Daily Papers

Recent large vision-language models (LVLMs) have demonstrated strong potential for device control. However, existing research has primarily focused on point-and-click (PnC) interaction, while remote-control (RC) interaction commonly encountered in everyday TV usage remains largely underexplored. To fill this gap, we introduce TVWorld, an offline graph-based abstraction of real-world TV navigation that enables reproducible and deployment-free evaluation. On this basis, we derive two complementary benchmarks that comprehensively assess TV-use capabilities: TVWorld-N for topology-aware navigation and TVWorld-G for focus-aware grounding. These benchmarks expose a key limitation of existing agents: insufficient topology awareness for focus-based, long-horizon TV navigation. Motivated by this finding, we propose a Topology-Aware Training framework that injects topology awareness into LVLMs. Using this framework, we develop TVTheseus, a foundation model specialized for TV navigation. TVTheseus achieves a success rate of 68.3% on TVWorld-N, surpassing strong closed-source baselines such as Gemini 3 Flash and establishing state-of-the-art (SOTA) performance. Additional analyses further provide valuable insights into the development of effective TV-use agents.

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}.

The Game of Life (Life), a well known algorithm within the broader class of cellular automata (CA), exhibits complex emergent dynamics, with extreme sensitivity to initial conditions. Modeling and predicting such intricate behavior without explicit knowledge of the system's underlying topology presents a significant challenge, motivating the development of algorithms that can generalize across various grid configurations and boundary conditions. We develop a decoder-only generative pretrained transformer model to solve this problem, showing that our model can simulate Life on a toroidal grid with no prior knowledge on the size of the grid, or its periodic boundary conditions (LifeGPT). LifeGPT is topology-agnostic with respect to its training data and our results show that a GPT model is capable of capturing the deterministic rules of a Turing-complete system with near-perfect accuracy, given sufficiently diverse training data. We also introduce the idea of an `autoregressive autoregressor' to recursively implement Life using LifeGPT. Our results pave the path towards true universal computation within a large language model (LLM) framework, synthesizing of mathematical analysis with natural language processing, and probing AI systems for situational awareness about the evolution of such algorithms without ever having to compute them. Similar GPTs could potentially solve inverse problems in multicellular self-assembly by extracting CA-compatible rulesets from real-world biological systems to create new predictive models, which would have significant consequences for the fields of bioinspired materials, tissue engineering, and architected materials design.

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.

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

While Retrieval-Augmented Generation (RAG) enhances the accuracy and relevance of responses by generative language models, it falls short in graph-based contexts where both textual and topological information are important. Naive RAG approaches inherently neglect the structural intricacies of textual graphs, resulting in a critical gap in the generation process. To address this challenge, we introduce Graph Retrieval-Augmented Generation (GRAG), which significantly enhances both the retrieval and generation processes by emphasizing the importance of subgraph structures. Unlike RAG approaches that focus solely on text-based entity retrieval, GRAG maintains an acute awareness of graph topology, which is crucial for generating contextually and factually coherent responses. Our GRAG approach consists of four main stages: indexing of k-hop ego-graphs, graph retrieval, soft pruning to mitigate the impact of irrelevant entities, and generation with pruned textual subgraphs. GRAG's core workflow-retrieving textual subgraphs followed by soft pruning-efficiently identifies relevant subgraph structures while avoiding the computational infeasibility typical of exhaustive subgraph searches, which are NP-hard. Moreover, we propose a novel prompting strategy that achieves lossless conversion from textual subgraphs to hierarchical text descriptions. Extensive experiments on graph multi-hop reasoning benchmarks demonstrate that in scenarios requiring multi-hop reasoning on textual graphs, our GRAG approach significantly outperforms current state-of-the-art RAG methods while effectively mitigating hallucinations.

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).

We present TopoMortar, a brick wall dataset that is the first dataset specifically designed to evaluate topology-focused image segmentation methods, such as topology loss functions. TopoMortar enables to investigate in two ways whether methods incorporate prior topological knowledge. First, by eliminating challenges seen in real-world data, such as small training set, noisy labels, and out-of-distribution test-set images, that, as we show, impact the effectiveness of topology losses. Second, by allowing to assess in the same dataset topology accuracy across dataset challenges, isolating dataset-related effects from the effect of incorporating prior topological knowledge. In these two experiments, it is deliberately difficult to improve topology accuracy without actually using topology information, thus, permitting to attribute an improvement in topology accuracy to the incorporation of prior topological knowledge. To this end, TopoMortar includes three types of labels (accurate, noisy, pseudo-labels), two fixed training sets (large and small), and in-distribution and out-of-distribution test-set images. We compared eight loss functions on TopoMortar, and we found that clDice achieved the most topologically accurate segmentations, Skeleton Recall loss performed best particularly with noisy labels, and the relative advantageousness of the other loss functions depended on the experimental setting. Additionally, we show that simple methods, such as data augmentation and self-distillation, can elevate Cross entropy Dice loss to surpass most topology loss functions, and that those simple methods can enhance topology loss functions as well. clDice and Skeleton Recall loss, both skeletonization-based loss functions, were also the fastest to train, making this type of loss function a promising research direction. TopoMortar and our code can be found at https://github.com/jmlipman/TopoMortar

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 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.

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

Topology reasoning aims to provide a precise understanding of road scenes, enabling autonomous systems to identify safe and efficient routes. In this paper, we present RoadPainter, an innovative approach for detecting and reasoning the topology of lane centerlines using multi-view images. The core concept behind RoadPainter is to extract a set of points from each centerline mask to improve the accuracy of centerline prediction. We start by implementing a transformer decoder that integrates a hybrid attention mechanism and a real-virtual separation strategy to predict coarse lane centerlines and establish topological associations. Then, we generate centerline instance masks guided by the centerline points from the transformer decoder. Moreover, we derive an additional set of points from each mask and combine them with previously detected centerline points for further refinement. Additionally, we introduce an optional module that incorporates a Standard Definition (SD) map to further optimize centerline detection and enhance topological reasoning performance. Experimental evaluations on the OpenLane-V2 dataset demonstrate the state-of-the-art performance of RoadPainter.

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.

Online scene perception and topology reasoning are critical for autonomous vehicles to understand their driving environments, particularly for mapless driving systems that endeavor to reduce reliance on costly High-Definition (HD) maps. However, recent advances in online scene understanding still face limitations, especially in long-range or occluded scenarios, due to the inherent constraints of onboard sensors. To address this challenge, we propose a Standard-Definition (SD) Map Enhanced scene Perception and Topology reasoning (SEPT) framework, which explores how to effectively incorporate the SD map as prior knowledge into existing perception and reasoning pipelines. Specifically, we introduce a novel hybrid feature fusion strategy that combines SD maps with Bird's-Eye-View (BEV) features, considering both rasterized and vectorized representations, while mitigating potential misalignment between SD maps and BEV feature spaces. Additionally, we leverage the SD map characteristics to design an auxiliary intersection-aware keypoint detection task, which further enhances the overall scene understanding performance. Experimental results on the large-scale OpenLane-V2 dataset demonstrate that by effectively integrating SD map priors, our framework significantly improves both scene perception and topology reasoning, outperforming existing methods by a substantial margin.

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.

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

Modern representation learning increasingly relies on unsupervised and self-supervised methods trained on large-scale unlabeled data. While these approaches achieve impressive generalization across tasks and domains, evaluating embedding quality without labels remains an open challenge. In this work, we propose Persistence, a topology-aware metric based on persistent homology that quantifies the geometric structure and topological richness of embedding spaces in a fully unsupervised manner. Unlike metrics that assume linear separability or rely on covariance structure, Persistence captures global and multi-scale organization. Empirical results across diverse domains show that Persistence consistently achieves top-tier correlations with downstream performance, outperforming existing unsupervised metrics and enabling reliable model and hyperparameter selection.

Recent breakthroughs in artificial intelligence (AI) have brought about increasingly capable systems that demonstrate remarkable abilities in reasoning, language understanding, and problem-solving. These advancements have prompted a renewed examination of AI awareness not as a philosophical question of consciousness, but as a measurable, functional capacity. AI awareness is a double-edged sword: it improves general capabilities, i.e., reasoning, safety, while also raising concerns around misalignment and societal risks, demanding careful oversight as AI capabilities grow. In this review, we explore the emerging landscape of AI awareness, which includes metacognition (the ability to represent and reason about its own cognitive state), self-awareness (recognizing its own identity, knowledge, limitations, inter alia), social awareness (modeling the knowledge, intentions, and behaviors of other agents and social norms), and situational awareness (assessing and responding to the context in which it operates). First, we draw on insights from cognitive science, psychology, and computational theory to trace the theoretical foundations of awareness and examine how the four distinct forms of AI awareness manifest in state-of-the-art AI. Next, we systematically analyze current evaluation methods and empirical findings to better understand these manifestations. Building on this, we explore how AI awareness is closely linked to AI capabilities, demonstrating that more aware AI agents tend to exhibit higher levels of intelligent behaviors. Finally, we discuss the risks associated with AI awareness, including key topics in AI safety, alignment, and broader ethical concerns.

