Spatial Representation

Embedding spaces define notions of semantic similarity and distance. We study whether those embeddings reflect physical measurements of mass, distance, time and volume, which admit a unique, objective notion of semantic equivalence and distance. We find that physical measurement is only weakly modeled in the embedding space, and that instead quite peculiar measurement patterns can be observed. Further analysis indicates that embedding representations of physical measurements are strongly influenced by superficial string similarity, and recalibration of similarity does not substantially improve the alignment.

Geospatial foundation models provide reusable representations of satellite imagery that support downstream mapping with limited task-specific modelling. We evaluate whether annual AlphaEarth embeddings support binary cultivated-versus-non-cultivated mapping in Maine, USA, using 192 spatially separated patches and labels derived from the USDA Cropland Data Layer (CDL). Without fine-tuning the foundation model, a lightweight classifier reaches 93.7% overall accuracy and 90.8% balanced accuracy on held-out patches. Logistic regression is within 0.3 percentage points of a gradient-boosted ensemble, while a nearest-class-centroid rule, which uses class centroids but fits no parameters, reaches 90.2%. A balanced sample of 60,000 labelled pixels is within 1.3 percentage points of the full pool of 8.6 million pixels; because pixels are spatially autocorrelated, this result concerns pixel-sample efficiency rather than 60,000 independent annotation sites. In a same-region transfer experiment, classifiers trained in one year remain accurate across 2018 to 2023. Against a blind, two-interpreter consensus at 385 randomly sampled points in one contiguous 2023 block, the AlphaEarth-plus-random-forest map agrees at 95.3% ($κ=0.82$), compared with 91.7% for the CDL ($κ=0.72$; exact two-sided McNemar $p=0.0161$). This local result is consistent with partial smoothing of CDL label noise, but it does not establish statewide correction of the reference product. On the same points, the difference from a fine-tuned TerraMind segmentation model is not statistically significant (95.3% versus 93.5%; $p=0.14$), and the experiment is not a controlled comparison of computational cost. These results support frozen geospatial embeddings as a low-compute candidate for regional cropland mapping, subject to the limits of a single-state study, a 30 m-derived training reference, and a one-block human validation.

Spatial Transcriptomics (ST) has transformed biomedical research by enabling the spatial mapping of gene expression across tissue sections. However, high operational costs, specialized equipment requirements, and sensitivity to experimental noise limit the accessibility and scalability of ST. Recent computer vision approaches aim to overcome these limitations by predicting spatial gene expression directly from histopathology images. While effective, current approaches often suffer from gene expression over-smoothing and overly uniform predictions across tissue regions, suggesting that further progress depends on learning representations that reflect the hierarchical and asymmetric structure of gene regulation and tissue morphology. To address these issues, we propose Hyperbolic Contrastive Learning with Entailment for Spatial Transcriptomics (HyCLoST), a hyperbolic contrastive learning model that captures the intrinsic hierarchical relationships within ST data. By leveraging hyperbolic geometry and a gene-to-image entailment loss, HyCLoST learns structured, biologically grounded representations that improve gene expression prediction accuracy, achieving a 6% reduction in MSE and an 8% increase in PCC across 26 ST datasets, over previous methods. Our source code is publicly available at https://github.com/BCV-Uniandes/HyCLoST

Pretrained vision embeddings are increasingly used as general-purpose representations for modelling how people appraise urban scenes, and are validated almost entirely by how well they predict human ratings. High predictive accuracy does not establish that these embeddings organise scenes as human perception does. We test the two properties separately against brain data. Using openly released EEG from 63 adults who viewed and rated 56 Berlin street scenes, we estimate the representational geometry of the scenes over time, the proportion of that geometry that is explainable at all, and its correspondence with seventeen feature spaces spanning language-supervised, self-supervised, category-supervised and dense-prediction training, two orders of magnitude of scale, and interpretable controls. Correspondence is low throughout: the best representation, DINOv2 ViT-B, reaches 29.6% of the lower bound of the noise ceiling, the panel spans 11.0% to 29.6%, and a Gabor energy descriptor is indistinguishable from the best model while outperforming every language-supervised model tested. Within a model, deeper layers still match later neural responses, so the hierarchical correspondence found for object recognition survives even at this low overall level. The same embeddings predict held-out appraisal ratings well, up to r = 0.87, and the two measures do not track each other across models; reweighting features towards the neural geometry lowers appraisal prediction for every model tested, against a control of matched dimensionality. Predicting how a street is appraised is therefore weak evidence that a model represents the street as the brain does. The benchmark uses only public data and requires no training, so evaluating a new representation needs only its embeddings for 55 images.

AI-generated image detectors generalize poorly when their training and test images originate from different generators or datasets. Despite the rich spatial representations produced by vision foundation models like DINO, existing detectors typically classify images using only the globally aggregated CLS token. We hypothesize that globally aggregating DINO features into a single CLS token obscures spatially distributed generation traces. To test this hypothesis, we introduce PatchHead, a lightweight spatial aggregation head that preserves the two-dimensional organization of DINO patch tokens and integrates evidence across neighboring regions. During training, we freeze the pretrained DINO backbone and optimize only the inserted LoRA adapters, PatchHead, and auxiliary projection head. Across nine cross-dataset benchmarks spanning manually curated and in-the-wild settings, PatchHead ranks first on seven datasets and second on the remaining two. It improves the strongest prior method from 91.6% to 94.6% in average balanced accuracy (+3.0 points) and raises the worst-case accuracy from 82.4% to 89.4% (+6.9 points), while introducing only 8.6% more trainable parameters and 0.08% additional FLOPs. Further qualitative analysis suggests that PatchHead (i) reduces class-conditional domain discrepancy, and (ii) redirects the representation from content-dominated saliency toward spatially distributed authenticity evidence. Together, these observations provide a representation-level account of why spatial patch aggregation transfers more reliably across generators and datasets than a single CLS-based global representation. Our code and models will be made available upon acceptance.

The plethora of readily available geospatial data offers exciting opportunities to learn high quality representations of the planet, but the sheer size of the Earth Observations (EO), differing modalities, and different sensor types pose significant challenges in doing so. Location encoders have emerged as an efficient way of compressing EOs into location-specific embeddings. However, current state-of-the-art location encoders rely on computationally expensive CLIP-style frameworks that require large batch sizes in the 16K--32K range, suffer from false negative samples, and scale poorly with additional modalities. We introduce the Scalable Location Encoder via Distillation (SLED), a distillation-based location encoder that uses geospatial location as a binding modality to pretrain location encoders with any modality of geospatial data. The resulting location encoder framework is lightweight, modular, and can flexibly incorporate multiple modes, while eliminating the need for spatiotemporal coregistration of samples. SLED is performant with batch sizes as small as 128, enabling pretraining at a fraction of the runtime and compute costs of current state-of-the-art models. We demonstrate our approach by pretraining unimodal and multimodal SLED models on Sentinel-1, Sentinel-2, and Landsat imagery. We show that both unimodal and multimodal SLED models keep pace with or outperform existing approaches on a diverse set of 19 human-centric benchmark tasks and explore the benefits of using additional modes in pretraining.

