Sparse Mixture-of-Experts

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Overview

Sparse mixture-of-experts models use a router to send each token or input to only a few expert networks, aiming to combine large model capacity with manageable computation. Common approaches include top-k and threshold routing, hierarchical or shared experts, load-balancing objectives, and upcycling dense models into expert-based ones. Research spans language models as well as vision, speech, forecasting, and multimodal tasks, with work on training stability, pruning, quantization, and efficient inference. A central tension is that balancing expert use can prevent collapse but may weaken specialization, while high stored capacity does not always translate into better results or lower end-to-end cost.

Latest papers

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121 papers16 papers in the last four weeks, up 33% on the four weeks before. 0.1% of all new papers.

May 1, 2026

Affinity Is Not Enough: Recovering the Free Energy Principle in Mixture-of-Experts

Sparse MoE routing fails at domain transitions, where the current token belongs to one distribution and the next to another. In a controlled experiment (4 experts, 5 seeds), standard affinity routing assigns only 0.006 +/- 0.001 probability to the correct expert at the transition. Three lightweight gate modifications raise this to 0.748 +/- 0.002 (124x), cutting experts needed for 99% coverage from infeasible to a small constant: temporal memory (beta), a per-expert LIF membrane potential accumulating routing context across tokens; precision-weighted gating (Pi), a per-expert inverse variance of recent prediction error, yielding 31x contrast between reliable and unreliable experts; and anticipatory routing, a next-state predictor conditioned on the beta-accumulated hidden state. The mechanisms draw from Friston's Free Energy Principle and use LIF dynamics from spiking neural networks. An ablation across all 2^3 subsets reveals a super-additive beta x Ant interaction: anticipation alone gives nothing (+0.000 +/- 0.001); beta alone gives modest gain (+0.295 +/- 0.013); combined they close 75% of the oracle gap (+0.741 +/- 0.002, exceeding the sum by +0.446 +/- 0.014). This is structural: a stateless predictor cannot detect approaching transitions because pre-transition tokens are distributionally identical to within-domain tokens. In a character-level MoE LM (5 seeds), beta-routing reduces transition-step BPC from 6.56 +/- 0.01 (Standard) to 4.01 +/- 0.15 (beta-MoE); the beta + Ant gate places 0.86 +/- 0.02 probability on the correct domain expert before that domain appears in input, vs 0.42 +/- 0.12 for Standard MoE. Reference implementations (~200 lines each): https://github.com/russellwmy/affinity-is-not-enough

Man Yung Wong

Russell · Independent Researcher

Sparse Mixture-of-ExpertsMixture-of-Experts InferenceFree Energy PrincipleExpert RoutingMixture-of-Experts Expert Specialization
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Apr 28, 2026

The Thinking Pixel: Recursive Sparse Reasoning in Multimodal Diffusion Latents

Diffusion models have achieved success in high-fidelity data synthesis, yet their capacity for more complex, structured reasoning like text following tasks remains constrained. While advances in language models have leveraged strategies such as latent reasoning and recursion to enhance text understanding capabilities, extending these to multimodal text-to-image generation tasks is challenging due to the continuous and non-discrete nature of visual tokens. To tackle this problem, we draw inspiration from modular human cognition and propose a recursive, sparse mixture-of-experts framework integrated into conventional diffusion models. Our approach introduces a recursive component within joint attention layers that iteratively refines visual tokens over multiple latent steps while efficiently sharing parameters via sparse selection of neural modules. At each step, a gating network is devised to dynamically select specialized neural modules, conditioned on the current visual tokens, the diffusion timestep, and the conditioning information. Comprehensive evaluation on class-conditioned ImageNet image generation tasks and additional studies on the GenEval and DPG benchmark demonstrate the superiority of the proposed method in enhancing model image generation performance.

Yuwei Sun, Yuxuan Yao, Hui Li +1

Shanghai Academy of AI for Science · Fudan University

Diffusion TransformerConditional Image GenerationSparse Mixture-of-ExpertsDiffusion ModelsMultimodal Diffusion Models
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Apr 24, 2026

Preserving Long-Tailed Expert Information in Mixture-of-Experts Tuning

Despite MoE models leading many benchmarks, supervised fine-tuning (SFT) for the MoE architectures remains difficult because its router layers are fragile. Methods such as DenseMixer and ESFT mitigate router collapse with dense mixing or auxiliary load-balancing losses, but these introduce noisy gradients that often degrade performance. In preliminary experiments, we systematically pruned experts and observed that while certain super experts are activated far more frequently, discarding less used experts still leads to notable performance degradation. This suggests that even rarely activated experts encode non-trivial knowledge useful for downstream tasks. Motivated by this, we propose an auxiliary-loss-free MoE SFT framework that combines bias-driven sparsification with always-active gated condenser experts. Rather than enforcing balanced activation across all experts, our method encourages task-relevant experts to remain active while pushing long-tailed experts toward inactivity. The condenser experts provide a persistent, learnable pathway that alleviates gradient starvation and facilitates consolidation of information that would otherwise remain fragmented across sparsely activated experts. Analysis further suggest that this design better preserves long-tailed expert information under sparse routing. Experiments on large-scale MoE models demonstrate that our approach outperforms state-of-the-art SFT baselines such as DenseMixer and ESFT, achieving average gain of 2.5%+ on both mathematical reasoning and commonsenseQA benchmarks.

