ICML 2025 Papers

Machine learning models are routinely trained on a mixture of different data domains. Different domain weights yield very different downstream performances. We propose the Soup-of-Experts, a novel architecture that can instantiate a model at test time for any domain weights with minimal computational cost and without re-training the model. Our architecture consists of a bank of expert parameters, which are linearly combined to instantiate one model. We learn the linear combination coefficients as a function of the input domain weights. To train this architecture, we sample random domain weights, instantiate the corresponding model, and backprop through one batch of data sampled with these domain weights. We demonstrate how our approach obtains small specialized models on several language modeling tasks quickly. Soup-of-Experts are particularly appealing when one needs to ship many different specialist models quickly under a size constraint.

Diffusion models have transformed generative modeling but suffer from scalability limitations due to computational overhead and inflexible architectures that process all generative stages and tokens uniformly. In this work, we introduce Diff-MoE, a novel framework that combines Diffusion Transformers with Mixture-of-Experts to exploit both temporarily adaptability and spatial flexibility. Our design incorporates expert-specific timestep conditioning, allowing each expert to process different spatial tokens while adapting to the generative stage, to dynamically allocate resources based on both the temporal and spatial characteristics of the generative task. Additionally, we propose a globally-aware feature recalibration mechanism that amplifies the representational capacity of expert modules by dynamically adjusting feature contributions based on input relevance. Extensive experiments on image generation benchmarks demonstrate that Diff-MoE significantly outperforms state-of-the-art methods. Our work demonstrates the potential of integrating diffusion models with expert-based designs, offering a scalable and effective framework for advanced generative modeling.

Graph Neural Networks (GNNs) have shown great promise in tasks like node and graph classification, but they often struggle to generalize, particularly to unseen or out-of-distribution (OOD) data. These challenges are exacerbated when training data is limited in size or diversity. To address these issues, we introduce a theoretical framework using Rademacher complexity to compute a regret bound on the generalization error and then characterize the effect of data augmentation. This framework informs the design of GRATIN, an efficient graph data augmentation algorithm leveraging the capability of Gaussian Mixture Models (GMMs) to approximate any distribution. Our approach not only outperforms existing augmentation techniques in terms of generalization but also offers improved time complexity, making it highly suitable for real-world applications.

Transformer models encounter inefficiency when scaling hidden dimensions due to the uniform expansion of parameters. When delving into the sparsity of hidden dimensions, we observe that only a small subset of dimensions are highly activated, where some dimensions are commonly activated across tokens, and some others uniquely activated for individual tokens. To leverage this, we propose MoHD (Mixture of Hidden Dimensions), a sparse architecture that combines shared sub-dimensions for common features and dynamically routes specialized sub-dimensions per token. To address the potential information loss from sparsity, we introduce activation scaling and group fusion mechanisms. MoHD efficiently expands hidden dimensions with minimal computational increases, outperforming vanilla Transformers in both parameter efficiency and task performance across 10 NLP tasks. MoHD achieves 1.7% higher performance with 50% fewer activatied parameters and 3.7% higher performance with 3× total parameters expansion at constant activated parameters cost. MoHD offers a new perspective for scaling the model, showcasing the potential of hidden dimension sparsity.

Expert parallelism has emerged as a key strategy for distributing the computational workload of sparsely-gated mixture-of-experts (MoE) models across multiple devices, enabling the processing of increasingly large-scale models. However, the All-to-All communication inherent to expert parallelism poses a significant bottleneck, limiting the efficiency of MoE models. Although existing optimization methods partially mitigate this issue, they remain constrained by the sequential dependency between communication and computation operations. To address this challenge, we propose ScMoE, a novel shortcut-connected MoE architecture integrated with an overlapping parallelization strategy. ScMoE decouples communication from its conventional sequential ordering, enabling up to 100\% overlap with computation. Compared to the prevalent top-2 MoE baseline, ScMoE achieves speedups of $1.49\times$ in training and $1.82\times$ in inference. Moreover, our experiments and analyses indicate that ScMoE not only achieves comparable but in some instances surpasses the model quality of existing approaches.

