Hessian–Vector Directional Propagation

In many machine learning applications, computing the full Hessian matrix (second derivatives) is too expensive. The Pearlmutter forward-over-reverse method allows propagating a specific direction through a gradient computation graph to reveal local curvature without forming a dense Hessian.

Experiment

You can interact with the directional propagation in the interactive module.

1. Set Point x to 1.
2. Set Point y to 1.
3. Set Direction to Diagonal.

Observe that at (1,1), the gradient is [0, 0] since it is the global minimum. The directional curvature is 202, showing positive curvature in this diagonal direction.