With the widespread adoption of Vision Transformers in modern AI, the need to analyze their inherent representational behavior has become increasingly important. While most existing studies emphasize token geometries and training dynamics, the evolution of representational covariance structures and class-level geometric organization remains comparatively underexplored. In this work, we investigate semantic geometry and class separability as representations evolve across the layers of ViT-Small/16 through TGO-III: Semantic Geometry Observatory. It is a framework designed to analyze the emergence of semantic organization, feature evolution, and class-wise representation geometry throughout training. The framework employs multiple complementary observatories, including Linear Probe Accuracy, Fisher Ratio, Class Centroid Distances, Local Intrinsic Dimension, and Local PCA Rank, to quantify the progressive evolution of discriminative representations. Our analysis reveals that class representations become progressively more linearly separable, Fisher discriminability increases, class centroids move farther apart, and local representation manifolds exhibit structured class-dependent geometric complexity. These observations provide empirical evidence supporting the Semantic Expansion Hypothesis, suggesting that the manifold expansion observed in previous observatories is accompanied by the progressive organization of representations into increasingly discriminative semantic structures. Collectively, TGO-III extends the Transformer Geometry Observatory framework by establishing a direct connection between manifold geometry, covariance evolution, and semantic organization during Transformer training.

As autonomous drone deployments scale from individual units to coordinated swarms, the human operator's role shifts from direct piloting to high-level supervision. Current interfaces often treat multi-drone control as a scaled-up version of single-drone operation. We instead investigate how reframing fleet supervision as spatial interaction can better support the spatial, temporal, and safety demands of complex missions. We present FleetScape, a Mixed Reality (MR) sandtable system that externalizes layered real-time mission, safety, and environmental data while enabling fluid transitions between manual intervention and autonomous supervision. We developed a high-fidelity building inspection simulation that generates and streams synchronized multi-drone and environmental data for MR visualizations. We used this prototype to conduct a user study with six experienced drone pilots managing fleets of up to 15 drones. Our findings show that FleetScape supports situational awareness through layered spatial representations and clarifies control mode transitions. However, a limit to situational awareness was observed as fleet size increases, leading to different supervisory strategies. Finally, we derive design implications for supporting scalable drone fleet supervision.

Search Trajectory Networks (STNs) are a graph-based tool for visualizing and characterizing the behavior of optimization algorithms. STNs' reliance on discretization of the search space has largely confined them to low-dimensional or combinatorial settings. We introduce a methodology for constructing STNs in semantic spaces, defined as the space of a model's predictions on a fixed sample set. Our approach discretizes semantic vectors and aggregates them into network nodes via agglomerative clustering with complete linkage under a normalized Hamming distance. Since any predictor can be summarized by its semantic vector, this method enables comparison of learning dynamics across otherwise incomparable algorithm families. We apply semantic space STNs to classification and regression tasks solved using different machine learning algorithms, recovering known qualitative differences between them. Additionally, we use semantic space STNs to study neural network generalization by contrasting standard training with the label randomization regime of Zhang et al. (2017). The resulting STNs exhibit consistent structural differences, training on real labels produces denser, more efficient and more centralized graphs than training on shuffled labels. Together, our results show that semantic space STNs capture functional training dynamics arising from the interaction between learning algorithms and data, providing a tool for analyzing and comparing learning dynamics across machine learning models and training regimes.

Spatial understanding is crucial for foundation models (FMs), and maps have long helped humans organize and reason about geographic information. This study examines whether choropleth maps remain useful for machine spatial understanding when models can directly process structured geodata. We introduce ChoroplethMap-Bench, a controlled benchmark containing 2,400 synthetic choropleth maps, corresponding GeoJSON data, and 12,000 questions across five cognitive dimensions: Identify, Spatial Recognition, Compare, Rank, and Delineate. We evaluate 22 open-source and proprietary models under three input conditions: Data Only, Map Only, and Data + Map. The results show that maps substantially improve spatial reasoning, especially when combined with symbolic data and for tasks requiring higher-level understanding of spatial patterns. We further analyze the effects of map type, color hue, and spatial structure, as well as prompting strategies, language, geographic context, decoding settings, classification methods, and response stability. Overall, the Data + Map condition achieves the strongest performance, demonstrating that maps remain valuable external representations for foundation model spatial reasoning.

Dense spatial perception is essential for physical intelligence, where visual systems are expected to recover structured, metric, and actionable representations from pixel observations. Modern visual foundation models tend to prioritize semantic invariance, often at the expense of detailed spatial understanding. In this work, we study vision pretraining through a boundary-centric lens, motivated by the premise that boundaries and shape discontinuities offer essential cues for perceiving geometric properties. Concretely, we propose masked boundary modeling, a self-supervised paradigm that dynamically learns sub-pixel boundary representations and subsequently leverages the discovered boundary-bearing tokens as masked targets to facilitate dense visual token learning. By scaling this framework, we develop LingBot-Vision and demonstrate its efficacy across a diverse set of downstream vision tasks with DINOv3 as a strong baseline. Remarkably, LingBot-Vision drives the progression from LingBot-Depth 1.0 to LingBot-Depth 2.0 for depth completion, and thereby yields enhanced depth estimation, a key pillar for embodied artificial intelligence. Our findings reveal that boundary modeling goes beyond simple line segments and instead serves as a scalable pretraining principle for learning spatially structured visual representations.

Self-supervised learning (SSL) is designed to learn generic, transferable representations rather than representations optimized for a single task. Most geospatial benchmarks evaluate representations solely through downstream tasks, providing limited insight into the information encoded within the representation itself. We ask a different question: do SSL representations of satellite imagery preserve statistical associations with environmental variables that co-vary with the imaging process? To answer this question, we probe SSL representations using co-located ERA5 reanalysis variables, a global dataset of physically consistent environmental variables, including temperature, precipitation, surface solar radiation, surface pressure, and volumetric soil water. These variables are physically related to the spectral reflectance and radar backscatter recorded by Sentinel-1 and Sentinel-2, making them meaningful evaluation targets despite not being used during SSL pretraining. We complement this probing analysis with intrinsic representation metrics to characterize representation geometry and investigate how these properties relate to downstream performance and the encoding of environmental signals. Using DINO, MAE, and MoCo models trained under identical conditions, we show that representation-level metrics distinguish models with similar downstream benchmark performance, providing complementary information beyond task-driven benchmarks. We further find that the linear accessibility of environmental signals is associated with performance on environmentally dependent tasks in the PANGAEA benchmark. Finally, we release ERA5 annotations co-located with the SSL4EO dataset to enable physically grounded representation evaluation for future geospatial foundation models.

We introduce a controlled subspace intervention framework to investigate how self-supervised Vision Transformers (ViTs) encode dense geometric information. While linear probing is widely used to assess geometric representations, it treats features as a black box, failing to disentangle the underlying topology. To address this issue, we decompose the weights of converged linear probes to isolate the low-rank subspaces containing explicit geometric signals using Singular Value Decomposition (SVD). Our perspective yields three key insights: (1) Pre-training objectives determine how features are encoded. DINOv2 aligns spatial features for efficient linear extraction, while Masked Autoencoders (MAE) tend to disperse these signals, requiring a broader spatial context. (2) Explicit geometric representations are highly compressible, suggesting dense predictive heads could potentially be constrained to low-rank subspaces with minimal performance loss. (3) The layer-wise task affinity suggests that geometric precision peaks at intermediate layers before yielding to semantic abstraction in the final layers. By connecting internal encoding mechanics with downstream performance, these findings provide a basis for effective feature selection and lightweight decoder design. The source code is available at https://github.com/Zhou-Weichen/Geosubprobe.

