Sparse Mixture-of-Experts

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

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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 5, 2026cs.LG

Distributionally Robust Mixture-of-Experts Training

Mixture-of-Experts (MoE) transformers scale capacity by activating only a few experts per token, but this sparsity creates a hidden reliability problem: when routing is imperfect, load-balanced models may send tokens to experts that are insufficiently trained for the assigned inputs. We propose Distributionally Robust MoE Training (DRMoET), a drop-in objective that treats layer-wise experts as endogenous robustness groups and optimizes high-loss routing outcomes rather than merely equalizing traffic. DRMoET updates a per-layer expert distribution by an entropy-regularized softmax rule on EMA-smoothed, activation-weighted expert losses, strengthening plausible non-top routing paths while preserving standard MoE computation. Under the FLAME-MoE recipe at 746M-total and 10.3B-total scales, DRMoET improves downstream averages over both standard FLAME-MoE and auxiliary-loss-free balancing. At 10.3B total parameters and 67B training tokens, DRMoET improves the seven-task average from 0.6625 to 0.6767, while the auxiliary-loss-free baseline achieves 0.6431. Mechanistic analyses show lower expert-loss variance with nearly unchanged mean loss, 4.3% lower excess loss under forced mid-

k

misrouting, and improved domain-expert specialization. These results position routing robustness-not only utilization balance-as a practical objective for reliable sparse MoE scaling. Project page and code are available at: https://drmoet.github.io/.

Xin Teng, Muxiao Li, Hongyi Wen

New York University Center for Data Science, NYU Shanghai

Mixture-of-Experts Language Models Sparse Mixture-of-Experts Distributionally Robust Optimization Mixture-of-Experts Models

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

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.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 28, 2026cs.LG

How to Loop MoE: Flatten the Experts, Untie the Attention

Looped Transformers reuse one block of layers several times: by spending extra computation they push a model of fixed size further, and so use its parameters more fully; while sparse mixture-of-experts (MoE) models activate only a few of many experts for each token. Looped MoE bridges these two design philosophies and gives MoE models new potential for better expert usage, but it raises a question: how to loop a MoE? We answer it with Foil. With the expert parameters and the expert compute per token held fixed, Foil (1) flattens the experts, halving the expert layers, doubling the experts per layer and doubling the passes, so that every routing decision chooses from a larger pool, and (2) unties the attention, giving each pass its own attention parameters while the experts and routers stay shared. Experiments show that Foil clearly outperforms the unflattened looped baseline: at 20B tokens every Foil model has lower pretraining loss than the baseline; at 100B tokens the loss improves monotonically with the degree of flattening, the most flattened Foil ending 0.012 nat below the baseline at equal parameters and compute, with downstream accuracy on par or better; untying the attention also yields more balanced and more confident routing at equal shape. Our ablations analyse why Foil works and turn the findings into design guidance for looped MoE: the returns of looping and of widening the expert layers amplify each other, routing confidence tracks healthy expert use better than load balance, and a sparse looped MoE should therefore use more experts per layer and more passes. Code and configurations are available at https://github.com/SR-A-W/how-to-loop-moe.

Shouren Wang, Chuang Ma, Mohsen Hariri +6

Case Western Reserve University · Kyoto University · NII LLMC

Mixture-of-Experts Language Models Sparse Mixture-of-Experts Transformer Attention Recurrent Transformers

Sep 17, 2026cs.LG

OceanMoE: Structured Conditional Sparse Computation for Long-Horizon Multivariate Ocean Forecasting

Multivariate ocean forecasting must exploit shared evolution in a coupled ocean system while adapting to the heterogeneous statistical and dynamical characteristics of different prediction variables and locations. Fully shared models may lack the flexibility to handle this heterogeneity, whereas fully independent models discard the common ocean context shared across variables. The key question is how to retain shared context in a unified model while allowing computation to specialize according to the prediction target and local state. We propose OceanMoE, a structured conditional sparse Mixture-of-Experts framework that combines sharing and specialization for multivariate ocean forecasting. OceanMoE fuses cross-variable information to construct target-specific local representations and uses them to perform content-conditioned sparse routing at each spatial location, with the number of active experts adapted to router confidence. In the decoder, routing is augmented with a learned geographic bias parameterized by spherical-harmonic spatial bases, while shared residual and seasonal pathways provide common cross-variable and month-dependent context. Experiments on long-horizon autoregressive ORAS5 forecasting show that OceanMoE lowers aggregate forecasting error in both evaluated settings and maintains lower geometric-mean normalized RMSE than the corresponding baselines over most later rollout months. Routing analyses further show that expert allocation varies with prediction targets and spatial locations. These results support structured conditional computation as a modeling strategy for balancing shared ocean context with adaptive specialization.

