Expert Routing

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Overview

Expert routing studies how models assign tokens, examples, or tasks to a small subset of experts, enabling conditional computation while storing many specialized networks. Common approaches include top-k token-choice and expert-choice gates, hierarchical and threshold-based routing, and adaptive policies driven by uncertainty, task information, or learned structure. Researchers test these methods in autoregressive language models, vision and multimodal systems, and diffusion models, measuring quality on benchmarks such as WikiText, MMLU, GSM8K, and ImageNet alongside load balance, latency, and memory use. A central tension is that balancing expert workloads can conflict with specialization and efficient execution, while analyses increasingly question whether routing patterns alone demonstrate genuine domain expertise or useful downstream effects.

Latest papers

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119 papers29 papers in the last four weeks, up 190% on the four weeks before. 0.2% of all new papers.

May 6, 2026

Adaptive Inverted-Index Routing for Granular Mixtures-of-Experts

Mixture-of-experts (MoE) models enable scalable transformer architectures by activating only a subset of experts per token. Recent evidence suggests that performance improves with increasingly granular experts, i.e., many small experts instead of a few large ones. However, this regime substantially increases routing cost, which can dominate computation. We introduce adaptive inverted-index routing for MoE (AIR-MoE), an inverted-index-inspired routing architecture based on vector quantization (VQ). In a first stage, AIR-MoE performs coarse shortlisting by assigning tokens to VQ codewords to construct a candidate set of experts. In a second stage, fine scoring computes exact routing scores restricted to this shortlist. This two-stage procedure approximates true top-k routing while avoiding full expert scoring and, in contrast to prior work, imposing no structural constraints on expert parameters. AIR-MoE serves as a drop-in replacement for standard routers and requires no modifications to the model architecture or loss function. We further provide a lower bound on the mass recall achieved by AIR-MoE that yields insights into its inner workings. Empirically, we demonstrate that AIR-MoE achieves improved performance compared to existing routing approaches in granular MoE settings.

Klaus-Rudolf Kladny, Maximilian Mordig, Bernhard Schölkopf +1

Max Planck Institute for Intelligent Systems, Tübingen · Tübingen AI Center · ETH Zurich +1

Mixture-of-Experts InferenceExpert RoutingMixture-of-Experts Models
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May 4, 2026

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 ak(x;φ)a_k(x;φ), the relevant local quantity is the top-two margin Δ(x;φ)Δ(x;φ), and the relevant global quantity is the boundary mass P(Δ(X;φ)≤w)\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 LτL_τ and the hard objective L0L_0, including an O(τα)O(τ^α) uniform comparison under a margin-tail condition, and yield ΓΓ-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)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-ExpertsExpert Routing
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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 27, 2026

SceneSelect: Selective Learning for Trajectory Scene Classification and Expert Scheduling

Accurate trajectory prediction is fundamentally challenging due to high scene heterogeneity - the severe variance in motion velocity, spatial density, and interaction patterns across different real-world environments. However, most existing approaches typically train a single unified model, expecting a fixed-capacity architecture to generalize universally across all possible scenarios. This conventional model-centric paradigm is fundamentally flawed when confronting such extreme heterogeneity, inevitably leading to a severe generalization gap, degraded accuracy, and massive computational waste. To overcome this bottleneck, rather than refining restricted model-centric architectures, we propose selective learning, a novel scene-centric paradigm. It explicitly analyzes the characteristics of the underlying scene to dynamically route inputs to the most appropriate expert models. As a concrete implementation of this paradigm, we introduce SceneSelect. Specifically, SceneSelect utilizes unsupervised clustering on interpretable geometric and kinematic features to discover a latent scene taxonomy. A highly decoupled classification module is then trained to assign real-time inputs to these scene categories, and a highly extensible, plug-and-play scheduling policy automatically dispatches the trajectory sequence to the optimal expert predictor. Crucially, this decoupled design ensures excellent generalization capabilities, allowing seamless integration with different off-the-shelf models and robust adaptation across new datasets without requiring computationally expensive joint retraining. Extensive experiments on three public benchmarks (ETH-UCY, SDD, and NBA) demonstrate that our method consistently outperforms strong single-model and ensemble baselines, achieving an average improvement of 10.5%, showcasing the effectiveness of scene-aware selective learning.