Locating a vehicle and determining its orientation in an uncertain environment is a critical challenge in autonomous vehicle navigation and path planning. To address these challenges, a vehicle estimates its pose while depending on sensor data that offer noisy measurements. These uncertainties in pose quantities are expressed mathematically as a covariance matrix. The real-time computation of the covariance matrix is critical because of the non-linearity involved in the kinematic model. The challenge is thus to evaluate the evolution of the covariance matrix of a vehicle's discretized stochastic kinematics. The purpose of this study is to obtain a near-accurate evolution of the covariance matrix of the rear-wheel bicycle kinematic model under uncertainties in wheel displacement and steering angle. We used Taylor's series to linearize the nonlinear trigonometric functions and provided closed-form expectations of random variables with the required accuracy. Our analytical findings are in good agreement with those obtained from Monte-Carlo simulations. Our contribution is probably the first detailed closed-form presentation of the covariance matrix constituents of the vehicle under evaluation, which were previously reported either incorrectly or incompletely. These findings aid in identifying the potential and constraints of the discretized kinematic model as well as its stochastic analysis. The techniques presented here are useful for the simultaneous localization and odometry self-calibration of certain mobile robots and autonomous vehicles.

Geolocation encoders, which map geographic coordinates to learned representations, are emerging as an effective means of capturing visual and non-visual characteristics from a latitude-longitude pair alone. However, existing approaches project coordinates onto fixed bases (e.g., spherical harmonics), allocating representational capacity uniformly and devoting equal resources to the open ocean and to a developing city. We introduce Tessellating the Earth (TTE), a location encoder built from learnable Spherical Voronoi partitions that concentrates representational capacity where it is needed in a fully differentiable, end-to-end manner. Each Voronoi site carries its own embedding and migrates during training toward discriminative areas. To bridge the gap between local spatial structure and global semantic understanding, we introduce \emph{global semantic tokens}: a set of shared learnable concept tokens that distill semantic knowledge from the satellite imagery into a compact vocabulary the location encoder can reference at inference, enabling geographically distant sites covering similar environments to share semantics. TTE sets a new state of the art for location encoders across a suite of geospatial classification and regression tasks, and achieves the strongest results when used as a geographic prior for fine-grained species classification on iNaturalist-2018. Code, and weights are available at https://github.com/mvrl/TTE.

Geographic implicit neural representations (INRs) learn to map any coordinate on Earth to a location embedding, implicitly encoding geospatial data into the weights of a neural network. Location embeddings are widely used off the shelf as general-purpose geospatial representations, yet users lack principled tools to audit what geographic or semantic information these embeddings capture. In this work, we analyze the information content of geographic INRs through their location embeddings. We decompose these embeddings into human-interpretable features$\unicode{x2014}$namely, (i) sparse latent concepts, (ii) natural language concepts, and (iii) visual features. The latent concept embeddings are learned using sparse autoencoders. To recover natural language concepts, we apply sparse linear concept embeddings (SpLiCE) over a predefined geospatial dictionary. Finally, visual features are extracted using saliency maps derived from CLIP Surgery. We show that location embeddings can be decomposed into human-interpretable representations while retaining high reconstruction capability, revealing interpretable geographic structures such as forests, deserts, and urban features. Across methods, sparse decompositions expose systematic differences in encoded information, ranging from urban structures to broader biome and climate signals, and pretraining-space saliency maps further highlight complementary features such as roads and landmarks. We hope this work provides a first step toward interpretable geospatial representations.

Geospatial vector data quality is a foundational research topic in GIS, yet classic rule-based quality assessment algorithms often struggle with diverse urban morphologies and massive data volumes. Recently, Geospatial Artificial Intelligence (GeoAI) shows promising potential for automating geospatial analysis, while its application to native vector data remains largely underexplored. To fill this research gap, we proposed Topo4Vec, an automated GeoAI framework, designed for scalable vector data quality assessment via advanced Spatial Representation Learning (SRL). Specifically, Topo4Vec relax the labor-intensive manual annotation process via topological error simulation, such as overlapping polygons and street network connectivity errors e.g., overshoots and undershoots. Then, it leverages state-of-the-art SRL approaches to encode complex, native vector geometries (e.g., polylines and polygons) into a latent space where topological errors are isolated from valid ones. A systematic performance evaluation across three study areas (Los Angeles, Munich, and Singapore) demonstrates the effectiveness and robustness of Topo4Vec, achieving a peak accuracy of 0.99 for detecting overlapping building footprints and 0.60 for overshoots and undershoots in street networks. Moreover, lessons learned from Topo4Vec shed a promising light into a scalable and autonomous GeoAI approach for large-scale vector data consistency and quality monitoring within the fast-growing geospatial data ecosystems. The code and data used in the paper are made openly available in https://figshare.com/s/612148eeb4bccadbd715.

Location encoders transform geographic coordinates into high dimensional embeddings for downstream machine learning, but it is unclear how well these representations capture interpretable spatial effects. We benchmark whether GeoShapley, a game-theoretic explainer that treats all location features as a single joint player, can recover spatially varying coefficients from models built on location-encoder embeddings. Eleven encoders from the TorchSpatial framework are evaluated against a synthetic process with known coefficients, across three scales (grid, county, global), with and without raw coordinates alongside the embedding, and under untrained and contrastively trained conditions. Measuring recovery as the correlation between estimated and true coefficients, we report how it varies with scale and encoder architecture and compare the embeddings against a raw-coordinate baseline. Recovery of the primary coefficient is consistently high across encoders, whereas recovery of a secondary coefficient is more scale-dependent, differing most at the global scale; the raw-coordinate baseline remains competitive throughout.

Learning Entropy (LE) has recently been extended to image analysis through Spatial Learning Entropy Maps (SLEMs), which are two-dimensional LE distributions that highlight unusually high learning activity across an image. Unlike conventional image descriptors, SLEMs are generated by incremental, sample-wise learning of a pretrained feedforward MLP network, where local pixel neighborhoods are presented sequentially in a fixed spatial order to predict the corresponding central pixels. Consequently, the learning activity at each image location depends not only on its local structure but also on the knowledge acquired from previously processed locations. This paper introduces Learning Entropy Signatures (LES), an image descriptor derived from SLEM using the K largest LE locations. LES captures the spatial organization of learning-relevant image structures and provides a compact representation of image content based on learning weight behavior. Experimental evaluation on image classification tasks shows that a relatively small number of K largest LE locations preserve substantial discriminative information. The results indicate a close relationship between the learning of neural weights and information relevance, extending the role of Learning Entropy from time series to images and, within images, from structural point extraction to compact image representation and classification.

Learned representations in intelligent sensing systems are often evaluated by reconstruction fidelity or downstream prediction accuracy, but these criteria do not specify which latent distinctions are justified by the sensing process. In sensor-conditioned environments, nuisance factors can change measurements without changing the scene, while distinct scenes may be indistinguishable under limited sensing capability. This paper formulates sensor-conditioned representation correctness as preserving sensing-supported scene distinctions while suppressing nuisance-induced and sensor-unsupported variation. We introduce the scene-relevant observation quotient, a representation target induced by sensing-supported distinguishability after nuisance canonicalization, and develop Observation-Quotient Tucker-Structured Autoencoding (OQ-TSAE), a scene-nuisance factorized framework with diagnostics for false distinction, false merge, nuisance sensitivity, and latent ordering consistency. Experiments on a controlled benchmark show that quotient-consistent supervision improves representation-correctness diagnostics over reconstruction-oriented, metric-learning, and contrastive-learning baselines. Sensitivity, perturbation, and ablation studies show the importance of quotient-aligned supervision, reliable quotient relations, and quotient geometry. Complementary real-radar experiments show that a reconstruction-only OQ-TSAE variant retains competitive downstream utility, robustness under observation degradation, and low seed-to-seed variability. These results suggest that sensor-conditioned representations should be evaluated not only by predictive utility, but also by whether their latent geometry preserves sensing-justified scene distinctions.

