Spatial perception is a fundamental component of intelligence. While many studies highlight that large multimodal language models (MLMs) struggle to reason about space, they only test for static spatial reasoning, such as categorizing the relative positions of objects. Meanwhile, real-world deployment requires dynamic capabilities like perspective-taking and egocentric action recognition. As a roadmap to improving spatial intelligence, we introduce SAT, Spatial Aptitude Training, which goes beyond static relative object position questions to the more dynamic tasks. SAT contains 218K question-answer pairs for 22K synthetic scenes across a training and testing set. Generated using a photo-realistic physics engine, our dataset can be arbitrarily scaled and easily extended to new actions, scenes, and 3D assets. We find that even MLMs that perform relatively well on static questions struggle to accurately answer dynamic spatial questions. Further, we show that SAT instruction-tuning data improves not only dynamic spatial reasoning on SAT, but also zero-shot performance on existing real-image spatial benchmarks: $23\%$ on CVBench, $8\%$ on the harder BLINK benchmark, and $18\%$ on VSR. When instruction-tuned on SAT, our 13B model matches larger proprietary MLMs like GPT4-V and Gemini-3-1.0 in spatial reasoning. Our data/code is available at http://arijitray1993.github.io/SAT/ .

Deep learning models often struggle with generalization when deploying on real-world data, due to the common distributional shift to the training data. Test-time adaptation (TTA) is an emerging scheme used at inference time to address this issue. In TTA, models are adapted online at the same time when making predictions to test data. Neighbor-based approaches have gained attention recently, where prototype embeddings provide location information to alleviate the feature shift between training and testing data. However, due to their inherit limitation of simplicity, they often struggle to learn useful patterns and encounter performance degradation. To confront this challenge, we study the TTA problem from a geometric point of view. We first reveal that the underlying structure of neighbor-based methods aligns with the Voronoi Diagram, a classical computational geometry model for space partitioning. Building on this observation, we propose the Test-Time adjustment by Voronoi Diagram guidance (TTVD), a novel framework that leverages the benefits of this geometric property. Specifically, we explore two key structures: 1) Cluster-induced Voronoi Diagram (CIVD): This integrates the joint contribution of self-supervision and entropy-based methods to provide richer information. 2) Power Diagram (PD): A generalized version of the Voronoi Diagram that refines partitions by assigning weights to each Voronoi cell. Our experiments under rigid, peer-reviewed settings on CIFAR-10-C, CIFAR-100-C, ImageNet-C, and ImageNet-R shows that TTVD achieves remarkable improvements compared to state-of-the-art methods. Moreover, extensive experimental results also explore the effects of batch size and class imbalance, which are two scenarios commonly encountered in real-world applications. These analyses further validate the robustness and adaptability of our proposed framework.

In warehousing systems, to enhance logistical efficiency amid surging demand volumes, much focus is placed on how to reasonably allocate tasks to robots. However, the robots labor is still inevitably wasted to some extent. In response to this, we propose a pre-scheduling enhanced warehousing framework that predicts task flow and acts in advance. It consists of task flow prediction and hybrid tasks allocation. For task prediction, we notice that it is possible to provide a spatio-temporal representation of task flow, so we introduce a periodicity-decoupled mechanism tailored for the generation patterns of aggregated orders, and then further extract spatial features of task distribution with novel combination of graph structures. In hybrid tasks allocation, we consider the known tasks and predicted future tasks simultaneously and optimize the allocation dynamically. In addition, we consider factors such as predicted task uncertainty and sector-level efficiency evaluation in warehousing to realize more balanced and rational allocations. We validate our task prediction model across actual datasets derived from real factories, achieving SOTA performance. Furthermore, we implement our compelte scheduling system in a real-world robotic warehouse for months of lifelong validation, demonstrating large improvements in key metrics of warehousing, such as empty running rate, by more than 50%.

Surgical workflow anticipation is the task of predicting the timing of relevant surgical events from live video data, which is critical in Robotic-Assisted Surgery (RAS). Accurate predictions require the use of spatial information to model surgical interactions. However, current methods focus solely on surgical instruments, assume static interactions between instruments, and only anticipate surgical events within a fixed time horizon. To address these challenges, we propose an adaptive graph learning framework for surgical workflow anticipation based on a novel spatial representation, featuring three key innovations. First, we introduce a new representation of spatial information based on bounding boxes of surgical instruments and targets, including their detection confidence levels. These are trained on additional annotations we provide for two benchmark datasets. Second, we design an adaptive graph learning method to capture dynamic interactions. Third, we develop a multi-horizon objective that balances learning objectives for different time horizons, allowing for unconstrained predictions. Evaluations on two benchmarks reveal superior performance in short-to-mid-term anticipation, with an error reduction of approximately 3% for surgical phase anticipation and 9% for remaining surgical duration anticipation. These performance improvements demonstrate the effectiveness of our method and highlight its potential for enhancing preparation and coordination within the RAS team. This can improve surgical safety and the efficiency of operating room usage.

This paper addresses the challenge of spectral-spatial feature extraction for hyperspectral image classification by introducing a novel tensor-based framework. The proposed approach incorporates circular convolution into a tensor structure to effectively capture and integrate both spectral and spatial information. Building upon this framework, the traditional Principal Component Analysis (PCA) technique is extended to its tensor-based counterpart, referred to as Tensor Principal Component Analysis (TPCA). The proposed TPCA method leverages the inherent multi-dimensional structure of hyperspectral data, thereby enabling more effective feature representation. Experimental results on benchmark hyperspectral datasets demonstrate that classification models using TPCA features consistently outperform those using traditional PCA and other state-of-the-art techniques. These findings highlight the potential of the tensor-based framework in advancing hyperspectral image analysis.

