About Momentum vs SGD
This page compares SGD and momentum on a narrow valley, f(x, y) = x squared + 10 y squared, with a learning rate of 0.01. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.
The valley is ten times steeper in y than in x. Plain SGD must use a rate small enough for the steep direction, so it crawls along the gentle one. Momentum keeps a velocity: along x the gradients keep the same sign, so the velocity builds up and the steps grow, while across y the gradients flip sign and the velocity cancels out.
With a momentum factor of 0.9 the effective step along a steady slope is about ten times the learning rate, which is why momentum reaches the bottom far sooner here.
How to use Momentum vs SGD
- Choose a function. The suggested learning rate for it is filled in.
- Change the learning rate if you like. Smaller is slower and safer, larger is faster until it blows up.
- Press Step to move every optimizer once, or Play to animate. "+25 steps" skips ahead.
- Tap the plot to move the starting point (the cross). The paths restart from there.
- Read the table for each optimizer's position, value and status: running, converged or diverged.
- Watch the log chart: a line that keeps falling is converging, and a line that climbs is diverging.
Features
- Seven functions: three curves and four 2D surfaces, including a narrow valley, Rosenbrock, Himmelblau and a saddle.
- SGD, Momentum, RMSprop and Adam, all from the same start with the same learning rate.
- Contour map for 2D functions and a curve for 1D, with a coloured path for each optimizer.
- Divergence detection that stops a run and says which optimizers blew up.
- A log-scale chart of the function value against step.
- Step, play and +25 steps controls, with slower playback if you prefer reduced motion.
- Tap the plot to choose the starting point.
Worked examples
Narrow valley, learning rate 0.01, 60 steps gives SGD 0.9066, Momentum 0.0644, RMSprop 29.8874, Adam 33.2263
Momentum is already about fourteen times lower than plain SGD, because it has built up speed along the gentle direction. RMSprop and Adam move about one learning rate per step, so at a rate this small they have barely begun.
Privacy: how it works
- Everything is computed in your browser tab. Nothing is sent to Ulkaa or anyone else.
Tips
- On the parabola, try a learning rate of 0.5: SGD jumps to the minimum in a single step because the step size matches the curvature exactly.
- On the double well, drag the start to the left side and see it settle in the other, shallower minimum.
- On Himmelblau, change the start point and see different optimizers choose different minima.
- If a path vanishes off the plot, check the status column: it probably diverged.
Frequently asked questions
Is it really free?
Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.
Do I need an account?
No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.
Does it run in my browser?
Yes. Your settings are processed by code running in your browser tab, on your own device.
Is my data uploaded?
No. Your settings are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.
How does momentum help gradient descent?
It adds up past gradients into a velocity, so steps grow along consistent directions and cancel where the gradient flips sign. That speeds up travel in valleys and damps zigzags.
What momentum value is typical?
0.9 is the common default, which this page uses. Values nearer 1 give more inertia and can overshoot.
More Gradient Descent Visualizer pages
- Gradient Descent VisualizerCompare SGD, Momentum, RMSprop and Adam side by side, step by step, on curves and contour maps.
- Learning Rate Too High: Gradient Descent DivergenceSee the error grow instead of shrink when the learning rate crosses its limit.
- SGD Learning Rate VisualizerChange the learning rate and watch plain gradient descent speed up, oscillate or stall.
- Adam Optimizer VisualizerSee Adam adapt its step per direction on the curved Rosenbrock valley.
- RMSprop Optimizer VisualizerSee RMSprop normalise its steps on a surface with four minima.
- Gradient Descent and Local MinimaStart on one side of a double well and see which minimum each optimizer reaches.
- Gradient Descent at a Saddle PointStart almost on a ridge and see how long each optimizer takes to escape the saddle.
- Gradient Descent on the Rosenbrock FunctionFollow gradient descent down the curved banana valley of the Rosenbrock function.
- Gradient Descent on a Bumpy LossSee how a bumpy loss traps plain gradient descent and how momentum helps.