Mixture-of-Experts Models

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Period ending 2026-09-21

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419 papers

Latest in Mixture-of-Experts Models

Jun 21, 2026cs.LG

Training-free Task Classification for Multi-Task Model Merging

Ever since the advent of foundation models and the pre-training-finetuning paradigm, there have been numerous efforts to merge multiple task-specific experts into a single multi-task model. Prior work largely focuses on finding a single merged model, but it often underperforms individual experts due to parameter interference. To resolve this, dynamic model merging employs routing to activate task-relevant parameters per input. However, existing routers typically require either additional training with abundant labeled datasets or assume the access to task IDs of each input at inference time. In this work, we aim to close the gap to expert performance without additional training or task-ID-access assumption. To this end, we formulate routing as training-free task classification for each test input. Using singular value decomposition (SVD)-based low-rank manifold approximations for each task, SiM scores tasks by the projection residual of the test input feature onto each task manifold and routes accordingly. The task manifolds are pre-computable offline from a pretrained backbone using a small per-task support set (e.g., 32 examples per task) prior to merging process, requiring no router training and no data during the merging process. Moreover, SiM integrates seamlessly with subspace-/mask-based merging that represents task-expert via lightweight compressed task vectors, avoiding the need to store full expert parameters. Experiments across computer vision and natural language processing benchmarks under task-unknown inference demonstrate that SiM substantially improves merged-model performance and consistently narrows the gap to individual task experts.
Jungyong Son, Jinwook Jung, Sungyong Baik
Jun 21, 2026cs.LG

Systematic Exploration of 4-Expert Heterogeneous Mixture-of-Experts via Automated Pipeline Search

We present an automated large-scale search pipeline for heterogeneous 4-Expert Mixture-of-Experts (MoE4) architectures within the LEMUR neural network dataset ecosystem. Building on a hand-crafted heterogeneous MoE reference model, we replace manual design with a deterministic code-assembly generator that systematically combines base architecture families drawn from the LEMUR database into MoE4 ensembles, each governed by a convolutional gating network with temperature scaling, mixup augmentation, and cosine-annealed learning rate scheduling. Over a 28-day campaign on an NVIDIA RTX 4090, the pipeline generated 4,463 candidate models across 197 batches, of which 1,021 were evaluated successfully. A critical finding emerged from the campaign: due to alphabetical enumeration via itertools.combinations, the entire explored search space (4.8% of the theoretical 23,751 possible 4-family combinations) is anchored to a single family, AirNet. We characterise this coverage bias precisely, identify the root cause in the generator, and propose a stratified random sampling fix. Within the AirNet anchored scope, ShuffleNet and MobileNetV3 consistently co-produce the highest-accuracy ensembles (mean accuracy up to 0.632), while FractalNet and MNASNet are identified as low-yield families warranting exclusion in future campaigns. The pipeline, analysis artefacts, and corrected generator are released as part of the open-source NNGPT project at https://github.com/ABrain-One/nn-gpt
Yashkumar R Lukhi, Harsh Rameshbhai Moradiya, Radu Timofte +1
Jun 20, 2026cs.LG

WiSP: A Working-Set View of Mixture-of-Experts Serving on Extremely Low-Resource Hardware

Modern local and agentic workloads often need large-model capacity at low concurrency, but run on GPUs that cannot keep a frontier-scale model resident. Mixture-of-Experts (MoE) models are a natural fit because they activate only a small subset of experts per token, but their sparsity saves computation, not residency: the full expert pool still has to be stored, and any expert used by a layer must be in GPU memory when that layer runs. Static layer-level CPU offload makes such models fit, but transfers the expert layer in bulk on every forward pass, losing much of the sparsity advantage. We view low-resource MoE serving as a working-set problem on the GPU. Routed expert weights and the KV cache are two memory-demand streams competing for the same limited VRAM. We implement this view in WiSP (Working-Set Paging), a routing-aware expert pager that plugs into an unmodified serving engine and preserves byte-identical outputs. On a real 24 GiB RTX 3090, WiSP achieves up to 2.0x the decode throughput of static offload at the same memory budget when the model does not fit. A natural next step is to predict future experts and prefetch them. We find that this does not help in single-stream decode: the bottleneck is PCIe bandwidth, not prediction quality, so speculative transfers compete with demand transfers instead of hiding them. This shifts the design question from prefetching to allocation: how should one VRAM budget be divided between resident experts and the KV cache? We answer with MV-WSA (Marginal-Value Working-Set Allocation), which splits memory by marginal latency benefit per byte while enforcing a KV-admission floor. As a startup configurator, MV-WSA is the only policy we test that stays near-best on both prefill and decode; as a live controller, it resizes both pools while serving and reduces end-to-end time by up to 1.19x over a fixed offline split, without changing model outputs.
Jiamu Zhang, Liang Wu, Mayank Darbari +1
Jun 19, 2026cs.PF

Does Mixture-of-Experts Actually Help Inference on Consumer and Edge Hardware? An Empirical Study

Mixture-of-Experts (MoE) language models are often described as ideal for resource-constrained inference. Each token activates only a small subset of experts, so the per-token compute cost, in floating-point operations (FLOPs), resembles that of a much smaller dense model. Whether that FLOP advantage survives in practice is far less clear. We ask whether MoE models actually run faster and cheaper than comparable dense models on consumer-grade and edge hardware. We benchmark OLMoE-1B-7B (1.3 B active of 6.9 B total) against three dense baselines on an Apple M2 Pro and an NVIDIA Jetson Orin Nano 8 GB through llama..cpp, measuring throughput, memory, and on-device energy. The answer is device-dependent: OLMoE's active-parameter advantage is only partly realised on the laptop (~10% behind the same-active Llama-3.2-1B) and erodes on the edge device (~31% behind, at 2.1×\times the energy per token, with peak memory at the 8 GB ceiling). Patching llama..cpp to time the decode graph node-by-node shows routing accounts for under 9% of MoE-block compute on the cleaner edge backend, so the gap reflects total-parameter memory footprint, expert dispatch, and KV-cache pressure rather than routing. The implication is that on bandwidth-bound edge hardware, inference cost tracks total parameters, not active ones, and sparse activation does not buy back what the device is constrained on. These findings are bounded to one MoE model at this parameter scale and two devices, and we release the full measurement harness and per-run data.
Alfarizy Alfarizy, Hung Truong Thanh Nguyen, René Richard +2
Jun 19, 2026cs.RO

Factor-Aware Mixture-of-Experts with Pretrained Encoder for Combinatorial Generalization

The integration of pretrained encoders with diffusion policies has become a dominant paradigm for visual robotic manipulation. However, it still struggles to generalize across complex environments with varying factors such as lighting and surface textures. To address this, we propose FAME, a framework that integrates a factor-aware mixture-of-experts (MoE) with a pretrained encoder to enhance generalization to environmental variations. FAME follows a three-stage training process: (1) policy warmup, where a diffusion policy is trained on standard-environment data with a frozen encoder; (2) factor-specific adapter training, where lightweight adapters inserted between the frozen encoder and the temporarily frozen policy are trained on customized datasets, each targeting a distinct environmental variation; and (3) joint fine-tuning, where a central router and the warmed policy are trained on mixed data to handle multiple factors jointly. FAME is ``factor-aware'' because the central router softly weights frozen factor-specific adapters as a dense MoE, enabling combinatorial generalization across multiple factors. Evaluations on the Meta-World benchmark show that FAME outperforms diffusion policy baselines by 34%. We further validate FAME in a real-world pick-and-place task using a compact model trained on newly collected data, where FAME achieves a 35% improvement in generalization under real-world variations.
Feihong Zhang, Guojian Zhan, Zeyu He +8
Jun 19, 2026eess.IV

MoECodec: Image Compression for joint human and machine perception via Mixture-of-Experts

Image compression for machines calls for a unified codec that serves multiple downstream vision tasks. Existing approaches either adopt task-specific end-to-end designs, raising parameter and deployment overhead, or rely on transfer-based adaptations that remain externally attached and heuristic task design. A key limitation shared by both lines of work is their largely static computation pattern, which applies similar transformations across tokens despite the fact that different image regions exhibit markedly different semantic importance and complexity for machine perception. We propose MoECodec, a token-aware image compression framework that supports multiple downstream tasks within a single model. MoECodec replaces the FFN layers in transformer-based compression model token-wise Mixture-of-Experts (MoE), enabling dynamic, token-level computation conditioned on the input content and task objective. To make MoE effective in compression model, we introduce a stable routing strategy that combines expert-choice routing with spatial total variation regularization to encourage spatially coherent assignments, and we propose a lightweight expert architecture, Group Shuffle MLP (GShMLP), to control parameter growth. Extensive experiments show consistent improvement against baselines on both conventional image reconstruction and machine tasks.
Jiancheng Zhao, Xiang Ji, Yifan Zhan +2
Jun 18, 2026cs.LG

Grouped Query Experts: Mixture-of-Experts on GQA Self-Attention

Self-attention is central to Transformer performance and is often the most expensive part of the Transformer at long context lengths because its pairwise token interactions scale quadratically with sequence length. Standard dense attention also applies the same set of attention heads to every token regardless of token difficulty or information content. This uniform activation can waste compute, especially as sequences grow longer and attention cost increases rapidly. We propose Grouped Query Experts (GQE), a mixture-of-experts layer on top of grouped-query attention (GQA). Within each GQA group, a router selects k query-head experts per token while all key-value (KV) heads remain dense and unchanged. Thus, GQE keeps the KV cache benefits of GQA and reduces only the active query-head computation. On a fixed 30B token budget at the 250M parameter scale, GQE matches the all-active GQA baseline in downstream accuracy while activating half the query heads per token.
Vishesh Tripathi, Abhay Kumar
Jun 18, 2026cs.AI

