[dnautics]

do we know if the rounding errors are a big deal for numerical methods that can tolerate inaccuracy (like gradient descent for machine learning)?

[nestorD]

It depends. I have seen some algorithms (the example that comes to mind was a clustering) become worse solely due to numerical error.

When that happens, if you are not equiped to measure the numerical error or at least trained to suspect it, you might think that it is just the algorithm that is not working.

[hamilyon2]

Rounding errors, underflows and instability in floats are very well known problems, a big deal if you do anything but graphics.

[klyrs]

You want to converge on a local minimum, don't you? We can't guarantee that with unstable algorithms.