges. The location trends of the apex possess a self-similar character that can be related to the cosmic web's hierarchical buildup. We find that persistence diagrams provide a significantly higher and more profound level of information on the structure formation process than more global summary statistics like Euler characteristic or Betti numbers.

Blood vessel networks in the brain play a crucial role in stroke research, where understanding their topology is essential for analyzing blood flow dynamics. However, extracting detailed topological vessel network information from microscopy data remains a significant challenge, mainly due to the scarcity of labeled training data and the need for high topological accuracy. This work combines synthetic data generation with deep learning to automatically extract vessel networks as graphs from volumetric microscopy data. To combat data scarcity, we introduce a comprehensive pipeline for generating large-scale synthetic datasets that mirror the characteristics of real vessel networks. Our three-stage approach progresses from abstract graph generation through vessel mask creation to realistic medical image synthesis, incorporating biological constraints and imaging artifacts at each stage. Using this synthetic data, we develop a two-stage deep learning pipeline of 3D U-Net-based models for node detection and edge prediction. Fine-tuning on real microscopy data shows promising adaptation, improving edge prediction F1 scores from 0.496 to 0.626 by training on merely 5 manually labeled samples. These results suggest that automated vessel network extraction is becoming practically feasible, opening new possibilities for large-scale vascular analysis in stroke research.

Graph representation learning is a fundamental task in various applications that strives to learn low-dimensional embeddings for nodes that can preserve graph topology information. However, many existing methods focus on static graphs while ignoring evolving graph patterns. Inspired by the success of graph convolutional networks(GCNs) in static graph embedding, we propose a novel k-core based temporal graph convolutional network, the CTGCN, to learn node representations for dynamic graphs. In contrast to previous dynamic graph embedding methods, CTGCN can preserve both local connective proximity and global structural similarity while simultaneously capturing graph dynamics. In the proposed framework, the traditional graph convolution is generalized into two phases, feature transformation and feature aggregation, which gives the CTGCN more flexibility and enables the CTGCN to learn connective and structural information under the same framework. Experimental results on 7 real-world graphs demonstrate that the CTGCN outperforms existing state-of-the-art graph embedding methods in several tasks, including link prediction and structural role classification. The source code of this work can be obtained from https://github.com/jhljx/CTGCN.

Graph Neural Networks (GNNs) have shown great promise in learning node embeddings for link prediction (LP). While numerous studies aim to improve the overall LP performance of GNNs, none have explored its varying performance across different nodes and its underlying reasons. To this end, we aim to demystify which nodes will perform better from the perspective of their local topology. Despite the widespread belief that low-degree nodes exhibit poorer LP performance, our empirical findings provide nuances to this viewpoint and prompt us to propose a better metric, Topological Concentration (TC), based on the intersection of the local subgraph of each node with the ones of its neighbors. We empirically demonstrate that TC has a higher correlation with LP performance than other node-level topological metrics like degree and subgraph density, offering a better way to identify low-performing nodes than using cold-start. With TC, we discover a novel topological distribution shift issue in which newly joined neighbors of a node tend to become less interactive with that node's existing neighbors, compromising the generalizability of node embeddings for LP at testing time. To make the computation of TC scalable, We further propose Approximated Topological Concentration (ATC) and theoretically/empirically justify its efficacy in approximating TC and reducing the computation complexity. Given the positive correlation between node TC and its LP performance, we explore the potential of boosting LP performance via enhancing TC by re-weighting edges in the message-passing and discuss its effectiveness with limitations. Our code is publicly available at https://github.com/YuWVandy/Topo_LP_GNN.

While many approaches to make neural networks more fathomable have been proposed, they are restricted to interrogating the network with input data. Measures for characterizing and monitoring structural properties, however, have not been developed. In this work, we propose neural persistence, a complexity measure for neural network architectures based on topological data analysis on weighted stratified graphs. To demonstrate the usefulness of our approach, we show that neural persistence reflects best practices developed in the deep learning community such as dropout and batch normalization. Moreover, we derive a neural persistence-based stopping criterion that shortens the training process while achieving comparable accuracies as early stopping based on validation loss.

Classical self-supervised networks suffer from convergence problems and reduced segmentation accuracy due to forceful termination. Qubits or bi-level quantum bits often describe quantum neural network models. In this article, a novel self-supervised shallow learning network model exploiting the sophisticated three-level qutrit-inspired quantum information system referred to as Quantum Fully Self-Supervised Neural Network (QFS-Net) is presented for automated segmentation of brain MR images. The QFS-Net model comprises a trinity of a layered structure of qutrits inter-connected through parametric Hadamard gates using an 8-connected second-order neighborhood-based topology. The non-linear transformation of the qutrit states allows the underlying quantum neural network model to encode the quantum states, thereby enabling a faster self-organized counter-propagation of these states between the layers without supervision. The suggested QFS-Net model is tailored and extensively validated on Cancer Imaging Archive (TCIA) data set collected from Nature repository and also compared with state of the art supervised (U-Net and URes-Net architectures) and the self-supervised QIS-Net model. Results shed promising segmented outcome in detecting tumors in terms of dice similarity and accuracy with minimum human intervention and computational resources.

Through the success of deep learning in various domains, artificial neural networks are currently among the most used artificial intelligence methods. Taking inspiration from the network properties of biological neural networks (e.g. sparsity, scale-freeness), we argue that (contrary to general practice) artificial neural networks, too, should not have fully-connected layers. Here we propose sparse evolutionary training of artificial neural networks, an algorithm which evolves an initial sparse topology (Erdos-R\'enyi random graph) of two consecutive layers of neurons into a scale-free topology, during learning. Our method replaces artificial neural networks fully-connected layers with sparse ones before training, reducing quadratically the number of parameters, with no decrease in accuracy. We demonstrate our claims on restricted Boltzmann machines, multi-layer perceptrons, and convolutional neural networks for unsupervised and supervised learning on 15 datasets. Our approach has the potential to enable artificial neural networks to scale up beyond what is currently possible.

The R-Learner is a powerful, theoretically-grounded framework for estimating heterogeneous treatment effects, prized for its robustness to nuisance model errors. However, its application to network data, where causal heterogeneity is often graph-dependent, presents a critical challenge to its core assumption of a well-specified final-stage model. In this paper, we conduct a large-scale empirical study to systematically dissect the R-Learner framework on graphs. We provide the first rigorous evidence that the primary driver of performance is the inductive bias of the final-stage CATE estimator, an effect that dominates the choice of nuisance models. Our central finding is the quantification of a catastrophic "representation bottleneck": we prove with overwhelming statistical significance (p < 0.001) that R-Learners with a graph-blind final stage fail completely (MSE > 4.0), even when paired with powerful GNN nuisance models. Conversely, our proposed end-to-end Graph R-Learner succeeds and significantly outperforms a strong, non-DML GNN T-Learner baseline. Furthermore, we identify and provide a mechanistic explanation for a subtle, topology-dependent "nuisance bottleneck," linking it to GNN over-squashing via a targeted "Hub-Periphery Trade-off" analysis. Our findings are validated across diverse synthetic and semi-synthetic benchmarks. We release our code as a reproducible benchmark to facilitate future research on this critical "final-stage bottleneck."

