可微规划张量网络
Differentiable Programming Tensor Networks
摘要：
可微分编程是一种新的编程范式，它构造参数化的算法组件，并使用自动微分（AD）来训练它们。这个概念来自深度学习，但不仅限于训练神经网络。我们目前的理论和实践的编程张量网络算法在一个完全可微的方式。通过将张量网络算法公式化为计算图，可以使用AD准确有效地计算程序的高阶导数。我们提出了通过张量网络收缩进行区分的基本技术，包括用于张量分解的稳定AD和通过定点迭代进行的有效反向传播。作为示范，我们直接通过对张量重整化群计算中得到的自由能进行二阶导数来计算伊辛模型的比热。其次，我们对量子反铁磁海森堡模型的无限投影纠缠对态进行了基于梯度的变分优化，并以适度的努力获得了最先进的变分能量和磁化强度。可微编程消除了在推导和实现张量网络程序的分析梯度方面的人工努力，这为张量网络算法和应用的更多创新打开了大门。
英文摘要：
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.
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