  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.
