What AlphaTensor found

AlphaTensor (Fawzi et al., 2022) is built on AlphaZero. A network looks at a game state and outputs a ranking of promising moves and an estimate of how many more moves the game will take — a measure of position learned from games, uphill moves included, where greedy had its count of nonzero cells. A tree search uses it to look ahead, and its games become training data.

From the paper:

• 4 × 4 matrices modulo 2: 47 multiplications, where Strassen applied twice gives 49.
• A 4 × 5 times a 5 × 5 matrix: 76, where the best known was 80.
• 4 × 4 in ordinary arithmetic: 49, matching the best known count, not beating it.

The 47-multiplication algorithm agrees with (A @ B) % 2 on all 1,000 random pairs and with A @ B on none. A count of multiplications always comes with the arithmetic it was counted in. The notebook and the widget train nothing: they check DeepMind’s published lists.