Accurate road topology reasoning is critical for autonomous driving, as it requires both perceiving road elements and understanding how lanes connect to each other (L2L) and to traffic elements (L2T). Existing methods often focus on either perception or L2L reasoning, leaving L2T underexplored and fall short of jointly optimizing perception and reasoning. Moreover, although topology prediction inherently involves relations, relational modeling itself is seldom incorporated into feature extraction or supervision. As humans naturally leverage contextual relationships to recognize road element and infer their connectivity, we posit that relational modeling can likewise benefit both perception and reasoning, and that these two tasks should be mutually enhancing. To this end, we propose RelTopo, a multi-level relational modeling approach that systematically integrates relational cues across three levels: 1) perception-level: a relation-aware lane detector with geometry-biased self-attention and curve-guided cross-attention enriches lane representations; 2) reasoning-level: relation-enhanced topology heads, including a geometry-enhanced L2L head and a cross-view L2T head, enhance topology inference via relational cues; and 3) supervision-level: a contrastive InfoNCE strategy regularizes relational embeddings. This design enables perception and reasoning to be optimized jointly. Extensive experiments on OpenLane-V2 demonstrate that RelTopo significantly improves both detection and topology reasoning, with gains of +3.1 in DET_l, +5.3 in TOP_{ll}, +4.9 in TOP_{lt}, and +4.4 overall in OLS, setting a new state-of-the-art. Code will be released.

Knot diagrams are among the most common visual tools in topology. Computer programs now make it possible to draw, manipulate and render them digitally, which proves to be useful in knot theory teaching and research. Still, an openly available tool to manipulate knot diagrams in a real-time, interactive way is yet to be developed. We introduce a method of operating on the geometry of the knot diagram itself without any underlying three-dimensional structure that can underpin such an application. This allows us to directly interact with vector graphics knot diagrams while at the same time computing knot invariants in ways proposed by previous work. An implementation of this method is provided.

We explore the use of topological data analysis (TDA) combined with machine learning for discriminating standard model backgrounds from the invisible decay of the Z^prime boson associated with monophoton emission at a 3 TeV muon collider. Reconstructed events are mapped into a six-dimensional kinematic space and aggregated into bags of events, from which persistent homology is used to extract Betti number distributions. Within the Multiple Instance Learning paradigm, classifiers trained on these topological descriptors demonstrate significantly improved classification accuracy compared to the conventional ML approaches based on event-wise kinematic inputs. We also draw exclusion contours at 95\% CL in the (m_{Z^prime}, m_chi) parameter space, highlighting the potential of topological features to extend the discovery reach of future collider experiments.

Vision-language models (VLMs) have made significant strides in reasoning, yet they often struggle with complex multimodal tasks and tend to generate overly verbose outputs. A key limitation is their reliance on chain-of-thought (CoT) reasoning, despite many tasks benefiting from alternative topologies like trees or graphs. To address this, we introduce STELAR-Vision, a training framework for topology-aware reasoning. At its core is TopoAug, a synthetic data pipeline that enriches training with diverse topological structures. Using supervised fine-tuning and reinforcement learning, we post-train Qwen2VL models with both accuracy and efficiency in mind. Additionally, we propose Frugal Learning, which reduces output length with minimal accuracy loss. On MATH-V and VLM-S2H, STELAR-Vision improves accuracy by 9.7% over its base model and surpasses the larger Qwen2VL-72B-Instruct by 7.3%. On five out-of-distribution benchmarks, it outperforms Phi-4-Multimodal-Instruct by up to 28.4% and LLaMA-3.2-11B-Vision-Instruct by up to 13.2%, demonstrating strong generalization. Compared to Chain-Only training, our approach achieves 4.3% higher overall accuracy on in-distribution datasets and consistently outperforms across all OOD benchmarks. We have released datasets, and code will be available.

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.

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

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.

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

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.

We focus on the utilisation of reactive trajectory imitation controllers for goal-directed mobile robot navigation. We propose a topological navigation graph (TNG) - an imitation-learning-based framework for navigating through environments with intersecting trajectories. The TNG framework represents the environment as a directed graph composed of deep neural networks. Each vertex of the graph corresponds to a trajectory and is represented by a trajectory identification classifier and a trajectory imitation controller. For trajectory following, we propose the novel use of neural object detection architectures. The edges of TNG correspond to intersections between trajectories and are all represented by a classifier. We provide empirical evaluation of the proposed navigation framework and its components in simulated and real-world environments, demonstrating that TNG allows us to utilise non-goal-directed, imitation-learning methods for goal-directed autonomous navigation.

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.

Autoencoders have been proposed as a powerful tool for model-independent anomaly detection in high-energy physics. The operating principle is that events which do not belong to the space of training data will be reconstructed poorly, thus flagging them as anomalies. We point out that in a variety of examples of interest, the connection between large reconstruction error and anomalies is not so clear. In particular, for data sets with nontrivial topology, there will always be points that erroneously seem anomalous due to global issues. Conversely, neural networks typically have an inductive bias or prior to locally interpolate such that undersampled or rare events may be reconstructed with small error, despite actually being the desired anomalies. Taken together, these facts are in tension with the simple picture of the autoencoder as an anomaly detector. Using a series of illustrative low-dimensional examples, we show explicitly how the intrinsic and extrinsic topology of the dataset affects the behavior of an autoencoder and how this topology is manifested in the latent space representation during training. We ground this analysis in the discussion of a mock "bump hunt" in which the autoencoder fails to identify an anomalous "signal" for reasons tied to the intrinsic topology of n-particle phase space.

A core aspect of human perception is situated awareness, the ability to relate ourselves to the surrounding physical environment and reason over possible actions in context. However, most existing benchmarks for multimodal foundation models (MFMs) emphasize environment-centric spatial relations (relations among objects in a scene), while largely overlooking observer-centric relationships that require reasoning relative to agent's viewpoint, pose, and motion. To bridge this gap, we introduce SAW-Bench (Situated Awareness in the Real World), a novel benchmark for evaluating egocentric situated awareness using real-world videos. SAW-Bench comprises 786 self-recorded videos captured with Ray-Ban Meta (Gen 2) smart glasses spanning diverse indoor and outdoor environments, and over 2,071 human-annotated question-answer pairs. It probes a model's observer-centric understanding with six different awareness tasks. Our comprehensive evaluation reveals a human-model performance gap of 37.66%, even with the best-performing MFM, Gemini 3 Flash. Beyond this gap, our in-depth analysis uncovers several notable findings; for example, while models can exploit partial geometric cues in egocentric videos, they often fail to infer a coherent camera geometry, leading to systematic spatial reasoning errors. We position SAW-Bench as a benchmark for situated spatial intelligence, moving beyond passive observation to understanding physically grounded, observer-centric dynamics.

Lane-level navigation is critical for geographic information systems and navigation-based tasks, offering finer-grained guidance than road-level navigation by standard definition (SD) maps. However, it currently relies on expansive global HD maps that cannot adapt to dynamic road conditions. Recently, online perception (OP) maps have become research hotspots, providing real-time geometry as an alternative, but lack the global topology needed for navigation. To address these issues, Online Navigation Refinement (ONR), a new mission is introduced that refines SD-map-based road-level routes into accurate lane-level navigation by associating SD maps with OP maps. The map-to-map association to handle many-to-one lane-to-road mappings under two key challenges: (1) no public dataset provides lane-to-road correspondences; (2) severe misalignment from spatial fluctuations, semantic disparities, and OP map noise invalidates traditional map matching. For these challenges, We contribute: (1) Online map association dataset (OMA), the first ONR benchmark with 30K scenarios and 2.6M annotated lane vectors; (2) MAT, a transformer with path-aware attention to aligns topology despite spatial fluctuations and semantic disparities and spatial attention for integrates noisy OP features via global context; and (3) NR P-R, a metric evaluating geometric and semantic alignment. Experiments show that MAT outperforms existing methods at 34 ms latency, enabling low-cost and up-to-date lane-level navigation.

We propose a novel approach for preserving topological structures of the input space in latent representations of autoencoders. Using persistent homology, a technique from topological data analysis, we calculate topological signatures of both the input and latent space to derive a topological loss term. Under weak theoretical assumptions, we construct this loss in a differentiable manner, such that the encoding learns to retain multi-scale connectivity information. We show that our approach is theoretically well-founded and that it exhibits favourable latent representations on a synthetic manifold as well as on real-world image data sets, while preserving low reconstruction errors.

