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Modern deep learning models employ considerably more parameters than requiredto fit the training data. Whereas conventional statistical wisdom suggests suchmodels should drastically overfit, in practice these models generalizeremarkably well. An emerging paradigm for describing this unexpected behavioris in terms of a \emph{double descent} curve, in which increasing a model'scapacity causes its test error to first decrease, then increase to a maximumnear the interpolation threshold, and then decrease again in theoverparameterized regime. Recent efforts to explain this phenomenontheoretically have focused on simple settings, such as linear regression orkernel regression with unstructured random features, which we argue are toocoarse to reveal important nuances of actual neural networks. We provide aprecise high-dimensional asymptotic analysis of generalization under kernelregression with the Neural Tangent Kernel, which characterizes the behavior ofwide neural networks optimized with gradient descent. Our results reveal thatthe test error has non-monotonic behavior deep in the overparameterized regimeand can even exhibit additional peaks and descents when the number ofparameters scales quadratically with the dataset size.

The Neural Tangent Kernel in High Dimensions: Triple Descent and a Multi-Scale Theory of Generalization