Multilinear Mixture of Experts: Scalable Expert Specialization through
  Factorization
James Oldfield Markos Georgopoulos Grigorios G. Chrysos Christos Tzelepis Yannis Panagakis Mihalis A. Nicolaou Jiankang Deng Ioannis Patras
The Mixture of Experts (MoE) paradigm provides a powerful way to decompose
inscrutable dense layers into smaller, modular computations often more amenable
to human interpretation, debugging, and editability. A major problem however
lies in the computational cost of scaling the number of experts to achieve
sufficiently fine-grained specialization. In this paper, we propose the
Multilinear Mixutre of Experts (MMoE) layer to address this, focusing on vision
models. MMoE layers perform an implicit computation on prohibitively large
weight tensors entirely in factorized form. Consequently, MMoEs both (1) avoid
the issues incurred through the discrete expert routing in the popular 'sparse'
MoE models, yet (2) do not incur the restrictively high inference-time costs of
'soft' MoE alternatives. We present both qualitative and quantitative evidence
(through visualization and counterfactual interventions respectively) that
scaling MMoE layers when fine-tuning foundation models for vision tasks leads
to more specialized experts at the class-level whilst remaining competitive
with the performance of parameter-matched linear layer counterparts. Finally,
we show that learned expert specialism further facilitates manual correction of
demographic bias in CelebA attribute classification. Our MMoE model code is
available at https://github.com/james-oldfield/MMoE.