The selection of initial parameter values for gradient-based optimization of
deep neural networks is one of the most impactful hyperparameter choices in
deep learning systems, affecting both convergence times and model performance.
Yet despite significant empirical and theoretical analysis, relatively little
has been proved about the concrete effects of different initialization schemes.
In this work, we analyze the effect of initialization in deep linear networks,
and provide for the first time a rigorous proof that drawing the initial
weights from the orthogonal group speeds up convergence relative to the
standard Gaussian initialization with iid weights. We show that for deep
networks, the width needed for efficient convergence to a global minimum with
orthogonal initializations is independent of the depth, whereas the width
needed for efficient convergence with Gaussian initializations scales linearly
in the depth. Our results demonstrate how the benefits of a good initialization
can persist throughout learning, suggesting an explanation for the recent
empirical successes found by initializing very deep non-linear networks
according to the principle of dynamical isometry.

本文研究在深度神经网络的梯度优化中最具影响力的超参数选择之一 —— 初始参数值的选择，分析了不同初始化方案的具体影响，证明了从正交组中绘制初始权重相对于具有独立同分布权重的标准高斯初始化会加速收敛，并且展示了如何通过基于动态等谱性的初始化原理初始化非线性网络以获得最佳效果。