Xinrun Wang, Deshun Xia, Yuxi Sun +1

School of Computer Science, China University of Geosciences (Wuhan) · School of Information Engineering, Wuhan University of Technology · School of Mathematics and Statistics, Wuhan University of Technology

Multi-Agent Trajectory PredictionExpert RoutingTrajectory Prediction
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Apr 27, 2026

SMoES: Soft Modality-Guided Expert Specialization in MoE-VLMs

Mixture-of-Experts (MoE) has become a prevalent backbone for large vision-language models (VLMs), yet how modality-specific signals should guide expert routing remains under-explored. Existing routing strategies are either hand-crafted or modality-agnostic, relying on idealized priors that ignore the layer-dependent modality fusion patterns in MoE-VLMs and provide little guidance for expert specialization. We propose Soft Modality-guided Expert Specialization (SMoES), which consists of dynamic soft modality scores that capture layer-dependent fusion patterns, an expert binning mechanism aligned with expert-parallel deployment, and an inter-bin mutual information regularization that encourages coherent modality specialization. Our method leverages attention-based or Gaussian-statistics modality scores to optimize mutual information regularization. Experiments across four MoE-based VLMs and 16 benchmarks demonstrate improvement on both effectiveness and efficiency: 0.9% and 4.2% average gain on multimodal and language-only tasks, 56.1% reduction in EP communication overhead, and 12.3% throughput improvement under realistic deployment. These results validate that aligning routing with modality-aware expert specialization unlocks MoE-VLM capacity and efficiency.

Zi-Hao Bo, Yaqian Li, Anzhou Hou +6

Li Auto Inc.

Vision-Language ModelsEfficient VLM InferenceMixture of ExpertsExpert RoutingMixture-of-Experts Models
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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 20, 2026

Multi-Domain Learning with Global Expert Mapping

Human perception generalizes well across different domains, but most vision models struggle beyond their training data. This gap motivates multi-dataset learning, where a single model is trained on diverse datasets to improve robustness under domain shifts. However, unified training remains challenging due to inconsistencies in data distributions and label semantics. Mixture-of-Experts (MoE) models provide a scalable solution by routing inputs to specialized subnetworks (experts). Yet, existing MoEs often fail to specialize effectively, as their load-balancing mechanisms enforce uniform input distribution across experts. This fairness conflicts with domain-aware routing, causing experts to learn redundant representations, and reducing performance especially on rare or out-of-distribution domains. We propose GEM (Global Expert Mapping), a planner-compiler framework that replaces the learned router with a global scheduler. Our planner, based on linear programming relaxation, computes a fractional assignment of datasets to experts, while the compiler applies hierarchical rounding to convert this soft plan into a deterministic, capacity-aware mapping. Unlike prior MoEs, GEM avoids balancing loss, resolves the conflict between fairness and specialization, and produces interpretable routing. Experiments show that GEM-DINO achieves state-of-the-art performance on the UODB benchmark, with notable gains on underrepresented datasets and solves task interference in few-shot adaptation scenarios.

Pourya Shamsolmoali, Masoumeh Zareapoor, Huiyu Zhou +3

Department of Computer Science, University of York, UK · School of Computing and Mathematical Sciences, University of Leicester, UK · Centre for Vision Speech and Signal Processing, University of Surrey, UK +2

Vision Foundation Model AdaptationExpert RoutingMixture-of-Experts ModelsCross-Dataset Generalization
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Apr 19, 2026

Layer-wise MoE Routing Locality under Shared-Prefix Code Generation: Token-Identity Decomposition and Compile-Equivalent Fork Redundancy

In LLM-based code generation, multiple code candidates are often generated in parallel from the same prompt -- for example, in best-of-N sampling or multi-candidate code completion. These requests can share KV caches through a common prefix, yet the extent to which their Mixture-of-Experts (MoE) expert routing overlaps, and how this overlap varies across layers, remains insufficiently understood. We study Qwen3.5-35B-A3B-FP8 (256 routed experts, top-8) by performing tree-search-based branching generation from a shared prefix (851 completed codes, temperature 0.7) and analyzing the results with a compiler-output-based alignment (gcc -S -O0 assembly) that controls for token-identity confounds. Our findings are threefold: (1) At positions where both sequences generated the same token, Jaccard similarity reaches 0.649 (40x random), while even at positions with different tokens it remains 0.175 (11x random). (2) A layer-wise decomposition reveals a crossing pattern: same-token routing similarity exceeds different-token similarity across all layers, but dips in the middle layers (L14-20), while different-token similarity peaks in the middle layers at 14x random. (3) In tree-search code generation, 67% of successfully compiled codes concentrate in the top three assembly-equivalent groups, and 99.6% of within-group differences consist of comments and blank lines. We show that diversity in top-P search, including beam search, poses a significant challenge. These results refine the "context-independent routing" claim of prior work through layer-wise decomposition and suggest opportunities for improving search efficiency in LLM code generation.

