Expert Routing

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13 papers in the last four weeks, up 225% on the four weeks before. 0.1% of all new papers.

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Latest papers 77

Jul 29, 2026cs.RO

Route by Kinematics, Act by Observation: Kinematics-Supervised Expert Routing in MoE-Augmented VLA

While MoE augments VLA via expert specialization, router suffers from ineffective expert routing owing to the kinematic heterogeneity of actions across manipulation tasks and, even worse, the unavailability of the kinematic signals at inference time. In this work, we first observe that most semantically distinct manipulation tasks reduce to multiple kinematic archetypes. Motivated by this finding, we propose Kinematics-supervised explicit routing (KinRT), a new paradigm that shifts from implicit, observation-driven expert routing to explicit, kinematics-guided expert dispatching. Specifically, we perform kinematic clustering on action trajectories into multiple kinematically coherent groups, whose IDs serve as ground truth to supervise the training of the router; at inference time, the router dispatches experts only using visual-language observations, without any reliance on action kinematics. KinRT actually introduces an asymmetric bridging mechanism that distills the task kinematics from the action space in training into the observation space at inference. In addition, to assess KinRT's cross-platform generalization, we build an economical, Do-It-Yourself robot (DIYRobot) platform from scratch using 3D-print technology (

<

2,000USD). Extensive experiments demonstrate KinRT's superiority over both dense and MoE-featured VLAs by more than 23.26% on RoboTwin benchmark and 20.27% on our introduced DIYRobot platform. Our code and DIYRobot platform will be open-sourced.

Tianhang Yang, Yanze Zheng, Junjie Wang +3

Tsinghua Shenzhen International Graduate School, Tsinghua University, Shenzhen, China · Pengcheng Lab, Shenzhen, China

Robot Policy Learning Expert Routing VLMs for Robotics

Jul 28, 2026cs.LG

Spend Experts Where You Are Unsure: Confidence-Adaptive Routing for Mixture-of-Experts LoRA

Mixture-of-Experts (MoE) variants of Low-Rank Adaptation (LoRA) route every token to a fixed number of experts

k

. Tokens differ in how uncertain the model is about them, so a single k over-spends on easy tokens and under-serves hard ones. We observe that the router's output distribution is already a per-token uncertainty signal: peaked mass indicates confidence, while a flat distribution indicates ambiguity. We introduce CARE (Confidence-Adaptive Routing of Experts), which admits experts in a nucleus fashion. Experts are activated in decreasing router weight until their cumulative mass reaches a threshold, with a small extension when the admitted experts disagree. A budget thermostat calibrates the threshold so that the average number of active experts matches any target. CARE is a drop-in, single-forward-pass rule with no extra parameters. Across eight commonsense benchmarks on LLaMA-3.1-8B and Qwen2.5-7B, as well as math, code, and knowledge tasks, CARE improves over fixed top-k MoE-LoRA at matched compute and matches the fixed-k=4 baseline while activating fewer experts. The same confidence and disagreement signals also improve out-of-distribution detection over MSP, entropy, and multi-pass proxies. We support the design with nucleus fidelity, budget optimality, and an epistemic reading of disagreement, and we release code.

Tom Saliencro, Rohan Desai, Priya Nair +2

University of California, Irvine · University of Washington

Parameter-Free Mixture-of-Experts Routing LLM Inference Acceleration Expert Routing LLM Uncertainty Estimation Mixture-of-Experts Models

Jul 27, 2026cs.CV

OPERA: Offline Policy-guided Expert Routing and Adaptation for Universal Biomedical Image Analysis

Biomedical image analysis spans diverse modalities and tasks, yet real-world deployment is hindered by severe distribution shifts across scanners, protocols, and patient populations. High-performing models consequently require repeated domain-specific fine-tuning, which is a costly cycle that becomes impractical when labels are scarce or privacy constraints limit data sharing. We propose OPERA (Offline Policy-guided Expert Routing and Adaptation), a multi-agent ensemble framework that addresses this deployment bottleneck by treating expert weight assignment as an offline policy learning problem: a routing policy is learned from a small validation set without gradient updates to any expert agent, then deployed with test-time adaptation to handle distribution shift. OPERA coordinates heterogeneous specialist agents through complementary mechanisms. The expert profiling module learns selection policies offline, enabling informed allocation of expertise. Each agent undergoes confidence calibration through temperature adjustment, ensuring more reliable probabilistic outputs. OPERA also incorporates distribution aware adaptation, where class weights are dynamically adjusted at the batch level using statistics derived from unlabeled test data. Instance level routing assigns each sample to the most suitable expert by leveraging inter model agreement and predictive entropy. We evaluate OPERA on 9 datasets covering fundus photography, chest X-ray, CT, MRI, and multimodal diagnostic benchmarks, comparing against 30+ baselines across classification, segmentation, and multimodal settings. OPERA consistently improves performance and calibration quality, demonstrating that offline policy-guided expert agents coordination is a practical path to deployable biomedical AI without retraining. Code is on GitHub.

