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Mar 18

The Topology and Geometry of Neural Representations

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.

TopoMortar: A dataset to evaluate image segmentation methods focused on topology accuracy

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

RoboSpatial: Teaching Spatial Understanding to 2D and 3D Vision-Language Models for Robotics

Spatial understanding is a crucial capability for robots to make grounded decisions based on their environment. This foundational skill enables robots not only to perceive their surroundings but also to reason about and interact meaningfully within the world. In modern robotics, these capabilities are taken on by visual language models, and they face significant challenges when applied to spatial reasoning context due to their training data sources. These sources utilize general-purpose image datasets, and they often lack sophisticated spatial scene understanding capabilities. For example, the datasets do not address reference frame comprehension - spatial relationships require clear contextual understanding, whether from an ego-centric, object-centric, or world-centric perspective, which allow for effective real-world interaction. To address this issue, we introduce RoboSpatial, a large-scale spatial understanding dataset consisting of real indoor and tabletop scenes captured as 3D scans and egocentric images, annotated with rich spatial information relevant to robotics. The dataset includes 1M images, 5K 3D scans, and 3M annotated spatial relationships, with paired 2D egocentric images and 3D scans to make it both 2D and 3D ready. Our experiments show that models trained with RoboSpatial outperform baselines on downstream tasks such as spatial affordance prediction, spatial relationship prediction, and robotics manipulation.

LaneSegNet: Map Learning with Lane Segment Perception for Autonomous Driving

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.

Sparkle: Mastering Basic Spatial Capabilities in Vision Language Models Elicits Generalization to Composite Spatial Reasoning

Vision language models (VLMs) have demonstrated impressive performance across a wide range of downstream tasks. However, their proficiency in spatial reasoning remains limited, despite its crucial role in tasks involving navigation and interaction with physical environments. Specifically, most of these tasks rely on the core spatial reasoning capabilities in two-dimensional (2D) environments, and our evaluation reveals that state-of-the-art VLMs frequently generate implausible and incorrect responses to composite spatial reasoning problems, including simple pathfinding tasks that humans can solve effortlessly at a glance. To address this, we explore an effective approach to enhance 2D spatial reasoning within VLMs by training the model solely on basic spatial capabilities. We begin by disentangling the key components of 2D spatial reasoning: direction comprehension, distance estimation, and localization. Our central hypothesis is that mastering these basic spatial capabilities can significantly enhance a model's performance on composite spatial tasks requiring advanced spatial understanding and combinatorial problem-solving, with generalized improvements in visual-spatial tasks. To investigate this hypothesis, we introduce Sparkle, a framework that fine-tunes VLMs on these three basic spatial capabilities by synthetic data generation and targeted supervision to form an instruction dataset for each capability. Our experiments demonstrate that VLMs fine-tuned with Sparkle achieve significant performance gains, not only in the basic tasks themselves but also in generalizing to composite and out-of-distribution spatial reasoning tasks. These findings underscore the effectiveness of mastering basic spatial capabilities in enhancing composite spatial problem-solving, offering insights into systematic strategies for improving VLMs' spatial reasoning capabilities.

Empowering Robotics with Large Language Models: osmAG Map Comprehension with LLMs

Recently, Large Language Models (LLMs) have demonstrated great potential in robotic applications by providing essential general knowledge for situations that can not be pre-programmed beforehand. Generally speaking, mobile robots need to understand maps to execute tasks such as localization or navigation. In this letter, we address the problem of enabling LLMs to comprehend Area Graph, a text-based map representation, in order to enhance their applicability in the field of mobile robotics. Area Graph is a hierarchical, topometric semantic map representation utilizing polygons to demark areas such as rooms, corridors or buildings. In contrast to commonly used map representations, such as occupancy grid maps or point clouds, osmAG (Area Graph in OpensStreetMap format) is stored in a XML textual format naturally readable by LLMs. Furthermore, conventional robotic algorithms such as localization and path planning are compatible with osmAG, facilitating this map representation comprehensible by LLMs, traditional robotic algorithms and humans. Our experiments show that with a proper map representation, LLMs possess the capability to understand maps and answer queries based on that understanding. Following simple fine-tuning of LLaMA2 models, it surpassed ChatGPT-3.5 in tasks involving topology and hierarchy understanding. Our dataset, dataset generation code, fine-tuned LoRA adapters can be accessed at https://github.com/xiefujing/LLM-osmAG-Comprehension.

Graph-based Topology Reasoning for Driving Scenes

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

3D Dynamic Scene Graphs: Actionable Spatial Perception with Places, Objects, and Humans

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

Reframing Spatial Reasoning Evaluation in Language Models: A Real-World Simulation Benchmark for Qualitative Reasoning

Spatial reasoning plays a vital role in both human cognition and machine intelligence, prompting new research into language models' (LMs) capabilities in this regard. However, existing benchmarks reveal shortcomings in evaluating qualitative spatial reasoning (QSR). These benchmarks typically present oversimplified scenarios or unclear natural language descriptions, hindering effective evaluation. We present a novel benchmark for assessing QSR in LMs, which is grounded in realistic 3D simulation data, offering a series of diverse room layouts with various objects and their spatial relationships. This approach provides a more detailed and context-rich narrative for spatial reasoning evaluation, diverging from traditional, toy-task-oriented scenarios. Our benchmark encompasses a broad spectrum of qualitative spatial relationships, including topological, directional, and distance relations. These are presented with different viewing points, varied granularities, and density of relation constraints to mimic real-world complexities. A key contribution is our logic-based consistency-checking tool, which enables the assessment of multiple plausible solutions, aligning with real-world scenarios where spatial relationships are often open to interpretation. Our benchmark evaluation of advanced LMs reveals their strengths and limitations in spatial reasoning. They face difficulties with multi-hop spatial reasoning and interpreting a mix of different view descriptions, pointing to areas for future improvement.

VisDiff: SDF-Guided Polygon Generation for Visibility Reconstruction and Recognition

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.