Shun-ichiro Hayashi, Daichi Mukunoki, Tetsuya Hoshino +1

Graduate School of Informatics, Nagoya University, Japan · Information Technology Center, Nagoya University, Japan

Expert RoutingEfficient Language Model InferenceLLM Code Generation
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Apr 18, 2026

CoGR-MoE: Concept-Guided Expert Routing with Consistent Selection and Flexible Reasoning for Visual Question Answering

Visual Question Answering (VQA) requires models to identify the correct answer options based on both visual and textual evidence. Recent Mixture-of-Experts (MoE) methods improve option reasoning by grouping similar concepts or routing based on examples. However, unstable routing can lead to inconsistent expert selection in the same question type, while overly stable routing may reduce flexibility. To address this, we propose Concept-Guided Routing framework (CoGR-MoE), which incorporates semantics of the answer options to guide expert selection in the training phase. Next, option features are used to reweight the selected experts, producing discriminative representations for each candidate option. These option-level representations are further used for option comparison and optimized via contrastive learning. The experimental results indicate that CoGR-MoE delivers strong performance across multiple VQA tasks, demonstrating the effectiveness of our approach.

Xiyin Zeng, Yi Lu, Hao Wang

Hong Kong University of Science and Technology (Guangzhou)

Visual Question AnsweringExpert RoutingMixture-of-Experts Models
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Apr 15, 2026

Equifinality in Mixture of Experts: Routing Topology Does Not Determine Language Modeling Quality

Sparse Mixture-of-Experts (MoE) architectures employ increasingly sophisticated routing mechanisms -- learned routers, multi-hop trajectories, token-dependent gating. We ask: does routing topology actually determine language modeling quality? We build a geometric MoE (ST-MoE) using cosine-similarity routing against learned centroids in a low-dimensional space (dspace=64d_{space} = 64), requiring 80% fewer routing parameters than standard linear routers. Through 62 controlled experiments on WikiText-103 at 76--84M parameters trained to convergence (50K steps, 1.64B tokens), we find that routing topology does not determine asymptotic perplexity (PPL): five cosine-routing variants are statistically equivalent within a 1-PPL margin (Two One-Sided Tests [TOST], p<0.05p < 0.05 for all 10 pairwise comparisons; 15 runs across 3 seeds, observed range 33.93--34.72). The finding extends to hash, random-fixed, and top-1 routing (single-seed; graceful 1.1--2.2 PPL degradation) and replicates on OpenWebText (0.03 PPL gap, 6 runs, 3 seeds each). A standard linear router with 5.3×\times more routing parameters reaches PPL 32.76, but iso-parameter cosine routing closes 67% of this gap -- the true mechanism advantage is ∼\sim1.2%. The mechanistic explanation is convergent redundancy: multi-hop updates are collinear (cos⁡(Δh0,Δh1)=0.805\cos(Δh_0, Δh_1) = 0.805), implementing magnitude amplification rather than compositional reasoning; a single learnable scalar replicates multi-hop performance. As a practical payoff, zero-shot relative-norm halting saves 25% of MoE FLOPs at +0.12% PPL. Expert-level specialization and causal controllability -- which coexist with topology-level equifinality -- are explored in a companion paper.

Ivan Ternovtsii, Yurii Bilak

Department of Software Systems, Uzhhorod National University Narodna sq. 3, Uzhhorod, Ukraine, 88000 · HengeBytes

Mixture-of-Experts Language ModelsExpert RoutingMixture-of-Experts Inference
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Apr 10, 2026

The Myth of Expert Specialization in MoEs: Why Routing Reflects Geometry, Not Necessarily Domain Expertise