Zihan Li, Feiyang Liu, Dandan Shan +2

University of Washington Seattle, USA · Delft University of Technology Delft, Netherlands · Xiamen University Xiamen, China

Test-Time Adaptation Medical Image Analysis Mixture-of-Experts Inference Expert Routing

Jul 25, 2026cs.LG

Hierarchical Copula-Gumbel-Top-\texorpdfstring{ $K$ }{K} Routing: Two-Sided Dependence Control for Frozen Mixture-of-Experts at Fixed Per-Token Routing Laws

A stochastic Gumbel-Top-

K

router defines, for every token of a mixture-of-experts (MoE) model, a \emph{routing law}: a distribution over ordered expert lists and mixture weights. We ask which \emph{joint} distributions over the routing choices of different tokens are reachable while every individual token's complete routing law is held exactly fixed. We give a two-sided construction, \emph{Hierarchical Copula-Gumbel-Top-

K

} (\CGA{}). Within a group of related tokens, an exchangeable Gaussian copula positively correlates the Gumbel perturbations at each expert coordinate, which can increase within-group expert-set coherence. Across disjoint pairs of groups, a tunable antithetic construction introduces a selectable amount of negative dependence. We prove that both operations leave each token's ordered Top-

K

sample, mixture weights, and inclusion probabilities identical in distribution to independent routing \emph{at a routing layer conditioned on its pre-routing logits}; conditional expected expert traffic is preserved as a consequence. We characterize the resulting trade-off: positive within-group coupling can only inflate the variance of realized expert loads relative to independent routing, while nonnegative cross-group opposition can only reduce it relative to flat coupling at the same within-group strength. Coherence and load dispersion are thus controlled by two complementary dependence dials on the invariance constraint surface. Because the base model is untouched, the dials can be driven by a small controller over frozen features, trainable with a score-function estimator: the frozen network is evaluated only in the forward direction, and gradients are confined to the controller. An initial small-scale pilot validates the mechanism and the training route, but does not establish task-level fine-tuning gains.

Richard Yi Da Xu

Hong Kong Baptist University and TadReamk Limited

Copula Models Expert Load Balancing Parameter-Free Mixture-of-Experts Routing Expert Routing Mixture-of-Experts Models

Jul 23, 2026cs.AI

Beyond Independent Optimization: Compression, MoE Routing, and Quantization Interactions in Multimodal Edge Intelligence

Efficient multimodal inference is increasingly constrained not only by model quality or FLOP count, but also by the cost of preserving, moving, routing, caching, and quantizing multimodal representations under latency, memory, and energy constraints. This paper reviews recent advances in efficient vision-language and multimodal large language models, covering visual token compression, video token management, KV-cache optimization, Mixture-of-Experts (MoE) routing, low-bit quantization, edge deployment, and hardware-aware benchmarking. We argue that these techniques cannot be treated as independent optimizations. Visual token compression alters downstream feature distributions and MoE routing decisions, routing behavior affects expert utilization and quantization sensitivity, quantized router logits influence expert assignment, KV-cache policies determine retained multimodal evidence, and hardware constraints often transform computational savings into memory and communication bottlenecks. We organize the literature around these interactions and identify key design trade-offs, including accuracy versus token budget, static versus adaptive compression, sparse routing efficiency versus expert collapse, and low-bit inference versus modality-specific degradation. Finally, we introduce Temporal Routing Consistency as a diagnostic for video MoE models and highlight open research directions in routing-aware compression, cross-modal cache management, hardware-aware co-design, and unified benchmarking for multimodal edge intelligence.

Jay Gor, Karm Dave, Akshita Abrol +3

Nirma University · Singapore Institute of Technology, Singapore · Department of CE-AI and Big Data, Marwadi University

Efficient Multimodal Inference VLM Quantization Multimodal Optimization Expert Routing Multimodal Token Compression Edge AI

Jul 17, 2026cs.CL

Multi-level context Modeling for consistent expert selection in Mixture-of-Experts

Mixture-of-Experts (MoE) enables efficient scaling of Transformer models by routing tokens to a small subset of experts. However, existing routers typically condition expert selection on shallow or isolated token representations, which often produce unstable and semantically inconsistent routing decisions across layers. In this work, we revisit expert selection from a representation perspective and identify context incompleteness as a key bottleneck limiting effective expert specialization. To address this issue, we propose Multi-level Context Fusion MOE (MCF-MOE), a framework that constructs context-aware representations by integrating complementary signals from cross-layer semantic aggregation and local token-level interactions, enabling more informative and consistent expert selection. Experiments on language modeling and understanding benchmarks demonstrate that MCF-MOE consistently improves routing consistency and downstream performance over strong MoE baselines, highlighting the importance of contextual completeness in expert routing. The code is available at https://github.com/shuhanhuang/MCF-MOE.

