Mixture-of-Experts Language Models

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18 papers in the last four weeks, up 38% on the four weeks before. 0.2% of all new papers.

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Oct 8, 2026cs.AI

RouterInterp: Understanding Superposed Specialisation in Mixture of Experts Routing

Sparse Mixture of Experts (MoE) models scale more efficiently than dense models by routing tokens to modular expert networks that are only active for processing a fraction of tokens. A leading hypothesis for the performance of MoE models is that each expert specialises in a single, coherent domain. However, interpretability efforts that assume this hypothesis have generally been unsuccessful. We propose and present evidence for an alternative account that we call the Superposed Specialisation Hypothesis (SSH): experts specialise in a disjoint union of fine-grained features rather than one broad domain. Leveraging the SSH, we introduce RouterInterp, a method for interpreting expert routing that identifies Sparse Autoencoder features most predictive of routing decisions and produces unified natural language explanations. On gpt-oss-20b, RouterInterp explains expert routing with

{\sim}65\%

higher detection accuracy than prior token statistics based methods. This work provides a scalable method for generating more accurate explanations of expert routing and increases our understanding of a previously uninterpretable component of foundation models.

Ilya Lasy, Nora Yinuo Cai, Kola Ayonrinde

Faculty of Informatics, TU Wien · Independent · UK AI Security Institute

Mixture of Experts Expert Routing Mixture-of-Experts Language Models Neural Network Interpretability

Oct 8, 2026cs.CL

Smoothing the Top-k Exposure Boundary for Sparse Mixture-of-Experts

Sparse Mixture-of-Experts models scale parameter capacity efficiently while maintaining a fixed compute budget per token. However, traditional training paradigms enforce a static choice of top-

k

experts, which converts a continuous routing distribution into a rigid step function. This constraint introduces a brittle boundary where highly competitive experts are arbitrarily separated into full-supervision and zero-feedback zones based on minor score fluctuations. To address this issue, we propose Elastic Expert Routing, which stochastically samples the active expert budget from a localized discrete distribution centered at

k

. Over multiple training iterations, this mechanism softens the sharp threshold into a gradual probability distribution. Because the sampling neighborhood remains symmetric, this approach matches the expected computational cost of deterministic training, while preserving the inference budget. Extensive experiments demonstrate the efficacy of our method on both supervised fine-tuning and from-scratch pretraining settings. During supervised fine-tuning, elastic routing improves downstream macro-averages on OLMoE-1B-7B and Qwen3-30B-A3B by

+0.84

and

+2.02

points, respectively. In addition, in from-scratch pretraining, it outperforms the static top-

k

baseline by

1.6

points on average across downstream tasks.

Yunkai Chai, Tong Zhu, Xiaoye Qu +4

Shanghai AI Laboratory, Shanghai, China · Shanghai Jiao Tong University, Shanghai, China · Nanyang Technological University, Singapore

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

Oct 7, 2026cs.CL

Expert Coupling in MoE Pretraining: Reducing All-to-All Overhead with Correlated Placement and Token Shuffling

Mixture-of-Experts (MoE) layers replace the feed-forward block of a Transformer with E expert networks, and each token is routed to k of these experts. Under expert parallelism (EP) the experts are distributed across GPUs, and every MoE layer runs all-to-all collectives in the forward and backward passes to dispatch tokens to their experts and then combine the results. On a cluster with 8 AMD Instinct MI300X GPUs per node, these collectives can take 45% of the training step at EP32 with top-2 routing and 60% with top-6 routing. We find that early in pretraining routers have already learned to assign tokens to experts in correlated patterns, both within a layer and across layers. At top-2, 0.8% of the expert pairs in a layer are selected together by 42% of tokens, and the experts a token selects at one layer predict the experts it selects at the next layer. We use these correlations to keep more token--expert assignments on the token's own GPU, which reduces communication across GPUs and across nodes. Correlated expert placement puts experts that are often selected together on the same GPU. Combined with a dispatcher that sends each token to each GPU once, it removes up to 58% of dispatched rows. Token shuffling applies when sequence parallelism shards tokens across the EP group. It moves each token to the GPU predicted to hold its next-layer experts during the reduce-scatter that follows attention. On one node this raises the share of token--expert assignments served on the token's GPU from 12.5% to 59%. In Megatron-LM, across EP degrees from 8 to 64 with top-2 and top-6 routing, the two methods reduce all-to-all time by 1.16-2.63X and end-to-end step time by up to 1.41X. Neither method changes the models' underlying routing decisions or expert parameters.

