ICLR 2026 论文列表

Recently, diffusion models have achieved a great performance with a small dataset of size $n$ and a fast optimization process. Despite the impressive performance, the estimation error suffers from the curse of dimensionality $n^{-1/D}$, where $D$ is the data dimension. Since images are usually a union of low-dimensional manifolds, current works model the data as a union of linear subspaces with Gaussian latent and achieve a $1/\sqrt{n}$ bound. Though this modeling reflects the multi-manifold property of data, the Gaussian latent can not capture the multi-modal property of the latent manifold. To bridge this gap, we propose the mixture subspace of low-rank mixture of Gaussian (MoLR-MoG) modeling, which models the target data as a union of $K$ linear subspaces, and each subspace admits a mixture of Gaussian latent ($n_k$ modals with dimension $d_k$). With this modeling, the corresponding score function naturally has a mixture of expert (MoE) structure, captures the multi-modal information, and contains nonlinear properties since each expert is a nonlinear latent MoG score. We first conduct real-world experiments to show that the generation results of MoE-latent MoG NN are much better than the results of MoE-latent Gaussian score. Furthermore, MoE-latent MoG NN achieves a comparable performance with MoE-latent Unet with $10 \times$ parameters. These results indicate that the MoLR-MoG modeling is reasonable and suitable for real-world data. After that, based on such MoE-latent MoG score, we provide a $R^4\sqrt{\Sigma_{k=1}^Kn_k}\sqrt{\Sigma_{k=1}^Kn_kd_k}/\sqrt{n}$ estimation error, which escapes the curse of dimensionality by using data structure. Finally, we study the optimization process and prove the convergence guarantee under the MoLR-MoG modeling. Combined with these results, under a setting close to real-world data, this work explains why diffusion models only require a small training sample and enjoy a fast optimization process to achieve a great performance.

The Mixture of Experts (MoE) is an effective architecture for scaling large language models by leveraging sparse expert activation to balance performance and efficiency. However, under expert parallelism, MoE suffers from inference inefficiencies due to imbalanced token-to-expert assignment, where underloaded experts complete computations early but must wait for overloaded experts, leading to global delays. We define this phenomenon as the \textbf{\textit{Straggler Effect}}, as the most burdened experts dictate the overall inference latency. To address this, we first propose \textit{\textbf{Capacity-Aware Token Drop}}, which enforces expert capacity limits by discarding excess tokens from overloaded experts, effectively reducing load imbalance with minimal performance impact (e.g., $30\%$ speedup with only $0.9\%$ degradation on OLMoE). Next, given the presence of low-load experts remaining well below the capacity threshold, we introduce \textit{\textbf{Capacity-Aware Expanded Drop}}, which allows tokens to include additional local experts in their candidate set before enforcing strict local capacity constraints, thereby improving load balance and enhancing the utilization of underused experts. Extensive experiments on both language and multimodal MoE models demonstrate the effectiveness of our approach, yielding substantial gains in expert utilization, model performance, and inference efficiency, e.g., applying Expanded Drop to Mixtral-8$\times$7B-Instruct yields a {0.2\%} average performance improvement and a {1.85$\times$} inference speedup. The code is released at: https://github.com/CASE-Lab-UMD/Capacity-Aware-MoE.

Language model (LM)-based embodied agents are increasingly deployed in real-world settings. Yet, their adaptability remains limited in dynamic environments, where constructing accurate and flexible world models is crucial for effective reasoning and decision-making. To address this challenge, we extend the Mixture-of-Experts (MoE) paradigm to embodied agents. While conventional MoE architectures modularize knowledge into expert components with pre-trained routing, they remain rigid once deployed, making them less effective for adapting to unseen domains in dynamic environments. We therefore propose Test-time Mixture of World Models (TMoW), a framework that enhances adaptability to unseen and evolving domains. TMoW updates its routing function over world models at test time, unlike conventional MoE where the function remains fixed, enabling agents to recombine existing models and integrate new ones for continual adaptation. It achieves this through (i) multi-granular prototype-based routing, which adapts mixtures across object- to scene-level similarities, (ii) test-time refinement that aligns unseen domain features with prototypes during inference, and (iii) distilled mixture-based augmentation, which efficiently constructs new models from few-shot data and existing prototypes. We evaluate TMoW on VirtualHome, ALFWorld, and RLBench benchmarks, demonstrating strong performance in both zero-shot adaptation and few-shot expansion scenarios, and showing that it enables embodied agents to operate effectively in dynamic environments.

