A recent line of work studies overparametrized neural networks in the ``kernel regime,'' i.e.~when the network behaves during training as a kernelized linear predictor, and thus training with gradient descent has the effect of finding the minimum RKHS norm solution. This stands in contrast to other studies which demonstrate how gradient descent on overparametrized multilayer networks can induce rich implicit biases that are not RKHS norms. Building on an observation by Chizat and Bach, we show how the scale of the initialization controls the transition between the ``kernel'' (aka lazy) and ``deep'' (aka active) regimes and affects generalization properties in multilayer homogeneous models. We provide a complete and detailed analysis for a simple two-layer model that already exhibits an interesting and meaningful transition between the kernel and deep regimes, and we demonstrate the transition for more complex matrix factorization models.

研究发现神经网络在过参量化后，当行为符合核化线性预测器时，在梯度下降的训练下能找到最小RKHS范数解；与此不同的是，梯度下降在过参量化的多层网络上可能引入不是RKHS范数的丰富隐性偏差。本文基于Chizat和Bach的观察，展示了初始化规模是如何控制多层同质模型中的“核”（也称惰性）和“丰富”（也称活动）区域之间的转换并影响泛化属性的。我们对一个简单的两层模型进行了全面而详细的分析，已经展示了核与丰富区域之间有一个有趣和有意义的转换，并展示了矩阵分解模型和多层非线性网络的转换。

过度参数化模型中的核心和丰富区域