Radha Gulhane, Quentin Anthony, Beren Millidge

Zyphra

Mixture-of-Experts Language Models Communication-Efficient Distributed Training Mixture-of-Experts Models Mixture of Experts

Oct 7, 2026cs.LG

Shared Low-rank Basis Factorization for Data-free Mixture-of-Experts Compression

Mixture-of-Experts (MoE) large language models decouple capacity from compute through sparse routing, but their large parameter count creates storage and serving challenges. We analyze three MoE compression families: expert pruning, expert merging, and weight reconstruction, and derive structural error bounds showing that pruning and merging can incur non-vanishing errors tied to routing and expert heterogeneity. In contrast, weight reconstruction avoids these structural costs by preserving expert structure and routing. Motivated by the analysis, we propose Shared Low-rank Basis Factorization (SLBF), a data-free weight reconstruction method that uses rank-

k

bases shared among experts, enabling richer cross-expert sharing, faster convergence, and lower reconstruction error. A post-hoc gauge fixing removes redundant parameters at no representational cost. Across five MoE architectures spanning 16B to 122B parameters, SLBF consistently outperforms methods from all three compression families.

Tianxiao Cao, Jiahe Shao, Yuning Qiu +3

Kyoto University · The University of Tokyo · RIKEN AIP

LLM Compression Mixture-of-Experts Language Models Matrix Factorization Low-Rank Matrix Decomposition

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 5, 2026cs.LG

How Sparse Probability Maps Shape Mixture-of-Experts Routing

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

Tomás Brogueira, Marcos Treviso, Miguel Couceiro

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

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

Oct 1, 2026cs.CL

Cross-Lingual Alignment for Decoder-Only Models using MoE Routers

Cross-lingual contrastive learning has been a core component of multilingual encoder training, but the ability to explicitly align representations is not possible in decoder-only LLMs because of varying multilingual tokenization. However, a growing amount of research suggests that even in LLMs, higher cross-lingual representational alignment leads to improved cross-lingual transfer. In this paper, we propose a novel approach to reimagine cross-lingual contrastive learning given the architectural constraints of modern LLMs. Rather than applying an auxiliary alignment loss on hidden states, we propose using the outputs of the mixture-of-experts (MoE) routers as the target for alignment. Router outputs lend themselves better to pooling over many tokens, enabling more reliable cross-lingual comparisons at the sequence-level. Controlled continual pre-training experiments on four open-source MoEs show that incorporating this routing loss also aligns the underlying hidden representations across languages. Most importantly, this loss improves multilingual performance on our diverse evaluation suite, demonstrating the potential of cross-lingual MoE router alignment.

Lucas Bandarkar, Clark Peng, Ahmed Haj Ahmed +2

University of California, Los Angeles∗ · Haverford College · MILA - Quebec AI Institute & McGill University

Mixture-of-Experts Language Models Cross-Lingual Representation Alignment Cross-Lingual Transfer

Oct 1, 2026cs.AI

ITC-MoE: Importance-guided Token-aware Compression for MoE Diffusion Language Models

Mixture-of-Experts (MoE) Diffusion Language Models (DLMs) offer flexible parallel decoding and increased model capacity, but their large number of expert parameters incurs substantial computation and storage costs. Existing low-rank MoE compression methods largely rely on static factorization and fixed rank allocation, which overlook the distinctive properties of MoE DLMs. Specifically, we identify two properties: cross-mode non-uniform redundancy, where parameter redundancy and sensitivity to rank truncation vary across the input, output, and expert modes, and token-wise utilization variation, where hot and cold tokens exhibit distinct spectral characteristics and expert activation patterns. To address these challenges, we propose ITC-MoE, an Importance-guided Token-aware Compression framework for MoE DLMs. ITC-MoE consists of two complementary components. First, Importance-guided Adaptive Tucker Compression (IATC) incorporates activation and gradient importance into expert weight transformation, jointly factorizes expert weights across multiple modes, and adaptively allocates ranks under a fixed parameter budget. Second, Token-aware Compensation and Routing (TCR) applies lightweight low-rank compensation to compression-sensitive hot tokens and restricts the candidate expert set for cold tokens with concentrated routing patterns. By jointly adapting compression capacity and inference execution to both parameter redundancy and token-wise variation, ITC-MoE substantially reduces the computation and storage costs of MoE DLMs while preserving their generation quality. For example, on SDAR-30B-A3B-Chat-b32, ITC-MoE maintains an accuracy of 96.33% on MultiArith under a 30% compression budget, while achieving up to a 7.22x end-to-end speedup. The code is publicly available at https://github.com/lianjunl13-sudo/ITC-MoE.

