The Math Behind The CHAT(GPT)
M. Ram Murty obtained his PhD from MIT (1980) and then held post-doctoral fellowships at IAS (Princeton) and TIFR (Mumbai). He was professor at McGill University (1982-1996), and now is Queen’s Research Chair and the A. V. Douglas Distinguished University Professor at Queen’s University. He is Fellow of the Royal Society of Canada (1990), Fields Institute (2003), Indian National Science Academy (2008), American Mathematical Society (2012) and Canadian Mathematical Society (2018). He received the E.W.R. Steacie Fellowship (1991), Killam Research Fellowship (1998) and the Simons Fellowship (2013). In 2024, he was awarded the CRM-Fields-PIMS Prize. He has written more than 300 research papers, 15 books, and supervised more than 25 doctoral students, 50 masters students and 50 post-doctoral fellows. He is cross-appointed to the Department of Philosophy at Queen’s University where he gives regular courses on mathematical logic and Indian philosophy. His introductory book on Indian philosophy was published by Broadview Press in 2012.
We present an informal outline of how ChatGPT works and describe the underlying mathematical concepts behind it. For instance, graph theory, vector calculus, linear algebra, Markov models, and probabilistic inference are all used in a fundamental way. We will also touch upon some philosophical questions that emerge such as the nature of knowledge, meaning and consciousness. The talk will not be too technical and is suitable for a general audience.
