Training a CNN-HMM model
CNN

Let's say you have $P$ phones $p_0,p_1,\ldots,p_{P-1}$ and the CNN generates the posterior probabilities $x_i = x(p_i)$ for $i=0,\ldots,P-1$.

HMM 

A Hidden Markov Model is a system that has $S$ states $s_0,\ldots,s_{S-1}$ that can produce $O$ observations $o_0,\ldots,o_{O-1}$. 

The probability of jumping from state $s_i$ to state $s_j$ is $a_{ij}$, and this is captured by the state transition (probability) matrix $\mathbf{A} = [a_{ij}]$.  

The output $o_i$ is generated by the state $s_j$ with probability $b_{ij}$ to form the output matrix $\mathbf{B} = [b_{ij}]$.

How to connect them?

So let's say that your phones $p_i$ are the states of the HMM $s_i$ (so that $S=P$).

But after that, I can't really say. The $x_i$ aren't really the $a_{ij}$. Nor are they the $b_{ij}$.

This paper contains the image below... but their explanation isn't really clear to me.

I'll read the paper again in the morning and see if that sheds any light.