Blogger writes a simplified proof of the Functional Scaling Law with help from GPT-6 Astra

Zhanpeng Zhou @zhanpeng_zhouOriginally posted 2026.09.23

Open original on X

Spend days to read Functional Scaling Law theory https://arxiv.org/abs/2509.19189 in details. Great math and tons of insights. I try to organize the proof logic in a simpler way. Here is my new blog: https://hammerhead-piano-5a0.notion.site/Blog-A-Simple-Proof-of-the-Functional-Scaling-Law-3df14499130181a0b9d2fbff030a54ba?source=copy_link Not fully hand-crafted. GPT-6 Astra helps with some proof. Still worth a read, if you want to understand more about loss dynamics and how LR schedule affects them.