Invited Talk 2: Expressiveness in Deep Learning via Tensor Networks and Quantum Entanglement

Understanding deep learning calls for addressing three fundamental questions: expressiveness, optimization and generalization. This talk will describe a series of works aimed at unraveling some of the mysteries behind expressiveness. I will begin by showing that state of the art deep learning architectures, such as convolutional networks, can be represented as tensor networks --- a prominent computational model for quantum many-body simulations. This connection will inspire the use of quantum entanglement for defining measures of data dependencies modeled by deep networks. Next, I will turn to derive a quantum max-flow / min-cut theorem characterizing the entanglement captured by deep networks. The theorem will give rise to new results that shed light on expressiveness in deep learning, and in addition, provide new tools for deep network design. Works covered in the talk were in collaboration with Yoav Levine, Or Sharir, Ronen Tamari, David Yakira and Amnon Shashua.