Haoze He, Xingyuan Ding, Xuan Jiang +5

Carnegie Mellon University · MIT · UCSD +1

Supervised Fine-TuningFine-TuningLong-Tail LearningSparse Mixture-of-ExpertsMixture-of-Experts ModelsMixture-of-Experts Fine-Tuning
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Apr 23, 2026

Teacher-Guided Routing for Sparse Vision Mixture-of-Experts

Recent progress in deep learning has been driven by increasingly large-scale models, but the resulting computational cost has become a critical bottleneck. Sparse Mixture of Experts (MoE) offers an effective solution by activating only a small subset of experts for each input, achieving high scalability without sacrificing inference speed. Although effective, sparse MoE training exhibits characteristic optimization difficulties. Because the router receives informative gradients only through the experts selected in the forward pass, it suffers from gradient blocking and obtains little information from unselected routes. This limited, highly localized feedback makes it difficult for the router to learn appropriate expert-selection scores and often leads to unstable routing dynamics, such as fluctuating expert assignments during training. To address this issue, we propose TGR-MoE: Teacher-Guided Routing for Sparse Vision Mixture-of-Experts, a simple yet effective method that stabilizes router learning using supervision derived from a pretrained dense teacher model. TGR-MoE constructs a teacher router from the teacher's intermediate representations and uses its routing outputs as pseudo-supervision for the student router, suppressing frequent routing fluctuations during training and enabling knowledge-guided expert selection from the early stages of training. Extensive experiments on ImageNet-1K and CIFAR-100 demonstrate that TGR consistently improves both accuracy and routing consistency, while maintaining stable training even under highly sparse configurations.

Masahiro Kada, Ryota Yoshihashi, Satoshi Ikehata +2

Institute of Science Tokyo · Tokyo, Japan · DENSO IT Laboratory

Adaptive Model RoutingSparse Mixture-of-ExpertsExpert Routing
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Apr 21, 2026

Quadruped Parkour Learning: Sparsely Gated Mixture of Experts with Visual Input

Robotic parkour provides a compelling benchmark for advancing locomotion over highly challenging terrain, including large discontinuities such as elevated steps. Recent approaches have demonstrated impressive capabilities, including dynamic climbing and jumping, but typically rely on sequential multilayer perceptron (MLP) architectures with densely activated layers. In contrast, sparsely gated mixture-of-experts (MoE) architectures have emerged in the large language model domain as an effective paradigm for improving scalability and performance by activating only a subset of parameters at inference time. In this work, we investigate the application of sparsely gated MoE architectures to vision-based robotic parkour. We compare control policies based on standard MLPs and MoE architectures under a controlled setting where the number of active parameters at inference time is matched. Experimental results on a real Unitree Go2 quadruped robot demonstrate clear performance gains, with the MoE policy achieving double the number of successful trials in traversing large obstacles compared to a standard MLP baseline. We further show that achieving comparable performance with a standard MLP requires scaling its parameter count to match that of the total MoE model, resulting in a 14.3% increase in computation time. These results highlight that sparsely gated MoE architectures provide a favorable trade-off between performance and computational efficiency, enabling improved scaling of control policies for vision-based robotic parkour. An anonymized link to the codebase is https://osf.io/v2kqj/files/github?view_only=7977dee10c0a44769184498eaba72e44.

Michael Ziegltrum, Jianhao Jiao, Tianhu Peng +2

Robot Perception and Learning Lab, Intelligent Robotics, Department of Computer Science, University College London, Gower Street, WC1E 6BT, London, UK.

Robot Policy LearningSparse Mixture-of-ExpertsRobot LocomotionVision-Based Robot ControlQuadruped Locomotion
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Apr 15, 2026

Design and Behavior of Sparse Mixture-of-Experts Layers in CNN-based Semantic Segmentation

Sparse mixture-of-experts (MoE) layers have been shown to substantially increase model capacity without a proportional increase in computational cost and are widely used in transformer architectures, where they typically replace feed-forward network blocks. In contrast, integrating sparse MoE layers into convolutional neural networks (CNNs) remains inconsistent, with most prior work focusing on fine-grained MoEs operating at the filter or channel levels. In this work, we investigate a coarser, patch-wise formulation of sparse MoE layers for semantic segmentation, where local regions are routed to a small subset of convolutional experts. Through experiments on the Cityscapes and BDD100K datasets using encoder-decoder and backbone-based CNNs, we conduct a design analysis to assess how architectural choices affect routing dynamics and expert specialization. Our results demonstrate consistent, architecture-dependent improvements (up to +3.9 mIoU) with little computational overhead, while revealing strong design sensitivity. Our work provides empirical insights into the design and internal dynamics of sparse MoE layers in CNN-based dense prediction. Our code is available at https://github.com/KASTEL-MobilityLab/moe-layers/.

Svetlana Pavlitska, Haixi Fan, Konstantin Ditschuneit +1

FZI Research Center for Information Technology · Karlsruhe Institute of Technology (KIT)

Sparse Mixture-of-ExpertsMixture-of-Experts ModelsConvolutional Neural NetworksSemantic Segmentation
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Apr 15, 2026

Enhancing Mixture-of-Experts Specialization via Cluster-Aware Upcycling

Sparse Upcycling provides an efficient way to initialize a Mixture-of-Experts (MoE) model from pretrained dense weights instead of training from scratch. However, since all experts start from identical weights and the router is randomly initialized, the model suffers from expert symmetry and limited early specialization. We propose Cluster-aware Upcycling, a strategy that incorporates semantic structure into MoE initialization. Our method first partitions the dense model's input activations into semantic clusters. Each expert is then initialized using the subspace representations of its corresponding cluster via truncated SVD, while setting the router's initial weights to the cluster centroids. This cluster-aware initialization breaks expert symmetry and encourages early specialization aligned with the data distribution. Furthermore, we introduce an expert-ensemble self-distillation loss that stabilizes training by providing reliable routing guidance using an ensemble teacher. When evaluated on CLIP ViT-B/32 and ViT-B/16, Cluster-aware Upcycling consistently outperforms existing methods across both zero-shot and few-shot benchmarks. The proposed method also produces more diverse and disentangled expert representations, reduces inter-expert similarity, and leads to more confident routing behavior. Project page: https://sanghyeokchu.github.io/cluster-aware-upcycling/