TopViewRS: Vision-Language Models as Top-View Spatial Reasoners

Top-view perspective denotes a typical way in which humans read and reason over different types of maps, and it is vital for localization and navigation of humans as well as of `non-human' agents, such as the ones backed by large Vision-Language Models (VLMs). Nonetheless, spatial reasoning capabilities of modern VLMs remain unattested and underexplored. In this work, we thus study their capability to understand and reason over spatial relations from the top view. The focus on top view also enables controlled evaluations at different granularity of spatial reasoning; we clearly disentangle different abilities (e.g., recognizing particular objects versus understanding their relative positions). We introduce the TopViewRS (Top-View Reasoning in Space) dataset, consisting of 11,384 multiple-choice questions with either realistic or semantic top-view map as visual input. We then use it to study and evaluate VLMs across 4 perception and reasoning tasks with different levels of complexity. Evaluation of 10 representative open- and closed-source VLMs reveals the gap of more than 50% compared to average human performance, and it is even lower than the random baseline in some cases. Although additional experiments show that Chain-of-Thought reasoning can boost model capabilities by 5.82% on average, the overall performance of VLMs remains limited. Our findings underscore the critical need for enhanced model capability in top-view spatial reasoning and set a foundation for further research towards human-level proficiency of VLMs in real-world multimodal tasks.

From Graphs to Hypergraphs: Hypergraph Projection and its Remediation

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

Topologically faithful image segmentation via induced matching of persistence barcodes

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.

A Framework for Fast and Stable Representations of Multiparameter Persistent Homology Decompositions

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.

Learning Navigational Visual Representations with Semantic Map Supervision

Being able to perceive the semantics and the spatial structure of the environment is essential for visual navigation of a household robot. However, most existing works only employ visual backbones pre-trained either with independent images for classification or with self-supervised learning methods to adapt to the indoor navigation domain, neglecting the spatial relationships that are essential to the learning of navigation. Inspired by the behavior that humans naturally build semantically and spatially meaningful cognitive maps in their brains during navigation, in this paper, we propose a novel navigational-specific visual representation learning method by contrasting the agent's egocentric views and semantic maps (Ego^2-Map). We apply the visual transformer as the backbone encoder and train the model with data collected from the large-scale Habitat-Matterport3D environments. Ego^2-Map learning transfers the compact and rich information from a map, such as objects, structure and transition, to the agent's egocentric representations for navigation. Experiments show that agents using our learned representations on object-goal navigation outperform recent visual pre-training methods. Moreover, our representations significantly improve vision-and-language navigation in continuous environments for both high-level and low-level action spaces, achieving new state-of-the-art results of 47% SR and 41% SPL on the test server.

Stable Vectorization of Multiparameter Persistent Homology using Signed Barcodes as Measures

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.

HaLo-NeRF: Learning Geometry-Guided Semantics for Exploring Unconstrained Photo Collections

Internet image collections containing photos captured by crowds of photographers show promise for enabling digital exploration of large-scale tourist landmarks. However, prior works focus primarily on geometric reconstruction and visualization, neglecting the key role of language in providing a semantic interface for navigation and fine-grained understanding. In constrained 3D domains, recent methods have leveraged vision-and-language models as a strong prior of 2D visual semantics. While these models display an excellent understanding of broad visual semantics, they struggle with unconstrained photo collections depicting such tourist landmarks, as they lack expert knowledge of the architectural domain. In this work, we present a localization system that connects neural representations of scenes depicting large-scale landmarks with text describing a semantic region within the scene, by harnessing the power of SOTA vision-and-language models with adaptations for understanding landmark scene semantics. To bolster such models with fine-grained knowledge, we leverage large-scale Internet data containing images of similar landmarks along with weakly-related textual information. Our approach is built upon the premise that images physically grounded in space can provide a powerful supervision signal for localizing new concepts, whose semantics may be unlocked from Internet textual metadata with large language models. We use correspondences between views of scenes to bootstrap spatial understanding of these semantics, providing guidance for 3D-compatible segmentation that ultimately lifts to a volumetric scene representation. Our results show that HaLo-NeRF can accurately localize a variety of semantic concepts related to architectural landmarks, surpassing the results of other 3D models as well as strong 2D segmentation baselines. Our project page is at https://tau-vailab.github.io/HaLo-NeRF/.

SoFar: Language-Grounded Orientation Bridges Spatial Reasoning and Object Manipulation

Spatial intelligence is a critical component of embodied AI, promoting robots to understand and interact with their environments. While recent advances have enhanced the ability of VLMs to perceive object locations and positional relationships, they still lack the capability to precisely understand object orientations-a key requirement for tasks involving fine-grained manipulations. Addressing this limitation not only requires geometric reasoning but also an expressive and intuitive way to represent orientation. In this context, we propose that natural language offers a more flexible representation space than canonical frames, making it particularly suitable for instruction-following robotic systems. In this paper, we introduce the concept of semantic orientation, which defines object orientations using natural language in a reference-frame-free manner (e.g., the ''plug-in'' direction of a USB or the ''handle'' direction of a knife). To support this, we construct OrienText300K, a large-scale dataset of 3D models annotated with semantic orientations that link geometric understanding to functional semantics. By integrating semantic orientation into a VLM system, we enable robots to generate manipulation actions with both positional and orientational constraints. Extensive experiments in simulation and real world demonstrate that our approach significantly enhances robotic manipulation capabilities, e.g., 48.7% accuracy on Open6DOR and 74.9% accuracy on SIMPLER.

