A Minimal Bifurcation Model of Load Imbalance in a Softmax Mixture-of-Experts Router
We propose a minimal dynamical model of adaptive softmax routing for a two-expert Mixture-of-Experts (MoE) layer. The model is obtained as a mean-field limit of a discrete reinforcement rule: the selected expert receives a small score increment, while all scores undergo regularizing decay. In the symmetric case the limiting system has a supercritical pitchfork bifurcation: for weak feedback there is a unique stable balanced state, whereas above a critical feedback strength two stable asymmetric states appear. When an external asymmetry is added, the pitchfork unfolds into a pair of fold bifurcations forming a cusp in the control-parameter plane. We derive exact parametric equations for the bifurcation set and the local normal form of the cusp catastrophe. Numerical experiments connect this picture to empirical expert load, a small trainable MoE model, hard top-1 PyTorch routing, and a small classification experiment on digits. The results provide a controlled low-dimensional mechanism for abrupt transitions to load imbalance in adaptive MoE routers.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
Imbalance Robust Softmax for Deep Embeeding Learning
Deep embedding learning is expected to learn a metric space in which features have smaller maximal intra-class distance than minimal inter-class distance. In recent years, one research focus is to solve the open-set prob…
Face RecognitionPerson Re-IdentificationMC#: Mixture Compressor for Mixture-of-Experts Large Models
Mixture-of-Experts (MoE) effectively scales large language models (LLMs) and vision-language models (VLMs) by increasing capacity through sparse activation. However, preloading all experts into memory and activating mult…
Expert Streaming: Accelerating Low-Batch MoE Inference via Multi-chiplet Architecture and Dynamic Expert Trajectory Scheduling
Mixture-of-Experts is a promising approach for edge AI with low-batch inference. Yet, on-device deployments often face limited on-chip memory and severe workload imbalance; the prevalent use of offloading further incurs …
A Replicate-and-Quantize Strategy for Plug-and-Play Load Balancing of Sparse Mixture-of-Experts LLMs
Sparse Mixture-of-Experts (SMoE) architectures are increasingly used to scale large language models efficiently, delivering strong accuracy under fixed compute budgets. However, SMoE models often suffer from severe load …
Least-Loaded Expert Parallelism: Load Balancing An Imbalanced Mixture-of-Experts
Mixture-of-Experts (MoE) models are typically pre-trained with explicit load-balancing constraints to ensure statistically balanced expert routing. Despite this, we observe that even well-trained MoE models exhibit signi…