Global information is essential for dense prediction problems, whose goal is to compute adiscrete or continuous label for each pixel in the images. Traditional convolutional layers in neural networks, initially designed for image classification, are restrictive in these problems since the filter size limits their receptive fields. In this work, we propose to replace any traditional convolutional layer with an autoregressivemoving-average (ARMA) layer,anovelmodule with an adjustable receptive field controlled by the learnable autoregressive coefficients.

Global information is essential for dense prediction problems, whose goal is to compute a discrete or continuous label for each pixel in the images. Traditional convolutional layers in neural networks, initially designed for image classification, are restrictive in these problems since the filter size limits their receptive fields. In this work, we propose to replace any traditional convolutional layer with an autoregressive moving-average (ARMA) layer, a novel module with an adjustable receptive field controlled by the learnable autoregressive coefficients. Compared with traditional convolutional layers, our ARMA layer enables explicit interconnections of the output neurons and learns its receptive field by adapting the autoregressive coefficients of the interconnections. ARMA layer is adjustable to different types of tasks: for tasks where global information is crucial, it is capable of learning relatively large autoregressive coefficients to allow for an output neuron's receptive field covering the entire input; for tasks where only local information is required, it can learn small or near zero autoregressive coefficients and automatically reduces to a traditional convolutional layer. We show both theoretically and empirically that the effective receptive field of networks with ARMA layers (named ARMA networks) expands with larger autoregressive coefficients. We also provably solve the instability problem of learning and prediction in the ARMA layer through a re-parameterization mechanism. Additionally, we demonstrate that ARMA networks substantially improve their baselines on challenging dense prediction tasks, including video prediction and semantic segmentation.

In the simulations in subsection 3.2, all linear networks have The backbone architecture consists of a stack of 12 Conv-LSTM modules, and each module contains 32 units (channels). The backbone architecture is illustrated in Figure 7. To demonstrate ARMA networks' applicability to image segmentation, we evaluate it on a challenging The network architecture is illustrated in Figure 15a. The experimental results are summarized in Table 5. Since image classifications tasks do not require convolu-tional layers to have large receptive fields, the learned autoregressive coefficients concentrate around 0, as shown in Figure 6.

Global information is essential for dense prediction problems, whose goal is to compute a discrete or continuous label for each pixel in the images. Traditional convolutional layers in neural networks, initially designed for image classification, are restrictive in these problems since the filter size limits their receptive fields. In this work, we propose to replace any traditional convolutional layer with an autoregressive moving-average (ARMA) layer, a novel module with an adjustable receptive field controlled by the learnable autoregressive coefficients. Compared with traditional convolutional layers, our ARMA layer enables explicit interconnections of the output neurons and learns its receptive field by adapting the autoregressive coefficients of the interconnections. ARMA layer is adjustable to different types of tasks: for tasks where global information is crucial, it is capable of learning relatively large autoregressive coefficients to allow for an output neuron's receptive field covering the entire input; for tasks where only local information is required, it can learn small or near zero autoregressive coefficients and automatically reduces to a traditional convolutional layer.

We propose an end-to-end framework based on a Graph Neural Network (GNN) to balance the power flows in energy grids. The balancing is framed as a supervised vertex regression task, where the GNN is trained to predict the current and power injections at each grid branch that yield a power flow balance. By representing the power grid as a line graph with branches as vertices, we can train a GNN that is accurate and robust to changes in topology. In addition, by using specialized GNN layers, we are able to build a very deep architecture that accounts for large neighborhoods on the graph, while implementing only localized operations. We perform three different experiments to evaluate: i) the benefits of using localized rather than global operations and the tendency of deep GNN models to oversmooth the quantities on the nodes; ii) the resilience to perturbations in the graph topology; and iii) the capability to train the model simultaneously on multiple grid topologies and the consequential improvement in generalization to new, unseen grids. The proposed framework is efficient and, compared to other solvers based on deep learning, is robust to perturbations not only to the physical quantities on the grid components, but also to the topology.

Global information is essential for dense prediction problems, whose goal is to compute a discrete or continuous label for each pixel in the images. Traditional convolutional layers in neural networks, originally designed for image classification, are restrictive in these problems since their receptive fields are limited by the filter size. In this work, we propose autoregressive moving-average (ARMA) layer, a novel module in neural networks to allow explicit dependencies of output neurons, which significantly expands the receptive field with minimal extra parameters. We show experimentally that the effective receptive field of neural networks with ARMA layers expands as autoregressive coefficients become larger. In addition, we demonstrate that neural networks with ARMA layers substantially improve the performance of challenging pixel-level video prediction tasks as our model enlarges the effective receptive field.

Recent graph neural networks implement convolutional layers based on polynomial filters operating in the spectral domain. In this paper, we propose a novel graph convolutional layer based on auto-regressive moving average (ARMA) filters that, compared to the polynomial ones, provides a more flexible response thanks to a rich transfer function that accounts for the concept of state. We implement the ARMA filter with a recursive and distributed formulation, obtaining a convolutional layer that is efficient to train, is localized in the node space and can be applied to graphs with different topologies. In order to learn more abstract and compressed representations in deeper layers of the network, we alternate pooling operations based on node decimation to reduce the dimensionality of the node space with convolutions on coarsened versions of the original graph. We consider three major graph inference problems: semi-supervised node classification, graph classification, and graph signal classification. Results show that the proposed graph neural network with ARMA filters outperform those based on polynomial filters and sets the new state-of-the-art in several tasks.