3DSRBench: A Comprehensive 3D Spatial Reasoning Benchmark

3D spatial reasoning is the ability to analyze and interpret the positions, orientations, and spatial relationships of objects within the 3D space. This allows models to develop a comprehensive understanding of the 3D scene, enabling their applicability to a broader range of areas, such as autonomous navigation, robotics, and AR/VR. While large multi-modal models (LMMs) have achieved remarkable progress in a wide range of image and video understanding tasks, their capabilities to perform 3D spatial reasoning on diverse natural images are less studied. In this work we present the first comprehensive 3D spatial reasoning benchmark, 3DSRBench, with 2,772 manually annotated visual question-answer pairs across 12 question types. We conduct robust and thorough evaluation of 3D spatial reasoning capabilities by balancing the data distribution and adopting a novel FlipEval strategy. To further study the robustness of 3D spatial reasoning w.r.t. camera 3D viewpoints, our 3DSRBench includes two subsets with 3D spatial reasoning questions on paired images with common and uncommon viewpoints. We benchmark a wide range of open-sourced and proprietary LMMs, uncovering their limitations in various aspects of 3D awareness, such as height, orientation, location, and multi-object reasoning, as well as their degraded performance on images with uncommon camera viewpoints. Our 3DSRBench provide valuable findings and insights about the future development of LMMs with strong 3D reasoning capabilities. Our project page and dataset is available https://3dsrbench.github.io.

Graphlets correct for the topological information missed by random walks

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.

Concept-Based Explainable Artificial Intelligence: Metrics and Benchmarks

Concept-based explanation methods, such as concept bottleneck models (CBMs), aim to improve the interpretability of machine learning models by linking their decisions to human-understandable concepts, under the critical assumption that such concepts can be accurately attributed to the network's feature space. However, this foundational assumption has not been rigorously validated, mainly because the field lacks standardised metrics and benchmarks to assess the existence and spatial alignment of such concepts. To address this, we propose three metrics: the concept global importance metric, the concept existence metric, and the concept location metric, including a technique for visualising concept activations, i.e., concept activation mapping. We benchmark post-hoc CBMs to illustrate their capabilities and challenges. Through qualitative and quantitative experiments, we demonstrate that, in many cases, even the most important concepts determined by post-hoc CBMs are not present in input images; moreover, when they are present, their saliency maps fail to align with the expected regions by either activating across an entire object or misidentifying relevant concept-specific regions. We analyse the root causes of these limitations, such as the natural correlation of concepts. Our findings underscore the need for more careful application of concept-based explanation techniques especially in settings where spatial interpretability is critical.

Expand VSR Benchmark for VLLM to Expertize in Spatial Rules

Distinguishing spatial relations is a basic part of human cognition which requires fine-grained perception on cross-instance. Although benchmarks like MME, MMBench and SEED comprehensively have evaluated various capabilities which already include visual spatial reasoning(VSR). There is still a lack of sufficient quantity and quality evaluation and optimization datasets for Vision Large Language Models(VLLMs) specifically targeting visual positional reasoning. To handle this, we first diagnosed current VLLMs with the VSR dataset and proposed a unified test set. We found current VLLMs to exhibit a contradiction of over-sensitivity to language instructions and under-sensitivity to visual positional information. By expanding the original benchmark from two aspects of tunning data and model structure, we mitigated this phenomenon. To our knowledge, we expanded spatially positioned image data controllably using diffusion models for the first time and integrated original visual encoding(CLIP) with other 3 powerful visual encoders(SigLIP, SAM and DINO). After conducting combination experiments on scaling data and models, we obtained a VLLM VSR Expert(VSRE) that not only generalizes better to different instructions but also accurately distinguishes differences in visual positional information. VSRE achieved over a 27\% increase in accuracy on the VSR test set. It becomes a performant VLLM on the position reasoning of both the VSR dataset and relevant subsets of other evaluation benchmarks. We open-sourced the expanded model with data and Appendix at https://github.com/peijin360/vsre and hope it will accelerate advancements in VLLM on VSR learning.

Latent Compass: Creation by Navigation

In Marius von Senden's Space and Sight, a newly sighted blind patient describes the experience of a corner as lemon-like, because corners "prick" sight like lemons prick the tongue. Prickliness, here, is a dimension in the feature space of sensory experience, an effect of the perceived on the perceiver that arises where the two interact. In the account of the newly sighted, an effect familiar from one interaction translates to a novel context. Perception serves as the vehicle for generalization, in that an effect shared across different experiences produces a concrete abstraction grounded in those experiences. Cezanne and the post-impressionists, fluent in the language of experience translation, realized that the way to paint a concrete form that best reflected reality was to paint not what they saw, but what it was like to see. We envision a future of creation using AI where what it is like to see is replicable, transferrable, manipulable - part of the artist's palette that is both grounded in a particular context, and generalizable beyond it. An active line of research maps human-interpretable features onto directions in GAN latent space. Supervised and self-supervised approaches that search for anticipated directions or use off-the-shelf classifiers to drive image manipulation in embedding space are limited in the variety of features they can uncover. Unsupervised approaches that discover useful new directions show that the space of perceptually meaningful directions is nowhere close to being fully mapped. As this space is broad and full of creative potential, we want tools for direction discovery that capture the richness and generalizability of human perception. Our approach puts creators in the discovery loop during real-time tool use, in order to identify directions that are perceptually meaningful to them, and generate interpretable image translations along those directions.

A Topological Perspective on Demystifying GNN-Based Link Prediction Performance

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.

Graph schemas as abstractions for transfer learning, inference, and planning

Transferring latent structure from one environment or problem to another is a mechanism by which humans and animals generalize with very little data. Inspired by cognitive and neurobiological insights, we propose graph schemas as a mechanism of abstraction for transfer learning. Graph schemas start with latent graph learning where perceptually aliased observations are disambiguated in the latent space using contextual information. Latent graph learning is also emerging as a new computational model of the hippocampus to explain map learning and transitive inference. Our insight is that a latent graph can be treated as a flexible template -- a schema -- that models concepts and behaviors, with slots that bind groups of latent nodes to the specific observations or groundings. By treating learned latent graphs (schemas) as prior knowledge, new environments can be quickly learned as compositions of schemas and their newly learned bindings. We evaluate graph schemas on two previously published challenging tasks: the memory & planning game and one-shot StreetLearn, which are designed to test rapid task solving in novel environments. Graph schemas can be learned in far fewer episodes than previous baselines, and can model and plan in a few steps in novel variations of these tasks. We also demonstrate learning, matching, and reusing graph schemas in more challenging 2D and 3D environments with extensive perceptual aliasing and size variations, and show how different schemas can be composed to model larger and more complex environments. To summarize, our main contribution is a unified system, inspired and grounded in cognitive science, that facilitates rapid transfer learning of new environments using schemas via map-induction and composition that handles perceptual aliasing.

