Abstract: Self-shrinkers model the singularities of the mean curvature flow. A Bernstein-type result for self-shrinkers says that any entire self-shrinking graph must be a hyperplane. In this talk, I will discuss a stronger rigidity result that any self-shrinker which is graphical in a large, but compact, ball must be a hyperplane. In fact, this rigidity holds within a larger class of almost stable self-shrinkers. A key ingredient of this result is a curvature estimate for almost stable shrinkers. This is joint work with Jonathan Zhu.