论文标题
量子懒训练
Quantum Lazy Training
论文作者
论文摘要
在通过梯度下降训练过度参数化模型函数时，有时参数不会显着变化，并且保持接近其初始值。该现象称为懒惰训练，并激发了对模型函数围绕初始参数的线性近似的考虑。在懒惰的制度中，这种线性近似模仿了参数化函数的行为，其相关内核称为切线内核，指定了模型的训练性能。众所周知，在宽度较大的（经典）神经网络的情况下进行懒惰训练。在本文中，我们表明，几何局部参数化量子电路的训练进入了大量Qubits的懒惰制度。更准确地说，我们证明了这种几何局部参数化量子电路的变化速率，以及相关量子模型函数的线性近似值的精度；随着Qubits数量的增加，这两个界限都趋于零。我们通过数值模拟支持我们的分析结果。
In the training of over-parameterized model functions via gradient descent, sometimes the parameters do not change significantly and remain close to their initial values. This phenomenon is called lazy training, and motivates consideration of the linear approximation of the model function around the initial parameters. In the lazy regime, this linear approximation imitates the behavior of the parameterized function whose associated kernel, called the tangent kernel, specifies the training performance of the model. Lazy training is known to occur in the case of (classical) neural networks with large widths. In this paper, we show that the training of geometrically local parameterized quantum circuits enters the lazy regime for large numbers of qubits. More precisely, we prove bounds on the rate of changes of the parameters of such a geometrically local parameterized quantum circuit in the training process, and on the precision of the linear approximation of the associated quantum model function; both of these bounds tend to zero as the number of qubits grows. We support our analytic results with numerical simulations.
