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AI & ML · Machine Learning Math

Activation & loss gradients

151 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

    The sigmoid activation satisfies σ′(z)=σ(z) (1−σ(z))\sigma'(z) = \sigma(z)\,(1 - \sigma(z)). At a certain pre-activation the sigmoid output is exactly σ(z)=16\sigma(z) = \dfrac{1}{6}. Compute the exact value of σ′(z)\sigma'(z) as a fraction.

  2. Warm-up

    The sigmoid activation satisfies σ′(z)=σ(z) (1−σ(z))\sigma'(z) = \sigma(z)\,(1 - \sigma(z)). At a certain pre-activation the sigmoid output is exactly σ(z)=15\sigma(z) = \dfrac{1}{5}. Compute the exact value of σ′(z)\sigma'(z) as a fraction.

  3. Warm-up

    The sigmoid activation satisfies σ′(z)=σ(z) (1−σ(z))\sigma'(z) = \sigma(z)\,(1 - \sigma(z)). At a certain pre-activation the sigmoid output is exactly σ(z)=23\sigma(z) = \dfrac{2}{3}. Compute the exact value of σ′(z)\sigma'(z) as a fraction.

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