Mixture of Experts with Soft Nearest Neighbor Loss: Resolving Expert Collapse via Representation Disentanglement

Sparse Mixture-of-Experts (SMoE) models improve scalability by routing input tokens to only a subset of expert networks, but they often suffer from representation collapse, in which multiple experts converge toward similar functions and lose their intended diversity. Prior work has addressed this limitation either by improving router architectures or by introducing auxiliary loss terms that implicitly penalize similarity among experts. However, router-based approaches remain vulnerable to routing collapses, and loss-based approaches can conflict with the task's original objective during optimization. In this work, we propose GaP-MoE (Gradient Accumulation and Projection in MoE), which induces expert specialization by directly manipulating expert output gradients rather than modifying the loss function. At each training step, GaP-MoE stochastically selects one of the $TopK$ routed experts as a leader based on normalized routing scores, and projects the gradients of the remaining follower experts onto the orthogonal complement of the subspace spanned by the leader's recent gradients. This removes directional overlap between expert gradients without altering the task loss, allowing specialization to emerge as a direct consequence of the optimization dynamics rather than an externally imposed constraint. We evaluate GaP-MoE in both fine-tuning settings (BERT-based, on GLUE) and from-scratch pretraining settings (GPT-2-based, on WikiText-103, enwik8, and text8), and further confirm its compatibility as a drop-in module for existing SMoE architectures. Experimental results show that GaP-MoE achieves performance comparable to or better than standard SMoE.

Sparse Mixture-of-Experts (MoE) architectures route each token through a subset of experts at each layer independently. We propose viewing MoE computation through the lens of expert paths -- the sequence of expert selections a token makes across all layers. This perspective reveals that, despite $N^L$ possible paths for $N$ experts across $L$ layers, tokens in practice cluster into a small fraction of paths that align with linguistic function, yet the vast majority of paths remain unexplored, representing a statistical inefficiency. This motivates architectures that constrain the effective path space to amplify this natural concentration. As one instantiation, we introduce \pathmoe{}, which shares router parameters across blocks of consecutive layers. Analysis confirms that \pathmoe{} amplifies the emergent path structure: it produces more concentrated path clusters, better cross-layer consistency, and greater robustness to routing perturbations. Experiments on 0.9B and 16B parameter \pathmoe{} models demonstrate consistent improvements on perplexity and downstream tasks over independent routing, while eliminating the need for auxiliary losses. These results establish expert paths as a useful design axis for MoE architectures, complementary to existing work on independent routing mechanisms.

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.