Toward Calibrated Mixture-of-Experts Under Distribution Shift

Calibration aligns a model's predictive uncertainty with the frequencies of its empirical outcomes and is important for understanding and trusting reported probabilities. Recent work shows that enforcing calibration at the level of individual predictors can improve ensemble accuracy and calibration, with mixture-of-experts (MoE) models showing strong empirical improvements in particular; however, the conditions under which calibration helps MoE are not well understood. In this work, we study how MoE models behave under distribution shift, focusing on how routing mechanisms interact with expert-level calibration. We show that expert calibration is sufficient to ensure calibration of the overall model under a broad class of distribution shifts in hard-routed models, but is insufficient for calibrating soft-routed models. To address this, we propose an adversarial reweighting that penalizes calibration errors of the routed aggregate under distribution shift, and we demonstrate that it improves the accuracy-calibration tradeoff both on average and on difficult subsets of the data, across model classes, prediction tasks, and distribution shifts.
Gina Wong, Drew Prinster, Suchi Saria +2
Jun 17, 2026cs.RO

CTS-MoE: Implicit Terrain Adaptation via Mixture-of-Experts for Perceptive Locomotion

Perceptive legged locomotion over discontinuous terrain (e.g., stairs, gaps, and obstacles) requires adaptive behavior, as a single conservative gait cannot produce the anticipatory maneuvers needed for abrupt topology changes. Cast as multi-task reinforcement learning, this problem introduces a tension between sharing and separation. Tasks use a common locomotion base but have conflicting rewards, so a policy must share behavior while avoiding value interference. Prior work addresses only one side, with monolithic policies sacrificing specialization and hierarchical sub-policies sacrificing generalization across transitions and unseen terrain. We propose CTS-MoE, which combines a dense mixture-of-experts actor with perception-based gating to compose shared behaviors and a multi-critic with task-specific value heads to prevent interference. The model is trained end-to-end in a single-stage concurrent teacher-student setup that handles partial observability and avoids sequential distillation, with task labels used only during training. At deployment, routing depends solely on perception, allowing terrain adaptation without a high-level selector or terrain classifier. Experiments on a Unitree Go1 in simulation and on hardware across seen and unseen terrains show task-aware specialization, with lower tracking error and higher success rates than monolithic baselines. Project Website: https://cts-moe.github.io/ .
Francisco Affonso, Matheus P. Angarola, Ana Luiza Mineiro +3
Jun 17, 2026cs.LG

Geometric and Stochastic Analysis of Discontinuities in Sparse Mixture-of-Experts

Sparse Mixture-of-Experts (SMoE) architectures are now widely deployed in state-of-the-art language and vision models, where conditional routing allows scaling to very large networks. However, this very Top-kk expert selection that enables conditional routing also renders the SMoE map inherently discontinuous. In the vicinity of these discontinuity surfaces, even inputs that are arbitrarily close may activate substantially different sets of experts resulting in significantly different outputs. In this work we give a rigorous geometric and stochastic analysis of these discontinuities. We first classify them by order, determined by the number of tied experts at a switching event. Using measure-theoretic slicing arguments, we establish asymptotic volume estimates for the thickened discontinuity surfaces, showing that lower-order discontinuity sets dominate, whereas higher-order ones occupy a vanishingly small relative volume. Next, modeling random perturbations in the input space via a diffusion process, we prove that the path eventually encounter a discontinuity, and moreover that the first hit almost surely occurs on an order-1 discontinuity with explicit finite-time probability bounds. We further derive occupation-time bounds that quantify the duration the random path spend in the neighborhoods of each discontinuity order. These theoretical results imply that inputs are more likely to lie near lower order discontinuities. Motivated by this insight, we propose a simple smoothing mechanism that can be directly applied to existing SMoEs, softly incorporating experts near discontinuities; our analysis guarantees that the added computational overhead remains small while providing localized smoothing near discontinuities, and experiments across language and vision tasks show that smoothing not only enforces continuity of the SMoE map but also enhances empirical performance.
Tho Tran Huu, Huu-Tuan Nguyen, Thien-Hai Nguyen +4
Jun 17, 2026cs.LG

FoMoE: Breaking the Full-Replica Barrier with a Federation of MoEs

Pre-training Large Language Models (LLMs) typically demands large-scale infrastructure with tightly coupled hardware accelerators. Mixture-of-Experts (MoEs) architectures partially decouple model capacity from per-token compute. This efficiency alone does not make MoE training feasible over ordinary Internet links or loosely connected commodity hardware since active expert routing still assumes high-speed datacenter fabrics. Low-communication methods such as DiLoCo and Photon reduce synchronization frequency across distributed sites, mitigating bandwidth constraints, yet still require full model replicas at every site. This creates a mismatch: modern MoEs have sparse data paths, but their distributed training infrastructure remains communication-dense and memory-inefficient, limiting attempts to pool geographically distributed compute. In this work, we introduce FoMoE, a system that breaks the full-replica paradigm by partitioning expert layers across workers and skipping non-resident experts during local training. We demonstrate that FoMoE: (I) reduces communication costs by up to 1.42x over efficient baselines and 45.44x over Distributed Data Parallelism (DDP) via partial expert replication in controlled regimes; (II) achieves empirical throughput speedups of up to 1.4x through the skip-token mechanism; and (III) shows stable routing in the trained regimes and projects the communication/memory benefits to 100B-scale configurations through system modeling.
Lorenzo Sani, Zeyu Cao, Meghdad Kurmanji +5
Jun 17, 2026cs.NE

Model Merging to Evolution: Parameter Space Exploration for Expert Models

Model merging integrates the capabilities of multiple expert models to create strong models for multiple tasks without additional training, thereby reducing computational resource requirements. However, existing methods operate within the convex combination space of expert models, failing to explore high-performance regions outside this space. This paper proposes the MERGEvolve framework, which unifies model merging and evolution within an evolution strategy by treating the merged model as the initialization for evolutionary exploration of the parameter space. During the merging phase, expert models act as deterministic sources to build a strong initial point. The evolution phase then explores the parameter space using random noise. Theoretical analysis shows that MERGEvolve explores regions outside the convex combination space. Extensive experiments on single-task and multi-task benchmarks demonstrate that MERGEvolve consistently achieves performance competitive with advanced model merging baselines. Ablation studies confirm that a high-quality initial point is critical for efficient exploration of the parameter space.
Chao Wang, Yuchen Guo, Zheng Tan +4
Jun 16, 2026cs.LG

SoftMoE: Soft Differentiable Routing for Mixture-of-Experts in LLMs

Sparse Mixture-of-Experts (MoE) architectures enable scaling LLM parameters under a fixed inference budget by activating only a small subset of experts via top-kk routing. While this preserves causality and suits autoregressive language models, the discrete top-kk operator is not differentiable, forcing a fixed number of active experts per input and resulting in inefficient use of computation. We propose SoftMoE, which replaces discrete routing with a truncated soft top-kk LapSum relaxation, allowing gradient-based optimization of expert routing. We further parameterize the mean number of active experts per layer and impose a global budget constraint, enabling the model to learn how to allocate expert capacity across layers. SoftMoE remains fully compatible with autoregressive modeling and achieves performance comparable to or better than sparse MoE on language modeling and downstream tasks, while activating significantly fewer experts. Notably, the learned allocation is highly non-uniform, with later layers activating more experts. The source code is publicly available†^\dagger.
Mikołaj Zasada, Łukasz Struski, Jacek Tabor +1
Jun 16, 2026cs.LG

Attribution-Guided and Coverage-Maximized Pruning for Structural MoE Compression

Mixture-of-Experts (MoE) models scale compute efficiently, yet remain expensive to deploy due to their substantial memory footprint and inference overhead. Prior compression methods mainly operate at the expert level, either removing entire experts or ranking experts by coarse-grained importance scores. However, such expert-wise decisions are often too coarse to capture fine-grained redundancy, leading to misallocated pruning budgets and limited compression. To address this problem, we observe that information within MoE experts is highly concentrated in a small subset of channels, leaving substantial redundancy even in experts deemed important. Based on this observation, we propose a structural pruning framework tailored for MoE models. Our method reformulates prune-ratio allocation as a channel-score coverage maximization problem and solves it efficiently using an attribution-based approximation. Experiments on DeepSeek and Qwen MoE models show that our method preserves model accuracy under 50% or 25% structured pruning when combined with 4-bit quantization. On Qwen3-30B-A3B, our approach reduces memory footprint by 5.27×\times and consistently outperforms state-of-the-art baselines across diverse benchmarks.
Yifu Ding, Jiacheng Wang, Ge Yang +4
Jun 15, 2026cs.LG

SPRI: SVD-Partitioned Residual Initialization for Data-Constrained MoE Upcycling

Mixture-of-Experts (MoE) models enable efficient scaling, but training them from scratch remains prohibitively expensive. MoE upcycling mitigates this cost by converting pretrained dense models into sparse MoE models. However, existing upcycling methods typically rely on large-scale continued training and often perform poorly under data-constrained supervised adaptation, due to either homogeneous experts or overly disruptive perturbations to pretrained parameters. In this setting, effective upcycling must leverage pretrained weight structure while introducing sufficient diversity among routed experts. To this end, we propose SVD-Partitioned Residual Initialization (SPRI), which distributes SVD-partitioned residuals derived from pretrained feed-forward network (FFN) weights across routed experts, introducing controlled expert diversity grounded in pretrained spectral structure. We further introduce a two-stage training strategy to improve adaptation stability. We evaluate SPRI on multilingual speech-to-text translation, where limited supervised data challenges MoE upcycling and multiple target languages provide natural routing heterogeneity. On CoVoST2 across 15 En-to-XX directions, SPRI improves average BLEU and COMET over fully fine-tuned dense models by 2.58 and 3.32 points, respectively, and outperforms the prior best MoE upcycling baseline by 3.39 BLEU and 4.34 COMET points.
Weiqiao Shan, Ruixiang Mao, Yuang Li +10
Jun 15, 2026cs.CV

