Scaling Laws for Fine-Grained Mixture of Experts

Mixture of Experts (MoE) models have emerged as a primary solution for reducing the computational cost of Large Language Models. In this work, we analyze their scaling properties, incorporating an expanded range of variables. Specifically, we introduce a new hyperparameter, granularity, whose adjustment enables precise control over the size of the experts. Building on this, we establish scaling laws for fine-grained MoE, taking into account the number of training tokens, model size, and granularity. Leveraging these laws, we derive the optimal training configuration for a given computational budget. Our findings not only show that MoE models consistently outperform dense Transformers but also highlight that the efficiency gap between dense and MoE models widens as we scale up the model size and training budget. Furthermore, we demonstrate that the common practice of setting the size of experts in MoE to mirror the feed-forward layer is not optimal at almost any computational budget. Contributions: Jakub implemented fine-grained MoE, ran experiments, and oversaw the course of the project. Jan designed and implemented the scaling laws, also optimized and tuned the fine-grained MoE implementation. Kamil A. provided significant advice on many aspects of the project. Maciej experimented with the block design and, with Michał, provided considerable technical support. Szymon, Kamil C., Krystian, and Tomasz contributed to the project and the engineering in various ways. Marek, along with Piotr, provided high-level scientific advice. Sebastian came up with the initial idea, started the project, and supervised it while setting the research direction and leading experiments and analyses. Correspondence to