Passenger demand forecasting helps optimize vehicle scheduling, thereby improving urban efficiency. Recently, attention-based methods have been used to adequately capture the dynamic nature of spatio-temporal data. However, existing methods that rely on heuristic masking strategies cannot fully adapt to the complex spatio-temporal correlations, hindering the model from focusing on the right context. These works also overlook the high-level correlations that exist in the real world. Effectively integrating these high-level correlations with the original correlations is crucial. To fill this gap, we propose the Aggregation Differential Transformer (ADFormer), which offers new insights to demand forecasting promotion. Specifically, we utilize Differential Attention to capture the original spatial correlations and achieve attention denoising. Meanwhile, we design distinct aggregation strategies based on the nature of space and time. Then, the original correlations are unified with the high-level correlations, enabling the model to capture holistic spatio-temporal relations. Experiments conducted on taxi and bike datasets confirm the effectiveness and efficiency of our model, demonstrating its practical value. The code is available at https://github.com/decisionintelligence/ADFormer.

Whilst spectral Graph Neural Networks (GNNs) are theoretically well-founded in the spectral domain, their practical reliance on polynomial approximation implies a profound linkage to the spatial domain. As previous studies rarely examine spectral GNNs from the spatial perspective, their spatial-domain interpretability remains elusive, e.g., what information is essentially encoded by spectral GNNs in the spatial domain? In this paper, to answer this question, we establish a theoretical connection between spectral filtering and spatial aggregation, unveiling an intrinsic interaction that spectral filtering implicitly leads the original graph to an adapted new graph, explicitly computed for spatial aggregation. Both theoretical and empirical investigations reveal that the adapted new graph not only exhibits non-locality but also accommodates signed edge weights to reflect label consistency among nodes. These findings thus highlight the interpretable role of spectral GNNs in the spatial domain and inspire us to rethink graph spectral filters beyond the fixed-order polynomials, which neglect global information. Built upon the theoretical findings, we revisit the state-of-the-art spectral GNNs and propose a novel Spatially Adaptive Filtering (SAF) framework, which leverages the adapted new graph by spectral filtering for an auxiliary non-local aggregation. Notably, our proposed SAF comprehensively models both node similarity and dissimilarity from a global perspective, therefore alleviating persistent deficiencies of GNNs related to long-range dependencies and graph heterophily. Extensive experiments over 13 node classification benchmarks demonstrate the superiority of our proposed framework to the state-of-the-art models.

Effective investment planning decisions are crucial to ensure cyber-physical infrastructures satisfy performance requirements over an extended time horizon. Computing these decisions often requires solving Capacity Expansion Problems (CEPs). In the context of regional-scale energy systems, these problems are prohibitively expensive to solve due to large network sizes, heterogeneous node characteristics, and a large number of operational periods. To maintain tractability, traditional approaches aggregate network nodes and/or select a set of representative time periods. Often, these reductions do not capture supply-demand variations that crucially impact CEP costs and constraints, leading to suboptimal decisions. Here, we propose a novel graph convolutional autoencoder approach for spatio-temporal aggregation of a generic CEP with heterogeneous nodes (CEPHN). Our architecture leverages graph pooling to identify nodes with similar characteristics and minimizes a multi-objective loss function. This loss function is tailored to induce desirable spatial and temporal aggregations with regard to tractability and optimality. In particular, the output of the graph pooling provides a spatial aggregation while clustering the low-dimensional encoded representations yields a temporal aggregation. We apply our approach to generation expansion planning of a coupled 88-node power and natural gas system in New England. The resulting aggregation leads to a simpler CEPHN with 6 nodes and a small set of representative days selected from one year. We evaluate aggregation outcomes over a range of hyperparameters governing the loss function and compare resulting upper bounds on the original problem with those obtained using benchmark methods. We show that our approach provides upper bounds that are 33% (resp. 10%) lower those than obtained from benchmark spatial (resp. temporal) aggregation approaches.