Spatial-temporal forecasting and imputation are important for real-world intelligent systems. Most existing methods are tailored for individual forecasting or imputation tasks but are not designed for both. Additionally, they are less effective for zero-shot and few-shot learning. While pre-trained language model (PLM) have exhibited strong pattern recognition and reasoning abilities across various tasks, including few-shot and zero-shot learning, their applications in spatial-temporal data understanding has been constrained by insufficient modeling of complex correlations such as the temporal correlations, spatial connectivity, non-pairwise and high-order spatial-temporal correlations within data. In this paper, we propose STD-PLM for understanding both spatial and temporal properties of Spatial-Temporal Data with PLM, which is capable of implementing both spatial-temporal forecasting and imputation tasks. STD-PLM understands spatial-temporal correlations via explicitly designed spatial and temporal tokenizers. Topology-aware node embeddings are designed for PLM to comprehend and exploit the topology structure of data in inductive manner. Furthermore, to mitigate the efficiency issues introduced by the PLM, we design a sandglass attention module (SGA) combined with a specific constrained loss function, which significantly improves the model's efficiency while ensuring performance. Extensive experiments demonstrate that STD-PLM exhibits competitive performance and generalization capabilities across the forecasting and imputation tasks on various datasets. Moreover, STD-PLM achieves promising results on both few-shot and zero-shot tasks.The code is made available at https://anonymous.4open.science/r/STD-PLM-F3BA{https://anonymous.4open.science/r/STD-PLM-F3BA}

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

Leaf-lesion segmentation is topology-sensitive: small merges, splits, or false holes can be biologically meaningful descriptors of biochemical pathways, yet they are weakly penalized by standard pixel-wise losses in Euclidean latents. I explore HyperTopo-Adapters, a lightweight, parameter-efficient head trained on top of a frozen vision encoder, which embeds features on a product manifold -- hyperbolic + Euclidean + spherical (H + E + S) -- to encourage hierarchical separation (H), local linear detail (E), and global closure (S). A topology prior complements Dice/BCE in two forms: (i) persistent-homology (PH) distance for evaluation and selection, and (ii) a differentiable surrogate that combines a soft Euler-characteristic match with total variation regularization for stable training. I introduce warm-ups for both the hyperbolic contrastive term and the topology prior, per-sample evaluation of structure-aware metrics (Boundary-F1, Betti errors, PD distance), and a min-PD within top-K Dice rule for checkpoint selection. On a Kaggle leaf-lesion dataset (N=2,940), early results show consistent gains in boundary and topology metrics (reducing Delta beta_1 hole error by 9%) while Dice/IoU remain competitive. The study is diagnostic by design: I report controlled ablations (curvature learning, latent dimensions, contrastive temperature, surrogate settings), and ongoing tests varying encoder strength (ResNet-50, DeepLabV3, DINOv2/v3), input resolution, PH weight, and partial unfreezing of late blocks. The contribution is an open, reproducible train/eval suite (available at https://github.com/ChimdiWalter/HyperTopo-Adapters) that isolates geometric/topological priors and surfaces failure modes to guide stronger, topology-preserving architectures.

To bridge the gaps between topology-aware Graph Neural Networks (GNNs) and inference-efficient Multi-Layer Perceptron (MLPs), GLNN proposes to distill knowledge from a well-trained teacher GNN into a student MLP. Despite their great progress, comparatively little work has been done to explore the reliability of different knowledge points (nodes) in GNNs, especially their roles played during distillation. In this paper, we first quantify the knowledge reliability in GNN by measuring the invariance of their information entropy to noise perturbations, from which we observe that different knowledge points (1) show different distillation speeds (temporally); (2) are differentially distributed in the graph (spatially). To achieve reliable distillation, we propose an effective approach, namely Knowledge-inspired Reliable Distillation (KRD), that models the probability of each node being an informative and reliable knowledge point, based on which we sample a set of additional reliable knowledge points as supervision for training student MLPs. Extensive experiments show that KRD improves over the vanilla MLPs by 12.62% and outperforms its corresponding teacher GNNs by 2.16% averaged over 7 datasets and 3 GNN architectures.

Time series reasoning treats time as a first-class axis and incorporates intermediate evidence directly into the answer. This survey defines the problem and organizes the literature by reasoning topology with three families: direct reasoning in one step, linear chain reasoning with explicit intermediates, and branch-structured reasoning that explores, revises, and aggregates. The topology is crossed with the main objectives of the field, including traditional time series analysis, explanation and understanding, causal inference and decision making, and time series generation, while a compact tag set spans these axes and captures decomposition and verification, ensembling, tool use, knowledge access, multimodality, agent loops, and LLM alignment regimes. Methods and systems are reviewed across domains, showing what each topology enables and where it breaks down in faithfulness or robustness, along with curated datasets, benchmarks, and resources that support study and deployment (https://github.com/blacksnail789521/Time-Series-Reasoning-Survey). Evaluation practices that keep evidence visible and temporally aligned are highlighted, and guidance is distilled on matching topology to uncertainty, grounding with observable artifacts, planning for shift and streaming, and treating cost and latency as design budgets. We emphasize that reasoning structures must balance capacity for grounding and self-correction against computational cost and reproducibility, while future progress will likely depend on benchmarks that tie reasoning quality to utility and on closed-loop testbeds that trade off cost and risk under shift-aware, streaming, and long-horizon settings. Taken together, these directions mark a shift from narrow accuracy toward reliability at scale, enabling systems that not only analyze but also understand, explain, and act on dynamic worlds with traceable evidence and credible outcomes.

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

This paper presents the computational challenge on differential geometry and topology that happened within the ICLR 2021 workshop "Geometric and Topological Representation Learning". The competition asked participants to provide creative contributions to the fields of computational geometry and topology through the open-source repositories Geomstats and Giotto-TDA. The challenge attracted 16 teams in its two month duration. This paper describes the design of the challenge and summarizes its main findings.

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.

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.

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

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

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.

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.

Large Vision-Language Models (LVLMs) typically align visual features from an encoder with a pre-trained Large Language Model (LLM). However, this makes the visual perception module a bottleneck, which constrains the overall capabilities of LVLMs. Conventional evaluation benchmarks, while rich in visual semantics, often contain unavoidable local shortcuts that can lead to an overestimation of models' perceptual abilities. Here, we introduce TopoPerception, a benchmark that leverages topological properties to rigorously evaluate the global visual perception capabilities of LVLMs across various granularities. Since topology depends on the global structure of an image and is invariant to local features, TopoPerception enables a shortcut-free assessment of global perception, fundamentally distinguishing it from semantically rich tasks. We evaluate state-of-the-art models on TopoPerception and find that even at the coarsest perceptual granularity, all models perform no better than random chance, indicating a profound inability to perceive global visual features. Notably, a consistent trend emerge within model families: more powerful models with stronger reasoning capabilities exhibit lower accuracy. This suggests that merely scaling up models is insufficient to address this deficit and may even exacerbate it. Progress may require new training paradigms or architectures. TopoPerception not only exposes a critical bottleneck in current LVLMs but also offers a lens and direction for improving their global visual perception. The data and code are publicly available at: https://github.com/Wenhao-Zhou/TopoPerception.

Given that visual foundation models (VFMs) are trained on extensive datasets but often limited to 2D images, a natural question arises: how well do they understand the 3D world? With the differences in architecture and training protocols (i.e., objectives, proxy tasks), a unified framework to fairly and comprehensively probe their 3D awareness is urgently needed. Existing works on 3D probing suggest single-view 2.5D estimation (e.g., depth and normal) or two-view sparse 2D correspondence (e.g., matching and tracking). Unfortunately, these tasks ignore texture awareness, and require 3D data as ground-truth, which limits the scale and diversity of their evaluation set. To address these issues, we introduce Feat2GS, which readout 3D Gaussians attributes from VFM features extracted from unposed images. This allows us to probe 3D awareness for geometry and texture via novel view synthesis, without requiring 3D data. Additionally, the disentanglement of 3DGS parameters - geometry (x, alpha, Sigma) and texture (c) - enables separate analysis of texture and geometry awareness. Under Feat2GS, we conduct extensive experiments to probe the 3D awareness of several VFMs, and investigate the ingredients that lead to a 3D aware VFM. Building on these findings, we develop several variants that achieve state-of-the-art across diverse datasets. This makes Feat2GS useful for probing VFMs, and as a simple-yet-effective baseline for novel-view synthesis. Code and data will be made available at https://fanegg.github.io/Feat2GS/.