Message Passing Neural Networks (MPNNs) are instances of Graph Neural Networks that leverage the graph to send messages over the edges. This inductive bias leads to a phenomenon known as over-squashing, where a node feature is insensitive to information contained at distant nodes. Despite recent methods introduced to mitigate this issue, an understanding of the causes for over-squashing and of possible solutions are lacking. In this theoretical work, we prove that: (i) Neural network width can mitigate over-squashing, but at the cost of making the whole network more sensitive; (ii) Conversely, depth cannot help mitigate over-squashing: increasing the number of layers leads to over-squashing being dominated by vanishing gradients; (iii) The graph topology plays the greatest role, since over-squashing occurs between nodes at high commute (access) time. Our analysis provides a unified framework to study different recent methods introduced to cope with over-squashing and serves as a justification for a class of methods that fall under graph rewiring.

Graph neural networks achieve high accuracy in link prediction by jointly leveraging graph topology and node attributes. Topology, however, is represented indirectly; state-of-the-art methods based on subgraph classification label nodes with distance to the target link, so that, although topological information is present, it is tempered by pooling. This makes it challenging to leverage features like loops and motifs associated with network formation mechanisms. We propose a link prediction algorithm based on a new pooling scheme called WalkPool. WalkPool combines the expressivity of topological heuristics with the feature-learning ability of neural networks. It summarizes a putative link by random walk probabilities of adjacent paths. Instead of extracting transition probabilities from the original graph, it computes the transition matrix of a "predictive" latent graph by applying attention to learned features; this may be interpreted as feature-sensitive topology fingerprinting. WalkPool can leverage unsupervised node features or be combined with GNNs and trained end-to-end. It outperforms state-of-the-art methods on all common link prediction benchmarks, both homophilic and heterophilic, with and without node attributes. Applying WalkPool to a set of unsupervised GNNs significantly improves prediction accuracy, suggesting that it may be used as a general-purpose graph pooling scheme.

Graphs have often been used to answer questions about the interaction between real-world entities by taking advantage of their capacity to represent complex topologies. Complex networks are known to be graphs that capture such non-trivial topologies; they are able to represent human phenomena such as epidemic processes, the dynamics of populations, and the urbanization of cities. The investigation of complex networks has been extrapolated to many fields of science, with particular emphasis on computing techniques, including artificial intelligence. In such a case, the analysis of the interaction between entities of interest is transposed to the internal learning of algorithms, a paradigm whose investigation is able to expand the state of the art in Computer Science. By exploring this paradigm, this thesis puts together complex networks and machine learning techniques to improve the understanding of the human phenomena observed in pandemics, pendular migration, and street networks. Accordingly, we contribute with: (i) a new neural network architecture capable of modeling dynamic processes observed in spatial and temporal data with applications in epidemics propagation, weather forecasting, and patient monitoring in intensive care units; (ii) a machine-learning methodology for analyzing and predicting links in the scope of human mobility between all the cities of Brazil; and, (iii) techniques for identifying inconsistencies in the urban planning of cities while tracking the most influential vertices, with applications over Brazilian and worldwide cities. We obtained results sustained by sound evidence of advances to the state of the art in artificial intelligence, rigorous formalisms, and ample experimentation. Our findings rely upon real-world applications in a range of domains, demonstrating the applicability of our methodologies.

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.

The natural world is full of complex systems characterized by intricate relations between their components: from social interactions between individuals in a social network to electrostatic interactions between atoms in a protein. Topological Deep Learning (TDL) provides a comprehensive framework to process and extract knowledge from data associated with these systems, such as predicting the social community to which an individual belongs or predicting whether a protein can be a reasonable target for drug development. TDL has demonstrated theoretical and practical advantages that hold the promise of breaking ground in the applied sciences and beyond. However, the rapid growth of the TDL literature has also led to a lack of unification in notation and language across Topological Neural Network (TNN) architectures. This presents a real obstacle for building upon existing works and for deploying TNNs to new real-world problems. To address this issue, we provide an accessible introduction to TDL, and compare the recently published TNNs using a unified mathematical and graphical notation. Through an intuitive and critical review of the emerging field of TDL, we extract valuable insights into current challenges and exciting opportunities for future development.

In the multiple unmanned aerial vehicle (UAV)- assisted downlink communication, it is challenging for UAV base stations (UAV BSs) to realize trajectory design and resource assignment in unknown environments. The cooperation and competition between UAV BSs in the communication network leads to a Markov game problem. Multi-agent reinforcement learning is a significant solution for the above decision-making. However, there are still many common issues, such as the instability of the system and low utilization of historical data, that limit its application. In this paper, a novel graph-attention multi-agent trust region (GA-MATR) reinforcement learning framework is proposed to solve the multi-UAV assisted communication problem. Graph recurrent network is introduced to process and analyze complex topology of the communication network, so as to extract useful information and patterns from observational information. The attention mechanism provides additional weighting for conveyed information, so that the critic network can accurately evaluate the value of behavior for UAV BSs. This provides more reliable feedback signals and helps the actor network update the strategy more effectively. Ablation simulations indicate that the proposed approach attains improved convergence over the baselines. UAV BSs learn the optimal communication strategies to achieve their maximum cumulative rewards. Additionally, multi-agent trust region method with monotonic convergence provides an estimated Nash equilibrium for the multi-UAV assisted communication Markov game.

Serving Large Language Models (LLMs) is a GPU-intensive task where traditional autoscalers fall short, particularly for modern Prefill-Decode (P/D) disaggregated architectures. This architectural shift, while powerful, introduces significant operational challenges, including inefficient use of heterogeneous hardware, network bottlenecks, and critical imbalances between prefill and decode stages. We introduce HeteroScale, a coordinated autoscaling framework that addresses the core challenges of P/D disaggregated serving. HeteroScale combines a topology-aware scheduler that adapts to heterogeneous hardware and network constraints with a novel metric-driven policy derived from the first large-scale empirical study of autoscaling signals in production. By leveraging a single, robust metric to jointly scale prefill and decode pools, HeteroScale maintains architectural balance while ensuring efficient, adaptive resource management. Deployed in a massive production environment on tens of thousands of GPUs, HeteroScale has proven its effectiveness, increasing average GPU utilization by a significant 26.6 percentage points and saving hundreds of thousands of GPU-hours daily, all while upholding stringent service level objectives.

We present a simple, highly modularized network architecture for image classification. Our network is constructed by repeating a building block that aggregates a set of transformations with the same topology. Our simple design results in a homogeneous, multi-branch architecture that has only a few hyper-parameters to set. This strategy exposes a new dimension, which we call "cardinality" (the size of the set of transformations), as an essential factor in addition to the dimensions of depth and width. On the ImageNet-1K dataset, we empirically show that even under the restricted condition of maintaining complexity, increasing cardinality is able to improve classification accuracy. Moreover, increasing cardinality is more effective than going deeper or wider when we increase the capacity. Our models, named ResNeXt, are the foundations of our entry to the ILSVRC 2016 classification task in which we secured 2nd place. We further investigate ResNeXt on an ImageNet-5K set and the COCO detection set, also showing better results than its ResNet counterpart. The code and models are publicly available online.