While imitation learning (IL) offers a promising framework for teaching robots various behaviors, learning complex tasks remains challenging. Existing IL policies struggle to generalize effectively across visual and spatial variations even for simple tasks. In this work, we introduce SPHINX: Salient Point-based Hybrid ImitatioN and eXecution, a flexible IL policy that leverages multimodal observations (point clouds and wrist images), along with a hybrid action space of low-frequency, sparse waypoints and high-frequency, dense end effector movements. Given 3D point cloud observations, SPHINX learns to infer task-relevant points within a point cloud, or salient points, which support spatial generalization by focusing on semantically meaningful features. These salient points serve as anchor points to predict waypoints for long-range movement, such as reaching target poses in free-space. Once near a salient point, SPHINX learns to switch to predicting dense end-effector movements given close-up wrist images for precise phases of a task. By exploiting the strengths of different input modalities and action representations for different manipulation phases, SPHINX tackles complex tasks in a sample-efficient, generalizable manner. Our method achieves 86.7% success across 4 real-world and 2 simulated tasks, outperforming the next best state-of-the-art IL baseline by 41.1% on average across 440 real world trials. SPHINX additionally generalizes to novel viewpoints, visual distractors, spatial arrangements, and execution speeds with a 1.7x speedup over the most competitive baseline. Our website (http://sphinx-manip.github.io) provides open-sourced code for data collection, training, and evaluation, along with supplementary videos.

Robotic perception is emerging as a crucial technology for navigation aids, particularly benefiting individuals with visual impairments through sonification. This paper presents a novel mapping framework that accurately represents spatial geometry for sonification, transforming physical spaces into auditory experiences. By leveraging depth sensors, we convert incrementally built 3D scenes into a compact 360-degree representation based on angular and distance information, aligning with human auditory perception. Our proposed mapping framework utilises a sensor-centric structure, maintaining 2D circular or 3D cylindrical representations, and employs the VDB-GPDF for efficient online mapping. We introduce two sonification modes-circular ranging and circular ranging of objects-along with real-time user control over auditory filters. Incorporating binaural room impulse responses, our framework provides perceptually robust auditory feedback. Quantitative and qualitative evaluations demonstrate superior performance in accuracy, coverage, and timing compared to existing approaches, with effective handling of dynamic objects. The accompanying video showcases the practical application of spatial sonification in room-like environments.

Urban flow prediction is a classic spatial-temporal forecasting task that estimates the amount of future traffic flow for a given location. Though models represented by Spatial-Temporal Graph Neural Networks (STGNNs) have established themselves as capable predictors, they tend to suffer from distribution shifts that are common with the urban flow data due to the dynamics and unpredictability of spatial-temporal events. Unfortunately, in spatial-temporal applications, the dynamic environments can hardly be quantified via a fixed number of parameters, whereas learning time- and location-specific environments can quickly become computationally prohibitive. In this paper, we propose a novel framework named Memory-enhanced Invariant Prompt learning (MIP) for urban flow prediction under constant distribution shifts. Specifically, MIP is equipped with a learnable memory bank that is trained to memorize the causal features within the spatial-temporal graph. By querying a trainable memory bank that stores the causal features, we adaptively extract invariant and variant prompts (i.e., patterns) for a given location at every time step. Then, instead of intervening the raw data based on simulated environments, we directly perform intervention on variant prompts across space and time. With the intervened variant prompts in place, we use invariant learning to minimize the variance of predictions, so as to ensure that the predictions are only made with invariant features. With extensive comparative experiments on two public urban flow datasets, we thoroughly demonstrate the robustness of MIP against OOD data.

Under a set of assumptions on a family of submanifolds $\subset {\mathbb R}^D$, we derive a series of geometric properties that remain valid after finite-dimensional and almost isometric Diffusion Maps (DM), including almost uniform density, finite polynomial approximation and local reach. Leveraging these properties, we establish rigorous bounds on the embedding errors introduced by the DM algorithm is $O\left((\frac{\log n}{n})^{\frac{1}{8d+16}}\right)$. These results offer a solid theoretical foundation for understanding the performance and reliability of DM in practical applications.

Recent advances in diffusion models have revolutionized 2D and 3D content creation, yet generating photorealistic dynamic 4D scenes remains a significant challenge. Existing dynamic 4D generation methods typically rely on distilling knowledge from pre-trained 3D generative models, often fine-tuned on synthetic object datasets. Consequently, the resulting scenes tend to be object-centric and lack photorealism. While text-to-video models can generate more realistic scenes with motion, they often struggle with spatial understanding and provide limited control over camera viewpoints during rendering. To address these limitations, we present PaintScene4D, a novel text-to-4D scene generation framework that departs from conventional multi-view generative models in favor of a streamlined architecture that harnesses video generative models trained on diverse real-world datasets. Our method first generates a reference video using a video generation model, and then employs a strategic camera array selection for rendering. We apply a progressive warping and inpainting technique to ensure both spatial and temporal consistency across multiple viewpoints. Finally, we optimize multi-view images using a dynamic renderer, enabling flexible camera control based on user preferences. Adopting a training-free architecture, our PaintScene4D efficiently produces realistic 4D scenes that can be viewed from arbitrary trajectories. The code will be made publicly available. Our project page is at https://paintscene4d.github.io/