Mixture of Experts (MoEs) are now ubiquitous in large language models, yet the mechanisms behind their "expert specialization" remain poorly understood. We show that, since MoE routers are linear maps, hidden state similarity is both necessary and sufficient to explain expert usage similarity, and specialization is therefore an emergent property of the representation space, not of the routing architecture itself. We confirm this at both token and sequence level across five pre-trained models. We additionally prove that load-balancing loss suppresses shared hidden state directions to maintain routing diversity, which might provide a theoretical explanation for specialization collapse under less diverse data, e.g. small batch. Despite this clean mechanistic account, we find that specialization patterns in pre-trained MoEs resist human interpretation: expert overlap between different models answering the same question is no higher than between entirely different questions (∼\sim60%); prompt-level routing does not predict rollout-level routing; and deeper layers exhibit near-identical expert activation across semantically unrelated inputs, especially in reasoning models. We conclude that, while the efficiency perspective of MoEs is well understood, understanding expert specialization is at least as hard as understanding LLM hidden state geometry, a long-standing open problem in the literature.

Xi Wang, Soufiane Hayou, Eric Nalisnick

Johns Hopkins University

Mixture-of-Experts Expert SpecializationMixture of ExpertsMixture-of-Experts ModelsExpert RoutingLLM InterpretabilityRepresentation Geometry in Language Models
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Apr 9, 2026

Seeing but Not Thinking: Routing Distraction in Multimodal Mixture-of-Experts

Multimodal Mixture-of-Experts (MoE) models have achieved remarkable performance on vision-language tasks. However, we identify a puzzling phenomenon termed Seeing but Not Thinking: models accurately perceive image content yet fail in subsequent reasoning, while correctly solving identical problems presented as pure text. Through systematic analysis, we first verify that cross-modal semantic sharing exists in MoE architectures, ruling out semantic alignment failure as the sole explanation. We then reveal that visual experts and domain experts exhibit layer-wise separation, with image inputs inducing significant routing divergence from text inputs in middle layers where domain experts concentrate. Based on these findings, we propose the Routing Distraction hypothesis: when processing visual inputs, the routing mechanism fails to adequately activate task-relevant reasoning experts. To validate this hypothesis, we design a routing-guided intervention method that enhances domain expert activation. Experiments on three multimodal MoE models across six benchmarks demonstrate consistent improvements, with gains of up to 3.17% on complex visual reasoning tasks. Our analysis further reveals that domain expert identification locates cognitive functions rather than sample-specific solutions, enabling effective transfer across tasks with different information structures.

Haolei Xu, Haiwen Hong, Hongxing Li +7

Zhejiang University · Alibaba Group

VLM ReasoningExpert RoutingMixture-of-Experts ModelsMultimodal Reasoning
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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 2, 2026

Expert-Choice Routing Enables Adaptive Computation in Diffusion Language Models

Diffusion language models (DLMs) enable parallel, non-autoregressive text generation, yet existing DLM mixture-of-experts (MoE) models inherit token-choice (TC) routing from autoregressive systems, leading to load imbalance and rigid computation allocation. We show that expert-choice (EC) routing is a better fit for DLMs: it provides deterministic load balancing by design, yielding higher throughput and faster convergence than TC. Building on the property that EC capacity is externally controllable, we introduce timestep-dependent expert capacity, which varies expert allocation according to the denoising step. We find that allocating more capacity to low-mask-ratio steps consistently achieves the best performance under matched FLOPs, and provide a mechanistic explanation: tokens in low-mask-ratio contexts exhibit an order-of-magnitude higher learning efficiency, so concentrating compute on these steps yields the largest marginal return. Finally, we show that existing pretrained TC DLMs can be retrofitted to EC by replacing only the router, achieving faster convergence and improved accuracy across diverse downstream tasks. Together, these results establish EC routing as a superior paradigm for DLM MoE models and demonstrate that computation in DLMs can be treated as an adaptive policy rather than a fixed architectural constant. Code is available at https://github.com/zhangshuibai/EC-DLM.

Shuibai Zhang, Caspian Zhuang, Chihan Cui +8

University of Wisconsin-Madison · Scitix · Cornell University +4

Expert RoutingMixture-of-Experts Language ModelsDiffusion Language ModelsAdaptive Computation
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Mar 26, 2026

MoE-GRPO: Optimizing Mixture-of-Experts via Reinforcement Learning in Vision-Language Models

