Evaluating foundation models for crystallographic reasoning requires benchmarks that isolate generalization behavior while enforcing physical constraints. This work introduces a multiscale multicrystal dataset with two physically grounded evaluation protocols to stress-test multimodal generative models. The Spatial-Exclusion benchmark withholds all supercells of a given radius from a diverse dataset, enabling controlled assessments of spatial interpolation and extrapolation. The Compositional-Exclusion benchmark omits all samples of a specific chemical composition, probing generalization across stoichiometries. Nine vision--language foundation models are prompted with crystallographic images and textual context to generate structural annotations. Responses are evaluated via (i) relative errors in lattice parameters and density, (ii) a physics-consistency index penalizing volumetric violations, and (iii) a hallucination score capturing geometric outliers and invalid space-group predictions. These benchmarks establish a reproducible, physically informed framework for assessing generalization, consistency, and reliability in large-scale multimodal models. Dataset and code are available at https://github.com/KurbanIntelligenceLab/StressTestingMMFMinCR.
Evaluating house prices is crucial for various stakeholders, including homeowners, investors, and policymakers. However, traditional spatial interpolation methods have limitations in capturing the complex spatial relationships that affect property values. To address these challenges, we have developed a new method called Multi-Head Gated Attention for spatial interpolation. Our approach builds upon attention-based interpolation models and incorporates multiple attention heads and gating mechanisms to capture spatial dependencies and contextual information better. Importantly, our model produces embeddings that reduce the dimensionality of the data, enabling simpler models like linear regression to outperform complex ensembling models. We conducted extensive experiments to compare our model with baseline methods and the original attention-based interpolation model. The results show a significant improvement in the accuracy of house price predictions, validating the effectiveness of our approach. This research advances the field of spatial interpolation and provides a robust tool for more precise house price evaluation. Our GitHub repository.contains the data and code for all datasets, which are available for researchers and practitioners interested in replicating or building upon our work.
Conditional diffusion models can create unseen images in various settings, aiding image interpolation. Interpolation in latent spaces is well-studied, but interpolation with specific conditions like text or poses is less understood. Simple approaches, such as linear interpolation in the space of conditions, often result in images that lack consistency, smoothness, and fidelity. To that end, we introduce a novel training-free technique named Attention Interpolation via Diffusion (AID). Our key contributions include 1) proposing an inner/outer interpolated attention layer; 2) fusing the interpolated attention with self-attention to boost fidelity; and 3) applying beta distribution to selection to increase smoothness. We also present a variant, Prompt-guided Attention Interpolation via Diffusion (PAID), that considers interpolation as a condition-dependent generative process. This method enables the creation of new images with greater consistency, smoothness, and efficiency, and offers control over the exact path of interpolation. Our approach demonstrates effectiveness for conceptual and spatial interpolation. Code and demo are available at https://github.com/QY-H00/attention-interpolation-diffusion.
Head-related transfer functions (HRTFs) are important for immersive audio, and their spatial interpolation has been studied to upsample finite measurements. Recently, neural fields (NFs) which map from sound source direction to HRTF have gained attention. Existing NF-based methods focused on estimating the magnitude of the HRTF from a given sound source direction, and the magnitude is converted to a finite impulse response (FIR) filter. We propose the neural infinite impulse response filter field (NIIRF) method that instead estimates the coefficients of cascaded IIR filters. IIR filters mimic the modal nature of HRTFs, thus needing fewer coefficients to approximate them well compared to FIR filters. We find that our method can match the performance of existing NF-based methods on multiple datasets, even outperforming them when measurements are sparse. We also explore approaches to personalize the NF to a subject and experimentally find low-rank adaptation to be effective.
The acquisition of accurate rainfall distribution in space is an important task in hydrological analysis and natural disaster pre-warning. However, it is impossible to install rain gauges on every corner. Spatial interpolation is a common way to infer rainfall distribution based on available raingauge data. However, the existing works rely on some unrealistic pre-settings to capture spatial correlations, which limits their performance in real scenarios. To tackle this issue, we propose the SSIN, which is a novel data-driven self-supervised learning framework for rainfall spatial interpolation by mining latent spatial patterns from historical observation data. Inspired by the Cloze task and BERT, we fully consider the characteristics of spatial interpolation and design the SpaFormer model based on the Transformer architecture as the core of SSIN. Our main idea is: by constructing rich self-supervision signals via random masking, SpaFormer can learn informative embeddings for raw data and then adaptively model spatial correlations based on rainfall spatial context. Extensive experiments on two real-world raingauge datasets show that our method outperforms the state-of-the-art solutions. In addition, we take traffic spatial interpolation as another use case to further explore the performance of our method, and SpaFormer achieves the best performance on one large real-world traffic dataset, which further confirms the effectiveness and generality of our method.
