Sparse Mixture-of-Experts

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11 papers in the last four weeks, up 57% on the four weeks before. 0.1% of all new papers.

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May 12, 2026cs.LG

Routers Learn the Geometry of Their Experts: Geometric Coupling in Sparse Mixture-of-Experts

Sparse Mixture-of-Experts (SMoE) models enable scaling language models efficiently, but training them remains challenging, as routing can collapse onto few experts and auxiliary load-balancing losses can reduce specialization. Motivated by these hurdles, we study how routing decisions in SMoEs are formed mechanistically. First, we reveal a geometric coupling between routers and their corresponding experts. For a given token, the router weights for the selected expert and the expert weights processing it receive gradients along the same input direction, differing only in scalar coefficients. Thus, matched router--expert directions accumulate the same routed token history. This theoretical coupling also appears empirically in routing dynamics. In a

1

B SMoE trained from scratch, higher router scores predict stronger expert neuron activations, showing that routing decisions are mirrored inside the selected expert. Next, we analyze the effects of auxiliary load balancing on the router--expert geometric coupling, showing that such losses break this structure by spreading input-directed gradients across router weights, making distinct router directions nearly three times more similar to each other. Last, we demonstrate the centrality of geometric coupling for effective routing with a parameter-free online K-Means router, in which each expert maintains a running average of the hidden states routed to it and tokens are assigned based on cosine similarity. Compared with auxiliary-loss and loss-free balancing, this router achieves the lowest load imbalance with only a modest perplexity increase, indicating that geometric coupling captures a substantial part of what the router learns. Overall, our results explain how routers form assignment geometry that supports an effective division of labor.

Sagi Ahrac, Noya Hochwald, Mor Geva

Blavatnik School of Computer Science and AI, Tel Aviv University

Expert Load Balancing Parameter-Free Mixture-of-Experts Routing Adaptive Model Routing Sparse Mixture-of-Experts Expert Routing Mixture-of-Experts Models

May 12, 2026cs.LG

Slicing and Dicing: Configuring Optimal Mixtures of Experts

Mixture-of-Experts (MoE) architectures have become standard in large language models, yet many of their core design choices - expert count, granularity, shared experts, load balancing, token dropping - have only been studied one or two at a time over narrow configuration ranges. It remains an open question whether these choices can be optimized independently, without considering interactions. We present the first systematic study of over 2,000 pretraining runs spanning models up to 6.6B total parameters, in which we exhaustively vary total experts, expert dimension, heterogeneous expert sizing within a single layer, shared expert size and load-balancing mechanisms. We find that at every active-parameter scale that we study, performance consistently improves with total MoE parameters even at extreme active expert parameter ratios like 128.Further, the optimal expert size is nearly invariant to total parameter count and depends only on active parameter count. Third, we see that other choices like shared experts, heterogeneous experts and load-balancing settings have small effects relative to expert count and granularity, although dropless routing yields a consistent gain. Overall, our results suggest a simpler recipe: focus on expert count and granularity, other choices have minimal effect on final quality.

Margaret Li, Sneha Kudugunta, Danielle Rothermel +1

Paul G Allen School of Computer Science University of Washington Seattle, USA · Courant School of Data Science New York University New York, USA

Mixture-of-Experts Language Models Mixture of Experts Sparse Mixture-of-Experts AI Scaling Laws

May 11, 2026cs.LG

DECO: Sparse Mixture-of-Experts with Dense-Comparable Performance on End-Side Devices

