How do high-speed trains avoid lifting off the tracks?

It's called aerodynamics and weight. Railroad tracks do not change elevation and direction like a roller coaster. They operate on much gentler grades and curves. That plus the overall weight of the engine and cars pretty much keeps them on the tracks. Extreme high-speed trains also get a bit of assistance from aerodynamic design.

The "just the slightest change in grade" is not enough. Something only lifts off if the change in grade is more than (v^2)/g, where v is the speed and g is the strength of the local gravitational field (on earth's surface, approximately 9.8 m/s^2 or 32 ft/s^2). High-speed trains run on special tracks that are designed not to have that much of a change in grade.

For the same reason race cars stay on the ground, aerodynamics. The forces that make an airplane lift off the ground used in reverse can hold a properly shaped body onto the ground.

You've seen the footage of race cars becoming airborne, the same would happen to high speed rail if it werent for the downward force or air at high speed.

I assume you mean passenger trains at speeds of 150 MPH and higher.

The locomotive might weigh 200,000 pounds or more so it would have about 100,000 pounds holding the front end down. The slope of the locomotive cab results in additional downward force at high speeds and the front cross section is small compared to the rest of the train. Crosswinds from the side at hurricane speeds might be more apt to cause problems. I'm sure the design engineers set limits on operational speeds and wind conditions as well as track geometry.

The front of the train is wedge shaped so the air pushes it downwards at high speed. And the changes of grade are gentle enough that the trains won't lift off.

Basically it's weight keeps it on the track.