Mixture-of-Experts Language Models

Overview

Mixture-of-Experts language models divide parts of a transformer into expert networks and use a router to select experts for each token, so a model can have many parameters without activating them all at once. Research explores top-k and other routing rules, load-balancing methods, and training strategies such as pretraining sparse models or converting dense models into experts; evaluations commonly include language-model loss and reasoning, coding, and multilingual benchmarks. A large body of work also aims to make these models easier to fine-tune, compress, interpret, and serve through pruning, quantization, expert sharing, and routing-aware systems. A central tension is how to encourage useful expert specialization while keeping routing reliable and balanced, since communication and memory costs can limit the practical gains from sparse computation.

Latest papers

229 papers37 papers in the last four weeks, up 42% on the four weeks before. 0.2% of all new papers.

Mar 17, 2026

Knowledge Localization in Mixture-of-Experts LLMs Using Cross-Lingual Inconsistency

Modern LLMs continue to exhibit significant variance in behavior across languages, such as being able to recall factual information in some languages but not others. While typically studied as a problem to be mitigated, in this work, we propose leveraging this cross-lingual inconsistency as a tool for interpretability in mixture-of-experts (MoE) LLMs. Our knowledge localization framework contrasts routing for sets of languages where the model correctly recalls information from languages where it fails. This allows us to isolate model components that play a functional role in answering about a piece of knowledge. Our method proceeds in two stages: (1) querying the model with difficult factual questions across a diverse set of languages to generate "success" and "failure" activation buckets and then (2) applying a statistical contrastive analysis to the MoE router logits to identify experts important for knowledge. To validate the necessity of this small number of experts for answering a knowledge question, we deactivate them and re-ask the question. We find that despite only deactivating about 20 out of 6000 experts, the model no longer answers correctly in over 40% of cases. Generally, this method provides a realistic and scalable knowledge localization approach to address increasingly complex LLMs.
Mar 17, 2026

EngGPT2: Sovereign, Efficient and Open Intelligence

EngGPT2-16B-A3B is the latest iteration of Engineering Group's Italian LLM and it's built to be a Sovereign, Efficient and Open model. EngGPT2 is trained on 2.5 trillion tokens - less than Qwen3's 36T or Llama3's 15T - and delivers performance on key benchmarks, including MMLU-Pro, GSM8K, IFEval and HumanEval, comparable to dense models in the 8B-16B range, while requiring one-fifth to half of the inference power, and between one-tenth to one-sixth of the training data and consequent needed training power. Designed as a trained-from-scratch Mixture-of-Experts (MoE) architecture, EngGPT2 features 16 billion parameters with 3 billion active per inference, with expert sizes positioned between those used in GPT-OSS and Qwen3. Approximately 25% of its training corpus consists of Italian-language data, to deliver strong capabilities for European and Italian NLP tasks among models of similar scale. This efficiency aims to position EngGPT2 as a key contributor to the growing portfolio of open-weight European models, combining performance and efficiency with full alignment to the EU AI Act. EngGPT2 is also a single model capable of multiple reasoning modes: non-reasoning, reasoning in Italian or English, and turbo-reasoning (a concise, bullet-point style reasoning available in both languages designed for real-time reasoning use cases). EngGPT2 aims to set a new standard for resource-conscious, high-performance LLMs tailored to European and Italian contexts.
Mar 13, 2026

LightMoE: Reducing Mixture-of-Experts Redundancy through Expert Replacing

Mixture-of-Experts (MoE) based Large Language Models (LLMs) have demonstrated impressive performance and computational efficiency. However, their deployment is often constrained by substantial memory demands, primarily due to the need to load numerous expert modules. While existing expert compression techniques like pruning or merging attempt to mitigate this, they often suffer from irreversible knowledge loss or high training overhead. In this paper, we propose a novel expert compression paradigm termed expert replacing, which replaces redundant experts with parameter-efficient modules and recovers their capabilities with low training costs. We find that even a straightforward baseline of this paradigm yields promising performance. Building on this foundation, we introduce LightMoE, a framework that enhances the paradigm by introducing adaptive expert selection, hierarchical expert construction, and an annealed recovery strategy. Experimental results show that LightMoE matches the performance of LoRA fine-tuning at a 30% compression ratio. Even under a more aggressive 50% compression rate, it outperforms existing methods and achieves average performance improvements of 5.6% across five diverse tasks. These findings demonstrate that LightMoE strikes a superior balance among memory efficiency, training efficiency, and model performance.
Mar 11, 2026

