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We present a novel form of Fourier analysis, and associated signal processing concepts, for signals (or data) indexed by edge-weighted directed acyclic graphs (DAGs). This means that our Fourier basis yields an eigendecomposition of a suitable notion of shift and convolution operators that we define. DAGs are the common model to capture causal relationships between data values and in this case our proposed Fourier analysis relates data with its causes under a linearity assumption that we define. The definition of the Fourier transform requires the transitive closure of the weighted DAG for which several forms are possible depending on the interpretation of the edge weights. Examples include level of influence, distance, or pollution distribution. Our framework is different from prior GSP: it is specific to DAGs and leverages, and extends, the classical theory of Moebius inversion from combinatorics. For a prototypical application we consider DAGs modeling dynamic networks in which edges change over time. Specifically, we model the spread of an infection on such a DAG obtained from real-world contact tracing data and learn the infection signal from samples assuming sparsity in the Fourier domain.

Novel view synthesis and 3D modeling using implicit neural field representation are shown to be very effective for calibrated multi-view cameras. Such representations are known to benefit from additional geometric and semantic supervision. Most existing methods that exploit additional supervision require dense pixel-wise labels or localized scene priors. These methods cannot benefit from high-level vague scene priors provided in terms of scenes' descriptions. In this work, we aim to leverage the geometric prior of Manhattan scenes to improve the implicit neural radiance field representations. More precisely, we assume that only the knowledge of the indoor scene (under investigation) being Manhattan is known -- with no additional information whatsoever -- with an unknown Manhattan coordinate frame. Such high-level prior is used to self-supervise the surface normals derived explicitly in the implicit neural fields. Our modeling allows us to cluster the derived normals and exploit their orthogonality constraints for self-supervision. Our exhaustive experiments on datasets of diverse indoor scenes demonstrate the significant benefit of the proposed method over the established baselines. The source code will be available at //github.com/nikola3794/normal-clustering-nerf.

Large pre-trained multimodal models have demonstrated significant success in a range of downstream tasks, including image captioning, image-text retrieval, visual question answering (VQA), etc. However, many of these methods rely on image-text pairs collected from the web as pre-training data and unfortunately overlook the need for fine-grained feature alignment between vision and language modalities, which requires detailed understanding of images and language expressions. While integrating VQA and dense captioning (DC) into pre-training can address this issue, acquiring image-question-answer as well as image-location-caption triplets is challenging and time-consuming. Additionally, publicly available datasets for VQA and dense captioning are typically limited in scale due to manual data collection and labeling efforts. In this paper, we propose a novel method called Joint QA and DC GEneration (JADE), which utilizes a pre-trained multimodal model and easily-crawled image-text pairs to automatically generate and filter large-scale VQA and dense captioning datasets. We apply this method to the Conceptual Caption (CC3M) dataset to generate a new dataset called CC3M-QA-DC. Experiments show that when used for pre-training in a multi-task manner, CC3M-QA-DC can improve the performance with various backbones on various downstream tasks. Furthermore, our generated CC3M-QA-DC can be combined with larger image-text datasets (e.g., CC15M) and achieve competitive results compared with models using much more data. Code and dataset are available at //github.com/johncaged/OPT_Questioner.

Surrogate-assisted evolutionary algorithms (SAEAs) aim to use efficient computational models with the goal of approximating the fitness function in evolutionary computation systems. This area of research has been active for over two decades and has received significant attention from the specialised research community in different areas, for example, single and many objective optimisation or dynamic and stationary optimisation problems. An emergent and exciting area that has received little attention from the SAEAs community is in neuroevolution. This refers to the use of evolutionary algorithms in the automatic configuration of artificial neural network (ANN) architectures, hyper-parameters and/or the training of ANNs. However, ANNs suffer from two major issues: (a) the use of highly-intense computational power for their correct training, and (b) the highly specialised human expertise required to correctly configure ANNs necessary to get a well-performing network. This work aims to fill this important research gap in SAEAs in neuroevolution by addressing these two issues. We demonstrate how one can use a Kriging Partial Least Squares method that allows efficient computation of good approximate surrogate models compared to the well-known Kriging method, which normally cannot be used in neuroevolution due to the high dimensionality of the data.

Efficient differential equation solvers have significantly reduced the sampling time of diffusion models (DMs) while retaining high sampling quality. Among these solvers, exponential integrators (EI) have gained prominence by demonstrating state-of-the-art performance. However, existing high-order EI-based sampling algorithms rely on degenerate EI solvers, resulting in inferior error bounds and reduced accuracy in contrast to the theoretically anticipated results under optimal settings. This situation makes the sampling quality extremely vulnerable to seemingly innocuous design choices such as timestep schedules. For example, an inefficient timestep scheduler might necessitate twice the number of steps to achieve a quality comparable to that obtained through carefully optimized timesteps. To address this issue, we reevaluate the design of high-order differential solvers for DMs. Through a thorough order analysis, we reveal that the degeneration of existing high-order EI solvers can be attributed to the absence of essential order conditions. By reformulating the differential equations in DMs and capitalizing on the theory of exponential integrators, we propose refined EI solvers that fulfill all the order conditions, which we designate as Refined Exponential Solver (RES). Utilizing these improved solvers, RES exhibits more favorable error bounds theoretically and achieves superior sampling efficiency and stability in practical applications. For instance, a simple switch from the single-step DPM-Solver++ to our order-satisfied RES solver when Number of Function Evaluations (NFE) $=9$, results in a reduction of numerical defects by $25.2\%$ and FID improvement of $25.4\%$ (16.77 vs 12.51) on a pre-trained ImageNet diffusion model.