Mixture-of-Experts (MoE) has emerged as an effective approach to reduce the computational overhead of Transformer architectures by sparsely activating a subset of parameters for each token while preserving high model capacity. This paradigm has recently been extended to Vision-Language Models (VLMs), enabling scalable multi-modal understanding with reduced computational cost. However, the widely adopted deterministic top-K routing mechanism may overlook more optimal expert combinations and lead to expert overfitting. To address this limitation and improve the diversity of expert selection, we propose MoE-GRPO, a reinforcement learning (RL)-based framework for optimizing expert routing in MoE-based VLMs. Specifically, we formulate expert selection as a sequential decision-making problem and optimize it using Group Relative Policy Optimization (GRPO), allowing the model to learn adaptive expert routing policies through exploration and reward-based feedback. Furthermore, we introduce a modality-aware router guidance that enhances training stability and efficiency by discouraging the router from exploring experts that are infrequently activated for a given modality. Extensive experiments on multi-modal image and video benchmarks show that MoE-GRPO consistently outperforms standard top-K routing and its variants by promoting more diverse expert selection, thereby mitigating expert overfitting and enabling a task-level expert specialization.

Dohwan Ko, Jinyoung Park, Seoung Choi +3

Korea University · KAIST

Expert RoutingMixture-of-Experts ModelsRL for VLMs
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Mar 25, 2026

LGEST: Dynamic Spatial-Spectral Expert Routing for Hyperspectral Image Classification

Deep learning methods, including Convolutional Neural Networks, Transformers and Mamba, have achieved remarkable success in hyperspectral image (HSI) classification. Nevertheless, existing methods exhibit inflexible integration of local-global representations, inadequate handling of spectral-spatial scale disparities across heterogeneous bands, and susceptibility to the Hughes phenomenon under high-dimensional sample heterogeneity. To address these challenges, we propose Local-Global Expert Spatial-Spectral Transformer (LGEST), a novel framework that synergistically combines three key innovations. The LGEST first employs a Deep Spatial-Spectral Autoencoder (DSAE) to generate compact yet discriminative embeddings through hierarchical nonlinear compression, preserving 3D neighborhood coherence while mitigating information loss in high-dimensional spaces. Secondly, a Cross-Interactive Mixed Expert Feature Pyramid (CIEM-FPN) leverages cross-attention mechanisms and residual mixture-of-experts layers to dynamically fuse multi-scale features, adaptively weighting spectral discriminability and spatial saliency through learnable gating functions. Finally, a Local-Global Expert System (LGES) processes decomposed features via sparsely activated expert pairs: convolutional sub-experts capture fine-grained textures, while transformer sub-experts model long-range contextual dependencies, with a routing controller dynamically selecting experts based on real-time feature saliency. Extensive experiments on four benchmark datasets demonstrate that LGEST consistently outperforms state-of-the-art methods.

Jiawen Wen, Suixuan Qiu, Zihang Luo +2

Information Hub, The Hong Kong University of Science and Technology (Guangzhou), Guangzhou, 511453, China · Faculty of Geographical Science, Beijing Normal University, Beijing, 100875, China · School of Electronic and Communication Engineering, Guangzhou University, Guangzhou University, Guangzhou, Guangzhou, 510006, China

Hyperspectral Image ClassificationHybrid CNN-Transformer ArchitecturesExpert RoutingMulti-Scale Feature FusionMixture-of-Experts Models
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Mar 25, 2026

MoE-Sieve: Routing-Guided LoRA for Efficient MoE Fine-Tuning

Standard LoRA fine-tuning of Mixture-of-Experts (MoE) models applies adapters to every expert, yet our profiling shows that per-layer expert routing is highly skewed: a small subset of experts handles most tokens in each layer, while many others are rarely activated ("cold"). We propose MoE-Sieve, a simple routing-guided framework for LoRA fine-tuning, and pair it with a systematic profiling study of expert routing across architectures and tasks. The method is simple: profile routing counts on a small calibration set, select the top-k most-routed experts per layer, and apply LoRA only to those experts. Across two architecturally distinct MoE models and three diverse tasks, tuning only the top 25% routed experts per layer remains competitive with full LoRA, with mean differences within +/-1 percentage point across all conditions. This reduces LoRA trainable parameters by 70-73%, adapter checkpoint size by 71-73%, and wall-clock training time by up to 50%. We also observe a non-monotonic relationship between expert count and seed-to-seed variance, consistent with the hypothesis that adapting cold experts can introduce gradient noise without improving accuracy. Further ablations show that random expert selection at matched budget is about 2.5 percentage points worse, indicating that the routing signal matters, while greedy per-layer budget optimization does not improve over uniform top-k.