Task-Conditioned Routing Signatures in Sparse Mixture-of-Experts Transformers

Sparse Mixture-of-Experts (MoE) architectures enable efficient scaling of large language models through conditional computation, yet the routing mechanisms responsible for expert selection remain poorly understood. In this work, we introduce routing signatures, a vector representation summarizing expert activation patterns across layers for a given prompt, and use them to study whether MoE routing exhibits task-conditioned structure. Using OLMoE-1B-7B-0125-Instruct as an empirical testbed, we show that prompts from the same task category induce highly similar routing signatures, while prompts from different categories exhibit substantially lower similarity. Within-category routing similarity (0.8435 +/- 0.0879) significantly exceeds across-category similarity (0.6225 +/- 0.1687), corresponding to Cohen's d = 1.44. A logistic regression classifier trained solely on routing signatures achieves 92.5% +/- 6.1% cross-validated accuracy on four-way task classification. To ensure statistical validity, we introduce permutation and load-balancing baselines and show that the observed separation is not explained by sparsity or balancing constraints alone. We further analyze layer-wise signal strength and low-dimensional projections of routing signatures, finding that task structure becomes increasingly apparent in deeper layers. These results suggest that routing in sparse transformers is not merely a balancing mechanism, but a measurable task-sensitive component of conditional computation. We release MOE-XRAY, a lightweight toolkit for routing telemetry and analysis.
Mar 9, 2026

Speculating Experts Accelerates Inference for Mixture-of-Experts

Mixture-of-Experts (MoE) models have gained popularity as a means of scaling the capacity of large language models (LLMs) while maintaining sparse activations and reduced per-token compute. However, in memory-constrained inference settings, expert weights must be offloaded to CPU, creating a performance bottleneck from CPU-GPU transfers during decoding. We propose an expert prefetching scheme that leverages currently computed internal model representations to speculate future experts, enabling memory transfers to overlap with computation. Across multiple MoE architectures, we demonstrate that future experts can be reliably predicted by these internal representations. We also demonstrate that executing speculated experts generally maintains downstream task accuracy, thus preserving more effective compute-memory overlap by eliminating the need to re-fetch true router-selected experts. Integrated into an optimized inference engine, our approach achieves up to 14% reduction in time per output token (TPOT) over on-demand loading of experts from CPU memory. For MoEs where speculative execution alone yields suboptimal accuracy, we further examine lightweight estimators that improve expert prediction hit rates, thereby reducing performance degradation. Our code is released in open-source at https://github.com/axonn-ai/yalis/tree/offload_prefetch.
Mar 6, 2026

MoE Lens -- An Expert Is All You Need

Mixture of Experts (MoE) models enable parameter-efficient scaling through sparse expert activations, yet optimizing their inference and memory costs remains challenging due to limited understanding of their specialization behavior. We present a systematic analysis of expert specialization in MoEs through two complementary approaches: domain-specific routing patterns and an early decoding framework that tracks expert contributions to output representations. Our analysis of the DeepSeekMoE model reveals that despite having 64 routed experts with 6 active for each layer's computation, the model predominantly relies on a few specialized experts, with the top-weighted expert's output closely approximating the full ensemble prediction. We quantitatively validate these findings through a systematic analysis of the token routing distribution, demonstrating that very few experts handle over 50% of routing decisions across different specialized domains. Hidden state similarity between single and ensemble experts for every layer is extremely high, with some layers having cosine similarity as high as 0.95 and perplexity increasing by only 5% when using a single expert across all three domains. Our results indicate that Mixture of Experts models exhibit concentrated expertise highlighting potential opportunities for inference optimization through targeted expert pruning while maintaining model performance and opening avenues towards studying localization of learned knowledge in these models.
Mar 5, 2026