Lianjun Liu, Shipeng Li, You Huang +5

Hainan University, Haikou, China · Xiamen University, Xiamen, China · Zhejiang Normal University, Jinhua, China

Mixture-of-Experts Language Models LLM Compression Mixture-of-Experts Inference Tensor Decomposition Diffusion Language Models

Oct 1, 2026cs.LG

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

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

Di He, Pengxiang Li, Da Chang +3

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

Mixture-of-Experts Language Models Recurrent Transformers Expert Routing

Sep 30, 2026cs.LG

Score the Update, Not the Token: Descent-Aligned Routing for Combinatorial LoRA Experts

Mixture-of-LoRA-experts methods raise the capacity of low-rank adaptation by routing each token to a few low-rank experts. Nearly all of them tie one input-side factor to one output-side factor per expert, and nearly all of them route by scoring the token: the router picks experts without seeing what any of them would write. We argue that the router should score the update. To first order, adding an expert's update to a layer output lowers the loss by the inner product between that update and the negative loss gradient at the output. This usefulness is quadratic in the token, so a router that is linear in the token sees only the part of it that runs through the token mean, and routers that rank experts by the norm of their own activations never see the output factor. If each expert is split into a reader (down-projection) and a writer (up-projection), the usefulness of every reader--writer pair becomes an inner product in the shared rank-

r

space, and all

N_AN_B

pairs can be scored from

N_A+N_B

vectors. We build VANE on this identity. A low-rank compass predicts the descent direction of each token. VANE scores every pair by the alignment between its update and the compass without forming any update, activates the top-

k

pairs with additive gates, and gives every pair its exact first-order router gradient. On single-domain commonsense reasoning and a four-domain multi-task mixture with Llama-3.2-3B and Llama-3.1-8B, VANE attains the best average among twelve PEFT and MoE-LoRA baselines, by 0.9--1.1 and 1.3--1.5 points respectively, with less than half the trainable parameters of an 8-expert MoE-LoRA. Its router scores also track the measured usefulness of experts far more closely than token routers do.

Priya Nair, Lukas Brenner, Maya Lindqvist +5

University of California, Irvine · University of Washington

Mixture-of-Experts Language Models Parameter-Free Mixture-of-Experts Routing Low-Rank Adaptation Mixture-of-Experts Models Parameter-Efficient Fine-Tuning

Sep 30, 2026cs.LG

Scaling Laws for Looped Mixture of Experts

Looped transformers and Mixture-of-Experts (MoE) offer complementary routes to efficient scaling: recurrence increases computational depth at fixed parameters, while MoE sparsity expands total capacity at fixed active compute. Yet existing scaling laws model recurrence or sparsity in isolation. In this work, we introduce Loop Scaling Laws, the first scaling law to jointly model recurrence and sparsity alongside model size and data. At its core is a bounded, sparsity-conditional recurrence mapping that characterizes the effective-parameter gain from looping and how sparsity raises this gain. The laws predict the held-out loss of looped models more accurately than prior alternatives, and recover the standard dense and MoE scaling laws as special cases. Beyond prediction, the fitted laws provide a principled foundation for designing looped MoE models under compute and memory constraints. Downstream evaluations further demonstrate the complementary benefits of the two axes: sparsity delivers ~3x active-parameter efficiency, recurrence yields ~2x total-parameter efficiency on reasoning, and joint scaling further advances the performance frontier. As a practical extension, we show these gains hold at trillion-token scale: at matched training compute, a looped MoE with law-derived recurrence matches a ~2x larger non-looped MoE on the reasoning benchmarks, while enabling test-time scaling through recurrence.

Yanbei Chen, Anirudh Goyal, Raghuraman Krishnamoorthi

Meta AI

Mixture-of-Experts Language Models Language Model Scaling Laws Inference-Time Scaling Recurrent Transformers AI Scaling Laws

Sep 30, 2026cs.LG

ID Balancing: Stable Training of Extremely Sparse MoE via PID-Based Load Control

Scaling Large Language Models (LLMs) via Mixture-of-Experts (MoE) enables massive parameter growth with nearly constant per-token computation. However, further scaling the parameter count requires increasingly sparse routing, where expert load imbalance becomes more severe. This imbalance reduces parameter utilization and training efficiency, and can undermine training stability, becoming a bottleneck to reliable scaling. In this work, we unify two representative auxiliary-loss-free methods as incomplete Proportional-Integral-Derivative (PID) controllers: DeepSeek's loss-free method acts as a fixed-step integral controller, while Kimi K3's Quantile Balancing functions as a generalized proportional controller. Building on this control perspective, we propose ID Balancing, an Integral-Derivative controller. It scales its integral term with load error and activates its derivative term only when imbalance worsens, enabling stronger corrections for large or worsening errors and smaller updates near balance. Evaluated across Top-

10

, Top-

5

, and Top-

3

routing over

768

experts, ID Balancing reduces worst-case backbone MaxVio and training-average backbone MinVio by over

50\%

and

12\%

, respectively, relative to the best baselines in the Top-

3

setting. When the total parameter count increases from

18.9

B to

69.9

B (Top-

10

-of-

768

), ID Balancing's worst-case backbone MaxVio remains nearly unchanged and is approximately

89.6\%

lower than that of the auxiliary-loss baseline. ID Balancing also maintains competitive language-modeling and downstream performance. The advantages of ID Balancing grow as sparsity increases, making it a promising solution for scaling larger, sparser MoE models.