DynFS-MoE: Dynamic Functional-Structural Mixture-of-Experts for Post-Traumatic Epilepsy Diagnosis

Post-traumatic epilepsy (PTE) is a severe complication of traumatic brain injury (TBI). Yet, early identification remains challenging due to the complex structural and functional alterations it induces in the brain. To address this, we propose a dynamic multimodal Mixture-of-Experts (MoE) framework that integrates functional and structural connectivity through time-aware functional-structural encoding and class-conditioned expert routing. Within this framework, modality-specific and cross-modal experts learn complementary representations, while a Modality-Class MoE (MCoE) module dynamically adjusts expert weights according to each classification objective. Experimental results across three binary classification tasks demonstrate that the framework consistently outperforms static fusion baselines, and high-interpretability analyses further reveal meaningful regions of interest (ROIs) interactions. This dynamic multimodal expert framework effectively captures class-dependent brain interaction patterns and provides an interpretable approach for PTE diagnosis and risk stratification.
Jun-En Ding, Spencer Chen, Henry Noren +6
Jun 14, 2026cs.LG

Conflict-Aware Federated Fine-Tuning of Large Language Models with Mixture-of-Experts

The continuous scaling of large language models (LLMs) incurs prohibitive computational costs, making Mixture-of-Experts (MoE) a scalable alternative for efficient fine-tuning via sparse activation. While federated learning (FL) emerges as the paradigm for privacy-preserving collaborative optimization, integrating MoE into FL under data heterogeneity may trigger conflicting expert optimizations. Client-specific data distributions force same-indexed experts to optimize under inconsistent or even conflicting feature-label correlations. This mismatch induces destructive interference during aggregation, thus destabilizing the optimization trajectory and degrading model performance. To address this issue, we propose FC-MoE, a federated conflict-aware framework for MoE fine-tuning. It employs an importance aware weighting scheme to prioritize reliable local updates and utilizes gradient consensus projection to suppress conflicting updates, ensuring a stable global optimization path. Moreover, a local knowledge retention mechanism further preserves specialized client expertise by re-anchoring domain-specific residuals. Extensive experiments demonstrate that FC-MoE accelerates convergence and enhances both global and local model performance in non-IID federated environments.
Yijun Lu, Zihan Fang, Pengpeng Qiao +6
Jun 14, 2026cs.LG

MoECa: Aligning Feature Reuse with Expert Decomposition in Diffusion Transformers

Diffusion Transformers with Mixture-of-Experts (DiT-MoE) improve model capacity under sparse activation, but diffusion inference is still bottlenecked by redundant computation across timesteps. Existing caching methods mainly operate at the token level, which becomes suboptimal in DiT-MoE because each token update is internally decomposed into multiple routed expert branches. Our analysis shows that cross-timestep redundancy in DiT-MoE is better characterized at the expert-branch level than at the whole-token level. Based on this observation, we propose MoECa, a fine-grained caching framework that performs branch-level feature reuse across timesteps. MoECa further introduces expert-aware adaptive control and synchronized cache updates across MoE and attention paths to maintain stable intermediate states. Experiments on multiple DiT-MoE models show that MoECa consistently achieves a better speed-quality trade-off than prior caching methods, with up to 2.83×\times inference speedup and minimal quality degradation.
Maoliang Li, Haojing Chen, Jiayu Chen +4
Jun 13, 2026cs.LG

Towards a Unified Generative Model for Scarce Time Series with Domain Experts

Synthesizing realistic time series with generative models has wide-ranging applications in real-world scenarios. Despite recent progress, most existing methods are trained under the assumption of abundant training data, which substantially limits their effectiveness in data-scarce settings. In this paper, we propose TimeMoDE, a novel framework that integrates Diffusion Transformers with Mixture-of-Experts to exploit both domain adaptability and diffusion-stage awareness for time series generation under data scarcity. It is pre-trained on a large-scale collection of multi-domain datasets to extract domain-agnostic temporal representations and domain-specific information benefiting generalization during fine-tuning. We propose Domain Prompts to condition expert assignment for indistinguishable noised tokens, mitigating the limitations of capturing inter-dataset relationships. Moreover, we incorporate diffusion timestep signals to equip the experts with awareness of time series degradation variations, facilitating adaptive calibrate to stage-dependent denoising requirements. Extensive experiments demonstrate that TimeMoDE outperforms existing methods under diverse low-data settings. It establishes an innovative paradigm for advanced time series few-shot generation.
Zihao Yao, Qi Zheng, Jiankai Zuo +1
Jun 13, 2026cs.LG

Director: Accelerating Distributed MoE Serving via Online Proactive Expert Placement

Expert parallelism has become the prevailing paradigm to serve Mixture-of-Experts (MoE) models. Its efficiency depends on the communication and computation latencies of the GPUs, which are linked to the placement of experts in the GPUs. Existing works for optimizing expert placement focus on leveraging past requests' expert activation patterns. However, they demonstrate deficiencies facing diverse and rapidly changing request patterns, calling for an online, proactive approach. Implementing such an approach requires addressing several challenges: the uncertainty associated with incoming requests' expert activation, the cost of expert migration, and the NP-hard complexity in optimization. Therefore, we present Director, a new distributed MoE serving system that minimizes end-to-end latency via prediction-driven, online expert placement. Director uses either a lightweight cascaded predictor or a low-bit quantized replica for expert activation patterns of incoming requests. An online migration module then enacts the changes with near-zero downtime by executing migrations in compute-bound phases, keeping disruption bounded. At its core, a relaxation-based expert placement optimizer operates under capacity constraints, runs in polynomial time, and achieves a (1+ε)(1+ε) approximation ratio. Finally, we implement a prototype and demonstrate, through extensive experiments, a reduction in end-to-end latency of 11∼55%11\sim55\% for popular MoE models (e.g., Mistral, DeepSeek and Qwen) compared to existing work.
Qianli Liu, Kaibin Guo, Zicong Hong +5
Jun 12, 2026cs.LG

Sticky Routing: Training MoE Models for Memory-Efficient Inference

Mixture-of-Experts (MoE) models activate only a sparse subset of experts per token, yet consecutive tokens frequently activate different experts -- causing constant weight swapping between slow storage and fast memory on edge devices. Existing remedies are either system-level (caching heuristics) or post-hoc (router fine-tuning), leaving the root cause unchanged during pretraining. We propose StickyMoE, a differentiable routing consistency loss that penalises abrupt expert switches between adjacent tokens, encouraging the router to maintain the same expert assignment across semantically coherent spans. StickyMoE requires no architectural changes, adds a single hyperparameter lambda, and unlike post-hoc methods, allows expert representations and routing decisions to co-adapt from the first training step. Experiments on small-scale MoE language models show that StickyMoE reduces the expert switch rate by up to 60% with less than 4% perplexity degradation, Pareto-dominating post-hoc fine-tuning on the quality-locality frontier. Routing temporal locality is most efficiently instilled at training time.
Ali Kayyam
Jun 12, 2026cs.CL

Nemotron 3 Ultra: Open, Efficient Mixture-of-Experts Hybrid Mamba-Transformer Model for Agentic Reasoning

We introduce Nemotron 3 Ultra, a 550 billion total and 55 billion active parameter Mixture-of-Experts Hybrid Mamba-Attention language model. We pre-trained Nemotron 3 Ultra on 20 trillion text tokens, then extended the context length to 1M tokens, and post-trained using Supervised Fine Tuning (SFT), Reinforcement Learning (RL), and Multi-teacher On-Policy Distillation (MOPD). Nemotron 3 Ultra is our most capable model yet, employing multiple key technologies - LatentMoE, Multi Token Prediction (MTP), NVFP4 pre-training, multi-environment RLVR, MOPD, and reasoning budget control. Nemotron 3 Ultra achieves up to ~6x higher inference throughput as compared to state-of-the-art publicly available LLMs while attaining on-par accuracy. The state-of-the-art accuracy, high inference throughput, and 1M token context length make Nemotron 3 Ultra ideal for long-running autonomous agentic tasks. We open-source the base, post-trained, and quantized checkpoints, along with the training data and recipe on HuggingFace.
NVIDIA, :, Aaron Blakeman +571
Jun 12, 2026cs.LG

iLENS: Interpretable LLM-Guided Mixture-of-Experts for Neuroimaging Survival Analysis

Alzheimer's Disease (AD) is a complex neurodegenerative disorder that continues to impact millions of people worldwide. Predicting AD conversion during the prodromal stage remains critical for disease understanding and patient care. As such, survival models are widely used for AD risk prediction, yet they are typically static predictors with limited interpretability and no capacity for natural language reasoning. In this work, we propose iLENS, an interpretable large language model (LLM) guided framework based on mixture-of-experts (MoE) for survival prediction in AD conversion. Our approach uses LLM to synthesize structured neuroimaging measurements and unstructured information to guide expert routing. Our framework demonstrates competitive predictive performance and capability in patient subtyping. Furthermore, our framework provides transparent, biologically grounded rationales for its routing decisions, bridging the gap between high-performance survival analysis and interpretable clinical decision support.
Farica Zhuang, Seong Woo Han, Zixuan Wen +3
Jun 12, 2026cs.SD