While Mixture-of-Experts (MoE) scales model capacity without proportionally increasing computation, its massive total parameter footprint creates significant storage and memory-access bottlenecks, which hinder efficient end-side deployment that simultaneously requires high performance, low computational cost, and small storage overhead. To achieve these properties, we present DECO, a sparse MoE architecture designed to match the performance of dense Transformers under identical total parameter budgets and training tokens. DECO utilizes the differentiable and flexible ReLU-based routing enhanced by learnable expert-wise scaling, which adaptively balances the contributions of routed and shared experts. Furthermore, we introduce NormSiLU, an activation function that normalizes inputs prior to SiLU operators, producing a more stable trend of routed-expert activation ratio and a higher intrinsic sparsity level. We also identify an empirical advantage in using non-gated MLP experts with ReLU-based routing, indicating the possibility of MoE architecture simplification. Experiments demonstrate that DECO, activating only 20% of routed experts, matches dense performance and outperforms established MoE baselines. Our specialized acceleration kernel delivers a 2.93

\times

speedup on Jetson AGX Orin compared with dense inference. Code and checkpoints are available at https://github.com/thunlp/DECO.

Chenyang Song, Weilin Zhao, Xu Han +3

Dept. of Comp. Sci. & Tech., Institute for AI, Tsinghua University, Beijing, China

Sparse Mixture-of-Experts Mixture-of-Experts Inference Expert Routing On-Device Inference

May 10, 2026cs.LG

FLAME: Adaptive Mixture-of-Experts for Continual Multimodal Multi-Task Learning

Real-world model deployment across multiple domains requires multimodal models to operate under two complementary regimes: (1) multi-task pretraining, tasks are co-available at design time where related tasks could borrow representational strength from one another, (2) continual adaptation, in which new tasks emerge after deployment with previously unseen modality combinations. However, neither regime alone suffices: the pretraining task set is never exhaustive, while bypassing joint training forfeits the transfer gains and efficiency among co-trainable tasks. Sparse Mixture-of-Experts (MoE) is a natural fit for this dual requirement: sparse activation enables modular capacity expansion as new tasks arrive, while routing decouples modality-level computation from task-level composition. In this work, we propose a scalable MoE framework for multitask pretraining and continual learning across flexible modality combinations. The framework is designed to support training on multimodal tasks with diverse modality configurations by leveraging modality-specific routers that process tokens from each modality across tasks. Furthermore, it enables continual learning over sequential multimodal tasks within a fixed-capacity MoE by compressing accumulated expert knowledge into low-rank memory subspaces, while expanding only the lightweight routers. We validate the effectiveness of our method on multiple healthcare multimodal benchmarks. It demonstrates competitive multitask pretraining performance while alleviating catastrophic forgetting and improving parameter efficiency.

Xing Han, Shravan Chaudhari, Tanvi Ranade +2

Department of Computer Science Johns Hopkins University · Department of ECE Johns Hopkins University · Department of Computer Science Johns Hopkins University, Bayesian Health

Cross-Modal Learning Healthcare Sparse Mixture-of-Experts Multi-Task Learning Multimodal Learning Multimodal Understanding

May 8, 2026cs.LG

SDG-MoE: Signed Debate Graph Mixture-of-Experts

Sparse MoE models achieve a good balance between capacity and compute by routing each token to a small subset of experts. However, in most MoE architectures, once a token is routed, the selected experts process it independently and their outputs are combined via a weighted sum. This leaves open whether enabling communication among them could improve performance. While prior work has raised this question, direct interaction among the active routed experts remains underexplored. In this paper, we propose SDG-MoE (Signed Debate Graph Mixture-of-Experts), a novel architecture that adds a lightweight, iterative deliberation step before final aggregation. SDG-MoE introduces three components: (i) two learned interaction matrices over the active experts, a support graph

A^+

and a critique graph

A^-

, capturing reinforcing and corrective influences; (ii) a signed message-passing step that updates expert representations before aggregation; and (iii) a disagreement-gated Friedkin-Johnsen-style anchoring that controls deliberation strength while preventing expert drift. Together, these enable a structured deliberation process where interaction strength scales with disagreement and specialization is preserved. We also provide a theoretical analysis establishing stability conditions on expert states and showing that deliberation adds only low-order overhead over the active set. In controlled three-seed pretraining experiments, SDG-MoE improves validation perplexity over both an unsigned graph communication baseline and vanilla MoE, outperforming the strongest baseline by 19.8%, and gives the best external perplexity on WikiText-103, C4, and Paloma among the compared systems.

