Hierarchical representations in machine learning and many-body quantum physics
Document typeMaster thesis
Rights accessOpen Access
Over the past few years a number of proofs have emerged revealing the many connections between the methods used in quantum-many body physics and those in machine learning. In particular, much attention has been given to tensor networks (TNs) and deep learning architectures which exhibit striking similarities. Finding those similarities has helped us gain a better understanding on why deep learning architectures have so much expressive efficiency. Recently, machine learning techniques have been used to approximate many-body physics problems. Conversely, TNs have been used for machine learning tasks. For example, state-of-the-art research has used one-dimensional TNs to solve image recognition problems with very limited scalability. The scalability problem, however, can be overcomed by using a two-dimensional hierarchical TNs and a training algorithm derived from the multipartite entanglement renormalization ansatz (MERA). Here we give further analysis of the inner structural resemblance between such hierarchical tensor networks (TNs) and pretrained convolutional neural networks (CNNs): this was achieved by analyzing their abstraction power layer by layer.
En col·laboració amb la Universitat Autònoma de Barcelona (UAB) i la Universitat de Barcelona (UB)