From Self-Supervised Speech Models to Mixture-of-Experts for Robust Anti-Spoofing

Recent advances in speech generation have significantly improved the naturalness of synthetic speech, making spoofing detection increasingly challenging. A key limitation of current anti-spoofing systems is their limited robustness to unseen synthesis methods. In this work, we transform a self-supervised speech representation model into a Mixture-of-Experts (MoE) architecture to improve generalization. Feed-forward blocks in selected encoder layers are replaced by multiple expert networks controlled by a layer-wise gating mechanism, allowing experts to capture complementary acoustic patterns while preserving the representations learned during self-supervised pretraining. We further analyze the architectural choices affecting the performance of this MoE conversion and investigate the activation behavior of the experts. The proposed approach is evaluated on 14 spoofing datasets and reduces the macro EER from 5.46% to 4.81%, corresponding to 11.9% relative improvement over the baseline.
Hugo Daumain, Driss Matrouf, Khaled Khelif +1
Jun 12, 2026cs.LG

Expert-Driven Survival Machines: Improving Stratification and Interpretability in Multiple Clinical Cohorts

Survival prediction plays a central role for healthcare providers and clinical researchers. Accurate risk stratification enables early intervention and improved patient management. Most existing deep survival models learn one common feature representation for all patients, which may hide important differences between patient subgroups. In contrast, a Mixture-of-Experts (MoE) framework allows different parts of the model to focus on different patient patterns, leading to more individualized representations. Therefore, in this work, we propose a mixture-of-experts enhanced adaptive deep clustering survival framework (AdaCSM) for modeling such heterogeneous survival patterns. We introduce a routing-based expert mechanism that enables conditional specialization within a parametric survival modeling framework. The proposed architecture allocates patients to specialized risk predictors dynamically while preserving the patient survival and subtype clustering objectives. We compare our method with state-of-the-art survival and deep clustering models on multiple real-world longitudinal clinical cohorts spanning diverse disease domains. The proposed method demonstrates improved predictive performance and leads to interpretable results in survival analysis.
Farica Zhuang, Zixuan Wen, Christos Davatzikos +1
Jun 12, 2026cs.LG

A theoretical model for task routing in mixture-of-expert transformers

Mixture-of-experts (MoE) layers enable the scaling of transformer models while keeping the inference compute fixed. While task-expert specialization has been observed in empirical studies of frontier MoE transformer models, existing theoretical work analyzes this using continuous mixture models that cannot be used to model natural language effectively. An important open question is to \textit{theoretically explain task-expert specialization in transformer MoE models using discrete models of language}. To address this, we represent structured knowledge via syntactic templates and finite key-value dictionaries, and prove formally that a single-layer MoE transformer can encode knowledge by using experts that specialize in the corresponding tasks. Our construction shows how queries are routed to unique, task-specific experts whose size depends solely on the intrinsic complexity of the given task (i.e. the combined size of its syntactic templates and factual dictionary). Our construction provides a theoretical support for empirical results on localized knowledge circuits in MoE models. We support our theoretical findings with experiments evaluating model performance under varying MoE loss functions.
Vinoth Nandakumar, Yongli Xiang, Yunzhi Yao +2
Jun 12, 2026cs.CL

Decoupled Mixture-of-Experts for Parametric Knowledge Injection

Knowledge injection aims to equip large language models (LLMs) with external, domain-specific, or time-sensitive knowledge. Existing approaches typically face a trade-off between flexibility and integration: retrieval-augmented generation keeps knowledge outside the model but only provides prompt-level augmentation, whereas post-training based methods encode new knowledge into shared parameters but may introduce catastrophic forgetting, knowledge conflict, and costly updates. In this paper, we propose Decoupled Mixture-of-Experts (DMoE), a modular architecture for parametric knowledge injection that decouples both experts and the router from the base model. DMoE converts external knowledge corpora into independently updatable expert modules and uses a lightweight uncertainty-aware router to activate relevant experts only when the base model lacks sufficient knowledge during generation. To support efficient auto-regressive inference, DMoE attaches experts only to the final-layer feed-forward network, preserving KV-cache reuse while enabling parameter-level knowledge augmentation. Experiments on knowledge-intensive benchmarks show that DMoE consistently improves answer quality over retrieval and adapter-based baselines.
Baoqing Yue, Weihang Su, Qingyao Ai +5
Jun 11, 2026cs.RO

AIR-VLA+: Decoupling Movement and Manipulation via Cascaded Dual-Action Decoders with Asymmetric MoE for Aerial Robots

Aerial manipulation systems have long suffered from representation coupling in end-to-end control, as platform-level Unmanned Aerial Vehicle (UAV) movement and end-effector-level arm manipulation differ substantially in action scale, dynamics, and control objectives. In this paper, we propose AIR-VLA+, a flow matching action generation architecture specifically designed for aerial manipulation, featuring cascaded dual-action decoders and an asymmetric feature-level Mixture of Experts (MoE). We construct cascaded manipulation and movement decoders, allowing the UAV to unidirectionally observe the manipulator's intent during movement to achieve workflow coordination, while isolating the impact of UAV movement information backpropagation on arm manipulation stability. Addressing the characteristic that UAV movement is highly dependent on high-level semantics and responsible for task state transitions in aerial manipulation, we design an input feature enhancement module for the UAV movement decoder. This module introduces an implicit visual grasp projector to perceive the interaction state between the gripper and the object, and injects compressed global semantic features. Within the UAV movement decoder, we deploy an implicit MoE architecture, enabling different movement experts to spontaneously exhibit capacity inclinations for various task stages during training. Through dense soft blending computation on the feature manifold, the UAV movement is endowed with stronger task-stage adaptability. Experiments on the standardized AIR-VLA benchmark demonstrate that our method comprehensively surpasses all baselines with an overall average score of 48.0. The overall task completion score improves by 80.2% compared to the single-head π0.5π_{0.5} policy, effectively mitigating the heterogeneous coordinated control conflicts of composite robots.
Jianli Sun, Bin Tian, Qiyao Zhang +6
Jun 10, 2026cs.LG

Redesign Mixture-of-Experts Routers with Manifold Power Iteration

Router is the cornerstone component to the Mixture-of-Experts models. Serving as expert proxies, the rows of the router matrix compute their similarity to the MoE inputs to determine which subset of experts is activated. Ideally, each router row is designed to encode the expert matrix into this representative vector, such that its dot-product with token can better reflect token-expert affinity. However, there exists no design principles to enforce this condensation. In this paper, we propose to align each router row with the principal singular direction of the associated expert, as this direction provides the most expressive mathematical description of a matrix. Based on this principle, we propose a router redesign with Manifold Power Iteration (MPI). Specifically, it introduces a "Power-then-Retract" paradigm, where a power iteration step is performed on the router weights, followed by a retraction to impose a norm constraint to ensure both efficiency and stability. Theoretically, we show that MPI drives router rows to converge toward the principal singular directions of associated experts. Empirically, we pretrain MoE model across scales from 1B to 11B parameters to confirm that this alignment facilitates more effective MoE models.
Songhao Wu, Ang Lv, Ruobing Xie +1
Jun 10, 2026cs.LG

Multi-Rate Mixture of Experts for Accelerating Liquid Neural Network Training

Multivariate time-series data often exhibit complex temporal dependencies, irregular sampling, and heterogeneous dynamics across multiple time scales, making accurate sequence modeling particularly challenging. Traditional recurrent neural networks (RNNs), such as Long Short-Term Memory (LSTM) networks, operate in discrete time and may struggle to effectively capture continuous and irregular temporal behaviors. Liquid Neural Networks (LNNs) address some of these limitations through continuous-time dynamics, but standard LNN architectures typically rely on a single dynamical system, limiting their ability to model heterogeneous temporal patterns. To address these challenges, we propose a Multi-Rate Mixture-of-Experts (MR-MoE) framework built on top of Liquid Neural Networks. In the proposed architecture, multiple LNN-based experts operate at distinct time scales, enabling the model to explicitly separate fast-changing dynamics from slow-evolving temporal trends. A gating network further enables adaptive expert specialization based on input conditions. In addition, we incorporate both feature-level and temporal attention mechanisms to improve robustness, interpretability, and long-range dependency modeling. Feature-level attention suppresses noisy or irrelevant variables, while temporal attention selectively focuses on informative historical states. We evaluate the proposed framework on a complex multivariate time-series prediction task and compare it against strong baselines, including LSTM, monolithic LNN, and standard MoE models. Experimental results demonstrate that the proposed MR-MoE framework consistently achieves improved AUROC and AUPRC performance while maintaining favorable computational efficiency. These results highlight the effectiveness of combining continuous-time dynamics, multi-scale expert decomposition, and adaptive attention mechanisms for time-series modeling.
Shilong Zong, Almuatazbellah Boker, Hoda Eldardiry
Jun 10, 2026cs.CV

MFEN:Multi-Frequency Expert Network for Visible-Infrared Person Re-ID

Visible-infrared person re-identification (VI-ReID) is challenging due to the large modality discrepancy between visible and infrared images. We contend that this discrepancy is largely related to differing lighting conditions, including differences in light wavelength and light source type. Recently, frequency-based VI-ReID approaches have achieved notable success because frequency information can better extract identity-relevant contours and details while excluding irrelevant lighting and color. However, existing methods either do not distinguish different frequency bands or focus on only one band, which is insufficient under diverse lighting conditions. To perform comprehensive frequency domain learning, we propose a Multi-Frequency Expert Network (MFEN) that enables multi-frequency modulation and adaptively combines different bands through a mixture-of-experts design. We further introduce Random Frequency Augmentation (RFA) and Frequency Auxiliary Optimization (FAO) to better train MFEN. The three modules are complementary and jointly capture critical frequency-domain details for robust representation learning. Extensive experiments on three VI-ReID datasets demonstrate the effectiveness of our approach.
Xulin Li, Yan Lu, Bin Liu +4
Jun 9, 2026cs.LG