Shuhan Huang, Naifan Zhang, Yuanbo Tang +2

Tsinghua Shenzhen International Graduate School, Tsinghua University · School of AI, The Chinese University of Hong Kong (Shenzhen)

Mixture-of-Experts Language Models Expert Routing LLM Routing

Jul 13, 2026cs.LG

From Global to Factor-Wise Expert Composition in Discrete Diffusion Models

Discrete diffusion models offer a powerful framework for solving complex reasoning tasks, particularly through compositional generation, which combines multiple pre-trained experts to generalize beyond their individual training data. Recent theoretical corrections introduce time-dependent mixing weights to better align composed diffusion dynamics with the intended target. However, these methods are fundamentally limited by working on a per-sample basis, treating each generated state monolithically and ignoring the potential spatial or functional specializations of different experts. In this work, we address this limitation by proposing FactorDiff - a factor-wise composition framework for diffusion models. We posit that samples can be further decomposed into smaller factors, and propose a sampling process that dynamically routes each factor to the most relevant expert. We instantiate this framework with spatial/pixel-level compositions and validate it on the ARC-AGI benchmark, demonstrating that simple factor-specific routing consistently outperforms complex global scalar weighting schemes on tasks that require logical consistency and spatial disentanglement.

Haozhe Huang, Yudong Xu, Abhijoy Mandal +1

Department of Computer Science, University of Toronto · Vector Institute for Artificial Intelligence · Department of Mechanical & Industrial Engineering, University of Toronto +1

Expert Routing Mixture-of-Experts Models Diffusion Models

Jul 2, 2026cs.SD

H-SAGE: Holistic Speaker-Aware Guided Experts for MoE-based Multi-Talker ASR

Multi-talker Automatic Speech Recognition (MTASR) faces significant challenges in accurately transcribing overlapping speech, particularly under complex high-overlap conditions. While recent Mixture-of-Experts (MoE) approaches have shown promise, they typically rely on frame-independent routing that leads to temporal myopia, and depend solely on the downstream ASR objective, which results in implicit and ungrounded representation learning. To address these limitations, we propose Holistic Speaker-Aware Guided Experts (H-SAGE) for MoE-based MTASR. Specifically, we introduce a Speaker-Aware Global Encoder to capture long-term dependencies, supervised by an auxiliary Overlap-Aware Loss that explicitly guides the model to discern acoustic states. Furthermore, we design a Holistic Gating Mechanism to arbitrate expert selection by jointly evaluating global context and local details. Experiments on LibriSpeechMix demonstrate that H-SAGE achieves consistent improvements over strong baselines, particularly in complex scenarios, validating that explicit acoustic guidance effectively enhances expert collaboration. Our code can be found at https://github.com/NKU-HLT/H-SAGE.

Yujie Guo, Jiaming Zhou, Yuhang Jia +2

TMCC, College of Computer Science, Nankai University, Tianjin, China

Automatic Speech Recognition Expert Routing Mixture-of-Experts Models

Jun 25, 2026cs.CV

Focusing on What Matters: Saliency-Harnessing Accurate Routing for Diffusion MoE

Mixture-of-Experts (MoE) architectures have emerged as a powerful paradigm for scaling diffusion models in visual generation. Recent advancements have focused on adaptively allocating computational resources across diverse tokens to improve efficiency and performance. However, we identify a routing assignment problem in existing diffusion MoE frameworks: the router fails to accurately allocate more computational resources to salient tokens. Our analysis attributes this failure to the router's reliance on noise-corrupted latent features throughout the denoising process. Such stochastic noise obscures the critical structural and textural information, thereby preventing the router from effectively distinguishing salient tokens. To address this, we propose SharpMoE, a post-training framework with a saliency-harnessing accurate routing mechanism, which utilizes clean latent features as a noise-free guidance signal for routing. By bypassing the noise-distorted inputs, SharpMoE provides the router with clear saliency guidance, enabling the identification of salient tokens even in high-noise stages. Furthermore, we introduce a trajectory routing loss to constrain the compute allocation throughout the multi-step denoising trajectory, ensuring precise resource allocation along the generation rollout. Extensive experiments demonstrate that SharpMoE serves as a versatile, plug-and-play solution that further enhances the pretrained, converged MoE models, achieving state-of-the-art performance in visual generation.

Haoyou Deng, Keyu Yan, Chaojie Mao +4

Key Laboratory of Image Processing and Intelligent Control, School of Artificial Intelligence and Automation, Huazhong University of Science and Technology · Tongyi Lab, Alibaba Group

Expert Routing Diffusion-Based Image Generation Diffusion Model Inference Acceleration

Jun 24, 2026cs.CV

GeMoE: Gating Entropy is All You Need for Uncertainty-aware Adaptive Routing in MoE-based Large Vision-Language Models

With the increase in model parameters and training data, the instruction following and generalization capabilities of Large VisionLanguage Models (LVLMs) have been significantly improved. Based on the Mixture of Experts (MoE) architecture, LVLMs expand their parameter capacity while maintaining the inference cost. However, traditional MoE methods employ a Top-k static routing strategy, which fails to account for variations in the input and adaptively select the number of experts, resulting in suboptimal resource utilization. In this paper, we propose viewing token routing as an information encoding task, framing dynamic routing as a Minimum Description Length (MDL) problem in encoding By validating the connection between MDL and gating entropy in the MoE scenario, we introduce Gating Entropy-based Uncertainty-aware Adaptive Routing (GeMoE) for MoE. Unlike traditional static or heuristic-based dynamic routing methods, GeMoE explicitly models the trade-off between model complexity and performance. By using gating entropy to assess the complexity of tokens, GeMoE adaptively determines the number of experts each token should engage. On a wide range of backbones and benchmarks, our method achieves 99.5% average performance retention compared to the original static routing, while improving average expert activation sparsity by 36.5%.