Despite advancements in real estate appraisal methods, this study primarily focuses on two pivotal challenges. Firstly, we explore the often-underestimated impact of Points of Interest (POI) on property values, emphasizing the necessity for a comprehensive, data-driven approach to feature selection. Secondly, we integrate road-network-based Areal Embedding to enhance spatial understanding for real estate appraisal. We first propose a revised method for POI feature extraction, and discuss the impact of each POI for house price appraisal. Then we present the Areal embedding-enabled Masked Multihead Attention-based Spatial Interpolation for House Price Prediction (AMMASI) model, an improvement upon the existing ASI model, which leverages masked multi-head attention on geographic neighbor houses and similar-featured houses. Our model outperforms current baselines and also offers promising avenues for future optimization in real estate appraisal methodologies.
Spatial interpolation is a class of estimation problems where locations with known values are used to estimate values at other locations, with an emphasis on harnessing spatial locality and trends. Traditional Kriging methods have strong Gaussian assumptions, and as a result, often fail to capture complexities within the data. Inspired by the recent progress of graph neural networks, we introduce Kriging Convolutional Networks (KCN), a method of combining the advantages of Graph Convolutional Networks (GCN) and Kriging. Compared to standard GCNs, KCNs make direct use of neighboring observations when generating predictions. KCNs also contain the Kriging method as a specific configuration. We further improve the model's performance by adding attention. Empirically, we show that this model outperforms GCNs and Kriging in several applications. The implementation of KCN using PyTorch is publicized at the GitHub repository: https://github.com/tufts-ml/kcn-torch.
We propose a novel nonparametric regression framework subject to the positive definiteness constraint. It offers a highly modular approach for estimating covariance functions of stationary processes. Our method can impose positive definiteness, as well as isotropy and monotonicity, on the estimators, and its hyperparameters can be decided using cross validation. We define our estimators by taking integral transforms of kernel-based distribution surrogates. We then use the iterated density estimation evolutionary algorithm, a variant of estimation of distribution algorithms, to fit the estimators. We also extend our method to estimate covariance functions for point-referenced data. Compared to alternative approaches, our method provides more reliable estimates for long-range dependence. Several numerical studies are performed to demonstrate the efficacy and performance of our method. Also, we illustrate our method using precipitation data from the Spatial Interpolation Comparison 97 project.
Spatial autocorrelation and spatial heterogeneity widely exist in spatial data, which make the traditional machine learning model perform badly. Spatial domain generalization is a spatial extension of domain generalization, which can generalize to unseen spatial domains in continuous 2D space. Specifically, it learns a model under varying data distributions that generalizes to unseen domains. Although tremendous success has been achieved in domain generalization, there exist very few works on spatial domain generalization. The advancement of this area is challenged by: 1) Difficulty in characterizing spatial heterogeneity, and 2) Difficulty in obtaining predictive models for unseen locations without training data. To address these challenges, this paper proposes a generic framework for spatial domain generalization. Specifically, We develop the spatial interpolation graph neural network that handles spatial data as a graph and learns the spatial embedding on each node and their relationships. The spatial interpolation graph neural network infers the spatial embedding of an unseen location during the test phase. Then the spatial embedding of the target location is used to decode the parameters of the downstream-task model directly on the target location. Finally, extensive experiments on thirteen real-world datasets demonstrate the proposed method's strength.
It is challenging to annotate large-scale datasets for supervised video shadow detection methods. Using a model trained on labeled images to the video frames directly may lead to high generalization error and temporal inconsistent results. In this paper, we address these challenges by proposing a Spatio-Temporal Interpolation Consistency Training (STICT) framework to rationally feed the unlabeled video frames together with the labeled images into an image shadow detection network training. Specifically, we propose the Spatial and Temporal ICT, in which we define two new interpolation schemes, \textit{i.e.}, the spatial interpolation and the temporal interpolation. We then derive the spatial and temporal interpolation consistency constraints accordingly for enhancing generalization in the pixel-wise classification task and for encouraging temporal consistent predictions, respectively. In addition, we design a Scale-Aware Network for multi-scale shadow knowledge learning in images, and propose a scale-consistency constraint to minimize the discrepancy among the predictions at different scales. Our proposed approach is extensively validated on the ViSha dataset and a self-annotated dataset. Experimental results show that, even without video labels, our approach is better than most state of the art supervised, semi-supervised or unsupervised image/video shadow detection methods and other methods in related tasks. Code and dataset are available at \url{https://github.com/yihong-97/STICT}.
The weather phenomenon of frost poses great threats to agriculture. As recent frost prediction methods are based on on-site historical data and sensors, extra development and deployment time are required for data collection in any new site. The aim of this article is to eliminate the dependency on on-site historical data and sensors for frost prediction methods. In this article, a frost prediction method based on spatial interpolation is proposed. The models use climate data from existing weather stations, digital elevation models surveys, and normalized difference vegetation index data to estimate a target site's next hour minimum temperature. The proposed method utilizes ensemble learning to increase the model accuracy. Climate datasets are obtained from 75 weather stations across New South Wales and Australian Capital Territory areas of Australia. The results show that the proposed method reached a detection rate up to 92.55%.
