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

Oct 8, 2026cs.AI

DivMoE: Fine-Grained MoE Upcycling via Cross-Domain Expert Composition

Mixture-of-Experts (MoE) architectures have become essential for scaling large language models, with recent work demonstrating the benefits of fine-grained expert designs. Training such models from scratch is expensive, and sparse upcycling from pre-trained dense models is an attractive alternative. However, we identify a structural pathology of fine-grained upcycling: when fine-grained experts are derived from a single source model, naive routing collapses and downstream accuracy drops to near-random (e.g., on Qwen3-1.7B, Drop-Upcycling-fine-grained reaches only 23.2% average accuracy across 15 benchmarks, essentially matching from-scratch training at 22.2%, while the same method's coarse-grained variant reaches 50.2%). We propose DivMoE, the first framework achieving fine-grained MoE Upcycling with structurally-balanced routing. DivMoE introduces domain-specialized fine-grained expert initialization, deriving experts from dense models that have undergone domain-adaptive continual pre-training, and diversity-constrained routing, a hard structural constraint guaranteeing that each token activates experts from distinct domain groups. Across two base models and 15 benchmarks, DivMoE consistently outperforms six upcycling baselines (55.6% vs. 51.6% for the strongest baseline on Qwen3-1.7B) and strictly improves over the dense base model on every benchmark after Stage 2 continual pre-training -- closing the regression gap that has plagued prior fine-grained upcycling. After supervised fine-tuning on a public reasoning mixture, our 12B-parameter DivMoE model matches Moonlight-MoE (16B) at 64.5% average accuracy while outperforming a controlled NVIDIA-Upcycling baseline by 6.1 percentage points.

Yuxuan Lou, Kai Yang, Geng Zhang +2

School of Computing, National University of Singapore, Singapore · Department of Computer Science and Engineering, Shanghai Jiao Tong University, Shanghai, China

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

Oct 6, 2026cs.LG

MASKerade: Token-Routed Mask Experts for Dense-to-MoE Upcycling

Sparsely activated Mixture-of-Experts (MoE) models increase model capacity without a proportional increase in per-token computation. Dense-to-MoE upcycling reuses pretrained dense models to construct such systems, commonly by copying feed-forward networks (FFNs) into independently trained experts. We introduce MASKerade, a dense-to-MoE training method that instead learns experts as sparse subnetworks of a frozen pretrained FFN. Each expert is defined by a learned binary mask, and a token-level router selects which masked FFNs to execute and combine. The router and mask scores are optimized jointly, while the underlying FFN weight values remain unchanged. This formulation supports neuron-structured, semi-structured, and unstructured experts within the same routing architecture. Our main configuration uses four 2:4 experts with top-2 routing, where two half-dense expert passes have the nominal FFN arithmetic of one dense pass, without requiring independent expert weight matrices. On five vision-language benchmarks with Qwen and Gemma backbones, this configuration achieves the highest performance among the compared baselines. Comparisons across mask granularities, routing interventions, and compute-matched controls distinguish the effects of learned connectivity from expert activation count. These results establish mask learning over frozen weights as a practical alternative for constructing token-routed MoE experts.

Mingyuan Zhang, Yue Bai, Zhongruo Wang +5

Department of Electrical and Computer Engineering, Northeastern University · Khoury College of Computer Science, Northeastern University

Expert Routing Sparse Neural Networks Mixture-of-Experts Models

Oct 5, 2026cs.LG

Structuring MoE Expert Selection for Agentic Reinforcement Learning

Long-horizon LLM agents are frequently implemented using sparse mixture-of-experts (MoE) models, yet the co-design of agentic behavior and MoE structures remains underexplored. In this work, we comprehensively study the connections between agentic post-training and MoE expert selection. In off-the-shelf MoE models, we observe expert selection exhibits a specialized structure that naturally aligns with agentic trajectories. Specifically, expert routing overlaps more between turns where the agent performs semantically similar operations (e.g., READ, UPDATE) than between turns with differing operations. However, standard RL algorithms ignore this specialization, allowing the MoE routing to go uncontrolled during training, which empirically limit task performance and inference efficiency. To address this, we introduce a hierarchical routing control framework for agentic tasks. We explicitly encourage turn-level expert selections to align with agentic operations while regularizing token-level expert selections to maintain local consistency. To resolve stability issues that arise during post-training with the proposed methods, we further introduce an entropy-gated control mechanism. Overall, our routing control framework achieves over 10-point improvements in success rate on all evaluated benchmarks. These results demonstrate that agentic trajectory structure provides an effective signal for optimizing MoE capacity during RL post-training.

Bolian Li, Ting-Yao Hu, Cheng-Yu Hsieh +3

Apple · Purdue University

Agentic RL Expert Routing RL Post-Training Mixture-of-Experts Models

Oct 5, 2026cs.LG

How Sparse Probability Maps Shape Mixture-of-Experts Routing

Mixture-of-experts (MoE) routers typically apply softmax to the router scores and keep the top-K experts, making every token use exactly K experts. Sparsity-inducing probability maps such as sparsemax, alpha-entmax and normmax can adaptively assign exact zeros to selected experts, and therefore appear to offer token-dependent expert participation, even when using the same top-K machinery. In this work, we study whether and how this sparsity survives training. We train matched 300M and 1B top-2 MoE language models with softmax, 1.5-entmax, sparsemax and 2-normmax, and find that the maps behave very differently once trained: at 1B, entmax discards 30% less probability mass than softmax while almost never dropping a selected expert, sparsemax retains the most mass, and normmax routes 21% of tokens to a single expert. These outcomes are not properties of the maps alone. Each map drops a selected expert only when the gap between the two largest scores reaches a fixed threshold, and the trained routers differ in the score distribution they learn: the entmax router learns scores with roughly half the spread of softmax's, which keeps its top-2 gaps below its threshold, while sparsemax and normmax, which share the same threshold, learn different gap distributions and hence different participation. Routers thus co-adapt their scores to the map, and a map's capacity to produce zeros does not by itself determine expert participation. While none of the sparse maps improves validation loss over softmax, they make the trained models far less sensitive to selecting more experts at inference: sparsemax trained with K=2 loses 0.02 nats when run with K=8, where softmax loses 0.58. Our results indicate that adaptive MoE routing has to be designed around the joint behavior of the probability map and the learned scores, rather than around the map alone.