Chaoxiang Cai, Minghe Weng, Jie Li +4

School of Software Technology, Zhejiang University · College of Computer Science and Technology, Zhejiang University

Efficient VLM Inference Large Vision-Language Models Expert Routing

Jun 24, 2026cs.CL

SARA: Unlocking Multilingual Knowledge in Mixture-of-Experts via Semantically Anchored Routing Alignment

Sparse Mixture-of-Experts (MoE) architectures have emerged as an increasingly influential paradigm as they offer a strategic balance between parameter scalability and computational efficiency. However, low-resource languages, which suffer from a scarcity of high-quality training data, often have their tokens routed to different experts than those predominantly activated by high-resource inputs, which limits cross-lingual expert sharing. This cross-lingual routing divergence consequently hinders their efficacy in multilingual contexts. To address this issue, we propose SARA (Semantically Anchored Routing Alignment), a framework designed to transfer specialized capabilities from high-resource languages as anchors to low-resource languages. SARA explicitly aligns the routing distribution of multilingual inputs with high-resource semantic anchors using a symmetric Jensen-Shannon (JS) divergence constraint. Unlike traditional distillation methods that operate on output logits, SARA directly aligns the internal routing distributions of MoE layers, encouraging mechanistic consistency in expert selection across languages. We conduct experiments on 2 LLMs across 5 low-resource languages and 3 benchmarks. Experiment results demonstrate that SARA outperforms standard instruction tuning, e.g., +0.8% on Qwen3-30B-A3B and +1.2% on Phi-3.5-MoE-instruct on Global-MMLU. Further analyses show that SARA effectively addresses performance bottlenecks in low-resource languages, providing a scalable pathway to enhance multilingual capabilities in sparse architectures.

Tianyu Dong, Yangyang Liu, Jiang Zhou +9

TJUNLP Lab, School of Computer Science and Technology, Tianjin University, China · Alibaba Group, China

Multilingual Language Models Sparse Mixture-of-Experts Expert Routing Low-Resource Language Processing Cross-Lingual Transfer

Jun 18, 2026cs.AI

Optimal Scheduling in a Question-Answering Forum of Knowledge Workers

As individuals turn to the Internet to find answers to questions they may have, several Question Answering (QA) forums have evolved, where users knowledgeable in certain topics can contribute their expertise to answering these requests for information. While these are currently volunteer based, we consider a future version employing knowledge workers who are experts in certain topics. In such a system, the request-answer processes forming the queuing system may utilize schedulers that assign requests in different topics to the experts in the forum, who may be able to answer them according to their expertise levels in different topics. With this model, we calculate the capacity of the system for handling the requests while keeping the system stable, and design schedulers that achieve capacity. We also investigate how collaboration between experts in answering requests can potentially increase capacity.

Rohit Negi, Mustafa Yilmaz

Carnegie Mellon University

Expert Load Balancing Question Answering Expert Routing

Jun 14, 2026cs.CV

Task-Instructed Causal Routing of Vision Foundation Models for Multi-Task Learning

Vision foundation models (VFMs) have demonstrated strong robustness and transferability across a wide range of visual tasks. However, each model typically encodes strong inductive biases shaped by its pre-training objective and data domain, resulting in fragmented yet complementary visual knowledge. As a result, a single model often struggles to capture the diverse visual representations required across multiple dense prediction tasks. To address this limitation, we propose TIGER (Task-Instruction-Guided Expert Routing), a framework that coordinates multiple heterogeneous VFMs for multi-task dense prediction. Instead of naively aggregating expert features, TIGER leverages natural-language task instructions to guide a routing network that assigns token-level expert weights conditioned on task semantics, enabling adaptive integration of complementary expert features. TIGER further introduces a counterfactual loss that aligns routing decisions with each expert's causal contribution by measuring prediction changes when experts are excluded, encouraging more reliable and interpretable routing. We evaluate TIGER on two multi-task dense prediction benchmarks, NYUD-v2 and Pascal Context, where it consistently outperforms recent multi-task learning baselines while keeping all VFMs frozen. These results demonstrate that combining instruction-guided expert routing with counterfactual causal alignment enables effective coordination of heterogeneous vision foundation models.

Donghyun Han, Yuseok Bae, Jung Uk Kim +1

Electronics and Telecommunications Research Institute (ETRI), Korea · Kyung Hee University, Korea · Chonnam National University, Korea

Vision Foundation Model Adaptation Multi-Task Learning Expert Routing Mixture-of-Experts Models

Jun 12, 2026cs.LG

Sticky Routing: Training MoE Models for Memory-Efficient Inference

Mixture-of-Experts (MoE) models activate only a sparse subset of experts per token, yet consecutive tokens frequently activate different experts -- causing constant weight swapping between slow storage and fast memory on edge devices. Existing remedies are either system-level (caching heuristics) or post-hoc (router fine-tuning), leaving the root cause unchanged during pretraining. We propose StickyMoE, a differentiable routing consistency loss that penalises abrupt expert switches between adjacent tokens, encouraging the router to maintain the same expert assignment across semantically coherent spans. StickyMoE requires no architectural changes, adds a single hyperparameter lambda, and unlike post-hoc methods, allows expert representations and routing decisions to co-adapt from the first training step. Experiments on small-scale MoE language models show that StickyMoE reduces the expert switch rate by up to 60% with less than 4% perplexity degradation, Pareto-dominating post-hoc fine-tuning on the quality-locality frontier. Routing temporal locality is most efficiently instilled at training time.