Mixture of Experts (MoE) models have emerged as the de-facto architecture for scaling up language models without significantly increasing the computational cost. Existing MoE methods optimize system efficiency or model architecture independently. We show that as MoE models get more granular and sparser, they become more memory-bound, and jointly optimizing the algorithms and the kernel design leads to a major improvement in MoE training throughput. We first propose a memory-efficient algorithm to compute the forward and backward of MoE with minimal activation saved. We then design GPU kernels that overlap memory IO latency with compute, benefiting all MoE architectures. Finally, we propose a novel "token rounding" method that minimizes the wasted compute brought by tile quantization. As a result, our method SNaX reduces activation memory by 45% and has 1.80x throughput improvement on NVidia H100 GPUs compared to ScatterMoE for a fine-grained 7B MoE. Moreover, SNaX on 64 H100s achieves a training throughput of 213 billion tokens a day comparable to ScatterMoE's 225 billion tokens a day on 96 H100s for a 7B MoE model training with token-choice routing while training with FSDP-2. Under high MoE sparsity settings, our tile-aware token rounding algorithm yields an additional 1.18x speedup on kernel execution time compared to vanilla top-$K$ routing while maintaining similar downstream performance.

Leveraging the intrinsic importance differences among experts, recent research has explored expert-level compression techniques to enhance the efficiency of Mixture-of-Experts (MoE) large language models (LLMs). However, existing approaches often rely on empirical heuristics to identify critical experts, while lacking a deeper understanding into the heterogeneous importance of experts and the inner workings of MoE LLMs. In this study, we report, for the first time, the discovery and systematic investigation of a distinct subset of experts that play a pivotal role in the model's forward inference. These experts are prevalent in open-source MoE LLMs, and despite their extremely limited number, pruning them results in a substantial decline in model performance (e.g., prune just three out of 6,144 causes Qwen3-30B-A3B to generate repetitive and uninformative outputs). We refer to these experts as Super Experts (SEs). Our comprehensive analysis provides progressively deeper insights into SEs: (i) SEs are characterized by rare but extreme activation outliers in the output of the down\_proj, which give rise to massive activations in the hidden states between decoder layers. Moreover, the distribution of SEs is model-specific, data-agnostic, and remains unaffected by post-training processes. (ii) By pruning SEs, we assess their significance across a variety of tasks, revealing their considerable impact on the model's overall performance, particularly in mathematical reasoning. (iii) We further investigate why compressing SEs exerts such a pronounced impact. We show that, in MoE LLMs, SEs serve as the primary source of the systematic outlier mechanism in Transformers, and that compressing them profoundly disrupts this process, ultimately causing the collapse of attention sinks. These findings advance the understanding of the internal dynamics of MoE LLMs, filling an important gap in the current knowledge. In addition, we developed an automated tool for rapid and accurate SE profiling. The code is provided in the supplementary materials.

Existing expert merging strategies for Sparse Mixture of Experts (SMoE) typically rely on input-dependent or input-independent averaging of expert parameters, but often lack a principled weighting mechanism. In this work, we reinterpret expert merging through the lens of game theory, revealing cooperative and competitive dynamics among experts. Based on this perspective, we introduce Nash Merging of Experts (NAMEx), a novel framework that incorporates Nash Bargaining into the merging process, enabling more balanced and efficient collaboration among experts. Additionally, we incorporate complex momentum into NAMEx to accelerate expert propagation with theoretical guarantees for convergence. Extensive experiments across language modeling, text classification, image classification, and zero-shot robustness under data corruption show that NAMEx consistently outperforms competing methods while integrating seamlessly with popular MoE architectures. Finally, we demonstrate NAMEx’s scalability by applying it to large-scale systems, including Qwen1.5-MoE (14B) and DeepSeek-MoE (16B), where it proves effective in both zero-shot and fine-tuning settings.

