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Presently the most successful approaches to semi-supervised learning arebased on consistency regularization, whereby a model is trained to be robust tosmall perturbations of its inputs and parameters. To understand consistencyregularization, we conceptually explore how loss geometry interacts withtraining procedures. The consistency loss dramatically improves generalizationperformance over supervised-only training; however, we show that SGD strugglesto converge on the consistency loss and continues to make large steps that leadto changes in predictions on the test data. Motivated by these observations, wepropose to train consistency-based methods with Stochastic Weight Averaging(SWA), a recent approach which averages weights along the trajectory of SGDwith a modified learning rate schedule. We also propose fast-SWA, which furtheraccelerates convergence by averaging multiple points within each cycle of acyclical learning rate schedule. With weight averaging, we achieve the bestknown semi-supervised results on CIFAR-10 and CIFAR-100, over many differentquantities of labeled training data. For example, we achieve 5.0% error onCIFAR-10 with only 4000 labels, compared to the previous best result in theliterature of 6.3%.

There Are Many Consistent Explanations of Unlabeled Data: Why You Should Average