Tensor networks for Green AI and signal processing

This course provides a solid mathematical foundation to tensor networks and discusses their use in machine learning and signal processing. Tensors are multi-dimensional generalization of matrices. Real-life data often comes in high dimensions, such as of a video stream, or multichannel EEG recorded from multiple patients under various conditions. Tensor-based tools are crucial to efficiently represent and process this data. Alternative (matrix-based) solutions artificially segment such high-dimensional data into shorter one- or two-dimensional arrays, causing information loss by destroying correlations in these data. The key idea of tensor networks is to write a tensor in terms of much smaller tensors that represent these correlations among the different dimensions. On one hand, such representations can reveal hidden structure in the data and can even lead to decompositions with physically interpretable terms. Moreover, in this way, the original tensor never needs to be kept explicitly in memory. This latter aspect becomes especially interesting considering the ever-increasing dataset sizes brought on by recent advances in sensor and imaging technology. Computations based on tensor networks enable faster training and inference of AI models based on such large datasets. Therefore, tensor networks facilitate the shift towards the direction of Green AI. Green AI aims to decrease the environmental footprint of AI computation and increase the inclusivity of AI research by becoming more independent of expensive computer hardware needed for training.

There are 4 assignments. Only the 4th assignment is graded and counts for 20% of the final grade. This 4th assignment is executed in groups of 2 or 3 students, and the topic is chosen from a list of several options depending on the interest of the students. The students will submit their code as well as a report about the assignment. In addition there will be a written exam that counts for 80% of the final grade. Both the 4th assignment and the written exam need to be passed. If the written exam was failed, then it will be redone while keeping the passing grade for the 4th assigment. If the 4th assignment was failed, then there will be a repair opportunity.