Mixture-of-Experts (MoE) architectures in large language models (LLMs) deliver exceptional performance and reduced inference costs compared to dense LLMs. However, their large parameter counts result in prohibitive memory requirements, limiting practical deployment. While existing pruning methods primarily focus on expert-level pruning, this coarse granularity often leads to substantial accuracy degradation. In this work, we introduce HEAPr, a novel pruning algorithm that decomposes experts into smaller, indivisible atomic experts, enabling more precise and flexible atomic expert pruning. To measure the importance of each atomic expert, we leverage second-order information based on principles similar to Optimal Brain Surgeon (OBS) theory. To address the computational and storage challenges posed by second-order information, HEAPr exploits the inherent properties of atomic experts to transform the second-order information from expert parameters into that of atomic expert parameters, and further simplifies it to the second-order information of atomic expert outputs. This approach reduces the space complexity from $O(d^4)$, where $d$ is the model’s dimensionality, to $O(d^2)$. HEAPr requires only two forward passes and one backward pass on a small calibration set to compute the importance of atomic experts. Extensive experiments on MoE models, including DeepSeek MoE and Qwen MoE family, demonstrate that HEAPr outperforms existing expert-level pruning methods across a wide range of compression ratios and benchmarks. Specifically, HEAPr achieves nearly lossless compression at compression ratios of $20\% \sim 25\%$ in most models, while also reducing FLOPs nearly by $20\%$. The code can be found at \href{https://anonymous.4open.science/r/anonymous-code-B927/}{anonymous-code-B927}.

Recent attempts to combine low-rank adaptation (LoRA) with mixture-of-experts (MoE) for multi-task adaptation of Large Language Models (LLMs) often replace whole attention/FFN layers with switch experts or append parallel expert branches, undermining parameter efficiency and limiting task specialization. We introduce **LoRA-Mixer**, a modular MoE framework that routes task-specific LoRA experts into the core projection matrices of the attention module (input/output linear layers), rather than primarily targeting FFN blocks. The design delivers fine-grained token-level specialization by fully exploiting the attention mechanism, while remaining drop-in compatible with Transformers and state-space models (SSMs) as the linear projection layers are ubiquitous. To train robust routers from limited data while promoting stable, selective decisions and high expert reuse, **LoRA-Mixer** employs an adaptive **Routing Specialization Loss (RSL)** that jointly enforces global load balance and input-aware specialization via an entropy-shaping objective. The framework supports two regimes: (i) joint optimization of adapters and router with a differentiable hard–soft top-k routing scheme, and (ii) plug-and-play routing over frozen, pre-trained LoRA modules sourced from public repositories. Across 15 benchmarks—including MedQA, GSM8K, HumanEval, and GLUE—RSL-optimized LoRA-Mixer outperforms state-of-the-art routing and LoRA-MoE baselines while using 48% of their trainable parameters, with gains of +3.79%, +2.90%, and +3.95% on GSM8K, CoLA, and ARC-C, respectively. Cross-model transfer and adapter reuse experiments further demonstrate the approach’s versatility and data efficiency.

Visual Prompt Tuning (VPT) has proven effective for parameter-efficient adaptation of pre-trained vision models to downstream tasks by inserting task-specific learnable prompt tokens. Despite its empirical success, a comprehensive theoretical understanding of VPT remains an active area of research. Building on the recently established connection between Mixture of Experts (MoE) and prompt-based methods, wherein each attention head can be conceptualized as a composition of multiple MoE models, we reinterpret VPT as the introduction of new *prompt experts* into these MoE structures. We identify a key limitation in existing VPT frameworks: the *restricted functional expressiveness* of prompt experts, which remain static and thus limited in their adaptability. To address this, we propose **Visual Adaptive Prompt Tuning (VAPT)**, a novel method that endows prompt experts with enhanced expressiveness while preserving parameter efficiency. Empirical evaluations on VTAB-1K and FGVC demonstrate that VAPT achieves *substantial performance improvements*, surpassing fully fine-tuned baselines by **7.34%** and **1.04%**, respectively. Moreover, VAPT consistently outperforms VPT while *requiring fewer additional parameters*. Furthermore, our theoretical analysis indicates that VAPT achieves optimal sample efficiency. Collectively, these results underscore the theoretical grounding and empirical advantages of our approach.

