Sketchpad: a 0.8B VLM certifies exact arbitrary-length arithmetic in the browser, verified in Lean
Mostafa 'Neo' Mohsenvand · hf · 2026-11-09
Sketchpad runs Qwen3.5-0.8B with a low-rank adapter on a rendered sheet in the browser: each forward pass reads a three-cell view and emits one digit, carry/borrow, and next operation, while a fixed runtime moves the view and writes no result digits. Because each step reads only a bounded external memory view, exactness becomes a finite, checkable property—they prove in Lean it holds for all input lengths iff it holds on the finite set of views, and that no finite test suffices if steps read earlier steps. All 2,446 views pass on a laptop GPU: signed arithmetic, long multiplication/division, square roots, GCDs at arbitrary length; 200/200 pre-registered problems and 220/220 up-to-1000-digit sums, beating ten models including GPT-6.1 Sol (217). A symbolic runtime built on it solves, expands and factors polynomials, and a multiplicative gate recovers the base model when the sheet is unused.
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