Peng Jin, Zihan Qiu, Zekun Wang +8

Qwen Team, Alibaba Token Hub, Alibaba Group

Expert Load Balancing Mixture-of-Experts Language Models Language Model Scaling Feedback Control

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 28, 2026cs.LG

MaskCoFT: Masked Co-Adaptive Fine-Tuning for Memory-Efficient MoE Inference

Mixture-of-experts (MoE) language models often exceed the memory of a single GPU. Expert offloading keeps most experts in host memory and loads them on demand, so decoding speed depends on how many experts each token must fetch. Caching and prefetching reduce this cost only as far as the routing allows. Router-only fine-tuning can reshape the routing to reuse experts, but it keeps the experts frozen, so they cannot adapt to the tokens the new routing sends them. We propose MaskCoFT, a masked co-adaptive fine-tuning method that trains routers and experts together with the cross-entropy loss alone. During fine-tuning, a learnable binary mask restricts the Top-K routing of each layer to a subset of experts, and the experts adapt to the tokens redirected to them. At inference, the learned mask becomes a soft prior that re-ranks experts, so every expert remains selectable. We simulate a GPU cache of 4 experts per layer for Mixtral-8x7B and 12 for DeepSeek-V2-Lite. MaskCoFT cuts expert fetches per token by 23.7% and 10.1% relative to the base model. In real offloading system serving, it lowers the time per output token by up to 16.4% and 5.5%, respectively. Its average accuracy over nine benchmarks stays above the base model by 0.92 and 0.53 points.

Junfeng Wu, Zehao Fan, Hadjer Benmeziane +3

Department of Industrial and Systems Engineering, Rensselaer Polytechnic Institute · Department of Electrical, Computer, and Systems Engineering, Rensselaer Polytechnic Institute · IBM Research

Expert Offloading Mixture-of-Experts Language Models Fine-Tuning Mixture-of-Experts Inference Memory-Efficient Inference LLM Routing

Sep 27, 2026cs.AI

EAT: Expert Account Tracker for Efficient MoE Inference

Mixture-of-Experts (MoE) models have emerged as a revolutionary method to scale Transformer models. However, traditional MoE architecture still suffers from inefficiency since a large number of experts are unnecessarily activated. Existing approaches for reducing the number of activated experts often overlook the historical performance of each expert. In this paper, we propose EAT, a novel method called Expert Account Tracker (EAT), which utilizes history-awareness metrics and adaptive thresholding to dynamically select the most important experts, thereby reducing the activated expert number while effectively maintaining the model performance. Experiments show that EAT outperforms the existing baseline Top-P method across multiple models and datasets, achieving over 25% an average reduction compared to the vanilla method in the number of activated experts and performing better token generation speed compared to the baseline. Furthermore, the performance of pruned models can be efficiently recovered via OPD using only 9K data. Additionally, through ablation studies, we find that excessively reducing the number of activated experts can significantly harm model performance, and the importance of experts varies across layers, with higher-level experts being generally more critical.

Yuexian Li, Yifei Yang, Zouying Cao +1

Paris Elite Institute of Technology, Shanghai Jiao Tong University · AGI Institute, School of Computer Science, Shanghai Jiao Tong University, Shanghai, China · Key Laboratory of Shanghai Education Commission for Intelligent Interaction and Cognitive Engineering, Shanghai Jiao Tong University +1

Mixture-of-Experts Pruning Mixture-of-Experts Language Models Mixture of Experts Mixture-of-Experts Inference

Sep 24, 2026cs.LG

RAZOR: Pruning Replaceable Experts in LLMs

Mixture-of-experts (MoE) models activate only a few experts per token but store the entire expert pool. Pruning this pool requires identifying experts whose removal preserves model behavior. Routing frequency and output magnitude do not fully describe deletion damage, which also depends on how the surviving and replacement experts compensate for the removed output. We introduce RAZOR, a training-free pruning method based on consensus residuals, the deviations of expert outputs from their original weighted mixture. At a fixed layer input, these residuals give the exact output change for a single deletion under survivor renormalization and router refill. RAZOR aggregates this damage by conditional root mean square and selects experts under a layerwise budget using forward computation alone, without gradients, subset search, or recovery training. Against frequency, activation-norm, and REAP baselines on GLM-4.7-Flash and Qwen3.6-35B-A3B at 25% and 50% expert removal, it attains the highest macro average over nine reasoning-intensive tasks in all four model-budget settings, gaining 2.12-5.59 points over REAP and lowering reverse KL in all four. On DeepSeek-V4-Flash-0731 and Hy3, it also achieves the highest macro average among the three residual criteria. Local exactness does not guarantee better joint pruning. Generation analyses show changes in diversity, formatting, and termination despite higher task scores.