Yishun Zhu, Jian Wang

Hangzhou Institute for Advanced Study, University of the Chinese Academy of Sciences Zhejiang, China · Computer Network Information Center, Chinese Academy of Sciences Beijing, China

Multivariate Time Series Forecasting Long-Term Time Series Forecasting Sparse Mixture-of-Experts Spatiotemporal Forecasting

Sep 16, 2026cs.LG

MoRE: Mixture of Reused Experts

Mixture-of-Experts (MoE) architectures decouple model capacity from computational cost, yet incur high memory footprints as parameters grow linearly with the number of experts. Recurrent Transformers achieve parameter efficiency by reusing layer weights, but typically lack the capacity for competitive language modeling. We propose Mixture of Reused Experts (MoRE), a hybrid that shares expert pools across groups of adjacent layers. Each layer retains its own router but selects from a larger shared pool, expanding the diversity of routing combinations without additional parameters. To enable shared experts to distinguish between layers, we introduce lightweight learnable depth embeddings that condition each layer's input before routing. Experiments across three model scales (114M-1.15B parameters) show that MoRE consistently achieves lower perplexity and stronger downstream performance than standard MoEs and state-of-the-art weight-sharing architectures at matched compute and parameter budgets, with only minimal modifications to existing MoE implementations.

Eric S. Qiu, Utku Umur Acikalin, Justin Lovelace +4

Department of Computer Science, Cornell University

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

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.CV

ExpertHTR: Unified Handwritten Text Recognition with Multi-Task Learning and Sparse Mixture-of-Experts

Handwritten text recognition resources are often small and distributed across collections that differ in language, script, document structure, and annotation format, making joint page-level training difficult. We propose ExpertHTR, a unified vision-language framework that addresses this problem through complementary supervision and conditional model capacity. Structural annotations from heterogeneous datasets are first organized through a common Page-Region-Line representation and used to construct four related training tasks for complete transcription, physical-line coverage, text localization, and localized recognition, without requiring additional manual labels. Building on a jointly trained dense model, ExpertHTR introduces a sparse Mixture-of-Experts architecture with an always-active shared branch and conditionally routed full-MLP experts. Sparsegen allows the number of active routed experts to vary with the hidden representation, while routing regularization reduces persistent concentration on a small subset of experts. Experiments on seven heterogeneous handwriting benchmarks show that complementary supervision consistently improves training with page transcription alone, while joint multi-source training provides further gains on most datasets. The proposed sparse expert model further improves the dense baseline on six of the seven sources. The final unified model also substantially outperforms the evaluated general-purpose OCR and vision-language systems on most benchmarks and achieves state-of-the-art performance on the IAM paragraph-level benchmark, while specialized HTR systems remain stronger on several challenging collections.

Dang Hoai Nam, Nguyen Duy Hieu, Quang Huu Hieu +1

University of Information Technology, Ho Chi Minh City, Vietnam · Vietnam National University, Ho Chi Minh City, Vietnam · AJ Technologies, Nagoya, Japan +1

Vision-Language Models Sparse Mixture-of-Experts Multi-Task Learning

Sep 10, 2026cs.LG

Data Scarcity and Model Sparsity: Mixtures-of-Experts Overfit More to Repeated Data