NeuronMoE: Neuron-Guided Mixture-of-Experts for Efficient Multilingual LLM Extension

Extending large language models to low-resource languages is essential for global accessibility, but training separate models per language is prohibitively expensive. Mixture-of-Experts (MoE) architectures address this by adding sparse language-specific parameters, but determining how many experts each layer needs remains an open question. Current approaches allocate experts based on layer-level similarity, yet language processing exhibits fine-grained specialization at individual neurons. We propose NeuronMoE\textbf{NeuronMoE}, a method that analyzes language-specific neurons across all transformer components to guide expert allocation per layer based on empirically measured cross-lingual neuron diversity. Applied to Llama-3.2-3B for low-resource languages (Greek, Turkish, and Hungarian), this approach achieves approximately 40% average parameter reduction while matching the performance of the LayerMoE baseline. We find that low-resource language experts independently develop neuron specialization patterns mirroring the high-resource language, which are concentrated in early and late layers. This reveals potential universal architectural principles in how multilingual models organize linguistic knowledge.
Mar 3, 2026

Robust Heterogeneous Analog-Digital Computing for Mixture-of-Experts Models with Theoretical Generalization Guarantees

Sparse Mixture-of-Experts (MoE) models enable efficient scalability by activating only a small sub-set of experts per input, yet their massive parameter counts lead to substantial memory and energy inefficiency during inference. Analog in-memory computing (AIMC) offers a promising solution by eliminating frequent data movement between memory and compute units. However, mitigating hardware nonidealities of AIMC typically requires noise-aware retraining, which is infeasible for large MoE models. In this paper, we propose a retraining-free heterogeneous computation framework in which noise-sensitive experts, which are provably identifiable by their maximum neuron norm, are computed digitally while the majority of the experts are executed on AIMC hardware. We further assign densely activated modules, such as attention layers, to digital computation due to their high noise sensitivity despite comprising a small fraction of parameters. Extensive experiments on large MoE language models, including DeepSeekMoE and OLMoE, across multiple benchmark tasks validate the robustness of our approach in maintaining accuracy under analog nonidealities.
Feb 19, 2026

Grassmannian Mixture-of-Experts: Concentration-Controlled Routing on Subspace Manifolds

Mixture-of-Experts models rely on learned routers to assign tokens to experts, yet standard softmax gating provides no principled mechanism to control the tradeoff between sparsity and utilization. We propose Grassmannian MoE (GrMoE), a routing framework that operates on the Grassmannian manifold of subspaces, where gating weights arise from the concentration parameters of Matrix Bingham distributions. This construction yields a single, interpretable knob -- the concentration matrix ΛΛ -- that continuously controls routing entropy, replacing discrete top-kk selection with a smooth, geometrically principled sparsity mechanism. We further develop an amortized variational inference procedure for posterior routing distributions, enabling uncertainty-aware expert assignment that naturally resists expert collapse. We formally prove tight bounds relating the Bingham concentration spectrum to routing entropy, expected top-kk mass, and an exponential bound on expert collapse, establishing the first formal theory of concentration-controlled sparsity. On synthetic routing tasks, a 350M-parameter MoE language model with 8 experts, a 1.3B-parameter model with 16 experts, and a 2.7B-parameter model with 32 experts, GrMoE achieves 0% routing collapse across all seeds, comparable or better perplexity with 15--30% improved load balance, and a smooth monotonic relationship between concentration and effective sparsity that enables post-hoc sparsity tuning without retraining. Token-level analysis reveals that experts learn heterogeneous concentration values that correlate with linguistic specialization, providing interpretable routing behavior.
Feb 19, 2026

