SuperTensor/references/semantics.md

Symbol semantics

Shape is not meaning. Two tensors of shape T×k can be a score matrix, a list of token positions, or a Boolean support, and drawing all three the same way is the fastest way to mislead a reader who is trying to follow the mechanism.

Classify every non-obvious symbol

For each symbol record: semantic kind, dtype/domain, what one entry means, and its range when meaningful. Kinds worth separating:

kind	example	domain
value / activation	X, H	ℝ
score / logit	S = QKᵀ/√d_h	ℝ
probability	A = softmax(S)	[0,1], rows sum to 1
index / coordinate	I = TopKIndices(G)	{0,…,E−1}
rank / order	selected-slot axis r	{1,…,k}
count	n_e tokens per expert	ℕ
id	token id, device id	opaque
mask / support	D, causal M	{0,1} or {0,−∞}
permutation	gather order	bijection
shape parameter	p, h	ℕ, not drawn as a tensor

One block, one object

Never merge a score, an index list and a mask under a label like M/S. Each conversion gets an explicit operator and arrow. For selection or routing, close the entire chain:

continuous scores → discrete indices/ids → gather / scatter / mask / route → selected values

TopKValues and TopKIndices are different tensors; if both are used, show both.

Three grammars, deliberately different

object	grammar	package
value / score / probability	magnitude — three separated lightness levels	\stface[pattern=dense]
index / id	discrete symbols in outlined cells, no lightness ramp	\stindexface{...}{entries}
mask / support	one flat level, exact structure, zeros unfilled	\stface[pattern=causal, level=3] or pattern=data

examples/moe-topk-gather.tex puts all three in one figure on purpose. The reason indices get no ramp: a ramp invites the reader to compare expert 3 > expert 0 as if the number were a size.

Notation duties

• Define index notation and range at first use: S_t = (s_{t,1},…,s_{t,k}), s_{t,r} ∈ {0,…,t}.
• Distinguish the source-position axis s from the selected-slot axis r, and say whether ordering, duplicates, padding or variable cardinality matter.
• Show the address mapping once: G[b,t,r,:] = X[b, S[b,t,r], :].
• If a mask is shown alongside the index tensor, state M[b,t,s] = 1[s ∈ S_{b,t}] — do not let the figure imply they are the same object.
• When one selector is shared across heads, ranks or branches, draw it once and mark the broadcast/reuse axis. A per-head copy of a shared mask is a false claim about memory and about the computation (examples/mha-causal.tex: M is a single face while A is a three-sheet stack).

Colors carry semantics too

One tensor role keeps one hue for the whole figure — that is what \stsetrole is for. A gathered, resharded or regrouped view of the same data keeps the same role color; a new hue means a new object. Derived tensors may reuse their parent's family rather than spending a hue (V → O → Y in the MHA example are all violet).

A \stgroup outline follows the same rule, because a group is a regrouped view: give it the role of the objects it wraps — the three-sheet q stack and the outline that names it as one composite are the same object, and a new hue there would claim a new tensor exists. Only when the members genuinely differ in role does the group take role=neutral; that is also the honest signal that the box is naming an arrangement rather than an object.