4-[(E)-3-Meth­oxy-5-nitro-4-(4-nitro­benz­yloxy)benzyl­idene­amino]-1,5-dimethyl-2-phenyl-1H-pyrazol-3(2H)-one

In the title compound, C26H23N5O7, the central benzene ring makes dihedral angles of 35.08 (6), 48.75 (7) and 69.55 (8)° with the pyrazolone ring, the nitro­benzene ring and the terminal phenyl ring, respectively. An intra­molecular C—H⋯O inter­action generates an S(6) ring. The packing is stabilized by weak nonclassical inter­molecular C—H⋯O=C hydrogen bonds that link adjacent mol­ecules into chains

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