The Surprising Simplicity of the Early-Time Learning Dynamics of Neural Networks
This work provides theoretical insight into neural network training dynamics, potentially simplifying analysis and optimization for researchers and practitioners, though it is incremental as it builds on existing NTK frameworks.
The paper demonstrates that the early learning dynamics of neural networks can be effectively approximated by training a simple linear model on inputs, challenging the perception of neural networks as complex black-box functions. This result is formally proven for two-layer networks and empirically extended to deeper and convolutional architectures.
Modern neural networks are often regarded as complex black-box functions whose behavior is difficult to understand owing to their nonlinear dependence on the data and the nonconvexity in their loss landscapes. In this work, we show that these common perceptions can be completely false in the early phase of learning. In particular, we formally prove that, for a class of well-behaved input distributions, the early-time learning dynamics of a two-layer fully-connected neural network can be mimicked by training a simple linear model on the inputs. We additionally argue that this surprising simplicity can persist in networks with more layers and with convolutional architecture, which we verify empirically. Key to our analysis is to bound the spectral norm of the difference between the Neural Tangent Kernel (NTK) at initialization and an affine transform of the data kernel; however, unlike many previous results utilizing the NTK, we do not require the network to have disproportionately large width, and the network is allowed to escape the kernel regime later in training.