minor cleanup

This commit is contained in:
NT
2021-04-19 12:01:39 +08:00
parent 0dd0c092c0
commit 760708d678
5 changed files with 77 additions and 88 deletions

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@@ -11,7 +11,9 @@ models, and there are lots of great introductions to deep learning.
Hence, we'll keep it short:
our goal is to approximate an unknown function
$f^*(x) = y^*$ ,
$$
f^*(x) = y^* ,
$$ (learn-base)
where $y^*$ denotes reference or "ground truth" solutions.
$f^*(x)$ should be approximated with an NN representation $f(x;\theta)$. We typically determine $f$
@@ -20,7 +22,9 @@ of the NN.
This gives a minimization problem to find $f(x;\theta)$ such that $e$ is minimized.
In the simplest case, we can use an $L^2$ error, giving
$\text{arg min}_{\theta} | f(x;\theta) - y^* |_2^2$
$$
\text{arg min}_{\theta} | f(x;\theta) - y^* |_2^2
$$ (learn-l2)
We typically optimize, i.e. _train_,
with some variant of a stochastic gradient descent (SGD) optimizer.