As the supply of human-written text is exhausted, it has become standard practice to repeat language model training data. Prior work has studied data repetition for densely activated Transformers, but the effects of data repetition remains largely unexplored for recently dominant sparse architectures such as Mixture-of-Experts (MoE), despite their increased compute efficiency. We vary data repetition rates across single- and multi-domain data mixes, and across MoE settings, including expert count and granularity. We consistently find, for models ranging from 80M to 1B active (8.5B total) parameters, that MoEs degrade more rapidly under data repetition. This effect increases with sparsity, dictated by total rather than active parameters. While 80M dense models can repeat data over 8x with minimal degradation, MoEs instead begin to suffer at 4x, and deteriorate rapidly, ceding their performance benefits in all-unique data settings to underperform dense models after 32x. We experiment with existing regularization methods as a potential remedy. We find that some methods, such as dropout, can mitigate overfitting. In particular, with strong masking-based regularization, MoEs are able to outperform dense models even when data is repeated more than 64 times. However, no method fully matches the performance of all-unique training data. Finally, we analyze internal mechanisms correlated with MoE overfitting in high repetition regimes, and find that MoE routing universally stabilizes early in training, and that expert specialization correlates with overfitting to repeated data. In sum, our work addresses the adverse interactions between sparsity and data repetition: we present evidence for the core mechanisms of overfitting and its potential remediation, and suggest promising avenues for future methods to reduce over-specialization in model parameters by disrupting memorization patterns.

Atindra Jha, Margaret Li, Jure Leskovec +2

Stanford University · Paul G. Allen School of Computer Science, University of Washington

Mixture of Experts Sparse Mixture-of-Experts LLM Training Data Repetition in Language Model Training

Sep 10, 2026cs.LG

Distribution-Consistent Inference for Dynamic Sparse Mixture-of-Experts

Mixture-of-Experts (MoE) architectures have emerged as a powerful paradigm for scaling model capacity while preserving efficient inference in large foundation models. However, most MoE models use a fixed top-

k

expert selection policy, assigning the same expert budget to every token even when fewer experts may be sufficient. Inference-time dynamic top-

k

routing can reduce computation without retraining, but existing methods often overlook the distributional shift caused by deviating from the training-time routing configuration. We show that reducing the number of activated experts consistently increases the RMS scale and variance of SMoE outputs, inducing a representation mismatch that contributes to downstream performance degradation in addition to the loss of expert capacity. To address this correctable component, we propose Layer-wise Distribution Alignment (LDA), a lightweight inference-time correction that uses layer-wise calibration statistics to align reduced-routing representations with the default configuration. Across multiple SMoE LLMs, benchmarks, and routing strategies, LDA recovers much of the performance lost induced by the distributional shift under reduced routing while preserving sparse-inference efficiency with negligible overhead.

Dohyeon Kim, Bedionita Soro, Sung Ju Hwang

KAIST

Parameter-Free Mixture-of-Experts Routing Sparse Mixture-of-Experts Mixture-of-Experts Inference LLM Inference Acceleration Mixture-of-Experts Models

Sep 8, 2026cs.LG

Hyperparameter Scaling Laws Across MoE Sparsity

Mixture-of-Experts (MoE) models expand model capacity without a proportional increase in training compute, but increasing sparsity makes reliable hyperparameter transfer challenging. In this work, we show that conventional hyperparameter scaling laws are insufficient for ultra-sparse MoEs: the optimal learning rate and batch size vary with activation ratio, and these shifts cannot be explained by either total or activated parameter count alone. To characterize this dependence, we conduct 1,800 pre-training runs spanning six activated-parameter scales and models with up to 6B total non-embedding parameters, processing approximately 20 trillion tokens at a cost of 200,000 equivalent H800 GPU-hours. Our results reconcile conflicting findings in prior work by revealing two scaling regimes. At fixed sparsity, the optimal batch size follows a power-law relationship with training tokens

D

, whereas the optimal learning rate scales with training compute

C

and remains robust to the allocation between model size and data. Across sparsity levels, the activation ratio

A

enters both relationships as an additional multiplicative power-law factor. These observations lead to unified hyperparameter scaling laws that transfer across MoE sparsity levels. Large-scale evaluation shows that the scaling form outperforms alternative functional forms. On a held-out ultra-sparse MoE with 12B total parameters and only 1/64 of its experts activated, the predicted hyperparameters remain close to the observed optima, supporting joint extrapolation across model scale and sparsity. Further experiments demonstrate transfer across expert granularities and isolate the effect of activation ratio from that of total expert count.

