In this section we provide visualizations to better understand the statistical power of our test, and to verify the claims in Section 2.3. We can see that R constructed from outlier images generally include a higher proportion of unexplained semantic information: comparing the CelebA residual in Fig.3(a) (second column) where the model is trained on CIFAR-10, to Fig.3(b) (first column) where CelebA is inlier, we can see that the facial structure in CelebA residual is more evident when the model is trained on CIFAR-10. Similarly, comparing the CIFAR-10 residual from both models, we can see that the structure of the vehicle (e.g. As the residual sequences constructed from outliers tend to have more natural image-like structures, they will also have stronger spatial autocorrelations, compared with residuals from inlier samples that should in principle be white noise. Note that while the residual sequences constructed from inliers also contain unexplained semantic information, this is due to estimation error of the deep AR model, and should not happen should we have access to the ground truth model, as we have shown in Section 2.2.

It is increasingly important to generate synthetic populations with explicit coordinates rather than coarse geographic areas, yet no established methods exist to achieve this. One reason is that latitude and longitude differ from other continuous variables, exhibiting large empty spaces and highly uneven densities. To address this, we propose a population synthesis algorithm that first maps spatial coordinates into a more regular latent space using Normalizing Flows (NF), and then combines them with other features in a Variational Autoencoder (VAE) to generate synthetic populations. This approach also learns the joint distribution between spatial and non-spatial features, exploiting spatial autocorrelations. We demonstrate the method by generating synthetic homes with the same statistical properties of real homes in 121 datasets, corresponding to diverse geographies. We further propose an evaluation framework that measures both spatial accuracy and practical utility, while ensuring privacy preservation. Our results show that the NF+VAE architecture outperforms popular benchmarks, including copula-based methods and uniform allocation within geographic areas. The ability to generate geolocated synthetic populations at fine spatial resolution opens the door to applications requiring detailed geography, from household responses to floods, to epidemic spread, evacuation planning, and transport modeling.

Increasing flood frequency and severity due to climate change threatens infrastructure and demands improved susceptibility mapping techniques. While traditional machine learning (ML) approaches are widely used, they struggle to capture spatial dependencies and poor boundary delineation between susceptibility classes. This study introduces the first application of a graph transformer (GT) architecture for flood susceptibility mapping to the flood-prone French Riviera (e.g., 2020 Storm Alex) using topography, hydrology, geography, and environmental data. GT incorporates watershed topology using Laplacian positional encoders (PEs) and attention mechanisms. The developed GT model has an AUC-ROC (0.9739), slightly lower than XGBoost (0.9853). However, the GT model demonstrated better clustering and delineation with a higher Moran's I value (0.6119) compared to the random forest (0.5775) and XGBoost (0.5311) with p-value lower than 0.0001. Feature importance revealed a striking consistency across models, with elevation, slope, distance to channel, and convergence index being the critical factors. Dimensionality reduction on Laplacian PEs revealed partial clusters, indicating they could capture spatial information; however, their importance was lower than flood factors. Since climate and land use changes aggravate flood risk, susceptibility maps are developed for the 2050 year under different Representative Concentration Pathways (RCPs) and railway track vulnerability is assessed. All RCP scenarios revealed increased area across susceptibility classes, except for the very low category. RCP 8.5 projections indicate that 17.46% of the watershed area and 54% of railway length fall within very-high susceptible zones, compared to 6.19% and 35.61%, respectively, under current conditions. The developed maps can be integrated into a multi-hazard framework.

This paper quantitatively investigates the crash severity of Autonomous Vehicles (AVs) with spatially localized machine learning and macroscopic measures of the urban built environment. Extending beyond the microscopic effects of individual infrastructure elements, we focus on the city-scale land use and behavioral patterns, while addressing spatial heterogeneity and spatial autocorrelation. We implemented a spatially localized machine learning technique called Geographical Random Forest (GRF) on the California AV collision dataset. Analyzing multiple urban measures, including points of interest, building footprint, and land use, we built a GRF model and visualized it as a crash severity risk map of San Francisco. This paper presents three findings. First, spatially localized machine learning outperformed regular machine learning in predicting AV crash severity. The bias-variance tradeoff was evident as we adjusted the localization weight hyperparameter. Second, land use was the most important predictor, compared to intersections, building footprints, public transit stops, and Points Of Interest (POIs). Third, AV crashes were more likely to result in low-severity incidents in city center areas with greater diversity and commercial activities, than in residential neighborhoods. Residential land use is likely associated with higher severity due to human behavior and less restrictive environments. Counterintuitively, residential areas were associated with higher crash severity, compared to more complex areas such as commercial and mixed-use areas. When robotaxi operators train their AV systems, it is recommended to: (1) consider where their fleet operates and make localized algorithms for their perception system, and (2) design safety measures specific to residential neighborhoods, such as slower driving speeds and more alert sensors.

Large Language Models (LLMs) have demonstrated unprecedented capabilities across various natural language processing tasks. Their ability to process and generate viable text and code has made them ubiquitous in many fields, while their deployment as knowledge bases and "reasoning" tools remains an area of ongoing research. In geography, a growing body of literature has been focusing on evaluating LLMs' geographical knowledge and their ability to perform spatial reasoning. However, very little is still known about the internal functioning of these models, especially about how they process geographical information. In this chapter, we establish a novel framework for the study of geospatial mechanistic interpretability - using spatial analysis to reverse engineer how LLMs handle geographical information. Our aim is to advance our understanding of the internal representations that these complex models generate while processing geographical information - what one might call "how LLMs think about geographic information" if such phrasing was not an undue anthropomorphism. We first outline the use of probing in revealing internal structures within LLMs. We then introduce the field of mechanistic interpretability, discussing the superposition hypothesis and the role of sparse autoencoders in disentangling polysemantic internal representations of LLMs into more interpretable, monosemantic features. In our experiments, we use spatial autocorrelation to show how features obtained for placenames display spatial patterns related to their geographic location and can thus be interpreted geospatially, providing insights into how these models process geographical information. We conclude by discussing how our framework can help shape the study and use of foundation models in geography.