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 enduring legacy of Euclidean geometry underpins classical machine learning, which, for decades, has been primarily developed for data lying in Euclidean space. Yet, modern machine learning increasingly encounters richly structured data that is inherently nonEuclidean. This data can exhibit intricate geometric, topological and algebraic structure: from the geometry of the curvature of space-time, to topologically complex interactions between neurons in the brain, to the algebraic transformations describing symmetries of physical systems. Extracting knowledge from such non-Euclidean data necessitates a broader mathematical perspective. Echoing the 19th-century revolutions that gave rise to non-Euclidean geometry, an emerging line of research is redefining modern machine learning with non-Euclidean structures. Its goal: generalizing classical methods to unconventional data types with geometry, topology, and algebra. In this review, we provide an accessible gateway to this fast-growing field and propose a graphical taxonomy that integrates recent advances into an intuitive unified framework. We subsequently extract insights into current challenges and highlight exciting opportunities for future development in this field.

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.

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

Persistent homology (PH) provides topological descriptors for geometric data, such as weighted graphs, which are interpretable, stable to perturbations, and invariant under, e.g., relabeling. Most applications of PH focus on the one-parameter case -- where the descriptors summarize the changes in topology of data as it is filtered by a single quantity of interest -- and there is now a wide array of methods enabling the use of one-parameter PH descriptors in data science, which rely on the stable vectorization of these descriptors as elements of a Hilbert space. Although the multiparameter PH (MPH) of data that is filtered by several quantities of interest encodes much richer information than its one-parameter counterpart, the scarceness of stability results for MPH descriptors has so far limited the available options for the stable vectorization of MPH. In this paper, we aim to bring together the best of both worlds by showing how the interpretation of signed barcodes -- a recent family of MPH descriptors -- as signed measures leads to natural extensions of vectorization strategies from one parameter to multiple parameters. The resulting feature vectors are easy to define and to compute, and provably stable. While, as a proof of concept, we focus on simple choices of signed barcodes and vectorizations, we already see notable performance improvements when comparing our feature vectors to state-of-the-art topology-based methods on various types of data.

We define and develop a homotopy invariant notion for the topological complexity of a map f:X to Y, denoted TC(f), that interacts with TC(X) and TC(Y) in the same way cat(f) interacts with cat(X) and cat(Y). Furthermore, TC(f) and cat(f) satisfy the same inequalities as TC(X) and cat(X). We compare it to other invariants defined in the papers [15,16,17,18,20]. We apply TC(f) to studying group homomorphisms f:Hto G.

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

We introduce a theoretical framework for differentiable surface evolution that allows discrete topology changes through the use of topological derivatives for variational optimization of image functionals. While prior methods for inverse rendering of geometry rely on silhouette gradients for topology changes, such signals are sparse. In contrast, our theory derives topological derivatives that relate the introduction of vanishing holes and phases to changes in image intensity. As a result, we enable differentiable shape perturbations in the form of hole or phase nucleation. We validate the proposed theory with optimization of closed curves in 2D and surfaces in 3D to lend insights into limitations of current methods and enable improved applications such as image vectorization, vector-graphics generation from text prompts, single-image reconstruction of shape ambigrams and multi-view 3D reconstruction.

Accurately segmenting thin tubular structures, such as vessels, nerves, roads or concrete cracks, is a crucial task in computer vision. Standard deep learning-based segmentation loss functions, such as Dice or Cross-Entropy, focus on volumetric overlap, often at the expense of preserving structural connectivity or topology. This can lead to segmentation errors that adversely affect downstream tasks, including flow calculation, navigation, and structural inspection. Although current topology-focused losses mark an improvement, they introduce significant computational and memory overheads. This is particularly relevant for 3D data, rendering these losses infeasible for larger volumes as well as increasingly important multi-class segmentation problems. To mitigate this, we propose a novel Skeleton Recall Loss, which effectively addresses these challenges by circumventing intensive GPU-based calculations with inexpensive CPU operations. It demonstrates overall superior performance to current state-of-the-art approaches on five public datasets for topology-preserving segmentation, while substantially reducing computational overheads by more than 90%. In doing so, we introduce the first multi-class capable loss function for thin structure segmentation, excelling in both efficiency and efficacy for topology-preservation.

Machine learning for point clouds has been attracting much attention, with many applications in various fields, such as shape recognition and material science. For enhancing the accuracy of such machine learning methods, it is often effective to incorporate global topological features, which are typically extracted by persistent homology. In the calculation of persistent homology for a point cloud, we choose a filtration for the point cloud, an increasing sequence of spaces. Since the performance of machine learning methods combined with persistent homology is highly affected by the choice of a filtration, we need to tune it depending on data and tasks. In this paper, we propose a framework that learns a filtration adaptively with the use of neural networks. In order to make the resulting persistent homology isometry-invariant, we develop a neural network architecture with such invariance. Additionally, we show a theoretical result on a finite-dimensional approximation of filtration functions, which justifies the proposed network architecture. Experimental results demonstrated the efficacy of our framework in several classification tasks.

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.

We present Topological Point Cloud Clustering (TPCC), a new method to cluster points in an arbitrary point cloud based on their contribution to global topological features. TPCC synthesizes desirable features from spectral clustering and topological data analysis and is based on considering the spectral properties of a simplicial complex associated to the considered point cloud. As it is based on considering sparse eigenvector computations, TPCC is similarly easy to interpret and implement as spectral clustering. However, by focusing not just on a single matrix associated to a graph created from the point cloud data, but on a whole set of Hodge-Laplacians associated to an appropriately constructed simplicial complex, we can leverage a far richer set of topological features to characterize the data points within the point cloud and benefit from the relative robustness of topological techniques against noise. We test the performance of TPCC on both synthetic and real-world data and compare it with classical spectral clustering.

Current visual foundation models are trained purely on unstructured 2D data, limiting their understanding of 3D structure of objects and scenes. In this work, we show that fine-tuning on 3D-aware data improves the quality of emerging semantic features. We design a method to lift semantic 2D features into an efficient 3D Gaussian representation, which allows us to re-render them for arbitrary views. Using the rendered 3D-aware features, we design a fine-tuning strategy to transfer such 3D awareness into a 2D foundation model. We demonstrate that models fine-tuned in that way produce features that readily improve downstream task performance in semantic segmentation and depth estimation through simple linear probing. Notably, though fined-tuned on a single indoor dataset, the improvement is transferable to a variety of indoor datasets and out-of-domain datasets. We hope our study encourages the community to consider injecting 3D awareness when training 2D foundation models. Project page: https://ywyue.github.io/FiT3D.

Micro-Aerial Vehicles (MAVs) have the advantage of moving freely in 3D space. However, creating compact and sparse map representations that can be efficiently used for planning for such robots is still an open problem. In this paper, we take maps built from noisy sensor data and construct a sparse graph containing topological information that can be used for 3D planning. We use a Euclidean Signed Distance Field, extract a 3D Generalized Voronoi Diagram (GVD), and obtain a thin skeleton diagram representing the topological structure of the environment. We then convert this skeleton diagram into a sparse graph, which we show is resistant to noise and changes in resolution. We demonstrate global planning over this graph, and the orders of magnitude speed-up it offers over other common planning methods. We validate our planning algorithm in real maps built onboard an MAV, using RGB-D sensing.

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.

The role of the attention mechanism in encoding linguistic knowledge has received special interest in NLP. However, the ability of the attention heads to judge the grammatical acceptability of a sentence has been underexplored. This paper approaches the paradigm of acceptability judgments with topological data analysis (TDA), showing that the geometric properties of the attention graph can be efficiently exploited for two standard practices in linguistics: binary judgments and linguistic minimal pairs. Topological features enhance the BERT-based acceptability classifier scores by 8%-24% on CoLA in three languages (English, Italian, and Swedish). By revealing the topological discrepancy between attention maps of minimal pairs, we achieve the human-level performance on the BLiMP benchmark, outperforming nine statistical and Transformer LM baselines. At the same time, TDA provides the foundation for analyzing the linguistic functions of attention heads and interpreting the correspondence between the graph features and grammatical phenomena.

Unsupervised learning for geometric perception (depth, optical flow, etc.) is of great interest to autonomous systems. Recent works on unsupervised learning have made considerable progress on perceiving geometry; however, they usually ignore the coherence of objects and perform poorly under scenarios with dark and noisy environments. In contrast, supervised learning algorithms, which are robust, require large labeled geometric dataset. This paper introduces SIGNet, a novel framework that provides robust geometry perception without requiring geometrically informative labels. Specifically, SIGNet integrates semantic information to make depth and flow predictions consistent with objects and robust to low lighting conditions. SIGNet is shown to improve upon the state-of-the-art unsupervised learning for depth prediction by 30% (in squared relative error). In particular, SIGNet improves the dynamic object class performance by 39% in depth prediction and 29% in flow prediction. Our code will be made available at https://github.com/mengyuest/SIGNet

We introduce a randomized topological augmentor based on Schur complements for Graph Contrastive Learning (GCL). Given a graph laplacian matrix, the technique generates unbiased approximations of its Schur complements and treats the corresponding graphs as augmented views. We discuss the benefits of our approach, provide theoretical justifications and present connections with graph diffusion. Unlike previous efforts, we study the empirical effectiveness of the augmentor in a controlled fashion by varying the design choices for subsequent GCL phases, such as encoding and contrasting. Extensive experiments on node and graph classification benchmarks demonstrate that our technique consistently outperforms pre-defined and adaptive augmentation approaches to achieve state-of-the-art results.