Understanding when and why deep neural networks are uncertain is crucial for deploying reliable machine learning systems in safety-critical domains. While existing uncertainty quantification methods provide scalar measures of model confidence, they offer limited insight into which spatial regions of an input contribute to different types of uncertainty. We propose a novel visualization framework, Uncertainty Activation Map (UAM), that combines Evidential Deep Learning (EDL) with Full-Gradient Class Activation Mapping (FullGrad) to generate interpretable spatial uncertainty activation maps. Our approach distinguishes between two fundamental types of uncertainty: vacuity, representing lack of evidence, and dissonance, capturing conflicting evidence between competing hypotheses. By leveraging the complete gradient decomposition property of FullGrad and the principled uncertainty quantification of Subjective Logic, our method produces theoretically grounded visualizations that highlight specific image regions responsible for model uncertainty. With this framework, vacuity and dissonance activation maps are generated by computing belief-weighted attributions, enabling identification of where models lack knowledge versus where they encounter ambiguous evidence. Extensive evaluations across multiple benchmark datasets demonstrate that the proposed framework effectively addresses the critical gap between uncertainty quantification and explainability, providing intuitive visual feedback to assess model reliability in complex visual recognition tasks.

Generative model-based imitation learning has become a widely adopted paradigm for robotic manipulation, where policy performance depends critically on the conditioned visual representations. Although spatial softmax-based representations have been adopted in prior visuomotor policies, their effectiveness and underlying mechanisms remain insufficiently understood. This work rethinks the use of spatial softmax pooling: do such implicit spatial representations provide effective and stable visual features for robotic manipulation? Through systematic studies of different pooling methods in visual encoders, we find that this pooling operation produces compact and stable spatial representations, which outperform feature-value representations, despite using substantially fewer dimensions. Complementary saliency analysis further suggests that these spatial representations guide the encoder to focus more consistently on task-relevant regions. However, this advantage is limited by a representation bottleneck in current visual encoders: repeated downsampling operations weaken fine-grained spatial information before the action-generation module can use it, especially under low-resolution observations. Motivated by these findings, we propose PRISM, a visual encoder that preserves multiscale implicit spatial information through top-down cross-attention fusion. Experiments across multiple tasks and policy backbones show consistent improvements. In particular, on the low-resolution, high-precision ToolHang task, PRISM shows clear gains, improving the average success rate from 5.0% to 13.4% while increasing parameters by only 15.4%. These results support the use of multiscale implicit spatial representations as an effective and efficient design principle for robotic manipulation.

Visual perception of urban streetscapes underpins evidence-based decisions in landscape planning, public health, and place-making. Yet models trained on a few well-photographed metropolises systematically misjudge underrepresented districts, propagating geographic bias into downstream policy. We address this gap with HVSP-LL, a lifelong learning framework that couples a stratified visual-semantic pivoting module with an equity-aware rehearsal mechanism. The pivoting module organises landscape concepts along a three-tier ontology (macro structure, meso composition, micro element) and aligns image features to learnable semantic anchors at each tier, providing transferable representations that resist distributional drift. The lifelong adaptation component sequentially absorbs new urban regions while constraining inter-region perception gaps through a worst-region sample-reweighting objective and a structurally-aware exemplar buffer. We evaluate HVSP-LL on a panoramic streetscape benchmark assembled from twelve cities across four continents and seven perceptual dimensions. The framework attains 0.834 Spearman correlation on the held-out city sequence, an absolute 6.1 point improvement over the strongest continual baseline, and shrinks the inter-city perception gap to 0.094 -- a 38% reduction relative to the strongest continual baseline (0.151) and a 57% reduction relative to a representative regularisation baseline (0.218). Ablations confirm that each tier of the pivoting hierarchy contributes monotonically, and the equity-aware rehearsal converts mean backward transfer from -0.038 (without retention) to +0.013, eliminating catastrophic forgetting on the held-out sequence. Our results indicate that hierarchical anchoring is a practical pathway toward geographically equitable streetscape inference at city scale.

Remote sensing vector mapping aims to generate structured maps of geospatial entities, such as buildings, roads, and water bodies, from remote sensing imagery. In practice, vector maps usually contain multiple category layers and heterogeneous entity structures, requiring a unified model for diverse mapping needs. However, existing methods typically represent vector objects as polygons or graphs, making them suitable only for specific categories: polygons poorly capture topological relations, while graphs often blur instance boundaries. We observe that language, as a natural medium for human communication, offers a flexible and expressive representation that can accommodate heterogeneous map elements, including geometry, semantics, and topolog. Motivated by this insight, we propose Vector Map as Language (VecLang), a unified paradigm that reformulates multiclass vector mapping as structured text generation. VecLang encodes the common elements of different geospatial entities into a GeoJSON-like vector language, enabling cross-category modeling within a shared textual format. To generate this language reliably, we design a progressive vision-language mapping framework that first localizes vectorization units and then generates structured map elements. We further introduce Hierarchical Vector Language Optimization, which uses reinforcement learning to improve syntax validity, content fidelity, and map executability. We also build VecMap-Bench with 54K images and 800K instances, supporting training and evaluation across standard and generalization settings. Extensive experiments demonstrate that VecLang handles both single-class and multiclass vector mapping while achieving strong cross-dataset and open-vocabulary generalization. The model and dataset are publicly available at https://github.com/yyyyll0ss/VecLang.

This paper extends the concept of Learning Entropy (LE) from temporal adaptive systems to spatial learning in multilayer perceptron networks (MLPs) applied to image data. Instead of evaluating image structure directly from gradients or covariance operators, as local neighborhood methods do, the proposed approach analyzes the learning process itself through Learning Entropy. An MLP is trained to predict the intensity of a center pixel from its surrounding spatial context, while LE is evaluated from the incremental adaptation of neural weights during learning across image-derived samples. The resulting Spatial Learning Entropy Maps (SLEM) identify unusual image points and regions that induce strong adaptation of the neural network and therefore have an important role in the learning process. The results indicate that spatial Learning Entropy provides a complementary perspective to conventional feature extraction and explainability methods by highlighting spatial locations that are particularly informative for network learning. Spatial Learning Entropy provides a complementary perspective to conventional feature extraction and explainability methods by identifying image points and regions according to their learning impact rather than their local structural properties. The proposed framework may open new directions for learning-driven image or scene analysis in computer vision, manufacturing, and robotics.

Geospatial understanding is a critical yet underexplored dimension in the development of machine learning systems for tasks such as image geolocation and spatial reasoning. In this work, we analyze the geospatial representations acquired by three model families: vision-only architectures (e.g., ViT), vision-language models (e.g., CLIP), and large-scale multimodal foundation models (e.g., LLaVA, Qwen, and Gemma). By evaluating across image clusters, including people, landmarks, and everyday objects, grouped based on the degree of localizability, we reveal systematic gaps in spatial accuracy and show that textual supervision enhances the learning of geospatial representations. Our findings suggest the role of language as an effective complementary modality for encoding spatial context and multimodal learning as a key direction for advancing geospatial AI.

Across contemplative, philosophical, and psychological accounts, human consciousness is often described along a similar spectrum, ranging from reactive and self-focused patterns to more integrative and coherent ones. Understanding whether language models encode such a structured, human-interpretable consciousness spectrum in representation space is important for model guidance, evaluation and alignment. In this work, we study the geometric structure and dynamics of patterns along this spectrum in transformer embedding spaces. We show that embeddings exhibit a globally organized geometry aligned with this spectrum: sentences associated with similar states cluster into locally coherent regions, forming a structured manifold. In particular, higher-level and lower-level regions exhibit convexity-like stability, while intermediate regions form a transition corridor. Dynamically, both utility-guided and geometry-only greedy trajectories consistently traverse from lower- to higher-level regions, passing through intermediate tiers, indicating that navigability is an intrinsic property of the representation space, guided but not dictated by a global directional signal. These results suggest that embedding spaces encode structured and navigable geometry aligned with a hypothesized consciousness-spectrum taxonomy, broadly inspired by recurring structural descriptions of human consciousness across contemplative traditions, philosophy, and modern psychology, providing a representation-level perspective for analyzing and guiding model behavior.