Since its 2009 genesis block, the Bitcoin network has processed >1.08 billion (B) transactions representing >8.72B BTC, offering rich potential for machine learning (ML); yet, its pseudonymity and obscured flow of funds inherent in its \utxo-based design, have rendered this data largely inaccessible for ML research. Addressing this gap, we present an ML-compatible graph modeling the Bitcoin's economic topology by reconstructing the flow of funds. This temporal, heterogeneous graph encompasses complete transaction history up to block \cutoffHeight, consisting of >2.4B nodes and >39.72B edges. Additionally, we provide custom sampling methods yielding node and edge feature vectors of sampled communities, tools to load and analyze the Bitcoin graph data within specialized graph databases, and ready-to-use database snapshots. This comprehensive dataset and toolkit empower the ML community to tackle Bitcoin's intricate ecosystem at scale, driving progress in applications such as anomaly detection, address classification, market analysis, and large-scale graph ML benchmarking. Dataset and code available at https://github.com/B1AAB/EBA{github.com/b1aab/eba}

Protein representation learning (PRL) is crucial for understanding structure-function relationships, yet current sequence- and graph-based methods fail to capture the hierarchical organization inherent in protein structures. We introduce Topotein, a comprehensive framework that applies topological deep learning to PRL through the novel Protein Combinatorial Complex (PCC) and Topology-Complete Perceptron Network (TCPNet). Our PCC represents proteins at multiple hierarchical levels -- from residues to secondary structures to complete proteins -- while preserving geometric information at each level. TCPNet employs SE(3)-equivariant message passing across these hierarchical structures, enabling more effective capture of multi-scale structural patterns. Through extensive experiments on four PRL tasks, TCPNet consistently outperforms state-of-the-art geometric graph neural networks. Our approach demonstrates particular strength in tasks such as fold classification which require understanding of secondary structure arrangements, validating the importance of hierarchical topological features for protein analysis.

Recent studies in using deep reinforcement learning (DRL) to solve Job-shop scheduling problems (JSSP) focus on construction heuristics. However, their performance is still far from optimality, mainly because the underlying graph representation scheme is unsuitable for modelling partial solutions at each construction step. This paper proposes a novel DRL-guided improvement heuristic for solving JSSP, where graph representation is employed to encode complete solutions. We design a Graph Neural-Network-based representation scheme, consisting of two modules to effectively capture the information of dynamic topology and different types of nodes in graphs encountered during the improvement process. To speed up solution evaluation during improvement, we present a novel message-passing mechanism that can evaluate multiple solutions simultaneously. We prove that the computational complexity of our method scales linearly with problem size. Experiments on classic benchmarks show that the improvement policy learned by our method outperforms state-of-the-art DRL-based methods by a large margin.

Multimodal contrastive learning aims to train a general-purpose feature extractor, such as CLIP, on vast amounts of raw, unlabeled paired image-text data. This can greatly benefit various complex downstream tasks, including cross-modal image-text retrieval and image classification. Despite its promising prospect, the security issue of cross-modal pre-trained encoder has not been fully explored yet, especially when the pre-trained encoder is publicly available for commercial use. In this work, we propose AdvCLIP, the first attack framework for generating downstream-agnostic adversarial examples based on cross-modal pre-trained encoders. AdvCLIP aims to construct a universal adversarial patch for a set of natural images that can fool all the downstream tasks inheriting the victim cross-modal pre-trained encoder. To address the challenges of heterogeneity between different modalities and unknown downstream tasks, we first build a topological graph structure to capture the relevant positions between target samples and their neighbors. Then, we design a topology-deviation based generative adversarial network to generate a universal adversarial patch. By adding the patch to images, we minimize their embeddings similarity to different modality and perturb the sample distribution in the feature space, achieving unviersal non-targeted attacks. Our results demonstrate the excellent attack performance of AdvCLIP on two types of downstream tasks across eight datasets. We also tailor three popular defenses to mitigate AdvCLIP, highlighting the need for new defense mechanisms to defend cross-modal pre-trained encoders.

Although graph neural networks (GNNs) have achieved impressive achievements in graph classification, they often need abundant task-specific labels, which could be extensively costly to acquire. A credible solution is to explore additional labeled graphs to enhance unsupervised learning on the target domain. However, how to apply GNNs to domain adaptation remains unsolved owing to the insufficient exploration of graph topology and the significant domain discrepancy. In this paper, we propose Coupled Contrastive Graph Representation Learning (CoCo), which extracts the topological information from coupled learning branches and reduces the domain discrepancy with coupled contrastive learning. CoCo contains a graph convolutional network branch and a hierarchical graph kernel network branch, which explore graph topology in implicit and explicit manners. Besides, we incorporate coupled branches into a holistic multi-view contrastive learning framework, which not only incorporates graph representations learned from complementary views for enhanced understanding, but also encourages the similarity between cross-domain example pairs with the same semantics for domain alignment. Extensive experiments on popular datasets show that our CoCo outperforms these competing baselines in different settings generally.

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

We introduce LeapfrogLayers, an invertible neural network architecture that can be trained to efficiently sample the topology of a 2D U(1) lattice gauge theory. We show an improvement in the integrated autocorrelation time of the topological charge when compared with traditional HMC, and look at how different quantities transform under our model. Our implementation is open source, and is publicly available on github at https://github.com/saforem2/l2hmc-qcd.

Quantum communication can enhance internet technology by enabling novel applications that are provably impossible classically. The successful execution of such applications relies on the generation of quantum entanglement between different users of the network which meets stringent performance requirements. Alongside traditional metrics such as throughput and jitter, one must ensure the generated entanglement is of sufficiently high quality. Meeting such performance requirements demands a careful orchestration of many devices in the network, giving rise to a fundamentally new scheduling problem. Furthermore, technological limitations of near-term quantum devices impose significant constraints on scheduling methods hoping to meet performance requirements. In this work, we propose the first end-to-end design of a centralized quantum network with multiple users that orchestrates the delivery of entanglement which meets quality-of-service (QoS) requirements of applications. We achieve this by using a centrally constructed schedule that manages usage of devices and ensures the coordinated execution of different quantum operations throughout the network. We use periodic task scheduling and resource-constrained project scheduling techniques, including a novel heuristic, to construct the schedules. Our simulations of four small networks using hardware-validated network parameters, and of a real-world fiber topology using futuristic parameters, illustrate trade-offs between traditional and quantum performance metrics.

We present a simple but powerful architecture of convolutional neural network, which has a VGG-like inference-time body composed of nothing but a stack of 3x3 convolution and ReLU, while the training-time model has a multi-branch topology. Such decoupling of the training-time and inference-time architecture is realized by a structural re-parameterization technique so that the model is named RepVGG. On ImageNet, RepVGG reaches over 80% top-1 accuracy, which is the first time for a plain model, to the best of our knowledge. On NVIDIA 1080Ti GPU, RepVGG models run 83% faster than ResNet-50 or 101% faster than ResNet-101 with higher accuracy and show favorable accuracy-speed trade-off compared to the state-of-the-art models like EfficientNet and RegNet. The code and trained models are available at https://github.com/megvii-model/RepVGG.

A map, as crucial information for downstream applications of an autonomous driving system, is usually represented in lanelines or centerlines. However, existing literature on map learning primarily focuses on either detecting geometry-based lanelines or perceiving topology relationships of centerlines. Both of these methods ignore the intrinsic relationship of lanelines and centerlines, that lanelines bind centerlines. While simply predicting both types of lane in one model is mutually excluded in learning objective, we advocate lane segment as a new representation that seamlessly incorporates both geometry and topology information. Thus, we introduce LaneSegNet, the first end-to-end mapping network generating lane segments to obtain a complete representation of the road structure. Our algorithm features two key modifications. One is a lane attention module to capture pivotal region details within the long-range feature space. Another is an identical initialization strategy for reference points, which enhances the learning of positional priors for lane attention. On the OpenLane-V2 dataset, LaneSegNet outperforms previous counterparts by a substantial gain across three tasks, i.e., map element detection (+4.8 mAP), centerline perception (+6.9 DET_l), and the newly defined one, lane segment perception (+5.6 mAP). Furthermore, it obtains a real-time inference speed of 14.7 FPS. Code is accessible at https://github.com/OpenDriveLab/LaneSegNet.