Sanghyeok Chu, Pyunghwan Ahn, Gwangmo Song +3

ECE, Seoul National University · LG AI Research · University of Michigan +1

Mixture-of-Experts Expert SpecializationMixture-of-Experts ModelsMixture of ExpertsSparse Mixture-of-ExpertsVision Foundation Models
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Apr 10, 2026

Plasticity-Enhanced Multi-Agent Mixture of Experts for Dynamic Objective Adaptation in UAVs-Assisted Emergency Communication Networks

Unmanned aerial vehicles serving as aerial base stations can rapidly restore connectivity after disasters, yet abrupt changes in user mobility and traffic demands shift the quality of service trade-offs and induce strong non-stationarity. Deep reinforcement learning policies suffer from plasticity loss under such shifts, as representation collapse and neuron dormancy impair adaptation. We propose plasticity enhanced multi-agent mixture of experts (PE-MAMoE), a centralized training with decentralized execution framework built on multi-agent proximal policy optimization. PE-MAMoE equips each UAV with a sparsely gated mixture of experts actor whose router selects a single specialist per step. A non-parametric Phase Controller injects brief, expert-only stochastic perturbations after phase switches, resets the action log-standard-deviation, anneals entropy and learning rate, and schedules the router temperature, all to re-plasticize the policy without destabilizing safe behaviors. We derive a dynamic regret bound showing the tracking error scales with both environment variation and cumulative noise energy. In a phase-driven simulator with mobile users and 3GPP-style channels, PE-MAMoE improves normalized interquartile mean return by 26.3% over the best baseline, increases served-user capacity by 12.8%, and reduces collisions by approximately 75%. Diagnostics confirm persistently higher expert feature rank and periodic dormant-neuron recovery at regime switches.

Wen Qiu, Zhiqiang He, Wei Zhao +1

Department of Information and Communication Engineering, Kitami Institute of Technology, Japan. · Graduate School of Informatics and Engineering, the University of Electro-Communications, Japan. · School of Computer Science and Technology, Anhui University of Technology, China. +1

UAV CommunicationReinforcement LearningNon-Stationary RLMulti-Agent Reinforcement LearningWireless CommunicationsSparse Mixture-of-Experts
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Apr 8, 2026

MoE Routing Testbed: Studying Expert Specialization and Routing Behavior at Small Scale

Sparse Mixture-of-Experts (MoE) architectures are increasingly popular for frontier large language models (LLM) but they introduce training challenges due to routing complexity. Fully leveraging parameters of an MoE model requires all experts to be well-trained and to specialize in non-redundant ways. Assessing this, however, is complicated due to lack of established metrics and, importantly, many routing techniques exhibit similar performance at smaller sizes, which is often not reflective of their behavior at large scale. To address this challenge, we propose the MoE Routing Testbed, a setup that gives clearer visibility into routing dynamics at small scale while using realistic data. The testbed pairs a data mix with clearly distinguishable domains with a reference router that prescribes ideal routing based on these domains, providing a well-defined upper bound for comparison. This enables quantifiable measurement of expert specialization. To demonstrate the value of the testbed, we compare various MoE routing approaches and show that balancing scope is the crucial factor that allows specialization while maintaining high expert utilization. We confirm that this observation generalizes to models 35x larger.

Tobias Falke, Nicolas Anastassacos, Samson Tan +6

Amazon AGI

Mixture of ExpertsSparse Mixture-of-ExpertsExpert RoutingExpert Load Balancing
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Apr 7, 2026

Efficient Quantization of Mixture-of-Experts with Theoretical Generalization Guarantees

Sparse Mixture-of-Experts (MoE) allows scaling of language and vision models efficiently by activating only a small subset of experts per input. While this reduces computation, the large number of parameters still incurs substantial memory overhead during inference. Post-training quantization has been explored to address this issue. Because uniform quantization suffers from significant accuracy loss at low bit-widths, mixed-precision methods have been recently explored; however, they often require substantial computation for bit-width allocation and overlook the varying sensitivity of model performance to the quantization of different experts. We propose a theoretically grounded expert-wise mixed precision strategy that assigns bit-width to each expert primarily based on their change in routers l2 norm during training. Experts with smaller changes are shown to capture less frequent but critical features, and model performance is more sensitive to the quantization of these experts, thus requiring higher precision. Furthermore, to avoid allocating experts to lower precision that inject high quantization noise, experts with large maximum intra-neuron variance are also allocated higher precision. Experiments on large-scale MoE models, including Switch Transformer and Mixtral, show that our method achieves higher accuracy than existing approaches, while also reducing inference cost and incurring only negligible overhead for bit-width assignment.

Mohammed Nowaz Rabbani Chowdhury, Kaoutar El Maghraoui, Hsinyu Tsai +4

Rensselaer Polytechnic Institute · IBM Research

Mixture-of-Experts QuantizationNeural Network QuantizationPost-Training QuantizationSparse Mixture-of-Experts
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Apr 7, 2026

Do Domain-specific Experts exist in MoE-based LLMs?

In the era of Large Language Models (LLMs), the Mixture of Experts (MoE) architecture has emerged as an effective approach for training extremely large models with improved computational efficiency. This success builds upon extensive prior research aimed at enhancing expert specialization in MoE-based LLMs. However, the nature of such specializations and how they can be systematically interpreted remain open research challenges. In this work, we investigate this gap by posing a fundamental question: Do domain-specific experts exist in MoE-based LLMs? To answer the question, we evaluate ten advanced MoE-based LLMs ranging from 3.8B to 120B parameters and provide empirical evidence for the existence of domain-specific experts. Building on this finding, we propose Domain Steering Mixture of Experts (DSMoE), a training-free framework that introduces zero additional inference cost and outperforms both well-trained MoE-based LLMs and strong baselines, including Supervised Fine-Tuning (SFT). Experiments on four advanced open-source MoE-based LLMs across both target and non-target domains demonstrate that our method achieves strong performance and robust generalization without increasing inference cost or requiring additional retraining. Our implementation is publicly available at https://github.com/giangdip2410/Domain-specific-Experts.