Arcee Trinity Large Technical Report

We present the technical report for Arcee Trinity Large, a sparse Mixture-of-Experts model with 400B total parameters and 13B activated per token. Additionally, we report on Trinity Nano and Trinity Mini, with Trinity Nano having 6B total parameters with 1B activated per token, Trinity Mini having 26B total parameters with 3B activated per token. The models' modern architecture includes interleaved local and global attention, gated attention, depth-scaled sandwich norm, and sigmoid routing for Mixture-of-Experts. For Trinity Large, we also introduce a new MoE load balancing strategy titled Soft-clamped Momentum Expert Bias Updates (SMEBU). We train the models using the Muon optimizer. All three models completed training with zero loss spikes. Trinity Nano and Trinity Mini were pre-trained on 10 trillion tokens, and Trinity Large was pre-trained on 17 trillion tokens. The model checkpoints are available at https://huggingface.co/arcee-ai.
Feb 17, 2026

ExpertWeaver: Unlocking the Inherent MoE in Dense LLMs with GLU Activation Patterns

Mixture-of-Experts (MoE) effectively scales model capacity while preserving computational efficiency through sparse expert activation. However, training high-quality MoEs from scratch is prohibitively expensive. A promising alternative is to convert pretrained dense models into sparse MoEs. Existing dense-to-MoE methods fall into two categories: dynamic structural pruning that converts dense models into MoE architectures with moderate sparsity to balance performance and inference efficiency, and downcycling approaches that use pretrained dense models to initialize highly sparse MoE architectures. However, existing methods break the intrinsic activation patterns within dense models, leading to suboptimal expert construction. In this work, we argue that the Gated Linear Unit (GLU) mechanism provides a natural blueprint for dense-to-MoE conversion. We show that the fine-grained neural-wise activation patterns of GLU reveal a coarse-grained structure, uncovering an inherent MoE architecture composed of consistently activated universal neurons and dynamically activated specialized neurons. Leveraging this discovery, we introduce ExpertWeaver, a training-free framework that partitions neurons according to their activation patterns and constructs shared experts and specialized routed experts with layer-adaptive configurations. Our experiments demonstrate that ExpertWeaver significantly outperforms existing methods, both as a training-free dynamic structural pruning technique and as a downcycling strategy for superior MoE initialization.
Feb 4, 2026

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

Mixture-of-Experts (MoE) language models introduce unique challenges for safety alignment due to their sparse routing mechanisms, which can enable degenerate optimization behaviors under standard full-parameter fine-tuning. In our preliminary experiments, we observe that naively applying full-parameter safety fine-tuning to MoE models can reduce attack success rates through routing or expert dominance effects, rather than by directly repairing Safety-Critical Experts. To address this challenge, we propose RASA, a routing-aware expert-level alignment framework that explicitly repairs Safety-Critical Experts while preventing routing-based bypasses. RASA identifies experts disproportionately activated by successful jailbreaks, selectively fine-tunes only these experts under fixed routing, and subsequently enforces routing consistency with safety-aligned contexts. Across two representative MoE architectures and a diverse set of jailbreak attacks, RASA achieves near-perfect robustness, strong cross-attack generalization, and substantially reduced over-refusal, while preserving general capabilities on benchmarks such as MMLU, GSM8K, and TruthfulQA. Our results suggest that robust MoE safety alignment benefits from targeted expert repair rather than global parameter updates, offering a practical and architecture-preserving alternative to prior approaches.
Jan 24, 2026

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. SETA shares an overlapping parameter block only when the new task's update passes a subspace-agreement test and a sign test against its prior expert; shared knowledge is protected by adaptive elastic anchoring, and independently gated routers retrieve the relevant experts at inference without task identifiers. 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, improving overall performance over the strongest baseline by 1.1 to 1.7 points on TRACE and by up to 5.5 points on the O-LoRA benchmark, with backward transfer between -2.2 and -1.3 on TRACE, against 4.6 to 6.3 points of forgetting for MoE-CL and 8 to 15 points for the other LoRA baselines.
Jan 20, 2026

