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AI at work · course 26 of 105

Neural Networks Without the Black Box

Work out by pencil and calculator what a neural network computes, from one node’s weighted sum to a forward pass, softmax, the losses and one step of gradient descent.

4 modules

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What it teaches

What a neural network actually computes, worked with your own pencil: one node’s weighted sum and activation (ReLU, sigmoid, tanh), a forward pass through a small two-layer network, softmax, the losses (MSE, RMSE, log loss), and one step of gradient descent, including what a too-big learning rate and a dead ReLU do. The AI asks 3 questions, places you, shows a short card per module, then gives you one problem at a time and checks your answer against an answer key: every number answer in it was computed by script.

How long

36 items. About 30-50 rounds plus a 12-item final: 2-3 sessions (estimate, not timed with a real student). The tutor gives a one-line save code at the end of each session.

The modules

4 modules, drilled one item at a time.

  1. M0

    The words

    Concept questions

  2. M1

    One node

    Weighted sums and activations

  3. M2

    A forward pass through a small network

    Forward passes through one small network, and softmax

  4. M3

    Loss and one step of learning

    Loss, gradient steps

Before it teaches, it asks

  1. 1
    Why are you learning this (a course, work with ML teams, curiosity), and how comfortable are you with algebra: weighted sums, e^x, logs?
    AI voice (ElevenLabs)
  2. 2
    Inputs x = (1, 2, 3), weights w = (0.2, 0.3, 0.5), bias b = −0.5, ReLU activation. Output?
  3. 3
    Network A, input x = (1, 2). What is the output?Network A: inputs x1, x2 → two hidden nodes with ReLU → one output, no activation.h1 = ReLU(1·x1 − 1·x2 + 0.5)h2 = ReLU(0.5·x1 + 1·x2 − 1)output = 2·h1 + 1·h2 + 0

What’s exact, and what isn’t

Show

Straight from the course’s own notes.

Computed by script
Every number key, in exact fractions (e^x and logs as floats, shown to 4 places), from numbers typed into the script. Every forward pass is computed two ways and must agree; every gradient is checked against a finite-difference estimate; 15 of the 18 listed wrong answers are reproduced by making the slip. The script does not read the question text, the working lines, the wrong-answer notes or the teach cards: a test run with AI-simulated students checked the question-to-answer links, the working sums and the card numbers with its own scripts and found no errors there.
Sourced
Definitions and formulas from Google’s Machine Learning Crash Course, 20 short quotes matched word for word on 2026-10-10.
Simplified on purpose
One-weight gradient steps only (the chain rule through several layers is not in yet); a calculator is fine for e^x and logs.
Not in it yet
Full backpropagation, convolutional/recurrent networks, transformers, code.