Multilinear Mixture of Experts: Scalable Expert Specialization through Factorization

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Abstract:The Mixture of Experts (MoE) paradigm provides a powerful way to decompose dense layers into smaller, modular computations often more amenable to human interpretation, debugging, and editability. However, a major challenge lies in the computational cost of scaling the number of experts high enough to achieve fine-grained specialization. In this paper, we propose the Multilinear Mixture of Experts ($mu$MoE) layer to address this, focusing on vision models. $mu$MoE layers enable scalable expert specialization by performing an implicit computation on prohibitively large weight tensors entirely in factorized form. Consequently, $mu$MoEs (1) avoid the restrictively high inference-time costs of dense MoEs, yet (2) do not inherit the training issues of the popular sparse MoEs’ discrete (non-differentiable) expert routing. We present both qualitative and quantitative evidence that scaling $mu$MoE layers when fine-tuning foundation models for vision tasks leads to more specialized experts at the class-level, further enabling manual bias correction in CelebA attribute classification. Finally, we show qualitative results demonstrating the expert specialism achieved when pre-training large GPT2 and MLP-Mixer models with parameter-matched $mu$MoE blocks at every layer, maintaining comparable accuracy. Our code is available at: this https URL.