Mingyang Song, Mao Zheng

Foundation Model Department, Tencent, China

Mixture-of-Experts Pruning LLM Pruning Mixture-of-Experts Language Models LLM Compression

Sep 22, 2026cs.LG

You Only Need 2/3 of the Chosen Experts: An Empirical Study of Dynamic Expert Pruning in Fine-Grained MoE LLMs

Fine-grained mixture-of-experts (MoE) architectures have become a mainstream design for open-weight LLMs, with hundreds of experts and increasingly many selected per token. This shift makes dynamic expert pruning an attractive route to cheaper inference. Yet existing evidence comes largely from coarser architectures and likelihood-scored multiple-choice benchmarks, leaving three central questions open in the fine-grained regime: how redundant per-token expert selection is, how effectively existing pruning methods exploit that redundancy, and what governs a model's sensitivity to pruning. We fill this gap with a systematic empirical study of twelve fine-grained MoE checkpoints spanning nine architecture families, with a core suite of eleven benchmarks covering knowledge QA, mathematics, code generation, and general reasoning. We find that expert selection is far more redundant than the field's operating points assume: uniformly retaining about two thirds of the selected experts preserves 98.8% of unpruned performance on average, requiring only a one-integer change and delivering 1.2-1.7x measured speedup across two serving backends. This simple baseline leaves little room for dynamic allocation at conservative budgets: even the best published rules differ from it by under 1% at matched expert budgets. Their value emerges under aggressive pruning, where the best rules recover up to 3.0% over uniform truncation, with gains concentrated in the generative tasks that suffer the sharpest degradation. Sensitivity to aggressive pruning also depends on the model: larger and thinking models are more resilient, whereas multimodal models are more vulnerable. Together, these findings reveal how much expert computation fine-grained MoEs can dispense with, and establish when dynamic allocation earns its complexity, informing both practical deployment and future pruning methods.

Yuanteng Chen, Qiwei Lai, Chen Tianqi +7

Institute of Automation, Chinese Academy of Sciences · School of Artificial Intelligence, University of Chinese Academy of Sciences · Zhongguancun Academy +1

Mixture-of-Experts Pruning Mixture-of-Experts Language Models Mixture-of-Experts Inference

Sep 22, 2026cs.LG

From Experts to Sub-experts: Fine-grained Parameter-Efficient Fine-Tuning for MoE LLMs

As large language models (LLMs) scale rapidly, dense full-parameter adaptation becomes increasingly expensive, motivating sparse and modular architectures such as Mixture-of-Experts (MoE) models. This shift raises a key question for parameter-efficient fine-tuning (PEFT): at what granularity should parameters be selected and updated? Existing PEFT methods such as LoRA operate on predefined weight matrices, while expert-level sparse tuning methods update entire selected experts. However, we observe that activated experts are internally sparse, with only a small fraction of intermediate channels strongly responding to downstream tasks, indicating that expert-level adaptation is still too coarse. We propose NSFT (Neural Sub-expert Fine-Tuning), a fine-grained PEFT framework that refines MoE adaptation from experts to sub-experts. NSFT decomposes each expert along the intermediate dimension into structured channel groups and selects task-relevant sub-experts by combining routing importance with intra-expert activation saliency. To optimize sparse partial updates, NSFT further introduces learning-rate scaling and dynamic gradient scaling to compensate for the reduced effective update magnitude. Experiments on OLMoE and Ling-mini-2.0 across challenging domain-specific tasks and general benchmarks show that NSFT consistently outperforms representative PEFT and expert-level sparse tuning baselines, while using substantially fewer trainable parameters and preserving competitive general capability. These results suggest that sub-expert-level adaptation is a more precise and efficient PEFT paradigm for MoE LLMs.

