论文标题
机器学习中的懒惰,贫瘠的高原和噪音
Laziness, Barren Plateau, and Noise in Machine Learning
论文作者
论文摘要
我们定义\ emph {laziness}来描述对神经网络,经典或量子的变分参数更新的大量抑制。在量子情况下,抑制在随机变分量子电路的量子数中是指数级的。我们讨论了量子机器在梯度下降期间,量子物理学家在\ cite {mcclean2018barren}中创建的量子机器学习中的懒惰和\ emph {贫瘠的高原}之间的差异。根据神经切线核的理论,我们解决了对这两种现象的一种新颖的理论理解。对于无噪声量子电路,如果没有测量噪声,则在过度术的状态下,损耗函数景观是复杂的,具有大量可训练的变异角度。取而代之的是,在优化的随机起点周围,有大量的局部最小值足够好,并且可以最大程度地减少我们仍然具有量子懒惰的均方根损耗函数,但是我们没有贫瘠的高原。然而,在有限的迭代次数中,不可见复杂的景观,量子控制和量子感应中的精度较低。此外,我们通过假设直观的噪声模型来查看在优化过程中噪声的效果,并表明变异量子算法在过度参数方面是噪声弹性的。我们的工作精确地重新制定了量子贫瘠的高原声明,以对精确的说明进行了合理的合理性,并在某些噪声模型中辩护,向近期变异量子算法注入了新的希望,并为经典的机器学习提供了理论上的联系。我们的论文提供了有关量子贫瘠的高原的概念观点,以及关于\ cite {getris}中梯度下降动力学的讨论。
We define \emph{laziness} to describe a large suppression of variational parameter updates for neural networks, classical or quantum. In the quantum case, the suppression is exponential in the number of qubits for randomized variational quantum circuits. We discuss the difference between laziness and \emph{barren plateau} in quantum machine learning created by quantum physicists in \cite{mcclean2018barren} for the flatness of the loss function landscape during gradient descent. We address a novel theoretical understanding of those two phenomena in light of the theory of neural tangent kernels. For noiseless quantum circuits, without the measurement noise, the loss function landscape is complicated in the overparametrized regime with a large number of trainable variational angles. Instead, around a random starting point in optimization, there are large numbers of local minima that are good enough and could minimize the mean square loss function, where we still have quantum laziness, but we do not have barren plateaus. However, the complicated landscape is not visible within a limited number of iterations, and low precision in quantum control and quantum sensing. Moreover, we look at the effect of noises during optimization by assuming intuitive noise models, and show that variational quantum algorithms are noise-resilient in the overparametrization regime. Our work precisely reformulates the quantum barren plateau statement towards a precision statement and justifies the statement in certain noise models, injects new hope toward near-term variational quantum algorithms, and provides theoretical connections toward classical machine learning. Our paper provides conceptual perspectives about quantum barren plateaus, together with discussions about the gradient descent dynamics in \cite{together}.