Slicing and Dicing: Configuring Optimal Mixtures of Experts

Mixture-of-Experts models increase parameter capacity while keeping the computation activated by each token bounded, but their architectural evolution cannot be explained by a chronological list of model releases alone. This technical survey synthesizes primary papers, official technical reports, and prior surveys to organize modern Mixture-of-Experts systems along five coupled dimensions: expert granularity, expert topology, routing freedom, the scope of load balancing, and execution structure. We describe eight architectural milestones as a dependency graph with six mainline developments and two orthogonal branches, rather than as eight successive generations. We then analyze individual systems through four control planes: Expert Topology, Routing, Balance, and Expert Parallelism. These planes specify which experts exist, which experts process each token, how aggregate load is controlled, and how selected computation is mapped onto physical devices. The framework connects algorithmic choices such as Top-k routing, shared experts, fine-grained experts, and dynamic expert composition with systems concerns including token dispatch, device placement, all-to-all communication, and communication-computation overlap. We conclude with equal-budget pretraining experiments, quality and systems metrics, and open research questions. The main trend is a shift from merely activating more sparse parameters toward decoupling semantic routing, computational budgets, and physical execution.

Mixture-of-Experts (MoE) architectures efficiently scale Large Language Models (LLMs) by activating only a small fraction of their experts per token, yet the full parameter count - dominated by the expert parameters - must be held in training and inference memory. To address this, we introduce Expert Tying, an architectural modification that shares expert parameters across consecutive transformer layers while preserving independent, layer-wise routing and attention. We evaluate this approach across common, state-of-the-art architectures, including OLMoE, Qwen3, and DeepSeek-style MoEs. Our pretraining experiments demonstrate that tying experts can reduce memory footprint by almost 2x at virtually no degradation in perplexity or downstream quality. By exploiting the parameter redundancy inherent in MoE pathways, our method provides a highly favorable compute-to-memory trade-off, advancing efficient training and scaling of next-generation LLMs.

Sparse Mixture-of-Experts (MoE) architectures enable scaling LLM parameters under a fixed inference budget by activating only a small subset of experts via top-$k$ routing. While this preserves causality and suits autoregressive language models, the discrete top-$k$ operator is not differentiable, forcing a fixed number of active experts per input and resulting in inefficient use of computation. We propose SoftMoE, which replaces discrete routing with a truncated soft top-$k$ LapSum relaxation, allowing gradient-based optimization of expert routing. We further parameterize the mean number of active experts per layer and impose a global budget constraint, enabling the model to learn how to allocate expert capacity across layers. SoftMoE remains fully compatible with autoregressive modeling and achieves performance comparable to or better than sparse MoE on language modeling and downstream tasks, while activating significantly fewer experts. Notably, the learned allocation is highly non-uniform, with later layers activating more experts. The source code is publicly available$^\dagger$.