Zhentao Tan, Chang Liu, Yao Liu +2

Alibaba Group · Southeast University

Mixture-of-Experts Language Models Sparse Fine-Tuning Selective Fine-Tuning Parameter-Efficient Fine-Tuning

Sep 16, 2026cs.LG

Higher-order pruning of experts in mixture-of-experts language models

Mixture-of-Experts (MoE) language models suffer from large parameter counts, which create a significant memory bottleneck. Expert pruning is the most direct approach for reducing this parameter count, yet existing methods make pruning decisions for each expert independently, and assume experts' contributions are purely additive. In reality, expert usage in MoEs is inherently cooperative. We derive HOPE (Higher-Order Pruning of Experts), a second-order pruning objective which provably minimizes an upper bound on the error resulting from pruning. We show that REAP (a state-of-the-art first-order pruning method) is a special case of HOPE where interaction terms are ignored. Across three frontier MoE models (up to 122B parameters), two distinct calibration sets, and multiple benchmarks (including math, instruction following, coding, and an agentic suite), we demonstrate that HOPE produces better pruning decisions than existing methods, and its advantage is most pronounced at high pruning rates and on challenging agentic workloads. At 50% pruning, HOPE outperforms all baselines and achieves an average rank of 1.58 out of 5 methods (versus 2.42 for the next-best method, REAP), with gains of up to +6.1% on agentic coding. Over all conditions, HOPE again achieves the best average rank and surpasses every other method in the majority of head-to-head comparisons. By preserving cooperative expert structure that first-order methods ignore, HOPE enables aggressive compression with minimal degradation, particularly on complex tasks where diverse expert combinations are invoked over long sequences.

Alex M. Tseng, Prannay Kaul, Luca Zancato +2

AI Fundamental Research AWS Agentic AI

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

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 9, 2026cs.LG

OMP-MoE: Efficient Expert Pruning for Mixture-of-Experts LLMs via Orthogonal Matching Pursuit

Mixture-of-Experts (MoE) models enable efficient scaling of large language models but face critical deployment challenges due to massive memory requirements. Existing pruning methods either incur prohibitive search costs or neglect the dynamic interdependencies between experts. To address these challenges, we present OMP-MoE, a novel training-free compression framework for reducing expert redundancy in MoE-based LLMs. Based on observations of expert contribution patterns, we reformulate the pruning problem as a sparse signal reconstruction task solved through Orthogonal Matching Pursuit. Specifically, our method first treats individual expert contributions as dictionary atoms and selects experts that greedily minimize reconstruction error with linear computational complexity. Then, we optimize cross-layer expert allocation through a water-filling strategy that accounts for both reconstruction quality and routing stability. Finally, we introduce OMP-MoE†, an adaptive inference mechanism that dynamically adjusts expert activation based on energy prediction. Comprehensive experiments on Qwen, DeepSeek-V2, GPT-OSS, and Mixtral MoE demonstrate consistent improvements over existing methods at 25-50% pruning ratios. For Qwen3-30B-A3B at 50% compression, we retain 93.3% of original performance, achieving 33

\times

faster search and 1.55

\times

inference speedup. Codes will be available after acceptance.

Dezhi Li, Lujun Li, Qiyuan Zhu +4

The Hong Kong University of Science and Technology

Mixture-of-Experts Pruning Mixture-of-Experts Language Models LLM Compression LLM Inference Acceleration

Sep 9, 2026cs.CR

How Fragile Is Safety Alignment at Frontier Scale? A Single-Direction Attack on a 320B MoE

Directional ablation removes an aligned language model's ability to refuse by projecting a single "refusal direction" out of the weights that write the residual stream. It needs no gradient-based training and no optimization, only a few hundred contrastive prompts, which makes it the canonical white-box attack on open-weight alignment. However, it has been established only on dense models up to roughly 70B parameters. We study whether it survives the shift to frontier mixture-of-experts (MoE) models whose residual streams are no longer a single tensor and whose weights ship quantized. We apply it to GLM-5.3-Flash (320B parameters, 288 routed experts, a four-wide hyper-connection residual, block-FP8). The attack survives the architecture, but what it reaches is no longer where a reader of the original recipe would look for it. Editing the attention, dense and routed-expert writers on their own removes 0.039, 0.016 and 0.148 of refusal respectively; editing all three together removes 0.776. As a result, 74% of the effect exists only under the joint intervention. The part the conventional recipe reaches by module-name matching accounts for 0.066 of that 0.776, which is why it fails silently on an MoE. The effect does not follow from removing just any direction: ablating a random direction orthogonal to it leaves refusal unchanged. A category-concentrated residue survives every edit we tried: subspaces fitted on violence, sexual content and hate leave measurable refusal at every rank from 1 to 12. We report the method, the 41-89 percentage-point reductions it achieves across seven harmful benchmarks with no detected change in capability, and the boundary where it stops.