From Observation to Intervention: A Causal Audit of Expert Importance in Mixture-of-Experts Models

Interpretability methods routinely use population-level summary statistics over observed model behaviour to license claims about the effects of targeted interventions on specific computations; in Pearl's terms, they treat rung-1 associational evidence as if it supported rung-2 interventional conclusions, a move whose validity is rarely tested. We examine one concrete instance: the use of routing statistics in Mixture-of-Experts (MoE) pruning, where utilization rates, activation norms, and routing weight distributions are treated as predictors of which experts can be removed without functional cost. A token-level interventional audit across three high-redundancy MoE architectures (OLMoE-1B-7B-0924, Qwen1.5-MoE-A2.7B, DeepSeek-V2-Lite) finds no observational metric predicts causal expert importance in any model: across all 60 metric-layer combinations effect sizes stay below Cohen's d=0.23d = 0.23, and no metric is reliably positive under our corrected, dual-test criterion. A per-token routing weight control, run with identical nn, rules out insufficient power, recovering a signal whose CI excludes zero at OLMoE's final MoE layer (d=+0.231d = +0.231, 95% CI [+0.09,+0.37][+0.09, +0.37], p=0.0013p = 0.0013). Existing pruning methods succeed in this regime not by identifying dispensable experts but because early-layer redundancy renders most selection criteria interchangeable. Our results provide an explicit counterexample to the common inferential step from population-level observational summaries to token-level interventional claims about expert importance, and illustrate how interventional audits can calibrate the evidential standards for interpretability claims.
Leonard Engmann, Christian Medeiros Adriano, Holger Giese
Jun 9, 2026cs.LG

MoE Enhanced Federated Learning for Spatiotemporal Prediction

Traffic prediction is fundamental to intelligent transportation systems and urban computing, yet many cities continue to suffer from traffic data scarcity due to limited sensor deployment and uneven urban development. Cross-city knowledge transfer has thus attracted increasing attention, enabling data-rich cities to assist data-scarce ones. However, centralized approaches raise privacy concerns, while existing federated methods struggle with pronounced spatiotemporal heterogeneity across cities. To address these challenges, we propose MoE-FedTP, a personalized federated cross-city spatiotemporal prediction framework based on lightweight Mixture-of-Experts (MoE) networks. MoE-FedTP first employs spatiotemporal neural networks to extract features from both source and target cities, then introduces a set of expert networks derived from different source cities through partial parameter sharing. A gating mechanism dynamically fuses the experts to capture diverse traffic dynamics, achieving fine-grained modeling of urban heterogeneity while preserving privacy. Experiments on four real-world traffic datasets show that MoE-FedTP consistently outperforms state-of-the-art cross-city and federated learning baselines, demonstrating its effectiveness in enhancing prediction accuracy for data-scarce cities.
Zhehao Dai, Xiao Han, Zhaolin Deng +4
Jun 9, 2026cs.DC

Achieving Cloud-Grade SLOs for Local Mixture-of-Experts Inference through CPU-GPU Hybrid Design

Local deployment of large Mixture-of-Experts (MoE) models falls short of the service quality achieved in cloud-scale environments, even under low-concurrency workloads. We identify four key gaps in local MoE inference: reliance on capacity-reduced models (quantized, distilled, rerouted), inability to meet 30-second TTFT for long prefills (more than 12K), sub-baseline decode throughput (under 20 tokens/s), and poor concurrency under mixed prefill-decode and batched decode workloads. We present a CPU-GPU hybrid system that achieves cloud-level SLOs on dual-socket commodity CPUs and consumer GPUs by (1) stream-loading prefill (SLP), boosting prefill throughput to 1,200 tokens/s and enabling 32K prompts within 30 seconds; (2) distributed SLP (DSLP) with SmallEP expert parallelism, reaching 1,800 tokens/s and 45K prompts in 30 seconds on two RTX 5090s; (3) intra-node prefill-decode disaggregation with zero-copy shared weights and a dual-batch attention-MoE overlap scheme, sustaining concurrency with under 15 percent latency increase and 50 percent throughput gains; (4) an AVX-512-optimized FP8 GEMV kernel, enabling native CPU FP8 inference while delivering 4-5x lower CPU latency; and (5) fine-grained CPU parallelism that attains 28 tokens/s on INT4 DeepSeek-V3 and 21.5 tokens/s on intact FP8 V3. Evaluations show our system delivers cloud-level QoS for flagship MoE models on consumer CPU-GPU platforms, reshaping local deployment with intact, original-precision inference and enabling high-quality, cost-effective access without datacenter infrastructure.
Wenxin Wang, Yule Hou, Yu Ji +2
Jun 9, 2026eess.AS

Entropy-Aware Domain-Routed Mixture-of-Experts Speech-LLM Framework: A Case Study of Multi-Domain Child-Adult ASR

While Speech Large Language Models (Speech-LLMs) have achieved strong performance on adult Automatic Speech Recognition (ASR), their effectiveness on child speech remains under-explored, and single models often struggle to handle diverse adult and child age groups simultaneously. This paper proposes a Mixture-of-Experts (MoE) Speech-LLM for unified ASR across adult and child speech spanning diverse environments and age groups. The framework employs a Classifier-based Domain Router (C-DR) with a coarse-to-fine strategy and integrates both a Mixture-of-Projectors (MoP) and a Mixture-of-LoRAs (MoL) to model domain-specific variations. To address routing uncertainty near domain boundaries, an Entropy-Aware Routing (EAR) mechanism is introduced to dynamically incorporate a shared expert. Experiments on public child corpora demonstrate consistent improvements over baselines while preserving adult ASR performance. To our knowledge, this is the first work leveraging Speech-LLMs for unified, multi-domain ASR encompassing both children and adults.
Mohan Shi, Kaiyuan Zhang, Zilai Wang +3
Jun 9, 2026cs.CL

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

As large language models (LLMs) continue to scale, it becomes increasingly challenging to grow model capacity under fixed computation budgets. We propose Path-Aligned Decompression Distillation (PADD), a framework for distilling knowledge from dense teachers without explicit routing into mixture-of-experts (MoE) students while learning high-quality routing policies. PADD organizes knowledge distillation into four stages in two phases: an initialization phase (Stage I) that builds diverse functionality in the student's experts through teacher neuron clustering and student-expert warmup, and a training phase (Stages II--IV) that integrates online adaptive distillation, path-refined policy optimization, and reward-augmented load balancing in a single training pipeline. Experiments on mathematical reasoning benchmarks demonstrate that PADD yields substantial gains over strong baselines at the same inference cost and that the MoE student can match or surpass its dense teacher. They also demonstrate effective teacher-to-student knowledge distillation and stable routing behavior.
Xinyue Peng, Yi Qian, Jiaojiao Lin +2
Jun 9, 2026cs.CL

Routing-Aware Expert Calibration for Machine Unlearning in Mixture-of-Experts Language Models

Machine unlearning is increasingly important for large language models, yet unlearning in Mixture-of-Experts (MoE) architectures remains underexplored. Unlike dense models, MoE architectures employ a router at each layer to assign each token to a sparse subset of experts. In this work, we observe that forget data often activates a small subset of experts disproportionately, while these experts may receive much weaker activation from retain data. This forget--retain routing mismatch can leave forget-critical experts under-regularized during unlearning. To address this, we propose \textbf{TRACE}, Targeted Routing-Aware Calibration of Experts, for MoE unlearning. TRACE first detects forget-critical experts from offline activation statistics, and then calibrates retain regularization by reweighting token-level retain losses so that each selected expert's retain-side activation frequency better matches its forget-side counterpart. Experiments on WMDP and MUSE-BOOKS across multiple MoE LLMs show that TRACE consistently improves the forget-utility trade-off, yielding a 9% relative utility improvement over the strongest baseline under comparable forgetting quality and the best performance on three out of four MUSE-BOOKS metrics.
Jingyi Xie, Yijun Lin, Yinjiang Xiong +2
Jun 8, 2026cs.RO

MosaicIMU: Composing Carrier Experts for Generalizable Neural Inertial Odometry

Robust inertial odometry is essential for various carriers when external sensing is unreliable. Learning-based methods reduce integration drift by capturing local motion priors, but these methods often remain tied to a particular carrier, limiting generalization across heterogeneous platforms. We present MosaicIMU, a carrier-conditioned Mixture-of-Experts (MoE) pretraining-and-adaptation framework for generalizable neural inertial odometry. MosaicIMU uses a prototype-based router to compose carrier-specific expert features, decodes local velocity and uncertainty constraints, and integrates them with a history-aware EKF. For unseen domain adaptation, it freezes the pretrained base model and learns a new lightweight expert residual branch. For edge-deployment, it further reuses the router to select informative online samples for efficient incremental updates. Experiments show that MosaicIMU consistently outperforms learning-based baselines, reducing average ATE and RTE-10s by 40% and 34%, respectively. These results highlight that MosaicIMU provides a scalable pretraining-to-deployment paradigm for generalizable and adaptive neural inertial odometry.
Junye Zou, Huiyi Yan, Xinning Xu +4
Jun 8, 2026cs.AI

FAME: Forecastability-Aware Mixture of Experts for Heterogeneous Time Series Forecasting

