M

M — the attention mask

A matrix of 0s and −∞ (minus infinity) added to the attention scores before softmax. A 0 leaves a position allowed; −∞ blocks it.

Adding $-\infty$ to a score before softmax removes that option. Since $e^{-\infty} = 0$ , that position gets exactly zero weight, contributes nothing, and receives no gradient.

The causal mask sets $M_{ij} = -\infty$ whenever $j > i$ , so token $i$ cannot look at later tokens. In code, a large negative number such as $-10^9$ is used in place of $-\infty$ to avoid arithmetic with true infinities.

Example

M = \begin{bmatrix} 0 & -\infty & -\infty \\ 0 & 0 & -\infty \\ 0 & 0 & 0 \end{bmatrix}

Causal mask for 3 tokens: row i may see columns up to i and nothing after.

Where the course uses it

6.2 Scaled Dot-Product Attention, by Hand · Module 6, Attentionfirst use
8.4 Decoder-Only: Predicting the Next Token · Module 8, Three Families: Encoder, Encoder-Decoder, Decoder

Related terms

The exponential functionRead "e to the z" (also written exp(z)). It raises e ≈ 2.718 to the power z. The result is always positive: e⁰ = 1, and it shrinks toward 0 as z becomes very negative.
Cases — an if/elseA large left brace with several lines is an if/else written vertically. Read each line as "this value, if this condition holds" and use the line whose condition is true.
Scaled dot-product attentionEach token scores every other token, turns the scores into weights that add up to 1, and takes the weighted average of their value vectors.