4+3 Phases of Compute-Optimal Neural Scaling Laws
This work provides theoretical insights into neural scaling laws, which is foundational for optimizing compute allocation in AI, though it is incremental as it builds on existing scaling models.
The paper tackles the problem of predicting compute-optimal neural scaling laws by analyzing a solvable model with parameters for data and target complexity, identifying 4 phases (+3 subphases) in the scaling behavior and deriving exponents for optimal model-parameter-count as a function of compute budget.
We consider the solvable neural scaling model with three parameters: data complexity, target complexity, and model-parameter-count. We use this neural scaling model to derive new predictions about the compute-limited, infinite-data scaling law regime. To train the neural scaling model, we run one-pass stochastic gradient descent on a mean-squared loss. We derive a representation of the loss curves which holds over all iteration counts and improves in accuracy as the model parameter count grows. We then analyze the compute-optimal model-parameter-count, and identify 4 phases (+3 subphases) in the data-complexity/target-complexity phase-plane. The phase boundaries are determined by the relative importance of model capacity, optimizer noise, and embedding of the features. We furthermore derive, with mathematical proof and extensive numerical evidence, the scaling-law exponents in all of these phases, in particular computing the optimal model-parameter-count as a function of floating point operation budget.