Changxin Tian, Kunlong Chen, Jia Liu +3

Ling Team, Ant Group

Language Model Scaling Laws Sparse Mixture-of-Experts Hyperparameter Transfer Scaling Laws Mixture-of-Experts Models

Sep 3, 2026stat.ML

Towards a Statistical Understanding of Mixture-of-Experts

Mixture-of-experts (MoE) architectures increase model capacity by combining a collection of expert predictors through input-dependent routing, while often activating only a small subset of experts for each input. Despite their growing importance in modern large-scale models, the statistical roles of their design choices, especially routing, sparse activation, and shared experts, remain only partially understood, as existing theory has largely focused on parametric or correctly specified MoE models. In this paper, we view MoE as a form of localized aggregation and show how this localization reshapes the approximation-estimation-computation tradeoff. We derive oracle risk bounds for learning dense and sparse routing with evolving experts, separating approximation, expert-learning, and router-estimation errors, and characterize how sparse Top-K routing can retain the benefits of localized aggregation while controlling per-input computation. We also interpret gating through the geometry of input space, relating routing performance to regions of local expert advantage, and show how shared experts, as adopted in architectures such as DeepSeekMoE, can extract common predictive structure so that routed experts focus on residual local variation. Together, these results provide a unified statistical framework for understanding MoE through input-dependent expert aggregation, in which expert specialization and computational tradeoffs are governed by local predictive structure.

Siyuan He, Bokai Yang, Jie Hu +2

Qiuzhen College, Tsinghua University, Beijing, China. · KLATASDS-MOE, School of Statistics, East China Normal University, Shanghai, China. · Yau Mathematical Sciences Center, Tsinghua University, Beijing, China. +1

Mixture of Experts Sparse Mixture-of-Experts Mixture-of-Experts Models Statistical Learning Theory

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

Aug 31, 2026cs.NI

WiSDoM: Wireless Sparse Decision Transformer with Mixture-of-Experts for Multi-Task Mobile Network Optimization

Emerging 6G wireless networks are expected to operate across diverse deployment scenarios, where variations in network topology, user mobility, traffic demand, and radio conditions challenge the scalability of conventional radio resource management (RRM). While offline reinforcement learning (RL) methods have demonstrated strong decision-making capabilities, learning a single policy that performs consistently across heterogeneous wireless environments remains difficult due to conflicting optimization objectives and limited model specialization. These challenges become particularly pronounced in coordinated multipoint (CoMP) transmission, where selecting the optimal serving-cell combination requires sequential decision-making under evolving network conditions. This paper presents the Wireless Sparse Decision Transformer with Mixture of Experts (WiSDoM), a sparse multi-task offline RL framework for adaptive multi-cell selection. WiSDoM combines Decision Transformers (DTs) with a Mixture-of-Experts (MoE) architecture that dynamically activates specialized experts according to task characteristics. This MoE mechanism improves model capacity without proportionally increasing inference cost, mitigates negative transfer, and enables expert specialization across tasks. WiSDoM is trained jointly on diverse network configurations spanning multiple base station and user equipment densities, mobility levels, and scheduler policies. Experimental results show that WiSDoM consistently outperforms heuristic methods, single-task models, and conventional multi-task DTs, improving quality of experience (QoE) by up to 55% while activating approximately one-third of the parameters of its dense counterpart during inference. Furthermore, WiSDoM exhibits strong task generalization and efficiently adapts to unseen wireless scenarios through few-shot prompting without retraining or fine-tuning.

Fatih Temiz, Shavbo Salehi, Melike Erol-Kantarci

School of Electrical Engineering and Computer Science, University of Ottawa, Ottawa, Canada

Sparse Mixture-of-Experts Decision Transformer Offline RL Multi-Task RL Wireless Resource Allocation

Aug 13, 2026cs.SD

HybridSB-MoE: Dual-Domain Schrödinger Bridges with Scene-Adaptive Expert Routing for Speech Enhancement

