15,504 research outputs found
Unsupervised Generative Modeling Using Matrix Product States
Generative modeling, which learns joint probability distribution from data
and generates samples according to it, is an important task in machine learning
and artificial intelligence. Inspired by probabilistic interpretation of
quantum physics, we propose a generative model using matrix product states,
which is a tensor network originally proposed for describing (particularly
one-dimensional) entangled quantum states. Our model enjoys efficient learning
analogous to the density matrix renormalization group method, which allows
dynamically adjusting dimensions of the tensors and offers an efficient direct
sampling approach for generative tasks. We apply our method to generative
modeling of several standard datasets including the Bars and Stripes, random
binary patterns and the MNIST handwritten digits to illustrate the abilities,
features and drawbacks of our model over popular generative models such as
Hopfield model, Boltzmann machines and generative adversarial networks. Our
work sheds light on many interesting directions of future exploration on the
development of quantum-inspired algorithms for unsupervised machine learning,
which are promisingly possible to be realized on quantum devices.Comment: 11 pages, 12 figures (not including the TNs) GitHub Page:
https://congzlwag.github.io/UnsupGenModbyMPS
Deep learning systems as complex networks
Thanks to the availability of large scale digital datasets and massive
amounts of computational power, deep learning algorithms can learn
representations of data by exploiting multiple levels of abstraction. These
machine learning methods have greatly improved the state-of-the-art in many
challenging cognitive tasks, such as visual object recognition, speech
processing, natural language understanding and automatic translation. In
particular, one class of deep learning models, known as deep belief networks,
can discover intricate statistical structure in large data sets in a completely
unsupervised fashion, by learning a generative model of the data using
Hebbian-like learning mechanisms. Although these self-organizing systems can be
conveniently formalized within the framework of statistical mechanics, their
internal functioning remains opaque, because their emergent dynamics cannot be
solved analytically. In this article we propose to study deep belief networks
using techniques commonly employed in the study of complex networks, in order
to gain some insights into the structural and functional properties of the
computational graph resulting from the learning process.Comment: 20 pages, 9 figure
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