Moran Eigenvector Spatial Filtering (ESF) approaches have shown promise in accounting for spatial effects in statistical models. Can this extend to machine learning? This paper examines the effectiveness of using Moran Eigenvectors as additional spatial features in machine learning models. We generate synthetic datasets with known processes involving spatially varying and nonlinear effects across two different geometries. Moran Eigenvectors calculated from different spatial weights matrices, with and without a priori eigenvector selection, are tested. We assess the performance of popular machine learning models, including Random Forests, LightGBM, XGBoost, and TabNet, and benchmark their accuracies in terms of cross-validated R2 values against models that use only coordinates as features. We also extract coefficients and functions from the models using GeoShapley and compare them with the true processes. Results show that machine learning models using only location coordinates achieve better accuracies than eigenvector-based approaches across various experiments and datasets. Furthermore, we discuss that while these findings are relevant for spatial processes that exhibit positive spatial autocorrelation, they do not necessarily apply when modeling network autocorrelation and cases with negative spatial autocorrelation, where Moran Eigenvectors would still be useful.

Objectives: Our research adopts computational techniques to analyze disease outbreaks weekly over a large geographic area while maintaining local-level analysis by incorporating relevant high-spatial resolution cultural and environmental datasets. The abundance of data about disease outbreaks gives scientists an excellent opportunity to uncover patterns in disease spread and make future predictions. However, data over a sizeable geographic area quickly outpace human cognition. Our study area covers a significant portion of the African continent (about 17,885,000 km2). The data size makes computational analysis vital to assist human decision-makers. Methods: We first applied global and local spatial autocorrelation for malaria, cholera, meningitis, and yellow fever case counts. We then used machine learning to predict the weekly presence of these diseases in the second-level administrative district. Lastly, we used machine learning feature importance methods on the variables that affect spread. Results: Our spatial autocorrelation results show that geographic nearness is critical but varies in effect and space. Moreover, we identified many interesting hot and cold spots and spatial outliers. The machine learning model infers a binary class of cases or none with the best F1 score of 0.96 for malaria. Machine learning feature importance uncovered critical cultural and environmental factors affecting outbreaks and variations between diseases. Conclusions: Our study shows that data analytics and machine learning are vital to understanding and monitoring disease outbreaks locally across vast areas. The speed at which these methods produce insights can be critical during epidemics and emergencies.

Prediction problems in geographic information science and transportation are often motivated by the possibility to enhance operational efficiency and thereby reduce emissions. Examples range from predicting car sharing demand for relocation planning to forecasting traffic congestion for navigation purposes. However, conventional accuracy metrics ignore the spatial distribution of the errors, despite its relevance for operations. Here, we put forward a spatially aware evaluation metric and loss function based on Optimal Transport (OT). Our framework leverages partial OT and can minimize relocation costs in any spatial prediction problem. We showcase the advantages of OT-based evaluation over conventional metrics and further demonstrate the application of an OT loss function for improving forecasts of bike sharing demand and charging station occupancy.

Neurons in the brain are spatially organized such that neighbors on tissue often exhibit similar response profiles. In the human language system, experimental studies have observed clusters for syntactic and semantic categories, but the mechanisms underlying this functional organization remain unclear. Here, building on work from the vision literature, we develop TopoLM, a transformer language model with an explicit two-dimensional spatial representation of model units. By combining a next-token prediction objective with a spatial smoothness loss, representations in this model assemble into clusters that correspond to semantically interpretable groupings of text and closely match the functional organization in the brain's language system. TopoLM successfully predicts the emergence of the spatio-functional organization of a cortical language system as well as the organization of functional clusters selective for fine-grained linguistic features empirically observed in human cortex. Our results suggest that the functional organization of the human language system is driven by a unified spatial objective, and provide a functionally and spatially aligned model of language processing in the brain.

Over the past few years, vision transformers (ViTs) have consistently demonstrated remarkable performance across various visual recognition tasks. However, attempts to enhance their robustness have yielded limited success, mainly focusing on different training strategies, input patch augmentation, or network structural enhancements. These approaches often involve extensive training and fine-tuning, which are time-consuming and resource-intensive. To tackle these obstacles, we introduce a novel approach named Spatial Autocorrelation Token Analysis (SATA). By harnessing spatial relationships between token features, SATA enhances both the representational capacity and robustness of ViT models. This is achieved through the analysis and grouping of tokens according to their spatial autocorrelation scores prior to their input into the Feed-Forward Network (FFN) block of the self-attention mechanism. Importantly, SATA seamlessly integrates into existing pre-trained ViT baselines without requiring retraining or additional fine-tuning, while concurrently improving efficiency by reducing the computational load of the FFN units. Experimental results show that the baseline ViTs enhanced with SATA not only achieve a new state-of-the-art top-1 accuracy on ImageNet-1K image classification (94.9%) but also establish new state-of-the-art performance across multiple robustness benchmarks, including ImageNet-A (top-1=63.6%), ImageNet-R (top-1=79.2%), and ImageNet-C (mCE=13.6%), all without requiring additional training or fine-tuning of baseline models.