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1. SBO-RNN: Reformulating Recurrent Neural Networks via Stochastic Bilevel Optimization

   Zhang, Z.; Yue, Y.; Wu, G.; Li, Y.; Zhang, H. (December 2021, Thirty-fifth Conference on Neural Information Processing Systems)

   In this paper we consider the training stability of recurrent neural networks (RNNs) and propose a family of RNNs, namely SBO-RNN, that can be formulated using stochastic bilevel optimization (SBO). With the help of stochastic gradient descent (SGD), we manage to convert the SBO problem into an RNN where the feedforward and backpropagation solve the lower and upper-level optimization for learning hidden states and their hyperparameters, respectively. We prove that under mild conditions there is no vanishing or exploding gradient in training SBO-RNN. Empirically we demonstrate our approach with superior performance on several benchmark datasets, with fewer parameters, less training data, and much faster convergence. Code is available at https://zhang-vislab.github.io. 

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2. Reverse engineering recurrent networks for sentiment classification reveals line attractor dynamics

   Maheswaranathan, N.; Williams, A; Golub, M; Ganguli, S; Sussillo, D. (December 2019, Advances in neural information processing systems)

   null (Ed.)

   Recurrent neural networks (RNNs) are a widely used tool for modeling sequential data, yet they are often treated as inscrutable black boxes. Given a trained recurrent network, we would like to reverse engineer it--to obtain a quantitative, interpretable description of how it solves a particular task. Even for simple tasks, a detailed understanding of how recurrent networks work, or a prescription for how to develop such an understanding, remains elusive. In this work, we use tools from dynamical systems analysis to reverse engineer recurrent networks trained to perform sentiment classification, a foundational natural language processing task. Given a trained network, we find fixed points of the recurrent dynamics and linearize the nonlinear system around these fixed points. Despite their theoretical capacity to implement complex, high-dimensional computations, we find that trained networks converge to highly interpretable, low-dimensional representations. In particular, the topological structure of the fixed points and corresponding linearized dynamics reveal an approximate line attractor within the RNN, which we can use to quantitatively understand how the RNN solves the sentiment analysis task. Finally, we find this mechanism present across RNN architectures (including LSTMs, GRUs, and vanilla RNNs) trained on multiple datasets, suggesting that our findings are not unique to a particular architecture or dataset. Overall, these results demonstrate that surprisingly universal and human interpretable computations can arise across a range of recurrent networks. 

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3. NeuroView-RNN: It’s About Time

   https://doi.org/10.1145/3531146.3533224  

   Barberan, Cj; Alemmohammad, Sina; Liu, Naiming; Balestriero, Randall; Baraniuk, Richard (June 2022, FAccT '22: 2022 ACM Conference on Fairness, Accountability, and Transparency)

   Recurrent Neural Networks (RNNs) are important tools for processing sequential data such as time-series or video. Interpretability is defined as the ability to be understood by a person and is different from explainability, which is the ability to be explained in a mathematical formulation. A key interpretability issue with RNNs is that it is not clear how each hidden state per time step contributes to the decision-making process in a quantitative manner. We propose NeuroView-RNN as a family of new RNN architectures that explains how all the time steps are used for the decision-making process. Each member of the family is derived from a standard RNN architecture by concatenation of the hidden steps into a global linear classifier. The global linear classifier has all the hidden states as the input, so the weights of the classifier have a linear mapping to the hidden states. Hence, from the weights, NeuroView-RNN can quantify how important each time step is to a particular decision. As a bonus, NeuroView-RNN also offers higher accuracy in many cases compared to the RNNs and their variants. We showcase the benefits of NeuroView-RNN by evaluating on a multitude of diverse time-series datasets. 

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4. 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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5. Mini-Batch Learning Strategies for modeling long term temporal dependencies: A study in environmental applications

   https://doi.org/10.1137/1.9781611977653.ch73  

   Xu, Shaoming; Khandelwal, Ankush; Li, Xiang; Jia, Xiaowei; Liu, Licheng; Willard, Jared; Ghosh, Rahul; Cutler, Kelly; Steinbach, Michael; Duffy, Christopher; et al (April 2023, Proceedings of the 2023 SIAM International Conference on Data Mining (SDM))

   Shekhar, Shashi; Zhou, Zhi-Hua; Chiang, Yao-Yi; Stiglic, Gregor (Ed.)

   In many environmental applications, recurrent neural networks (RNNs) are often used to model physical variables with long temporal dependencies. However, due to minibatch training, temporal relationships between training segments within the batch (intra-batch) as well as between batches (inter-batch) are not considered, which can lead to limited performance. Stateful RNNs aim to address this issue by passing hidden states between batches. Since Stateful RNNs ignore intra-batch temporal dependency, there exists a trade-off between training stability and capturing temporal dependency. In this paper, we provide a quantitative comparison of different Stateful RNN modeling strategies, and propose two strategies to enforce both intra- and inter-batch temporal dependency. First, we extend Stateful RNNs by defining a batch as a temporally ordered set of training segments, which enables intra-batch sharing of temporal information. While this approach significantly improves the performance, it leads to much larger training times due to highly sequential training. To address this issue, we further propose a new strategy which augments a training segment with an initial value of the target variable from the timestep right before the starting of the training segment. In other words, we provide an initial value of the target variable as additional input so that the network can focus on learning changes relative to that initial value. By using this strategy, samples can be passed in any order (mini-batch training) which significantly reduces the training time while maintaining the performance. In demonstrating the utility of our approach in hydrological modeling, we observe that the most significant gains in predictive accuracy occur when these methods are applied to state variables whose values change more slowly, such as soil water and snowpack, rather than continuously moving flux variables such as streamflow. 

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