Traditional fluorescence staining is phototoxic to live cells, slow, and expensive; thus, the subcellular structure prediction (SSP) from transmitted light (TL) images is emerging as a label-free, faster, low-cost alternative. However, existing approaches utilize 3D networks for one-to-one voxel level dense prediction, which necessitates a frequent and time-consuming Z-axis imaging process. Moreover, 3D convolutions inevitably lead to significant computation and GPU memory overhead. Therefore, we propose an efficient framework, SparseSSP, predicting fluorescent intensities within the target voxel grid in an efficient paradigm instead of relying entirely on 3D topologies. In particular, SparseSSP makes two pivotal improvements to prior works. First, SparseSSP introduces a one-to-many voxel mapping paradigm, which permits the sparse TL slices to reconstruct the subcellular structure. Secondly, we propose a hybrid dimensions topology, which folds the Z-axis information into channel features, enabling the 2D network layers to tackle SSP under low computational cost. We conduct extensive experiments to validate the effectiveness and advantages of SparseSSP on diverse sparse imaging ratios, and our approach achieves a leading performance compared to pure 3D topologies. SparseSSP reduces imaging frequencies compared to previous dense-view SSP (i.e., the number of imaging is reduced up to 87.5% at most), which is significant in visualizing rapid biological dynamics on low-cost devices and samples.

Feature vectors provided by pre-trained deep artificial neural networks have become a dominant source for image representation in recent literature. Their contribution to the performance of image analysis can be improved through finetuning. As an ultimate solution, one might even train a deep network from scratch with the domain-relevant images, a highly desirable option which is generally impeded in pathology by lack of labeled images and the computational expense. In this study, we propose a new network, namely KimiaNet, that employs the topology of the DenseNet with four dense blocks, fine-tuned and trained with histopathology images in different configurations. We used more than 240,000 image patches with 1000x1000 pixels acquired at 20x magnification through our proposed "highcellularity mosaic" approach to enable the usage of weak labels of 7,126 whole slide images of formalin-fixed paraffin-embedded human pathology samples publicly available through the The Cancer Genome Atlas (TCGA) repository. We tested KimiaNet using three public datasets, namely TCGA, endometrial cancer images, and colorectal cancer images by evaluating the performance of search and classification when corresponding features of different networks are used for image representation. As well, we designed and trained multiple convolutional batch-normalized ReLU (CBR) networks. The results show that KimiaNet provides superior results compared to the original DenseNet and smaller CBR networks when used as feature extractor to represent histopathology images.

This paper addresses the challenges of registering two rigid semantic scene graphs, an essential capability when an autonomous agent needs to register its map against a remote agent, or against a prior map. The hand-crafted descriptors in classical semantic-aided registration, or the ground-truth annotation reliance in learning-based scene graph registration, impede their application in practical real-world environments. To address the challenges, we design a scene graph network to encode multiple modalities of semantic nodes: open-set semantic feature, local topology with spatial awareness, and shape feature. These modalities are fused to create compact semantic node features. The matching layers then search for correspondences in a coarse-to-fine manner. In the back-end, we employ a robust pose estimator to decide transformation according to the correspondences. We manage to maintain a sparse and hierarchical scene representation. Our approach demands fewer GPU resources and fewer communication bandwidth in multi-agent tasks. Moreover, we design a new data generation approach using vision foundation models and a semantic mapping module to reconstruct semantic scene graphs. It differs significantly from previous works, which rely on ground-truth semantic annotations to generate data. We validate our method in a two-agent SLAM benchmark. It significantly outperforms the hand-crafted baseline in terms of registration success rate. Compared to visual loop closure networks, our method achieves a slightly higher registration recall while requiring only 52 KB of communication bandwidth for each query frame. Code available at: http://github.com/HKUST-Aerial-Robotics/SG-Reg{http://github.com/HKUST-Aerial-Robotics/SG-Reg}.

Graph neural networks (GNNs) emerged recently as a standard toolkit for learning from data on graphs. Current GNN designing works depend on immense human expertise to explore different message-passing mechanisms, and require manual enumeration to determine the proper message-passing depth. Inspired by the strong searching capability of neural architecture search (NAS) in CNN, this paper proposes Graph Neural Architecture Search (GNAS) with novel-designed search space. The GNAS can automatically learn better architecture with the optimal depth of message passing on the graph. Specifically, we design Graph Neural Architecture Paradigm (GAP) with tree-topology computation procedure and two types of fine-grained atomic operations (feature filtering and neighbor aggregation) from message-passing mechanism to construct powerful graph network search space. Feature filtering performs adaptive feature selection, and neighbor aggregation captures structural information and calculates neighbors' statistics. Experiments show that our GNAS can search for better GNNs with multiple message-passing mechanisms and optimal message-passing depth. The searched network achieves remarkable improvement over state-of-the-art manual designed and search-based GNNs on five large-scale datasets at three classical graph tasks. Codes can be found at https://github.com/phython96/GNAS-MP.

Recent advancements in large language model (LLM)-based agents have demonstrated that collective intelligence can significantly surpass the capabilities of individual agents, primarily due to well-crafted inter-agent communication topologies. Despite the diverse and high-performing designs available, practitioners often face confusion when selecting the most effective pipeline for their specific task: Which topology is the best choice for my task, avoiding unnecessary communication token overhead while ensuring high-quality solution? In response to this dilemma, we introduce G-Designer, an adaptive, efficient, and robust solution for multi-agent deployment, which dynamically designs task-aware, customized communication topologies. Specifically, G-Designer models the multi-agent system as a multi-agent network, leveraging a variational graph auto-encoder to encode both the nodes (agents) and a task-specific virtual node, and decodes a task-adaptive and high-performing communication topology. Extensive experiments on six benchmarks showcase that G-Designer is: (1) high-performing, achieving superior results on MMLU with accuracy at 84.50% and on HumanEval with pass@1 at 89.90%; (2) task-adaptive, architecting communication protocols tailored to task difficulty, reducing token consumption by up to 95.33% on HumanEval; and (3) adversarially robust, defending against agent adversarial attacks with merely 0.3% accuracy drop.

Skeleton sequence representation learning has shown great advantages for action recognition due to its promising ability to model human joints and topology. However, the current methods usually require sufficient labeled data for training computationally expensive models, which is labor-intensive and time-consuming. Moreover, these methods ignore how to utilize the fine-grained dependencies among different skeleton joints to pre-train an efficient skeleton sequence learning model that can generalize well across different datasets. In this paper, we propose an efficient skeleton sequence learning framework, named Skeleton Sequence Learning (SSL). To comprehensively capture the human pose and obtain discriminative skeleton sequence representation, we build an asymmetric graph-based encoder-decoder pre-training architecture named SkeletonMAE, which embeds skeleton joint sequence into Graph Convolutional Network (GCN) and reconstructs the masked skeleton joints and edges based on the prior human topology knowledge. Then, the pre-trained SkeletonMAE encoder is integrated with the Spatial-Temporal Representation Learning (STRL) module to build the SSL framework. Extensive experimental results show that our SSL generalizes well across different datasets and outperforms the state-of-the-art self-supervised skeleton-based action recognition methods on FineGym, Diving48, NTU 60 and NTU 120 datasets. Additionally, we obtain comparable performance to some fully supervised methods. The code is avaliable at https://github.com/HongYan1123/SkeletonMAE.