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

Characteristic classes, which are abstract topological invariants associated with vector bundles, have become an important notion in modern physics with surprising real-world consequences. As a representative example, the incredible properties of topological insulators, which are insulators in their bulk but conductors on their surface, can be completely characterized by a specific characteristic class associated with their electronic band structure, the first Chern class. Given their importance to next generation computing and the computational challenge of calculating them using first-principles approaches, there is a need to develop machine learning approaches to predict the characteristic classes associated with a material system. To aid in this program we introduce the {Haldane bundle dataset}, which consists of synthetically generated complex line bundles on the 2-torus. We envision this dataset, which is not as challenging as noisy and sparsely measured real-world datasets but (as we show) still difficult for off-the-shelf architectures, to be a testing ground for architectures that incorporate the rich topological and geometric priors underlying characteristic classes.

Representation learning has become an invaluable approach for learning from symbolic data such as text and graphs. However, while complex symbolic datasets often exhibit a latent hierarchical structure, state-of-the-art methods typically learn embeddings in Euclidean vector spaces, which do not account for this property. For this purpose, we introduce a new approach for learning hierarchical representations of symbolic data by embedding them into hyperbolic space -- or more precisely into an n-dimensional Poincar\'e ball. Due to the underlying hyperbolic geometry, this allows us to learn parsimonious representations of symbolic data by simultaneously capturing hierarchy and similarity. We introduce an efficient algorithm to learn the embeddings based on Riemannian optimization and show experimentally that Poincar\'e embeddings outperform Euclidean embeddings significantly on data with latent hierarchies, both in terms of representation capacity and in terms of generalization ability.

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.

Recent 3D generative models produce high-quality textures for 3D mesh objects. However, they commonly rely on the heavy assumption that input 3D meshes are accompanied by manual mesh parameterization (UV mapping), a manual task that requires both technical precision and artistic judgment. Industry surveys show that this process often accounts for a significant share of asset creation, creating a major bottleneck for 3D content creators. Moreover, existing automatic methods often ignore two perceptually important criteria: (1) semantic awareness (UV charts should align semantically similar 3D parts across shapes) and (2) visibility awareness (cutting seams should lie in regions unlikely to be seen). To overcome these shortcomings and to automate the mesh parameterization process, we present an unsupervised differentiable framework that augments standard geometry-preserving UV learning with semantic- and visibility-aware objectives. For semantic-awareness, our pipeline (i) segments the mesh into semantic 3D parts, (ii) applies an unsupervised learned per-part UV-parameterization backbone, and (iii) aggregates per-part charts into a unified UV atlas. For visibility-awareness, we use ambient occlusion (AO) as an exposure proxy and back-propagate a soft differentiable AO-weighted seam objective to steer cutting seams toward occluded regions. By conducting qualitative and quantitative evaluations against state-of-the-art methods, we show that the proposed method produces UV atlases that better support texture generation and reduce perceptible seam artifacts compared to recent baselines. Our implementation code is publicly available at: https://github.com/AHHHZ975/Semantic-Visibility-UV-Param.

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.

Spatial embodied intelligence requires agents to act to acquire information under partial observability. While multimodal foundation models excel at passive perception, their capacity for active, self-directed exploration remains understudied. We propose Theory of Space, defined as an agent's ability to actively acquire information through self-directed, active exploration and to construct, revise, and exploit a spatial belief from sequential, partial observations. We evaluate this through a benchmark where the goal is curiosity-driven exploration to build an accurate cognitive map. A key innovation is spatial belief probing, which prompts models to reveal their internal spatial representations at each step. Our evaluation of state-of-the-art models reveals several critical bottlenecks. First, we identify an Active-Passive Gap, where performance drops significantly when agents must autonomously gather information. Second, we find high inefficiency, as models explore unsystematically compared to program-based proxies. Through belief probing, we diagnose that while perception is an initial bottleneck, global beliefs suffer from instability that causes spatial knowledge to degrade over time. Finally, using a false belief paradigm, we uncover Belief Inertia, where agents fail to update obsolete priors with new evidence. This issue is present in text-based agents but is particularly severe in vision-based models. Our findings suggest that current foundation models struggle to maintain coherent, revisable spatial beliefs during active exploration.

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

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

Image segmentation is a largely researched field where neural networks find vast applications in many facets of technology. Some of the most popular approaches to train segmentation networks employ loss functions optimizing pixel-overlap, an objective that is insufficient for many segmentation tasks. In recent years, their limitations fueled a growing interest in topology-aware methods, which aim to recover the correct topology of the segmented structures. However, so far, none of the existing approaches achieve a spatially correct matching between the topological features of ground truth and prediction. In this work, we propose the first topologically and feature-wise accurate metric and loss function for supervised image segmentation, which we term Betti matching. We show how induced matchings guarantee the spatially correct matching between barcodes in a segmentation setting. Furthermore, we propose an efficient algorithm to compute the Betti matching of images. We show that the Betti matching error is an interpretable metric to evaluate the topological correctness of segmentations, which is more sensitive than the well-established Betti number error. Moreover, the differentiability of the Betti matching loss enables its use as a loss function. It improves the topological performance of segmentation networks across six diverse datasets while preserving the volumetric performance. Our code is available in https://github.com/nstucki/Betti-matching.

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

In this paper, we propose REASON, a novel framework that enables the automatic discovery of both intra-level (i.e., within-network) and inter-level (i.e., across-network) causal relationships for root cause localization. REASON consists of Topological Causal Discovery and Individual Causal Discovery. The Topological Causal Discovery component aims to model the fault propagation in order to trace back to the root causes. To achieve this, we propose novel hierarchical graph neural networks to construct interdependent causal networks by modeling both intra-level and inter-level non-linear causal relations. Based on the learned interdependent causal networks, we then leverage random walks with restarts to model the network propagation of a system fault. The Individual Causal Discovery component focuses on capturing abrupt change patterns of a single system entity. This component examines the temporal patterns of each entity's metric data (i.e., time series), and estimates its likelihood of being a root cause based on the Extreme Value theory. Combining the topological and individual causal scores, the top K system entities are identified as root causes. Extensive experiments on three real-world datasets with case studies demonstrate the effectiveness and superiority of the proposed framework.

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.

We develop information geometric techniques to understand the representations learned by deep networks when they are trained on different tasks using supervised, meta-, semi-supervised and contrastive learning. We shed light on the following phenomena that relate to the structure of the space of tasks: (1) the manifold of probabilistic models trained on different tasks using different representation learning methods is effectively low-dimensional; (2) supervised learning on one task results in a surprising amount of progress even on seemingly dissimilar tasks; progress on other tasks is larger if the training task has diverse classes; (3) the structure of the space of tasks indicated by our analysis is consistent with parts of the Wordnet phylogenetic tree; (4) episodic meta-learning algorithms and supervised learning traverse different trajectories during training but they fit similar models eventually; (5) contrastive and semi-supervised learning methods traverse trajectories similar to those of supervised learning. We use classification tasks constructed from the CIFAR-10 and Imagenet datasets to study these phenomena.

Complex prediction models such as deep learning are the output from fitting machine learning, neural networks, or AI models to a set of training data. These are now standard tools in science. A key challenge with the current generation of models is that they are highly parameterized, which makes describing and interpreting the prediction strategies difficult. We use topological data analysis to transform these complex prediction models into pictures representing a topological view. The result is a map of the predictions that enables inspection. The methods scale up to large datasets across different domains and enable us to detect labeling errors in training data, understand generalization in image classification, and inspect predictions of likely pathogenic mutations in the BRCA1 gene.

Understanding and mapping a new environment are core abilities of any autonomously navigating agent. While classical robotics usually estimates maps in a stand-alone manner with SLAM variants, which maintain a topological or metric representation, end-to-end learning of navigation keeps some form of memory in a neural network. Networks are typically imbued with inductive biases, which can range from vectorial representations to birds-eye metric tensors or topological structures. In this work, we propose to structure neural networks with two neural implicit representations, which are learned dynamically during each episode and map the content of the scene: (i) the Semantic Finder predicts the position of a previously seen queried object; (ii) the Occupancy and Exploration Implicit Representation encapsulates information about explored area and obstacles, and is queried with a novel global read mechanism which directly maps from function space to a usable embedding space. Both representations are leveraged by an agent trained with Reinforcement Learning (RL) and learned online during each episode. We evaluate the agent on Multi-Object Navigation and show the high impact of using neural implicit representations as a memory source.

