Google DeepMind利用AlphaEvolve优化矩阵乘法理论界
Google DeepMind just used AlphaEvolve to improve the best-known theoretical boun…
展示了AlphaEvolve在数学证明领域的突破能力，不仅刷新了矩阵乘法指数的理论纪录，还详细披露了参数规模与性能贡献的量化细节，对探索AI辅助科研路径极具参考价值。
Google DeepMind just used AlphaEvolve to improve the best-known theoretical bound for matrix multiplication.
Google DeepMind 刚刚利用 AlphaEvolve 改进了矩阵乘法的最佳已知理论界。
And they did it with the help of AI.
而这一切是在 AI 的帮助下完成的。
AlphaEvolve repeatedly modified and improved the researchers’ optimization code, helping them find a better matrix-multiplication bound than the previous record, which the team then rigorously verified.
AlphaEvolve 反复修改并优化研究人员的优化代码，帮助他们找到了比此前纪录更好的矩阵乘法界，随后团队对其进行了严格验证。
The matrix multiplication exponent ω tracks how arithmetic cost scales with matrix size. The previous best was ω < 2.371339. This work reaches ω < 2.371177, a gain the authors say is comparable in magnitude to most improvements over the past 40 years.
矩阵乘法指数 ω 追踪算术成本随矩阵规模的增长情况。此前的最佳结果为 ω < 2.371339。这项工作将结果提升至 ω < 2.371177，作者表示这一增益幅度与过去 40 年中的大多数改进相当。
The mathematical framework is not new. Combination loss analysis turns the proof into a huge non-convex optimization problem.
该数学框架并非全新。组合损失分析（Combination loss analysis）将证明过程转化为一个巨大的非凸优化问题。
The team rebuilt that optimization around gradients, JAX, and parallel tensor operations, allowing recursion level 4 instead of 3. That grows the optimizable parameters from roughly 25k to 7 million. Gradient descent supplied about 0.97×10^-4 of the improvement; AlphaEvolve modified the optimization code and raised the total to about 1.62×10^-4.
团队基于梯度、JAX 和并行张量操作重构了该优化过程，使得递归层级从 3 提升至 4。这使得可优化参数数量从约 2.5 万激增至 700 万。梯度下降贡献了约 0.97×10^-4 的改进；AlphaEvolve 修改了优化代码，将总提升幅度提高至约 1.62×10^-4。
They then certified the result with exact rational arithmetic.
随后，他们通过精确有理算术对结果进行了认证。
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