Quantum maximum likelihood prediction via Hilbert space embeddings

Maximum likelihood prediction plays a major (hidden) role in modern large language models via the next token prediction task. In this talk, we propose and study a simplified version, based on an i.i.d. data model. The model is based on a quantum maximum likelihood predictor, which is obtained by embedding empirical distributions into quantum states and minimizing quantum relative entropy over a prescribed model class.
We interpret this predictor via quantum reverse information projection and a quantum Pythagorean theorem, under structural assumptions such as unitary invariance and closure under pinching. We extend this theorem to non-self-adjoint mixture families in finite dimensions and establish a related infinite-dimensional inequality under additional regularity conditions. Finally, we present non-asymptotic guarantees, including convergence rates and concentration inequalities in trace norm and quantum relative entropy. 
Joint work with Sreejith Sreekumar. 

Bio : Nir Weinberger is an Associate Professor at the The Viterbi Faculty of Electrical and Computer Engineering, Technion - Israel Institute ofTechnology. Previously, from 2017 to 2018 he was a post-doctoral fellow at Tel-Aviv University, and from 2018-2020 he was a Technion-MIT post-doctoral fellow at the Massachusetts Institute of Technology, Cambridge, MA, USA. He has received the B.Sc. and M.Sc. degrees from Tel-Aviv University, Tel-Aviv, Israel, in 2006 and 2009, respectively, and his Ph.D.degree in 2017, from the Technion, Israel Institute of Technology.