In this work, we present a simple, highly efficient and modularized Dual Path Network (DPN) for image classification which presents a new topology of connection paths internally. By revealing the equivalence of the state-of-the-art Residual Network (ResNet) and Densely Convolutional Network (DenseNet) within the HORNN framework, we find that ResNet enables feature re-usage while DenseNet enables new features exploration which are both important for learning good representations. To enjoy the benefits from both path topologies, our proposed Dual Path Network shares common features while maintaining the flexibility to explore new features through dual path architectures. Extensive experiments on three benchmark datasets, ImagNet-1k, Places365 and PASCAL VOC, clearly demonstrate superior performance of the proposed DPN over state-of-the-arts. In particular, on the ImagNet-1k dataset, a shallow DPN surpasses the best ResNeXt-101(64x4d) with 26% smaller model size, 25% less computational cost and 8% lower memory consumption, and a deeper DPN (DPN-131) further pushes the state-of-the-art single model performance with about 2 times faster training speed. Experiments on the Places365 large-scale scene dataset, PASCAL VOC detection dataset, and PASCAL VOC segmentation dataset also demonstrate its consistently better performance than DenseNet, ResNet and the latest ResNeXt model over various applications.

In biological research, fluorescence staining is a key technique to reveal the locations and morphology of subcellular structures. However, it is slow, expensive, and harmful to cells. In this paper, we model it as a deep learning task termed subcellular structure prediction (SSP), aiming to predict the 3D fluorescent images of multiple subcellular structures from a 3D transmitted-light image. Unfortunately, due to the limitations of current biotechnology, each image is partially labeled in SSP. Besides, naturally, subcellular structures vary considerably in size, which causes the multi-scale issue of SSP. To overcome these challenges, we propose Re-parameterizing Mixture-of-Diverse-Experts (RepMode), a network that dynamically organizes its parameters with task-aware priors to handle specified single-label prediction tasks. In RepMode, the Mixture-of-Diverse-Experts (MoDE) block is designed to learn the generalized parameters for all tasks, and gating re-parameterization (GatRep) is performed to generate the specialized parameters for each task, by which RepMode can maintain a compact practical topology exactly like a plain network, and meanwhile achieves a powerful theoretical topology. Comprehensive experiments show that RepMode can achieve state-of-the-art overall performance in SSP.

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.

Federated learning is an active research topic since it enables several participants to jointly train a model without sharing local data. Currently, cross-silo federated learning is a popular training setting that utilizes a few hundred reliable data silos with high-speed access links to training a model. While this approach has been widely applied in real-world scenarios, designing a robust topology to reduce the training time remains an open problem. In this paper, we present a new multigraph topology for cross-silo federated learning. We first construct the multigraph using the overlay graph. We then parse this multigraph into different simple graphs with isolated nodes. The existence of isolated nodes allows us to perform model aggregation without waiting for other nodes, hence effectively reducing the training time. Intensive experiments on three public datasets show that our proposed method significantly reduces the training time compared with recent state-of-the-art topologies while maintaining the accuracy of the learned model. Our code can be found at https://github.com/aioz-ai/MultigraphFL

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

Fully decentralized learning enables the distribution of learning resources and decision-making capabilities across multiple user devices or nodes, and is rapidly gaining popularity due to its privacy-preserving and decentralized nature. Importantly, this crowdsourcing of the learning process allows the system to continue functioning even if some nodes are affected or disconnected. In a disaster scenario, communication infrastructure and centralized systems may be disrupted or completely unavailable, hindering the possibility of carrying out standard centralized learning tasks in these settings. Thus, fully decentralized learning can help in this case. However, transitioning from centralized to peer-to-peer communications introduces a dependency between the learning process and the topology of the communication graph among nodes. In a disaster scenario, even peer-to-peer communications are susceptible to abrupt changes, such as devices running out of battery or getting disconnected from others due to their position. In this study, we investigate the effects of various disruptions to peer-to-peer communications on decentralized learning in a disaster setting. We examine the resilience of a decentralized learning process when a subset of devices drop from the process abruptly. To this end, we analyze the difference between losing devices holding data, i.e., potential knowledge, vs. devices contributing only to the graph connectivity, i.e., with no data. Our findings on a Barabasi-Albert graph topology, where training data is distributed across nodes in an IID fashion, indicate that the accuracy of the learning process is more affected by a loss of connectivity than by a loss of data. Nevertheless, the network remains relatively robust, and the learning process can achieve a good level of accuracy.

Graphs can be used to represent and reason about systems and a variety of metrics have been devised to quantify their global characteristics. However, little is currently known about how to construct a graph or improve an existing one given a target objective. In this work, we formulate the construction of a graph as a decision-making process in which a central agent creates topologies by trial and error and receives rewards proportional to the value of the target objective. By means of this conceptual framework, we propose an algorithm based on reinforcement learning and graph neural networks to learn graph construction and improvement strategies. Our core case study focuses on robustness to failures and attacks, a property relevant for the infrastructure and communication networks that power modern society. Experiments on synthetic and real-world graphs show that this approach can outperform existing methods while being cheaper to evaluate. It also allows generalization to out-of-sample graphs, as well as to larger out-of-distribution graphs in some cases. The approach is applicable to the optimization of other global structural properties of graphs.

Despite the impressive advancements of Large Language Models (LLMs) in generating text, they are often limited by the knowledge contained in the input and prone to producing inaccurate or hallucinated content. To tackle these issues, Retrieval-augmented Generation (RAG) is employed as an effective strategy to enhance the available knowledge base and anchor the responses in reality by pulling additional texts from external databases. In real-world applications, texts are often linked through entities within a graph, such as citations in academic papers or comments in social networks. This paper exploits these topological relationships to guide the retrieval process in RAG. Specifically, we explore two kinds of topological connections: proximity-based, focusing on closely connected nodes, and role-based, which looks at nodes sharing similar subgraph structures. Our empirical research confirms their relevance to text relationships, leading us to develop a Topology-aware Retrieval-augmented Generation framework. This framework includes a retrieval module that selects texts based on their topological relationships and an aggregation module that integrates these texts into prompts to stimulate LLMs for text generation. We have curated established text-attributed networks and conducted comprehensive experiments to validate the effectiveness of this framework, demonstrating its potential to enhance RAG with topological awareness.

Masked graph autoencoders have emerged as a powerful graph self-supervised learning method that has yet to be fully explored. In this paper, we unveil that the existing discrete edge masking and binary link reconstruction strategies are insufficient to learn topologically informative representations, from the perspective of message propagation on graph neural networks. These limitations include blocking message flows, vulnerability to over-smoothness, and suboptimal neighborhood discriminability. Inspired by these understandings, we explore non-discrete edge masks, which are sampled from a continuous and dispersive probability distribution instead of the discrete Bernoulli distribution. These masks restrict the amount of output messages for each edge, referred to as "bandwidths". We propose a novel, informative, and effective topological masked graph autoencoder using bandwidth masking and a layer-wise bandwidth prediction objective. We demonstrate its powerful graph topological learning ability both theoretically and empirically. Our proposed framework outperforms representative baselines in both self-supervised link prediction (improving the discrete edge reconstructors by at most 20%) and node classification on numerous datasets, solely with a structure-learning pretext. Our implementation is available at https://github.com/Newiz430/Bandana.

The use of graph neural networks has produced significant advances in point cloud problems, such as those found in high energy physics. The question of how to produce a graph structure in these problems is usually treated as a matter of heuristics, employing fully connected graphs or K-nearest neighbors. In this work, we elevate this question to utmost importance as the Topology Problem. We propose an attention mechanism that allows a graph to be constructed in a learned space that handles geometrically the flow of relevance, providing one solution to the Topology Problem. We test this architecture, called GravNetNorm, on the task of top jet tagging, and show that it is competitive in tagging accuracy, and uses far fewer computational resources than all other comparable models.

