Frontier models have 'memoized' 2x2-digit multiplication, no intermediate steps needed

ctjlewis · x · 2026-09-26

Responding to a demo, ctjlewis argues frontier and top OSS models now have internal circuits that compute 2x2 and 3x3 digit arithmetic in a single step, without intermediate work.

He coins "memoized" for operations a model can perform reliably via dedicated circuits: a 2x2-digit multiplication comes out correct for any inputs without thinking, while 12x12-digit still requires working it out on paper — until those get memoized too. He likens it to memorizing multiplication tables: bigger models memorize bigger tables (3x3, 3x2, 4x2 digits), though they can still do un-memoized arithmetic via reasoning.

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