What do the symbols in this image mean in relation to autoencoding? (which concepts do they represent and why?)
The question seems more about notation than autoencoders:
$ a,b = argmin_{a,b}f(a,b)$ simply means that $a$ and $b$ are chosen to minimize $f$.
w.r.t. autoencoders, the argmin statement is saying that we want the decoding of the encoded data $X$ to be as similar as possible to the original $X$.
To represent &quot;decoding of the encoding&quot;, we can use function composition: $\psi\circ\phi X$ which means $\psi(\phi(X))$, hence the decoding of the encoding of $X$.
So overall, we are saying that we choose the encoding and decoding functions to minimize the delta between input $X$ and encoded/decoded $X$.

Where the question asks:

what does the arg min section and beyond mean?

The latter half &quot;and beyond&quot; should be more specific.