arXiv 论文给出 ω≤9/4 的构造性证明，回应 OpenAI 此前论断
Matrix Multiplication from Polynomial Packings: A Constructive and Elementary Proof of $ω\le9/4$
OpenAI 刚用非构造性方法给出 ω≤9/4，这篇论文把构造写出来了，矩阵乘法复杂度爱好者可以直接看推导。
一篇 arXiv 论文给出矩阵乘法指数 ω≤9/4 的自包含构造性证明。该上界此前由 OpenAI 通过 Strassen 渐近谱框架下的非构造性论证声称，其计算口径为复数域上的精确标量算术运算。作者显式构造了一个 Strassen 风格的矩阵乘法恒等式，并通过普通分块递归得到该上界。对任意 γ>0，所得算法用 O(n^{9/4+γ}) 次整数算术运算完成两个 n×n 整数矩阵的乘法。
Matrix Multiplication from Polynomial Packings: A Constructive and Elementary Proof of $ω\le9/4$
We give a self-contained constructive proof that the matrix multiplication exponent satisfies $ω\le9/4$. This bound was recently claimed by OpenAI~\cite{original} through non-constructive arguments in Strassen's asymptotic spectral framework, counting exact scalar arithmetic operations over the complex numbers. We explicitly construct a Strassen-style matrix multiplication identity and obtain the bound by ordinary block recursion. For every $γ>0$, the resulting algorithm multiplies two $n\times n$ integer matrices using $O(n^{9/4+γ})$ integer arithmetic operations.
- Artificial Analysis10-20 16:13原文
