연세대학교 계산과학공학

Wednesday, September 30, 2026 14:00-16:00

Advanced Science & Technology Center (Building 117) #516, Yonsei University (연세대 첨단관 516호, https://naver.me/G1wS9KYn)

Taehun Cha (Korea University)

From Chain Rule to Large Language Model Alignment: Virtual Covariance, Target Linearity, and Concept Gradient

The chain rule plays a fundamental role in how artificial intelligence is trained today: thanks to it, we need not compute the gradient at each layer of a neural network one by one, but can obtain them successively through backpropagation. Under the current paradigm of training against a scalar loss, however, it is far from easy to tell what is actually happening inside the network. This "Wallfacer" problem (borrowing the term from the novel The Three-Body Problem) is likely to become far more serious in the years ahead, as decisions large and small increasingly come to rest on the outputs of AI.

This seminar introduces the Feature Learning equation, derived from the simple chain rule, which connects weight gradients to feature gradients, and uses it to examine what happens inside a neural network. Three concepts follow from this single expression: (1) Virtual Covariance: a neural network learns the covariance structure of virtually updated hidden states; (2) Target Linearity: a neural network learns to sequentially linearize non-linear input data; and (3) Concept Gradient: which makes it possible to directly manipulate the hidden states of an LLM to elicit a desired response. Taken together, they show how a theoretical understanding of AI grounded in elementary principles can lead all the way to practical alignment methods.

Host: Dohyun Kwon