Many time series are generated by a set of entities that interact with one another over time. This paper introduces a broad, flexible framework to learn from multiple inter-dependent time series generated by such entities. Our framework explicitly models the entities and their interactions through time. It achieves this by building on the capabilities of Recurrent Neural Networks, while also offering several ways to incorporate domain knowledge constraints into the model architecture. The capabilities of our approach are showcased through an application to weather prediction, which shows gains over strong baselines.
A similar model has been proposed for learning on spatio-temporal graphs ( @cite_11 ). Unlike our models however, the RNNs in their model cannot affect each other. In their setting, each node and each edge has an input feature vector at every time step. Since the RNNs on the edges do not take input from RNNs at nodes, the forward pass through their model is equivalent to running independent siloed RNNs, with one set of RNNs for each node. In contrast, we do not have any data input on edges. Additionally, in our case, summaries flow along each edge which are computed using hidden states of RNNs nearby and thus, all RNNs evolve together. Another assumption in their approach is that the same RNN on the edge provides input to RNNs on both sides. In our case, the edges can be directed and hence the interactions can be modeled differently. Finally we note that this model is a special case of our model with each edge replaced by a node and creating a disconnected graph with one connected component per node in the original graph.
@cite_11
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Deep Recurrent Neural Network architectures, though remarkably capable at modeling sequences, lack an intuitive high-level spatio-temporal structure. That is while many problems in computer vision inherently have an underlying high-level structure and can benefit from it. Spatio-temporal graphs are a popular tool for imposing such high-level intuitions in the formulation of real world problems. In this paper, we propose an approach for combining the power of high-level spatio-temporal graphs and sequence learning success of Recurrent Neural Networks (RNNs). We develop a scalable method for casting an arbitrary spatio-temporal graph as a rich RNN mixture that is feedforward, fully differentiable, and jointly trainable. The proposed method is generic and principled as it can be used for transforming any spatio-temporal graph through employing a certain set of well defined steps. The evaluations of the proposed approach on a diverse set of problems, ranging from modeling human motion to object interactions, shows improvement over the state-of-the-art with a large margin. We expect this method to empower new approaches to problem formulation through high-level spatio-temporal graphs and Recurrent Neural Networks. Deep Recurrent Neural Network architectures, though remarkably capable at modeling sequences, lack an intuitive high-level spatio-temporal structure. That is while many problems in computer vision inherently have an underlying high-level structure and can benefit from it. Spatiotemporal graphs are a popular tool for imposing such high-level intuitions in the formulation of real world problems. In this paper, we propose an approach for combining the power of high-level spatio-temporal graphs and sequence learning success of Recurrent Neural Networks (RNNs). We develop a scalable method for casting an arbitrary spatio-temporal graph as a rich RNN mixture that is feedforward, fully differentiable, and jointly trainable. The proposed method is generic and principled as it can be used for transforming any spatio-temporal graph through employing a certain set of well defined steps. The evaluations of the proposed approach on a diverse set of problems, ranging from modeling human motion to object interactions, shows improvement over the state-of-the-art with a large margin. We expect this method to empower new approaches to problem formulation through high-level spatio-temporal graphs and Recurrent Neural Networks. Recurrent neural networks (RNNs) have achieved state-of-the-art performances in many natural language processing tasks, such as language modeling and machine translation. However, when the vocabulary is large, the RNN model will become very big (e.g., possibly beyond the memory capacity of a GPU device) and its training will become very inefficient. In this work, we propose a novel technique to tackle this challenge. The key idea is to use 2-Component (2C) shared embedding for word representations. We allocate every word in the vocabulary into a table, each row of which is associated with a vector, and each column associated with another vector. Depending on its position in the table, a word is jointly represented by two components: a row vector and a column vector. Since the words in the same row share the row vector and the words in the same column share the column vector, we only need @math vectors to represent a vocabulary of @math unique words, which are far less than the @math vectors required by existing approaches. Based on the 2-Component shared embedding, we design a new RNN algorithm and evaluate it using the language modeling task on several benchmark datasets. The results show that our algorithm significantly reduces the model size and speeds up the training process, without sacrifice of accuracy (it achieves similar, if not better, perplexity as compared to state-of-the-art language models). Remarkably, on the One-Billion-Word benchmark Dataset, our algorithm achieves comparable perplexity to previous language models, whilst reducing the model size by a factor of 40-100, and speeding up the training process by a factor of 2. We name our proposed algorithm to reflect its very small model size and very high training speed. Recursive neural networks (RNNs) and graph neural networks (GNNs) are two connectionist models that can directly process graphs. RNNs and GNNs exploit a similar processing framework, but they can be applied to different input domains. RNNs require the input graphs to be directed and acyclic, whereas GNNs can process any kind of graphs. The aim of this paper consists in understanding whether such a difference affects the behaviour of the models on a real application. An experimental comparison on an image classification problem is presented, showing that GNNs outperforms RNNs. Moreover the main differences between the models are also discussed w.r.t. their input domains, their approximation capabilities and their learning algorithms.