Recent works (Chen et al., 2022; Suzuki et al., 2023b) have demonstrated In this work, we improve the dependence on logarithmic Sobolev inequality (LSI) constants in their particle approximation errors which can exponentially deteriorate with the regularization coefficient. One may consider adding Gaussian noise to the gradient descent to make the method more stable.

Recurrent Neural Networks (RNNs) frequently exhibit complicated dynamics, and their sensitivity to the initialization process often renders them notoriously hardtotrain.

Then,fk is Li-Yorkechaoticwith constant (albeitsmall) probability. There suchthatk (whose minimumvalue ),fk is 3-periodic 1 .

"Gated Orthogonal Recurrent Units: On Learningto Forget".

Theirdifference,albeitobvious,shouldalsobeemphasized: GD isdeterministic, and the same constant initial condition will always lead to the same iterates.

In the case of coupled skew tent maps, theproposedmethodconsistently outperforms afivelayerDeepNeuralNetwork (DNN) and Long Short Term Memory (LSTM) architecture for unidirectional coupling coefficient values ranging from0.1 to 0.7.