Spatial reasoning is a crucial component of both biological and artificial intelligence. In this work, we present a comprehensive study of the capability of current state-of-the-art large language models (LLMs) on spatial reasoning. To support our study, we created and contribute a novel Spatial Reasoning Characterization (SpaRC) framework and Spatial Reasoning Paths (SpaRP) datasets, to enable an in-depth understanding of the spatial relations and compositions as well as the usefulness of spatial reasoning chains. We found that all the state-of-the-art LLMs do not perform well on the datasets -- their performances are consistently low across different setups. The spatial reasoning capability improves substantially as model sizes scale up. Finetuning both large language models (e.g., Llama-2-70B) and smaller ones (e.g., Llama-2-13B) can significantly improve their F1-scores by 7--32 absolute points. We also found that the top proprietary LLMs still significantly outperform their open-source counterparts in topological spatial understanding and reasoning.

Road network representation learning aims to learn compressed and effective vectorized representations for road segments that are applicable to numerous tasks. In this paper, we identify the limitations of existing methods, particularly their overemphasis on the distance effect as outlined in the First Law of Geography. In response, we propose to endow road network representation with the principles of the recent Third Law of Geography. To this end, we propose a novel graph contrastive learning framework that employs geographic configuration-aware graph augmentation and spectral negative sampling, ensuring that road segments with similar geographic configurations yield similar representations, and vice versa, aligning with the principles stated in the Third Law. The framework further fuses the Third Law with the First Law through a dual contrastive learning objective to effectively balance the implications of both laws. We evaluate our framework on two real-world datasets across three downstream tasks. The results show that the integration of the Third Law significantly improves the performance of road segment representations in downstream tasks.

While there is no replacement for the learned expertise, devotion, and social benefits of a guide dog, there are cases in which a robot navigation assistant could be helpful for individuals with blindness or low vision (BLV). This study investigated the potential for an industrial agile robot to perform guided navigation tasks. We developed two interface prototypes that allowed for spatial information between a human-robot pair: a voice-based app and a flexible, responsive handle. The participants (n=21) completed simple navigation tasks and a post-study survey about the prototype functionality and their trust in the robot. All participants successfully completed the navigation tasks and demonstrated the interface prototypes were able to pass spatial information between the human and the robot. Future work will include expanding the voice-based app to allow the robot to communicate obstacles to the handler and adding haptic signals to the handle design.

Exposure assessment is fundamental to air pollution cohort studies. The objective is to predict air pollution exposures for study subjects at locations without data in order to optimize our ability to learn about health effects of air pollution. In addition to generating accurate predictions to minimize exposure measurement error, understanding the mechanism captured by the model is another crucial aspect that may not always be straightforward due to the complex nature of machine learning methods, as well as the lack of unifying notions of variable importance. This is further complicated in air pollution modeling by the presence of spatial correlation. We tackle these challenges in two datasets: sulfur (S) from regulatory United States national PM2.5 sub-species data and ultrafine particles (UFP) from a new Seattle-area traffic-related air pollution dataset. Our key contribution is a leave-one-out approach for variable importance that leads to interpretable and comparable measures for a broad class of models with separable mean and covariance components. We illustrate our approach with several spatial machine learning models, and it clearly highlights the difference in model mechanisms, even for those producing similar predictions. We leverage insights from this variable importance measure to assess the relative utilities of two exposure models for S and UFP that have similar out-of-sample prediction accuracies but appear to draw on different types of spatial information to make predictions.

Topological Data Analysis (TDA) allows us to extract powerful topological and higher-order information on the global shape of a data set or point cloud. Tools like Persistent Homology or the Euler Transform give a single complex description of the global structure of the point cloud. However, common machine learning applications like classification require point-level information and features to be available. In this paper, we bridge this gap and propose a novel method to extract node-level topological features from complex point clouds using discrete variants of concepts from algebraic topology and differential geometry. We verify the effectiveness of these topological point features (TOPF) on both synthetic and real-world data and study their robustness under noise.

