My own understanding of the flat minima idea is that it’s a different thing. It’s not really about noise, it’s about gradient descent in general being a pretty shitty optimization method, which converges very poorly to sharp minima (more precisely, minima with a high condition number). (Continuous gradient flow circumvents that, but using step sizes small enough to circumvent the problem in practice would make GD prohibitively slow. The methods we actually use are not a good approximation of continuous flow, as I understand it.) If you want flat minima, then an optimization algorithm which converges very poorly to sharp minima could actually be a good thing, so long as you combine it with some way to escape the basin of the sharp minimum (e.g. noise in SGD).
That said, I haven’t read the various papers on this, so I’m at high risk of misunderstanding.
Also worth noting that there are reasons to expect convergence to flat minima besides bias in SGD itself. A flatter basin fills more of the parameter space than a sharper basin, so we’re more likely to initialize in a flat basin (relevant to the NTK/GP/Mingard et al picture) or accidentally stumble into one.
My own understanding of the flat minima idea is that it’s a different thing. It’s not really about noise, it’s about gradient descent in general being a pretty shitty optimization method, which converges very poorly to sharp minima (more precisely, minima with a high condition number). (Continuous gradient flow circumvents that, but using step sizes small enough to circumvent the problem in practice would make GD prohibitively slow. The methods we actually use are not a good approximation of continuous flow, as I understand it.) If you want flat minima, then an optimization algorithm which converges very poorly to sharp minima could actually be a good thing, so long as you combine it with some way to escape the basin of the sharp minimum (e.g. noise in SGD).
That said, I haven’t read the various papers on this, so I’m at high risk of misunderstanding.
Also worth noting that there are reasons to expect convergence to flat minima besides bias in SGD itself. A flatter basin fills more of the parameter space than a sharper basin, so we’re more likely to initialize in a flat basin (relevant to the NTK/GP/Mingard et al picture) or accidentally stumble into one.