Modality fusion is a cornerstone of multimodal learning, enabling information integration from diverse data sources. However, existing approaches are limited by $\textbf{(a)}$ their focus on modality correspondences, which neglects heterogeneous interactions between modalities, and $\textbf{(b)}$ the fact that they output a single multimodal prediction without offering interpretable insights into the multimodal interactions present in the data. In this work, we propose $\texttt{I$^2$MoE}$ ($\underline{I}$nterpretable Multimodal $\underline{I}$nteraction-aware $\underline{M}$ixture-$\underline{o}$f-$\underline{E}$xperts), an end-to-end MoE framework designed to enhance modality fusion by explicitly modeling diverse multimodal interactions, as well as providing interpretation on a local and global level. First, $\texttt{I$^2$MoE}$ utilizes different interaction experts with weakly supervised interaction losses to learn multimodal interactions in a data-driven way. Second, $\texttt{I$^2$MoE}$ deploys a reweighting model that assigns importance scores for the output of each interaction expert, which offers sample-level and dataset-level interpretation. Extensive evaluation of medical and general multimodal datasets shows that $\texttt{I$^2$MoE}$ is flexible enough to be combined with different fusion techniques, consistently improves task performance, and provides interpretation across various real-world scenarios. Code is available at https://github.com/Raina-Xin/I2MoE.

On-device LLMs have gained increasing attention for their ability to enhance privacy and provide a personalized user experience. To facilitate private learning with scarce data, Federated Learning has become a standard approach. However, it faces challenges such as computational resource heterogeneity and data heterogeneity among end users. We propose CoMiGS ($\textbf{Co}$llaborative learning with a $\textbf{Mi}$xture of $\textbf{G}$eneralists and $\textbf{S}$pecialists), the first approach to address both challenges. A key innovation of our method is the bi-level optimization formulation of the Mixture-of-Experts learning objective, where the router is optimized using a separate validation set to ensure alignment with the target distribution. We solve our objective with alternating minimization, for which we provide a theoretical analysis. Our method shares generalist experts across users while localizing a varying number of specialist experts, thereby adapting to users’ computational resources and preserving privacy. Through extensive experiments, we show CoMiGS effectively balances general and personalized knowledge for each token generation. We demonstrate that CoMiGS remains robust against overfitting—due to the generalists' regularizing effect—while adapting to local data through specialist expertise. We open source our codebase for collaborative LLMs.

Diffusion models approximate the denoising distribution as a Gaussian and predict its mean, whereas flow matching models reparameterize the Gaussian mean as flow velocity. However, they underperform in few-step sampling due to discretization error and tend to produce over-saturated colors under classifier-free guidance (CFG). To address these limitations, we propose a novel Gaussian mixture flow matching (GMFlow) model: instead of predicting the mean, GMFlow predicts dynamic Gaussian mixture (GM) parameters to capture a multi-modal flow velocity distribution, which can be learned with a KL divergence loss. We demonstrate that GMFlow generalizes previous diffusion and flow matching models where a single Gaussian is learned with an $L_2$ denoising loss. For inference, we derive GM-SDE/ODE solvers that leverage analytic denoising distributions and velocity fields for precise few-step sampling. Furthermore, we introduce a novel probabilistic guidance scheme that mitigates the over-saturation issues of CFG and improves image generation quality. Extensive experiments demonstrate that GMFlow consistently outperforms flow matching baselines in generation quality, achieving a Precision of 0.942 with only 6 sampling steps on ImageNet 256$\times$256.