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

In computer vision, keypoint detection is a fundamental task, with applications spanning from Ideally, a good feature detector should provide keypoints robotics to image retrieval; however, existing with the following desirable properties: high repeatability learning-based methods suffer from scale dependency, (i.e., consistent across image pairs) and scale-invariance, and lack flexibility. This paper introduces while being robust to noise and distortion (Ghahremani et al., a novel approach that leverages Morse theory and 2020; Revaud et al., 2019; Lowe, 2004). Scale-Space theory persistent homology, powerful tools rooted in algebraic (Lindeberg, 1994) provides a formulation of the concept topology. We propose a novel loss function of keypoint that guarantees the properties mentioned above based on the recent introduction of a notion (Lindeberg, 1994; Lowe, 2004; Ghahremani et al., 2020), of subgradient in persistent homology, paving the and it operates by building a scale-space feature pyramid way toward topological learning. Our detector, from the image, in which keypoints are detected as local MorseDet, is the first topology-based learning extrema. Many classical handcrafted detectors exploit this model for feature detection, which achieves competitive theoretical framework (Mikolajczyk & Schmid, 2004; Bay performance in keypoint repeatability and et al., 2006), the most popular of which is SIFT (Lowe, introduces a principled and theoretically robust 2004).

Cognitive Language Processing (CLP), situated at the intersection of Natural Language Processing (NLP) and cognitive science, plays a progressively pivotal role in the domains of artificial intelligence, cognitive intelligence, and brain science. Among the essential areas of investigation in CLP, Cognitive Signal Decoding (CSD) has made remarkable achievements, yet there still exist challenges related to insufficient global dynamic representation capability and deficiencies in multi-domain feature integration. In this paper, we introduce a novel paradigm for CLP referred to as Disentangled Frequency-Spatial-Temporal Attention(D-FaST). Specifically, we present an novel cognitive signal decoder that operates on disentangled frequency-space-time domain attention. This decoder encompasses three key components: frequency domain feature extraction employing multi-view attention, spatial domain feature extraction utilizing dynamic brain connection graph attention, and temporal feature extraction relying on local time sliding window attention. These components are integrated within a novel disentangled framework. Additionally, to encourage advancements in this field, we have created a new CLP dataset, MNRED. Subsequently, we conducted an extensive series of experiments, evaluating D-FaST's performance on MNRED, as well as on publicly available datasets including ZuCo, BCIC IV-2A, and BCIC IV-2B. Our experimental results demonstrate that D-FaST outperforms existing methods significantly on both our datasets and traditional CSD datasets including establishing a state-of-the-art accuracy score 78.72% on MNRED, pushing the accuracy score on ZuCo to 78.35%, accuracy score on BCIC IV-2A to 74.85% and accuracy score on BCIC IV-2B to 76.81%.

Large foundation models have recently emerged as a prominent focus of interest, attaining superior performance in widespread scenarios. Due to the scarcity of 3D data, many efforts have been made to adapt pre-trained transformers from vision to 3D domains. However, such 2D-to-3D approaches are still limited, due to the potential loss of spatial geometries and high computation cost. More importantly, their frameworks are mainly designed for 2D models, lacking a general any-to-3D paradigm. In this paper, we introduce Any2Point, a parameter-efficient method to empower any-modality large models (vision, language, audio) for 3D understanding. Given a frozen transformer from any source modality, we propose a 3D-to-any (1D or 2D) virtual projection strategy that correlates the input 3D points to the original 1D or 2D positions within the source modality. This mechanism enables us to assign each 3D token with a positional encoding paired with the pre-trained model, which avoids 3D geometry loss caused by the true projection and better motivates the transformer for 3D learning with 1D/2D positional priors. Then, within each transformer block, we insert an any-to-3D guided adapter module for parameter-efficient fine-tuning. The adapter incorporates prior spatial knowledge from the source modality to guide the local feature aggregation of 3D tokens, compelling the semantic adaption of any-modality transformers. We conduct extensive experiments to showcase the effectiveness and efficiency of our method. Code and models are released at https://github.com/Ivan-Tang-3D/Any2Point.

Intuitively, there is a relation between measures of spatial dependence and information theoretical measures of entropy. For instance, we can provide an intuition of why spatial data is special by stating that, on average, spatial data samples contain less than expected information. Similarly, spatial data, e.g., remotely sensed imagery, that is easy to compress is also likely to show significant spatial autocorrelation. Formulating our (highly specific) core concepts of spatial information theory in the widely used language of information theory opens new perspectives on their differences and similarities and also fosters cross-disciplinary collaboration, e.g., with the broader AI/ML communities. Interestingly, however, this intuitive relation is challenging to formalize and generalize, leading prior work to rely mostly on experimental results, e.g., for describing landscape patterns. In this work, we will explore the information theoretical roots of spatial autocorrelation, more specifically Moran's I, through the lens of self-information (also known as surprisal) and provide both formal proofs and experiments.