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1. Complex Unitary Recurrent Neural Networks Using Scaled Cayley Transform

   https://doi.org/10.1609/aaai.v33i01.33014528  

   Maduranga, Kehelwala D. ; Helfrich, Kyle E. ; Ye, Qiang ( July 2019 , Proceedings of the AAAI Conference on Artificial Intelligence)

   Recurrent neural networks (RNNs) have been successfully used on a wide range of sequential data problems. A well known difficulty in using RNNs is the vanishing or exploding gradient problem. Recently, there have been several different RNN architectures that try to mitigate this issue by maintaining an orthogonal or unitary recurrent weight matrix. One such architecture is the scaled Cayley orthogonal recurrent neural network (scoRNN) which parameterizes the orthogonal recurrent weight matrix through a scaled Cayley transform. This parametrization contains a diagonal scaling matrix consisting of positive or negative one entries that can not be optimized by gradient descent. Thus the scaling matrix is fixed before training and a hyperparameter is introduced to tune the matrix for each particular task. In this paper, we develop a unitary RNN architecture based on a complex scaled Cayley transform. Unlike the real orthogonal case, the transformation uses a diagonal scaling matrix consisting of entries on the complex unit circle which can be optimized using gradient descent and no longer requires the tuning of a hyperparameter. We also provide an analysis of a potential issue of the modReLU activiation function which is used in our work and several other unitary RNNs. In the experiments conducted, the scaled Cayley unitary recurrent neural network (scuRNN) achieves comparable or better results than scoRNN and other unitary RNNs without fixing the scaling matrix. 

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2. MomentumRNN: Integrating Momentum into Recurrent Neural Networks

   Nguyen, Tan M. ; Baraniuk, Richard G. ; Bertozzi, Andrea L. ; Osher, Stanley L. ; Wang, Bao ( December 2020 , Advances in neural information processing systems)

   null (Ed.)

   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 {\em 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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3. 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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4. Sparse RNNs can support high-capacity classification

   https://doi.org/10.1371/journal.pcbi.1010759  

   Turcu, Denis ; Abbott, L. F. ( December 2022 , PLOS Computational Biology)

   Soltani, Alireza (Ed.)

   Feedforward network models performing classification tasks rely on highly convergent output units that collect the information passed on by preceding layers. Although convergent output-unit like neurons may exist in some biological neural circuits, notably the cerebellar cortex, neocortical circuits do not exhibit any obvious candidates for this role; instead they are highly recurrent. We investigate whether a sparsely connected recurrent neural network (RNN) can perform classification in a distributed manner without ever bringing all of the relevant information to a single convergence site. Our model is based on a sparse RNN that performs classification dynamically. Specifically, the interconnections of the RNN are trained to resonantly amplify the magnitude of responses to some external inputs but not others. The amplified and non-amplified responses then form the basis for binary classification. Furthermore, the network acts as an evidence accumulator and maintains its decision even after the input is turned off. Despite highly sparse connectivity, learned recurrent connections allow input information to flow to every neuron of the RNN, providing the basis for distributed computation. In this arrangement, the minimum number of synapses per neuron required to reach maximum memory capacity scales only logarithmically with network size. The model is robust to various types of noise, works with different activation and loss functions and with both backpropagation- and Hebbian-based learning rules. The RNN can also be constructed with a split excitation-inhibition architecture with little reduction in performance. 

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5. E-RNN: Design Optimization for Efficient Recurrent Neural Networks in FPGAs

   https://doi.org/10.1109/HPCA.2019.00028  

   Li, Zhe ; Ding, Caiwen ; Wang, Siyue ; Wen, Wujie ; Zhuo, Youwei ; Liu, Chang ; Qiu, Qinru ; Xu, Wenyao ; Lin, Xue ; Qian, Xuehai ; et al ( February 2019 , 2019 IEEE International Symposium on High Performance Computer Architecture (HPCA))

   Recurrent Neural Networks (RNNs) are becoming increasingly important for time series-related applications which require efficient and real-time implementations. The two major types are Long Short-Term Memory (LSTM) and Gated Recurrent Unit (GRU) networks. It is a challenging task to have real-time, efficient, and accurate hardware RNN implementations because of the high sensitivity to imprecision accumulation and the requirement of special activation function implementations. Recently two works have focused on FPGA implementation of inference phase of LSTM RNNs with model compression. First, ESE uses a weight pruning based compressed RNN model but suffers from irregular network structure after pruning. The second work C-LSTM mitigates the irregular network limitation by incorporating block-circulant matrices for weight matrix representation in RNNs, thereby achieving simultaneous model compression and acceleration. A key limitation of the prior works is the lack of a systematic design optimization framework of RNN model and hardware implementations, especially when the block size (or compression ratio) should be jointly optimized with RNN type, layer size, etc. In this paper, we adopt the block-circulant matrixbased framework, and present the Efficient RNN (E-RNN) framework for FPGA implementations of the Automatic Speech Recognition (ASR) application. The overall goal is to improve performance/energy efficiency under accuracy requirement. We use the alternating direction method of multipliers (ADMM) technique for more accurate block-circulant training, and present two design explorations providing guidance on block size and reducing RNN training trials. Based on the two observations, we decompose E-RNN in two phases: Phase I on determining RNN model to reduce computation and storage subject to accuracy requirement, and Phase II on hardware implementations given RNN model, including processing element design/optimization, quantization, activation implementation, etc. 1 Experimental results on actual FPGA deployments show that E-RNN achieves a maximum energy efficiency improvement of 37.4× compared with ESE, and more than 2× compared with C-LSTM, under the same accuracy. 

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