Recent large language models (LLMs) often appear to exhibit spatial reasoning ability; however, this capability is largely \emph{symbolic}, arising from pattern matching over spatial language rather than true \emph{geometric} reasoning over space. Because LLMs operate on discrete tokens, they lack native support for continuous spatial representations, explicit geometric computation, and structured spatial operators. To address this limitation, we introduce the \emph{Spatial Language Model (SLM)}, the first multimodal LLM that treats location information as a first-class modality and enables geometric spatial reasoning within the model's inference process. SLM directly operates on learned spatial representations rather than textual descriptions of spatial relations. To support effective training, we construct a \emph{Spatial Instruction Dataset} that aligns spatial representations, atomic geometric operations, and natural language instructions. We further propose a new benchmark named \emph{SpatialEval}, which is designed to evaluate spatial reasoning across attributes, distance, topology, and relative-position tasks. Extensive experiments show that SLM significantly outperforms existing LLM-based approaches that rely on symbolic reasoning via prompt engineering or textual abstraction, demonstrating the benefits of integrating geometric spatial representations for robust spatial reasoning. Our instruction dataset, evaluation benchmark, model training codes, and models' checkpoints can be found at: \hyperlink{https://github.com/chuchen2017/SLM}{https://github.com/chuchen2017/SLM}.

Event-based tactile sensing offers low-latency signal acquisition for contact-rich robotic interaction. This paper investigates contact-angle estimation using event streams from an event-based tactile sensor (NeuroTac) and compares three event-derived spatial contour representations: a dynamic representation capturing recent event activity, a static representation recovering a more persistent contact state, and their combined representation. Across the evaluated motion scenarios, all representation pipelines exhibited P99 processing latency below 10 ms at all tested sampling intervals, demonstrating their potential for high-frequency event-based tactile angle estimation in robotic manipulation. The static representation consistently achieved marginally better performance than the dynamic and combined representations under scenario-specific training, yielding a mean overall MAE of 0.160° during continuous sensor rolling and a stop-phase mean MAE of 0.251° during randomly inserted motion interruptions. It also exhibited smaller performance fluctuations across speed and indentation depth variations than the other two representations.

Earth Observation (EO) has fundamentally transformed the monitoring of environmental processes and human activities up to planetary scale. Recent advances in self-supervised learning have given rise to Earth Observation Foundation Models (EOFMs), which leverage petabyte-scale unlabeled EO data to learn transferable representations across a wide range of downstream geospatial tasks. Despite these advances, current EOFMs remain largely confined to raster modalities, overlooking the rich, structured information encoded in openly-accessible vector data sources such as OpenStreetMap and Overture. Vector data provides explicit and compact representations of geographic entities, including geometry, topology, and semantic relationships, offering critical contextual signals that are often ambiguous or inaccessible in imagery alone. Raster and vector data thus represent complementary views of geographic space: raster data captures continuous physical and spectral patterns, while vector data encodes discrete objects and their relational structure and often represents more of the human rather than the physical systems (e.g. social or demographic data). However, existing geospatial representation learning paradigms treat these modalities in isolation, relying on imperfect and often lossy transformations to bridge them. This perspective paper calls for a paradigm shift toward joint Spatial Representation Learning (SRL) in an unified embedding space that integrate raster perception with vector-based reasoning. Building on emerging efforts in multimodal geospatial learning, we highlight conceptual foundations, technical challenges, and promising directions for aligning heterogeneous spatial data sources. We contend that such integration is essential for developing next-generation geospatial AI systems capable of more accurate, interpretable, and semantically grounded understanding of the Earth.

Large Language Model (LLM)-based navigation systems commonly construct explicit spatial representations (e.g., topological graphs, semantic raster maps) and translate them into textual descriptions as LLMs' inputs. However, the linguistic structures of such text-based spatial representations and the choices of contextual features (e.g., topology, geometry) they contain are often treated as neutral engineering decisions rather than key factors that shape LLMs' behavior. To fill the gap, we propose a dual-interventional framework that disentangles linguistic structures from different contextual cues to evaluate the linguistic inductive bias of LLMs for navigation planning. In the framework, representation intervention varies the linguistic format and the degree of linguistic compression, clarifying when linguistic representations support or inhibit navigation planning. Context intervention, combined with contextual feature combination and conflict probing, explicitly clarifies the preferences and weaknesses of LLMs when processing different contextual cues. Experiments across diverse spatial reasoning tasks and multiple model scales reveal a consistent pattern: topological information is a sturdy shield and the backbone of robust planning; linguistic format is a double-edged sword whose effect depends on model size, task demands, and the compression level; and semantic information is a fatal Achilles' heel -- incorrect semantic cues can systematically derail the planning process. Overall, our study shows that effective text-based spatial representations in LLM-based navigation should preserve topological integrity, calibrate representational compression to model capacity, and ensure semantic correctness, rather than simply adopting a single representation. Our code is publicly available at https://github.com/jonesdong150/LLM-Navigation-Inductive-Bias.

Vision-language models (VLMs) achieve strong performance on spatial reasoning benchmarks, yet it remains unclear whether this reflects structured 3D understanding or reliance on statistical shortcuts in natural images. We introduce a representation-level analysis framework that constructs minimal contrastive pairs to measure how spatial axes are organized and disentangled within VLM embeddings. Our analysis across multiple model families reveals a consistent vertical-distance entanglement: models conflate vertical image position with distance, mirroring the perspective bias of natural photographs. This bias produces a significant accuracy gap between perspective-consistent and counter-heuristic examples, and intensifies under data scaling even as overall benchmark accuracy improves. We further show that models with similar benchmark scores can exhibit different internal representations, and that these differences predict accuracy and robustness across diverse spatial reasoning benchmarks. To isolate this bias from evaluation-set skew, we introduce SpatialTunnel, a synthetic benchmark designed to expose spatial shortcut biases by removing common correlations present in natural images. Experiments confirm that the entanglement is model-intrinsic, and that models with well-separated spatial axes exhibit greater robustness, suggesting that well-structured spatial representations lead to more reliable spatial reasoning across diverse benchmarks. Code and benchmark are available on the project page: https://cheolhong0916.github.io/whyfarlooksup.github.io/.

Positional embeddings (PEs) in Vision Transformers (ViTs) are known to impact performance and robustness, but their role in shaping internal spatial representations is not well understood. In this work, we study how different forms of PEs influence the representational geometry of ViTs and how these changes relate to robustness under content-disrupting distribution shifts. We introduce a metric, the Spatial Similarity Distance Correlation (SSDC), to quantify spatial structure in token representations. Using this metric, we show that ViTs trained without PEs still develop non-trivial spatial structure, but this structure is driven by visual content and collapses under token permutation. In contrast, we find that all PEs considered (learned absolute, sinusoidal, and rotary) are associated with a consistent shift toward an index-anchored spatial organization. Representations in these models remain stable under perturbations that disrupt content, and exhibit substantially improved robustness to such distributional shifts. We further show that while different PEs produce distinct depth-wise trajectories of spatial structure, their robustness properties are largely similar (with secondary variation across encoding schemes), suggesting that robustness appears to depend on the presence of a stable positional reference frame more than it depends on the specific encoding mechanism. These results offer a geometric account of how positional encodings shape internal representations, with implications for the principled design of future encoding schemes.