ButterflyMoE: Compression-Scalable Ternary Experts via Structured Butterfly Orbits

In current Mixture of Experts (MoE) architectures, linear memory scaling is present, the memory grows as the number of experts increases. NN independent expert weight matrices require O(N⋅d2)\mathcal{O}(N \cdot d^2) memory which exceeds the memory budget of edge devices. Current compression methods like quantization, pruning, and low-rank factorization reduce constant factors, but the scaling bottleneck is still unresolved. We introduce ButterflyMoE, a method which treats experts not as independent matrices but as geometric reorientations of a shared quantized substrate. Diversity amongst the experts arises from viewing different angles of the shared capacity and not from redundant storage. Learned rotations are applied to a shared ternary prototype. With this, each expert yields O(d2+N⋅dlog⁡d)\mathcal{O}(d^2 + N \cdot d \log d) memory-reducing per-expert cost from O(d2)\mathcal{O}(d^2) to O(dlog⁡d)\mathcal{O}(d \log d). The key insight is that training these rotations with quantization reduces activation outliers and stabilizes extreme low-bit training where other static methods collapse. Across language modeling benchmarks, ButterflyMoE achieves 80×\times memory reduction at 8 experts with a highly favorable memory-accuracy tradeoff.At this 80x compression ButterflyMoE outperforms an equal memory dense baseline, showing that orbital parameterization extracts fundamentally more utility per byte. When scaled up to 256 experts, ButterflyMoE asymptotically compresses the memory by 150 ×\times. ButterflyMoE reduces the constant factor of linear scaling with compression ratio growing with the expert count.
Jan 8, 2026

DR-LoRA: Dynamic Rank LoRA for Fine-Tuning Mixture-of-Experts Models

Mixture-of-Experts (MoE) has become a prominent paradigm for scaling Large Language Models (LLMs). Parameter-efficient fine-tuning methods, such as LoRA, are widely adopted to adapt pretrained MoE LLMs to downstream tasks. However, existing approaches typically assign identical LoRA ranks to all expert modules, ignoring the heterogeneous specialization of pretrained experts. This uniform allocation leads to a resource mismatch: task-relevant experts are under-provisioned, while less relevant ones receive redundant parameters. To address this, we propose DR-LoRA, a Dynamic Rank LoRA framework for fine-tuning pretrained MoE models. Specifically, DR-LoRA initializes all expert LoRA modules with a small active rank and uses an expert saliency score, which combines routing frequency and gradient-based rank importance, to identify which experts would benefit most from additional capacity. It then periodically expands the active ranks of the task-critical expert LoRA, progressively constructing a heterogeneous rank distribution tailored to the target task. Experiments on three MoE models across six tasks show that DR-LoRA consistently outperforms LoRA and other strong baselines, demonstrating that task-adaptive heterogeneous rank allocation is an effective strategy to improve active capacity utilization in MoE fine-tuning.
Nov 9, 2025

Mixtures of SubExperts for Large Language Continual Learning

Enabling lifelong learning in LLMs demands resolving the stability-plasticity dilemma (i.e., models must incorporate new knowledge without overwriting prior representations) while maintaining scalability under bounded parameter growth. Existing PEFT methods fail to satisfy this triad; shared-parameter approaches suffer from catastrophic interference, while task-isolated expansions preclude knowledge transfer and scale linearly. We propose Mixtures of SubExperts (MoSEs), a modular and sparse framework that factorizes model capacity into reusable, compositional primitives. MoSEs augment transformer layers with lightweight SubExperts and a learned sub-routing function that dynamically selects and composes a sparse subset of modules conditioned on task inputs. This induces a structured decomposition of the parameter space where knowledge is localized yet accessible, mitigating interference while preserving reuse. Specifically, MoSEs balance the dilemma via three pillars: (i) stability by isolating knowledge within sparsely activated modules, (ii) plasticity through routing-driven recombination and selective expansion, and (iii) scalability via sublinear growth in effective capacity. Notably, the routing mechanism enables compositional generalization, allowing new tasks to be represented as combinations of previously acquired sub-functions. We empirically validate MoSEs on TRACE and SuperNI, showing reduced forgetting, improved forward transfer, and better parameter efficiency over strong PEFT baselines. MoSEs establish a new Pareto frontier, achieving state-of-the-art performance while maintaining strict parameter budgets. Our results suggest that modular sparsity and compositional routing are key inductive biases for building foundation models that continually learn without saturation.
Sep 30, 2025

