When I first began learning about machine learning, I struggled with the notion that lowering the loss on the training data does not necessarily guarantee performance on the test data, since training data and test data are different. In this article, I will carefully explain why the performance on test data is theoretically guaranteed, aiming […]
A Gentle Introduction to Machine Learning Theory Read Post »
I came across an intriguing post while browsing X during New Year’s holidays. Historically, humanity has pursued the idea that truth is inherently simple, exemplified by equations like \(E = mc^2\) or \(F = ma\). However, the idea presented was that such truths may represent only a small subset of the entire truth, suggesting the
The Hidden Information AI Understands but Humans Miss Read Post »
It is well known that eigenvalues of a real symmetric matrix are real values, and eigenvectors of a real symmetric matrix form an orthonormal basis. This theorem plays important roles in many fields. For example, the principal component analysis relies on this theorem. Although every textbook on linear algebra contains a proof of this theorem,