Giang Do, Hung Le, Truyen Tran

Applied Artificial Intelligence Intiative (A2I2), Deakin University

Mixture-of-Experts Language ModelsMixture-of-Experts ModelsSparse Mixture-of-ExpertsDomain Adaptation for LLMs
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Apr 6, 2026

HI-MoE: Hierarchical Instance-Conditioned Mixture-of-Experts for Object Detection

Mixture-of-Experts (MoE) architectures enable conditional computation by activating only a subset of model parameters for each input. Although sparse routing has been highly effective in language models and has also shown promise in vision, most vision MoE methods operate at the image or patch level. This granularity is poorly aligned with object detection, where the fundamental unit of reasoning is an object query corresponding to a candidate instance. We propose Hierarchical Instance-Conditioned Mixture-of-Experts (HI-MoE), a DETR-style detection architecture that performs routing in two stages: a lightweight scene router first selects a scene-consistent expert subset, and an instance router then assigns each object query to a small number of experts within that subset. This design aims to preserve sparse computation while better matching the heterogeneous, instance-centric structure of detection. In the current draft, experiments are concentrated on COCO with preliminary specialization analysis on LVIS. Under these settings, HI-MoE improves over a dense DINO baseline and over simpler token-level or instance-only routing variants, with especially strong gains on small objects. We also provide an initial visualization of expert specialization patterns. We present the method, ablations, and current limitations in a form intended to support further experimental validation.

Vadim Vashkelis, Natalia Trukhina

Object DetectionMixture-of-Experts ModelsSparse Mixture-of-ExpertsDetection Transformer
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Apr 5, 2026

SARES-DEIM: Sparse Mixture-of-Experts Meets DETR for Clutter-Aware SAR Ship Detection

Ship detection in Synthetic Aperture Radar (SAR) imagery is challenged by coherent speckle noise, complex coastal clutter, and the prevalence of small-scale targets. Conventional detectors, primarily designed for optical imagery, often exhibit limited adaptability to SAR-specific degradation and suffer from the loss of fine-grained ship signatures during spatial downsampling. To address these limitations, we propose SARES-DEIM, a domain-aware detection framework grounded in the DEtection TRansformer (DETR) paradigm. Central to our approach is SARESMoE (SAR-aware Expert Selection Mixture-of-Experts), a module leveraging a sparse gating mechanism to selectively route features toward specialized wavelet, spatial, and frequency-oriented experts. This sparsely activated architecture enhances clutter-aware representation while keeping the active inference cost controlled. Furthermore, we introduce the Space-to-Depth Enhancement Pyramid (SDEP) neck to preserve high-resolution spatial cues from shallow stages and improve the localization of small targets. Experiments on HRSID and SAR-Ship-Dataset show that SARES-DEIM achieves competitive results across both public benchmarks, with more prominent advantages on the challenging HRSID dataset. Specifically, SARES-DEIM achieves 76.4% mAP50:95 and 93.8% mAP50 on HRSID, while keeping the active computation at 72.6 GFLOPs and 136.5 FPS on a single NVIDIA A40 GPU with batch size 8; the batch-size-1 latency is 37.6 ms.

Fenghao Song, Shaojing Yang, Xi Zhou

Yunnan Normal University, No. 768, Jucheng Avenue, Chenggong District, Kunming 650500, China.

Object DetectionRemote Sensing Small Object DetectionSynthetic Aperture RadarSparse Mixture-of-ExpertsDetection Transformer
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Apr 3, 2026

Adaptive Semantic Communication for Wireless Image Transmission Leveraging Mixture-of-Experts Mechanism

Deep learning based semantic communication has achieved significant progress in wireless image transmission, but most existing schemes rely on fixed models and thus lack robustness to diverse image contents and dynamic channel conditions. To improve adaptability, recent studies have developed adaptive semantic communication strategies that adjust transmission or model behavior according to either source content or channel state. More recently, MoE-based semantic communication has emerged as a sparse and efficient adaptive architecture, although existing designs still mainly rely on single-driven routing. To address this limitation, we propose a novel multi-stage end-to-end image semantic communication system for multi-input multi-output (MIMO) channels, built upon an adaptive MoE Swin Transformer block. Specifically, we introduce a dynamic expert gating mechanism that jointly evaluates both real-time CSI and the semantic content of input image patches to compute adaptive routing probabilities. By selectively activating only a specialized subset of experts based on this joint condition, our approach breaks the rigid coupling of traditional adaptive methods and overcomes the bottlenecks of single-driven routing. Simulation results indicate a significant improvement in reconstruction quality over existing methods while maintaining the transmission efficiency.

