Learned positional lookup P[:T]

Background

GPT-2 uses learned positional embeddings: a table P ∈ ℝ^{block_size × C} indexed by position, not token id. For a sequence of length T, you take the first T rows — position t gets row P[t]:

$$\text{pos\_emb} = P[0{:}T], \qquad \text{shape } (T, C)$$

These broadcast across the batch when added to the token embeddings.

Problem statement

Implement positional_lookup(P, T) returning the position rows for a length-T sequence.

Input

• P — learned positional table, shape (block_size, C).
• T — int, sequence length.

Output

Returns an np.ndarray of shape (T, C): the first T rows of P.

Examples

Example 1

Input:  P = [[0, 0], [1, 1], [2, 2], [3, 3]], T = 2
Output: [[0, 0], [1, 1]]

Constraints

• Return P[:T] (positions 0..T-1).
• Result shape (T, C).

Notes

• Unlike the token table (indexed by token id), this is indexed by arange(T) — the same positions every forward pass, regardless of which tokens appear.