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1. MomentumRNN: Integrating Momentum into Recurrent Neural Networks

   Nguyen, Tan M.; Bertozzi, Andrea L; Osher, Stanley J; Wang, Bao (January 2020, 34th Conference on Neural Information Processing Systems (NeurIPS 2020), Vancouver, Canada)

   Designing deep neural networks is an art that often involves an expensive search over candidate architectures. To overcome this for recurrent neural nets (RNNs), we establish a connection between the hidden state dynamics in an RNN and gradient descent (GD). We then integrate momentum into this framework and propose a new family of RNNs, called MomentumRNNs. We theoretically prove and numerically demonstrate that MomentumRNNs alleviate the vanishing gradient issue in training RNNs. We study the momentum long-short term memory (MomentumLSTM) and verify its advantages in convergence speed and accuracy over its LSTM counterpart across a variety of benchmarks. We also demonstrate that MomentumRNN is applicable to many types of recurrent cells, including those in the state-of-the-art orthogonal RNNs. Finally, we show that other advanced momentum-based optimization methods, such as Adam and Nesterov accelerated gradients with a restart, can be easily incorporated into the MomentumRNN framework for designing new recurrent cells with even better performance. 

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2. Eigenvalue Normalized Recurrent Neural Networks for Short Term Memory

   https://doi.org/10.1609/aaai.v34i04.5831  

   Helfrich, Kyle; Ye, Qiang (June 2020, Proceedings of the AAAI Conference on Artificial Intelligence)

   Several variants of recurrent neural networks (RNNs) with orthogonal or unitary recurrent matrices have recently been developed to mitigate the vanishing/exploding gradient problem and to model long-term dependencies of sequences. However, with the eigenvalues of the recurrent matrix on the unit circle, the recurrent state retains all input information which may unnecessarily consume model capacity. In this paper, we address this issue by proposing an architecture that expands upon an orthogonal/unitary RNN with a state that is generated by a recurrent matrix with eigenvalues in the unit disc. Any input to this state dissipates in time and is replaced with new inputs, simulating short-term memory. A gradient descent algorithm is derived for learning such a recurrent matrix. The resulting method, called the Eigenvalue Normalized RNN (ENRNN), is shown to be highly competitive in several experiments. 

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3. Representation learning for neural population activity with Neural Data Transformers

   https://doi.org/10.51628/001c.27358  

   Ye, Joel; Pandarinath, Chethan (January 2021, Neurons, Behavior, Data analysis, and Theory)

   Neural population activity is theorized to reflect an underlying dynamical structure. This structure can be accurately captured using state space models with explicit dynamics, such as those based on recurrent neural networks (RNNs). However, using recurrence to explicitly model dynamics necessitates sequential processing of data, slowing real-time applications such as brain-computer interfaces. Here we introduce the Neural Data Transformer (NDT), a non-recurrent alternative. We test the NDT’s ability to capture autonomous dynamical systems by applying it to synthetic datasets with known dynamics and data from monkey motor cortex during a reaching task well-modeled by RNNs. The NDT models these datasets as well as state-of-the-art recurrent models. Further, its non-recurrence enables 3.9ms inference, well within the loop time of real-time applications and more than 6 times faster than recurrent baselines on the monkey reaching dataset. These results suggest that an explicit dynamics model is not necessary to model autonomous neural population dynamics. Code: https://github.com/snel-repo/neural-data-transformers 

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4. The Recurrent Neural Tangent Kernel

   Alemohammad, Sina; Wang, Zichao; Balestriero, Randall; Baraniuk, Richard (May 2021, The International Conference on Learning Representations)

   The study of deep neural networks (DNNs) in the infinite-width limit, via the so-called neural tangent kernel (NTK) approach, has provided new insights into the dynamics of learning, generalization, and the impact of initialization. One key DNN architecture remains to be kernelized, namely, the recurrent neural network (RNN). In this paper we introduce and study the Recurrent Neural Tangent Kernel (RNTK), which provides new insights into the behavior of overparametrized RNNs. A key property of the RNTK should greatly benefit practitioners is its ability to compare inputs of different length. To this end, we characterize how the RNTK weights different time steps to form its output under different initialization parameters and nonlinearity choices. A synthetic and 56 real-world data experiments demonstrate that the RNTK offers significant performance gains over other kernels, including standard NTKs, across a wide array of data sets. 

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5. Scene Parsing via Dense Recurrent Neural Networks with Attentional Selection

   Fan, Heng; Chu, Peng; Latecki, Longin Jan; Ling, Haibin (January 2019, IEEE Winter Conference on Applications of Computer Vision)

   Recurrent neural networks (RNNs) have shown the ability to improve scene parsing through capturing long-range dependencies among image units. In this paper, we propose dense RNNs for scene labeling by exploring various longrange semantic dependencies among image units. Different from existing RNN based approaches, our dense RNNs are able to capture richer contextual dependencies for each image unit by enabling immediate connections between each pair of image units, which significantly enhances their discriminative power. Besides, to select relevant dependencies and meanwhile to restrain irrelevant ones for each unit from dense connections, we introduce an attention model into dense RNNs. The attention model allows automatically assigning more importance to helpful dependencies while less weight to unconcerned dependencies. Integrating with convolutional neural networks (CNNs), we develop an end-to-end scene labeling system. Extensive experiments on three large-scale benchmarks demonstrate that the proposed approach can improve the baselines by large margins and outperform other state-of-the-art algorithms. 

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