Ali Kayyam

BrainChip Inc., Laguna Hills, CA

Mixture-of-Experts Inference Memory-Efficient Inference Expert Routing Mixture-of-Experts Models

Jun 10, 2026cs.LG

Redesign Mixture-of-Experts Routers with Manifold Power Iteration

Router is the cornerstone component to the Mixture-of-Experts models. Serving as expert proxies, the rows of the router matrix compute their similarity to the MoE inputs to determine which subset of experts is activated. Ideally, each router row is designed to encode the expert matrix into this representative vector, such that its dot-product with token can better reflect token-expert affinity. However, there exists no design principles to enforce this condensation. In this paper, we propose to align each router row with the principal singular direction of the associated expert, as this direction provides the most expressive mathematical description of a matrix. Based on this principle, we propose a router redesign with Manifold Power Iteration (MPI). Specifically, it introduces a "Power-then-Retract" paradigm, where a power iteration step is performed on the router weights, followed by a retraction to impose a norm constraint to ensure both efficiency and stability. Theoretically, we show that MPI drives router rows to converge toward the principal singular directions of associated experts. Empirically, we pretrain MoE model across scales from 1B to 11B parameters to confirm that this alignment facilitates more effective MoE models.

Songhao Wu, Ang Lv, Ruobing Xie +1

Gaoling School of Artificial Intelligence, Renmin University of China · Large Language Model Department, Tencent

Mixture-of-Experts Language Models Expert Routing Mixture-of-Experts Models

Jun 9, 2026cs.CL

PADD: Path-Aligned Decompression Distillation for Non-Router Teacher to Guide MoE Student Learning

As large language models (LLMs) continue to scale, it becomes increasingly challenging to grow model capacity under fixed computation budgets. We propose Path-Aligned Decompression Distillation (PADD), a framework for distilling knowledge from dense teachers without explicit routing into mixture-of-experts (MoE) students while learning high-quality routing policies. PADD organizes knowledge distillation into four stages in two phases: an initialization phase (Stage I) that builds diverse functionality in the student's experts through teacher neuron clustering and student-expert warmup, and a training phase (Stages II--IV) that integrates online adaptive distillation, path-refined policy optimization, and reward-augmented load balancing in a single training pipeline. Experiments on mathematical reasoning benchmarks demonstrate that PADD yields substantial gains over strong baselines at the same inference cost and that the MoE student can match or surpass its dense teacher. They also demonstrate effective teacher-to-student knowledge distillation and stable routing behavior.

Xinyue Peng, Yi Qian, Jiaojiao Lin +2

Intel Corporation, China · Zhejiang University, China

Mixture-of-Experts Language Models Expert Routing Teacher-Student Learning Knowledge Distillation

Jun 7, 2026cs.AI

STAR: Rethinking MoE Routing as Structure-Aware Subspace Learning

Mixture-of-Experts (MoE) scales model capacity efficiently by selectively routing inputs to a specialized subset of experts. However, input-expert specialization, the core motivation of MoE, critically depends on whether the router is actually aware of input structure. In practice, MoE routing is typically implemented as a shallow linear projection with limited awareness of input representation, which often leads to unstable routing. We propose STAR, a Structure Aware Routing that rethinks MoE routing as a subspace learning problem by augmenting standard learnable routing with an evolving principal subspace that tracks dominant input structure via Generalized Hebbian Algorithm (GHA). By aligning routing decisions directly with input structure, STAR enables stable expert specialization. We evaluate STAR on controlled synthetic setup and large-scale language and vision tasks, where it consistently improves routing quality and downstream performance over strong MoE baselines. Moreover, optional test-time subspace updates further enhance routing robustness and generalization under input distribution shifts.

Sumin Park, Noseong Park

Korea Advanced Institute of Science and Technology (KAIST), Daejeon, Republic of Korea.

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

Jun 4, 2026cs.CL

Value-and-Structure Alignment for Routing-Consistent Quantization of Mixture-of-Experts Models

Mixture-of-Experts (MoE) models scale foundation models efficiently by activating only a subset of experts for each token, but their large number of expert parameters still makes quantization essential for practical deployment. Unlike dense models, however, MoE models are sensitive to routing instability: small quantization-induced perturbations can change the top-

k

expert selection, altering the computation path and degrading model quality. We propose Value-and-Structure Routing Alignment for Quantization (VSRAQ), a MoE-specific post-training quantization objective that preserves pre-quantization expert-selection behavior under quantization. VSRAQ combines two complementary objectives that jointly preserve expert-selection behavior: value alignment, which matches routing-relevant logits or scores, and structure alignment, which preserves expert ordering and top-

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decision boundaries. By maintaining routing consistency, VSRAQ reduces quantization-induced degradation without introducing any inference-time overhead and can be integrated into existing quantization frameworks. Experiments on recent MoE foundation models show that VSRAQ improves expert-selection consistency and consistently outperforms reconstruction-only and router-aware baselines.

