Path-Constrained Mixture-of-Experts

Mixture-of-Experts (MoE) architectures scale Large Language Model (LLM) capacity efficiently by activating a sparse subset of experts per token. However, modern MoE inference remains heavily constrained by the rigid, whole-expert abstraction. Existing frameworks manage, schedule, or prune experts as atomic execution units, which fixes the optimization boundary too early and leaves fine-grained intra-expert computational redundancy underexplored. In this work, we present PCoMoE, a path-compositional execution framework that shifts MoE inference from coarse-grained expert selection to fine-grained path composition. PCoMoE incorporates a path-level formulation of expert computation, a compatibility-aware layer-wise pruning strategy to suppress low-value path combinations, and a hardware-friendly execution engine to exploit reusable sub-expert structures under strictly bounded overheads. Experimental results demonstrate that PCoMoE achieves up to a 1.31x end-to-end inference speedup while enhancing model accuracy by 10%. The code is available at https://github.com/gzyyy0/PCoMoE

Sparse Mixture-of-Experts (MoE) architectures employ increasingly sophisticated routing mechanisms -- learned routers, multi-hop trajectories, token-dependent gating. We ask: does routing topology actually determine language modeling quality? We build a geometric MoE (ST-MoE) using cosine-similarity routing against learned centroids in a low-dimensional space ($d_{space} = 64$), requiring 80% fewer routing parameters than standard linear routers. Through 62 controlled experiments on WikiText-103 at 76--84M parameters trained to convergence (50K steps, 1.64B tokens), we find that routing topology does not determine asymptotic perplexity (PPL): five cosine-routing variants are statistically equivalent within a 1-PPL margin (Two One-Sided Tests [TOST], $p < 0.05$ for all 10 pairwise comparisons; 15 runs across 3 seeds, observed range 33.93--34.72). The finding extends to hash, random-fixed, and top-1 routing (single-seed; graceful 1.1--2.2 PPL degradation) and replicates on OpenWebText (0.03 PPL gap, 6 runs, 3 seeds each). A standard linear router with 5.3$\times$ more routing parameters reaches PPL 32.76, but iso-parameter cosine routing closes 67% of this gap -- the true mechanism advantage is $\sim$1.2%. The mechanistic explanation is convergent redundancy: multi-hop updates are collinear ($\cos(Δh_0, Δh_1) = 0.805$), implementing magnitude amplification rather than compositional reasoning; a single learnable scalar replicates multi-hop performance. As a practical payoff, zero-shot relative-norm halting saves 25% of MoE FLOPs at +0.12% PPL. Expert-level specialization and causal controllability -- which coexist with topology-level equifinality -- are explored in a companion paper.

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$^\dagger$.