V-STaR: Benchmarking Video-LLMs on Video Spatio-Temporal Reasoning

Human processes video reasoning in a sequential spatio-temporal reasoning logic, we first identify the relevant frames ("when") and then analyse the spatial relationships ("where") between key objects, and finally leverage these relationships to draw inferences ("what"). However, can Video Large Language Models (Video-LLMs) also "reason through a sequential spatio-temporal logic" in videos? Existing Video-LLM benchmarks primarily focus on assessing object presence, neglecting relational reasoning. Consequently, it is difficult to measure whether a model truly comprehends object interactions (actions/events) in videos or merely relies on pre-trained "memory" of co-occurrences as biases in generating answers. In this work, we introduce a Video Spatio-Temporal Reasoning (V-STaR) benchmark to address these shortcomings. The key idea is to decompose video understanding into a Reverse Spatio-Temporal Reasoning (RSTR) task that simultaneously evaluates what objects are present, when events occur, and where they are located while capturing the underlying Chain-of-thought (CoT) logic. To support this evaluation, we construct a dataset to elicit the spatial-temporal reasoning process of Video-LLMs. It contains coarse-to-fine CoT questions generated by a semi-automated GPT-4-powered pipeline, embedding explicit reasoning chains to mimic human cognition. Experiments from 14 Video-LLMs on our V-STaR reveal significant gaps between current Video-LLMs and the needs for robust and consistent spatio-temporal reasoning.

Landscaping Linear Mode Connectivity

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

Pruning-based Topology Refinement of 3D Mesh using a 2D Alpha Mask

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.

MapGPT: Map-Guided Prompting for Unified Vision-and-Language Navigation

Embodied agents equipped with GPT as their brain have exhibited extraordinary thinking and decision-making abilities across various tasks. However, existing zero-shot agents for vision-and-language navigation (VLN) only prompt the GPT to handle excessive environmental information and select potential locations within localized environments, without constructing an effective ''global-view'' (e.g., a commonly-used map) for the agent to understand the overall environment. In this work, we present a novel map-guided GPT-based path-planning agent, dubbed MapGPT, for the zero-shot VLN task. Specifically, we convert a topological map constructed online into prompts to encourage map-guided global exploration, and require the agent to explicitly output and update multi-step path planning to avoid getting stuck in local exploration. Extensive experiments demonstrate that our MapGPT is effective, achieving impressive performance on both the R2R and REVERIE datasets (38.8% and 28.4% success rate, respectively) and showcasing the newly emerged global thinking and path planning capabilities of the GPT model. Unlike previous VLN agents, which require separate parameters fine-tuning or specific prompt design to accommodate various instruction styles across different datasets, our MapGPT is more unified as it can adapt to different instruction styles seamlessly, which is the first of its kind in this field.

Do Vision-Language Models Really Understand Visual Language?

Visual language is a system of communication that conveys information through symbols, shapes, and spatial arrangements. Diagrams are a typical example of a visual language depicting complex concepts and their relationships in the form of an image. The symbolic nature of diagrams presents significant challenges for building models capable of understanding them. Yet, recent studies seem to suggest that Large Vision-Language Models (LVLMs) can even tackle complex reasoning tasks involving diagrams. In this paper, we investigate this phenomenon by developing a comprehensive test suite to evaluate the diagram comprehension capability of LVLMs. Our test suite uses a variety of questions focused on concept entities and their relationships over a set of synthetic as well as real diagrams across several domains to evaluate the recognition and reasoning abilities of models. Our evaluation of three LVLMs (GPT-4V, GPT-4o, and Gemini) shows that while these models can accurately identify and reason about entities, their ability to understand relationships is notably limited. Further testing reveals that the decent performance on diagram understanding largely stems from leveraging their background knowledge as shortcuts to identify and reason about the relational information. Thus, we conclude that LVLMs have a limited capability for genuine diagram understanding, and their impressive performance in diagram reasoning is an illusion emanating from other confounding factors, such as the background knowledge in the models.

GPT4Scene: Understand 3D Scenes from Videos with Vision-Language Models

In recent years, 2D Vision-Language Models (VLMs) have made significant strides in image-text understanding tasks. However, their performance in 3D spatial comprehension, which is critical for embodied intelligence, remains limited. Recent advances have leveraged 3D point clouds and multi-view images as inputs, yielding promising results. However, we propose exploring a purely vision-based solution inspired by human perception, which merely relies on visual cues for 3D spatial understanding. This paper empirically investigates the limitations of VLMs in 3D spatial knowledge, revealing that their primary shortcoming lies in the lack of global-local correspondence between the scene and individual frames. To address this, we introduce GPT4Scene, a novel visual prompting paradigm in VLM training and inference that helps build the global-local relationship, significantly improving the 3D spatial understanding of indoor scenes. Specifically, GPT4Scene constructs a 3D Bird's Eye View (BEV) image from the video and marks consistent object IDs across both frames and the BEV image. The model then inputs the concatenated BEV image and video frames with markers. In zero-shot evaluations, GPT4Scene improves performance over closed-source VLMs like GPT-4o. Additionally, we prepare a processed video dataset consisting of 165K text annotation to fine-tune open-source VLMs, achieving state-of-the-art performance on all 3D understanding tasks. Surprisingly, after training with the GPT4Scene paradigm, VLMs consistently improve during inference, even without visual prompting and BEV image as explicit correspondence. It demonstrates that the proposed paradigm helps VLMs develop an intrinsic ability to understand 3D scenes, which paves the way for a noninvasive approach to extending pre-trained VLMs for 3D scene understanding.