Stepan Kulibaba, Kirill Labzin, Artem Dzhalilov +4

Innopolis University, Innopolis · Sirius University, Sirius · Innopolis University, Innopolis; Sirius University, Sirius +1

Mixture-of-Experts Language Models Mixture of Experts Sparse Mixture-of-Experts Mixture-of-Experts Models

May 8, 2026cs.LG

Hierarchical Mixture-of-Experts with Two-Stage Optimization

Sparse Mixture-of-Experts (MoE) models scale capacity by routing each token to a small subset of experts. However, their routers exhibit a fundamental trade-off: strong load balancing can suppress expert specialization, while aggressive diversity often causes routing collapse. We propose Hi-MoE, a grouped MoE framework that decomposes routing control into two coupled levels: (i) inter-group balancing that enforces fair traffic across expert groups, and (ii) intra-group specialization that promotes complementary expert behaviors while preventing within-group collapse. Our analysis provides a principled explanation of how our hierarchical objectives reshape the router, thereby promoting stable specialization and mitigating collapse. We observe consistent improvements over recent sparse-routing and grouped-MoE baselines across NLP and vision benchmarks, and confirm robustness via scaling studies (model size, expert count) and targeted ablations. In large-scale pre-training on 58B tokens, Hi-MoE-7B achieves a 5.6% perplexity reduction and a 40% improvement in expert balance over OLMoE-7B across diverse evaluation domains.

Gleb Molodtsov, Alexander Miasnikov, Aleksandr Beznosikov

BRAIn Lab, Moscow, Russia

Expert Load Balancing Mixture of Experts Sparse Mixture-of-Experts Expert Routing Mixture-of-Experts Models

May 8, 2026cs.LG

Geometric Asymmetry in MoE Specialization: Functional Decorrelation and Representational Overlap

Mixture-of-Experts (MoE) architectures achieve scalable capacity through sparse routing, yet the geometric structure of expert specialization remains poorly understood. We introduce a unified Jacobian-PCA-Grassmann framework for analyzing MoE layers in both function space and representation space. Across pretrained MoE Transformers (Mistral, Qwen), we find a consistent structural asymmetry: experts exhibit strong functional decorrelation (consistently low, near-zero cross-expert Jacobian alignment) while their routed representations occupy distinct but partially overlapping subspaces. This indicates that functional decorrelation and representation overlap coexist rather than coincide in MoE specialization. Controlled routing experiments further indicate that routing sparsity appears to be a key factor shaping this geometry: top-k routing induces sharper functional separation and larger subspace divergence, whereas fully soft routing yields more entangled expert structure. Together, these results suggest a geometric interpretation in which MoE layers may be viewed as implementing locally decorrelated operators over overlapping submanifolds on a shared representation manifold, and provide a general diagnostic framework for studying conditional computation in modern Transformer architectures.

Feilong Liu

Transformer Interpretability Neural Representation Geometry Sparse Mixture-of-Experts Mixture-of-Experts Models

May 7, 2026cs.LG

UniPool: Learning Expert-to-Layer Ownership from Brief Global Access

Most Mixture-of-Experts (MoE) transformers preassign each expert to one layer for the whole of training. We study whether a brief global-access phase can learn a compatible expert-to-layer allocation that is then executed privately. UniPool-Lock gives every layer its own router over one global pool, balances aggregate pool usage, and scores experts with a scale-stable NormRouter. After the short ownership-learning phase, it assigns each expert to one layer, locks the disjoint allocation, and continues training as a layer-private MoE. With the same expert-FFN budget and routed expert FLOPs, this recipe lowers held-out loss relative to vanilla MoE by 0.024-0.037 across five dense-equivalent scales from 182M to 1.5B, including -0.0247 at 1.5B after 60B tokens. The ownership-learning phase lasts 2K steps, about 3.3% of training, and post-lock step time is within -0.7% to +2.8% of vanilla MoE in our throughput measurements. Controls locate the gain in full-pool training and in the allocation it produces: a random disjoint allocation fixed at initialization, trained with the same router and losses, matches vanilla, whereas locking the allocation learned during the full-pool phase recovers nearly all of the persistent full-pool gain, and substituting a random allocation at the lock forfeits about half of it. Keeping full-pool access throughout training (UniPool-Full) also improves over vanilla MoE at four scales and outperforms it with only 66.7% (182M) to 50% (469M and 650M) of its expert parameters.