Tomás Brogueira, Marcos Treviso, Miguel Couceiro

Técnico, Universidade de Lisboa · INESC-ID · Instituto de Telecomunicações +2

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

Oct 5, 2026cs.LG

CIPHER-MoE: Balancing Efficiency and Routing Fidelity in Trillion-Scale MoE Training

Mixture-of-Experts (MoE) has been widely adopted in recent large language model (LLM) architectures. However, scaling up MoE in LLM training introduces system-level challenges on training, where non-uniform token routing can lead to highly imbalanced workloads across experts and devices, further destabilizing the training process. With trillion-scale LLMs, imbalanced expert workloads further amplify the resource cost of MoE training, resulting in degraded training efficiency and hardware utilization for underloaded experts, while hot experts require additional resources to accommodate excessive workloads. Recent studies address imbalanced MoE training through intricate parallelism strategies or resource reallocation. However, these system-level approaches often introduce additional resource requirements and considerable orchestration complexity, which become increasingly difficult to afford when training trillion-parameter LLMs under constrained computational resources. This work introduces CIPHER-MoE, which mitigates MoE workload imbalance while keeping the router's token-side Top-K selection unchanged. CIPHER-MoE applies affinity-aware Expert-to-Token filtering with explicit capacity control to reduce hotspot expert workloads without additional hardware resources or complex runtime design. The proposed method has been evaluated on large-scale MoE models, including DeepSeek-V4-Pro, showing up to 64.9 percentage points Top-1 expert workload reduction and 1.10

\times

-1.94

\times

training acceleration, while preserving the training quality. The source code will be released soon.

Jing Li, Jian Meng, Yingmeng Gao +8

Tongji University · Cornell University · Harbin Institute of Technology, Shenzhen +1

Expert Load Balancing Expert Routing Mixture-of-Experts Models LLM Training

Oct 2, 2026cs.LG

Conditional Capacity and Routing in Mixture-of-Experts Particle Transformers

Mixture-of-Experts (MoE) models can increase parameter capacity without proportionally increasing active computation, but it is unclear how this trade-off behaves in particle-physics transformers. We study dense and MoE Particle Transformers on 188-class JetClass-II, varying expert count, routing capacity, top-K, and auxiliary loss. We find that, when token dropping is avoided, top-1 MoE models improve over the dense baseline at nearly unchanged nominal forward compute, while further increasing the number of stored experts produces little additional accuracy gain. Activating multiple experts per token yields additional predictive improvements at higher computational cost. Routing analyses show that expert assignments become more strongly associated with particle identity and kinematics in some configurations, but this structure does not increase monotonically with classification performance. These results highlight the need to distinguish stored parameter capacity, active computation, routing capacity, and routing organization when evaluating sparse expert models for jet classification. Code and experiment configurations are available at https://github.com/kpendiyala/MPT.

Kaushik Pendiyala, Haris Zia, Trevin Lee +8

University of California Davis, Davis, CA, USA · University of California San Diego, San Diego, CA, USA · University of Illinois at Chicago, Chicago, IL, USA +1

Mixture-of-Experts Models Sparse Mixture-of-Experts Expert Routing Jet Tagging High-Energy Physics

Oct 1, 2026cs.AI

Auditing Routing Entropy as an Uncertainty Signal in Attention-Residual Transformers

Dynamic architectures leave a per-example routing trace beside each prediction, and diffuse routing is easy to read as a sign that the prediction is unreliable. We audit that reading for routing entropy in Attention-Residual (AR) variants of Swin-Tiny and DeiT-Small, trained from scratch on CIFAR-10/100 with a soft-binned calibration auxiliary loss, asking whether the trace carries information about correctness beyond what the model's own confidence already reveals. Three checks probe this increment: does a routing signal appear at fixed confidence, does it replicate across training seeds, and can a held-out predictor exploit it against output-only and shuffled-trace controls? A sensitivity audit then injects effects of known size and measures the fraction of each that the probes recover. No test in the fixed 30-test binned family survives multiplicity correction, and neither the nominal hit nor a borderline result recurs in its sibling seeds. Across 24 paired runs a scalar routing probe yields no pooled improvement in routing-stratified calibration, and an entropy-profile probe predicts correctness better than the same probe given shuffled profiles yet worse than a confidence-only predictor in both binary log-loss and Brier score: a gain over shuffled traces does not become a gain over the output. Conditioning on the complete logit vector leaves the corresponding comparison unresolved. The audit bounds how far these non-detections can be read: at an injected effect of 0.010 nats the profile probe recovers 24-59% of the oracle gain, and a reference-preserving correction probe recovers 8% and 23% in the two CIFAR-100 settings, below the threshold we fixed for applying it to real labels. The results establish control-dependent gains and incomplete estimator recovery, not the absence of conditional routing information.

