Typicality of thermal states in isolated quantum systems corresponds to ubiquity of global minima in wide artificial neural networks

The Neural Tangent Kernel theory theoretically guarantees the existence of global minima of the cost functional in the neighborhood of an arbitrary random initialized parameters in wide artificial neural networks. In this paper, we show that the ubiquity of the global minima directly corresponds to the typicality of pure thermal states in isolated quantum systems by identifying a common underlying mechanism characterized by the restriction to a few observables and the role of a Wishart-type matrix. Moreover, we demonstrate that the increase in distinguishability of the reduced density matrices of typical pure states with subsystem size corresponds to the double descent phenomenon observed by varying the width of layers in finite-width artificial neural networks. Thereby, the threshold for the reduced state become thermal is determined by essentially the same condition as the fitting threshold. In this manner, we reveal a structural correspondence between thermalization in isolated quantum systems and wide neural network.