Haowen Wan, Qianqian Yang

Polytechnic Institute, Zhejiang University, Hangzhou, China · College of Information Science and Electronic Engineering, Zhejiang University, Hangzhou, China

Adaptive Model RoutingSparse Mixture-of-ExpertsSemantic CommunicationWireless Communications
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Mar 21, 2026

Distilled Large Language Model-Driven Dynamic Sparse Expert Activation Mechanism

High inter-class similarity, extreme scale variation, and limited computational budgets hinder reliable visual recognition across diverse real-world data. Existing vision-centric and cross-modal approaches often rely on rigid fusion mechanisms and heavy annotation pipelines, leading to sub-optimal generalization. We propose the Distilled Large Language Model (LLM)-Driven Sparse Mixture-of-Experts (DS-MoE) framework, which integrates text-guided dynamic routing and lightweight multi-scale comprehension. The DS-MoE framework dynamically aligns textual semantics with defect-specific visual patterns through a sparse MoE architecture, where task-relevant experts are adaptively activated based on semantic relevance, resolving inter-class ambiguity. A lightweight MobileSAM encoder enables real-time inference while preserving multi-scale defect details. Extensive experiments on PCB, aluminum foil, and mold defect datasets demonstrate that our framework achieves superior performance compared to existing pure vision models. DS-MoE surpasses YOLOv8/YOLOX with gains of +13.9, +1.4, and +2.0 pp mAP@ 0.5:0.95 on BBMP, aluminum, and PCB, respectively, while also improving precision and recall.

Qinghui Chen, Zekai Zhang, Zaigui Zhang +5

School of Control Science and Engineering, Shandong University, Jinan, China · Laoshan Laboratory, Qingdao, China · Jinan Inspur Data Technology Co., Ltd, Jinan, China +2

Industrial Anomaly DetectionIndustrial InspectionSparse Mixture-of-Experts
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Mar 18, 2026

Path-Constrained Mixture-of-Experts

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 NLN^L possible paths for NN experts across LL 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.

Zijin Gu, Tatiana Likhomanenko, Vimal Thilak +2

Apple · †Google

Mixture-of-Experts Language ModelsSparse Mixture-of-ExpertsExpert Routing
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Mar 12, 2026

Expert Threshold Routing for Autoregressive Language Modeling with Dynamic Computation Allocation and Load Balancing

Token-choice Mixture-of-Experts (TC-MoE) routes each token to a fixed number of experts, limiting dynamic computation allocation and requiring auxiliary losses to maintain load balance. We propose Expert Threshold (ET) routing, where each expert maintains an exponential moving average (EMA) threshold estimated from the global token distribution. At both training and inference, each token is independently routed to an expert if its score exceeds the expert's threshold, enabling dynamic computation allocation while achieving load balance without auxiliary losses. This fully causal mechanism eliminates dependence on other tokens in the batch, making it well-suited for autoregressive language modeling. In pretraining experiments scaling to 2.4B parameters on FineWeb-Edu, ET achieves 0.067 lower cross-entropy loss than TC-MoE, equivalent to reaching the same performance with 1.6×\times fewer tokens.

Hanchi Sun, Yixin Liu, Yonghui Wu +1

Computer Science and Engineering, Lehigh University, Bethlehem, PA, USA · MD-HOBI-BIOMED INFORMATICS, University of Florida, Gainesville, FL, USA

Expert RoutingMixture-of-Experts ModelsSparse Mixture-of-ExpertsExpert Load BalancingAutoregressive Language Modeling
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Mar 11, 2026

Task-Conditioned Routing Signatures in Sparse Mixture-of-Experts Transformers

Sparse Mixture-of-Experts (MoE) architectures enable efficient scaling of large language models through conditional computation, yet the routing mechanisms responsible for expert selection remain poorly understood. In this work, we introduce routing signatures, a vector representation summarizing expert activation patterns across layers for a given prompt, and use them to study whether MoE routing exhibits task-conditioned structure. Using OLMoE-1B-7B-0125-Instruct as an empirical testbed, we show that prompts from the same task category induce highly similar routing signatures, while prompts from different categories exhibit substantially lower similarity. Within-category routing similarity (0.8435 +/- 0.0879) significantly exceeds across-category similarity (0.6225 +/- 0.1687), corresponding to Cohen's d = 1.44. A logistic regression classifier trained solely on routing signatures achieves 92.5% +/- 6.1% cross-validated accuracy on four-way task classification. To ensure statistical validity, we introduce permutation and load-balancing baselines and show that the observed separation is not explained by sparsity or balancing constraints alone. We further analyze layer-wise signal strength and low-dimensional projections of routing signatures, finding that task structure becomes increasingly apparent in deeper layers. These results suggest that routing in sparse transformers is not merely a balancing mechanism, but a measurable task-sensitive component of conditional computation. We release MOE-XRAY, a lightweight toolkit for routing telemetry and analysis.

Mynampati Sri Ranganadha Avinash

Independent Researcher | Asthra Labs

Mixture-of-Experts InterpretabilityMixture-of-Experts Language ModelsExpert RoutingSparse Mixture-of-ExpertsTransformer InterpretabilityNeural Network Interpretability
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Mar 9, 2026

FineRMoE: Dimension Expansion for Finer-Grained Expert with Its Upcycling Approach

As revealed by the scaling law of fine-grained MoE, model performance ceases to be improved once the granularity of the intermediate dimension exceeds the optimal threshold, limiting further gains from single-dimension fine-grained design. To address this bottleneck, we propose FineRMoE (FineR-Grained MoE), an architecture that extends fine-grained expert design to both intermediate and output dimensions, aiming to enhance expert specialization beyond the single-dimension limit. We further introduce a bi-level sparse forward computation paradigm and a specialized routing mechanism to govern the activation. In addition, to obviate the prohibitive cost of training FineRMoE from scratch, we devise a generalized upcycling method to build FineRMoE in a cost-effective manner. Extensive experiments demonstrate the superior performance achieved by FineRMoE across ten standard benchmarks. Compared with the strongest baseline, FineRMoE achieves 6 times higher parameter efficiency, 281 times lower prefill latency, and 136 timese higher decoding throughput during inference.