Wenhao Liang, Lin Yue, Wei Emma Zhang +3

Adelaide University, Adelaide, Australia

Uncertainty Quantification Model Calibration Expert Routing

Oct 1, 2026cs.AI

SpikeMoE: Brain-Inspired Competitive Routing for Flexible Spiking Mixture-of-Experts

Spiking Neural Networks (SNNs) enable event-driven computation through biologically inspired dynamics at the neuronal scale, while Mixture-of-Experts (MoE) perform conditional computation through expert selection at the model scale. Integrating their strengths offers potential for flexible neural architectures. A key challenge, however, lies in designing an expert selection mechanism based on spiking activity. To address this, we introduce a spike-based k-WTA Router inspired by competition-inhibition observed in the hippocampal CA1 region. The router incorporates lateral inhibition and refractory period to select Top-K experts according to discrete spike counts. Building on this, we present SpikeMoE, a framework that integrates neuronal-scale spiking dynamics with model-scale expert selection. To address incomplete multisensory inputs in multimodal tasks, we further equip SpikeMoE with a two-stage missing-modality modeling module that combines empirical prototypes from an observed-modality pool with modality-specific learnable embeddings to construct missing-modality representations. Experiments on vision, language, and multimodal benchmarks demonstrate that SpikeMoE achieves state-of-the-art performance among the SNN baselines, matches or exceeds the performance of ANN counterparts, and maintains robustness across diverse missing-modality conditions. These results demonstrate a favorable trade-off between performance and energy efficiency, validating the integration of spiking dynamics with sparse expert computation and highlighting SpikeMoE as a promising approach to energy-efficient brain-inspired computing.

Xiaoli Liu, Yujie Liang, Jialin Li +1

School of Computer Science and Engineering, University of Electronic Science and Technology of China

Spiking Neural Networks Expert Routing Mixture-of-Experts Models Multimodal Learning

Oct 1, 2026cs.LG

Looping Beyond Twice: A Scalable Recipe for Looped Mixture-of-Experts

Looped Transformers introduce recurrent depth as a new scaling axis for LLMs: by repeatedly applying shared Transformer blocks, they increase effective depth without increasing parameter count. However, the benefits of looping remain unclear for large MoE LLMs under FLOPs-matched comparisons. The main reason is that the gains from additional iterations diminish quickly and can even turn into degradation, so the extra FLOPs spent on looping yield little substantial improvement. Consequently, prior work typically settles on two loops. We identify two main obstacles to scaling looped MoE. First, looping inherits and amplifies the curse of depth: hidden-state variance grows with each iteration as residual updates accumulate, which destabilizes deep recurrence and causes representations to drift. Second, looped MoE suffers from expert selection collapse: routers repeatedly select the same experts across loops, so extra iterations add computation without adding computational diversity. Guided by this diagnosis, we propose LOOM, built on a single principle: each loop should contribute new computation while keeping the recurrent state stable. LOOM stabilizes recurrence by scaling residual updates to bound variance growth and re-injecting the input embedding at every loop, and diversifies it through per-loop routers that engage different experts and a Looping Residual that carries earlier outputs forward. Experiments across 100M-1.7B models show stable scaling to 9-12 loops. Under near-iso-FLOP, the 700M model performs best at 5 loops, reducing perplexity from 18.36 to 16.54 and improving average zero-shot accuracy from 38.84% to 39.53% over the non-looped baseline. Without FLOP matching, the 1.7B model trained on 60B tokens peaks at 9 loops, reducing perplexity from 9.62 to 7.77 and improving average zero-shot accuracy from 42.4% to 47.7%. Code is available https://github.com/hed-ucas/LOOM.

Di He, Pengxiang Li, Da Chang +3

Shenzhen Institutes of Advanced Technology, Chinese Academy of Sciences · Peng Cheng Laboratory · University of Chinese Academy of Sciences +5

Mixture-of-Experts Language Models Recurrent Transformers Expert Routing

Sep 30, 2026cs.LG

Raw-Routed Mixture of Adapters: A Causal Intervention for Routing Collapse in Time Series Foundation Models

Time series foundation models (TSFMs) commonly adapt to new data by attaching a single trainable head to a frozen backbone, a one-size-fits-all setup that underfits heterogeneous regimes. Replacing the head with a mixture of experts is the standard upgrade, but on instance-normalized backbones (the dominant TSFM design class) it fails: routing entropy collapses to zero and one expert absorbs every input, a failure we call normalization-induced routing collapse. Standard MoE rescue mechanisms do not repair it, because the cause is in the router's input, not its optimization. Pre-encoder normalization strips the statistics a router would need to tell regimes apart. A mutual-information decomposition makes this precise and yields a signal-ratio that, computed before training, predicts dataset vulnerability (Spearman

ρ= -0.88

). Eight causal controls, including a vision-modality replication, isolate instance normalization as the cause. The prescription is a minimal causal intervention: Raw-Routed Mixture of Adapters (RR-MoA), which routes on the raw, pre-normalization input. Under a strictly frozen backbone, RR-MoA wins 54/54 comparisons against the strongest fixed adapter and significantly outperforms LoRA, TRACE, AdaMix, and full fine-tuning. The effect generalizes across six backbones and an imputation task. Frozen RR-MoA also beats full fine-tuning by 12-79% (the Frozen Paradox); two architecturally distinct variants confirm the principle generalizes beyond this specific router.

Hung Phan, Thuy T. Nguyen, Minh Ngoc Dinh +1

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

Sep 30, 2026cs.LG

MoRA: MoE Pruning via Router Bias Learning and Expert Approximation

Mixture-of-Experts (MoE) models enable parameter scaling with limited per-token computation by activating only a small subset of experts for each token, but deploying them still requires loading the complete expert pool into memory. Structured expert pruning can effectively reduce the memory usage by removing experts. However, existing pruning methods either use expert ranking criteria that are not well aligned with model performance or rely on effective expert subset searching that is computationally expensive. Moreover, these methods typically overlook the routing-behavior redundancy among the retained experts. In this paper, we propose MoE Pruning via Router Bias Learning and Expert Approximation (MoRA), a framework for structured MoE expert pruning. We introduce a learnable router bias for each expert and optimize these biases by minimizing the language-modeling loss and a routing-diversity regularizer. The learned router biases sharpen the routing probability distributions to identify experts critical to model performance while encouraging the selection of experts with diverse routing preferences. In addition, we introduce an expert approximation mechanism as a post-pruning enhancement. It leverages the remaining experts to approximate the outputs of pruned experts by affine transformation, further improving the performance of the pruned model. We evaluate MoRA on Qwen3-30B-A3B, DeepSeek-V2-Lite, and Moonlight-16B-A3B, removing 25% and 50% of the routed experts in each MoE layer. Extensive experiments on nine zero-shot benchmarks show that MoRA outperforms state-of-the-art pruning algorithms. Our code will be released.

