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Noisy recurrent neural networks: the discrete-time case
1Department of Electrical and Computer Engineering, MS 1G5, George Mason University, Fairfax, VA 22030, USA.
IEEE Transactions on Neural Networks
|February 8, 2008
Summary
This study analyzes discrete-time recurrent neural networks (RNNs), establishing uniform boundedness for their trajectory moments. Practical bounds for bias and variance are derived for stochastic RNNs, aiding in network design.
Area of Science:
- Machine Learning
- Artificial Intelligence
- Dynamical Systems
Background:
- Recurrent Neural Networks (RNNs) are crucial for sequential data processing.
- Understanding the behavior of discrete-time RNNs is essential for reliable applications.
- Previous work established continuous-time RNN behavior.
Purpose of the Study:
- Specialize continuous-time RNN results to discrete-time (time-lagged) RNNs.
- Establish theoretical bounds for discrete-time RNNs.
- Provide practical tools for analyzing stochastic discrete-time RNNs.
Main Methods:
- Theoretical analysis of discrete-time recurrent neural network dynamics.
- Derivation of uniform boundedness for moment sequences.
- Development of estimation methods for bias and variance bounds.
Main Results:
- Uniform boundedness of first and second moment sequences for discrete-time RNN trajectories is proven.
- Estimates and bounds for bias and variance sequences of stochastic discrete-time RNNs are derived.
- A script for estimating variance bounds is provided.
Conclusions:
- The study provides a rigorous mathematical framework for discrete-time RNNs.
- Derived bounds offer practical guidance for designing and analyzing stochastic RNNs.
- The provided script facilitates the application of these findings in practice.
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