Ning Liao, Xiaoxing Wang, Xiaohan Qin +1

Shanghai Jiao Tong University

Sparse Mixture-of-ExpertsMixture-of-Experts ModelsMixture-of-Experts Inference
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Mar 9, 2026

Mixture of experts architectures for machine learning interatomic potentials

Machine Learning Interatomic Potentials (MLIPs) enable accurate large-scale atomistic simulations, yet improving their expressive capacity efficiently remains challenging. Here we systematically investigate Mixture-of-Experts (MoE) and Mixture-of-Linear-Experts (MoLE) architectures within the DPA3 framework for MLIPs and analyze the effects of routing strategies and expert designs. We show that sparse activation combined with shared experts yields substantial performance gains, and that nonlinear MoE formulations outperform MoLE when shared experts are present, underscoring the importance of nonlinear expert specialization. Furthermore, element-wise routing consistently surpasses configuration-level routing, while global MoE routing often leads to numerical instability. The resulting element-wise MoE model consistently outperforms all DPA3-based baselines across the OMol25, OMat24, and OC20M benchmarks. Analysis of routing patterns reveals chemically interpretable expert specialization aligned with periodic-table trends, indicating that the model effectively captures element-specific chemical characteristics for precise interatomic modeling.

Yuzhi Liu, Duo Zhang, Anyang Peng +3

AI for Science Institute, Beijing 100080, P. R. China. · DP Technology, Beijing 100080, P. R. China. · Academy for Advanced Interdisciplinary Studies, Peking University, Beijing 100871, P. R. China. +3

Machine Learning Interatomic PotentialsMixture-of-Experts ModelsSparse Mixture-of-ExpertsExpert Routing
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Mar 6, 2026

Swimba: Switch Mamba Model Scales State Space Models

Mixture-of-experts (MoE) is a common approach for increasing parameter capacity, but applying MoE to state space model (SSM) token mixers can multiply the cost of the recurrent state update. We study how to introduce expert specialization into selective SSMs while preserving computational efficiency. We show that MoE--SSM can refer to two designs: (1) MoE over separated SSMs, which maintains multiple state trajectories and thus scales compute with the number of experts; and (2) MoE-parameterized SSM, which mixes experts in parameter space, maintains a single state trajectory, and evaluates the recurrence once. Our method, Switch Mamba (Swimba), follows the second design by routing over expert-produced SSM streams. Theoretically, we establish well-definedness and stability for MoE-parameterized SSMs and characterize the relationship between the two designs. Empirically, we evaluate Swimba on standard benchmark tasks and measure real-time throughput and latency. Under matched FLOPs, Swimba achieves slightly better average performance than the baseline, with a small slowdown in real-time latency and throughput. Overall, these results suggest that parameter-space MoE can increase SSM capacity while keeping the dominant recurrence cost fixed.

Zhixu Du, Krishna Teja Chitty-Venkata, Murali Emani +3

Duke University · Red Hat, Inc. · Argonne National Laboratory

State Space ModelsSelective SSMsMixture-of-Experts ModelsSparse Mixture-of-Experts
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Mar 6, 2026

EvoESAP: Non-Uniform Expert Pruning for Sparse MoE

Sparse Mixture-of-Experts (SMoE) language models achieve strong capability at low per-token compute, yet deployment remains constrained by memory footprint and throughput because the full expert pool must still be stored and served. Post-training expert pruning reduces this cost, but most methods focus on which experts to prune within each layer and default to a uniform layer-wise sparsity allocation, even though the layer-wise allocation can strongly affect performance. We decouple pruning into within-layer expert ranking and across-layer budget allocation, and introduce Expected Speculative Acceptance Proxy (ESAP), a speculative-decoding-inspired, teacher-forced metric that measures how well a pruned model matches the full model without costly autoregressive decoding. ESAP is bounded and stable, enabling cheap comparison of many candidates. Building on ESAP, we propose EvoESAP, an evolutionary search framework that finds an improved non-uniform layer-wise sparsity allocation under a fixed global budget while holding the within-layer pruning order fixed, making it a plug-and-play method for criteria such as Frequency, EAN, SEER, and REAP. Across 7B--30B SMoE LLMs at 25% and 50% sparsity, EvoESAP consistently discovers non-uniform allocations that improve open-ended generation (up to +19.6% on MATH-500 at 50% sparsity) while preserving competitive multiple-choice accuracy compared with uniform pruning at the same sparsity. Code is available at https://github.com/ZongfangLiu/EvoESAP.

Zongfang Liu, Shengkun Tang, Boyang Sun +2

Zhejiang University, Hangzhou, Zhejiang, China · Westlake University, Hangzhou, Zhejiang, China · Mohamed bin Zayed University of Artificial Intelligence, Abu Dhabi, United Arab Emirates

Mixture-of-Experts PruningLLM PruningSparse Mixture-of-ExpertsNeural Network Pruning
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Mar 3, 2026

Robust Heterogeneous Analog-Digital Computing for Mixture-of-Experts Models with Theoretical Generalization Guarantees

Sparse Mixture-of-Experts (MoE) models enable efficient scalability by activating only a small sub-set of experts per input, yet their massive parameter counts lead to substantial memory and energy inefficiency during inference. Analog in-memory computing (AIMC) offers a promising solution by eliminating frequent data movement between memory and compute units. However, mitigating hardware nonidealities of AIMC typically requires noise-aware retraining, which is infeasible for large MoE models. In this paper, we propose a retraining-free heterogeneous computation framework in which noise-sensitive experts, which are provably identifiable by their maximum neuron norm, are computed digitally while the majority of the experts are executed on AIMC hardware. We further assign densely activated modules, such as attention layers, to digital computation due to their high noise sensitivity despite comprising a small fraction of parameters. Extensive experiments on large MoE language models, including DeepSeekMoE and OLMoE, across multiple benchmark tasks validate the robustness of our approach in maintaining accuracy under analog nonidealities.