Large-scale retail and industrial forecasting systems contain many heterogeneous time series whose lifecycle, sparsity, volatility, seasonality, spectral patterns, and contextual sensitivity differ substantially. A single forecasting model rarely performs well across all regimes, while dense ensembles increase inference cost and provide limited insight into expert suitability. This paper studies forecastability-aware expert routing: learning how data characteristics determine the suitability of forecasting experts. We propose \method{}, a sparse mixture-of-experts framework that represents each series with a multidimensional forecastability fingerprint, mines expert-suitability targets from validation performance, and trains a cost-aware sparse router to activate a small budgeted set of experts for each series. Using a production-scale vending-machine sales dataset from Shandong New Beiyang (SNBC), where the forecasting component has been integrated into the replenishment-planning pipeline, together with public retail benchmarks, we show that expert suitability varies systematically across data regimes. On the industrial dataset with 5,000+ machines and 60M+ transactions, \method{} Top-2 reduces MSE by 12.4% over the strongest single expert, LightGBM, while executing 1.92 experts per series on average. The deployed component produces demand forecasts, while inventory-oriented gains are estimated by an offline replay simulator under a fixed replenishment policy rather than by online intervention. The framework turns heterogeneous sales forecasting from heuristic model selection into data mining of forecastability patterns and expert specialization. Code is available at https://github.com/hit636/FAME
Qianyang Li, Xingjun Zhang, Shaoxun Wang +2
Jun 7, 2026cs.AI

STAR: Rethinking MoE Routing as Structure-Aware Subspace Learning

Mixture-of-Experts (MoE) scales model capacity efficiently by selectively routing inputs to a specialized subset of experts. However, input-expert specialization, the core motivation of MoE, critically depends on whether the router is actually aware of input structure. In practice, MoE routing is typically implemented as a shallow linear projection with limited awareness of input representation, which often leads to unstable routing. We propose STAR, a Structure Aware Routing that rethinks MoE routing as a subspace learning problem by augmenting standard learnable routing with an evolving principal subspace that tracks dominant input structure via Generalized Hebbian Algorithm (GHA). By aligning routing decisions directly with input structure, STAR enables stable expert specialization. We evaluate STAR on controlled synthetic setup and large-scale language and vision tasks, where it consistently improves routing quality and downstream performance over strong MoE baselines. Moreover, optional test-time subspace updates further enhance routing robustness and generalization under input distribution shifts.
Sumin Park, Noseong Park
Jun 7, 2026cs.CV

NGram-MoSE: Efficient Remote Sensing Super-Resolution via N-Gram Context and Mixture-of-Experts

Remote sensing applications for environmental monitoring and disaster management are frequently constrained by a spatial--temporal trade-off: imagery with fine spatial detail is often acquired less frequently, whereas more temporally available observations are typically coarser. Single-image super-resolution provides a practical means to enhance coarse imagery without changing acquisition schedules, yet many Transformer-based SR models remain computationally expensive and can be sensitive to limited or geographically biased training data, which degrades robustness under out-of-distribution conditions. This paper presents NGram-MoSE, a lightweight Transformer architecture designed to improve both efficiency and texture continuity. NGram-MoSE introduces N-Gram Context Injection to strengthen cross-window local consistency and mitigate window-boundary artifacts, and incorporates a Mixture-of-Experts (MoE) feed-forward design to scale capacity through sparse activation without proportional growth in inference cost. Experiments on a geographically disjoint OOD test set show that NGram-MoSE achieves 31.68,dB PSNR while reducing FLOPs by 14×14\times relative to a heavyweight Transformer reference. Downstream evaluation on a landslide segmentation benchmark further demonstrates that restoring degraded inputs to the detector training scale improves performance, yielding a 4.47% absolute gain in mAP@50 over bicubic upsampling, and exhibits stronger cross-scale consistency under scale extrapolation. These results indicate that NGram-MoSE provides an effective SR module for resource-constrained remote sensing pipelines requiring robust generalization.
Yun-Hsuan Huang, Trong-An Bui, Chih-Hung Chuang
Jun 6, 2026stat.ML

Variational Proximal Policy Optimization

Reinforcement Learning from Human Feedback via Proximal Policy Optimization often suffers from policy mode collapse, brittle exploration loops, and distribution drift. This paper introduces Variational Proximal Policy Optimization (\textscVP2\textscO\textsc{VP}_2\textsc{O}), a particle-based variational inference framework that maps policy optimization to Stein Variational Gradient Descent within a Mixture-of-Experts architecture. By leveraging functional kernels over localized expert prototypes alongside an expert orthogonalization loss, \textscVP2\textscO\textsc{VP}_2\textsc{O} introduces a geometry-based proximal-control mechanism that can reduce reliance on fixed clipping or KL schedules. Our results on a 33B/4B sparse Mixture-of-Experts model show several improvements across complex reasoning benchmarks, establishing a +179+\mathbf{179} ELO gain on Codeforces and a 32%\mathbf{32\%} reduction in token count on AIME mathematical reasoning tasks.
Ousmane Amadou Dia
Jun 6, 2026cs.LG

LongMoE: Longitudinal Multimodal Learning via Trajectory-Aware Mixture-of-Experts

Multimodal clinical learning is increasingly important for integrating diverse patient data, including imaging, text, and personalised health records. However, it faces two fundamental challenges: i) modality missingness, where arbitrary subsets of modalities are unavailable at a given patient visit, ii) longitudinal dynamics, where the diagnostic significance of an observation depends on the patient's evolving disease trajectory over time. Existing methods address these challenges in isolation: missing-modality frameworks treat each visit as an independent static snapshot and discard temporal context, while longitudinal models often assume complete modality availability and degrade under systematic modality incompleteness. We propose LongMoE (Longitudinal Mixture-of-Experts), the unified framework to jointly address both challenges. LongMoE combines a context-aware imputation module with an attentional tokenization module that captures frequency-domain temporal patterns across irregular visit sequences, a trajectory-aware encoder for modeling disease progression, and context-conditioned Sparse MoE routing for patient-specific expert selection. Experiments on ADNI, OASIS-3, and MIMIC-IV show that LongMoE improves robustness under missing or weak contemporaneous modalities and remains competitive in full-modality settings, establishing a strong foundation for longitudinally-aware multimodal clinical learning.
Maxx Richard Rahman, Prakhar Kumar, Wolfgang Maass
Jun 5, 2026cs.LG

Sparse Subspace-to-Expert Sharing for Task-Agnostic Continual Learning

Continual learning in Large Language Models (LLMs) is hindered by the plasticity-stability dilemma, where acquiring new capabilities often leads to catastrophic forgetting of previous knowledge. Existing methods typically treat parameters uniformly, failing to distinguish between specific task knowledge and shared capabilities. We introduce Mixture of Sparse Experts for Task Agnostic Continual Learning (SETA), a framework that resolves the plasticity-stability conflict through adaptive sparse subspace decomposition into task-specific expert modules. Unlike standard updates, where tasks compete for the same parameters, SETA separates knowledge into unique experts, designed to isolate task-specific patterns, and shared experts, responsible for capturing common features. This structure is maintained through adaptive elastic anchoring and a routing-aware regularization that jointly protect shared knowledge at both the weight and routing levels and enable a unified gating network to automatically retrieve the correct expert combination during inference. Extensive experiments across diverse domain-specific benchmarks demonstrate that SETA achieves competitive or superior overall performance relative to state-of-the-art continual learning baselines, with particularly strong retention of early-task knowledge and improved backward transfer on LLaMA-2 7B and Qwen3-4B.
Fatema Siddika, Md Anwar Hossen, Tanwi Mallick +1
Jun 5, 2026cs.LG

Reversible Foundations: Training a 120B Sparse MoE through State-Preserving Scaling

This paper reports on training a hundred-billion-parameter sparse mixture of experts on a single eight-GPU node, end to end. LightningLM 0.1V is a recurrence-backbone language model family grown in four stages from a small dense seed, through a 5B and a 9B mixture of experts, to a 120B model with 460 routed experts under top-12 routing. Each larger model is grown from the trained weights of the smaller one; active parameters rise monotonically from 1.78B at the dense seed to 5.93B at 120B (about 5% of the 118.67B stored). The full lineage runs on single nodes, the larger stages at 8K context, reaching a released training loss of 1.78 at 120B scale. This is a systems and experience report. It is organized around three disciplines. Reversibility: a reversible recurrence stack reconstructs activations in the backward pass instead of storing them, holding activation memory flat as the model grows. State-preserving growth: each expansion (dense to MoE, shallow to deep, few experts to many) is given as a reproducible principle paired with the failure that results from getting it wrong; several failures are silent. Single-node economics: the 120B trains through TQP, a strategy of quantized base expert weights and trained low-rank adapters that carries optimizer state on 2.26B adapter parameters rather than 100B+ resident in routed experts, cutting expert-path optimizer state by a factor of ~45. What is new is the integration of known primitives, not any primitive in isolation: one grown lineage running end to end on a single node, documented at practitioner level, with per-domain held-out loss as evidence that targeted capabilities (multilingual Indic competence, code) were learned by construction. Model family, tokenizer, and training code are released.
Rohan Shravan
Jun 4, 2026cs.LG

