On the Implicit Bias of Gradient Descent for Temporal Extrapolation

When using recurrent neural networks (RNNs) it is common practice to apply trained models to sequences longer than those seen in training. This ``extrapolating'' usage deviates from the traditional statistical learning setup where guarantees are provided under the assumption that train and test distributions are identical. Here we set out to understand when RNNs can extrapolate, focusing on a simple case where the data generating distribution is memoryless. We first show that even with infinite training data, there exist RNN models that interpolate perfectly (i.e., they fit the training data) yet extrapolate poorly to longer sequences. We then show that if gradient descent is used for training, learning will converge to perfect extrapolation under certain assumptions on initialization.Our results complement recent studies on the implicit bias of gradient descent, showing that it plays a key role in extrapolation when learning temporal prediction models.