Mohammed Nowaz Rabbani Chowdhury, Hsinyu Tsai, Geoffrey W. Burr +3

Rensselaer Polytechnic Institute · IBM Research

Mixture-of-Experts InferenceHeterogeneous ComputingMixture-of-Experts Language ModelsSparse Mixture-of-ExpertsCompute-in-Memory
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Mar 2, 2026

DynaMoE: Dynamic Token-Level Expert Activation with Layer-Wise Adaptive Capacity for Mixture-of-Experts Neural Networks

Mixture-of-Experts (MoE) architectures have emerged as a powerful paradigm for scaling neural networks while maintaining computational efficiency. However, standard MoE implementations rely on two rigid design assumptions: (1) fixed Top-K routing where exactly K experts are activated per token, and (2) uniform expert allocation across all layers. This paper introduces DynaMoE, a novel MoE framework that relaxes both constraints through dynamic token-level expert activation and layer-wise adaptive capacity allocation. DynaMoE introduces a principled routing mechanism where the number of active experts per token varies based on input complexity. Concurrently, the framework implements six distinct scheduling strategies for distributing expert capacity across network depth, including descending, ascending, pyramid, and wave patterns. We theoretically analyze the expressivity gains of dynamic routing and derive bounds on computational efficiency. Through extensive experiments on MNIST, Fashion-MNIST, CIFAR-10 (image classification), and Recycling-the-Web (language modeling) across multiple model scales, we demonstrate that DynaMoE achieves superior parameter efficiency compared to static baselines. Our key finding is that optimal expert schedules are task- and scale-dependent: descending schedules (concentrating capacity in early layers) outperform uniform baselines on image classification. For language modeling, optimal schedules vary by model size, descending for Tiny, ascending for Small, and uniform for Medium. Furthermore, dynamic routing reduces gradient variance during training, leading to improved convergence stability. DynaMoE establishes a new framework for adaptive computation in neural networks, providing principled guidance for MoE architecture design.

Gökdeniz Gülmez

Machine Learning Research, Stuttgart, Germany

Mixture-of-Experts ModelsExpert RoutingSparse Mixture-of-ExpertsNeural Network Expressivity
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Feb 25, 2026

Excitation: Momentum For Experts

We propose Excitation, a novel optimization framework designed to accelerate learning in sparse architectures such as Mixture-of-Experts (MoEs). Unlike traditional optimizers that treat all parameters uniformly, Excitation dynamically modulates updates using batch-level expert utilization. It introduces a competitive update dynamic that amplifies updates to highly-utilized experts and can selectively suppress low-utilization ones, effectively sharpening routing specialization. Notably, we identify a phenomenon of "structural confusion" in deep MoEs, where standard optimizers fail to establish functional signal paths; Excitation acts as a specialization catalyst, "rescuing" these models and enabling stable training where baselines remain trapped. Excitation is optimizer-, domain-, and model-agnostic, requires minimal integration effort, and introduces neither additional per-parameter optimizer state nor learnable parameters, making it highly viable for memory-constrained settings. Across language and vision tasks, Excitation consistently improves convergence speed and final performance in MoE models, indicating that active update modulation is a key mechanism for effective conditional computation.

Sagi Shaier

Aleph Alpha Research, Heidelberg, Germany.

Sparse Mixture-of-ExpertsMixture of ExpertsMixture-of-Experts Models
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Feb 24, 2026

Modality-Guided Mixture of Structured Experts with Entropy-Triggered Routing for Multimodal Recommendation

Multimodal recommenders combine collaborative behavior with visual and textual item evidence, whose usefulness varies across user-item interactions. Independently trained source-specific diagnostic probes partition held-out interactions into behavior-, appearance-, semantics-, and mixed-evidence regimes across five benchmarks, within which capacity-matched fixed fusion rules exhibit systematic regime-dependent performance crossovers. This diagnostic observation motivates MAGNET, a multimodal graph recommender with two core mechanisms. First, a calibrated expert bank organizes trainable experts by anchor source (behavior, appearance, or semantics) and fusion family (dominant, balanced, or complementary), while an interaction-conditioned router selects a sparse composition using all three evidence sources. Second, an entropy-triggered, coverage-aware progressive schedule decouples population-level routing-mass coverage from per-instance decisiveness, transitioning from broad routing exploration to confident specialization once sufficient coverage is sustained, while preserving coverage thereafter. MAGNET separately encodes the observed interaction graph and a filtered content-induced structural view, applying cross-view alignment after independent propagation. We evaluate MAGNET on four Amazon domains and the non-Amazon MicroLens-100K benchmark, including tail-item and low-history warm-start user evaluation alongside matched expert-design controls. Under the shared-feature, fixed-split protocol, MAGNET-DV exceeds the strongest protocol-compatible non-MAGNET baseline in every reported main-table cell, supported by seed-wise difference tests. Both the fixed and KL-anchored structured variants achieve higher five-seed mean NDCG@20 than matched homogeneous and free-mixture alternatives across all five datasets. MAGNET supports route-level diagnostics through explicit expert semantics.

Ji Dai, Quan Fang, DeSheng Cai

Beijing University of Posts and Telecommunications, China · Beijing University of Posts and Telecommunications, Beijing, China · Tianjin University of Technology, China

Sparse Mixture-of-ExpertsRecommender SystemsMultimodal RecommendationMultimodal Graph LearningMixture-of-Experts Models
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Feb 23, 2026

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 imbalance across experts, where a small subset of experts receives most tokens while others are underutilized. Prior work has focused mainly on training-time solutions such as routing regularization or auxiliary losses, leaving inference-time behavior, which is critical for deployment, less explored. We present a systematic analysis of expert routing during inference and identify three findings: (i) load imbalance persists and worsens with larger batch sizes, (ii) selection frequency does not reliably reflect expert importance, and (iii) overall expert workload and importance can be estimated using a small calibration set. These insights motivate inference-time mechanisms that rebalance workloads without retraining or router modification. We propose Replicate-and-Quantize (R&Q), a training-free and near-lossless framework for dynamic workload rebalancing. In each layer, heavy-hitter experts are replicated to increase parallel capacity, while less critical experts and replicas are quantized to remain within the original memory budget. We also introduce a Load-Imbalance Score (LIS) to measure routing skew by comparing heavy-hitter load to an equal allocation baseline. Experiments across representative SMoE models and benchmarks show up to 1.4x reduction in imbalance with accuracy maintained within +/-0.6%, enabling more predictable and efficient inference.

