energy landscape of multi classification energy based model

Hello all,

i would like to ask what is the shape of energy function multi classification energy based model - if we want to classify numbers form 0-9:

• The energy landscape has 10 valleys on different places of the surface - each valley represent number of from 0-9. If we get new sample it the new sample is placed near some of the valley and using gradient descend we get move down to the valley of the number - and we classified it as that number.

or

• For each possible y we compute different landscape - for 1 we compute landscape where the 1 is the deeper valley and other numbers has not so deep energy holes. We examine the compatibility of the new sample with all landscapes (for all possible 10 landscape )

So basically we have single landscape with 10 valleys or we have 10 landscapes (each for possible discrete result - y)

Thank you all!