# Learning an identity function with convolutional networks

I am trying to train networks to achieve what I expected to be a trivial task: learn the identity mapping. However, this is very hard to achieve, and the optimization is hard. Moreover, I don't want to learn $$f_\theta(x)=x\;\;\forall x$$, but only $$f_\theta(x_1)=x_1$$ for one particular example (I am trying to overfit!).

Any ideas why this optimization is so hard? The learning curves oscillate and most of the points are not visually satisfactory.