Mathematically, convergence just means that the distance to some limit point goes to 0 in the limit. There’s no implication that the limit point has to be unique, or optimal. Eg. in the case of Newton fractals, there are multiple roots and the trajectory converges to one of the roots, but which one it converges to depends on the starting point of the trajectory. Once the weight updates become small enough, we should say the net has converged, regardless of whether it achieved the “optimal” loss or not.
If even “converged” is not good enough, I’m not sure what one could say instead. Probably the real problem in such cases is people being doofuses, and probably they will continue being doofuses no matter what word we force them to use.
You raise good points. I agree that the mathematical definition of convergence does not insinuate uniqueness or optimality, thanks for reminding me of that.
Mathematically, convergence just means that the distance to some limit point goes to 0 in the limit. There’s no implication that the limit point has to be unique, or optimal. Eg. in the case of Newton fractals, there are multiple roots and the trajectory converges to one of the roots, but which one it converges to depends on the starting point of the trajectory. Once the weight updates become small enough, we should say the net has converged, regardless of whether it achieved the “optimal” loss or not.
If even “converged” is not good enough, I’m not sure what one could say instead. Probably the real problem in such cases is people being doofuses, and probably they will continue being doofuses no matter what word we force them to use.
You raise good points. I agree that the mathematical definition of convergence does not insinuate uniqueness or optimality, thanks for reminding me of that.