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.

Videos are continuous 2D projections of 3D worlds. After training on large video data, will global 3D understanding naturally emerge? We study this by quantifying the 3D understanding of existing Video Foundation Models (VidFMs) pretrained on vast video data. We propose the first model-agnostic framework that measures the 3D awareness of various VidFMs by estimating multiple 3D properties from their features via shallow read-outs. Our study presents meaningful findings regarding the 3D awareness of VidFMs on multiple axes. In particular, we show that state-of-the-art video generation models exhibit a strong understanding of 3D objects and scenes, despite not being trained on any 3D data. Such understanding can even surpass that of large expert models specifically trained for 3D tasks. Our findings, together with the 3D benchmarking of major VidFMs, provide valuable observations for building scalable 3D models.

Vision-Language Pretraining (VLP) has shown impressive results on diverse downstream tasks by offline training on large-scale datasets. Regarding the growing nature of real-world data, such an offline training paradigm on ever-expanding data is unsustainable, because models lack the continual learning ability to accumulate knowledge constantly. However, most continual learning studies are limited to uni-modal classification and existing multi-modal datasets cannot simulate continual non-stationary data stream scenarios. To support the study of Vision-Language Continual Pretraining (VLCP), we first contribute a comprehensive and unified benchmark dataset P9D which contains over one million product image-text pairs from 9 industries. The data from each industry as an independent task supports continual learning and conforms to the real-world long-tail nature to simulate pretraining on web data. We comprehensively study the characteristics and challenges of VLCP, and propose a new algorithm: Compatible momentum contrast with Topology Preservation, dubbed CTP. The compatible momentum model absorbs the knowledge of the current and previous-task models to flexibly update the modal feature. Moreover, Topology Preservation transfers the knowledge of embedding across tasks while preserving the flexibility of feature adjustment. The experimental results demonstrate our method not only achieves superior performance compared with other baselines but also does not bring an expensive training burden. Dataset and codes are available at https://github.com/KevinLight831/CTP.

Accurately depicting the complex traffic scene is a vital component for autonomous vehicles to execute correct judgments. However, existing benchmarks tend to oversimplify the scene by solely focusing on lane perception tasks. Observing that human drivers rely on both lanes and traffic signals to operate their vehicles safely, we present OpenLane-V2, the first dataset on topology reasoning for traffic scene structure. The objective of the presented dataset is to advance research in understanding the structure of road scenes by examining the relationship between perceived entities, such as traffic elements and lanes. Leveraging existing datasets, OpenLane-V2 consists of 2,000 annotated road scenes that describe traffic elements and their correlation to the lanes. It comprises three primary sub-tasks, including the 3D lane detection inherited from OpenLane, accompanied by corresponding metrics to evaluate the model's performance. We evaluate various state-of-the-art methods, and present their quantitative and qualitative results on OpenLane-V2 to indicate future avenues for investigating topology reasoning in traffic scenes.

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.

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

With the development of large language models (LLMs), particularly with the introduction of the long reasoning chain technique, the reasoning ability of LLMs in complex problem-solving has been significantly enhanced. While acknowledging the power of long reasoning chains, we cannot help but wonder: Why do different reasoning chains perform differently in reasoning? What components of the reasoning chains play a key role? Existing studies mainly focus on evaluating reasoning chains from a functional perspective, with little attention paid to their structural mechanisms. To address this gap, this work is the first to analyze and evaluate the quality of the reasoning chain from a structural perspective. We apply persistent homology from Topological Data Analysis (TDA) to map reasoning steps into semantic space, extract topological features, and analyze structural changes. These changes reveal semantic coherence, logical redundancy, and identify logical breaks and gaps. By calculating homology groups, we assess connectivity and redundancy at various scales, using barcode and persistence diagrams to quantify stability and consistency. Our results show that the topological structural complexity of reasoning chains correlates positively with accuracy. More complex chains identify correct answers sooner, while successful reasoning exhibits simpler topologies, reducing redundancy and cycles, enhancing efficiency and interpretability. This work provides a new perspective on reasoning chain quality assessment and offers guidance for future optimization.

While Large Language Models require more and more data to train and scale, rather than looking for any data to acquire, we should consider what types of tasks are more likely to benefit from data scaling. We should be intentional in our data acquisition. We argue that the topology of data itself informs which tasks to prioritize in data scaling, and shapes the development of the next generation of compute paradigms for tasks where data scaling is inefficient, or even insufficient.

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

The Airbnb search system grapples with many unique challenges as it continues to evolve. We oversee a marketplace that is nuanced by geography, diversity of homes, and guests with a variety of preferences. Crafting an efficient search system that can accommodate diverse guest needs, while showcasing relevant homes lies at the heart of Airbnb's success. Airbnb search has many challenges that parallel other recommendation and search systems but it has a unique information retrieval problem, upstream of ranking, called location retrieval. It requires defining a topological map area that is relevant to the searched query for homes listing retrieval. The purpose of this paper is to demonstrate the methodology, challenges, and impact of building a machine learning based location retrieval product from the ground up. Despite the lack of suitable, prevalent machine learning based approaches, we tackle cold start, generalization, differentiation and algorithmic bias. We detail the efficacy of heuristics, statistics, machine learning, and reinforcement learning approaches to solve these challenges, particularly for systems that are often unexplored by current literature.

Visual navigation in robotics traditionally relies on globally-consistent 3D maps or learned controllers, which can be computationally expensive and difficult to generalize across diverse environments. In this work, we present a novel RGB-only, object-level topometric navigation pipeline that enables zero-shot, long-horizon robot navigation without requiring 3D maps or pre-trained controllers. Our approach integrates global topological path planning with local metric trajectory control, allowing the robot to navigate towards object-level sub-goals while avoiding obstacles. We address key limitations of previous methods by continuously predicting local trajectory using monocular depth and traversability estimation, and incorporating an auto-switching mechanism that falls back to a baseline controller when necessary. The system operates using foundational models, ensuring open-set applicability without the need for domain-specific fine-tuning. We demonstrate the effectiveness of our method in both simulated environments and real-world tests, highlighting its robustness and deployability. Our approach outperforms existing state-of-the-art methods, offering a more adaptable and effective solution for visual navigation in open-set environments. The source code is made publicly available: https://github.com/podgorki/TANGO.

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.

Multi-camera 3D object detection for autonomous driving is a challenging problem that has garnered notable attention from both academia and industry. An obstacle encountered in vision-based techniques involves the precise extraction of geometry-conscious features from RGB images. Recent approaches have utilized geometric-aware image backbones pretrained on depth-relevant tasks to acquire spatial information. However, these approaches overlook the critical aspect of view transformation, resulting in inadequate performance due to the misalignment of spatial knowledge between the image backbone and view transformation. To address this issue, we propose a novel geometric-aware pretraining framework called GAPretrain. Our approach incorporates spatial and structural cues to camera networks by employing the geometric-rich modality as guidance during the pretraining phase. The transference of modal-specific attributes across different modalities is non-trivial, but we bridge this gap by using a unified bird's-eye-view (BEV) representation and structural hints derived from LiDAR point clouds to facilitate the pretraining process. GAPretrain serves as a plug-and-play solution that can be flexibly applied to multiple state-of-the-art detectors. Our experiments demonstrate the effectiveness and generalization ability of the proposed method. We achieve 46.2 mAP and 55.5 NDS on the nuScenes val set using the BEVFormer method, with a gain of 2.7 and 2.1 points, respectively. We also conduct experiments on various image backbones and view transformations to validate the efficacy of our approach. Code will be released at https://github.com/OpenDriveLab/BEVPerception-Survey-Recipe.

The concept of 3D scene graphs is increasingly recognized as a powerful semantic and hierarchical representation of the environment. Current approaches often address this at a coarse, object-level resolution. In contrast, our goal is to develop a representation that enables robots to directly interact with their environment by identifying both the location of functional interactive elements and how these can be used. To achieve this, we focus on detecting and storing objects at a finer resolution, focusing on affordance-relevant parts. The primary challenge lies in the scarcity of data that extends beyond instance-level detection and the inherent difficulty of capturing detailed object features using robotic sensors. We leverage currently available 3D resources to generate 2D data and train a detector, which is then used to augment the standard 3D scene graph generation pipeline. Through our experiments, we demonstrate that our approach achieves functional element segmentation comparable to state-of-the-art 3D models and that our augmentation enables task-driven affordance grounding with higher accuracy than the current solutions. See our project page at https://fungraph.github.io.