Minbin Huang, Han Shi, Chuanyang Zheng +5

The Chinese University of Hong Kong · Huawei Technologies · The University of Hong Kong

Mixture-of-Experts Language Models Mixture of Experts Sparse Mixture-of-Experts

May 7, 2026cs.LG

E = T*H/(O+B): A Dimensionless Control Parameter for Mixture-of-Experts Ecology

We introduce E = T*H/(O+B), a dimensionless control parameter that predicts whether Mixture-of-Experts (MoE) models will develop a healthy expert ecology or collapse into dead experts. E combines four hyperparameters -- routing temperature T, routing entropy weight H, oracle weight O, and balance weight B -- into a single quantity. Through 12 controlled experiments (8 vision, 4 language) totaling over 11,000 training epochs, we establish that E >= 0.5 alone is sufficient to guarantee zero dead experts, removing the necessity for handcrafted load-balancing auxiliary losses. We validate this cross-modally on CIFAR-10, CIFAR-100, TinyImageNet-200, WikiText-2, and WikiText-103. Six additional findings emerge: (1) dead experts can resuscitate -- triggered by balance loss driving router re-exploration; (2) ortho toxicity is dataset-dependent, not universal; (3) task complexity shifts the critical E threshold; (4) model overfitting is decoupled from expert ecological health; (5) three-tier MoE spontaneously collapses into a two-tier functional structure; (6) ecological structure is temperature-invariant across a 50x range. We propose that E serves as a unified diagnostic for MoE training, analogous to the Reynolds number in fluid dynamics.

Qingjun Zhang

School of Integrated Circuits, Wuxi Taihu University Department of Communication Engineering · Department of Communication Engineering

Expert Load Balancing Mixture of Experts Sparse Mixture-of-Experts Mixture-of-Experts Models

May 5, 2026cs.LG

Toward Structural Multimodal Representations: Specialization, Selection, and Sparsification via Mixture-of-Experts

We propose S3 (Specialization, Selection, Sparsification), a framework that rethinks multimodal learning through a structural perspective. Instead of encoding all signals into a fixed embedding, S3 decomposes multimodal inputs into semantic experts and selectively routes them for each task. Specialization forms concept-level experts in a shared latent space, Selection adapts routing for task-specific needs, and Sparsification prunes low-utility paths to yield compact, information-minimal representations. Across four MultiBench benchmarks, S3 improves accuracy and shows a consistent reverse U-shaped sparsity-performance trend, with peak performance at intermediate sparsity. These results suggest that structuring multimodal representations as selectable semantic components provides a practical and principled alternative to contrastive learning or InfoMax-driven approaches.

Hahyeon Choi, Nojun Kwak

Seoul National University, Seoul, South Korea.

Cross-Modal Representation Learning Sparse Mixture-of-Experts Multimodal Learning Multimodal Understanding

May 4, 2026cs.LG

Soft-to-Hard Routing in Sparse Mixture-of-Experts Models

Softmax routing approaches hard top-1 routing as the temperature tends to zero, but the limiting passage is singular at router ties. This paper develops a boundary-layer calculus for this soft-to-hard limit in population squared-loss mixture-of-experts regression. For a router with logits

a_k(x;φ)

, the relevant local quantity is the top-two margin

Δ(x;φ)

, and the relevant global quantity is the boundary mass

\mathbb{P}(Δ(X;φ)\le w)