Differentiability and Optimization of Multiparameter Persistent Homology

Real-valued functions on geometric data -- such as node attributes on a graph -- can be optimized using descriptors from persistent homology, allowing the user to incorporate topological terms in the loss function. When optimizing a single real-valued function (the one-parameter setting), there is a canonical choice of descriptor for persistent homology: the barcode. The operation mapping a real-valued function to its barcode is differentiable almost everywhere, and the convergence of gradient descent for losses using barcodes is relatively well understood. When optimizing a vector-valued function (the multiparameter setting), there is no unique choice of descriptor for multiparameter persistent homology, and many distinct descriptors have been proposed. This calls for the development of a general framework for differentiability and optimization that applies to a wide range of multiparameter homological descriptors. In this article, we develop such a framework and show that it encompasses well-known descriptors of different flavors, such as signed barcodes and the multiparameter persistence landscape. We complement the theory with numerical experiments supporting the idea that optimizing multiparameter homological descriptors can lead to improved performances compared to optimizing one-parameter descriptors, even when using the simplest and most efficiently computable multiparameter descriptors.

Re-Thinking Inverse Graphics With Large Language Models

Inverse graphics -- the task of inverting an image into physical variables that, when rendered, enable reproduction of the observed scene -- is a fundamental challenge in computer vision and graphics. Disentangling an image into its constituent elements, such as the shape, color, and material properties of the objects of the 3D scene that produced it, requires a comprehensive understanding of the environment. This requirement limits the ability of existing carefully engineered approaches to generalize across domains. Inspired by the zero-shot ability of large language models (LLMs) to generalize to novel contexts, we investigate the possibility of leveraging the broad world knowledge encoded in such models in solving inverse-graphics problems. To this end, we propose the Inverse-Graphics Large Language Model (IG-LLM), an inverse-graphics framework centered around an LLM, that autoregressively decodes a visual embedding into a structured, compositional 3D-scene representation. We incorporate a frozen pre-trained visual encoder and a continuous numeric head to enable end-to-end training. Through our investigation, we demonstrate the potential of LLMs to facilitate inverse graphics through next-token prediction, without the use of image-space supervision. Our analysis opens up new possibilities for precise spatial reasoning about images that exploit the visual knowledge of LLMs. We will release our code and data to ensure the reproducibility of our investigation and to facilitate future research at https://ig-llm.is.tue.mpg.de/

Reasoning Paths with Reference Objects Elicit Quantitative Spatial Reasoning in Large Vision-Language Models

Despite recent advances demonstrating vision-language models' (VLMs) abilities to describe complex relationships in images using natural language, their capability to quantitatively reason about object sizes and distances remains underexplored. In this work, we introduce a manually annotated benchmark, Q-Spatial Bench, with 271 questions across five categories designed for quantitative spatial reasoning and systematically investigate the performance of state-of-the-art VLMs on this task. Our analysis reveals that reasoning about distances between objects is particularly challenging for SoTA VLMs; however, some VLMs significantly outperform others, with an over 40-point gap between the two best performing models. We also make the surprising observation that the success rate of the top-performing VLM increases by 19 points when a reasoning path using a reference object emerges naturally in the response. Inspired by this observation, we develop a zero-shot prompting technique, SpatialPrompt, that encourages VLMs to answer quantitative spatial questions using reference objects as visual cues. By instructing VLMs to use reference objects in their reasoning paths via SpatialPrompt, Gemini 1.5 Pro, Gemini 1.5 Flash, and GPT-4V improve their success rates by over 40, 20, and 30 points, respectively. We emphasize that these significant improvements are obtained without needing more data, model architectural modifications, or fine-tuning.

From Occlusion to Insight: Object Search in Semantic Shelves using Large Language Models

How can a robot efficiently extract a desired object from a shelf when it is fully occluded by other objects? Prior works propose geometric approaches for this problem but do not consider object semantics. Shelves in pharmacies, restaurant kitchens, and grocery stores are often organized such that semantically similar objects are placed close to one another. Can large language models (LLMs) serve as semantic knowledge sources to accelerate robotic mechanical search in semantically arranged environments? With Semantic Spatial Search on Shelves (S^4), we use LLMs to generate affinity matrices, where entries correspond to semantic likelihood of physical proximity between objects. We derive semantic spatial distributions by synthesizing semantics with learned geometric constraints. S^4 incorporates Optical Character Recognition (OCR) and semantic refinement with predictions from ViLD, an open-vocabulary object detection model. Simulation experiments suggest that semantic spatial search reduces the search time relative to pure spatial search by an average of 24% across three domains: pharmacy, kitchen, and office shelves. A manually collected dataset of 100 semantic scenes suggests that OCR and semantic refinement improve object detection accuracy by 35%. Lastly, physical experiments in a pharmacy shelf suggest 47.1% improvement over pure spatial search. Supplementary material can be found at https://sites.google.com/view/s4-rss/home.

GeoX: Geometric Problem Solving Through Unified Formalized Vision-Language Pre-training

Despite their proficiency in general tasks, Multi-modal Large Language Models (MLLMs) struggle with automatic Geometry Problem Solving (GPS), which demands understanding diagrams, interpreting symbols, and performing complex reasoning. This limitation arises from their pre-training on natural images and texts, along with the lack of automated verification in the problem-solving process. Besides, current geometric specialists are limited by their task-specific designs, making them less effective for broader geometric problems. To this end, we present GeoX, a multi-modal large model focusing on geometric understanding and reasoning tasks. Given the significant differences between geometric diagram-symbol and natural image-text, we introduce unimodal pre-training to develop a diagram encoder and symbol decoder, enhancing the understanding of geometric images and corpora. Furthermore, we introduce geometry-language alignment, an effective pre-training paradigm that bridges the modality gap between unimodal geometric experts. We propose a Generator-And-Sampler Transformer (GS-Former) to generate discriminative queries and eliminate uninformative representations from unevenly distributed geometric signals. Finally, GeoX benefits from visual instruction tuning, empowering it to take geometric images and questions as input and generate verifiable solutions. Experiments show that GeoX outperforms both generalists and geometric specialists on publicly recognized benchmarks, such as GeoQA, UniGeo, Geometry3K, and PGPS9k.