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

Visual navigation using only a single camera and a topological map has recently become an appealing alternative to methods that require additional sensors and 3D maps. This is typically achieved through an "image-relative" approach to estimating control from a given pair of current observation and subgoal image. However, image-level representations of the world have limitations because images are strictly tied to the agent's pose and embodiment. In contrast, objects, being a property of the map, offer an embodiment- and trajectory-invariant world representation. In this work, we present a new paradigm of learning "object-relative" control that exhibits several desirable characteristics: a) new routes can be traversed without strictly requiring to imitate prior experience, b) the control prediction problem can be decoupled from solving the image matching problem, and c) high invariance can be achieved in cross-embodiment deployment for variations across both training-testing and mapping-execution settings. We propose a topometric map representation in the form of a "relative" 3D scene graph, which is used to obtain more informative object-level global path planning costs. We train a local controller, dubbed "ObjectReact", conditioned directly on a high-level "WayObject Costmap" representation that eliminates the need for an explicit RGB input. We demonstrate the advantages of learning object-relative control over its image-relative counterpart across sensor height variations and multiple navigation tasks that challenge the underlying spatial understanding capability, e.g., navigating a map trajectory in the reverse direction. We further show that our sim-only policy is able to generalize well to real-world indoor environments. Code and supplementary material are accessible via project page: https://object-react.github.io/

Hypergraphs are marked by complex topology, expressing higher-order interactions among multiple nodes with hyperedges, and better capturing the topology is essential for effective representation learning. Recent advances in generative self-supervised learning (SSL) suggest that hypergraph neural networks learned from generative self supervision have the potential to effectively encode the complex hypergraph topology. Designing a generative SSL strategy for hypergraphs, however, is not straightforward. Questions remain with regard to its generative SSL task, connection to downstream tasks, and empirical properties of learned representations. In light of the promises and challenges, we propose a novel generative SSL strategy for hypergraphs. We first formulate a generative SSL task on hypergraphs, hyperedge filling, and highlight its theoretical connection to node classification. Based on the generative SSL task, we propose a hypergraph SSL method, HypeBoy. HypeBoy learns effective general-purpose hypergraph representations, outperforming 16 baseline methods across 11 benchmark datasets.

We present a topology-informed inverse rendering approach for reconstructing high-genus surface meshes from multi-view images. Compared to 3D representations like voxels and point clouds, mesh-based representations are preferred as they enable the application of differential geometry theory and are optimized for modern graphics pipelines. However, existing inverse rendering methods often fail catastrophically on high-genus surfaces, leading to the loss of key topological features, and tend to oversmooth low-genus surfaces, resulting in the loss of surface details. This failure stems from their overreliance on Adam-based optimizers, which can lead to vanishing and exploding gradients. To overcome these challenges, we introduce an adaptive V-cycle remeshing scheme in conjunction with a re-parametrized Adam optimizer to enhance topological and geometric awareness. By periodically coarsening and refining the deforming mesh, our method informs mesh vertices of their current topology and geometry before optimization, mitigating gradient issues while preserving essential topological features. Additionally, we enforce topological consistency by constructing topological primitives with genus numbers that match those of ground truth using Gauss-Bonnet theorem. Experimental results demonstrate that our inverse rendering approach outperforms the current state-of-the-art method, achieving significant improvements in Chamfer Distance and Volume IoU, particularly for high-genus surfaces, while also enhancing surface details for low-genus surfaces.

We adapt previous research on category theory and topological unsupervised learning to develop a functorial perspective on manifold learning, also known as nonlinear dimensionality reduction. We first characterize manifold learning algorithms as functors that map pseudometric spaces to optimization objectives and that factor through hierarchical clustering functors. We then use this characterization to prove refinement bounds on manifold learning loss functions and construct a hierarchy of manifold learning algorithms based on their equivariants. We express several popular manifold learning algorithms as functors at different levels of this hierarchy, including Metric Multidimensional Scaling, IsoMap, and UMAP. Next, we use interleaving distance to study the stability of a broad class of manifold learning algorithms. We present bounds on how closely the embeddings these algorithms produce from noisy data approximate the embeddings they would learn from noiseless data. Finally, we use our framework to derive a set of novel manifold learning algorithms, which we experimentally demonstrate are competitive with the state of the art.

Medical image classification requires not only high predictive performance but also interpretability to ensure clinical trust and adoption. Graph Neural Networks (GNNs) offer a powerful framework for modeling relational structures within datasets; however, standard GNNs often operate as black boxes, limiting transparency and usability, particularly in clinical settings. In this work, we present an interpretable graph-based learning framework named FireGNN that integrates trainable fuzzy rules into GNNs for medical image classification. These rules embed topological descriptors - node degree, clustering coefficient, and label agreement - using learnable thresholds and sharpness parameters to enable intrinsic symbolic reasoning. Additionally, we explore auxiliary self-supervised tasks (e.g., homophily prediction, similarity entropy) as a benchmark to evaluate the contribution of topological learning. Our fuzzy-rule-enhanced model achieves strong performance across five MedMNIST benchmarks and the synthetic dataset MorphoMNIST, while also generating interpretable rule-based explanations. To our knowledge, this is the first integration of trainable fuzzy rules within a GNN. Source Code: https://github.com/basiralab/FireGNN

Recent advances in artificial intelligence reveal the limits of purely predictive systems and call for a shift toward causal and collaborative reasoning. Drawing inspiration from the revolution of Grothendieck in mathematics, we introduce the relativity of causal knowledge, which posits structural causal models (SCMs) are inherently imperfect, subjective representations embedded within networks of relationships. By leveraging category theory, we arrange SCMs into a functor category and show that their observational and interventional probability measures naturally form convex structures. This result allows us to encode non-intervened SCMs with convex spaces of probability measures. Next, using sheaf theory, we construct the network sheaf and cosheaf of causal knowledge. These structures enable the transfer of causal knowledge across the network while incorporating interventional consistency and the perspective of the subjects, ultimately leading to the formal, mathematical definition of relative causal knowledge.

The impressive capabilities of recent generative models to create texts that are challenging to distinguish from the human-written ones can be misused for generating fake news, product reviews, and even abusive content. Despite the prominent performance of existing methods for artificial text detection, they still lack interpretability and robustness towards unseen models. To this end, we propose three novel types of interpretable topological features for this task based on Topological Data Analysis (TDA) which is currently understudied in the field of NLP. We empirically show that the features derived from the BERT model outperform count- and neural-based baselines up to 10\% on three common datasets, and tend to be the most robust towards unseen GPT-style generation models as opposed to existing methods. The probing analysis of the features reveals their sensitivity to the surface and syntactic properties. The results demonstrate that TDA is a promising line with respect to NLP tasks, specifically the ones that incorporate surface and structural information.

Open World Object Detection (OWOD) is a challenging and realistic task that extends beyond the scope of standard Object Detection task. It involves detecting both known and unknown objects while integrating learned knowledge for future tasks. However, the level of "unknownness" varies significantly depending on the context. For example, a tree is typically considered part of the background in a self-driving scene, but it may be significant in a household context. We argue that this contextual information should already be embedded within the known classes. In other words, there should be a semantic or latent structure relationship between the known and unknown items to be discovered. Motivated by this observation, we propose Hyp-OW, a method that learns and models hierarchical representation of known items through a SuperClass Regularizer. Leveraging this representation allows us to effectively detect unknown objects using a similarity distance-based relabeling module. Extensive experiments on benchmark datasets demonstrate the effectiveness of Hyp-OW, achieving improvement in both known and unknown detection (up to 6 percent). These findings are particularly pronounced in our newly designed benchmark, where a strong hierarchical structure exists between known and unknown objects. Our code can be found at https://github.com/tldoan/-HYP-OW-AAAI-2024-

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

Temporal knowledge graphs represent temporal facts (s,p,o,tau) relating a subject s and an object o via a relation label p at time tau, where tau could be a time point or time interval. Temporal knowledge graphs may exhibit static temporal patterns at distinct points in time and dynamic temporal patterns between different timestamps. In order to learn a rich set of static and dynamic temporal patterns and apply them for inference, several embedding approaches have been suggested in the literature. However, as most of them resort to single underlying embedding spaces, their capability to model all kinds of temporal patterns was severely limited by having to adhere to the geometric property of their one embedding space. We lift this limitation by an embedding approach that maps temporal facts into a product space of several heterogeneous geometric subspaces with distinct geometric properties, i.e.\ Complex, Dual, and Split-complex spaces. In addition, we propose a temporal-geometric attention mechanism to integrate information from different geometric subspaces conveniently according to the captured relational and temporal information. Experimental results on standard temporal benchmark datasets favorably evaluate our approach against state-of-the-art models.