Knowledge distillation has become a crucial technique to transfer the capacities of large language models (LLMs) to smaller, more efficient models for practical deployment. While recent work exploits rich information from intermediate states of the teacher model for more effective knowledge transfer, imperfect knowledge from the teacher can also mislead student learning, restricting the student’s generalization capacity. In this work, we propose a two-stage distillation framework that is effective for diverse knowledge distillation scenarios. In the first stage, we pretrain projectors to extract and compress teacher knowledge into a low-dimensional vector space via self-reconstruction. In the second stage, we perform distillation with a hybrid objective that combines learning from the compressed teacher representations with standard supervised fine-tuning on ground-truth data. Our key innovation is residual learning for LLM distillation, where the student learns to make predictions based on the differential between its representations and projected states from the teacher. This approach encourages the student to further improve its representations beyond potentially erroneous teacher knowledge. For Mixture-of-Experts (MoE) teacher models, we further fuse the experts’ outputs using a self-attention mechanism for better utilizing the teacher knowledge. Moreover, to support the cross-tokenizer distillation setting, where the teacher and student models have different vocabularies, we adopt a cross-model attention mechanism that eliminates the need for explicit token alignment rules. Experimental results show the superior performance of our proposed framework under both same- and cross-tokenizer settings, demonstrating the effectiveness in preserving teacher knowledge and improving student generalization capability.

Mixture-of-Experts (MoE) architectures have demonstrated remarkable capabilities and scalability for large language models, but incur a prohibitive memory footprint due to duplicated expert parameters. Existing compression approaches, particularly those based on low-rank decomposition, typically operate at the granularity of individual experts. However, such per-expert methods overlook structural redundancies across experts, limiting their compression efficiency and effectiveness. In this work, we introduce TD-MoE (Tensor Decomposition for MoE Compression), a data-aware framework that jointly and holistically factorizes expert weights. Our contributions are threefold: (i) Cross-expert tensorization with joint 3D decomposition, which unifies all experts within a layer into a single tensor and captures shared structure beyond per-expert scope; (ii) A multi-linear whitening strategy, which decorrelates input and output features, yielding a more balanced and data-adaptive decomposition; (iii) A 3D rank allocation mechanism, which dynamically assigns 3D decomposition ranks across dimensions to best meet a target compression ratio while minimizing the reconstruction error. Extensive experiments on Qwen2-57B-A14 and Mixtral-8×7B across seven commonsense reasoning benchmarks demonstrate that TD-MoE achieves almost lossless performance under 20\% parameter reduction, and delivers more than 11\% and 14\% gains over state-of-the-art decomposition-based baselines at 40\% and 60\% compression. Further ablation studies validate the effectiveness of each component, highlighting the importance of joint factorization, whitening, and rank allocation. The code is available at \href{https://anonymous.4open.science/r/TD-MoE}{https://anonymous.4open.science/r/TD-MoE}.

We study the problem of federated clustering when the total number of clusters $K$ across clients is unknown, and the clients have heterogeneous but potentially overlapping cluster sets in their local data. To that end, we develop FedGEM: a federated generalized expectation-maximization algorithm for the training of mixture models with an unknown number of components. Our proposed algorithm relies on each of the clients performing EM steps locally, and constructing an uncertainty set around the maximizer associated with each local component. The central server utilizes the uncertainty sets to learn potential cluster overlaps between clients, and infer the global number of clusters via closed-form computations. We perform a thorough theoretical study of our algorithm, presenting probabilistic convergence guarantees under common assumptions. Subsequently, we study the specific setting of isotropic GMMs, providing tractable, low-complexity computations to be performed by each client during each iteration of the algorithm, as well as rigorously verifying assumptions required for algorithm convergence. We perform various numerical experiments, where we empirically demonstrate that our proposed method achieves comparable performance to centralized EM, and that it outperforms various existing federated clustering methods.