Visual Language Maps for Robot Navigation

Grounding language to the visual observations of a navigating agent can be performed using off-the-shelf visual-language models pretrained on Internet-scale data (e.g., image captions). While this is useful for matching images to natural language descriptions of object goals, it remains disjoint from the process of mapping the environment, so that it lacks the spatial precision of classic geometric maps. To address this problem, we propose VLMaps, a spatial map representation that directly fuses pretrained visual-language features with a 3D reconstruction of the physical world. VLMaps can be autonomously built from video feed on robots using standard exploration approaches and enables natural language indexing of the map without additional labeled data. Specifically, when combined with large language models (LLMs), VLMaps can be used to (i) translate natural language commands into a sequence of open-vocabulary navigation goals (which, beyond prior work, can be spatial by construction, e.g., "in between the sofa and TV" or "three meters to the right of the chair") directly localized in the map, and (ii) can be shared among multiple robots with different embodiments to generate new obstacle maps on-the-fly (by using a list of obstacle categories). Extensive experiments carried out in simulated and real world environments show that VLMaps enable navigation according to more complex language instructions than existing methods. Videos are available at https://vlmaps.github.io.

Spatially-Aware Transformer for Embodied Agents

Episodic memory plays a crucial role in various cognitive processes, such as the ability to mentally recall past events. While cognitive science emphasizes the significance of spatial context in the formation and retrieval of episodic memory, the current primary approach to implementing episodic memory in AI systems is through transformers that store temporally ordered experiences, which overlooks the spatial dimension. As a result, it is unclear how the underlying structure could be extended to incorporate the spatial axis beyond temporal order alone and thereby what benefits can be obtained. To address this, this paper explores the use of Spatially-Aware Transformer models that incorporate spatial information. These models enable the creation of place-centric episodic memory that considers both temporal and spatial dimensions. Adopting this approach, we demonstrate that memory utilization efficiency can be improved, leading to enhanced accuracy in various place-centric downstream tasks. Additionally, we propose the Adaptive Memory Allocator, a memory management method based on reinforcement learning that aims to optimize efficiency of memory utilization. Our experiments demonstrate the advantages of our proposed model in various environments and across multiple downstream tasks, including prediction, generation, reasoning, and reinforcement learning. The source code for our models and experiments will be available at https://github.com/junmokane/spatially-aware-transformer.

Hierarchical multi-class segmentation of glioma images using networks with multi-level activation function

For many segmentation tasks, especially for the biomedical image, the topological prior is vital information which is useful to exploit. The containment/nesting is a typical inter-class geometric relationship. In the MICCAI Brain tumor segmentation challenge, with its three hierarchically nested classes 'whole tumor', 'tumor core', 'active tumor', the nested classes relationship is introduced into the 3D-residual-Unet architecture. The network comprises a context aggregation pathway and a localization pathway, which encodes increasingly abstract representation of the input as going deeper into the network, and then recombines these representations with shallower features to precisely localize the interest domain via a localization path. The nested-class-prior is combined by proposing the multi-class activation function and its corresponding loss function. The model is trained on the training dataset of Brats2018, and 20% of the dataset is regarded as the validation dataset to determine parameters. When the parameters are fixed, we retrain the model on the whole training dataset. The performance achieved on the validation leaderboard is 86%, 77% and 72% Dice scores for the whole tumor, enhancing tumor and tumor core classes without relying on ensembles or complicated post-processing steps. Based on the same start-of-the-art network architecture, the accuracy of nested-class (enhancing tumor) is reasonably improved from 69% to 72% compared with the traditional Softmax-based method which blind to topological prior.

DendroMap: Visual Exploration of Large-Scale Image Datasets for Machine Learning with Treemaps

In this paper, we present DendroMap, a novel approach to interactively exploring large-scale image datasets for machine learning (ML). ML practitioners often explore image datasets by generating a grid of images or projecting high-dimensional representations of images into 2-D using dimensionality reduction techniques (e.g., t-SNE). However, neither approach effectively scales to large datasets because images are ineffectively organized and interactions are insufficiently supported. To address these challenges, we develop DendroMap by adapting Treemaps, a well-known visualization technique. DendroMap effectively organizes images by extracting hierarchical cluster structures from high-dimensional representations of images. It enables users to make sense of the overall distributions of datasets and interactively zoom into specific areas of interests at multiple levels of abstraction. Our case studies with widely-used image datasets for deep learning demonstrate that users can discover insights about datasets and trained models by examining the diversity of images, identifying underperforming subgroups, and analyzing classification errors. We conducted a user study that evaluates the effectiveness of DendroMap in grouping and searching tasks by comparing it with a gridified version of t-SNE and found that participants preferred DendroMap. DendroMap is available at https://div-lab.github.io/dendromap/.

Spatial As Deep: Spatial CNN for Traffic Scene Understanding

Convolutional neural networks (CNNs) are usually built by stacking convolutional operations layer-by-layer. Although CNN has shown strong capability to extract semantics from raw pixels, its capacity to capture spatial relationships of pixels across rows and columns of an image is not fully explored. These relationships are important to learn semantic objects with strong shape priors but weak appearance coherences, such as traffic lanes, which are often occluded or not even painted on the road surface as shown in Fig. 1 (a). In this paper, we propose Spatial CNN (SCNN), which generalizes traditional deep layer-by-layer convolutions to slice-byslice convolutions within feature maps, thus enabling message passings between pixels across rows and columns in a layer. Such SCNN is particular suitable for long continuous shape structure or large objects, with strong spatial relationship but less appearance clues, such as traffic lanes, poles, and wall. We apply SCNN on a newly released very challenging traffic lane detection dataset and Cityscapse dataset. The results show that SCNN could learn the spatial relationship for structure output and significantly improves the performance. We show that SCNN outperforms the recurrent neural network (RNN) based ReNet and MRF+CNN (MRFNet) in the lane detection dataset by 8.7% and 4.6% respectively. Moreover, our SCNN won the 1st place on the TuSimple Benchmark Lane Detection Challenge, with an accuracy of 96.53%.

