Deep neural networks come in many sizes and architectures. The choice of architecture, in conjunction with the dataset and learning algorithm, is commonly understood to affect the learned neural representations. Yet, recent results have shown that different architectures learn representations with striking qualitative similarities. Here we derive an effective theory of representation learning under the assumption that the encoding map from input to hidden representation and the decoding map from representation to output are arbitrary smooth functions. This theory schematizes representation learning dynamics in the regime of complex, large architectures, where hidden representations are not strongly constrained by the parametrization. We show through experiments that the effective theory describes aspects of representation learning dynamics across a range of deep networks with different activation functions and architectures, and exhibits phenomena similar to the "rich" and "lazy" regime. While many network behaviors depend quantitatively on architecture, our findings point to certain behaviors that are widely conserved once models are sufficiently flexible.

翻译：深度神经网络存在多种尺寸与架构。架构选择与数据集及学习算法相结合，通常被认为会影响所学习的神经表示。然而，近期研究结果表明，不同架构学习的表示在定性上具有显著相似性。本文基于编码映射（从输入到隐藏表示）与解码映射（从表示到输出）均为任意光滑函数的假设，推导了表示学习的有效理论。该理论描述了在复杂大型架构体系（其中隐藏表示不受强参数化约束）下的表示学习动态。通过实验表明，该有效理论能够刻画不同激活函数与架构的多种深度网络中的表示学习动态特征，并展现出与"丰富"和"懒惰"机制相似的现象。虽然许多网络行为在定量上依赖于架构，我们的发现指出，一旦模型具备足够灵活性，某些行为会呈现出广泛保守性。