A method performed by one or more computers, the method comprising: determining an architecture for a task neural network that is configured to perform a particular machine learning task, comprising: obtaining data specifying a current set of candidate architectures for the task neural network, wherein the current set of candidate architectures is determined by expanding cells of one or more previous candidate architectures; for each candidate architecture in the current set: processing the data specifying the candidate architecture using a performance prediction neural network having a plurality of performance prediction parameters, wherein the performance prediction neural network is configured to process the data specifying the candidate architecture in accordance with current values of the performance prediction parameters to generate a performance prediction that characterizes how well a neural network having the candidate architecture would perform after being trained on the particular machine learning task; and generating an updated set of candidate architectures by selecting one or more of the candidate architectures in the current set based on the performance predictions for the candidate architectures in the current set, the generating comprising pruning the current set of candidate architectures based on the respective performance predictions to reduce the size of the current set; and wherein the task neural network is configured to process an image, the particular machine learning task comprises image classification, and the task neural network is configured to generate one or more scores for each of a set of object categories, with each score representing an estimated likelihood that the image contains an image of an object belonging to the category; or wherein the task neural network is configured to process an image, the particular machine learning task comprises object detection, and the task neural network is configured to identify locations in the input image at which particular types of objects are depicted; or wherein the task neural network is configured to process audio data, the particular machine learning task comprises speech recognition, and the task neural network is configured to generate an output that determines, for a given spoken utterance, the term or terms that the utterance represents. obtaining data specifying a current set of candidate architectures for the task neural network, wherein the current set of candidate architectures is determined by expanding cells of one or more previous candidate architectures; for each candidate architecture in the current set: processing the data specifying the candidate architecture using a performance prediction neural network having a plurality of performance prediction parameters, wherein the performance prediction neural network is configured to process the data specifying the candidate architecture in accordance with current values of the performance prediction parameters to generate a performance prediction that characterizes how well a neural network having the candidate architecture would perform after being trained on the particular machine learning task; and processing the data specifying the candidate architecture using a performance prediction neural network having a plurality of performance prediction parameters, wherein the performance prediction neural network is configured to process the data specifying the candidate architecture in accordance with current values of the performance prediction parameters to generate a performance prediction that characterizes how well a neural network having the candidate architecture would perform after being trained on the particular machine learning task; and generating an updated set of candidate architectures by selecting one or more of the candidate architectures in the current set based on the performance predictions for the candidate architectures in the current set, the generating comprising pruning the current set of candidate architectures based on the respective performance predictions to reduce the size of the current set; and wherein the task neural network is configured to process an image, the particular machine learning task comprises image classification, and the task neural network is configured to generate one or more scores for each of a set of object categories, with each score representing an estimated likelihood that the image contains an image of an object belonging to the category; or wherein the task neural network is configured to process an image, the particular machine learning task comprises object detection, and the task neural network is configured to identify locations in the input image at which particular types of objects are depicted; or wherein the task neural network is configured to process audio data, the particular machine learning task comprises speech recognition, and the task neural network is configured to generate an output that determines, for a given spoken utterance, the term or terms that the utterance represents.