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

In the literature, it has been shown that the evolution of the known explicit 3D surface to the target one can be learned from 2D images using the instantaneous flow field, where the known and target 3D surfaces may largely differ in topology. We are interested in capturing 4D shapes whose topology changes largely over time. We encounter that the straightforward extension of the existing 3D-based method to the desired 4D case performs poorly. In this work, we address the challenges in extending 3D neural evolution to 4D under large topological changes by proposing two novel modifications. More precisely, we introduce (i) a new architecture to discretize and encode the deformation and learn the SDF and (ii) a technique to impose the temporal consistency. (iii) Also, we propose a rendering scheme for color prediction based on Gaussian splatting. Furthermore, to facilitate learning directly from 2D images, we propose a learning framework that can disentangle the geometry and appearance from RGB images. This method of disentanglement, while also useful for the 4D evolution problem that we are concentrating on, is also novel and valid for static scenes. Our extensive experiments on various data provide awesome results and, most importantly, open a new approach toward reconstructing challenging scenes with significant topological changes and deformations. Our source code and the dataset are publicly available at https://github.com/insait-institute/N4DE.

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

In neural networks, it is often desirable to work with various representations of the same space. For example, 3D rotations can be represented with quaternions or Euler angles. In this paper, we advance a definition of a continuous representation, which can be helpful for training deep neural networks. We relate this to topological concepts such as homeomorphism and embedding. We then investigate what are continuous and discontinuous representations for 2D, 3D, and n-dimensional rotations. We demonstrate that for 3D rotations, all representations are discontinuous in the real Euclidean spaces of four or fewer dimensions. Thus, widely used representations such as quaternions and Euler angles are discontinuous and difficult for neural networks to learn. We show that the 3D rotations have continuous representations in 5D and 6D, which are more suitable for learning. We also present continuous representations for the general case of the n-dimensional rotation group SO(n). While our main focus is on rotations, we also show that our constructions apply to other groups such as the orthogonal group and similarity transforms. We finally present empirical results, which show that our continuous rotation representations outperform discontinuous ones for several practical problems in graphics and vision, including a simple autoencoder sanity test, a rotation estimator for 3D point clouds, and an inverse kinematics solver for 3D human poses.

Graph mining workloads aim to extract structural properties of a graph by exploring its subgraph structures. General purpose graph mining systems provide a generic runtime to explore subgraph structures of interest with the help of user-defined functions that guide the overall exploration process. However, the state-of-the-art graph mining systems remain largely oblivious to the shape (or pattern) of the subgraphs that they mine. This causes them to: (a) explore unnecessary subgraphs; (b) perform expensive computations on the explored subgraphs; and, (c) hold intermediate partial subgraphs in memory; all of which affect their overall performance. Furthermore, their programming models are often tied to their underlying exploration strategies, which makes it difficult for domain users to express complex mining tasks. In this paper, we develop Peregrine, a pattern-aware graph mining system that directly explores the subgraphs of interest while avoiding exploration of unnecessary subgraphs, and simultaneously bypassing expensive computations throughout the mining process. We design a pattern-based programming model that treats "graph patterns" as first class constructs and enables Peregrine to extract the semantics of patterns, which it uses to guide its exploration. Our evaluation shows that Peregrine outperforms state-of-the-art distributed and single machine graph mining systems, and scales to complex mining tasks on larger graphs, while retaining simplicity and expressivity with its "pattern-first" programming approach.

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.

Large-scale pre-training has shown promising results on the vision-and-language navigation (VLN) task. However, most existing pre-training methods employ discrete panoramas to learn visual-textual associations. This requires the model to implicitly correlate incomplete, duplicate observations within the panoramas, which may impair an agent's spatial understanding. Thus, we propose a new map-based pre-training paradigm that is spatial-aware for use in VLN. Concretely, we build a local metric map to explicitly aggregate incomplete observations and remove duplicates, while modeling navigation dependency in a global topological map. This hybrid design can balance the demand of VLN for both short-term reasoning and long-term planning. Then, based on the hybrid map, we devise a pre-training framework to learn a multimodal map representation, which enhances spatial-aware cross-modal reasoning thereby facilitating the language-guided navigation goal. Extensive experiments demonstrate the effectiveness of the map-based pre-training route for VLN, and the proposed method achieves state-of-the-art on four VLN benchmarks.

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.

We present a case study in semi-autonomous mathematics discovery, using Gemini to systematically evaluate 700 conjectures labeled 'Open' in Bloom's Erdős Problems database. We employ a hybrid methodology: AI-driven natural language verification to narrow the search space, followed by human expert evaluation to gauge correctness and novelty. We address 13 problems that were marked 'Open' in the database: 5 through seemingly novel autonomous solutions, and 8 through identification of previous solutions in the existing literature. Our findings suggest that the 'Open' status of the problems was through obscurity rather than difficulty. We also identify and discuss issues arising in applying AI to math conjectures at scale, highlighting the difficulty of literature identification and the risk of ''subconscious plagiarism'' by AI. We reflect on the takeaways from AI-assisted efforts on the Erdős Problems.

Structural understanding of complex visual objects is an important unsolved component of artificial intelligence. To study this, we develop a new technique for the recently proposed Break-and-Make problem in LTRON where an agent must learn to build a previously unseen LEGO assembly using a single interactive session to gather information about its components and their structure. We attack this problem by building an agent that we call \ours that is able to make its own visual instruction book. By disassembling an unseen assembly and periodically saving images of it, the agent is able to create a set of instructions so that it has the information necessary to rebuild it. These instructions form an explicit memory that allows the model to reason about the assembly process one step at a time, avoiding the need for long-term implicit memory. This in turn allows us to train on much larger LEGO assemblies than has been possible in the past. To demonstrate the power of this model, we release a new dataset of procedurally built LEGO vehicles that contain an average of 31 bricks each and require over one hundred steps to disassemble and reassemble. We train these models using online imitation learning which allows the model to learn from its own mistakes. Finally, we also provide some small improvements to LTRON and the Break-and-Make problem that simplify the learning environment and improve usability.

To achieve human-level dexterity, robots must infer spatial awareness from multimodal sensing to reason over contact interactions. During in-hand manipulation of novel objects, such spatial awareness involves estimating the object's pose and shape. The status quo for in-hand perception primarily employs vision, and restricts to tracking a priori known objects. Moreover, visual occlusion of objects in-hand is imminent during manipulation, preventing current systems to push beyond tasks without occlusion. We combine vision and touch sensing on a multi-fingered hand to estimate an object's pose and shape during in-hand manipulation. Our method, NeuralFeels, encodes object geometry by learning a neural field online and jointly tracks it by optimizing a pose graph problem. We study multimodal in-hand perception in simulation and the real-world, interacting with different objects via a proprioception-driven policy. Our experiments show final reconstruction F-scores of 81% and average pose drifts of 4.7,mm, further reduced to 2.3,mm with known CAD models. Additionally, we observe that under heavy visual occlusion we can achieve up to 94% improvements in tracking compared to vision-only methods. Our results demonstrate that touch, at the very least, refines and, at the very best, disambiguates visual estimates during in-hand manipulation. We release our evaluation dataset of 70 experiments, FeelSight, as a step towards benchmarking in this domain. Our neural representation driven by multimodal sensing can serve as a perception backbone towards advancing robot dexterity. Videos can be found on our project website https://suddhu.github.io/neural-feels/

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

Lane segment topology reasoning provides comprehensive bird's-eye view (BEV) road scene understanding, which can serve as a key perception module in planning-oriented end-to-end autonomous driving systems. Existing lane topology reasoning methods often fall short in effectively leveraging temporal information to enhance detection and reasoning performance. Recently, stream-based temporal propagation method has demonstrated promising results by incorporating temporal cues at both the query and BEV levels. However, it remains limited by over-reliance on historical queries, vulnerability to pose estimation failures, and insufficient temporal propagation. To overcome these limitations, we propose FASTopoWM, a novel fast-slow lane segment topology reasoning framework augmented with latent world models. To reduce the impact of pose estimation failures, this unified framework enables parallel supervision of both historical and newly initialized queries, facilitating mutual reinforcement between the fast and slow systems. Furthermore, we introduce latent query and BEV world models conditioned on the action latent to propagate the state representations from past observations to the current timestep. This design substantially improves the performance of temporal perception within the slow pipeline. Extensive experiments on the OpenLane-V2 benchmark demonstrate that FASTopoWM outperforms state-of-the-art methods in both lane segment detection (37.4% v.s. 33.6% on mAP) and centerline perception (46.3% v.s. 41.5% on OLS).