Generative speech enhancement faces three gaps: spectral models capture harmonic structure but often disrupt phase, waveform models preserve phase but miss harmonics, and Schrödinger Bridges (SB) shorten transport from noise to clean speech but leave inference cost only loosely tied to training. We propose HybridSB-MoE, a dual-domain framework that fills these gaps through three contributions unified by a single asymmetric design principle. (i) Asymmetric uncertainty fusion: The spectral path captures epistemic uncertainty via expert disagreement, while the waveform bridge models aleatoric variance through stochastic dynamics. We fuse them asymmetrically, allowing the mixing weight to adapt to distinct error regimes rather than average predictions. (ii) Heterogeneous MoE with top-k=2 routing across five distinct architectural archetypes, where architectural diversity makes the epistemic signal indicate which inductive bias fails rather than small perturbations among similar experts. (iii) Discretization bound (Theorem 1): path-consistency and trajectory regularizers together bound the K-step bridge sampling error in 2-Wasserstein distance at rate K-alpha, making small-K inference an objective-level guarantee rather than an empirical claim. On VoiceBank+DEMAND, HybridSB-MoE outperforms diffusion- and SB-based baselines at their step budgets while remaining competitive with consistency-distilled few-step methods.

Zhengyi Lu, Aswini Sivakumar, Jie Hu +1

Department of Computer Science and Engineering, Oakland University, Rochester, MI 48309

Sparse Mixture-of-Experts Schrödinger Bridges Speech Enhancement

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 12, 2026cs.CV

STAR: A Spatial-Topology Aware Routing Framework for Generalizable 3D Scene Understanding

Constructing a unified 3D scene understanding model has long been hindered by the topological discrepancies across sensor modalities. While applying the Mixture-of-Experts (MoE) architecture is a flexible approach for multi-domain 3D understanding, we observe that conventional feature-only MoE routers may underrepresent local sampling topology under semantic supervision, making expert allocation difficult when semantic consistency coexists with geometric heterogeneity. To overcome this challenge, we propose STAR (Spatial-Topology Aware Routing Framework). Specifically, we introduce a multi-attribute self-supervised pre-training branch, covering topological and textural variations, to anchor cross-domain structural priors. Building upon this, we design a domain-aware expert branch with two mechanisms: Domain-Spatial-Guided Routing (DSR), which captures local topological variations from spatial context, and Entropy-controlled Dynamic Allocation (EDA), which adjusts the number of activated experts according to routing uncertainty. Together, these branches combine stable cross-domain representation learning with adaptive expert allocation. Extensive experiments across various tasks, encompassing both indoor and outdoor scenes, demonstrate the effectiveness of STAR. It achieves 80.1% mIoU on the ScanNet validation set and 77.2% mIoU on S3DIS, consistently improving over strong baselines. Code is available at our project page (https://xmw666.github.io/STAR/).

Mingwei Xing, Xinliang Wang, Yifeng Shi

KE Holdings Inc.

Sparse Mixture-of-Experts Domain Generalization 3D Semantic Segmentation 3D Representation Learning 3D Scene Understanding

Aug 10, 2026cs.CV

Disentangling Co-Occurring Retinal Pathologies with Saliency-Guided Sparse Expert Routing

Retinal fundus images frequently exhibit multiple co-occurring pathologies, yet standard deep learning classifiers apply static, identical computation to every image regardless of the underlying disease distribution. We propose a novel architecture that resolves this via sparse conditional computation, pairing a Guided Context Gating (GCG) spatial attention front-end with a sparsely-routed Mixture-of-Experts (MoE) block operating over feature tokens. Crucially, this routing yields an interpretable, data-driven decomposition. Expert allocation is significantly disease-dependent (p < 0.001), with the healthy Normal state and morphologically distinct pathologies (e.g., ERM, AMD) isolating to dedicated experts. On a five-class, patient-disjoint 5-fold cross-validation benchmark, our model achieves 0.912 +/- 0.008 macro AUC and 0.653 +/- 0.014 macro F1. Furthermore, Grad-CAM++ and post-MoE t-SNE visualizations confirm that expert routing aligns with localized lesions and geometrically maps co-occurring cases between their constituent clusters, positioning sparse MoE as an interpretable approach to multi-disease retinal screening.

