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Stability of recurrent models is closely linked with trainability,generalizability and in some applications, safety. Methods that train stablerecurrent neural networks, however, do so at a significant cost toexpressibility. We propose an implicit model structure that allows for a convexparametrization of stable models using contraction analysis of non-linearsystems. Using these stability conditions we propose a new approach to modelinitialization and then provide a number of empirical results comparing theperformance of our proposed model set to previous stable RNNs and vanilla RNNs.By carefully controlling stability in the model, we observe a significantincrease in the speed of training and model performance.

Contracting Implicit Recurrent Neural Networks: Stable Models with Improved Trainability