Diffusion models have driven the advancement of vision generation over the past years. However, it is often difficult to apply these large models in downstream tasks, due to massive fine-tuning cost. Recently, Low-Rank Adaptation (LoRA) has been applied for efficient tuning of diffusion models. Unfortunately, the capabilities of LoRA-tuned diffusion models are limited, since the same LoRA is used for different timesteps of the diffusion process. To tackle this problem, we introduce a general and concise TimeStep Master (TSM) paradigm with two key fine-tuning stages. In the fostering stage (1-stage), we apply different LoRAs to fine-tune the diffusion model at different timestep intervals. This results in different TimeStep LoRA experts that can effectively capture different noise levels. In the assembling stage (2-stage), we design a novel asymmetrical mixture of TimeStep LoRA experts, via core-context collaboration of experts at multi-scale intervals. For each timestep, we leverage TimeStep LoRA expert within the smallest interval as the core expert without gating, and use experts within the bigger intervals as the context experts with time-dependent gating. Consequently, our TSM can effectively model the noise level via the expert in the finest interval, and adaptively integrate contexts from the experts of other scales, boosting the versatility of diffusion models. To show the effectiveness of our TSM paradigm, we conduct extensive experiments on three typical and popular LoRA-related tasks of diffusion models, including domain adaptation, post-pretraining, and model distillation. Our TSM achieves the state-of-the-art results on all these tasks, throughout various model structures (UNet, DiT and MM-DiT) and visual data modalities (Image, Video), showing its remarkable generalization capacity.

Diffusion models have emerged as mainstream framework in visual generation. Building upon this success, the integration of Mixture of Experts (MoE) methods has shown promise in enhancing model scalability and performance. In this paper, we introduce Race-DiT, a novel MoE model for diffusion transformers with a flexible routing strategy, Expert Race. By allowing tokens and experts to compete together and select the top candidates, the model learns to dynamically assign experts to critical tokens. Additionally, we propose per-layer regularization to address challenges in shallow layer learning, and router similarity loss to prevent mode collapse, ensuring better expert utilization. Extensive experiments on ImageNet validate the effectiveness of our approach, showcasing significant performance gains while promising scaling properties.

Mixture-of-Experts (MoE) models mostly use a router to assign tokens to specific expert modules, activating only partial parameters and often outperforming dense models. We argue that the separation between the router's decision-making and the experts' execution is a critical yet overlooked issue, leading to suboptimal expert selection and learning. To address this, we propose Autonomy-of-Expert (AoE), a novel MoE paradigm in which experts autonomously select themselves to process inputs. AoE is based on the insight that an expert is aware of its own capacity to effectively process a token, an awareness reflected in the scale of its internal activations. In AoE, routers are removed; instead, experts pre-compute internal activations for inputs and are ranked based on their activation norms. Only the top-ranking experts proceed with the forward pass, while the others abort. The overhead of pre-computing activations is reduced through a low-rank weight factorization. This self-evaluating-then-partner-comparing approach ensures improved expert selection and effective learning. We pre-train language models having 700M up to 4B parameters, demonstrating that AoE outperforms traditional MoE models with comparable efficiency.

Mixture of Experts (MoE) architectures have significantly increased computational efficiency in both research and real-world applications of large-scale machine learning models. However, their scalability and efficiency under memory constraints remain relatively underexplored. In this work, we present joint scaling laws for dense and MoE models, incorporating key factors such as the number of active parameters, dataset size, and the number of experts. Our findings provide a principled framework for selecting the optimal MoE configuration under fixed memory and compute budgets. Surprisingly, we show that MoE models can be more memory-efficient than dense models, contradicting conventional wisdom. Extensive empirical validation confirms the theoretical predictions of our scaling laws. These results offer actionable insights for designing and deploying MoE models in practical large-scale training scenarios.

Neurons in large language models often exhibit \emph{polysemanticity}, simultaneously encoding multiple unrelated concepts and obscuring interpretability. Instead of relying on post-hoc methods, we present \textbf{MoE-X}, a mixture-of-experts (MoE) language model designed to be \emph{intrinsically} interpretable. Our approach is motivated by the observation that, in language models, wider networks with sparse activations are more likely to capture interpretable factors. however, directly training such large sparse networks is computationally prohibitive. MoE architectures offer a scalable alternative by activating only a subset of experts for any given input, inherently aligning with interpretability objectives. In MoE-X, we establish this connection by rewriting the MoE layer as an equivalent sparse, large MLP. This approach enables efficient scaling of the hidden size while maintaining sparsity. To further enhance interpretability, we enforce sparse activation within each expert and redesign the routing mechanism to prioritize experts with the highest activation sparsity. These designs ensure that only the most salient features are routed and processed by the experts. We evaluate MoE-X on chess and natural language tasks, showing that it achieves performance comparable to dense models while significantly improving interpretability. MoE-X achieves a perplexity better than GPT-2, with interpretability surpassing even sparse autoencoder (SAE)-based approaches.

