A Resource Model For Neural Scaling Law
Jinyeop Song Ziming Liu Max Tegmark Jeff Gore
Neural scaling laws characterize how model performance improves as the model
size scales up. Inspired by empirical observations, we introduce a resource
model of neural scaling. A task is usually composite hence can be decomposed
into many subtasks, which compete for resources (measured by the number of
neurons allocated to subtasks). On toy problems, we empirically find that: (1)
The loss of a subtask is inversely proportional to its allocated neurons. (2)
When multiple subtasks are present in a composite task, the resources acquired
by each subtask uniformly grow as models get larger, keeping the ratios of
acquired resources constants. We hypothesize these findings to be generally
true and build a model to predict neural scaling laws for general composite
tasks, which successfully replicates the neural scaling law of Chinchilla
models reported in arXiv:2203.15556. We believe that the notion of resource
used in this paper will be a useful tool for characterizing and diagnosing
neural networks.