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Autoregressive neural network models have been used successfully for sequence generation, feature extraction, and hypothesis scoring. This paper presents yet another use for these models: allocating more computation to more difficult inputs. In our model, an autoregressive model is used both to extract features and to predict observations in a stream of input observations. The surprisal of the input, measured as the negative log-likelihood of the current observation according to the autoregressive model, is used as a measure of input difficulty. This in turn determines whether a small, fast network, or a big, slow network, is used. Experiments on two speech recognition tasks show that our model can match the performance of a baseline in which the big network is always used with 15% fewer FLOPs.