Graph neural networks (GNNs) provide a powerful and scalable solution for modeling continuous spatial data. However, they often rely on Euclidean distances to construct the input graphs. This assumption can be improbable in many real-world settings, where the spatial structure is more complex and explicitly non-Euclidean (e.g., road networks). Here, we propose PE-GNN, a new framework that incorporates spatial context and correlation explicitly into the models. Building on recent advances in geospatial auxiliary task learning and semantic spatial embeddings, our proposed method (1) learns a context-aware vector encoding of the geographic coordinates and (2) predicts spatial autocorrelation in the data in parallel with the main task. On spatial interpolation and regression tasks, we show the effectiveness of our approach, improving performance over different state-of-the-art GNN approaches. We observe that our approach not only vastly improves over the GNN baselines, but can match Gaussian processes, the most commonly utilized method for spatial interpolation problems.
The interpolation of spatial data can be of tremendous value in various applications, such as forecasting weather from only a few measurements of meteorological or remote sensing data. Existing methods for spatial interpolation, such as variants of kriging and spatial autoregressive models, tend to suffer from at least one of the following limitations: (a) the assumption of stationarity, (b) the assumption of isotropy, and (c) the trade-off between modelling local or global spatial interaction. Addressing these issues in this work, we propose the use of Markov reward processes (MRPs) as a spatial interpolation method, and we introduce three variants thereof: (i) a basic static discount MRP (SD-MRP), (ii) an accurate but mostly theoretical optimised MRP (O-MRP), and (iii) a transferable weight prediction MRP (WP-MRP). All variants of MRP interpolation operate locally, while also implicitly accounting for global spatial relationships in the entire system through recursion. Additionally, O-MRP and WP-MRP no longer assume stationarity and are robust to anisotropy. We evaluated our proposed methods by comparing the mean absolute errors of their interpolated grid cells to those of 7 common baselines, selected from models based on spatial autocorrelation, (spatial) regression, and deep learning. We performed detailed evaluations on two publicly available datasets (local GDP values, and COVID-19 patient trajectory data). The results from these experiments clearly show the competitive advantage of MRP interpolation, which achieved significantly lower errors than the existing methods in 23 out of 40 experimental conditions, or 35 out of 40 when including O-MRP.
Machine learning is gaining popularity in a broad range of areas working with geographic data, such as ecology or atmospheric sciences. Here, data often exhibit spatial effects, which can be difficult to learn for neural networks. In this study, we propose SXL, a method for embedding information on the autoregressive nature of spatial data directly into the learning process using auxiliary tasks. We utilize the local Moran's I, a popular measure of local spatial autocorrelation, to "nudge" the model to learn the direction and magnitude of local spatial effects, complementing the learning of the primary task. We further introduce a novel expansion of Moran's I to multiple resolutions, thus capturing spatial interactions over longer and shorter distances simultaneously. The novel multi-resolution Moran's I can be constructed easily and as a multi-dimensional tensor offers seamless integration into existing machine learning frameworks. Throughout a range of experiments using real-world data, we highlight how our method consistently improves the training of neural networks in unsupervised and supervised learning tasks. In generative spatial modeling experiments, we propose a novel loss for auxiliary task GANs utilizing task uncertainty weights. Our proposed method outperforms domain-specific spatial interpolation benchmarks, highlighting its potential for downstream applications. This study bridges expertise from geographic information science and machine learning, showing how this integration of disciplines can help to address domain-specific challenges. The code for our experiments is available on Github: https://github.com/konstantinklemmer/sxl.
Stochastic processes provide a mathematically elegant way model complex data. In theory, they provide flexible priors over function classes that can encode a wide range of interesting assumptions. In practice, however, efficient inference by optimisation or marginalisation is difficult, a problem further exacerbated with big data and high dimensional input spaces. We propose a novel variational autoencoder (VAE) called the prior encoding variational autoencoder ($\pi$VAE). The $\pi$VAE is finitely exchangeable and Kolmogorov consistent, and thus is a continuous stochastic process. We use $\pi$VAE to learn low dimensional embeddings of function classes. We show that our framework can accurately learn expressive function classes such as Gaussian processes, but also properties of functions to enable statistical inference (such as the integral of a log Gaussian process). For popular tasks, such as spatial interpolation, $\pi$VAE achieves state-of-the-art performance both in terms of accuracy and computational efficiency. Perhaps most usefully, we demonstrate that the low dimensional independently distributed latent space representation learnt provides an elegant and scalable means of performing Bayesian inference for stochastic processes within probabilistic programming languages such as Stan.