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This paper introduces DOT-MoE, a framework that reformulates the conversion of dense layers in Large Language Models (LLMs) into sparse Mixture of Experts (MoEs) as a Differentiable Optimal Transport problem. By employing differentiable Sinkhorn-Knopp iterations, DOT-MoE ensures balanced transport and strict expert capacity constraints, allowing for an end-to-end learning of neuron assignments and routing policies. Experimental results show that DOT-MoE retains 90% of the performance of the original dense model while halving the number of active parameters, outperforming existing methods like structured pruning and heuristic clustering.
Achieving a 50% reduction in active parameters while maintaining 90% of the original model's performance could redefine efficiency benchmarks for LLMs.
The scaling of Large Language Models (LLMs) has driven significant performance gains but created substantial challenges in inference efficiency. While Mixture of Experts (MoEs) architectures address this by decoupling model size from inference cost, training MoEs from scratch is often unstable and compute intensive. Conversion of pre-trained dense models into sparse MoEs has emerged as an alternative solution; however, existing methods typically rely on heuristic neuron clustering or random splitting to partition the Feed-Forward Network (FFN) into experts. In this work, we propose DOT-MoE, a novel framework that formulates the decomposition of dense layers as a Differentiable Optimal Transport (DOT) problem. Instead of static heuristics, we model neuron assignment as a balanced transport problem, utilizing differentiable Sinkhorn-Knopp iterations to enforce strict expert capacity constraints. Furthermore, we utilize Straight-Through Estimators (STE) to jointly learn the discrete neuron-to-expert assignment and the token-to-expert routing policy end-to-end. Extensive experiments across multiple architectures and benchmarks demonstrate that DOT-MoE significantly outperforms structured pruning, heuristic clustering, and random-split baselines, retaining 90% of the original dense model's performance while reducing active parameters by 50%.