Hancheol Park, Geonho Lee, Tairen Piao +1

Nota Inc., South Korea.

LLM Quantization Mixture-of-Experts Quantization Expert Routing Mixture-of-Experts Models Post-Training Quantization Neural Network Quantization

Jun 2, 2026cs.CL

Expert-Aware Refusal Steering

Safety alignment in instruction-tuned large language models (LLMs) depends on a model's ability to reliably refuse to respond to harmful or disallowed requests. Recent work has shown that a steering vector can be applied to a dense LLM during inference to effectively suppress refusal behavior, inducing response to harmful requests. We extend this refusal steering method to three open-source Mixture-of-Experts (MoE) LLMs and find that steering performance is uninhibited by the complex routing patterns inherent to the MoE architecture. We then propose two expert-aware refusal steering methods that leverage refusal-specific expert routing patterns and expert-specific steering directions to suppress normal refusal behavior. We find that refusal behavior can be effectively steered based on the output of a single expert. Our results show that refusal signals captured by steering methods differ from expert routing behavior, suggesting a substantial role for attention in MoE refusal behavior.

Anna C. Marbut, Daniel R. Olson, Travis J. Wheeler

Department of Interdisciplinary Studies University of Montana Missoula, MT, USA · Department of Pharmacy Practice & Science University of Arizona Tucson, AZ, USA · European Bioinformatics Institute European Molecular Biology Laboratory Wellcome Genome Campus, Hinxton, United Kingdom

Mixture-of-Experts Language Models Language Model Steering LLM Safety Alignment LLM Refusal Behavior Expert Routing Refusal Behavior in Language Models

Jun 1, 2026cs.LG

ProbMoE: Differentiable Probabilistic Routing for Mixture-of-Experts

Mixture-of-Experts (MoE) models scale by activating only a small subset of experts per token. However, training such models remains challenging because top-

k

routing is discrete and non-differentiable, requiring gradient estimators for expert selection whose design remains a central open problem. We introduce ProbMoE, a probabilistic routing framework that models expert selection as a distribution over cardinality-constrained expert subsets and formulates routing as probabilistic inference in this discrete subset space. We first propose ProbMoE Exact-

k

routing, which samples

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-expert subsets in the forward pass, and the backward pass uses gradients through each expert's exact marginal probability as a tractable surrogate for the true gradient. ProbMoE naturally generalizes to a dynamic-

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routing setting, where both training and inference constrain the routing cardinality to the same predefined range, allowing adaptive expert allocation per token. Across benchmarks and model backbones, ProbMoE Exact-

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achieves strong performance compared to competitive baselines, with improved expert utilization and routing diversity; ProbMoE Dynamic-

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achieves comparable performance with fewer activated experts.

Heng Zhao, Zilei Shao, Guy Van den Broeck +1

Department of Computer Science, University of Virginia, Charlottesville, USA · Department of Computer Science, University of California, Los Angeles, Los Angeles, USA

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

May 29, 2026cs.LG

PR2: Predictive Routing Replay for MoE-Based LLM Reinforcement Learning

Mixture of Experts (MoE) Large Language Models (LLMs) achieve strong performance at scale. However, reinforcement learning (RL) on MoE-based LLMs often suffers from training instability. A root cause is router drift, i.e., expert activations can change drastically across model updates and differ between disaggregated rollout and training phases, causing large rollout--training mismatch and unstable importance sampling weights in PPO-style RL algorithms. Routing replay mitigates this issue by freezing the replay route within each reasoning trajectory, but it ignores how the router evolves under off-policy updates and thus causes router staleness. To address this limitation, we propose Predictive Routing Replay (PR2), which augments each router with a lightweight evolution predictor that learns to anticipate short-horizon router evolution. During the rollout phase, we use the predictive routing distribution to apply top-

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routing, enabling gradients to reach experts that are likely to become active after updates. During the training phase, we replay the resulting predicted route to retain consistency for stable importance estimation. Theoretical analysis and experiments support that PR2 reduces routing-induced mismatch, improves RL stability, and yields stronger performance across various reasoning benchmarks.

Daize Dong, Junlin Chen, Haolong Jia +9

♣Rutgers University · ♦AMD · ⋆MBZUAI

RL for Language Model Reasoning Expert Routing LLM Routing RL Post-Training Off-Policy RL

May 27, 2026math.DS

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.

