The bench — five tenants and one dangerous tile

The full world first: Q, K, V, O are tall thin matrices (N = 1024 rows, d = 64 wide) living in HBM, and the score matrix S = QKT is the N × N monster — drawn to the same scale below. None of this fits on the bench. The machine works on blocks: Br asker rows, Bc shelf rows, and the small tile of S where they cross.

Q K V O S = QKᵀ — N × N, never materialized ← only these small blocks ever visit the bench: Bᵣ = 64 asker rows of Q, O Bᶜ = 391 shelf rows of K, V one Bᵣ × Bᶜ tile of S
the bench — every tenant drawn to scale (1 seat = 1 unit of area)

Q-block Bᵣ·d
K-block Bᶜ·d
V-block Bᶜ·d
O-block Bᵣ·d
tile Bᵣ·Bᶜ
total
budget M100,000
free seats
rounds N/Bᶜ
64

fixed: d = 64   Bᶜ = 391   N = 1024   M = 100,000 numbers   (A100-class bench)