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 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.

Graph neural networks are popular architectures for graph machine learning, based on iterative computation of node representations of an input graph through a series of invariant transformations. A large class of graph neural networks follow a standard message-passing paradigm: at every layer, each node state is updated based on an aggregate of messages from its neighborhood. In this work, we propose a novel framework for training graph neural networks, where every node is viewed as a player that can choose to either 'listen', 'broadcast', 'listen and broadcast', or to 'isolate'. The standard message propagation scheme can then be viewed as a special case of this framework where every node 'listens and broadcasts' to all neighbors. Our approach offers a more flexible and dynamic message-passing paradigm, where each node can determine its own strategy based on their state, effectively exploring the graph topology while learning. We provide a theoretical analysis of the new message-passing scheme which is further supported by an extensive empirical analysis on a synthetic dataset and on real-world datasets.

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

Recently, graph neural networks (GNNs) have shown prominent performance in semi-supervised node classification by leveraging knowledge from the graph database. However, most existing GNNs follow the homophily assumption, where connected nodes are more likely to exhibit similar feature distributions and the same labels, and such an assumption has proven to be vulnerable in a growing number of practical applications. As a supplement, heterophily reflects dissimilarity in connected nodes, which has gained significant attention in graph learning. To this end, data engineers aim to develop a powerful GNN model that can ensure performance under both homophily and heterophily. Despite numerous attempts, most existing GNNs struggle to achieve optimal node representations due to the constraints of undirected graphs. The neglect of directed edges results in sub-optimal graph representations, thereby hindering the capacity of GNNs. To address this issue, we introduce AMUD, which quantifies the relationship between node profiles and topology from a statistical perspective, offering valuable insights for Adaptively Modeling the natural directed graphs as the Undirected or Directed graph to maximize the benefits from subsequent graph learning. Furthermore, we propose Adaptive Directed Pattern Aggregation (ADPA) as a new directed graph learning paradigm for AMUD. Empirical studies have demonstrated that AMUD guides efficient graph learning. Meanwhile, extensive experiments on 14 benchmark datasets substantiate the impressive performance of ADPA, outperforming baselines by significant margins of 3.96\%.

Graph neural networks (GNNs) based methods have achieved impressive performance on node clustering task. However, they are designed on the homophilic assumption of graph and clustering on heterophilic graph is overlooked. Due to the lack of labels, it is impossible to first identify a graph as homophilic or heterophilic before a suitable GNN model can be found. Hence, clustering on real-world graph with various levels of homophily poses a new challenge to the graph research community. To fill this gap, we propose a novel graph clustering method, which contains three key components: graph reconstruction, a mixed filter, and dual graph clustering network. To be graph-agnostic, we empirically construct two graphs which are high homophily and heterophily from each data. The mixed filter based on the new graphs extracts both low-frequency and high-frequency information. To reduce the adverse coupling between node attribute and topological structure, we separately map them into two subspaces in dual graph clustering network. Extensive experiments on 11 benchmark graphs demonstrate our promising performance. In particular, our method dominates others on heterophilic graphs.

A graph homomorphism is a map between two graphs that preserves adjacency relations. We consider the problem of sampling a random graph homomorphism from a graph into a large network. We propose two complementary MCMC algorithms for sampling random graph homomorphisms and establish bounds on their mixing times and the concentration of their time averages. Based on our sampling algorithms, we propose a novel framework for network data analysis that circumvents some of the drawbacks in methods based on independent and neighborhood sampling. Various time averages of the MCMC trajectory give us various computable observables, including well-known ones such as homomorphism density and average clustering coefficient and their generalizations. Furthermore, we show that these network observables are stable with respect to a suitably renormalized cut distance between networks. We provide various examples and simulations demonstrating our framework through synthetic networks. We also demonstrate the performance of our framework on the tasks of network clustering and subgraph classification on the Facebook100 dataset and on Word Adjacency Networks of a set of classic novels.

Node centralities play a pivotal role in network science, social network analysis, and recommender systems. In temporal data, static path-based centralities like closeness or betweenness can give misleading results about the true importance of nodes in a temporal graph. To address this issue, temporal generalizations of betweenness and closeness have been defined that are based on the shortest time-respecting paths between pairs of nodes. However, a major issue of those generalizations is that the calculation of such paths is computationally expensive. Addressing this issue, we study the application of De Bruijn Graph Neural Networks (DBGNN), a causality-aware graph neural network architecture, to predict temporal path-based centralities in time series data. We experimentally evaluate our approach in 13 temporal graphs from biological and social systems and show that it considerably improves the prediction of both betweenness and closeness centrality compared to a static Graph Convolutional Neural Network.

In this paper, we present a new MTL framework that searches for structures optimized for multiple tasks with diverse graph topologies and shares features among tasks. We design a restricted DAG-based central network with read-in/read-out layers to build topologically diverse task-adaptive structures while limiting search space and time. We search for a single optimized network that serves as multiple task adaptive sub-networks using our three-stage training process. To make the network compact and discretized, we propose a flow-based reduction algorithm and a squeeze loss used in the training process. We evaluate our optimized network on various public MTL datasets and show ours achieves state-of-the-art performance. An extensive ablation study experimentally validates the effectiveness of the sub-module and schemes in our framework.

Random network models play a prominent role in modeling, analyzing and understanding complex phenomena on real-life networks. However, a key property of networks is often neglected: many real-world networks exhibit spatial structure, the tendency of a node to select neighbors with a probability depending on physical distance. Here, we introduce a class of random spatial networks (RSNs) which generalizes many existing random network models but adds spatial structure. In these networks, nodes are placed randomly in space and joined in edges with a probability depending on their distance and their individual expected degrees, in a manner that crucially remains analytically tractable. We use this network class to propose a new generalization of small-world networks, where the average shortest path lengths in the graph are small, as in classical Watts-Strogatz small-world networks, but with close spatial proximity of nodes that are neighbors in the network playing the role of large clustering. Small-world effects are demonstrated on these spatial small-world networks without clustering. We are able to derive partial integro-differential equations governing susceptible-infectious-recovered disease spreading through an RSN, and we demonstrate the existence of traveling wave solutions. If the distance kernel governing edge placement decays slower than exponential, the population-scale dynamics are dominated by long-range hops followed by local spread of traveling waves. This provides a theoretical modeling framework for recent observations of how epidemics like Ebola evolve in modern connected societies, with long-range connections seeding new focal points from which the epidemic locally spreads in a wavelike manner.

The topology of the hyperlink graph among pages expressing different opinions may influence the exposure of readers to diverse content. Structural bias may trap a reader in a polarized bubble with no access to other opinions. We model readers' behavior as random walks. A node is in a polarized bubble if the expected length of a random walk from it to a page of different opinion is large. The structural bias of a graph is the sum of the radii of highly-polarized bubbles. We study the problem of decreasing the structural bias through edge insertions. Healing all nodes with high polarized bubble radius is hard to approximate within a logarithmic factor, so we focus on finding the best k edges to insert to maximally reduce the structural bias. We present RePBubLik, an algorithm that leverages a variant of the random walk closeness centrality to select the edges to insert. RePBubLik obtains, under mild conditions, a constant-factor approximation. It reduces the structural bias faster than existing edge-recommendation methods, including some designed to reduce the polarization of a graph.

