• Course code:63835E
  • Credits:5
  • Semester: winter
  • Contents

Tensor Networks for Machine Learning

Tensor networks are decompositions of multi-dimensional tensors with exponential reduction of parameters. They have been introduced to quantum mechanics approximately 20 ago. Since then, they have become one of the most important technical tools to understand quantum states’ structure, especially in one dimension. They are a vital ingredient of the state-of-the-art numerical techniques of many-body quantum mechanics. In many-body quantum mechanics and quantum information, tensor networks are now a well-established and understood tool with well-known geometric properties and robust optimization algorithms. In the last seven years, they also appeared in mathematical literature (particularly matrix product states or tensor trains) in linear algebra with large matrices. Over the previous four years, they increasingly appear in machine learning literature, where they have been applied to various practical problems from parameter compression, classification to anomaly detection. Theoretically, tensor networks have been related to Born machines, hidden Markov models, and probabilistic and quadratic automata from the formal language’s literature. The course will focus on recently developed tensor network applications for machine learning (mainly from an experimental/numerical perspective). We will guide students in reproducing recent results involving tensor network decompositions in machine learning and then trying to go beyond by improving or applying the learned techniques to a slightly different problem. The proposed projects will be adapted to fit student interests, time, and expertise.

Restrictions/Prerequisites: Basic linear algebra, basic machine learning

  • Study programmes
  • Distribution of hours per semester
15
hours
lectures
15
hours
tutorials
20
hours
tutorials
  • Professor
Instructor
Room:R2.26 - Laboratorij LKM
Course Organiser
Room:R2.17 - Kabinet