O. M. Kiselev

Innopolis University, Innopolis, Russia

Dynamical Systems Expert Load Balancing Adaptive Model Routing Expert Routing Mixture-of-Experts Models

May 24, 2026cs.LG

AME-TS: Anchored Mixture-of-Experts for Time Series Forecasting

Time series forecasting models are increasingly scaled through large Transformer backbones, yet most existing approaches process all series through a shared dense computation path despite substantial heterogeneity in temporal structure. Mixture-of-Experts (MoE) offers a natural alternative by enabling conditional computation, but standard MoE routing leaves expert specialization weakly identified and often unstable during downstream adaptation. We propose AME-TS, a structure-guided sparse time series foundation model that aligns expert routing with interpretable temporal structure. AME-TS first uses a lightweight regime predictor to estimate series-level descriptors, including forecastability, seasonality, trend, and sparsity, and maps them to a soft structural prior over experts. This series-level prior guides token-level routing during training, encouraging structure-aligned specialization. On the GIFT-Eval benchmark, AME-TS delivers a strong accuracy-efficiency tradeoff across model scales: it substantially outperforms existing time series foundation models at small model scales and remains competitive with the strongest models at larger scales, while activating substantially fewer parameters through sparse routing. We further show that AME-TS learns more interpretable routing geometry and substantially more stable expert specialization than standard MoE during fine-tuning on the M5 dataset. These results suggest that structure-aware routing is an effective and reliable way to realize the benefits of sparse expert models for time series forecasting.

Rui Wang, Renhao Xue, Ray Razi +2

Amazon Web Services

Sparse Mixture-of-Experts Time Series Forecasting Expert Routing Time-Series Foundation Models

May 22, 2026cs.AI

Safety-Oriented Routing Analysis of Mixtral MoE Under Benign and Harmful Prompts

Sparse mixture-of-experts (MoE) language models activate only a small subset of parameters for each token, making router behavior a central part of model computation. This paper studies routing behavior of Mixtral 8x7B-Instruct under benign and harmful prompts using two complementary signals: activation-based routing scores derived from expert selection frequencies and gradient-based scores derived from router-gate sensitivities. We analyze expert- and layer-level routing behavior and conduct expert-suppression interventions. The results show that activation-based expert usage is broad and long-tailed, whereas gradient-based importance is concentrated. At expert level, benign and harmful prompt groups remain close under both signals with modest separation. At layer level, activation-based routing is most selective around layers 8-15, while gradient-based importance is concentrated in final layers. Expert classification shows most experts are shared across benign and harmful prompts, though a limited subset shows clear group preference. Top-ranked expert sets show stronger benign-malicious overlap under gradient scores than activation scores, suggesting concentration on a common late-layer expert set. In intervention experiments, suppressing top five benign-dominant experts from activation scores reduces restricted responses from 24 to 14 over 100 prompts, while suppressing gradient-derived experts reduces them from 34 to 22 with fewer unintended reversals. Overall, safety-relevant routing in Mixtral is subtle, depth-dependent, and distributed rather than dominated by a fixed set of experts.

Md Nurul Absar Siddiky

Department of Electrical and Computer Engineering University of Hawai’i at M¯anoa Honolulu, HI, USA

Mixture-of-Experts Language Models Expert Routing LLM Safety LLM Routing

May 21, 2026cs.CL

Can AI Guess What You Know? Performance Comparison of Large Language Models for Human Domain Knowledge Estimation From Communication Logs

Employees often struggle to identify ``who knows what,'' leading to organizational productivity losses. We investigate whether Large Language Models (LLMs) can infer individual domain knowledge directly from long-term Slack logs. Analyzing 27,188 messages from 43 users, we evaluated seven models (including Gemini, Claude, and GPT families) by comparing their zero-shot estimates against self-reported skill ratings from 27 participants. Gemini 2.5 Flash achieved the lowest error (MAE 21.13%), while GPT models showed significantly larger discrepancies. Notably, estimation accuracy depended only weakly on message volume, indicating that more text alone does not guarantee better inference. These findings demonstrate the feasibility and current limits of automated expertise mapping, highlighting the need for privacy-preserving deployments and richer, structure-aware representations of human knowledge.

Ko Watanabe, Shoya Ishimaru

DFKI, Kaiserslautern, Germany · Osaka Metropolitan University, Osaka, Japan

LLM Evaluation Expert Routing User Modeling

May 17, 2026cs.CL

Mixture of Experts for Low-Resource LLMs

Mixture-of-Experts (MoE) architectures enable efficient model scaling, yet expert routing behavior across underrepresented languages remains poorly understood. We analyze routing dynamics in two architecturally distinct MoE models -- a pure Transformer (Qwen3-30B-A3B) and a hybrid Mamba-Transformer (Nemotron-3-Nano-30B-A3B) -- using Hebrew as a morphologically rich, low-resource testbed. Both pre-trained models exhibit \emph{deep-layer routing collapse}: usage entropy drops sharply in final layers and tokens concentrate on a narrow expert subset, a pattern largely absent for English. Continual pre-training (CPT) on balanced bilingual data substantially corrects this imbalance, increasing entropy and shifting routing toward shared, language-agnostic experts; supervised fine-tuning (SFT) alone achieves less complete correction. Extending the analysis to Japanese reveals quantitatively consistent collapse signatures, providing cross-linguistic evidence that the phenomenon is a systematic consequence of pre-training underrepresentation rather than any language-intrinsic property. Routing improvements correlate with consistent downstream benchmark gains, positioning routing entropy and expert specialization as principled diagnostics for multilingual capacity in MoE systems.

