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

Identification of male- and female-specific olfaction genes in antennae of the oriental fruit fly (Bactrocera dorsalis)

The oriental fruit fly (Bactrocera dorsalis) is a species of tephritid fruit fly, endemic to Southeast Asia but also introduced to many regions of the US, and it is one of the major pest species with a broad host range of cultivated and wild fruits. Although males of B. dorsalis respond strongly to methyl eugenol and this is used for monitoring and estimating populations, the molecular mechanism of the oriental fruit fly olfaction has not been elucidated yet. Therefore, in this project, using next generation sequencing technologies, we sequenced the transcriptome of the antennae of male and female adults of B. dorsalis. We identified a total of 20 candidate odorant binding proteins (OBPs), 5 candidate chemosensory proteins (CSPs), 35 candidate odorant receptors (ORs), 12 candidate ionotropic receptors (IRs) and 4 candidate sensory neuron membrane proteins (SNMPs). The sex-specific expression of these genes was determined and a subset of 9 OR genes was further characterized by qPCR with male and female antenna, head, thorax, abdomen, leg and wing samples. In the male antennae, 595 genes showed a higher expression, while 128 genes demonstrated a higher expression in the female antennae. Interestingly, 2 ORs (BdorOR13 and BdorOR14) were highly and specifically expressed in the antennae of males, and 4 ORs (BdorOR13, BdorOR16, BdorOR18 and BdorOR35) clustered with DmOR677, suggesting pheromone reception. We believe this study with these antennae-enriched OBPs, CSPs, ORs, IRs and SNMPs can play an important role in the detection of pheromones and general odorants, and so in turn our data improve our current understanding of insect olfaction at the molecular level and provide important information for disrupting the behavior of the oriental fruit fly using chemical communication methods

Differentiable Programming Tensor Networks

Differentiable programming is a fresh programming paradigm which composes parameterized algorithmic components and trains them using automatic differentiation (AD). The concept emerges from deep learning but is not only limited to training neural networks. We present theory and practice of programming tensor network algorithms in a fully differentiable way. By formulating the tensor network algorithm as a computation graph, one can compute higher order derivatives of the program accurately and efficiently using AD. We present essential techniques to differentiate through the tensor networks contractions, including stable AD for tensor decomposition and efficient backpropagation through fixed point iterations. As a demonstration, we compute the specific heat of the Ising model directly by taking the second order derivative of the free energy obtained in the tensor renormalization group calculation. Next, we perform gradient based variational optimization of infinite projected entangled pair states for quantum antiferromagnetic Heisenberg model and obtain start-of-the-art variational energy and magnetization with moderate efforts. Differentiable programming removes laborious human efforts in deriving and implementing analytical gradients for tensor network programs, which opens the door to more innovations in tensor network algorithms and applications.Comment: Typos corrected, discussion and refs added; revised version accepted for publication in PRX. Source code available at https://github.com/wangleiphy/tensorgra

First-forbidden transition of nuclear β\beta decay by projected shell model

The first-forbidden transition of nuclear $\beta$ decay is expected to play crucial roles in many aspects in nuclear physics, nuclear astrophysics and particle physics such as the stellar $\beta$-decay rates and the reactor anti-neutrino spectra. In this work we develop the projected shell model (PSM) for description of first-forbidden transition of nuclear $\beta$ decay for the first time. Detailed theoretical framework and logics are provided, and 35 dominant first-forbidden transitions that are expected to be important for the reactor anti-neutrino spectra problems are calculated and compared systematically with the data to test the new development of the PSM. The corresponding experimental Log$f_0 t$ values are described reasonably, and the quenching factors of nuclear matrix elements are found to affect the Log$f_0 t$ values as well as the related shape factors, which may be helpful for better understanding of the reactor anti-neutrino spectra problems