While spatial foundation models have demonstrated impressive performance on standard datasets, a critical question remains: are they truly all-round players capable of generalizing robustly across diverse downstream tasks, arbitrary viewpoints, shifting scene domains, varying input densities, and specific hardware constraints? Answering this overarching question requires a holistic assessment, yet current models are mainly evaluated on specific domains for which they were specifically designed or trained. Such evaluations are intrinsically limited by narrow paradigm coverage, limited scene domains, and arbitrary frame sampling, making it fundamentally difficult to assess their true generalization capabilities. To address this gap, we present SpatialBench, a cross-paradigm, domain-diverse benchmark for spatial foundation models with deterministic sampling. SpatialBench features unprecedented scale and rigorous deterministic design, comprising 19 datasets and 546 scenes across 5 diverse spatial domains. It comprehensively evaluates 41 models across 6 paradigms on 5 task suites under 4 different input density settings. Our extensive evaluation reveals that current models are not yet all-round players, and uncovers crucial insights for future advancement. Specifically, we demonstrate that full-context attention maximizes accuracy while bounded-memory strategies unlock long-sequence scalability. Moreover, our empirical evaluations in challenging embodied and egocentric tasks demonstrate that strict domain alignment and high data quality are far more critical to performance than simple dataset scaling. Furthermore, to address the largest data gap identified in our analysis, we go beyond evaluation by introducing a large-scale dataset, DA-Next-5M, and a strong baseline model, DA-Next, pushing the boundaries of spatial representation learning.

Representation learning with Vision Transformers (ViTs) has advanced rapidly, yet the utility of large-scale models in spatially sensitive tasks is hindered by spurious tokens. Prior efforts to mitigate this have been limited, often defining these artifacts narrowly, for example, as simple high-norm outliers. We argue that this scope is insufficient. For dense prediction tasks, we posit that any token failing to encode location-aligned semantics should be treated as a spurious artifact. This broader definition reveals a more complex problem, leading us to systematically categorize and characterize three fundamental types of spurious tokens that corrupt spatial representations. Based on this comprehensive diagnosis, we propose UniRefiner, a universal refinement framework that teaches pre-trained ViTs to self-dispose of these artifacts. UniRefiner uses contrastive registers to explicitly isolate and redistribute spurious tokens via a dual objective: (i) it aligns image tokens with filtered regular tokens to preserve semantics, and (ii) it aligns register tokens with detected spurious tokens to capture the spurious signals. Our method requires only a few epochs of fine-tuning on ~5k images to refine diverse ViTs, including massive models like EVA-CLIP-8B and InternViT-6B. Experiments demonstrate consistent and significant improvements: notably, the refined EVA-CLIP-8B achieves 51.9% mIoU on ADE20K (+9.4%), surpassing specialized vision models like DINOv2 (49.1%), while zero-shot segmentation accuracy improves by up to 22%. UniRefiner unlocks the latent spatial potential of existing large-scale foundation models, paving the way for their broader application.

Large-scale pretraining on Earth observation imagery has yielded powerful representations of the natural and built environment. However, most existing geospatial foundation models do not directly model the structured socioeconomic covariates typically stored in tabular form. This modality gap limits their ability to capture the complete total environment, which is critical for reasoning about complex environmental, social, and health-related outcomes. In this work, we propose GeoViSTA (Geospatial Vision-Tabular Transformer), a vision-tabular architecture that learns unified geospatial embeddings from co-registered gridded imagery and tabular data. GeoViSTA utilizes bilateral cross-attention to exchange spatial and semantic information across modalities, guided by a geography-aware attention mechanism that aligns continuous image patches with irregular census-tract tokens. We train GeoViSTA with a self-supervised joint masked-autoencoding objective, forcing it to recover missing image patches and tabular rows using local spatial context and cross-modal cues. Empirically, GeoViSTA's unified embeddings improve linear probing performance on high-impact downstream tasks, outperforming baselines in predicting disease-specific mortality and fire hazard frequency across held-out regions. These results demonstrate that jointly modeling the physical environment alongside structured socioeconomic context yields highly transferable representations for holistic geospatial inference.

Learning latent representations that capture both semantic and spatial information is central to efficient spatio-semantic reasoning. However, many existing approaches rely on implicit latent structures combined with dense feature maps or task-specific heads, limiting computational efficiency and flexibility. We propose WorldComp2D, a novel lightweight representation learning framework that explicitly structures latent space geometry according to object identity and spatial proximity using multiscale local receptive fields. This framework consists of (i) a proximity-dependent encoder that maps a given observation into a spatio-semantic latent space and (ii) a localizer that infers the coordinates of objects in the input from the resulting spatio-semantic representation. Using facial landmark localization as a proof-of-concept, we show that, compared to SoTA lightweight models, WorldComp2D reduces the numbers of parameters and FLOPs by up to 4.0X and 2.2X, respectively, while maintaining real-time performance on CPU. These results demonstrate that explicitly structured latent spaces provide an efficient and general foundation for spatio-semantic reasoning. This framework is open-sourced at https://github.com/JinSeongmin/WorldComp2D.

Recent advancements in Large Vision-Language Models (VLMs) have demonstrated exceptional semantic understanding, yet these models consistently struggle with spatial reasoning, often failing at fundamental geometric tasks such as depth ordering and precise coordinate grounding. Recent efforts introduce spatial supervision from scene-centric datasets (e.g., multi-view scans or indoor video), but are constrained by the limited number of underlying scenes. As a result, the scale and diversity of such data remain significantly smaller than those of web-scale 2D image collections. To address this limitation, we propose SpatialForge, a scalable data synthesis pipeline that transforms in-the-wild 2D images into spatial reasoning supervision. Our approach decomposes spatial reasoning into perception and relation, and constructs structured supervision signals covering depth, layout, and viewpoint-dependent reasoning, with automatic verification to ensure data quality. Based on this pipeline, we build SpatialForge-10M, a large-scale dataset containing 10 million spatial QA pairs. Extensive experiments across multiple spatial reasoning benchmarks demonstrate that training on SpatialForge-10M significantly improves the spatial reasoning ability of standard VLMs, highlighting the effectiveness of scaling 2D data for 3D-aware spatial reasoning.

Chest radiograph interpretation requires temporal reasoning over prior and current studies, yet most vision-language models are trained on static image-report pairs and lack explicit supervision for modeling longitudinal change. We introduce CheXTemporal, a dataset for temporally grounded reasoning in chest radiography consisting of paired prior-current chest X-rays (CXR) with finding-level temporal and spatial annotations. The dataset includes a five-class progression taxonomy (new, worse, stable, improved, resolved), localized spatial supervision of pathology, explicit spatial-temporal alignment across paired studies, and multi-source coverage for cross-domain evaluation. We additionally construct a 280K-pair silver dataset with automatically derived temporal and anatomical supervision for large-scale evaluation under weaker supervision. Using these resources, we evaluate multiple state-of-the-art vision-language CXR models on grounding and progression-classification tasks in a zero-shot setting. Across both gold and silver evaluations, current models exhibit consistent limitations in spatial grounding, fine-grained temporal reasoning, and robustness under distribution shift. In particular, models perform substantially better on salient progression categories such as worse than on temporally subtle states such as stable and resolved, suggesting limited modeling of longitudinal disease evolution in chest radiography.