Yushuai Sun, Zikun Zhou, Lin Gao +2

Harbin Institute of Technology, Shenzhen

Mixture-of-Experts Pruning LLM Compression Expert Routing Mixture-of-Experts Models

Sep 30, 2026cs.IR

RouteRec: Behavior-Guided Sparse Routing for Sequential Recommendation

Sessionized interaction histories contain behavioral patterns that can improve sequential recommendation. However, existing models process all sessions through the same parameterized blocks, regardless of their behavioral differences. Mixture of Experts (MoE) enables conditional computation, but it leaves open what should guide expert allocation. We propose RouteRec, a sequential recommender that uses observed session behavior as the routing criterion. RouteRec summarizes four types of behavioral evidence from sessionized histories: interaction tempo, item-group focus, repetition and carryover, and popularity tendency. It uses these cues to route computation at macro, mid, and micro scopes. Cue-derived scores first select expert groups; within each selected group, the current backbone state then refines expert selection. Across six public datasets and 18 dataset-metric combinations, RouteRec ranks first in 12 and second in three, yielding the best overall average rank of 1.61 compared with 4.11 for the next-best baseline. Additional analyses suggest that the behavioral cues guide expert allocation beyond added capacity and produce routing patterns aligned with observed behavior. Our code is available at https://github.com/jy1559/RouteRec

Junyeong Song, Jaemin Yoo

Korea Advanced Institute of Science and Technology Daejeon, Republic of Korea · Seoul National University Seoul, Republic of Korea

Sequential Recommendation Sparse Mixture-of-Experts Expert Routing

Sep 29, 2026cs.CV

Breaking the Uniformity Trap: Scaling Video Diffusion Model via SplitMoE

Mixture-of-Experts (MoE), popularized by large language models, is a promising paradigm for scaling visual generative models. However, conventional token-wise MoE routes tokens independently within a homogeneous expert pool and regularizes expert usage toward uniformity, making it poorly matched to video data that is spatiotemporally redundant and semantically long-tailed. We show that existing visual MoEs fall into a uniformity trap: semantically under-organized routing, compounded by uniform expert-usage regularization, scatters coherent patches across disparate experts, causing routing fragmentation and structural distortion. To address this, we propose SplitMoE, a split-role sparse architecture that breaks the shackles of uniformity. To accommodate the inherent semantic imbalance, we explicitly bifurcate the expert pool into semantic experts and generic experts, with semantic experts capturing high-level semantic abstraction and generic experts preserving residual visual information and flexible generative capacity. Leveraging prototype-guided routing and pull-push regularization, SplitMoE enables tokens to cluster naturally by semantic attributes rather than arbitrary balancing constraints. Extensive results show that under an equivalent activated-parameter budget, SplitMoE outperforms traditional load-balanced MoEs in convergence speed, routing coherence, and video generation quality across standard benchmarks. By revealing an emergent coarse-to-fine denoising logic, SplitMoE provides the community with a modality-aware scaling path, serving as a critical reference for building large-scale video world models.

Yu Xu, Yuxin Zhang, Xiao Yang +7

University of Chinese Academy of Sciences · ByteDance · Canva Research +1

Video Diffusion Models Video Generation Expert Routing Mixture-of-Experts Models

Sep 29, 2026cs.AI

Cross-Entropy Guided Routing in Mixture-of-Experts Large Language Models

Sparse mixture-of-experts (MoE) large language models scale model capacity by routing each token to a small subset of experts. Their routers are regularized with load balancing terms and learn affinity scores through the language-model objective. However, these objectives do not provide direct alignment between routing affinities and token-level error. We introduce token-error supervision for sparse routing in two forms. The first form predicts an error score per expert. The affinity-weighted aggregate of these scores is aligned to the next-token cross-entropy loss, while the individual scores attenuate affinity before top-

K

selection. The second directly aligns the router's affinities to the model's objective without requiring an additional head or inference-time modification. Both formulations use the Itakura--Saito divergence or an exponential negative log-likelihood for aligning affinities and token errors. Across two sparse MoE backbones and four multiple-choice question-answering benchmarks, we evaluate both supervision mechanisms. On Granite, our method improves accuracy by approximately 2.3 percentage points on average over a parameter-matched routing baseline. With stronger supervision, the gain on ARC-Challenge reaches 2.94 points. Both mechanisms preserve the native sparse execution budget and aggregation policy. Our code is available in the supplementary materials.

Yury Nahshan, Nati Daniel, Jacob Goldberger +1

Bar-Ilan University, Ramat-Gan, Israel · NVIDIA, Israel

Mixture-of-Experts Language Models Parameter-Free Mixture-of-Experts Routing Sparse Mixture-of-Experts Expert Routing LLM Routing

Sep 23, 2026cs.LG

Exact Quantile Balancing and Load-Error Injection for Mixture-of-Experts

Mixture-of-Experts (MoE) training requires global load balance to prevent expert under-utilization and local balance for efficient expert-parallel execution. Existing distributed Quantile Balancing (QB) uses shard-dependent or approximate global quantiles, while token-independent expert biases cannot ensure microbatch-level balance. We introduce Exact Quantile Balancing (EQB), which computes exact global-batch BF16 quantiles with negligible communication, and Load-Error Injection (LEI), which injects local load errors directly into router-score gradients. On 7.5B-parameter MoEs trained for up to 500B tokens, EQB improves global balance and downstream performance over naive QB, while LEI improves local balance and outperforms the GShard loss at comparable quality.

