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Bulletin of the American Physical Society

Generative quantum models over tensor network architectures

Khadijeh Najafi, Ahmadreza Azizi, Carlos Fuertes, Miles Stoudenmire, Masoud Mohseni

Published Mar 6, 2020• 0 citations
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TextTN: Probabilistic Encoding of Language on Tensor Network

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As a novel model that bridges machine learning and quantum theory, tensor network (TN) has recently gained increasing attention and successful applications for processing natural images. However, for natural languages, it is unclear how to design a probabilistic encoding architecture to efficiently and accurately learn and classify texts based on TN. This paper proposes a general two-step scheme of text classification based on Tensor Network, which is named as TextTN. TextTN first encodes the word vectors in a probabilistic space by a generative TN (word-GTN), and then classifies a text sentence using a discriminative TN (sentence-DTN). Moreover, in sentence-DTN, its hyper-parameter (i.e., bond-dimension) can be analyzed and selected by the theoretical property of TextTN's expressive power. In experiments, our TextTN also obtains the state-of-the-art result on SST-5 sentiment classification task.

•May 4, 2021•4 citations
Tensor networks have found a wide use in a variety of applications in physics and computer science, recently leading to both theoretical insights as well as practical algorithms in machine learning. In this work we explore the connection between tensor networks and probabilistic graphical models, and show that it motivates the definition of generalized tensor networks where information from a tensor can be copied and reused in other parts of the network. We discuss the relationship between generalized tensor network architectures used in quantum physics, such as string-bond states, and architectures commonly used in machine learning. We provide an algorithm to train these networks in a supervised-learning context and show that they overcome the limitations of regular tensor networks in higher dimensions, while keeping the computation efficient. A method to combine neural networks and tensor networks as part of a common deep learning architecture is also introduced. We benchmark our algorithm for several generalized tensor network architectures on the task of classifying images and sounds, and show that they outperform previously introduced tensor-network algorithms. The models we consider also have a natural implementation on a quantum computer and may guide the development of near-term quantum machine learning architectures.
Tensor networks have found a wide use in a variety of applications in physics and computer science, recently leading to both theoretical insights as well as practical algorithms in machine learning. In this work we explore the connection between tensor networks and probabilistic graphical models, and show that it motivates the definition of generalized tensor networks where information from a tensor can be copied and reused in other parts of the network. We discuss the relationship between generalized tensor network architectures used in quantum physics, such as String-Bond States and Entangled Plaquette States, and architectures commonly used in machine learning. We provide an algorithm to train these networks in a supervised learning context and show that they overcome the limitations of regular tensor networks in higher dimensions, while keeping the computation efficient. A method to combine neural networks and tensor networks as part of a common deep learning architecture is also introduced. We benchmark our algorithm for several generalized tensor network architectures on the task of classifying images and sounds, and show that they outperform previously introduced tensor network algorithms. Some of the models we consider can be realized on a quantum computer and may guide the development of near-term quantum machine learning architectures.
As a novel model that bridges machine learning and quantum theory, tensor network (TN) has recently gained increasing attention and successful applications for processing natural images. However, for natural languages, it is unclear how to design a probabilistic encoding architecture to efficiently and accurately learn and classify texts based on TN. This paper proposes a general two-step scheme of text classification based on Tensor Network, which is named as TextTN. TextTN first encodes the word vectors in a probabilistic space by a generative TN (word-GTN), and then classifies a text sentence using a discriminative TN (sentence-DTN). Moreover, in sentence-DTN, its hyper-parameter (i.e., bond-dimension) can be analyzed and selected by the theoretical property of TextTN's expressive power. In experiments, our TextTN also obtains the state-of-the-art result on SST-5 sentiment classification task.