Yi Shi, Tanyu Chen, Kai Shen

Continuum AI

Mixture-of-Experts Language Models LLM Alignment Adversarial Attacks on LLMs Refusal Behavior in Language Models

Sep 7, 2026cs.AI

ProtLingo: Efficient Protein Language Modeling via Conditional Memory and Expert Routing

Proteins perform diverse cellular functions, and even single amino-acid substitutions can alter stability, activity, or molecular interactions. Protein language models (PLMs) provide a scalable approach for modeling such sequence--function relationships from unlabeled sequences, but increasing the size of dense Transformer backbones often brings substantial computational cost without consistently improving mutation-sensitive prediction. We introduce ProtLingo, an efficient PLM framework that augments a pretrained single-sequence backbone with conditional local memory and sparse expert routing. ProtLingo maps contextual residue representations into route-specific discrete codes, composes centered local windows into latent

N

-gram addresses, and retrieves reusable residual signals associated with recurring local sequence contexts. In parallel, selected feed-forward blocks are upcycled into sparse Mixture-of-Experts layers with shared and routed experts, enabling residue-dependent computation while activating only a subset of parameters. Experiments on protein fitness prediction, FLIP benchmarks, and supervised contact prediction show that ProtLingo achieves competitive performance with a 150M-scale backbone, including strong parameter efficiency on mutation-effect prediction and preserved long-range structural representations.

Mingrui Li, Sixian Shen, Minzhang Li +4

ShanghaiTech University

Mixture-of-Experts Language Models Protein Fitness Prediction Memory-Augmented Language Models Protein Language Models Molecular Property Prediction

Sep 1, 2026cs.CL

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

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

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

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

Mixture-of-Experts Language Models Expert Routing

Sep 1, 2026cs.CL

Instella-MoE Technical Report

In this work, we introduce Instella-MoE, a fully open Mixture-of-Experts (MoE) language model with 16 billion total parameters and 2.8 billion active parameters per token, trained entirely from scratch on AMD Instinct MI300X and MI325X GPUs. Instella-MoE combines a sparsely activated MoE design with architectural and system-level innovations, including Gated Multi-head Latent Attention (Gated MLA) and FarSkip-Collective connectivity, enabling efficient large-scale training and inference. The model is developed through a multi-stage pipeline comprising pre-training, mid-training, long-context extension, supervised fine-tuning with feedback-driven data curation, direct preference optimization, and reinforcement learning with Multi-Teacher On-Policy Distillation. Instella-MoE achieves an average score of 76.7 across standard pre-training benchmarks, outperforming prior fully open models including OLMo-3-7B, SmolLM3-3B, and OLMoE-1B-7B, while remaining competitive with open-weight MoE and dense baselines at comparable active-parameter scales, including Moonlight-16B-A3B and Qwen3.5-4B. After post-training, our final Think checkpoint achieves an average score of 73.2 across instruction-following, reasoning, math, coding, and chat benchmarks, outperforming both fully open and open-weight models with comparable or larger active parameter counts in our evaluation. To support transparent and reproducible research, we release the complete Instella-MoE model flow, including model weights, training configurations, data mixtures, and training code. Together, these contributions establish Instella-MoE a strong, fully open foundation for efficient, high-performing MoE models and reproducible research.

Jiang Liu, Sudhanshu Ranjan, Prakamya Mishra +10

Mixture-of-Experts Language Models Language Model Post-Training LLM Training

Sep 1, 2026cs.AI

Residual Sparsification via Output Importance for Compressing Mixture-of-Experts LLMs

Mixture-of-experts (MoE) architectures scale large language models efficiently, but they demand massive GPU memory. To cope with such demand, models are commonly compressed to reduce their memory footprint. Residual sparsification is a representative compression technique that decomposes each projection matrix of an expert into a shared base matrix and per-expert residual matrix, and then compresses the residuals. Existing sparsification methods compress each residual matrix independently by minimizing its compression error, thereby minimizing the error of each projection matrix. However, our analysis shows that this objective is misaligned with preserving model accuracy after compression. In an expert, the final output is produced through computations coupled across multiple projections and hidden representations. Therefore, even small errors in individual matrices can propagate through hidden representations and projection interactions, leading to large expert output errors and accuracy degradation. To address this misalignment, we propose PARSER, a new residual sparsification method that shifts the compression objective from minimizing isolated matrix errors to preserving the expert output error. PARSER achieves this by introducing output importance, which measures the actual contribution to the expert output error. Our experiments show that, compared with existing methods, PARSER narrows the accuracy gap to the uncompressed model by 1.41

\times

on Qwen and 1.44

\times

on DeepSeek, while achieving the same peak memory reduction. Our code is available at https://github.com/OSSS-KU/PARSER.