Nagur Shareef Shaik, Jeongwoo Park, Yeong-Jin Kim +3

Department of Computer Science, Georgia State University, Atlanta, GA 30324, USA · Piehealthcare Inc., Suwon-si, Gyeonggi-do, 16311, Republic of Korea

Medical Imaging Sparse Mixture-of-Experts Medical Image Classification Fundus Imaging Explainable Medical Image Analysis

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 7, 2026cs.CR

Policy-Masked Private Experts: Auditable and Reversible Capability Access Control in Sparse MoE Models

Most language-model access controls regulate behavior while leaving the same computation available to every request. We study a different systems question: can trusted authorization determine which newly trained parameters are reachable by the forward pass? Policy-Masked Private Experts freezes a pretrained sparse Mixture-of-Experts (MoE) model, trains a disjoint expert branch, and selects the public or private pool before top-k routing. The resulting claim is narrow but testable: under the declared trusted computing base (TCB), an unauthorized request executes no private expert. It does not imply that the public model lacks the same semantic capability. We test this separation between execution control and task utility in Qwen3-30B-A3B and DeepSeek-V2-Lite. Three Qwen BF16 seeds update all 32 private experts while the public fingerprint remains unchanged. Across 64 adversarial scenarios and 96 deny/fail-closed events, unauthorized private execution is zero; independent hooks exactly match 11,616 routed private rows and allow-deny-allow recovery is exact. On two prospectively frozen Qwen benchmarks, the private branch improves exact tool use by 5.0 percentage points (pp) (five versus zero discordances; one-sided Holm p = 0.03125, corresponding two-sided exact p = 0.0625) and 21.3 pp (percentile-bootstrap 95% CI [13.3, 29.3], Holm p = 0.000031). Three arm-blinded model evaluators retain a positive external effect of 18.7 pp (95% CI [9.3, 28.0]). A parameter-matched Lora has similar external utility, but a post-hoc request gate leaves 1,225 adapter calls under deny; the disjoint expert branch leaves none. DeepSeek reproduces the route invariant and gains 27.0 pp. A valid sealed evaluation is near-neutral. These results support auditable, reversible control over a trained parameter path, while showing that useful transfer remains distribution dependent.

Zhuoheng Huang, Mukesh Singh

Independent Researcher

LLM Auditing Sparse Mixture-of-Experts LLM Security Mixture-of-Experts Models

Aug 2, 2026cs.CV

One Query, Many Scales: Sparse Mixture-of-Experts for Efficient Hierarchical Cross-View Geo-Localization

Cross-view geo-localization (CVGL) retrieves geo-tagged satellite imagery for a ground-view query. Most systems exhaustively search a flat, fixed-resolution gallery, incurring high cost over large areas and adapting poorly to satellite resolution changes. Autoregressive coarse-to-fine alternatives reduce comparisons but bind later predictions to earlier decisions and a predefined hierarchy. We introduce GeoMoE, a sparse mixture-of-experts dual encoder that decouples global multi-scale representation learning from local hierarchical search. Global multi-scale supervision and content-adaptive routing map ground and satellite images across resolutions into a globally comparable embedding space. At inference, each image is encoded once, and probabilistic beam search follows parent--child links to score a small candidate subset. Later levels reuse these descriptors rather than features generated by preceding levels, limiting feature-level error propagation and hierarchy coupling. We further introduce VIGOR-M, a four-city benchmark with an explicit parent--child satellite hierarchy and held-out half-step galleries for single-resolution, cross-resolution, and hierarchical evaluation. GeoMoE achieves 95.78% R@40m on Just Zoom In, 2.77 percentage points above the previous best, and 62.39% R@1 on VIGOR-M. The latter requires 0.885 MMAC/query for descriptor matching, 5.27% of an exhaustive L3 scan, while exceeding the strongest exhaustive baseline by 3.12 percentage points in R@1. One model trained on L1, L2, and L3 also outperforms a matched dense control across all six galleries and transfers to three withheld resolutions. By decoupling globally trained embeddings from local hierarchical search, GeoMoE jointly improves localization accuracy, search efficiency, and cross-resolution transfer.

