How Feature Learning Can Improve Neural Scaling Laws
This work provides theoretical insights into compute-optimal strategies for scaling neural networks, particularly benefiting researchers in deep learning theory and optimization.
The authors tackled the problem of understanding how feature learning affects neural scaling laws, showing that for hard tasks outside the RKHS of the initial NTK, feature learning can nearly double the scaling exponent with training time and compute, while it does not change scaling for easy tasks.
We develop a solvable model of neural scaling laws beyond the kernel limit. Theoretical analysis of this model shows how performance scales with model size, training time, and the total amount of available data. We identify three scaling regimes corresponding to varying task difficulties: hard, easy, and super easy tasks. For easy and super-easy target functions, which lie in the reproducing kernel Hilbert space (RKHS) defined by the initial infinite-width Neural Tangent Kernel (NTK), the scaling exponents remain unchanged between feature learning and kernel regime models. For hard tasks, defined as those outside the RKHS of the initial NTK, we demonstrate both analytically and empirically that feature learning can improve scaling with training time and compute, nearly doubling the exponent for hard tasks. This leads to a different compute optimal strategy to scale parameters and training time in the feature learning regime. We support our finding that feature learning improves the scaling law for hard tasks but not for easy and super-easy tasks with experiments of nonlinear MLPs fitting functions with power-law Fourier spectra on the circle and CNNs learning vision tasks.