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Reservoir computing systems, a class of recurrent neural networks, have recently been exploited for model-free, data-based prediction of the state evolution of a variety of chaotic dynamical systems. The prediction horizon demonstrated has been about half dozen Lyapunov time. Is it possible to significantly extend the prediction time beyond what has been achieved so far? We articulate a scheme incorporating time-dependent but sparse data inputs into reservoir computing and demonstrate that such rare updates of the actual state practically enable an arbitrarily long prediction horizon for a variety of chaotic systems. A physical understanding based on the theory of temporal synchronization is developed.
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Recommender systems objectives can be broadly characterized as modeling user preferences over short-or long-term time horizon. A large body of previous research studied long-term recommendation through dimensionality reduction techniques applied to the historical user-item interactions. A recently introduced session-based recommendation setting highlighted the importance of modeling short-term user preferences. In this task, Recurrent Neural Networks (RNN) have shown to be successful at capturing the nuances of users interactions within a short time window. In this paper, we evaluate RNN-based models on both short-term and long-term recommendation tasks. Our experimental results suggest that RNNs are capable of predicting immediate as well as distant user interactions. We also find the best performing configuration to be a stacked RNN with layer normalization and tied item embeddings.
It is well known that it is challenging to train deep neural networks and recurrent neural networks for tasks that exhibit long term dependencies. The vanishing or exploding gradient problem is a well known issue associated with these challenges. One approach to addressing vanishing and exploding gradients is to use either soft or hard constraints on weight matrices so as to encourage or enforce orthogonality. Orthogonal matrices preserve gradient norm during backpropagation and may therefore be a desirable property. This paper explores issues with optimization convergence, speed and gradient stability when encouraging or enforcing orthogonality. To perform this analysis, we propose a weight matrix factorization and parameterization strategy through which we can bound matrix norms and therein control the degree of expansivity induced during backpropagation. We find that hard constraints on orthogonality can negatively affect the speed of convergence and model performance.
A key attribute that drives the unprecedented success of modern Recurrent Neural Networks (RNNs) on learning tasks which involve sequential data, is their ability to model intricate long-term temporal dependencies. However, a well established measure of RNNs long-term memory capacity is lacking, and thus formal understanding of the effect of depth on their ability to correlate data throughout time is limited. Specifically, existing depth efficiency results on convolutional networks do not suffice in order to account for the success of deep RNNs on data of varying lengths. In order to address this, we introduce a measure of the networks ability to support information flow across time, referred to as the Start-End separation rank, which reflects the distance of the function realized by the recurrent network from modeling no dependency between the beginning and end of the input sequence. We prove that deep recurrent networks support Start-End separation ranks which are combinatorially higher than those supported by their shallow counterparts. Thus, we establish that depth brings forth an overwhelming advantage in the ability of recurrent networks to model long-term dependencies, and provide an exemplar of quantifying this key attribute which may be readily extended to other RNN architectures of interest, e.g. variants of LSTM networks. We obtain our results by considering a class of recurrent networks referred to as Recurrent Arithmetic Circuits, which merge the hidden state with the input via the Multiplicative Integration operation, and empirically demonstrate the discussed phenomena on common RNNs. Finally, we employ the tool of quantum Tensor Networks to gain additional graphic insight regarding the complexity brought forth by depth in recurrent networks.
We investigate the multi-step prediction of the drivable space, represented by Occupancy Grid Maps (OGMs), for autonomous vehicles. Our motivation is that accurate multi-step prediction of the drivable space can efficiently improve path planning and navigation resulting in safe, comfortable and optimum paths in autonomous driving. We train a variety of Recurrent Neural Network (RNN) based architectures on the OGM sequences from the KITTI dataset. The results demonstrate significant improvement of the prediction accuracy using our proposed difference learning method, incorporating motion related features, over the state of the art. We remove the egomotion from the OGM sequences by transforming them into a common frame. Although in the transformed sequences the KITTI dataset is heavily biased toward static objects, by learning the difference between subsequent OGMs, our proposed method provides accurate prediction over both the static and moving objects.
The rise of deep learning technologies has quickly advanced many fields, including that of generative music systems. There exist a number of systems that allow for the generation of good sounding short snippets, yet, these generated snippets often lack an overarching, longer-term structure. In this work, we propose CM-HRNN: a conditional melody generation model based on a hierarchical recurrent neural network. This model allows us to generate melodies with long-term structures based on given chord accompaniments. We also propose a novel, concise event-based representation to encode musical lead sheets while retaining the notes relative position within the bar with respect to the musical meter. With this new data representation, the proposed architecture can simultaneously model the rhythmic, as well as the pitch structures in an effective way. Melodies generated by the proposed model were extensively evaluated in quantitative experiments as well as a user study to ensure the musical quality of the output as well as to evaluate if they contain repeating patterns. We also compared the system with the state-of-the-art AttentionRNN. This comparison shows that melodies generated by CM-HRNN contain more repeated patterns (i.e., higher compression ratio) and a lower tonal tension (i.e., more tonally concise). Results from our listening test indicate that CM-HRNN outperforms AttentionRNN in terms of long-term structure and overall rating.
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