Less is MoE: Trimming Experts in Domain-Specialist Language Models

Mixture-of-Experts (MoE) models achieve strong performance through conditional computation, but their large parameter footprint poses deployment challenges. Prior MoE compression approaches catastrophically fail when evaluated on general-purpose benchmarks beyond commonsense reasoning. We trace this failure to the granularity of compression: important capabilities are distributed across experts but concentrated in FFN sparse intermediate dimensions. To identify these dimensions, we use Fisher importance which outperforms activation-, router-score-, and magnitude-based alternatives, and identifies tiny sets of task-critical dimensions: in Qwen1.5-MoE, removing as few as 12 of 1.35M routed-FFN intermediate dimensions collapses GSM8K accuracy while largely preserving factual-knowledge performance. Building on this, we propose Fisher-MoE, which operates within FFN to remove intermediate dimensions ranked by Fisher importance. At the same 50% MoE compression ratio, Fisher-MoE preserves model capability, while reducing weight memory by ~45% and improving inference throughput by 21%. These findings suggest intermediate dimension granularity is an effective unit for both compression and ranking where capability concentrates in MoE models.
Haoze He, Xinkai Zou, Xuan Jiang +4
Jun 3, 2026cs.CV

HD-DinoMoE: A Class-Aware Hierarchical Dual Mixture-of-Experts Network for Scleral Anomaly Segmentation in Complex Acquisition Scenarios

Traditional Chinese Medicine (TCM) ocular inspection provides empirical cues for assessing scleral surface anomalies, but its clinical use remains subjective and difficult to quantify. To support intelligent and quantifiable ocular inspection, this study presents the TCM-inspired Artificial Intelligence Ocular Auxiliary Diagnosis System (TAO) and focuses on pixel-level scleral surface anomaly segmentation. For clinical and user-acquired images affected by multi-source distributional discrepancies, diverse anomaly morphologies, and scleral specular reflection (SSR), we propose HD-DinoMoE, a class-aware hierarchical dual mixture-of-experts network. HD-DinoMoE combines class-aware dual-stream DINOv3 feature fusion with class-specific multi-expert decoding to segment Vessels, Yellow and Black Spots, and Blood Spots. A three-stage backbone-frozen routing strategy stabilizes dual-backbone adaptation; Progressive Confidence Penalty (PCP) Loss reduces high-confidence false positives and segmentation leakage in SSR regions; and Class-Aware Adaptive Sample Weighting (CA-ASW) balances sample- and class-level training contributions. We further construct the Multi-label Scleral Anomaly Segmentation Dataset (ML-SASD), a new benchmark with Clinical, Wild, and Mix settings and pixel-wise annotations for three anomaly categories. On ML-SASD-Mix, HD-DinoMoE achieves a mean Dice of 72.11% and a mean Intersection-over-Union of 58.44%, while maintaining favorable boundary localization and specular-region false-positive control. It also shows competitive generalization on the Vessels subset of the public SBVPI dataset. These results indicate that HD-DinoMoE provides a feasible segmentation solution for TAO under complex acquisition scenarios. The code and data access information are available at https://github.com/FX-CMX/HD-DinoMoE.
Yinxiang Yu, Maoxiang Chu, Qi Niu +7
Jun 3, 2026cs.RO

D3^3-MoE:Dual Disentangled Diffusion Mixture-of-Experts for Style-Controllable End-to-End Autonomous Driving

Traditional end-to-end autonomous driving frameworks frequently suffer from the "style-averaging" dilemma when trained on high-variance human demonstrations, yielding homogenized, style-uncontrollable, and even kinematically unsafe policies. To overcome this limitation, we present D3^3-MoE (Dual Disentangled Diffusion Mixture-of-Experts), which disentangles trajectory modeling along two complementary axes. On the behavioral axis, generation is decoupled from selection: a style-conditioned diffusion process synthesizes multi-style candidate trajectories in parallel within a single scene, allowing a downstream module to select the optimal trajectory based on user preference or an evaluation score. On the physical axis, decoupled longitudinal and lateral routers activate their respective experts during inference time, trained without manual labels using self-supervised targets from orthogonal ground-truth kinematics. These activated experts, architected as Diffusion Transformers (DiT) and equipped with style-conditioned AdaLN and asymmetric lateral-fusion cross-attention, independently predict their corresponding physical state before being reassembled into a unified, kinematically coherent trajectory. Extensive evaluations on the challenging NAVSIM benchmark demonstrate that D3^3-MoE achieves state-of-the-art planning performance, reaching 88.2 PDMS and 84.3 EPDMS by default. Moreover, our Best-of-Three ensemble strategy effectively broadens the multi-modal solution space, raising performance to 91.3 PDMS and 87.5 EPDMS. Both quantitative and qualitative analyses jointly confirm the framework's advantages in planning quality and style controllability.
Renju Feng, Rukang Wang, Ning Xi +4
Jun 3, 2026cs.CV

Physics-Informed Video Generation via Mixture-of-Experts Latent Alignment

Large-scale video generation models have made remarkable progress in semantic consistency and visual quality, producing videos that are increasingly coherent and visually convincing. Nevertheless, the dynamics induced by pixel-level fitting do not naturally accommodate the regularities that govern real-world motion and interaction, resulting in persistent shortcomings in physical plausibility. To address this limitation, we propose \textbf{PILA} (Physics-Informed Latent Alignment), a framework that injects physics-structured latent guidance into the frozen flow-matching dynamics of pretrained video models. Specifically, PILA first employs anchored field estimation to map frozen-generator latents into an operational physical attribute bank organized by field-proxy slots, using observable motion as a kinematic anchor for constructing less directly observed proxies. To handle the heterogeneity of real-world dynamics, PILA adopts a mixture-of-experts design over physical categories. Label-prior masked expert routing selects category-specific operator experts, whose refinements are regularized by operational residuals abstracted from physical relations. Finally, the refined proxies are fused into the physical attribute bank and decoded into a correction to the flow-matching vector field, injecting physics-aware guidance while preserving the visual prior of the pretrained backbone. With staged adapter training on Wan 2.1-1.3B and direct transfer of the learned adapter to Wan 2.2-14B, PILA achieves state-of-the-art results on VBench-2.0, VideoPhy-2, and PhyGenBench in both visual quality and benchmark-measured physical plausibility.
Cong Wang, Hanxin Zhu, Jiayi Luo +6
Jun 3, 2026cs.LG

SHAPE: Coalition-Aware Expert Pruning for Sparse Mixture-of-Experts LLMs

Sparse Mixture-of-Experts (MoE) large language models achieve strong quality with low per-token compute, yet their deployment is often limited by the memory wall: the full expert pool must remain resident to support token-dependent routing. Expert pruning is a direct remedy, but prior criteria typically score experts independently and overlook that MoE inference is inherently \emph{coalitional}, where outputs arise from routed top-kk expert combinations. We propose \textbf{SHAPE}, a task-driven pruning framework that explicitly models \emph{intra-layer} expert cooperation. SHAPE formulates routing traces on a small calibration set as an empirical cooperative game and assigns interaction-aware expert values via a Shapley-style attribution over observed top-kk coalitions, enabling the identification of experts that are essential for high-utility collaborations rather than merely frequent. To preserve MoE topology under a global pruning budget, SHAPE further introduces a \emph{quality-coverage} selection rule that retains, in each layer, the minimal expert subset covering an αα fraction of non-negative Shapley mass, while using bisection to match a target keep rate. Experiments on three modern MoE backbones (Qwen3-30B-A3B, GPT-OSS-20B, and DeepSeek-V2-Lite) across diverse benchmarks show that SHAPE consistently improves robustness over global and layer-wise pruning variants, maintaining competitive accuracy under 20% and 40% expert pruning without additional training and delivering clear reductions in peak GPU memory footprint. The open-source code is available at https://github.com/Alizen-1009/Shapley-Moe.
Yuhao Zhang
Jun 3, 2026cs.LG

TENP: Trapezoidal Expert Neuron Pruning For Mixture-of-Experts

Mixture-of-Experts large language models (LLMs) scale efficiently through sparse activation, yet their deployment is fundamentally constrained by the large static parameter footprint of experts. Existing compression approaches either remove entire experts, disrupting routing topology and harming performance, or rely on unstructured weight pruning with limited practical efficiency. To address the limitations, we propose TENP, a structured Trapezoidal ExpertNeuron Pruning framework. Using a few samples, we identify and retain important experts, while applying expert neuron pruning (ENP) to less important experts, reserving model parameters in a trapezoidal pattern from shallow to deep layers. When evaluating expert importance, we jointly consider both the magnitude of the expert output and its ability to change the direction of the input vector. For ENP, we measure each neuron's projected contribution to the expert output to identify and retain important neurons. We conduct extensive experiments on the Qwen and DeepSeek models. Under a routing expert sparsity of 40% and an average of 63.76% activated expert parameters, the DeepSeek model suffers only a 1-point drop in accuracy compared to the full-parameter model. Moreover, it outperforms the full-parameter model by 10% on code generation tasks.
Jiangyang He, Shaolin Zhu, Deyi Xiong
Jun 3, 2026cs.NI

Treat Traffic Like Trees: A Semantic-Preserving Hierarchical Graph-Based Expert Framework for Encrypted Traffic Analysis

Graph-based deep learning methods have been widely employed in encrypted traffic analysis to exploit latent correlations across different granularities. However, while complex preprocessing pipelines and sophisticated model structures often achieve strong performance, they may obscure inherent protocol semantics during representation learning. Moreover, the hierarchical structure of protocol layers and their corresponding fields, defined by protocol specifications and routinely utilized in manual traffic analysis, remains underexplored in existing learning frameworks. In this paper, we propose Protocol Tree Graph Attention with Mixture of Experts (PTGAMoE), a semantic-preserving hierarchical graph-based expert framework for encrypted traffic analysis. The field-based graph construction and expert committee design enable PTGAMoE to quantify the model's preferences for specific fields and protocols. Extensive experimental results on representative benchmark datasets under strict no-data-leakage settings demonstrate that PTGAMoE significantly outperforms state-of-the-art (SOTA) models. Furthermore, the semantic-preserving design provides interpretable insights into protocol-level feature importance and expert-level contributions, reflecting the model's decision-making logic in encrypted traffic classification tasks.
Yuantu Luo, Jun Tao, Linxiao Yu +1
Jun 3, 2026cs.LG