Pit Neitemeier, Jiaze Li, Alessio Serra +2

Aleph Alpha

Expert Load Balancing Expert Routing Mixture-of-Experts Models

Sep 16, 2026cs.AI

The Other Half of the Memory Wall: Serving 35B MoEs from SSD with Trained Routing Prediction

Mixture-of-experts (MoE) inference on consumer hardware is bounded by weight memory: a 35B-class model is 19.5GB at 4-bit, and sparsity shrinks the compute per token, not the bytes that must be held. Naive offloading to SSD does not help on its own, because layer N+1's experts must be chosen before layer N's output exists, so the reads cannot start early enough to hide behind compute. We present Edge0, a streaming MoE inference engine that closes the gap with a prerouter: a per-layer head predicts the next layer's routing one token ahead, and the prediction is consumed as the routing itself, so the staged expert set equals the routed set and nothing is dropped. An unmerged recovery LoRA, trained on the student path, pays back the quality lost to int4 quantization and routing replacement. On a single 24GB machine, Edge0 serves a 35B MoE at 20tok/s inside 3GiB of peak active memory, within a few points of its fp16 teacher on average across five public benchmarks. An 8B tier runs on the same framework, and the framework, checkpoints, and adapters are open source.

Yu Lin, Yiming Wang, Runyuan Cai +2

AutoArk

Expert Offloading Mixture-of-Experts Inference Memory-Efficient Inference LLM Inference Acceleration Expert Routing

Sep 15, 2026cs.LG

Beyond the Previous Layer: Residual Predictive Structure in Sparse MoE Routing

Sparse mixture-of-experts models route each token through a sequence of expert selections. We ask whether the immediately preceding selection adequately summarizes this trajectory for predicting the next router. Using frozen OLMoE and JetMoE models, we measure the held-out predictive gain from earlier expert selections while retaining the most recent selection as a common baseline. In OLMoE, extending the history from one to eleven layers raises router-logit

R^2

from 0.59879 to 0.66544. A preregistered JetMoE replication yields four-layer gains of 0.14275 and 0.20528 at two target depths, with paired bootstrap intervals above zero. These gains survive nonlinear decoding: adding history to a small multilayer perceptron improves

R^2

by 0.17137 and 0.21861, whereas nonlinear decoding of the recent state alone adds 0.00139 and 0.00936 over a linear probe. Parameter-matched controls preserve the advantage, and cross-fitted history residuals predict target residuals with

R^2

of 0.20549 and 0.23556. These findings identify residual predictive structure in expert-selection trajectories beyond adjacent-layer persistence.

Hao Li, Yasuyuki Tahara, Yuichi Sei

Department of Informatics, Graduate School of Informatics and Engineering, The University of Electro-Communications, Tokyo, Japan

Sparse Mixture-of-Experts Expert Routing LLM Routing

Sep 14, 2026cs.CL

Expert-Space Exploration in MoE Reinforcement Learning

Reinforcement learning (RL) has become central to post-training of large language models. Recent advances in RL for Mixture-of-Experts (MoE) models have primarily focused on improving optimization stability and training efficiency, while treating the expert selection as a fixed component. Since routing determines the sparse computation paths that induce output distributions, expert selection offers an additional source of rollout diversity. Through empirical analysis, we find that perturbing expert routing effectively alters model output and increases rollout diversity, which is similar to increasing the decoding temperature. However, direct perturbation can activate unsuitable experts and substantially degrade rollout quality. Motivated by these observations, we introduce Expert-Space Exploration Reinforcement Learning (ESRL), an architecture-aware framework that explicitly explores the expert-routing space of MoE models. ESRL preserves high-confidence experts as anchors, and restricts stochastic routing to a plausible candidate pool, thereby retaining reliable computation paths. The perturbation strength is further adapted according to router entropy to avoid over-perturbation. To mitigate the routing mismatch introduced by perturbation, ESRL records the expert paths used during rollout and replays them during policy optimization. Experiments demonstrate that ESRL achieves the best performance across MoE backbones with top-K, top-1, and shared-expert routing, as well as across mathematics, science, and code tasks without additional sampling or computational cost. Specifically, ESRL on Qwen3-30B-A3B achieves the best among all compared methods, improving average Pass@1 and Pass@8 over GRPO by 3.2 and 4.5 percentage points, respectively. Further analyses of expert utilization and training dynamics provide insights into how exploiting MoE-specific routing structure benefits RL training.

Hongyi He, Zhenghao Lin, Xiao Liu +3

Tsinghua University · Microsoft Research

Reinforcement Learning Expert Routing RL Post-Training Mixture-of-Experts Models

Sep 2, 2026cs.LG

Evidence for Shared Routing Geometry and Dynamics in Sparse Mixture-of-Experts

Sparse mixture-of-experts (MoE) models use an independently parameterized router at each sparse layer to select experts for every token. Prior work has shown that routing decisions across depth can often be predicted from earlier routing signals, suggesting that routing is not fully independent across layers. However, the structure behind this predictability remains unclear. In this work, we provide evidence that routing-relevant states across layers share a common geometric structure that is obscured by layer-specific coordinate systems. We isolate the control subspace of each router and align these spaces into a shared canonical representation using generalized orthogonal Procrustes analysis. After alignment, a single linear transition reaches

R^2=0.39

--

0.71

and retains 79--90% of the predictive power of separately fitted layer-specific dynamics, indicating that much of routing-state evolution follows a reusable process across depth. We then ask whether this shared dynamics is specific to routing or simply reflects the smooth evolution of hidden representations. A matched-rank comparison shows that residual representations are often easier to predict across layers, while router-control states preserve the model's expert choices much more faithfully. This separates generic cross-layer predictability from routing-specific information. Finally, we test whether the predicted canonical states remain meaningful when used in place of native routing states. The transported states preserve local routing behavior, while learned state evolution reduces

Δ\mathrm{NLL}

relative to simple persistence by 15.7% on OLMoE and 6.2% over a 10-router horizon on Phi.