Mixture-of-Experts (MoE) has been a prevalent method for scaling up large language models at a reduced computational cost. Despite its effectiveness, the routing mechanism of MoE still lacks a clear understanding from the perspective of cross-layer mechanistic interpretability. We propose a light-weight methodology at which we can break down the routing decision for MoE to contribution of model components, in a recursive fashion. We use our methodology to dissect the routing mechanism by decomposing the input of routers into model components. We study how different model components contribute to the routing in different widely used open models. Our findings on four different LLMs reveal common patterns such as: a) MoE layer outputs contribute more than attention layer outputs to the routing decisions of latter layers, b) \emph{MoE entanglement} at which MoE firing up in layers consistently correlate with firing up of MoE in latter layers, and c) some components can persistently influence the routing in many following layers. Our study also includes findings on how different models have different patterns when it comes to long range and short range inhibiting/promoting effects that components can have over MoE in latter layers. Our results indicate importance of quantifying the impact of components across different layers on MoE to understand the mechanism of routing.

Knowledge editing (KE) is crucial for making precise modifications to factual knowledge within large language models (LLMs). Existing KE methods, however, are primarily designed for dense architectures, limiting their applicability to the increasingly popular sparse Mixture-of-Experts (MoE) models that power modern scalable LLMs. While MoEs offer remarkable efficiency and capacity scaling, their unique structure introduces new challenges for KE. Naively adapting dense-model editors to MoEs is not only computationally expensive but also induces routing distribution shifts that degrade model stability and consistency. To address these challenges, we introduce MoEEdit, the first systematic framework for routing-stable knowledge editing in MoE LLMs. Our approach reparameterizes expert updates through per-expert null-space projections, ensuring router inputs remain invariant to suppress these shifts, and solves the resulting block-structured optimization with an efficient block coordinate descent (BCD) solver. Experiments demonstrate that MoEEdit achieves state-of-the-art efficacy and generalization, while maintaining high specificity, routing stability, and superior computational and memory efficiency. Our work establishes a robust foundation for scalable and precise knowledge editing in modern sparse LLMs by highlighting the necessity of routing-stable interventions.

Prompt-based methods have recently gained prominence in Continual Learning (CL) due to their strong performance and memory efficiency. A prevalent strategy in this paradigm assigns a dedicated subset of prompts to each task, which, while effective, incurs substantial computational overhead and causes memory requirements to scale linearly with the number of tasks. Conversely, approaches employing a single shared prompt across tasks offer greater efficiency but often suffer from degraded performance due to knowledge interference. To reconcile this trade-off, we propose **SMoPE**, a novel framework that integrates the benefits of both task-specific and shared prompt strategies. Inspired by recent findings on the relationship between Prefix Tuning and Mixture of Experts (MoE), SMoPE organizes a shared prompt into multiple "prompt experts" within a sparse MoE architecture. For each input, only a select subset of relevant experts is activated, effectively mitigating interference. To facilitate expert selection, we introduce a prompt-attention score aggregation mechanism that computes a unified proxy score for each expert, enabling dynamic and sparse activation. Additionally, we propose an adaptive noise mechanism to encourage balanced expert utilization while preserving knowledge from prior tasks. To further enhance expert specialization, we design a prototype-based loss function that leverages prefix keys as implicit memory representations. Extensive experiments across multiple CL benchmarks demonstrate that SMoPE consistently outperforms task-specific prompt methods and achieves performance competitive with state-of-the-art approaches, all while significantly reducing parameter counts and computational costs.