Ruijie Fan, Junyan Ye, Qi Zhu +1

Tsinghua Shenzhen International Graduate School, Tsinghua University · School of Geospatial Engineering and Science, Sun Yat-sen University

Cross-View Geo-Localization Geospatial Representation Learning Sparse Mixture-of-Experts Remote Sensing Benchmarks

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

Jul 30, 2026cs.LG

From Expert Reduction to Behavioral Divergence: Tracing Numerical State through Sparse MoE Inference

Mathematically equivalent expert-reduction orders can produce observably different sparse-MoE executions. We isolate this effect in native DeepSeek-V4-Flash by freezing local MoE state and varying only aggregation semantics. Four schemes separate operand representation from accumulator precision. At one layer-5 fork, 720 A-mode orders yield 10 continuation basins; 720 B-mode orders form 360 exact structural classes and 11 basins. Under one Chinese prompt, the B classes split into 202 layoffs, 113 hiring, and 45 other continuations. Maximum-L-infinity B-branch selection separates 12, 24, and 36 of 50 prompts by 8, 16, and 32 tokens. Across 192 persistent trajectories per scheme, P32, A, and B change every native-reference route trajectory, while C preserves routes, token sequences, and texts. A separate 192-trajectory C check matches native MoE, post-mHC, next-router, and LM states bitwise. For one controlled B branch, exact post-mHC endpoint reconstruction reproduces the measured downstream trajectory. At the next decode boundary, exact FP64 reconstruction of the branch's full persistent state yields agreement for 301 downstream post-mHC states, 301 persistent-state checkpoints, 301 routes, predictions, and text over seven steps, given the same naturally generated next input. These controls identify post-mHC as an intra-token boundary and full persistent state as a cross-token continuation boundary. Identical tokens need not imply identical autoregressive state: divergence can survive a token boundary and become visible later. These results make expert operand conversion, accumulator precision, and reduction order part of a numerical compatibility contract for sparse-MoE runtimes and hardware backends. They establish controlled causal possibility, not deployment incidence; C's order invariance is limited to evaluated six-term states and schedules.

Tianyang Zhu

Independent Researcher

Sparse Mixture-of-Experts Mixture-of-Experts Inference State Tracking ML Reproducibility

Jul 29, 2026cs.LG

TIER-MoE: Trust-Informed Expert Routing via Conditional Modality Risk for Multimodal Fusion in Biomedical Classification

The promise of multimodal fusion lies in combining complementary sources of evidence, yet more evidence does not always yield a better prediction. Recent multimodal models have advanced fusion through richer cross-modal interaction and sample-adaptive fusion. However, the influence assigned to a modality during fusion does not reveal whether that source is unreliable, redundant, or poorly matched to a specialized expert. To address this limitation, we introduce TIER-MoE, a risk-guided subspace mixture-of-experts model that defines sample-specific modality reliability as the prediction loss its unimodal predictor is expected to incur. This risk is learned from out-of-fold predictions generated by models that were not trained on the corresponding sample. TIER-MoE combines the estimated risk with expert-specific subspace compatibility for sparse modality-expert routing, while an always-active shared path preserves multimodal complementarity. We evaluate TIER-MoE on four public multimodal biomedical datasets spanning Alzheimer's disease status, skin-lesion malignancy, and retinal classification. Results demonstrate its superiority over state-of-the-art methods in predictive performance and probability calibration, with consistent improvements in Macro-F1 and Brier score and strong zero-shot generalization to an external cohort.

Yu Chang, Anzhe Cheng, Chenwei Wu +7

University of Southern California · University of Michigan · 3The University of British Columbia +1

Sparse Mixture-of-Experts Multimodal Classification Mixture-of-Experts Models Multimodal Fusion

Jul 7, 2026cs.CV

SpecTrack: Spectral Prompt Guided Adaptive Experts for Multispectral Object Tracking

Multispectral image(MSI) and hyperspectral image(HSI) object tracking object tracking exploits recorded band-wise observations to improve target--background discrimination under similar RGB appearance, mixed pixels, illumination variation, occlusion, and clutter. However, existing trackers commonly process all search regions through a fixed capacity spectral--spatial path, ignoring that tracking difficulty varies substantially across frames and target states. Clear regions may require only lightweight local discrimination, whereas ambiguous boundaries and spectrally similar distractors often demand stronger contextual reasoning. To address this limitation, we propose SpecTrack, a spectral--spatial complexity-aware tracker that formulates MSI tracking as search-region-level adaptive capacity allocation. Its core component, the Spectral Adaptive Mixture-of-Experts (SAMoE) module, provides a capacity-ordered expert pool with progressively increasing latent rank, receptive field, and depth. Expert selection is guided by a Spectral Prompt Router, which fuses semantic context, spatial boundary cues, and a latent channel-variation cue computed after multispectral patch embedding to activate a sparse subset of SAMoE experts for each search region. In parallel, a Shared Global Expert supplies common latent spectral--spatial context to reduce fragmented sparse-routing decisions. Experiments on MUST, MSITrack, and HOTC20 demonstrate a favorable accuracy--efficiency trade-off. The accuracy-oriented SpecTrack-L384 achieves state-of-the-art or highly competitive AUCs of 65.2%, 51.9%, and 72.6% on the three benchmarks, while the balanced SpecTrack-B224 reaches 62.4% AUC at 43.7 FPS on MUST. An additional GOT-10k evaluation indicates RGB-domain architectural generalization, with SpecTrack-L384 achieving 79.3% AO.