Andrea Manzoni

Mixture-of-Experts Fine-TuningFine-TuningSelective Fine-TuningSparse Fine-TuningLow-Rank AdaptationExpert Routing
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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

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 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 28, 2026

MME: Mixture of Mesh Experts with Random Walk Transformer Gating

In recent years, various methods have been proposed for mesh analysis, each offering distinct advantages and often excelling on different object classes. We present a novel Mixture of Experts (MoE) framework designed to harness the complementary strengths of these diverse approaches. We propose a new gate architecture that encourages each expert to specialise in the classes it excels in. Our design is guided by two key ideas: (1) random walks over the mesh surface effectively capture the regions that individual experts attend to, and (2) an attention mechanism that enables the gate to focus on the areas most informative for each expert's decision-making. To further enhance performance, we introduce a dynamic loss balancing scheme that adjusts a trade-off between diversity and similarity losses throughout the training, where diversity prompts expert specialization, and similarity enables knowledge sharing among the experts. Our framework achieves state-of-the-art results in mesh classification, retrieval, and semantic segmentation tasks. Our code is available at: https://github.com/amirbelder/MME-Mixture-of-Mesh-Experts.

Amir Belder, Ayellet Tal

Technion - Israel Institute of Technology, Israel

Mixture-of-Experts ModelsExpert RoutingClassification3D Semantic Segmentation
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Feb 22, 2026

Grouter: Decoupling Routing from Representation for Accelerated MoE Training

Traditional Mixture-of-Experts (MoE) training typically proceeds without any structural priors, effectively requiring the model to simultaneously train expert weights while searching for an optimal routing policy within a vast combinatorial space. This entanglement often leads to sluggish convergence and training instabilities. This paper introduces Grouter, a preemptive routing method that by distilling high-quality structures from fully-trained MoE models and serving as a fixed router for target models. By decoupling structural optimization from weight updates, Grouter significantly accelerates both the speed and quality of model convergence. To ensure the framework's versatility, we also introduce expert folding to adapt Grouter across varying model configurations and expert tuning to rebalance workloads across different data distributions. Furthermore, by leveraging the structural priors provided by preemptive routing, we can implement targeted optimizations to further enhance training throughput. Experiments demonstrate that Grouter achieves superior performance and efficiency which boosts pre-training data utilization by 4.28x and achieves up to 33.5% throughput acceleration, establishing preemptive routing as a fundamental paradigm for scalable MoE training. We publicly release our code and pretrained Grouter checkpoints at https://github.com/JimmyAwoe/Grouter.

Yuqi Xu, Rizhen Hu, Zihan Liu +2

School of Mathematical Sciences, Peking University, Beijing, China · Zhejiang Lab, Hangzhou, China · Yuanpei College, Peking University, Beijing, China +1

Mixture-of-Experts ModelsExpert Routing
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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

Phase-Aware Mixture of Experts for Agentic Reinforcement Learning

Reinforcement learning (RL) has equipped LLM agents with a strong ability to solve complex tasks. However, existing RL methods normally use a single policy network, causing simplicity bias where simple tasks occupy most parameters and dominate gradient updates, leaving insufficient capacity for complex tasks. A plausible remedy could be employing the Mixture-of-Experts (MoE) architecture in the policy network, as MoE allows different parameters (experts) to specialize in different tasks, preventing simple tasks from dominating all parameters. However, a key limitation of traditional MoE is its token-level routing, where the router assigns each token to specialized experts, which fragments phase-consistent patterns into scattered expert assignments and thus undermines expert specialization. In this paper, we propose Phase-Aware Mixture of Experts (PA-MoE). It first features a lightweight phase router that learns latent phase boundaries directly from the RL objective without pre-defining phase categories. Then, the phase router allocates temporally consistent assignments to the same expert, allowing experts to preserve phase-specific expertise. Experimental results demonstrate the effectiveness of our proposed PA-MoE.

