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Recurrent neural networks (RNNs) have been successfully applied to a variety of problems involving sequential data, but their optimization is sensitive to parameter initialization, architecture, and optimizer hyperparameters. Considering RNNs as dynamical systems, a natural way to capture stability, i.e., the growth and decay over long iterates, are the Lyapunov Exponents (LEs), which form the Lyapunov spectrum. The LEs have a bearing on stability of RNN training dynamics since forward propagation of information is related to the backward propagation of error gradients. LEs measure the asymptotic rates of expansion and contraction of non-linear system trajectories, and generalize stability analysis to the time-varying attractors structuring the non-autonomous dynamics of data-driven RNNs. As a tool to understand and exploit stability of training dynamics, the Lyapunov spectrum fills an existing gap between prescriptive mathematical approaches of limited scope and computationally-expensive empirical approaches. To leverage this tool, we implement an efficient way to compute LEs for RNNs during training, discuss the aspects specific to standard RNN architectures driven by typical sequential datasets, and show that the Lyapunov spectrum can serve as a robust readout of training stability across hyperparameters. With this exposition-oriented contribution, we hope to draw attention to this under-studied, but theoretically grounded tool for understanding training stability in RNNs.
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Tracking of Dynamical Processes with Model Switching Using Temporal Convolutional Networks
This paper considers the problem of tracking and predicting dynamical processes with model switching. The classical approach to this problem has been to use an interacting multiple model (IMM) which uses multiple Kalman filters and an auxiliary system to estimate the posterior probability of each model given the observations. More recently, data-driven approaches such as recurrent neural networks (RNNs) have been used for tracking and prediction in a variety of settings. An advantage of data-driven approaches like the RNN is that they can be trained to provide good performance even when the underlying dynamic models are unknown. This paper studies the use of temporal convolutional networks (TCNs) in this setting since TCNs are also data-driven but have certain structural advantages over RNNs. Numerical simulations demonstrate that a TCN matches or exceeds the performance of an IMM and other classical tracking methods in two specific settings with model switching: (i) a Gilbert-Elliott burst noise communication channel that switches between two different modes, each modeled as a linear system, and (ii) a maneuvering target tracking scenario where the target switches between a linear constant velocity mode and a nonlinear coordinated turn mode. In particular, the results show that the TCN tends to identify a mode switch as fast or faster than an IMM and that, in some cases, the TCN can perform almost as well as an omniscient Kalman filter with perfect knowledge of the current mode of the dynamical system.
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- Award ID(s):
- 1836695
- PAR ID:
- 10349348
- Date Published:
- Journal Name:
- 2021 IEEE Aerospace Conference
- Page Range / eLocation ID:
- 1 to 9
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/AERO50100.2021.9438450
