Velocity Settles At Ten Times

Keras implements SGD with momentum as

velocity = momentum * velocity - learning_rate * g
w = w + velocity

A job trains stably with plain SGD at learning_rate=0.1. You turn on momentum=0.9 and leave the learning rate alone. Over a stretch where the gradient $g$ is roughly constant, what does the velocity settle at, and which learning rate restores the old step size?

Velocity grows without bound on a constant gradient, so momentum is only usable when the gradient changes sign regularly.

Velocity settles at $-g$ , so each step moves ten times further than plain SGD's $-0.1g$ ; learning_rate=0.01 restores the original step.

Velocity settles at $-0.1g$ , the same as plain SGD. Momentum only smooths noisy gradients, so keep 0.1.

Velocity settles at $-0.09g$ , so momentum shrinks the step by the factor 0.9; raise the learning rate to about 0.11.