Convolutional neural networks (CNNs) are one of the most successful computer vision systems to solve object recognition. Furthermore, CNNs have major applications in understanding the nature of visual representations in the human brain. Yet it remains poorly understood how CNNs actually make their decisions, what the nature of their internal representations is, and how their recognition strategies differ from humans. Specifically, there is a major debate about the question of whether CNNs primarily rely on surface regularities of objects, or whether they are capable of exploiting the spatial arrangement of features, similar to humans. Here, we develop a novel feature-scrambling approach to explicitly test whether CNNs use the spatial arrangement of features (i.e. object parts) to classify objects. We combine this approach with a systematic manipulation of effective receptive field sizes of CNNs as well as minimal recognizable configurations (MIRCs) analysis. In contrast to much previous literature, we provide evidence that CNNs are in fact capable of using relatively long-range spatial relationships for object classification. Moreover, the extent to which CNNs use spatial relationships depends heavily on the dataset, e.g. texture vs. sketch. In fact, CNNs even use different strategies for different classes within heterogeneous datasets (ImageNet), suggesting CNNs have a continuous spectrum of classification strategies. Finally, we show that CNNs learn the spatial arrangement of features only up to an intermediate level of granularity, which suggests that intermediate rather than global shape features provide the optimal trade-off between sensitivity and specificity in object classification. These results provide novel insights into the nature of CNN representations and the extent to which they rely on the spatial arrangement of features for object classification.

The Eleventh International Workshop on Qualitative Reasoning was held in Cortona, Italy, on 3 to 6 June 1997. Participants included scientists from both qualitative reasoning and quantitative mathematical modeling communities. This article summarizes the significant issues and discussion raised during the workshop. Given the organizational context, an additional goal in our minds in preparing the workshop was to establish a basis for interaction between the qualitative and quantitative communities. To this end, in addition to the presentation of full papers, posters, and short talks, in line with past workshop schedules, we planned invited talks, the focuses of which were problem domains for qualitative reasoning in real-world applications, and a tutorial on system identification.

Reasoning about spatial data is a key task in many applications, including geographic information systems, meteorological and fluid-flow analysis, computer-aided design, and protein structure databases. Such applications often require the identification and manipulation of qualitative spatial representations, for example, to detect whether one object will soon occlude another in a digital image or efficiently determine relationships between a proposed road and wetland regions in a geographic data set. Qualitative spatial reasoning (QSR) provides representational primitives (a spatial "vocabulary") and inference mechanisms for these tasks. This article first reviews representative work on QSR for data-poor scenarios, where the goal is to design representations that can answer qualitative queries without much numeric information. It then turns to the data-rich case, where the goal is to derive and manipulate qualitative spatial representations that efficiently and correctly abstract important spatial aspects of the underlying data for use in subsequent tasks.

Satellite imagery and remote sensing provide explanatory variables at relatively high resolutions for modeling geospatial phenomena, yet regional summaries are often desirable for analysis and actionable insight. In this paper, we propose a novel method of inducing spatial aggregations as a component of the machine learning process, yielding regional model features whose construction is driven by model prediction performance rather than prior assumptions. Our results demonstrate that Genetic Programming is particularly well suited to this type of feature construction because it can automatically synthesize appropriate aggregations, as well as better incorporate them into predictive models compared to other regression methods we tested. In our experiments we consider a specific problem instance and real-world dataset relevant to predicting snow properties in high-mountain Asia.

Visual thinking plays an important role in scientific reasoning. Based on the research in automating diverse reasoning tasks about dynamical systems, nonlinear controllers, kinematic mechanisms, and fluid motion, we have identified a style of visual thinking, imagistic reasoning. Imagistic reasoning organizes computations around image-like, analogue representations so that perceptual and symbolic operations can be brought to bear to infer structure and behavior. Programs incorporating imagistic reasoning have been shown to perform at an expert level in domains that defy current analytic or numerical methods. We have developed a computational paradigm, spatial aggregation, to unify the description of a class of imagistic problem solvers. A program written in this paradigm has the following properties. It takes a continuous field and optional objective functions as input, and produces high-level descriptions of structure, behavior, or control actions. It computes a multi-layer of intermediate representations, called spatial aggregates, by forming equivalence classes and adjacency relations. It employs a small set of generic operators such as aggregation, classification, and localization to perform bidirectional mapping between the information-rich field and successively more abstract spatial aggregates. It uses a data structure, the neighborhood graph, as a common interface to modularize computations. To illustrate our theory, we describe the computational structure of three implemented problem solvers -- KAM, MAPS, and HIPAIR --- in terms of the spatial aggregation generic operators by mixing and matching a library of commonly used routines.