<i>But what does Knowing Why The Network Works mean exactly?</i><p>I would say it means: Why do these algorithms <i>seem</i> to be doing &quot;well&quot; despite their well-known theoretical intractability? Is it something about the instances? Or is it simply a matter of scale (so the local optima they are getting stuck in are not as obvious)? Or is there something &quot;deep&quot; we do not understand yet about these algorithms (or the theory)?<p>Either way, there is something going on here for sure.