Outliers have emerged as a fundamental bottleneck in preserving accuracy for low-precision large models, particularly within Mixture-of-Experts (MoE) architectures that are increasingly central to large-scale language modeling. Under post-training quantization (PTQ), these outliers induce substantial quantization errors, leading to severe accuracy degradation. While recent rotation-based smoothing techniques alleviate the problem by redistributing outlier magnitudes, residual errors remain and continue to impede reliable low-precision deployment. In this work, we tackle this challenge by introducing a unified quantization-and-clustering scheme that contains smoothing activation outliers via learnable rotation and absorbing weight outliers into fine-tuned cluster centroids for MoE. This design reduces the influence of extreme values by fitting them within cluster centroids, thereby lowering quantization error while maintaining expressive capacity. We introduce~\textit{CodeQuant}, a unified quantization-and-clustering framework tailored for MoEs. Coupled with a dedicated kernel design for GPU and CPU, CodeQuant achieves up to $4.15\times$ speedup while delivering significantly higher accuracy than state-of-the-art quantization approaches across diverse MoE models. Our results highlight CodeQuant as a promising direction for efficient and accurate deployment of MoE-based large language models under low-precision constraints.

Mixture-of-Experts (MoE) architectures employ sparse activation to deliver faster training and inference with higher accuracy than dense LLMs. However, in production serving, MoE models require batch inference to optimize hardware efficiency, which may cause excessive expert activation and thus slow the memory-bound decoding stage. To address the fundamental tension between batch decoding and expert sparsity, we present **SERE**, a **S**imilarity-based **E**xpert **R**e-routing method for **E**fficient batch decoding in MoE models. SERE dynamically reduces the number of active experts in an input-aware manner by re-routing tokens from secondary experts to their most similar primary counterparts. It also leverages similarity patterns to identify and preserve critical experts, thereby preventing capability loss. Notably, SERE avoids static expert pruning or merging, instead enabling dynamic expert skipping based on batch-level expert redundancy. Additionally, we provide an efficient custom CUDA kernel for SERE, enabling plug-and-play use in vLLM with only a single-line code change. Extensive experiments on various complex reasoning benchmarks demonstrate that SERE achieves up to $2.0\times$ speedup with minimal quality loss, providing a practical solution for cost-efficient and latency-sensitive large-scale MoE deployment.

Mixture-of-Experts (MoE) has demonstrated strong performance in video understanding tasks, yet its adversarial robustness remains underexplored. Existing attack methods often treat MoE as a unified architecture, overlooking the independent and collaborative weaknesses of key components such as routers and expert modules. To fill this gap, we propose Temporal Lipschitz-Guided Attacks (TLGA) to thoroughly investigate component-level vulnerabilities in video MoE models. We first design attacks on the router, revealing its independent weaknesses. Building on this, we introduce Joint Temporal Lipschitz-Guided Attacks (J-TLGA), which collaboratively perturb both routers and experts. This joint attack significantly amplifies adversarial effects and exposes the Achilles’ Heel (collaborative weaknesses) of the MoE architecture. Based on these insights, we further propose Joint Temporal Lipschitz Adversarial Training (J-TLAT). J-TLAT performs joint training to further defend against collaborative weaknesses, enhancing component-wise robustness. Our framework is plug-and-play and reduces inference cost by more than 60% compared with dense models. It consistently enhances adversarial robustness across diverse video datasets and model architectures, effectively mitigating both the independent and collaborative weaknesses of MoE.

General continual learning (GCL) challenges intelligent systems to learn from single-pass, non-stationary data streams without clear task boundaries. While recent advances in continual parameter-efficient tuning (PET) of pretrained models show promise, they typically rely on multiple training epochs and explicit task cues, limiting their effectiveness in GCL scenarios. Moreover, existing methods often lack targeted design and fail to address two fundamental challenges in continual PET: how to allocate expert parameters to evolving data distributions, and how to improve their representational capacity under limited supervision. Inspired by the fruit fly's hierarchical memory system characterized by sparse expansion and modular ensembles, we propose FlyPrompt, a brain-inspired framework that decomposes GCL into two subproblems: expert routing and expert competence improvement. FlyPrompt introduces a randomly expanded analytic router for instance-level expert activation and a temporal ensemble of output heads to dynamically adapt decision boundaries over time. Extensive theoretical and empirical evaluations demonstrate FlyPrompt's superior performance, achieving up to 11.23%, 12.43%, and 7.62% gains over state-of-the-art baselines on CIFAR-100, ImageNet-R, and CUB-200, respectively. Our source code is available at https://github.com/AnAppleCore/FlyGCL.