Ori Bar Joseph, Smadar Arvatz, Noam Kayzer +2

Mixture-of-Experts Language Models Expert Routing LLM Routing Low-Resource Language Processing

May 17, 2026cs.CV

Stable Routing for Mixture-of-Experts in Class-Incremental Learning

Class-incremental learning (CIL) requires models to learn new classes sequentially while preserving prior knowledge. Recently, approaches that combine pre-trained models with mixture-of-experts (MoE) have received increasing attention in CIL: they typically expand experts during learning and employ a router to assign weights across experts. However, existing MoE methods often overlook routing drift induced by expert expansion. Once new experts are introduced, the router may reassign samples from earlier classes to newly added experts, thereby perturbing previously established expert compositions and causing interference even when old experts remain frozen. We argue that expandable MoE in CIL requires two complementary properties: stable old-class routing for knowledge preservation and sufficient capacity utilization for new-class adaptation. To this end, we propose Stable Routing for MoE (StaR-MoE), a routing-level framework for expandable MoE in CIL. By incorporating sensitivity-aware routing alignment, StaR-MoE aligns current old-class routing behavior with historical routing distributions through sensitivity-guided constraints. Complementarily, StaR-MoE introduces asymmetric capacity regularization to encourage effective utilization of the expanded expert pool without compromising class-specific routing specialization. Extensive experiments across four standard CIL benchmarks demonstrate that StaR-MoE consistently improves both average and last accuracy over state-of-the-art methods, highlighting the importance of stable routing.

Zirui Guo, Quan Cheng, Da-Wei Zhou +1

State Key Laboratory of Novel Software Technology, Nanjing University, Nanjing, China · School of Artificial Intelligence, Nanjing University, Nanjing, China

Class-Incremental Learning Expert Routing Incremental Learning Mixture-of-Experts Models

May 15, 2026cs.CV

When Does Sparse MoE Help in Vision? The Role of Backbone Compute Leverage in Sparse Routing

Mixture-of-Experts (MoE) networks promise favorable accuracy-compute trade-offs, yet practical vision deployments are hindered by expert collapse and limited end-to-end efficiency gains. We study when sparse top-

k

routing with hard capacity constraints helps in vision classification, evaluated under multi-seed protocols on four benchmarks (CIFAR-10/100, Tiny-ImageNet, ImageNet-1K). We observe a \emph{compute-leverage pattern}: positive accuracy gaps require a substantial fraction

ρ

of total FLOPs to be routed; at ImageNet scale this is necessary but not sufficient, as multi-expert routing (

k \geq 2

) is additionally required. Two controlled experiments isolate these factors. A hidden-size sweep on CIFAR-10 yields both predicted sign reversals across standard and depthwise backbones, ruling out backbone family as the active variable. An ImageNet-1K ablation that varies only top-

k

-- holding architecture, initialization, and

ρ

fixed -- reverses the gap from positive to negative across all five seeds. A per-sample variant of Soft MoE that softmaxes over experts rather than the batch rescues CIFAR-100 above the dense baseline, identifying batch-axis dispatch as the dominant failure mode in per-sample CNN settings. Code and aggregate results: https://github.com/libophd/sparse-moe-vision-rho.

Libo Sun, Po-wei Harn, Peixiong He +1

Department of Computer Science and Software Engineering Auburn University, Auburn, AL 36849, USA · Department of Information Management National Central University, Taoyuan 320317, Taiwan · Department of Computer Science and Software Engineering Auburn University

Sparse Mixture-of-Experts Expert Routing Mixture-of-Experts Models Image Classification

May 12, 2026cs.CV

Sparse Mixture-of-Experts Routing in Visual Diffusion Transformers:Diagnosis, Boundary Calibration and Evolutionary Roadmap from Routing Collapse to Selective Deadlock

This paper systematically diagnoses the training failure modes of Token-Choice sparse Mixture-of-Experts (MoE) on video Diffusion Transformers. Starting from a pretrained dense model of about 5 billion parameters, we convert it into an MoE architecture following three laws: routed experts exactly clone the original FFN weights, shared experts are initialized to zero for verification and then to extremely small non-zero noise for actual training, while only the gating networks start from random initialization. Experiments reveal a hierarchy of five failure modes: (1) linear routers suffer global soft saturation with complete expert homogenization; (2) MLP routers introduce selective deadlock, where roughly one-third of layers degenerate into a single-expert mode that cannot be prevented by increasing the auxiliary loss; (3) cross-attention routers exhibit preliminary self-recovery, yet about nine layers remain stubbornly deadlocked; (4) deadlocked layers display a U-shaped distribution, concentrated in shallow visual processing layers and deep semantic integration layers; (5) bfloat16 mixed precision causes tiny weight updates to be truncated to zero by hardware. Based on routing decision time series over 65 million tokens across 5,000 training steps, we propose the Functional Redundancy Hypothesis: deadlock is a rational waiting strategy before the shared expert matures within the gate-shared expert-routed expert triadic system. This hypothesis is supported by the theory of functional redundancy in systems biology. On the engineering side, we summarize the Three Laws of dense-to-MoE conversion and provide a complete solution for the bfloat16 precision trap. We calibrate the current capability boundary of the Token-Choice paradigm and outline a three-step evolutionary roadmap from visual unification to a world model.

Haiying Sha

Independent Researcher

Video Diffusion Models Diffusion Transformer Sparse Mixture-of-Experts Expert Routing Mixture-of-Experts Models

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