Mixture of Experts (MoE), an ensemble of specialized models equipped with a router that dynamically distributes each input to appropriate experts, has achieved successful results in the field of machine learning. However, theoretical understanding of this architecture is falling behind due to its inherent complexity. In this paper, we theoretically study the sample and runtime complexity of MoE following the stochastic gradient descent when learning a regression task with an underlying cluster structure of single index models. On the one hand, we show that a vanilla neural network fails in detecting such a latent organization as it can only process the problem as a whole. This is intrinsically related to the concept of *information exponent* which is low for each cluster, but increases when we consider the entire task. On the other hand, with a MoE, we show that it succeeds in dividing the problem into easier subproblems by leveraging the ability of each expert to weakly recover the simpler function corresponding to an individual cluster. To the best of our knowledge, this work is among the first to explore the benefits of the MoE framework by examining its SGD dynamics in the context of nonlinear regression.

The problem of learning to defer with multiple experts consists of optimally assigning input instances to experts, balancing the trade-off between their accuracy and computational cost. This is a critical challenge in natural language generation, but also in other fields such as image processing, and medical diagnostics. Recent studies have proposed surrogate loss functions to optimize deferral, but challenges remain in ensuring their consistency properties. This paper introduces novel surrogate loss functions and efficient algorithms with strong theoretical learning guarantees. We address open questions regarding realizable $H$-consistency, $H$-consistency bounds, and Bayes-consistency for both single-stage (jointly learning predictor and deferral function) and two-stage (learning only the deferral function with a fixed expert) learning scenarios. For single-stage deferral, we introduce a family of new realizable $H$-consistent surrogate losses and further prove $H$-consistency for a selected member. For two-stage deferral, we derive new surrogate losses that achieve realizable $H$-consistency, $H$-consistency bounds, and Bayes-consistency for the two-expert scenario and, under natural assumptions, multiple-expert scenario. Additionally, we provide enhanced theoretical guarantees under low-noise assumptions for both scenarios. Finally, we report the results of experiments using our proposed surrogate losses, comparing their performance against existing baselines.

Mixture-of-Experts (MoE) large language models (LLMs), which leverage dynamic routing and sparse activation to enhance efficiency and scalability, have achieved higher performance while reducing computational costs. However, these models face significant memory overheads, limiting their practical deployment and broader adoption. Post-training quantization (PTQ), a widely used method for compressing LLMs, encounters severe accuracy degradation and diminished generalization performance when applied to MoE models. This paper investigates the impact of MoE’s sparse and dynamic characteristics on quantization and identifies two primary challenges: (1) Inter-expert imbalance, referring to the uneven distribution of samples across experts, which leads to insufficient and biased calibration for less frequently utilized experts; (2) Intra-expert imbalance, arising from MoE's unique aggregation mechanism, which leads to varying degrees of correlation between different samples and their assigned experts. To address these challenges, we propose MoEQuant, a novel quantization framework tailored for MoE LLMs. MoEQuant includes two novel techniques: 1) Expert-Balanced Self-Sampling (EBSS) is an efficient sampling method that efficiently constructs a calibration set with balanced expert distributions by leveraging the cumulative probabilities of tokens and expert balance metrics as guiding factors. 2) Affinity-Guided Quantization (AGQ), which incorporates affinities between experts and samples into the quantization process, thereby accurately assessing the impact of individual samples on different experts within the MoE layer. Experiments demonstrate that MoEQuant achieves substantial performance gains (more than 10 points accuracy gain in the HumanEval for DeepSeekMoE-16B under 4-bit quantization) and boosts efficiency.