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Sparsely activated Mixture-of-Experts (SMoE) has shown promise to scale upthe learning capacity of neural networks, however, they have issues like (a)High Memory Usage, due to duplication of the network layers into multiplecopies as experts; and (b) Redundancy in Experts, as common learning-basedrouting policies suffer from representational collapse. Therefore, vanilla SMoEmodels are memory inefficient and non-scalable, especially forresource-constrained downstream scenarios. In this paper, we ask: Can we crafta compact SMoE model by consolidating expert information? What is the bestrecipe to merge multiple experts into fewer but more knowledgeable experts? Ourpilot investigation reveals that conventional model merging methods fail to beeffective in such expert merging for SMoE. The potential reasons are: (1)redundant information overshadows critical experts; (2) appropriate neuronpermutation for each expert is missing to bring all of them in alignment. Toaddress this, we propose M-SMoE, which leverages routing statistics to guideexpert merging. Specifically, it starts with neuron permutation alignment forexperts; then, dominant experts and their "group members" are formed; lastly,every expert group is merged into a single expert by utilizing each expert'sactivation frequency as their weight for merging, thus diminishing the impactof insignificant experts. Moreover, we observed that our proposed mergingpromotes a low dimensionality in the merged expert's weight space, naturallypaving the way for additional compression. Hence, our final method, MC-SMoE(i.e., Merge, then Compress SMoE), further decomposes the merged experts intolow-rank and structural sparse alternatives. Extensive experiments across 8benchmarks validate the effectiveness of MC-SMoE. For instance, our MC-SMoEachieves up to 80% memory and a 20% FLOPs reduction, with virtually no loss inperformance.

Merge, Then Compress: Demystify Efficient SMoE with Hints from Its Routing Policy