Seungwoo Jung, Dohyeok Kwon, Seungmin Cha +4

Department of Computer Science and Engineering, Korea University · Department of Computer Science and Artificial Intelligence, Dongguk University

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

Aug 31, 2026cs.AI

TuringLLM: Efficiently Scaling Foundation Models Toward Physical AI

We present Turing-20B-A2B, a 20B-parameter Mixture-of-Experts language model that activates approximately 2B parameters per token, designed for long-context and latency-sensitive physical AI applications. The model adopts Quantile Routing in a dynamic top-k configuration, enabling token-adaptive expert allocation while maintaining balanced expert utilization and a controlled average compute budget. During deployment, we further apply capacity-constrained routing to prompt prefill for more regular and efficient expert execution, while retaining dropless routing during pretraining. Turing-20B-A2B also employs a hybrid attention architecture that combines Lightning Attention with a small number of full-attention layers for efficient long-context modeling. The model is pretrained with a progressive three-stage curriculum and extended to a native context length of 128K through continued pretraining, with further inference-time extension to 512K using YaRN. Despite its compact active-parameter budget, Turing-20B-A2B achieves, at the base-model stage, overall general capability exceeding Qwen3-8B Base and approaching Qwen3.5-9B Base, while maintaining strong long-context performance and favorable prefill-latency scaling. These results demonstrate an effective balance among model capability, long-context scalability, and practical inference efficiency.

Yuheng Zhang, Yizhao Wang, Da Zhu +19

Foundation Model Team, Xpeng Inc.

Mixture-of-Experts Language Models Long-Context Language Model Inference LLM Routing Efficient Language Model Inference

Aug 31, 2026cs.LG

Q-Strata: Hierarchical Bit Allocation for Mixed-Precision Quantization of Mixture-of-Experts LLMs

Mixed-precision quantization (MPQ) assigns a different bitwidth to each linear layer of a large language model (LLM) to minimize the quantization-induced quality loss under a fixed budget, but Mixture-of-Experts (MoE) models contain these layers in every expert of every MoE block, so the allocation space grows far larger than in a dense model. Existing methods either allocate within each block under a uniform per-block budget, or allocate across blocks through an additive proxy, and neither directly optimizes a model-level objective over the choices that couple the blocks. We propose Q-Strata, a bi-level allocator that ranks within-block assignments with a cheap proxy and allocates across blocks with a model-level objective evaluated on the assembled quantized model. Its inner stage caches a Pareto frontier of candidates per block over finely spaced budgets, leaving the outer stage to set one budget per block instead of a bitwidth for every linear layer. With the search reduced to one budget per block, the outer stage optimizes this model-level objective directly, capturing the inter-block coupling that additive proxies miss. On Mixtral-8x7B-Instruct, Qwen1.5-MoE-A2.7B, and DeepSeek-V2-Lite, Q-Strata consistently achieves lower WikiText2 perplexity than uniform-bitwidth GPTQ and the state-of-the-art MoE MPQ methods MxMoE and GEMQ in the low-bit regime. The code is available at https://github.com/snu-mllab/Q-Strata/tree/main.

Deokjae Lee, Sihun Chu, Hyun Oh Song

Department of Computer Science and Engineering, Seoul National University · Neural Processing Research Center · 3Neural Processing Research Center +2

Mixed-Precision Quantization LLM Quantization Mixture-of-Experts Language Models Mixture-of-Experts Quantization Neural Network Quantization

Aug 31, 2026cs.AI

A.X K2 Technical Report

We introduce A.X K2, a 688B-parameter Mixture-of-Experts (MoE) language model trained from scratch as a high-performance foundation for \emph{agentic} applications. Trained on approximately 8.5T tokens---fewer than its predecessor, A.X K1---on a smaller but higher-quality mixture with substantially expanded agentic and software-engineering data, it nonetheless improves over A.X K1 across the board, by over 30 percentage points on some benchmarks, reflecting large gains in token efficiency. To support long contexts efficiently, we introduce Sparse Gated Attention (SGA), which combines sparse attention with gated attention, and adopt Gated Norm (GN) to stabilize large-scale training. SGA is trained natively at 128K through a \emph{sparse} indexer warmup that optimizes the indexer against its own sparse top-

k

selection rather than the dense attention distribution, making adaptation markedly cheaper: each query reads only 2,048 positions, yet long-context quality is unchanged and A.X K2 scores 94.6 on RULER out to 256K. The outlier suppression of GN in turn keeps 4-bit NVFP4 serving within one point of FP8 accuracy. A simple yet effective Think-Fusion recipe further lets users switch between thinking and non-thinking modes within a single unified model. Extensive evaluations show that A.X K2 performs competitively against strong open-weight baselines, matching or exceeding them on math and Korean-language benchmarks.

Cheolseung Baek, Dhammiko Arya, Eunki Kim +40

Mixture-of-Experts Language Models Long-Context Language Modeling Sparse Attention