Title: Meta-Learning General-Purpose Learning Algorithms with Transformers. Abstract: Modern machine learning requires system designers to specify aspects of the learning pipeline, such as losses, architectures, and optimizers. Meta-learning, or learning-to-learn, instead aims to learn those aspects, and promises to unlock greater capabilities with less manual effort. One particularly ambitious goal of meta-learning is to train general purpose learning algorithms from scratch, using only black box models with minimal inductive bias. A general purpose learning algorithm is one which takes in training data, and produces test-set predictions across a wide range of problems, without any explicit definition of an inference model, training loss, or optimization algorithm. In this paper we show that Transformers and other black-box models can be meta-trained to act as general purpose learning algorithms, and can generalize to learn on different datasets than used during meta-training. We characterize phase transitions between algorithms that generalize, algorithms that memorize, and algorithms that fail to meta-train at all, induced by changes in model size, number of tasks used during meta-training, and meta-optimization hyper-parameters. We further show that the capabilities of meta-trained algorithms are bottlenecked by the accessible state size determining the next prediction, unlike standard models which are thought to be bottlenecked by parameter count. Finally, we propose practical interventions such as biasing the training distribution that improve the meta-training and meta-generalization of general purpose learning algorithms.