LoopMoE: Unifying Iterative Computation with Mixture-of-Experts for Language Modeling

Mixture-of-Experts (MoE) and looped architectures scale models along two orthogonal axes, namely parameter capacity and effective depth. However, mainstream looped architectures rely on dense backbones that couple parameter count with per-token FLOPs, which makes it impossible to isolate the effect of iterative computation under matched budgets. To this end, we present LoopMoE, a looped MoE language model that integrates sparse routing with iterative weight-shared computation through two designs. The first is IterAdaLN, which resolves weight-sharing symmetry via a modulation signal jointly conditioned on the iteration index and the per-token hidden state. The second is a capacity-balancing strategy that recovers the attention-to-FFN active parameter ratio of well-tuned non-looped references. Together, these designs enable the first strictly controlled, head-to-head evaluation of a looped MoE against a Vanilla MoE under identical total parameters, per-token FLOPs, and active sublayer ratios. At the 3B scale, LoopMoE outperforms the Vanilla MoE on 8 of 9 downstream benchmarks with an average improvement exceeding 1 point. At the 9B scale, LoopMoE continues to outperform the matched Vanilla MoE, indicating that the architectural gain persists at larger scale. Our work establishes a controlled synthesis of sparsity and recurrence, and suggests a promising direction for looped language models.
Wenkai Chen, Tianshu Li, Wenyong Huang +3
Jun 2, 2026cs.LG

Sparse Mixture-of-Experts Reward Models Learn Interpretable and Specialized Experts for Personalized Preference Modeling

Preference modeling plays a central role in reinforcement learning from human feedback (RLHF), enabling large language models (LLMs) to align with human values. However, most existing approaches assume a universal reward function, neglecting the diversity and heterogeneity of human preferences. To address this limitation without additional annotation costs, recent work has proposed learning multiple preference components from binary data and combining them to model individual preferences. Nevertheless, these components often fail to capture coherent and disentangled patterns, limiting their interpretability and effectiveness for personalization. In this work, we propose a sparse Mixture-of-Experts (MoE) reward model that encourages sparse routing and expert diversity during training on binary preference data. Across controlled and real-world experiments, sparse MoE learns interpretable routing patterns and specialized experts. It also improves test-time personalization, and post-adaptation shifts in expert weights provide a qualitative lens for analyzing how the model adapts to personalized preferences.
Yifan Wang, Jinyi Mu, Mayank Jobanputra +5
Jun 2, 2026cs.CL

Expert-Aware Refusal Steering

Safety alignment in instruction-tuned large language models (LLMs) depends on a model's ability to reliably refuse to respond to harmful or disallowed requests. Recent work has shown that a steering vector can be applied to a dense LLM during inference to effectively suppress refusal behavior, inducing response to harmful requests. We extend this refusal steering method to three open-source Mixture-of-Experts (MoE) LLMs and find that steering performance is uninhibited by the complex routing patterns inherent to the MoE architecture. We then propose two expert-aware refusal steering methods that leverage refusal-specific expert routing patterns and expert-specific steering directions to suppress normal refusal behavior. We find that refusal behavior can be effectively steered based on the output of a single expert. Our results show that refusal signals captured by steering methods differ from expert routing behavior, suggesting a substantial role for attention in MoE refusal behavior.
Anna C. Marbut, Daniel R. Olson, Travis J. Wheeler
Jun 2, 2026cs.DC

UltraEP: Unleash MoE Training and Inference on Rack-Scale Nodes with Near-Optimal Load Balancing

Large-scale expert parallelism (EP) is becoming pivotal for training and serving frontier MoE models, but it also amplifies device-level expert load imbalance into compute stragglers, token all-to-all bottlenecks, and activation-memory spikes. Existing balancers redistribute experts periodically based on historical load, which becomes unreliable for production deployments with non-stationary load patterns. We present UltraEP, the first exact-load, real-time balancer for large-EP MoE training and serving prefill on rack-scale nodes (RSNs). Leveraging the extended scale-up connectivity among dozens of GPUs within RSNs, UltraEP rebalances every microbatch and layer on critical paths, which requires nontrivial co-design of plan solving and expert replication communication to minimize exposed overhead. To this end, UltraEP eagerly reacts to post-gating load with an efficient quota-driven planner, and executes the resulting irregular expert-state transfers with RSN-native persistent tile streaming and relay-based fan-out mitigation. We evaluate UltraEP in a multi-RSN deployment of up to 256 GPUs, using cutting-edge MoE models from 106B to 671B parameters. Averaged across training and serving, UltraEP achieves 94.3% of the force-balanced ideal throughput, delivering 1.49×\times improvement over no-balancing, while reducing the final inter-rank imbalance from 1.30−-4.01 to 1.01−-1.04.
Xinming Wei, Chao Jin, Tuo Dai +10
Jun 2, 2026cs.CL

Expert-Aware Causal Tracing of Factual Recall in Sparse MoE Language Models

Activation patching can identify a mixture-of-experts (MoE) block whose clean output restores a corrupted factual prediction. However, because the block output combines contributions from multiple routed experts, block-level rescue does not establish whether the recovery localizes to an individual expert or depends on the routed expert set. We study this question on single-token COUNTERFACT contrasts by corrupting subject-token embeddings, restoring clean block outputs, and then restoring clean-minus-noised expert updates under fixed routing. In Qwen3-30B-A3B-Base, a discovery sweep selects layer 44, and held-out analysis identifies L44E069 as a recurrent routed contributor with positive specificity over same-layer active experts. Its effect is fact-matched and improves true-token probability and rank, which explains part of the layer rescue. In Mixtral-8x7B-v0.1, the selected recurrent singleton is not specific; matched-size controls instead show specificity of the clean-routed top-2 set. These findings show that successful MoE-block restoration does not necessarily imply localization to a single expert.
Yuetian Lu, Ali Modarressi, Yihong Liu +1
Jun 2, 2026cs.LG

AnchorMoE: Interpretable Time Series Classification via Anchor-Routed MoE

Multivariate time series classification (MTSC) is pivotal in high-stakes domains, such as clinical diagnosis and industrial fault detection, where safe deployment necessitates transparent decision-making. However, isolating the temporal segments that drive model predictions is challenging because discriminative signals in real-world time series are typically sparse, heterogeneous, and heavily obscured by background noise. This paper, therefore, proposes AnchorMoE, an interpretable-by-construction classification framework. Built upon a Mixture-of-Experts (MoE) architecture, AnchorMoE encodes multi-view representations of local patches and routes them to specialized experts, ensuring that the final prediction is formulated as an exact additive decomposition over the input segments, facilitating ante-hoc transparency rather than relying on post-hoc estimations. To maintain the reliability of this decomposition under sparse signal distributions, we introduce a geometric orthogonality constraint that penalizes representational redundancy, compelling distinct experts to specialize in heterogeneous predictive patterns. Furthermore, an uncertainty-aware reliability gate is designed to dynamically calibrate the contribution of each segment, effectively suppressing residual background noise. Extensive experiments on real-world and synthetic benchmarks demonstrate that AnchorMoE achieves highly competitive classification performance while faithfully grounding its decisions in the raw time series.
Tao Xie, Zexi Tan, Haoyi Xiao +5
Jun 2, 2026cs.CV

PRISM: Synergizing Vision Foundation Models via Self-organized Expert Specialization

Unifying the complementary strengths of diverse Vision Foundation Models (VFMs) into a single efficient model is highly desirable but challenged by the negative transfer inherent in monolithic distillation. To address these feature conflicts, we introduce \textbf{PRISM}, a novel dual-stream Mixture-of-Experts (MoE) framework that synergizes VFMs via modular specialization. We propose a two-stage paradigm: (1) expertise deconstruction, where a teacher-conditional router guides experts to specialize in distinct representational subspaces to mitigate interference, followed by (2) dynamic recomposition, where the router learns to assemble these experts into tailored computational pathways for downstream tasks. Experiments on PASCAL-Context and NYUD-v2 show that \textbf{PRISM} establishes a new state of the art, validating that sparse, emergent specialization is a scalable approach for integrating diverse visual knowledge.
Ying Tang, Dong Li, Youjia Zhang +3
Jun 2, 2026cs.LG

When Model Merging Breaks Routing: Training-Free Calibration for MoE

Model merging has emerged as a cost-effective approach for consolidating the capabilities of multiple LLMs without retraining. However, existing merging techniques, largely based on linear parameter arithmetic or optimization, struggle when applied to Mixture-of-Experts (MoE) architectures. We identify a critical failure mode in MoE merging, termed routing breakdown, in which the merged router fails to dispatch tokens to suitable experts. Routing breakdown stems from the sensitivity of the non-linear softmax and discrete Top-k routing mechanisms to parameter perturbations from merging, a sensitivity further amplified by load-balancing constraints imposed during MoE pretraining. Because fine-tuned experts exhibit distinct specializations, even modest misrouting can cause severe performance degradation. To address this issue, we propose Hessian-Aware Router Calibration (HARC), a training-free framework that leverages second-order curvature information to realign the merged router. This approach admits a closed-form solution that can be efficiently solved using a matrix-free conjugate gradient method. Experiments on mathematical reasoning and code generation tasks show that HARC effectively mitigates routing breakdown across diverse MoE merging baselines and leads to substantial performance improvements. Our code is available at https://github.com/huangcb01/HARC.
Canbin Huang, Tianyuan Shi, Xiaojun Quan +3