论文信息 - Global Asymptotic Stability and Stabilization of Long Short-Term Memory Neural Networks with Constant Weights and Biases

Global Asymptotic Stability and Stabilization of Long Short-Term Memory Neural Networks with Constant Weights and Biases

In this paper, a global asymptotic stability condition for Long Short-Term Memory neural networks is presented. Since this condition is formulated in terms of the networks’ weight matrices and biases that are essentially control variables, the same condition can be viewed as a way to globally asymptotically stabilize these networks. The condition and how to compute numerical values for the weight matrices and biases are illustrated by a number of numerical examples.

[1] Jürgen Schmidhuber,et al. Long Short-Term Memory , 1997, Neural Computation.

[2] Donato Trigiante,et al. THEORY OF DIFFERENCE EQUATIONS Numerical Methods and Applications (Second Edition) , 2002 .

[3] M. Hirsch,et al. Differential Equations, Dynamical Systems, and an Introduction to Chaos , 2003 .

[4] Charles R. Johnson,et al. Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[5] J. P. Lasalle. The stability and control of discrete processes , 1986 .

[6] Nils Bertschinger,et al. Real-Time Computation at the Edge of Chaos in Recurrent Neural Networks , 2004, Neural Computation.

[7] R. E. Kalman,et al. Control System Analysis and Design Via the “Second Method” of Lyapunov: I—Continuous-Time Systems , 1960 .

[8] Boris Murmann,et al. Some Local Stability Properties of an Autonomous Long Short-Term Memory Neural Network Model , 2018, 2018 IEEE International Symposium on Circuits and Systems (ISCAS).

[9] W. Fleming. Functions of Several Variables , 1965 .

[10] P. Holmes,et al. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields , 1983, Applied Mathematical Sciences.

[11] Dragoslav D. Šiljak,et al. Decentralized control of complex systems , 2012 .

[12] Alex Graves,et al. Generating Sequences With Recurrent Neural Networks , 2013, ArXiv.

[13] Jürgen Schmidhuber,et al. LSTM: A Search Space Odyssey , 2015, IEEE Transactions on Neural Networks and Learning Systems.