Accurate load forecasting plays a vital role in numerous sectors, but accurately capturing the complex dynamics of dynamic power systems remains a challenge for traditional statistical models. For these reasons, time-series models (ARIMA) and deep-learning models (ANN, LSTM, GRU, etc.) are commonly deployed and often experience higher success. In this paper, we analyze the efficacy of the recently developed Transformer-based Neural Network model in Load forecasting. Transformer models have the potential to improve Load forecasting because of their ability to learn long-range dependencies derived from their Attention Mechanism. We apply several metaheuristics namely Differential Evolution to find the optimal hyperparameters of the Transformer-based Neural Network to produce accurate forecasts. Differential Evolution provides scalable, robust, global solutions to non-differentiable, multi-objective, or constrained optimization problems. Our work compares the proposed Transformer based Neural Network model integrated with different metaheuristic algorithms by their performance in Load forecasting based on numerical metrics such as Mean Squared Error (MSE) and Mean Absolute Percentage Error (MAPE). Our findings demonstrate the potential of metaheuristic-enhanced Transformer-based Neural Network models in Load forecasting accuracy and provide optimal hyperparameters for each model.

Recently, graph neural networks have been gaining a lot of attention to simulate dynamical systems due to their inductive nature leading to zero-shot generalizability. Similarly, physics-informed inductive biases in deep-learning frameworks have been shown to give superior performance in learning the dynamics of physical systems. There is a growing volume of literature that attempts to combine these two approaches. Here, we evaluate the performance of thirteen different graph neural networks, namely, Hamiltonian and Lagrangian graph neural networks, graph neural ODE, and their variants with explicit constraints and different architectures. We briefly explain the theoretical formulation highlighting the similarities and differences in the inductive biases and graph architecture of these systems. We evaluate these models on spring, pendulum, gravitational, and 3D deformable solid systems to compare the performance in terms of rollout error, conserved quantities such as energy and momentum, and generalizability to unseen system sizes. Our study demonstrates that GNNs with additional inductive biases, such as explicit constraints and decoupling of kinetic and potential energies, exhibit significantly enhanced performance. Further, all the physics-informed GNNs exhibit zero-shot generalizability to system sizes an order of magnitude larger than the training system, thus providing a promising route to simulate large-scale realistic systems.

Graph Convolutional Networks (GCNs) have been widely applied in various fields due to their significant power on processing graph-structured data. Typical GCN and its variants work under a homophily assumption (i.e., nodes with same class are prone to connect to each other), while ignoring the heterophily which exists in many real-world networks (i.e., nodes with different classes tend to form edges). Existing methods deal with heterophily by mainly aggregating higher-order neighborhoods or combing the immediate representations, which leads to noise and irrelevant information in the result. But these methods did not change the propagation mechanism which works under homophily assumption (that is a fundamental part of GCNs). This makes it difficult to distinguish the representation of nodes from different classes. To address this problem, in this paper we design a novel propagation mechanism, which can automatically change the propagation and aggregation process according to homophily or heterophily between node pairs. To adaptively learn the propagation process, we introduce two measurements of homophily degree between node pairs, which is learned based on topological and attribute information, respectively. Then we incorporate the learnable homophily degree into the graph convolution framework, which is trained in an end-to-end schema, enabling it to go beyond the assumption of homophily. More importantly, we theoretically prove that our model can constrain the similarity of representations between nodes according to their homophily degree. Experiments on seven real-world datasets demonstrate that this new approach outperforms the state-of-the-art methods under heterophily or low homophily, and gains competitive performance under homophily.

High spectral dimensionality and the shortage of annotations make hyperspectral image (HSI) classification a challenging problem. Recent studies suggest that convolutional neural networks can learn discriminative spatial features, which play a paramount role in HSI interpretation. However, most of these methods ignore the distinctive spectral-spatial characteristic of hyperspectral data. In addition, a large amount of unlabeled data remains an unexploited gold mine for efficient data use. Therefore, we proposed an integration of generative adversarial networks (GANs) and probabilistic graphical models for HSI classification. Specifically, we used a spectral-spatial generator and a discriminator to identify land cover categories of hyperspectral cubes. Moreover, to take advantage of a large amount of unlabeled data, we adopted a conditional random field to refine the preliminary classification results generated by GANs. Experimental results obtained using two commonly studied datasets demonstrate that the proposed framework achieved encouraging classification accuracy using a small number of data for training.

While it is nearly effortless for humans to quickly assess the perceptual similarity between two images, the underlying processes are thought to be quite complex. Despite this, the most widely used perceptual metrics today, such as PSNR and SSIM, are simple, shallow functions, and fail to account for many nuances of human perception. Recently, the deep learning community has found that features of the VGG network trained on the ImageNet classification task has been remarkably useful as a training loss for image synthesis. But how perceptual are these so-called "perceptual losses"? What elements are critical for their success? To answer these questions, we introduce a new Full Reference Image Quality Assessment (FR-IQA) dataset of perceptual human judgments, orders of magnitude larger than previous datasets. We systematically evaluate deep features across different architectures and tasks and compare them with classic metrics. We find that deep features outperform all previous metrics by huge margins. More surprisingly, this result is not restricted to ImageNet-trained VGG features, but holds across different deep architectures and levels of supervision (supervised, self-supervised, or even unsupervised). Our results suggest that perceptual similarity is an emergent property shared across deep visual representations.