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Circuits of biological neurons, such as in the functional parts of the braincan be modeled as networks of coupled oscillators. Inspired by the ability ofthese systems to express a rich set of outputs while keeping (gradients of)state variables bounded, we propose a novel architecture for recurrent neuralnetworks. Our proposed RNN is based on a time-discretization of a system ofsecond-order ordinary differential equations, modeling networks of controllednonlinear oscillators. We prove precise bounds on the gradients of the hiddenstates, leading to the mitigation of the exploding and vanishing gradientproblem for this RNN. Experiments show that the proposed RNN is comparable inperformance to the state of the art on a variety of benchmarks, demonstratingthe potential of this architecture to provide stable and accurate RNNs forprocessing complex sequential data.

Coupled Oscillatory Recurrent Neural Network (coRNN): An accurate and (gradient) stable architecture for learning long time dependencies