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AI & ML · Machine Learning Math

Jacobians & Hessians for networks

120 problems in this skill, each with a solver-verified answer key. Answers are checked the moment you submit — with a hint if you want one and a worked solution afterwards.

What the problems look like

A few statements from this skill. Answers, hints and worked solutions live in the practice session.

  1. Warm-up

    A two-layer scalar network computes y=x+2y = x + 2 followed by z=2y2z = 2y^{2}. By the chain rule, dz/dx=(dz/dy)(dy/dx)dz/dx = (dz/dy)(dy/dx). Compute dz/dxdz/dx at x=2x = 2.

  2. Warm-up

    A two-layer scalar network computes y=2x+1y = 2x + 1 followed by z=3y2z = 3y^{2}. By the chain rule, dz/dx=(dz/dy)(dy/dx)dz/dx = (dz/dy)(dy/dx). Compute dz/dxdz/dx at x=−2x = -2.

  3. Warm-up

    A two-layer scalar network computes y=2x+3y = 2x + 3 followed by z=3y2z = 3y^{2}. By the chain rule, dz/dx=(dz/dy)(dy/dx)dz/dx = (dz/dy)(dy/dx). Compute dz/dxdz/dx at x=−1x = -1.

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