3D-Mem: 3D Scene Memory for Embodied Exploration and Reasoning

Constructing compact and informative 3D scene representations is essential for effective embodied exploration and reasoning, especially in complex environments over extended periods. Existing representations, such as object-centric 3D scene graphs, oversimplify spatial relationships by modeling scenes as isolated objects with restrictive textual relationships, making it difficult to address queries requiring nuanced spatial understanding. Moreover, these representations lack natural mechanisms for active exploration and memory management, hindering their application to lifelong autonomy. In this work, we propose 3D-Mem, a novel 3D scene memory framework for embodied agents. 3D-Mem employs informative multi-view images, termed Memory Snapshots, to represent the scene and capture rich visual information of explored regions. It further integrates frontier-based exploration by introducing Frontier Snapshots-glimpses of unexplored areas-enabling agents to make informed decisions by considering both known and potential new information. To support lifelong memory in active exploration settings, we present an incremental construction pipeline for 3D-Mem, as well as a memory retrieval technique for memory management. Experimental results on three benchmarks demonstrate that 3D-Mem significantly enhances agents' exploration and reasoning capabilities in 3D environments, highlighting its potential for advancing applications in embodied AI.

NAPA-VQ: Neighborhood Aware Prototype Augmentation with Vector Quantization for Continual Learning

Catastrophic forgetting; the loss of old knowledge upon acquiring new knowledge, is a pitfall faced by deep neural networks in real-world applications. Many prevailing solutions to this problem rely on storing exemplars (previously encountered data), which may not be feasible in applications with memory limitations or privacy constraints. Therefore, the recent focus has been on Non-Exemplar based Class Incremental Learning (NECIL) where a model incrementally learns about new classes without using any past exemplars. However, due to the lack of old data, NECIL methods struggle to discriminate between old and new classes causing their feature representations to overlap. We propose NAPA-VQ: Neighborhood Aware Prototype Augmentation with Vector Quantization, a framework that reduces this class overlap in NECIL. We draw inspiration from Neural Gas to learn the topological relationships in the feature space, identifying the neighboring classes that are most likely to get confused with each other. This neighborhood information is utilized to enforce strong separation between the neighboring classes as well as to generate old class representative prototypes that can better aid in obtaining a discriminative decision boundary between old and new classes. Our comprehensive experiments on CIFAR-100, TinyImageNet, and ImageNet-Subset demonstrate that NAPA-VQ outperforms the State-of-the-art NECIL methods by an average improvement of 5%, 2%, and 4% in accuracy and 10%, 3%, and 9% in forgetting respectively. Our code can be found in https://github.com/TamashaM/NAPA-VQ.git.

CHORUS: Learning Canonicalized 3D Human-Object Spatial Relations from Unbounded Synthesized Images

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

IRWE: Inductive Random Walk for Joint Inference of Identity and Position Network Embedding

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.

CoMPaSS: Enhancing Spatial Understanding in Text-to-Image Diffusion Models

Text-to-image diffusion models excel at generating photorealistic images, but commonly struggle to render accurate spatial relationships described in text prompts. We identify two core issues underlying this common failure: 1) the ambiguous nature of spatial-related data in existing datasets, and 2) the inability of current text encoders to accurately interpret the spatial semantics of input descriptions. We address these issues with CoMPaSS, a versatile training framework that enhances spatial understanding of any T2I diffusion model. CoMPaSS solves the ambiguity of spatial-related data with the Spatial Constraints-Oriented Pairing (SCOP) data engine, which curates spatially-accurate training data through a set of principled spatial constraints. To better exploit the curated high-quality spatial priors, CoMPaSS further introduces a Token ENcoding ORdering (TENOR) module to allow better exploitation of high-quality spatial priors, effectively compensating for the shortcoming of text encoders. Extensive experiments on four popular open-weight T2I diffusion models covering both UNet- and MMDiT-based architectures demonstrate the effectiveness of CoMPaSS by setting new state-of-the-arts with substantial relative gains across well-known benchmarks on spatial relationships generation, including VISOR (+98%), T2I-CompBench Spatial (+67%), and GenEval Position (+131%). Code will be available at https://github.com/blurgyy/CoMPaSS.

Navigation-Oriented Scene Understanding for Robotic Autonomy: Learning to Segment Driveability in Egocentric Images

This work tackles scene understanding for outdoor robotic navigation, solely relying on images captured by an on-board camera. Conventional visual scene understanding interprets the environment based on specific descriptive categories. However, such a representation is not directly interpretable for decision-making and constrains robot operation to a specific domain. Thus, we propose to segment egocentric images directly in terms of how a robot can navigate in them, and tailor the learning problem to an autonomous navigation task. Building around an image segmentation network, we present a generic affordance consisting of 3 driveability levels which can broadly apply to both urban and off-road scenes. By encoding these levels with soft ordinal labels, we incorporate inter-class distances during learning which improves segmentation compared to standard "hard" one-hot labelling. In addition, we propose a navigation-oriented pixel-wise loss weighting method which assigns higher importance to safety-critical areas. We evaluate our approach on large-scale public image segmentation datasets ranging from sunny city streets to snowy forest trails. In a cross-dataset generalization experiment, we show that our affordance learning scheme can be applied across a diverse mix of datasets and improves driveability estimation in unseen environments compared to general-purpose, single-dataset segmentation.