Training Matryoshka Mixture-of-Experts for Elastic Inference-Time Expert Utilization

Mixture-of-Experts (MoE) has emerged as a promising paradigm for efficiently scaling large language models without a proportional increase in computational cost. However, the standard training strategy of Top-K router prevents MoE models from realizing their full potential for elastic inference. When the number of activated experts is altered at inference time, these models exhibit precipitous performance degradation. In this work, we introduce Matryoshka MoE (M-MoE), a training framework that instills a coarse-to-fine structure directly into the expert ensemble. By systematically varying the number of activated experts during training, M-MoE compels the model to learn a meaningful ranking: top-ranked experts collaborate to provide essential, coarse-grained capabilities, while subsequent experts add progressively finer-grained detail. We explore this principle at multiple granularities, identifying a layer-wise randomization strategy as the most effective. Our experiments demonstrate that a single M-MoE model achieves remarkable elasticity, with its performance at various expert counts closely matching that of an entire suite of specialist models, but at only a fraction of the total training cost. This flexibility not only unlocks elastic inference but also enables optimizing performance by allocating different computational budgets to different model layers. Our work paves the way for more practical and adaptable deployments of large-scale MoE models.
Mar 13, 2025

Ensemble Learning for Large Language Models in Text and Code Generation: A Survey

Generative Pretrained Transformers (GPTs) are foundational Large Language Models (LLMs) for text generation. However, individual LLMs often produce inconsistent outputs and exhibit biases, limiting their representation of diverse language patterns. The closed-source nature of many powerful LLMs further restricts industry applications due to data privacy concerns. Inspired by successes in text generation, LLM ensemble techniques are now increasingly explored for code generation. This article reviews these emerging ensemble approaches to enhance understanding, encourage further research, and promote practical implementation in both text and code generation. We categorize LLM ensembles into seven main methods - weight merging, knowledge fusion, mixture-of-experts, reward ensemble, output ensemble, routing, and cascading - analyzing capabilities of those approaches. Our findings highlight key benefits such as improved diversity representation, enhanced output quality, and greater application flexibility. These insights aid model selection for real-world tasks and crucially, lay groundwork for extending ensemble strategies to multimodal LLMs.
Apr 25, 2024

Prediction Is All MoE Needs: Expert Load Distribution Goes from Fluctuating to Stabilizing

MoE facilitates the development of large models by making the computational complexity of the model no longer scale linearly with increasing parameters. The learning sparse gating network selects a set of experts for each token to be processed; however, this may lead to differences in the number of tokens processed by each expert over several successive iterations, i.e., the expert load fluctuations, which reduces computational parallelization and resource utilization. To this end, we traced and analyzed loads of each expert in the training iterations for several large language models in this work, and defined the transient state with "obvious load fluctuation" and the stable state with "temporal locality". Moreover, given the characteristics of these two states and the computational overhead, we deployed three classical prediction algorithms that achieve accurate expert load prediction results. For the GPT3 350M model, the average error rates for predicting the expert load proportion over the next 1,000 and 2,000 steps are approximately 1.3% and 1.8%, respectively. This work can provide valuable guidance for expert placement or resource allocation for MoE model training. Based on this work, we will propose an expert placement scheme for transient and stable states in our coming work.