Accelerating Real-Time ML with Symbolic Python Interpreter
chalk.ai3 pointsby Derander1 comments
x + 2 * dx * step, y * 2 * dy * step.
What you've done is double the step-multiplier, not the gradient itself (<dx, dy>). This means that the optimization process jumps further at each step. However, the step size that OP chose is somewhat arbitrary to begin with, so it's not clear why any particular choice would be better or worse. The reason that the step size matters is that if your step size is too large your optimization process might jump over a minimum location or something similarly bad -- there are pathological functions like the Rosenbrock Function [1] which are notoriously hard to optimize with gradient ascent. In practice, you'll often choose your step size more intelligently based on a few different tests, or vary it as the optimization process progresses.
To make Python faster, I built a Symbolic Python Interpreter to make Chalk’s “Python resolvers” into optimized Velox-native expressions — enabling high-performance execution without sacrificing developer experience.
This post explains the problem I encountered, why it’s so challenging, and how we solved for it.