Kirill Labzin, Stepan Kulibaba, Artem Dzhalilov +1

Central University, Moscow · Innopolis University, Innopolis · Independent Researcher

Sparse Mixture-of-Experts Expert Routing

Sep 1, 2026cs.CL

Beyond Magnitude: Contrastive Routing for Modular Mixture-of-Experts

In current Mixture-of-Experts architectures, routing is performed based on representations dominated by structure shared across all tokens, limiting expert specialization. We show that contrasting each token against an Exponential Moving Average of the layer's hidden states, rather than routing on absolute magnitude, concentrates the routing signal onto a low-dimensional, highly separable subspace. Building on this, we propose the Contrastive Routing Mechanism (CoRM), which scores each expert by the gap between its affinity for the incoming token and its affinity for this shared reference state, interpreted through a distinct per-expert projection. The resulting experts have routing boundaries that align with linguistic structure significantly more than the Top-k baseline. Our experiments show that CoRM improves average zero-shot accuracy by +0.67 to +1.69 points (Top-1) and +1.38 to +1.77 points (Top-2) over standard Top-k MoE baselines on nine zero-shot reasoning benchmarks, at the minimal cost of 2.9% added parameters and 2.6% added FLOPs per token.

Nikolaos Xiros, Dimitrios Damianos, Maria-Eleni Zoumpoulidi +3

Institute for Language and Speech Processing, Athena Research Center, Greece

Mixture-of-Experts Language Models Expert Routing

Aug 12, 2026cs.LG

TradingMoE: Routing the Right Experts in Evolving Markets

Large language models (LLMs) have shown strong potential for financial analysis and trading, but direct trading remains challenging because the predictive capabilities required can vary across assets, decision fields, and market conditions. Existing LLM-based trading systems either coordinate human-defined external experts or adopt conventional internal Mixture-of-Experts (MoE) routers that do not directly evaluate how individual experts contribute to trading decisions. Moreover, these routers receive no direct signal indicating when an inactive expert has become more suitable as market conditions change. We find that native router scores poorly reflect how much individual experts improve trading decisions, frequently leaving better alternatives unselected. We further reveal that token-specific expert usefulness exhibits a compact low-dimensional structure. Based on these findings, we propose TradingMoE, a trading-oriented sparse MoE that augments a frozen dense LLM with lightweight residual experts. We introduce a Query-Key router that represents the expertise required by each token under the current market context as a low-dimensional query and matches it with learnable expert keys. We further propose a sparse expert selection update mechanism that samples a few inactive experts during training and estimates whether they should replace the weakest expert in the current Top-k route. This mechanism enables the router to update expert selection as market conditions change while preserving sparse computation. Experiments against 22 baselines on stock and cryptocurrency markets show that TradingMoE improves cumulative return over the best-performing baselines by 30.89% and 30.7%, respectively. Rolling paper-trading experiments further demonstrate that its advantage persists under forward-only deployment.

Chang Zhou, Xingtong Yu, Minbin Huang +4

University of Science and Technology of China · The Chinese University of Hong Kong · The University of Tokyo +1

Mixture-of-Experts Language Models Sparse Mixture-of-Experts Expert Routing LLM Routing Algorithmic Trading

Aug 11, 2026cs.LG

Share First, Route What Remains: A Unified Framework for Token-Adaptive MoE Computation

Mixture-of-experts (MoE) models have recently moved beyond routing a fixed number of complete experts. Shared-expert designs preserve reusable knowledge, fine-grained methods vary computation within experts, and dynamic routers adapt the number of active experts. Yet these decisions are usually made independently, overlooking a basic dependency: extracting reusable computation changes both what remains and how much expert capacity the remainder needs. We study this dependency by decomposing sparsely upcycled feed-forward experts into key-value channels. Co-activated experts align at a subset of value positions; removing these positions changes expert preference; and greater shared coverage is associated with lower residual expert demand. These observations lead to one principle: share first, then route what remains. We instantiate it in UniF-MoE, a unified framework for token-adaptive MoE computation. Each expert is partitioned into aligned blocks. A shared-demand score sets the shared block count and pathway weight, key prototypes select the shared content, and the complementary demand determines the residual expert count through cumulative routing mass. A Gram regularizer separates and normalizes router embeddings, promoting diverse routing directions, sparse expert overlap, and a simple routing geometry. Experiments on DomainBed and GLUE show that this unified design improves predictive performance over representative static and dynamic MoEs while reducing activated computation, inference latency, and memory. Code is available at https://github.com/existence0420/UniF-MoE.

Gongli Zhang, Zhulin Liu, C. L. Philip Chen

Guangdong Provincial Key Laboratory of Computational AI Models and Cognitive Intelligence, School of Computer Science and Engineering, South China University of Technology, Guangzhou 510006, China · Pazhou Lab, Guangzhou 510335, China · Engineering Research Center of the Ministry of Education on Health Intelligent Perception and Paralleled Digital-Human, Guangzhou 510641, China

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

Aug 9, 2026cs.LG

Beyond Routing: Decoupling Expert Dispatch and Aggregation in Sparse Mixture-of-Experts

Sparse Mixture-of-Experts (MoE) routers commonly use the same scores both to select experts and to weight their already-computed outputs. We study whether these two roles, dispatch and aggregation, should be coupled. On pretrained OLMoE-1B-7B, we keep selected Top-8 expert IDs, expert computation, and total selected router mass fixed and change only within-set aggregation. A structured oracle improves full-horizon cross-entropy by 0.0160 +/- 0.0039 across three seeds; the router's top-scored expert is the counterfactual-best vertex only 17.2% of the time, with router-utility Spearman 0.030. We therefore train Fixed-Dispatch Adaptive Aggregation (FDAA), a 301K-parameter post-compute head optimized directly with the language-modeling objective while freezing the backbone, router, and experts. On OLMoE, FDAA improves fresh WikiText-103 test by Delta CE = -0.1523 +/- 0.0031 across three seeds, and mixed-domain training gives robust gains on WikiText-103, C4, and held-out Penn Treebank under frozen confirmatory evaluation. We also replicate the fixed-dispatch audit on DeepSeek-V2-Lite, which uses Top-6 routed experts plus shared experts. Best-vertex headroom remains significant on WikiText and C4, while router Top1 identifies the best selected expert in only 12.5% and 16.7% of audited examples. In a one-seed mixed-domain replication, FDAA improves locked WikiText and PTB, while C4 is statistically neutral. These results support a cross-architecture distinction between expert selection and expert commitment.