Xingyu Tan, Yunrong Qin, Mengjie Hu

Beijing University of Posts and Telecommunications, China

Visual Object Tracking Sparse Mixture-of-Experts

Jul 7, 2026cs.LG

TriRoute: Unified Learned Routing for Joint Adaptive Attention, Experts, and KV-Cache Allocation

Conditional computation can decouple language model quality from per-token inference cost, yet leading techniques act on a single axis in isolation: Mixture-of-Experts (MoE) sparsifies the FFN, Mixture-of-Depths (MoD) skips whole transformer blocks, and KV-cache quantization compresses attention memory. We argue these three decisions (attention resolution, expert selection, and cache bit-width) are strongly coupled and should be made jointly: a token rare enough to warrant full attention may also need high-precision caching regardless of which expert processes it. We introduce TriRoute, a single lightweight controller shared across all three axes that, for every token at every layer, emits a coordinated policy: (i) an attention mode (skip/local/full), (ii) a sparse set of FFN experts (with a null expert recovering MoD), and (iii) a KV-cache bit-width. The controller trains end-to-end via a heterogeneous relaxation (Gumbel-Softmax with straight-through estimation for categorical decisions and load-balanced top-k gating for experts) under a Lagrangian budget constraint that turns the average compute and memory cost into a controllable knob. We identify a cross-axis routing-collapse cascade in naive joint training, where collapse on one axis propagates to the others, and address it with per-axis normalization and a coupling-aware balancing loss. On decoder-only models from 160M to 1.3B parameters at compute-optimal token counts, TriRoute Pareto-dominates the best independent MoD+MoE+KV-quantization combination at matched inference FLOPs and memory, while better preserving tail-case robustness on rare entities, code, and arithmetic that pure perplexity optimization erodes. Post-hoc analysis reveals interpretable structure: the controller allocates full attention and high-precision cache to sentence-initial positions, rare subwords, and named entities, while cheaply routing function words.

Andrii Balashov, Olena Ponomarova

Ukrainian State University of Science and Technologies

Sparse Mixture-of-Experts LLM Routing KV-Cache Quantization Conditional Computation

Jul 2, 2026cs.AI

Generic Expert Coverage for Pruning SparseMixture-of-Experts Language Models

Sparsely activated Mixture-of-Experts (MoE) language models contain substantial structured redundancy among routed experts, but pruning them without downstream calibration data remains challenging. Existing expert-pruning methods typically rely on a single aggregated importance score, which can bias the retained set toward experts favored by dominant calibration patterns. We propose \textbf{Generic TB-Coverage}, a coverage-aware expert pruning method that uses only generic text corpora (WikiText2 and C4) for calibration. Instead of collapsing expert utility into one score, our method profiles per-expert utility separately on each corpus and enforces a fixed-budget coverage rule that preserves high-utility experts from each corpus before constructing the final pruning mask. Across Qwen1.5-MoE-A2.7B and DeepSeek-MoE-16B-Base at 25%, 50%, and 75% retention budgets, our method improves average accuracy on six common zero-shot benchmarks over random pruning, REAP, and ExpertSparsity, while also reducing perplexity degradation on WikiText2 and C4. The gains are largest under aggressive pruning (25% and 50% retain), suggesting that preserving cross-corpus expert coverage is an effective generic-data prior for MoE pruning. Our improvements hold with fixed pruning budgets and no downstream calibration data.

Yongqin Zeng, Sicheng Pan, Jiale Wang +4

Mixture-of-Experts Pruning LLM Pruning Mixture-of-Experts Language Models Sparse Mixture-of-Experts Neural Network Pruning