Zijie Liu, Jie Peng, Jinhao Duan +7

University of North Carolina at Chapel Hill · University of Minnesota Twin Cities · North Carolina State University +2

Expert Load BalancingMixture of ExpertsSparse Mixture-of-ExpertsMixture-of-Experts Inference
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Feb 19, 2026

Grassmannian Mixture-of-Experts: Concentration-Controlled Routing on Subspace Manifolds

Mixture-of-Experts models rely on learned routers to assign tokens to experts, yet standard softmax gating provides no principled mechanism to control the tradeoff between sparsity and utilization. We propose Grassmannian MoE (GrMoE), a routing framework that operates on the Grassmannian manifold of subspaces, where gating weights arise from the concentration parameters of Matrix Bingham distributions. This construction yields a single, interpretable knob -- the concentration matrix ΛΛ -- that continuously controls routing entropy, replacing discrete top-kk selection with a smooth, geometrically principled sparsity mechanism. We further develop an amortized variational inference procedure for posterior routing distributions, enabling uncertainty-aware expert assignment that naturally resists expert collapse. We formally prove tight bounds relating the Bingham concentration spectrum to routing entropy, expected top-kk mass, and an exponential bound on expert collapse, establishing the first formal theory of concentration-controlled sparsity. On synthetic routing tasks, a 350M-parameter MoE language model with 8 experts, a 1.3B-parameter model with 16 experts, and a 2.7B-parameter model with 32 experts, GrMoE achieves 0% routing collapse across all seeds, comparable or better perplexity with 15--30% improved load balance, and a smooth monotonic relationship between concentration and effective sparsity that enables post-hoc sparsity tuning without retraining. Token-level analysis reveals that experts learn heterogeneous concentration values that correlate with linguistic specialization, providing interpretable routing behavior.

Ibne Farabi Shihab, Sanjeda Akter, Anuj Sharma

Department of Computer Science, Iowa State University · Department of Civil, Construction and Environmental Engineering, Iowa State University

Expert RoutingMixture-of-Experts Language ModelsSparse Mixture-of-Experts
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Feb 19, 2026

Arcee Trinity Large Technical Report

We present the technical report for Arcee Trinity Large, a sparse Mixture-of-Experts model with 400B total parameters and 13B activated per token. Additionally, we report on Trinity Nano and Trinity Mini, with Trinity Nano having 6B total parameters with 1B activated per token, Trinity Mini having 26B total parameters with 3B activated per token. The models' modern architecture includes interleaved local and global attention, gated attention, depth-scaled sandwich norm, and sigmoid routing for Mixture-of-Experts. For Trinity Large, we also introduce a new MoE load balancing strategy titled Soft-clamped Momentum Expert Bias Updates (SMEBU). We train the models using the Muon optimizer. All three models completed training with zero loss spikes. Trinity Nano and Trinity Mini were pre-trained on 10 trillion tokens, and Trinity Large was pre-trained on 17 trillion tokens. The model checkpoints are available at https://huggingface.co/arcee-ai.

Varun Singh, Lucas Krauss, Sami Jaghouar +23

Arcee AI · Prime Intellect · DatologyAI

LLM TrainingMixture-of-Experts Language ModelsLanguage Model PretrainingSparse Mixture-of-Experts
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Aug 3, 2025

Shape Distribution Matters: Shape-Specific Mixture-of-Experts for Amodal Segmentation Under Diverse Occlusions

Amodal segmentation aims to predict complete object masks covering both visible and occluded regions, serving as a critical foundation for robust multimedia scene understanding and interactive media editing. This task poses significant challenges in complex visual media due to severe occlusions and extreme shape variation, ranging from rigid furniture to highly deformable clothing. Existing one-size-fits-all approaches struggle to reason about diverse amodal shapes in multimedia content due to limited representation capacity. While a mixture-of-experts framework is a natural solution, naively applying it without considering the underlying shape distribution leads to mismatched routing and redundant experts. To address these issues, we introduce ShapeMoE, a shape-specific sparse mixture-of-experts framework designed for complex visual scene parsing. The key idea is to learn a latent shape distribution space and dynamically route each object to a lightweight expert tailored to its geometric characteristics. Specifically, ShapeMoE encodes each object into a compact Gaussian embedding that captures key shape features. A Shape-Aware Sparse Router then maps the object to the most suitable expert, enabling precise shape-aware routing. Each expert is lightweight and specializes in recovering occluded regions for specific shape patterns. ShapeMoE is designed for shape-specific expert specialization while maintaining computational efficiency. Extensive experiments on three challenging benchmarks demonstrate that ShapeMoE consistently outperforms state-of-the-art methods. Beyond advancing fundamental visual reasoning, ShapeMoE provides a robust and efficient visual prior for downstream multimedia applications, particularly in occlusion-heavy immersive environments.

Zhixuan Li, Yujia Liu, Chen Hui +3

College of Computing and Data Science, Nanyang Technological University, Singapore · School of Computer Science, Peking University, Beijing, China · National Key Laboratory for Multimedia Information Processing, Peking University, Beijing, China +3

Amodal SegmentationOcclusion ReasoningMixture-of-Experts ModelsSparse Mixture-of-Experts
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