Parameters vs FLOPs: Scaling Laws for Optimal Sparsity for
  Mixture-of-Experts Language Models
Authors: name: Samira Abnar, name: Harshay Shah, name: Dan Busbridge, name: Alaaeldin Mohamed Elnouby Ali, name: Josh Susskind, name: Vimal Thilak

Scaling the capacity of language models has consistently proven to be a
reliable approach for improving performance and unlocking new capabilities.
Capacity can be primarily defined by two dimensions: the number of model
parameters and the compute per example. While scaling typically involves
increasing both, the precise interplay between these factors and their combined
contribution to overall capacity remains not fully understood. We explore this
relationship in the context of sparse Mixture-of-Experts (MoEs), which allow
scaling the number of parameters without proportionally increasing the FLOPs
per example. We investigate how varying the sparsity level, i.e., the fraction
of inactive parameters, impacts model's performance during pretraining and
downstream few-shot evaluation. We find that under different constraints (e.g.,
parameter size and total training compute), there is an optimal level of
sparsity that improves both training efficiency and model performance. These
results provide a better understanding of the impact of sparsity in scaling
laws for MoEs and complement existing works in this area, offering insights for
designing more efficient architectures.