Maximum Score Routing For Mixture-of-Experts

TL;DR

MaxScore introduces a novel routing method for mixture-of-experts models that models routing as a minimum-cost maximum-flow problem, improving training loss and evaluation scores without capacity constraints.

Contribution

It proposes MaxScore, a new MoE routing paradigm that overcomes limitations of existing methods by modeling routing as a flow problem with a SoftTopk operator.

Findings

Lower training losses compared to baselines

Higher evaluation scores at same FLOPs

Effective routing without expert capacity constraints

Abstract

Routing networks in sparsely activated mixture-of-experts (MoE) dynamically allocate input tokens to top-k experts through differentiable sparse transformations, enabling scalable model capacity while preserving computational efficiency. Traditional MoE networks impose an expert capacity constraint to ensure GPU-friendly computation. However, this leads to token dropping when capacity is saturated and results in low hardware efficiency due to padding in underutilized experts. Removing the capacity constraint, in turn, compromises load balancing and computational efficiency. To address these issues, we propose Maximum Score Routing ($\mathbf{MaxScore}$), a novel MoE routing paradigm that models routing as a minimum-cost maximum-flow problem and integrates a SoftTopk operator. MaxScore resolves the fundamental limitations of iterative rerouting and optimal transport formulations, achieving lower training losses and higher evaluation scores at equivalent FLOPs compared to both constrained and unconstrained baselines. Implementation details and experimental configurations can be obtained from $\href{https://github.com/dongbw18/MaxScore.git}{MaxScore}$.