Shengtian Yang, Yu Li, Shuo He +4

School of Computer Science and Engineering, Southeast University, Nanjing, China · Kuaishou Technology, Beijing, China · College of Computing and Data Science, Nanyang Technological University, Singapore

Reinforcement LearningRL for LLM AgentsMixture-of-Experts ModelsAgentic RLExpert Routing
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Feb 5, 2026

OmniMoE: An Efficient MoE by Orchestrating Atomic Experts at Scale

Mixture-of-Experts (MoE) architectures are evolving towards finer granularity to improve parameter efficiency. However, existing MoE designs face an inherent trade-off between the granularity of expert specialization and hardware execution efficiency. We propose OmniMoE, a system-algorithm co-designed framework that pushes expert granularity to its logical extreme. OmniMoE introduces vector-level Atomic Experts, enabling scalable routing and execution within a single MoE layer, while retaining a shared dense MLP branch for general-purpose processing. Although this atomic design maximizes capacity, it poses severe challenges for routing complexity and memory access. To address these, OmniMoE adopts a system-algorithm co-design: (i) a Cartesian Product Router that decomposes the massive index space to reduce routing complexity from O(N) to O(sqrt(N)); and (ii) Expert-Centric Scheduling that inverts the execution order to turn scattered, memory-bound lookups into efficient dense matrix operations. Validated on seven benchmarks, OmniMoE (with 1.7B active parameters) achieves 50.9% zero-shot accuracy across seven benchmarks, outperforming coarse-grained (e.g., DeepSeekMoE) and fine-grained (e.g., PEER) baselines. Crucially, OmniMoE reduces inference latency from 73ms to 6.7ms (a 10.9-fold speedup) compared to PEER, demonstrating that massive-scale fine-grained MoE can be fast and accurate. Our code is open-sourced at https://github.com/flash-algo/omni-moe.

Jingze Shi, Zhangyang Peng, Yizhang Zhu +3

The Hong Kong University of Science and Technology (Guangzhou) · Beijing Academy of Artificial Intelligence

Mixture-of-Experts InferenceLLM Inference AccelerationExpert RoutingMixture-of-Experts Models
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Feb 4, 2026

Routing-Aware Safety Alignment for Mixture-of-Experts Models

Mixture-of-Experts (MoE) language models introduce unique challenges for safety alignment due to their sparse routing mechanisms, which can enable degenerate optimization behaviors under standard full-parameter fine-tuning. In our preliminary experiments, we observe that naively applying full-parameter safety fine-tuning to MoE models can reduce attack success rates through routing or expert dominance effects, rather than by directly repairing Safety-Critical Experts. To address this challenge, we propose RASA, a routing-aware expert-level alignment framework that explicitly repairs Safety-Critical Experts while preventing routing-based bypasses. RASA identifies experts disproportionately activated by successful jailbreaks, selectively fine-tunes only these experts under fixed routing, and subsequently enforces routing consistency with safety-aligned contexts. Across two representative MoE architectures and a diverse set of jailbreak attacks, RASA achieves near-perfect robustness, strong cross-attack generalization, and substantially reduced over-refusal, while preserving general capabilities on benchmarks such as MMLU, GSM8K, and TruthfulQA. Our results suggest that robust MoE safety alignment benefits from targeted expert repair rather than global parameter updates, offering a practical and architecture-preserving alternative to prior approaches.

Jiacheng Liang, Yuhui Wang, Tanqiu Jiang +1

Department of Computer Science Stony Brook University

Mixture-of-Experts Language ModelsLLM AlignmentExpert RoutingAdversarial Robustness of Language Models
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Jan 29, 2026

L2R: Low-Rank and Lipschitz-Controlled Routing for Mixture-of-Experts

Mixture-of-Experts (MoE) models scale neural networks by conditionally activating a small subset of experts, where the router plays a central role in determining expert specialization and overall model performance. However, many modern MoE systems still adopt linear routers in raw high-dimensional representation spaces, where representation mismatch, angular concentration, and scale-sensitive scoring can jointly undermine routing discriminability and stable expert specialization. In this work, we propose Low-rank & Lipschitz-controlled Routing (L2R), a unified routing framework that reshapes both the routing space and scoring geometry. L2R performs expert assignment in a shared low-rank latent routing space and introduces Saturated Inner-Product Scoring (SIPS) to explicitly control the Lipschitz behavior of routing functions, yielding smoother and more stable routing geometry. In addition, L2R incorporates a parameter-efficient multi-anchor routing mechanism to enhance expert expressiveness. Experiments on an OLMoE-based language MoE model and a ViT-based ImageNet setting show improved overall performance in both domains; OLMoE diagnostics further show improved routing geometry and expert discrimination.

Minghao Yang, Ren Togo, Guang Li +2

Hokkaido University

Expert RoutingMixture-of-Experts Models
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