Prediction tasks over nodes and edges in networks require careful effort in engineering features used by learning algorithms. Recent research in the broader field of representation learning has led to significant progress in automating prediction by learning the features themselves. However, present feature learning approaches are not expressive enough to capture the diversity of connectivity patterns observed in networks. Here we propose node2vec, an algorithmic framework for learning continuous feature representations for nodes in networks. In node2vec, we learn a mapping of nodes to a low-dimensional space of features that maximizes the likelihood of preserving network neighborhoods of nodes. We define a flexible notion of a node's network neighborhood and design a biased random walk procedure, which efficiently explores diverse neighborhoods. Our algorithm generalizes prior work which is based on rigid notions of network neighborhoods, and we argue that the added flexibility in exploring neighborhoods is the key to learning richer representations. We demonstrate the efficacy of node2vec over existing state-of-the-art techniques on multi-label classification and link prediction in several real-world networks from diverse domains. Taken together, our work represents a new way for efficiently learning state-of-the-art task-independent representations in complex networks.

Graph Neural Networks (GNNs) have demonstrated superior performance on various graph learning tasks, including recommendation, where they leverage user-item collaborative filtering signals in graphs. However, theoretical formulations of their capability are scarce, despite their empirical effectiveness in state-of-the-art recommender models. Recently, research has explored the expressiveness of GNNs in general, demonstrating that message passing GNNs are at most as powerful as the Weisfeiler-Lehman test, and that GNNs combined with random node initialization are universal. Nevertheless, the concept of "expressiveness" for GNNs remains vaguely defined. Most existing works adopt the graph isomorphism test as the metric of expressiveness, but this graph-level task may not effectively assess a model's ability in recommendation, where the objective is to distinguish nodes of different closeness. In this paper, we provide a comprehensive theoretical analysis of the expressiveness of GNNs in recommendation, considering three levels of expressiveness metrics: graph isomorphism (graph-level), node automorphism (node-level), and topological closeness (link-level). We propose the topological closeness metric to evaluate GNNs' ability to capture the structural distance between nodes, which aligns closely with the objective of recommendation. To validate the effectiveness of this new metric in evaluating recommendation performance, we introduce a learning-less GNN algorithm that is optimal on the new metric and can be optimal on the node-level metric with suitable modification. We conduct extensive experiments comparing the proposed algorithm against various types of state-of-the-art GNN models to explore the explainability of the new metric in the recommendation task. For reproducibility, implementation codes are available at https://github.com/HKUDS/GTE.

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.

The study of network robustness is a critical tool in the characterization and sense making of complex interconnected systems such as infrastructure, communication and social networks. While significant research has been conducted in all of these areas, gaps in the surveying literature still exist. Answers to key questions are currently scattered across multiple scientific fields and numerous papers. In this survey, we distill key findings across numerous domains and provide researchers crucial access to important information by--(1) summarizing and comparing recent and classical graph robustness measures; (2) exploring which robustness measures are most applicable to different categories of networks (e.g., social, infrastructure; (3) reviewing common network attack strategies, and summarizing which attacks are most effective across different network topologies; and (4) extensive discussion on selecting defense techniques to mitigate attacks across a variety of networks. This survey guides researchers and practitioners in navigating the expansive field of network robustness, while summarizing answers to key questions. We conclude by highlighting current research directions and open problems.

We present an agentic, autonomous graph expansion framework that iteratively structures and refines knowledge in situ. Unlike conventional knowledge graph construction methods relying on static extraction or single-pass learning, our approach couples a reasoning-native large language model with a continually updated graph representation. At each step, the system actively generates new concepts and relationships, merges them into a global graph, and formulates subsequent prompts based on its evolving structure. Through this feedback-driven loop, the model organizes information into a scale-free network characterized by hub formation, stable modularity, and bridging nodes that link disparate knowledge clusters. Over hundreds of iterations, new nodes and edges continue to appear without saturating, while centrality measures and shortest path distributions evolve to yield increasingly distributed connectivity. Our analysis reveals emergent patterns, such as the rise of highly connected 'hub' concepts and the shifting influence of 'bridge' nodes, indicating that agentic, self-reinforcing graph construction can yield open-ended, coherent knowledge structures. Applied to materials design problems, we present compositional reasoning experiments by extracting node-specific and synergy-level principles to foster genuinely novel knowledge synthesis, yielding cross-domain ideas that transcend rote summarization and strengthen the framework's potential for open-ended scientific discovery. We discuss other applications in scientific discovery and outline future directions for enhancing scalability and interpretability.

We study a new connection between a technical measure called mu-conductance that arises in the study of Markov chains for sampling convex bodies and the network community profile that characterizes size-resolved properties of clusters and communities in social and information networks. The idea of mu-conductance is similar to the traditional graph conductance, but disregards sets with small volume. We derive a sequence of optimization problems including a low-rank semi-definite program from which we can derive a lower bound on the optimal mu-conductance value. These ideas give the first theoretically sound bound on the behavior of the network community profile for a wide range of cluster sizes. The algorithm scales up to graphs with hundreds of thousands of nodes and we demonstrate how our framework validates the predicted structures of real-world graphs.

Message-passing graph neural networks (MPNNs) emerged as powerful tools for processing graph-structured input. However, they operate on a fixed input graph structure, ignoring potential noise and missing information. Furthermore, their local aggregation mechanism can lead to problems such as over-squashing and limited expressive power in capturing relevant graph structures. Existing solutions to these challenges have primarily relied on heuristic methods, often disregarding the underlying data distribution. Hence, devising principled approaches for learning to infer graph structures relevant to the given prediction task remains an open challenge. In this work, leveraging recent progress in exact and differentiable k-subset sampling, we devise probabilistically rewired MPNNs (PR-MPNNs), which learn to add relevant edges while omitting less beneficial ones. For the first time, our theoretical analysis explores how PR-MPNNs enhance expressive power, and we identify precise conditions under which they outperform purely randomized approaches. Empirically, we demonstrate that our approach effectively mitigates issues like over-squashing and under-reaching. In addition, on established real-world datasets, our method exhibits competitive or superior predictive performance compared to traditional MPNN models and recent graph transformer architectures.

Adversarially perturbed images of text can cause sophisticated OCR systems to produce misleading or incorrect transcriptions from seemingly invisible changes to humans. Some of these perturbations even survive physical capture, posing security risks to high-stakes applications such as document processing, license plate recognition, and automated compliance systems. Existing defenses, such as adversarial training, input preprocessing, or post-recognition correction, are often model-specific, computationally expensive, and affect performance on unperturbed inputs while remaining vulnerable to unseen or adaptive attacks. To address these challenges, TopoReformer is introduced, a model-agnostic reformation pipeline that mitigates adversarial perturbations while preserving the structural integrity of text images. Topology studies properties of shapes and spaces that remain unchanged under continuous deformations, focusing on global structures such as connectivity, holes, and loops rather than exact distance. Leveraging these topological features, TopoReformer employs a topological autoencoder to enforce manifold-level consistency in latent space and improve robustness without explicit gradient regularization. The proposed method is benchmarked on EMNIST, MNIST, against standard adversarial attacks (FGSM, PGD, Carlini-Wagner), adaptive attacks (EOT, BDPA), and an OCR-specific watermark attack (FAWA).

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

Motivated by applications in chemistry and other sciences, we study the expressive power of message-passing neural networks for geometric graphs, whose node features correspond to 3-dimensional positions. Recent work has shown that such models can separate generic pairs of non-isomorphic geometric graphs, though they may fail to separate some rare and complicated instances. However, these results assume a fully connected graph, where each node possesses complete knowledge of all other nodes. In contrast, often, in application, every node only possesses knowledge of a small number of nearest neighbors. This paper shows that generic pairs of non-isomorphic geometric graphs can be separated by message-passing networks with rotation equivariant features as long as the underlying graph is connected. When only invariant intermediate features are allowed, generic separation is guaranteed for generically globally rigid graphs. We introduce a simple architecture, EGENNET, which achieves our theoretical guarantees and compares favorably with alternative architecture on synthetic and chemical benchmarks. Our code is available at https://github.com/yonatansverdlov/E-GenNet.

