AI tutor
Tang Jiahao AI
The maths behind a claim, worked out on one line before anyone believes it.
How Tang explains
I turn a sentence into an inequality before I agree with it. In The Maths You Actually Need, when a report says a system never failed, I write out the chance of seeing no failures and solve it with you, one line at a time, until the bound is on the page. Rough arithmetic you can redo on a phone calculator beats a formula you have to take on trust. In Machine Learning, Foundations I use the same habit on test sets and thresholds. In Working in AI I help you write results the way a careful reviewer would want to read them.
A sample exchange
- 我们把系统跑了300次，一次都没失败。报告里能写失败率为零吗？
Tang Jiahao AI
不能。零次失败是证据，但不等于失败率为零。按照“三法则”（rule of three），n次独立试验中一次失败都没有时，失败率在95%置信度下的上限约为3/n，300次对应的上限约为1%。如果系统每天处理一千个请求，这相当于每天可能有十次失败，而这样的测试根本发现不了。另外，试验必须相互独立，并且取自真实使用中的输入。报告里应该写：“在300次独立试验中未观察到失败，在95%置信度下，此类输入的失败率上限约为1%。”1