Zongfei Li

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

Aug 9, 2026cs.CL

The Evolution of Mixture-of-Experts Architectures in Large Language Models: Routing, Topology, Load Balancing, and Expert Parallelism

Mixture-of-Experts models increase parameter capacity while keeping the computation activated by each token bounded, but their architectural evolution cannot be explained by a chronological list of model releases alone. This technical survey synthesizes primary papers, official technical reports, and prior surveys to organize modern Mixture-of-Experts systems along five coupled dimensions: expert granularity, expert topology, routing freedom, the scope of load balancing, and execution structure. We describe eight architectural milestones as a dependency graph with six mainline developments and two orthogonal branches, rather than as eight successive generations. We then analyze individual systems through four control planes: Expert Topology, Routing, Balance, and Expert Parallelism. These planes specify which experts exist, which experts process each token, how aggregate load is controlled, and how selected computation is mapped onto physical devices. The framework connects algorithmic choices such as Top-k routing, shared experts, fine-grained experts, and dynamic expert composition with systems concerns including token dispatch, device placement, all-to-all communication, and communication-computation overlap. We conclude with equal-budget pretraining experiments, quality and systems metrics, and open research questions. The main trend is a shift from merely activating more sparse parameters toward decoupling semantic routing, computational budgets, and physical execution.

Jiguo Li

This report was completed with the assistance of Codex.

Expert Parallelism Expert Load Balancing Mixture-of-Experts Inference Expert Routing Mixture-of-Experts Models

Aug 5, 2026cs.LG

Elbow-Based MoE Routing: A Training-Free Inference Time Plugin for Expert Selection

Mixture-of-Experts (MoE) models enable model scaling while maintaining low inference-time compute by activating only a subset of experts per token. However, conventional routing relies on a fixed top-k selection, forcing the model to spend the same compute regardless of how many experts are relevant. We introduce elbow-based routing, a training-free inference-time modification that dynamically adjusts the number of experts on a per-token basis. Our method examines the sorted router probability distribution and identifies an elbow point that separates high- and low-probability experts. We find that most router distributions exhibit clear inflection points suitable for this strategy, and we show both theoretically and empirically that elbow-based routing preserves expert load balance. Experiments on a state-of-the-art MoE model demonstrate an average latency reduction of 5.3% while maintaining accuracy across six benchmarks.

Robin Pan, Raymond Liu, Daniel Fang +2

John A. Paulson School of Engineering and Applied Sciences, Harvard University · Department of Mathematics, Harvard University

Mixture-of-Experts Inference LLM Inference Acceleration Expert Routing

Aug 3, 2026cs.LG

Uncertainty Is Not Enough: Value-of-Information Routing for Mixtures of LoRA Experts

Mixtures of low-rank adaptation experts increase parameter-efficient capacity by routing each input through a subset of adapters. Recent dynamic routers activate more experts when the router or prediction is uncertain. This rule silently equates uncertainty with useful additional computation: an uncertain example may contain complementary, unqueried expert evidence, but it may instead remain ambiguous after every expert agrees. We formulate routing as certified value-of-information allocation. VI-MoLE learns the counterfactual risk remaining after each expert prefix, converts these predictions into simultaneous upper-risk certificates on held-out calibration data, and spends a global adapter budget on the token--layer action with the largest certified marginal risk reduction per unit cost. A terminal certificate then decides whether to answer or abstain. Unlike an uncertainty gate, this procedure distinguishes present ambiguity from recoverable and residual risk. We prove simultaneous certificate validity, optimal greedy allocation under diminishing certified gains, and allocation regret under value-estimation error. The evaluation protocol tests matched-compute accuracy, certificate coverage, risk--coverage, distribution shift, and tail latency against fixed and dynamic MoE-LoRA routers.

Tom Saliencro, Rohan Desai, Priya Nair +2

University of California, Irvine · University of Washington

Adaptive Model Routing Selective Prediction Value of Information Cost-Aware Inference Mixture-of-Experts Inference Low-Rank Adaptation+1

Aug 1, 2026cs.NI

HetRoute Heterogeneous and Cost-aware Collaborative Routing Framework for Distributed Edge MoE Inference

Mixture-of-Experts (MoE) models have become a dominant architecture for large-scale AI services, yet deploying them over geo-distributed heterogeneous edge servers remains challenging. When the Top-k activated experts of a token are spread across multiple servers, the optimal routing depends jointly on cross-server link bandwidth, heterogeneous GPU computing capability, GPU-CPU expert loading delay, instantaneous queueing backlog, and replica-level quantization quality loss. Existing distributed inference and MoE serving methods address these factors separately and do not provide a unified framework for online multi-server collaborative routing. In this paper, we propose HetRoute, a heterogeneous-cost-aware collaborative routing framework for distributed edge MoE inference. HetRoute introduces a unified per-assignment cost model that explicitly captures four cost components: cross-server transmission, GPU-CPU offloading, GPU computation with queueing, and quantization-induced quality penalty. Guided by this model, the offline stage determines expert server placement, GPU-CPU residency, and replica precision through a routing-cost-coupled deployment algorithm, while the online stage routes the Top-k activated expert set as a whole by minimizing the bottleneck layer cost via exact enumeration or beam search. Theoretical analysis establishes fallback feasibility, a bound on the number of participating servers, per-layer optimality for small candidate domains, and online computational complexity. Trace-driven evaluation on three MoE models over a heterogeneous 10-server edge testbed shows that HetRoute reduces average inference latency by up to 59.0% and P99 latency by up to 58.0%, cuts cross-server traffic by up to 72.1%, and achieves 2.13x throughput improvement compared with representative baselines, while keeping quality degradation within the configured budget.

