TensorGame

TensorGame — the AlphaTensor paper’s name for the search for a short factorization, played as a one-player game. Spanish: TensorGame (el juego del tensor).

• The game starts from the tensor T.
• A move is three vectors (u, v, w) from a small fixed set of entries; it subtracts their block from the current state.
• The game ends when every cell is 0.
• Every move costs −1: the score is minus the number of moves.

A game won in R moves is an algorithm with R multiplications. On the 2 × 2 tensor with entries −1, 0 and 1 there are 128,000 different moves, and about 10³² sets of seven. For 4 × 4 with the five values −2 … 2 the paper allows, a single move has 5⁴⁸ ≈ 3.6 × 10³³ choices.