Pixel-level slum mapping has long been constrained by limited cross-city generalisation, the absence of continuous density estimation, and weak global comparability. AlphaEarth Foundations (AEF), a globally consistent 64-dimensional annual surface embedding at 10 m, offers a new analysis-ready basis for lightweight slum monitoring, but its applicability to slum detection - an indirectly coupled task shaped by both built form and socio-economic processes - remains untested. We evaluate AEF on slum classification and sub-pixel density estimation across 12 cities and 69 city-year pairs (2017-2024), using GRAM pseudo-masks as supervisory labels. The evaluation spans four training strategies, two protocols (random split and 3x3 spatial block cross-validation), six auxiliary feature configurations, and five baseline models, complemented by representation-level analyses (PCA, SHAP) and full-AOI mapping. Five findings emerge. (1) Same-city cross-year training is optimal under both protocols (median spatial F1 = 0.616, R^2 = 0.466); temporal expansion outperforms cross-city transfer, indicating city-scale representational drift. (2) Regression R^2 is driven primarily by zero/non-zero boundary discrimination: positive-pixel R^2 is consistently negative across all cities, revealing limited capacity to model intra-pixel density gradients at 10 m. (3) PC36 is consistently top-ranked across tasks; classification saturates at k = 32 while regression remains unsaturated at k = 64. (4) POI features yield the largest density gain (Delta R^2 = +0.064). (5) For six cities meeting dual-task usability thresholds, full-AOI inference across 2017-2024 preserves slum cluster structure (mean SSIM = 0.926). The study delineates the capabilities and complementarity needs of foundation-model embeddings for slum monitoring.

Existing self-supervised learning (SSL) methods primarily learn object-invariant representations but often neglect the spatial structure and relationships among object parts. To address this limitation, we introduce Spatial Prediction (SP), a spatially aware pretext regression task that predicts the relative position and scale between a pair of disentangled local views from the same image. By modeling part-to-part relationships in a continuous geometric space, SP encourages representations to capture fine-grained spatial dependencies beyond invariant categorical semantics, thereby learning the compositional structure of visual scenes. SP is implemented as a decoupled plug-in and can be seamlessly integrated into diverse SSL frameworks. Extensive experiments show consistent improvements across image recognition, fine-grained classification, semantic segmentation, and depth estimation, as well as substantial gains in out-of-distribution robustness for object recognition. To evaluate spatial reasoning, we introduce (1) a position and scale prediction task on image patch pairs and (2) a jigsaw understanding task requiring patch reordering and recognition after reconstruction. Strong performance on these tasks indicates improved spatial structure and geometric awareness. Overall, explicitly modeling spatial information provides an effective inductive bias for SSL, leading to more structured representations and better generalization. Code and models will be released.

Cross-modal knowledge distillation has emerged as an effective strategy for integrating point cloud and image features in 3D perception tasks. However, the modality heterogeneity, spatial misalignment, and the representation crisis of multiple modalities often limit the efficient of these cross-modal distillation methods. To address these limitations in existing approaches, we propose a hyperbolic constrained cross-modal distillation method for multimodal 3D object detection (HGC-Det). The proposed HGC-Det framework includes an image branch and a point cloud branch to extract semantic features from two different modalities. The point cloud branch comprises three core components: a 2D semantic-guided voxel optimization component (SGVO), a hyperbolic geometry constrained cross-modal feature transfer component (HFT), and a feature aggregation-based geometry optimization component (FAGO). Specifically, the SGVO component adaptively refines the spatial representation of the 3D branch by leveraging semantic cues from the image branch, thereby mitigating the issue of inadequate representation fusion. The HFT component exploits the intrinsic geometric properties of hyperbolic space to alleviate semantic loss during the fusion of high-dimensional image features and low-dimensional point cloud features. Finally, the FAGO compensates for potential spatial feature degradation introduced by the 2D semantic-guided voxel optimization component. Extensive experiments on indoor datasets (SUN RGB-D, ARKitScenes) and outdoor datasets (KITTI, nuScenes) demonstrate that our method achieves a better trade-off between detection accuracy and computational cost.

Self-supervised learning (SSL) has transformed representation learning for large models, yet remains unexplored for microcontroller (MCU)-class models with fewer than 500K parameters. We identify three obstacles at this scale -- projection head dominance, representation bottleneck, and augmentation sensitivity -- and propose Capacity-Aware Distilled Self-Supervised Learning (CA-DSSL), a teacher-guided framework that overcomes them without labels or text supervision. CA-DSSL combines asymmetric distillation from a frozen DINO ViT-S/16 teacher, multi-scale feature distillation for spatial representations, and a progressive augmentation curriculum. On a MobileNetV2-0.35 backbone (396K parameters) pretrained on CIFAR-100, CA-DSSL reaches 62.7 0.5% linear-probe accuracy (3-seed mean) -- surpassing SimCLR-Tiny by 18 pp, matching SEED (61.7%) with 10 fewer projection parameters (426K vs. 3.15M), and reaching 94.0% of a supervised upper bound. Standard SSL methods (BYOL-Tiny, DINO-Tiny) collapse entirely at this scale. On Pascal VOC detection, CA-DSSL achieves 2.3 the mAP of random initialization and +3 pp over SEED, though SimCLR-Tiny matches CA-DSSL on detection mAP. The deployed backbone occupies 378 KB (INT8) with no inference overhead from pretraining. Preliminary ImageNet-100 experiments reveal that CA-DSSL's advantage is specific to small-data regimes; scaling to ImageNet-1K is discussed as future work.

Neural representations carry rich geometric structure; but does that structure causally shape behavior? To address this question, we intervene along paths through activation space defined by different geometries, and measure the behavioral trajectories they induce. In particular, we test whether interventions that respect the geometry of activation space will yield behaviors close to those the model exhibits naturally. Concretely, we first fit an activation manifold $M_h$ to representations and a behavior manifold $M_y$ to output probability distributions. We then test the link $M_h \leftrightarrow M_y$ via interventions: we find that steering along $M_h$, which we term manifold steering, yields behavioral trajectories that follow $M_y$, while linear steering -- which assumes a Euclidean geometry -- cuts through off-manifold regions and hence produces unnatural outputs. Moreover, optimizing interventions in activation space to produce paths along $M_y$ recovers activation trajectories that trace the curvature of $M_h$. We demonstrate this bidirectional relationship between the geometry of representation and behavior across tasks and modalities. In language models, we use reasoning tasks with cyclic and sequential geometries as well as in-context learning tasks with more complex graph geometries. In a video world model, we use a task with geometry corresponding to physical dynamics. Overall, our work shows that geometry in neural representation is not merely incidental, but is in fact the proper object for enabling principled control via intervention on internals. This recasts the core problem of steering from finding the right direction to finding the right geometry.

Deep convolutional neural networks (DCNNs) have rivaled humans on many visual tasks, yet they remain vulnerable to near-imperceptible perturbations generated by adversarial attacks. Recent work shows that aligning DCNN representations with human visual cortex activity improves adversarial robustness, but the mechanisms driving this advantage are unclear. One hypothesis suggests that neural alignment confers robustness by biasing models away from brittle high-frequency details and towards the low spatial frequencies (LSF). However, recent work shows that human object recognition critically depends on a narrow, mid-frequency "human channel". Interestingly, this band was partially preserved in prior LSF-focused studies. Here, we investigate whether a spectral bias towards the LSF or the human channel is the primary driver of the adversarial robustness observed in neurally aligned DCNNs. We first show that DCNNs aligned to higher-order regions of the human ventral visual stream systematically increase reliance on both LSF and the human channel. However, directly steering DCNNs towards these bands revealed a clear dissociation. Biasing models towards the human channel, either alone or together with LSF, does not improve robustness and even impairs it. LSF bias produced some robustness gains, but such improvements are modest despite inducing much larger shifts in spatial-frequency reliance than neurally aligned models. Spatial-frequency-biased models overall show little, if any, increase in similarity to human neural representational geometry. Together, our results suggest that altered spatial-frequency reliance is likely an emergent property of learning more human-like representations rather than the primary mechanism by which neural alignment confers adversarial robustness, and motivate the need for future research examining representational properties beyond spatial-frequency profiles.