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.

Network embedding has been intensively studied in the literature and widely used in various applications, such as link prediction and node classification. While previous work focus on the design of new algorithms or are tailored for various problem settings, the discussion of initialization strategies in the learning process is often missed. In this work, we address this important issue of initialization for network embedding that could dramatically improve the performance of the algorithms on both effectiveness and efficiency. Specifically, we first exploit the graph partition technique that divides the graph into several disjoint subsets, and then construct an abstract graph based on the partitions. We obtain the initialization of the embedding for each node in the graph by computing the network embedding on the abstract graph, which is much smaller than the input graph, and then propagating the embedding among the nodes in the input graph. With extensive experiments on various datasets, we demonstrate that our initialization technique significantly improves the performance of the state-of-the-art algorithms on the evaluations of link prediction and node classification by up to 7.76% and 8.74% respectively. Besides, we show that the technique of initialization reduces the running time of the state-of-the-arts by at least 20%.

Graph neural networks (GNNs) are a powerful architecture for tackling graph learning tasks, yet have been shown to be oblivious to eminent substructures such as cycles. We present TOGL, a novel layer that incorporates global topological information of a graph using persistent homology. TOGL can be easily integrated into any type of GNN and is strictly more expressive (in terms the Weisfeiler--Lehman graph isomorphism test) than message-passing GNNs. Augmenting GNNs with TOGL leads to improved predictive performance for graph and node classification tasks, both on synthetic data sets, which can be classified by humans using their topology but not by ordinary GNNs, and on real-world data.

Analyzing network topologies and communication graphs plays a crucial role in contemporary network management. However, the absence of a cohesive approach leads to a challenging learning curve, heightened errors, and inefficiencies. In this paper, we introduce a novel approach to facilitate a natural-language-based network management experience, utilizing large language models (LLMs) to generate task-specific code from natural language queries. This method tackles the challenges of explainability, scalability, and privacy by allowing network operators to inspect the generated code, eliminating the need to share network data with LLMs, and concentrating on application-specific requests combined with general program synthesis techniques. We design and evaluate a prototype system using benchmark applications, showcasing high accuracy, cost-effectiveness, and the potential for further enhancements using complementary program synthesis techniques.

This paper studies the problem of embedding very large information networks into low-dimensional vector spaces, which is useful in many tasks such as visualization, node classification, and link prediction. Most existing graph embedding methods do not scale for real world information networks which usually contain millions of nodes. In this paper, we propose a novel network embedding method called the "LINE," which is suitable for arbitrary types of information networks: undirected, directed, and/or weighted. The method optimizes a carefully designed objective function that preserves both the local and global network structures. An edge-sampling algorithm is proposed that addresses the limitation of the classical stochastic gradient descent and improves both the effectiveness and the efficiency of the inference. Empirical experiments prove the effectiveness of the LINE on a variety of real-world information networks, including language networks, social networks, and citation networks. The algorithm is very efficient, which is able to learn the embedding of a network with millions of vertices and billions of edges in a few hours on a typical single machine. The source code of the LINE is available online.

Topology reasoning aims to comprehensively understand road scenes and present drivable routes in autonomous driving. It requires detecting road centerlines (lane) and traffic elements, further reasoning their topology relationship, i.e., lane-lane topology, and lane-traffic topology. In this work, we first present that the topology score relies heavily on detection performance on lane and traffic elements. Therefore, we introduce a powerful 3D lane detector and an improved 2D traffic element detector to extend the upper limit of topology performance. Further, we propose TopoMLP, a simple yet high-performance pipeline for driving topology reasoning. Based on the impressive detection performance, we develop two simple MLP-based heads for topology generation. TopoMLP achieves state-of-the-art performance on OpenLane-V2 benchmark, i.e., 41.2% OLS with ResNet-50 backbone. It is also the 1st solution for 1st OpenLane Topology in Autonomous Driving Challenge. We hope such simple and strong pipeline can provide some new insights to the community. Code is at https://github.com/wudongming97/TopoMLP.

The presence of linear paths in parameter space between two different network solutions in certain cases, i.e., linear mode connectivity (LMC), has garnered interest from both theoretical and practical fronts. There has been significant research that either practically designs algorithms catered for connecting networks by adjusting for the permutation symmetries as well as some others that more theoretically construct paths through which networks can be connected. Yet, the core reasons for the occurrence of LMC, when in fact it does occur, in the highly non-convex loss landscapes of neural networks are far from clear. In this work, we take a step towards understanding it by providing a model of how the loss landscape needs to behave topographically for LMC (or the lack thereof) to manifest. Concretely, we present a `mountainside and ridge' perspective that helps to neatly tie together different geometric features that can be spotted in the loss landscape along the training runs. We also complement this perspective by providing a theoretical analysis of the barrier height, for which we provide empirical support, and which additionally extends as a faithful predictor of layer-wise LMC. We close with a toy example that provides further intuition on how barriers arise in the first place, all in all, showcasing the larger aim of the work -- to provide a working model of the landscape and its topography for the occurrence of LMC.

Despite its outstanding performance in various graph tasks, vanilla Message Passing Neural Network (MPNN) usually fails in link prediction tasks, as it only uses representations of two individual target nodes and ignores the pairwise relation between them. To capture the pairwise relations, some models add manual features to the input graph and use the output of MPNN to produce pairwise representations. In contrast, others directly use manual features as pairwise representations. Though this simplification avoids applying a GNN to each link individually and thus improves scalability, these models still have much room for performance improvement due to the hand-crafted and unlearnable pairwise features. To upgrade performance while maintaining scalability, we propose Neural Common Neighbor (NCN), which uses learnable pairwise representations. To further boost NCN, we study the unobserved link problem. The incompleteness of the graph is ubiquitous and leads to distribution shifts between the training and test set, loss of common neighbor information, and performance degradation of models. Therefore, we propose two intervention methods: common neighbor completion and target link removal. Combining the two methods with NCN, we propose Neural Common Neighbor with Completion (NCNC). NCN and NCNC outperform recent strong baselines by large margins. NCNC achieves state-of-the-art performance in link prediction tasks. Our code is available at https://github.com/GraphPKU/NeuralCommonNeighbor.

Given a node-attributed graph, and a graph task (link prediction or node classification), can we tell if a graph neural network (GNN) will perform well? More specifically, do the graph structure and the node features carry enough usable information for the task? Our goals are (1) to develop a fast tool to measure how much information is in the graph structure and in the node features, and (2) to exploit the information to solve the task, if there is enough. We propose NetInfoF, a framework including NetInfoF_Probe and NetInfoF_Act, for the measurement and the exploitation of network usable information (NUI), respectively. Given a graph data, NetInfoF_Probe measures NUI without any model training, and NetInfoF_Act solves link prediction and node classification, while two modules share the same backbone. In summary, NetInfoF has following notable advantages: (a) General, handling both link prediction and node classification; (b) Principled, with theoretical guarantee and closed-form solution; (c) Effective, thanks to the proposed adjustment to node similarity; (d) Scalable, scaling linearly with the input size. In our carefully designed synthetic datasets, NetInfoF correctly identifies the ground truth of NUI and is the only method being robust to all graph scenarios. Applied on real-world datasets, NetInfoF wins in 11 out of 12 times on link prediction compared to general GNN baselines.