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

Top quark decays with flavor violation in the B-LSSM

The decays of top quark $t\rightarrow c\gamma,\;t\rightarrow cg,\;t\rightarrow cZ,\;t\rightarrow ch$ are extremely rare processes in the standard model (SM). The predictions on the corresponding branching ratios in the SM are too small to be detected in the future, hence any measurable signal for the processes at the LHC is a smoking gun for new physics. In the extension of minimal supersymmetric standard model with an additional local $U(1)_{B-L}$ gauge symmetry (B-LSSM), new gauge interaction and new flavor changing interaction affect the theoretical evaluations on corresponding branching ratios of those processes. In this work, we analyze those processes in the B-LSSM, under a minimal flavor violating assumption for the soft breaking terms. Considering the constraints from updated experimental data, the numerical results imply $Br(t\rightarrow c\gamma)\sim5\times10^{-7}$, $Br(t\rightarrow cg)\sim2\times10^{-6}$, $Br(t\rightarrow cZ)\sim4\times10^{-7}$ and $Br(t\rightarrow ch)\sim3\times10^{-9}$ in our chosen parameter space. Simultaneously, new gauge coupling constants $g_{_B},\;g_{_{YB}}$ in the B-LSSM can also affect the numerical results of $Br(t\rightarrow c\gamma,\;cg,\;cZ,\;ch)$.Comment: 20 pages, 4 figures, published in EPJC. arXiv admin note: substantial text overlap with arXiv:1803.0990

Single dose of morphine produced a prolonged effect on dopamine neuron activities

<p>Abstract</p> <p>Background</p> <p>Clinical observation and experimental studies have indicated that a single exposure to morphine could induce tolerance and dependence. It has become a concern in clinical antinociceptive practice. However, the underling mechanism remains unknown. This study was designed to explore the changes of dopamine (DA) neuron activities in the ventral tegmental area (VTA) by employing a spectral analysis followed single morphine treatment.</p> <p>Results</p> <p>Acute morphine treatment significantly increased not only the firing rate and firing population but also the power of slow oscillation of DA neurons in naïve rats. These changes lasted at least for 3 days following the morphine treatment. During this period of time, responses of the DA neurons to subsequent morphine challenge were diminished. We further demonstrated a transient desensitization of opiate receptors as monitored by GTPγS binding to G-proteins. The present study provided first direct evidence for the temporal changes in the VTA DA neuron activities and opiate receptors desensitization.</p> <p>Conclusion</p> <p>Prolonged VTA DA neuron activation and opiate receptors desensitization followed single morphine exposure may underlie the development of dependence and tolerance that may associate with the acute analgesic tolerance and acute addiction of morphine.</p