\forall

∀ and ∃ — for all, there exists

∀ (an upside-down A) reads "for all" or "for every". ∃ (a backwards E) reads "there exists", meaning at least one.

$\dots = 0 \;\forall j > i$ says the statement holds for every index $j$ larger than $i$ , with no exceptions. That is the guarantee a causal mask must give: no token receives any weight from a later token.

Example

x^2 \ge 0 \;\; \forall x \in \mathbb{R}

Read: x squared is at least zero for every real number x.

Where the course uses it

8.4 Decoder-Only: Predicting the Next Token · Module 8, Three Families: Encoder, Encoder-Decoder, Decoderfirst use

Related terms

⟹ — impliesRead "implies" or "therefore". If the left side is true, the right side follows.
M — the attention maskA matrix of 0s and −∞ (minus infinity) added to the attention scores before softmax. A 0 leaves a position allowed; −∞ blocks it.