Beginner explanation
A simple artificial neuron combines numbers using adjustable weights and a bias. These are mathematical components, not miniature biological brains. Training changes the numbers so the network performs a task better on examples.
Intermediate explanation
For inputs x, a neuron first computes z = w·x + b. Weights control how inputs contribute and bias shifts the result. An activation then transforms z. Input scaling matters because features measured in different units can behave very differently.
Advanced explanation
A layer applies an affine map followed by an activation: a = φ(Wx + b). Dimensions must agree. Large coefficients do not automatically imply global feature importance, especially when inputs are correlated or differently scaled.
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A worked example
With x₁ = 2, x₂ = 3, w₁ = 0.5, w₂ = −1 and b = 1, the pre-activation is 1 − 3 + 1 = −1. This is an intermediate value, not a probability unless a suitable output transformation is applied.
TRY IT YOURSELF
Practice the idea
Calculate z for x = (4, 2), w = (0.5, −1) and b = 3.
Reveal the answer guide
z = 0.5×4 − 1×2 + 3 = 3. Changing the bias to 0 would make z = 0 without changing how either input is weighted.
Go further: advanced challenge
Explain why comparing two raw weight magnitudes is misleading when one feature is measured in dollars and another in thousands of dollars.
An open-ended discussion task. Explain your assumptions and evidence; there may be more than one defensible answer.
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Original AstraCruz explanations and fictional exercises. These primary references provide broader technical context; linked materials may change.
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