. Under smoothness and transversality assumptions, coarea and tubular-neighborhood estimates show how this mass scales with the slab width; in the binary case the leading coefficient is an explicit surface integral over the routing interface. These geometric estimates give quantitative bounds between the soft objective

L_τ

and the hard objective

L_0

, including an

O(τ^α)

uniform comparison under a margin-tail condition, and yield

Γ

-convergence of the soft objectives on compact parameter spaces. The main conclusion is that the zero-temperature approximation is controlled by the probability carried by an

O(τ)

neighborhood of the routing interfaces, not by temperature alone. After isolating this boundary-layer part of the problem, we record a conditional landscape-transfer theorem from hard to small-temperature soft routing and a reduced two-expert Gaussian calculation illustrating local symmetry breaking. Synthetic diagnostics are included only as controlled checks of the boundary-layer predictions.

Reza Rastegar

Meta Platforms, Inc Woodinville, WA

Sparse Mixture-of-Experts Expert Routing

May 1, 2026cs.LG

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-Experts Mixture-of-Experts Inference Free Energy Principle Expert Routing

Apr 28, 2026cs.CV

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 Transformer Conditional Image Generation Sparse Mixture-of-Experts Diffusion Models Multimodal Diffusion Models

Apr 24, 2026cs.LG

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-Tuning Fine-Tuning Long-Tail Learning Sparse Mixture-of-Experts Mixture-of-Experts Models

Apr 23, 2026cs.CV

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 Routing Sparse Mixture-of-Experts Expert Routing

Apr 21, 2026cs.RO

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 Learning Sparse Mixture-of-Experts Robot Locomotion Vision-Based Robot Control Quadruped Locomotion

Apr 3, 2026cs.LG

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 Routing Sparse Mixture-of-Experts Semantic Communication Wireless Communications

Feb 24, 2026cs.AI

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-Experts Recommender Systems Multimodal Recommendation Multimodal Graph Learning Mixture-of-Experts Models

Feb 23, 2026cs.LG

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 Balancing Mixture of Experts Sparse Mixture-of-Experts Mixture-of-Experts Inference

Jul 14, 2019stat.ME

Regularized Estimation and Feature Selection in Mixtures of Generalized Linear Experts

Mixtures of experts (MoE) are conditional mixture models in which both the mixing proportions and the component densities depend on the predictors, and are widely used for regression, classification and model-based clustering of heterogeneous data. Fitting MoE by maximum likelihood becomes unstable, and sometimes infeasible, when the predictors are numerous or correlated. We propose a regularized maximum likelihood framework for simultaneous parameter estimation and feature selection in MoE whose experts belong to the generalized linear model family, covering Gaussian, Poisson and multinomial responses within a single formulation. Sparsity is induced in both the gating network and the experts through

\ell_1

penalties, and the penalized log-likelihood is maximized by a proximal Newton-EM algorithm whose M-step reduces to weighted Lasso problems with closed-form coordinate-ascent updates. Unlike existing penalized MoE procedures, the algorithm requires neither a local quadratic approximation of the penalty nor any matrix inversion, it returns exactly sparse estimates without thresholding, and a proximal Newton-type variant guarantees a monotone increase of the penalized objective at every iteration. On simulated data and five real data sets, the method recovers the actual sparsity support and delivers prediction and clustering accuracy that is competitive with, and often better than, state-of-the-art regularized MoE. The source codes of our developed algorithms and their documentation are publicly available on Github at https://github.com/nv-thin/GLM-RMoE.

Thin Nguyen-Van, Faicel Chamroukhi, Ha Hoang Van +1

Faculty of Mathematics and Computer Science, University of Science, Ho Chi Minh City, Vietnam · Vietnam National University, Ho Chi Minh City, Vietnam · IRT SystemX, 91120 Palaiseau, France +1

Mixture of Experts Sparse Mixture-of-Experts Expectation-Maximization Feature Selection Generalized Linear Models