6 problems

Non-singularity conjecture. The Jacobian matrix

Noisy-typewriter test-channel conjecture. The optimal test-channel from $\mathsf{Z}$ to $\mathsf{Y}$ should also be a noisy typewriter channel.

Let $x-t-z$ be a Markov chain, with $y=x+n$, where $x$ and $n$ are independent, $n\sim N(0,1)$, and the input satisfies $\mathbb{E}[x^2]=P$. Suppose that the bottleneck output $z$…

Let $\mathcal{Y}$ be the set of classes in a classification problem, and let $|\mathcal{Y}|$ denote the number of classes. A phase transition is a transition in the information bot…

The variables $X$, $Y$, and $Z$ describe, respectively, input data, a binary classification target, and a finite-valued compressed representation of $X$. Shannon's entropy of the r…

A deep neural network has layers whose input and output variables form successive representations, and the information bottleneck (IB) framework describes the tradeoff between pres…