Xin Yuan, Ning Li, Wenchao Xu +2

School of Ocean Engineering, Harbin Institute of Technology, Heilongjiang, China · School of Artificial Intelligence, University of Science and Technology Beijing, China · Division of Integrative Systems and Design, Hong Kong University of Science and Technology, Hong Kong +1

Edge Inference Cost-Aware Inference Mixture-of-Experts Inference Expert Routing Distributed Inference

Aug 1, 2026cs.CV

Relax Within, Balance Across: Geometry-Guided Load Balancing for Vision-Language Mixture-of-Experts

Vision-language MoE batches contain different numbers of image and text tokens. Image resolution, image count, tiling, and prompt length all change this token mix. We call the standard token-level Switch auxiliary loss Std-Aux. Std-Aux balances only the mixed load, so large image and text load errors can cancel at one mix. On our main model, the same trained router shows more than a fivefold change in load imbalance across image resolutions. We hold the image and text load profiles fixed and derive the exact load curve as the token mix varies. The image-text load gap controls sensitivity to the token mix. Physical preprocessing can also change the conditional profiles. The fixed-profile law excludes such changes. To design a remedy, we examine the router input structure. Image and text occupy distinct regions, while visual tokens group strongly by source image. The modality boundary motivates separate image and text terms. The image boundary motivates one equal-weight routing instance per image. ReBA, or Relax Within, Balance Across, implements both choices. Across four split backbones, ReBA lowers load on every reported benchmark input while keeping mean task accuracy comparable to Std-Aux. ReBA also lowers average load over the tested range and worst physical load under resolution and tiling shifts. Code is available at https://github.com/ZiangWu-77/ReBA.

Ziang Wu, Peng Jin, Qishen Yin +4

2Peng Cheng Laboratory · School of Software and Microelectronics, Peking University · 1Shenzhen Graduate School, Peking University +2

Expert Load Balancing Vision-Language Models Expert Routing

Jul 31, 2026cs.AI

EntropyMoE: Entropy-Aware Sparse Expert Routing for Tokenizer-Free LLMs

Recent byte-level large language models (LLMs) have made tokenizer-free modeling increasingly competitive by grouping bytes into dynamically sized patches. However, existing byte-patch architectures still apply the same dense feed-forward computation to every patch. This uniform computation cannot adapt model capacity to variations in patch semantics and granularity. We address this limitation with EntropyMoE, a Mixture-of-Experts (MoE) architecture designed for dynamic byte patches. EntropyMoE replaces the dense feed-forward modules in the global patch Transformer with Top-K expert layers. Each dynamic patch serves as the basic unit of expert routing, and its byte coverage determines its contribution to workload accounting. The router selects experts directly from patch entropy, using the same granularity signal that underlies dynamic patch construction to organize sparse computation. Patch entropy and length jointly define the feature space for regulating expert specialization. Experiments show that EntropyMoE achieves the lowest held-out bits-per-byte among matched dense and sparse baselines while maintaining comparable downstream accuracy. These results establish patch entropy as an effective routing coordinate for sparse conditional computation and extend Mixture-of-Experts modeling beyond tokenizer-based representations.

Bo Liu, Muxuab Yu, Yu Zhang +2

University of Bristol · School of Automation Science and Electrical Engineering,Beihang University, Beijing, China · University of Manchester

Sparse Mixture-of-Experts Byte-Level Language Model Expert Routing Language Modeling LLM Routing

Jul 30, 2026cs.LG

Beyond Geometric Complementarity: Coherent Overlap in Sparse Mixture-of-Experts Routing

Sparse mixture-of-experts (MoE) language models route each token to multiple experts, suggesting a geometric account of their benefit: co-selected experts should contribute distinct representation directions. Existing evidence often conflates route coherence, candidate quality, and candidate-by-context interaction. We distinguish these quantities using an Expert Subspace Separation Index (ESSI), matched-route residuals, and a prefix-controlled

2\times2

factorial; frozen-route interventions and a controlled Top-

k

study assess functional value. Three paired contrasts organize the findings. First, across six MoE architectures, expert subspaces overlap substantially, yet actual routes explain token representations better than matched alternatives. Second, across the 39 factorial cells in OLMoE, Mixtral, and DeepSeek, the selected candidate explains more of the residual representation than the strongest unselected rival in every cell, yet the actual prefix narrows this advantage throughout: all interactions are negative, and every 95% confidence interval lies below zero. Third, this geometric narrowing does not imply functional redundancy: adding later experts improves next-token prediction in 24 of 39 frozen-route comparisons, while the other 15 estimates are inconclusive; a controlled training study also favors Top-2 over Top-1 in all three seeds. We call this joint pattern coherent overlap: routing selects token-relevant experts from a shared geometric neighborhood, while useful multi-expert computation persists without disjoint linear coverage. Separating these quantities clarifies why geometric similarity alone cannot determine redundancy or pruning value.

Huiyuan Tian, Bonan Xu, Shijian Li

College of Computer Science and Technology, Zhejiang University, Hangzhou, China · Department of Aeronautical and Aviation Engineering, The Hong Kong Polytechnic University

Sparse Mixture-of-Experts Expert Routing Representation Geometry in Language Models