Multimodal Self-Instruct: Synthetic Abstract Image and Visual Reasoning Instruction Using Language Model

Although most current large multimodal models (LMMs) can already understand photos of natural scenes and portraits, their understanding of abstract images, e.g., charts, maps, or layouts, and visual reasoning capabilities remains quite rudimentary. They often struggle with simple daily tasks, such as reading time from a clock, understanding a flowchart, or planning a route using a road map. In light of this, we design a multi-modal self-instruct, utilizing large language models and their code capabilities to synthesize massive abstract images and visual reasoning instructions across daily scenarios. Our strategy effortlessly creates a multimodal benchmark with 11,193 instructions for eight visual scenarios: charts, tables, simulated maps, dashboards, flowcharts, relation graphs, floor plans, and visual puzzles. This benchmark, constructed with simple lines and geometric elements, exposes the shortcomings of most advanced LMMs like Claude-3.5-Sonnet and GPT-4o in abstract image understanding, spatial relations reasoning, and visual element induction. Besides, to verify the quality of our synthetic data, we fine-tune an LMM using 62,476 synthetic chart, table and road map instructions. The results demonstrate improved chart understanding and map navigation performance, and also demonstrate potential benefits for other visual reasoning tasks. Our code is available at: https://github.com/zwq2018/Multi-modal-Self-instruct.

VectorMapNet: End-to-end Vectorized HD Map Learning

Autonomous driving systems require High-Definition (HD) semantic maps to navigate around urban roads. Existing solutions approach the semantic mapping problem by offline manual annotation, which suffers from serious scalability issues. Recent learning-based methods produce dense rasterized segmentation predictions to construct maps. However, these predictions do not include instance information of individual map elements and require heuristic post-processing to obtain vectorized maps. To tackle these challenges, we introduce an end-to-end vectorized HD map learning pipeline, termed VectorMapNet. VectorMapNet takes onboard sensor observations and predicts a sparse set of polylines in the bird's-eye view. This pipeline can explicitly model the spatial relation between map elements and generate vectorized maps that are friendly to downstream autonomous driving tasks. Extensive experiments show that VectorMapNet achieve strong map learning performance on both nuScenes and Argoverse2 dataset, surpassing previous state-of-the-art methods by 14.2 mAP and 14.6mAP. Qualitatively, VectorMapNet is capable of generating comprehensive maps and capturing fine-grained details of road geometry. To the best of our knowledge, VectorMapNet is the first work designed towards end-to-end vectorized map learning from onboard observations. Our project website is available at https://tsinghua-mars-lab.github.io/vectormapnet/.

Poincaré ResNet

This paper introduces an end-to-end residual network that operates entirely on the Poincar\'e ball model of hyperbolic space. Hyperbolic learning has recently shown great potential for visual understanding, but is currently only performed in the penultimate layer(s) of deep networks. All visual representations are still learned through standard Euclidean networks. In this paper we investigate how to learn hyperbolic representations of visual data directly from the pixel-level. We propose Poincar\'e ResNet, a hyperbolic counterpart of the celebrated residual network, starting from Poincar\'e 2D convolutions up to Poincar\'e residual connections. We identify three roadblocks for training convolutional networks entirely in hyperbolic space and propose a solution for each: (i) Current hyperbolic network initializations collapse to the origin, limiting their applicability in deeper networks. We provide an identity-based initialization that preserves norms over many layers. (ii) Residual networks rely heavily on batch normalization, which comes with expensive Fr\'echet mean calculations in hyperbolic space. We introduce Poincar\'e midpoint batch normalization as a faster and equally effective alternative. (iii) Due to the many intermediate operations in Poincar\'e layers, we lastly find that the computation graphs of deep learning libraries blow up, limiting our ability to train on deep hyperbolic networks. We provide manual backward derivations of core hyperbolic operations to maintain manageable computation graphs.

Measuring the Intrinsic Dimension of Objective Landscapes

Many recently trained neural networks employ large numbers of parameters to achieve good performance. One may intuitively use the number of parameters required as a rough gauge of the difficulty of a problem. But how accurate are such notions? How many parameters are really needed? In this paper we attempt to answer this question by training networks not in their native parameter space, but instead in a smaller, randomly oriented subspace. We slowly increase the dimension of this subspace, note at which dimension solutions first appear, and define this to be the intrinsic dimension of the objective landscape. The approach is simple to implement, computationally tractable, and produces several suggestive conclusions. Many problems have smaller intrinsic dimensions than one might suspect, and the intrinsic dimension for a given dataset varies little across a family of models with vastly different sizes. This latter result has the profound implication that once a parameter space is large enough to solve a problem, extra parameters serve directly to increase the dimensionality of the solution manifold. Intrinsic dimension allows some quantitative comparison of problem difficulty across supervised, reinforcement, and other types of learning where we conclude, for example, that solving the inverted pendulum problem is 100 times easier than classifying digits from MNIST, and playing Atari Pong from pixels is about as hard as classifying CIFAR-10. In addition to providing new cartography of the objective landscapes wandered by parameterized models, the method is a simple technique for constructively obtaining an upper bound on the minimum description length of a solution. A byproduct of this construction is a simple approach for compressing networks, in some cases by more than 100 times.

Self-supervised Video Representation Learning by Uncovering Spatio-temporal Statistics

This paper proposes a novel pretext task to address the self-supervised video representation learning problem. Specifically, given an unlabeled video clip, we compute a series of spatio-temporal statistical summaries, such as the spatial location and dominant direction of the largest motion, the spatial location and dominant color of the largest color diversity along the temporal axis, etc. Then a neural network is built and trained to yield the statistical summaries given the video frames as inputs. In order to alleviate the learning difficulty, we employ several spatial partitioning patterns to encode rough spatial locations instead of exact spatial Cartesian coordinates. Our approach is inspired by the observation that human visual system is sensitive to rapidly changing contents in the visual field, and only needs impressions about rough spatial locations to understand the visual contents. To validate the effectiveness of the proposed approach, we conduct extensive experiments with four 3D backbone networks, i.e., C3D, 3D-ResNet, R(2+1)D and S3D-G. The results show that our approach outperforms the existing approaches across these backbone networks on four downstream video analysis tasks including action recognition, video retrieval, dynamic scene recognition, and action similarity labeling. The source code is publicly available at: https://github.com/laura-wang/video_repres_sts.