Slide 8 (about 19 minutes into the video) of the Stanford Seminar - Information Theory of Deep Learning, Naftali Tishby has the following (rather informally stated) theorem.

Theorem (Information Plane) For large typical $\mathbf{X}$, the sample complexity of a DNN is completely determined by the encoder mutual information $\mathbf{I(X;T)}$, of the last hidden layer; the accuracy (generalization error) is determined by the decoder information, $\mathbf{I(T;Y)}$, of the last hidden layers.

I am having difficulty following what is meant by "the sample complexity is completely determined". What is the precise statement of this theorem?