Sketchpad：小视觉语言模型实现可证明的精确算术
原标题：Paper page - Sketchpad: certified exact arithmetic with a small vision-language model
AI 摘要
该论文提出 Sketchpad 方法：使用 Qwen3.5-0.8B 加低秩适配器，在渲染的“草稿纸”上执行算术步骤，每次前向只读取外部工作内存的三格视图并输出一步（数字、进位/借位、下一操作），由固定运行时移动视图。作者在 Lean 中证明：只要每步只读有界视图，模型在所有长度输入上的精确性等价于在运行时呈现的有限视图集合上的精确性，并证明若步骤可读取先前步骤则无有限测试可保证、该保证可容忍有界数值扰动且可组合。部署设备（浏览器中的笔记本 GPU）上全部 2,446 个视图通过，模型支持任意长度的加减乘除、平方根与最大公约数，在 220 道预注册题中全部解出，超过 GPT-6.1 Sol 等模型。
正文节选
Sketchpad: certified exact arithmetic with a small vision-language model Abstract Language models are accurate on most long-arithmetic problems, but their accuracy is estimated on samples and carries no guarantee for an unseen input; tool use is exact but moves the computation outside the network. We show that exactness at all input lengths becomes a finite, checkable property of a network when each of its steps reads only a bounded view of an external working memory. In Sketchpad, Qwen3.5-0.8B