Low-dimensional projections of text embeddings support visual analysis of document collections, but their spatial organization may not reflect the relationships an analyst intends to examine. Existing semantic interaction approaches encode semantic intent indirectly through geometric constraints or model updates, limiting interpretability and flexibility. We introduce LLM-augmented semantic steering, which enables analysts to express semantic intent by grouping a small set of example documents within the projection. A large language model externalizes this intent as natural-language representations and selectively extends it to related documents; the resulting semantic information is then incorporated into document representations via text augmentation or embedding-level blending, without retraining the underlying models. A case study illustrates how the same corpus can be reorganized from different semantic perspectives, while simulation-based evaluation shows that semantic steering improves global and local alignment with target semantic structures using only minimal interaction. Embedding-level blending further enables continuous and controllable steering of projection layouts. These results position projection spaces as intent-dependent semantic workspaces that can be reshaped through explicit, interpretable, language-mediated interaction.

Heat exposure connects the built environment and public health, directly shaping the livability and sustainability of urban areas. Understanding the spatial heterogeneity of heat exposure and its drivers is vital for climate-adaptive urban planning. However, most planning-oriented studies rely on land surface temperature (LST), and whether LST adequately represents human heat exposure and how it differs from physiologically relevant heat stress remains insufficiently examined. Here, using Landsat-retrieved 30-m LST and GPU-accelerated 1-m universal thermal climate index (UTCI) in Singapore, this study establishes a comprehensive "Modeling-Comparing-Assessing" framework to systematically evaluate the spatial and mechanistic differences between these two metrics. We further investigate their pronounced non-stationary and threshold-based relationships with urban factors using a novel geographically weighted XGBoost (GW-XGBoost) and generalized additive model (GAM) workflow. Our results reveal substantial differences in the spatial patterns of LST and UTCI, along with marked spatial heterogeneity in how 2D and 3D urban factors impact these thermal metrics, as demonstrated by explainable GW-XGBoost models (test R2 = 0.855 for LST and 0.905 for UTCI). Crucially, spatially explicit SHAP shows that sky view factor plays a central role in explaining UTCI variability but exhibits a comparatively marginal independent contribution to LST, indicating that LST inadequately captures shading-driven and radiative processes governing actual human heat stress. Moreover, SHAP-GAM analysis indicates that higher albedo is associated with increased UTCI. These findings provide model-informed planning implications for integrating physiologically relevant thermal indices to support targeted heat risk management and human-centric urban planning.

Vector Symbolic Architectures (VSAs) provide a well-defined algebraic framework for compositional representations in hyperdimensional spaces. We introduce HyperSpace, an open-source framework that decomposes VSA systems into modular operators for encoding, binding, bundling, similarity, cleanup, and regression. Using HyperSpace, we analyze and benchmark two representative VSA backends: Holographic Reduced Representations (HRR) and Fourier Holographic Reduced Representations (FHRR). Although FHRR provides lower theoretical complexity for individual operations, HyperSpaces modularity reveals that similarity and cleanup dominate runtime in spatial domains. As a result, HRR and FHRR exhibit comparable end-to-end performance. Differences in memory footprint introduce additional deployment trade-offs where HRR requires approximately half the memory of FHRR vectors. By enabling modular, system-level evaluation, HyperSpace reveals practical trade-offs in VSA pipelines that are not apparent from theoretical or operator-level comparisons alone.

Standard attribution heatmaps show where a vision-language model (VLM) focuses, but they do not reveal whether the recovered evidence is organized by the queried spatial relation or merely reflects image layout. To address this problem, we introduce CREG (Compass Relational Evidence Graph), a training-free diagnostic framework that converts token-level attribution into a reference-centered compass distribution and measures its directional alignment. CREG provides a shared directional readout across attribution methods and makes comparison with geometric controls explicit. Across three spatial-relation benchmarks, box-only geometry achieves Direction Alignment Error 28.4 to 34.4 degrees lower than the best current model-based attribution method on each dataset, leaving a substantial gap between attribution structure and simple target localization. To examine this gap, we apply a diagnostic battery including target intervention, reference-center randomization, and variance partition. Taken together, the results suggest that the directional structure recoverable from current attribution methods is limited and often mixed with image layout. We further find that higher task accuracy does not reliably coincide with better directional attribution: small-scale LoRA training and newer model generations can improve task accuracy while leaving Direction Alignment Error unchanged or worse. These findings characterize what current attribution methods reveal rather than the model's internal spatial representation. CREG provides a controlled protocol for testing whether improvements in spatial reasoning are accompanied by more directionally organized evidence.

End-to-end autonomous driving methods built on vision language models (VLMs) have undergone rapid development driven by their universal visual understanding and strong reasoning capabilities obtained from the large-scale pretraining. However, we find that current VLMs struggle to understand fine-grained 3D spatial relationships which is a fundamental requirement for systems interacting with the physical world. To address this issue, we propose SpaceDrive, a spatial-aware VLM-based driving framework that treats spatial information as explicit positional encodings (PEs) instead of textual digit tokens, enabling joint reasoning over semantic and spatial representations. SpaceDrive employs a universal positional encoder to all 3D coordinates derived from multi-view depth estimation, historical ego-states, and text prompts. These 3D PEs are first superimposed to augment the corresponding 2D visual tokens. Meanwhile, they serve as a task-agnostic coordinate representation, replacing the digit-wise numerical tokens as both inputs and outputs for the VLM. This mechanism enables the model to better index specific visual semantics in spatial reasoning and directly regress trajectory coordinates rather than generating digit-by-digit, thereby enhancing planning accuracy. Extensive experiments validate that SpaceDrive achieves state-of-the-art open-loop performance on the nuScenes dataset and the second-best Driving Score of 78.02 on the Bench2Drive closed-loop benchmark over existing VLM-based methods. Code is available at: https://github.com/zhenghao2519/SpaceDrive.

Embodied AI requires agents that perceive, act, and anticipate how actions reshape future world states. World models serve as internal simulators that capture environment dynamics, enabling forward and counterfactual rollouts to support perception, prediction, and decision making. This survey presents a unified framework for world models in embodied AI. Specifically, we formalize the problem setting and learning objectives, and propose a three-axis taxonomy encompassing: (1) Functionality, Decision-Coupled vs. General-Purpose; (2) Temporal Modeling, Sequential Simulation and Inference vs. Global Difference Prediction; (3) Spatial Representation, Global Latent Vector, Token Feature Sequence, Spatial Latent Grid, and Decomposed Rendering Representation. We systematize data resources and metrics across robotics, autonomous driving, and general video settings, covering pixel prediction quality, state-level understanding, and task performance. Furthermore, we offer a quantitative comparison of state-of-the-art models and distill key open challenges, including the scarcity of unified datasets and the need for evaluation metrics that assess physical consistency over pixel fidelity, the trade-off between model performance and the computational efficiency required for real-time control, and the core modeling difficulty of achieving long-horizon temporal consistency while mitigating error accumulation. Finally, we maintain a curated bibliography at https://github.com/Li-Zn-H/AwesomeWorldModels.