MME: Mixture of Mesh Experts with Random Walk Transformer Gating

Mixture-of-experts (MoE) models have become an important approach for scaling model parameters. Modern MoE architectures increasingly combine two design choices: fine-grained expert segmentation and shared experts. The former increases expressiveness by enabling more expert combinations at a fixed activation ratio, and the latter introduces experts that are active for every token. We identify an exploration dilemma between these designs: shared experts can make routing less exploratory by reducing the variability of token representations. This conflicts with the greater need for exploration induced by fine-grained expert segmentation due to the combinatorially enlarged routing space. Consequently, the additional expressiveness offered by fine-grained segmentation may not be fully realized in practice. MirrorMoE is proposed to reconcile this exploration dilemma by shrinking the exploration space through token-adaptive suppression of unnecessary experts. MirrorMoE consistently improves performance across model scales.

The Mixture-of-Experts (MoE) model uses a set of expert networks that specialize on subsets of a dataset under the supervision of a gating network. A common issue in MoE architectures is ``expert collapse'' where overlapping class boundaries in the raw input feature space cause multiple experts to learn redundant representations, thus forcing the gating network into rigid routing to compensate. We propose an enhanced MoE architecture that utilizes a feature extractor network optimized using Soft Nearest Neighbor Loss (SNNL) prior to feeding input features to the gating and expert networks. By pre-conditioning the latent space to minimize distances among class-similar data points, we resolve structural expert collapse which results to experts learning highly orthogonal weights. We employ Expert Specialization Entropy and Pairwise Embedding Similarity to quantify this dynamic. We evaluate our experimental approach across four benchmark image classification datasets (MNIST, FashionMNIST, CIFAR10, and CIFAR100), and we show our SNNL-augmented MoE models demonstrate structurally diverse experts which allow the gating network to adopt a more flexible routing strategy. This paradigm significantly improves classification accuracy on the FashionMNIST, CIFAR10, and CIFAR100 datasets.

Neural Architecture Search (NAS) has so far rarely been applied to Mixture-of-Experts (MoE) models, and existing MoE designs leave the alignment between experts and the structure of the data to emerge on its own. We propose an architecture search framework that makes this alignment an explicit search variable: the assignment of data clusters to experts is optimised jointly with the per-expert architectures. We cast the joint problem as a cluster-aware likelihood maximisation, show that it coincides with the incomplete-data maximum likelihood of a latent-variable mixture, and solve it by a generalised Expectation-Maximisation procedure whose otherwise intractable expert-quality term is supplied by an adaptively refined surrogate. We prove that the iterates converge whenever the surrogate errors are summable, and that at every limit point no candidate the search produces improves the true objective. On a heterogeneous image-classification mixture the method recovers the underlying domain partition on 95% of clusters without ever observing domain labels, and on that benchmark and a four-domain time-series forecasting one alike it outperforms the MoE and NAS baselines that likewise use no label information.