Mixture-of-Experts Models

Generalist vision--language--action (VLA) policies are typically trained on heterogeneous mixtures of robot demonstrations spanning diverse embodiments, action spaces, and observation configurations. Modeling such heterogeneity with a shared dense action module can induce negative transfer, particularly when action spaces or visual observations differ across data sources. We address this issue with HiMoE-VLA, a VLA framework built around a Hierarchical Mixture-of-Experts (HiMoE) action module. HiMoE uses Action-Space MoE layers at the input/output boundaries to specialize computation for distinct action spaces, Heterogeneity-Balancing MoE layers in neighboring layers to provide balanced capacity for residual variation in observations, scenes, and embodiments, and dense Transformer blocks in the middle to integrate shared representations. Two auxiliary objectives further guide this hierarchy: a contrastive Action-Space Regularization objective for boundary specialization and a load-balancing objective for stable expert utilization. HiMoE-VLA reaches 3.98 on CALVIN, 98.0% on LIBERO, and 75.0% and 63.7% average success on real xArm7 and ALOHA tasks; under controlled heterogeneous co-training, it turns the negative transfer observed in strong baselines into positive transfer. The code and models are publicly available at https://github.com/ZhiyingDu/HiMoE-VLA.

Mixture-of-Experts (MoE) models have shown strong potential in scaling language models efficiently by activating only a small subset of experts per input. However, their widespread deployment remains limited due to the high memory overhead associated with storing all expert parameters, particularly as the number of experts increases. To address this challenge, prior works have explored expert dropping and merging strategies, yet they often suffer from performance drop at high compression ratios. In this paper, we introduce PuzzleMoE, a training-free MoE compression method that achieves both high accuracy and efficient inference through two key innovations: First, PuzzleMoE performs sparse expert merging by identifying element-wise weight redundancy and specialization. It uses a dual-mask to capture both shared and expert-specific parameters. Second, to avoid the overhead of storing binary masks and signs, PuzzleMoE introduces a bit-packed encoding scheme that reuses underutilized exponent bits, enabling efficient MoE inference on GPUs. Extensive experiments demonstrate that PuzzleMoE can compress MoE models by up to 50% while maintaining accuracy across various tasks. Specifically, it outperforms prior MoE compression methods by up to 16.7% on MMLU at 50% compression ratio, and achieves up to 1.28\times inference speedup.

Dementia disorders such as Alzheimer's disease (AD) and frontotemporal dementia (FTD) exhibit overlapping electrophysiological signatures in EEG that challenge accurate diagnosis. Existing EEG-based methods are limited by full-band frequency analysis, which hinders the precise differentiation of dementia subtypes and severity stages. To address this limitation, we propose a Variational Mixture of Graph Neural Experts (VMoGE) framework that integrates multi-band EEG analysis with variational graph neural networks and a mixture-of-experts architecture. Each expert specializes in a specific EEG frequency band and models brain connectivity using a Gaussian Markov random field prior, while a variational gating mechanism adaptively integrates the expert outputs. This design enables the model to learn frequency-specific brain network representations while modeling latent uncertainty through variational inference. Experimental results on two EEG dementia datasets show that VMoGE achieves strong performance, with an AUC of 0.89 for HC vs. AD classification in the main comparison and competitive results across dementia subtyping and CDR staging tasks. Clinically, VMoGE offers three key translational values: the expert gating weights correlate with MMSE scores and CDR severity; slow-wave $δ$- and $θ$-band contributions are associated with AD-related EEG slowing and disease progression; and spatially localized activation maps reveal posterior $θ$- and $α$-band alterations and region-specific $β$-band changes, providing neurophysiologically interpretable markers aligned with known AD neuropathology.

This paper uses classical high-rate quantization theory to provide new insights into mixture-of-experts (MoE) models for regression tasks. Our MoE is defined by a segmentation of the input space to regions, each with a single-parameter expert that acts as a constant predictor with zero-compute at inference. Motivated by high-rate quantization theory assumptions, we assume that the number of experts is sufficiently large to make their input-space regions very small. This lets us study the approximation error of our MoE model class: (i) for one-dimensional inputs, we formulate the test error and its minimizing segmentation and experts; (ii) for multidimensional inputs, we formulate an upper bound for the test error and study its minimization. Moreover, we consider the learning of the expert parameters from a training dataset, given an input-space segmentation, and formulate their statistical learning properties. This leads us to theoretically and empirically show how the tradeoff between approximation and estimation errors in MoE learning depends on the number of experts.

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.

Encoder-Decoder architectures are widely used in deep learning-based Deformable Image Registration (DIR), where the encoder extracts multi-scale features and the decoder predicts deformation fields by recovering spatial locations. However, current methods lack specialized extraction of features (that are useful for registration) and predict deformation jointly and homogeneously in all three directions. In this paper, we propose a novel expert-guided DIR network with Mixture of Experts (MoE) mechanism applied in both encoder and decoder, named SHMoAReg. Specifically, we incorporate Mixture of Attention heads (MoA) into encoder layers, while Spatial Heterogeneous Mixture of Experts (SHMoE) into the decoder layers. The MoA enhances the specialization of feature extraction by dynamically selecting the optimal combination of attention heads for each image token. Meanwhile, the SHMoE predicts deformation fields heterogeneously in three directions for each voxel using experts with varying kernel sizes. Extensive experiments conducted on two publicly available datasets show consistent improvements over various methods, with a notable increase from 60.58% to 65.58% in Dice score for the abdominal CT dataset. Furthermore, SHMoAReg enhances model interpretability by differentiating experts' utilities across/within different resolution layers. To the best of our knowledge, we are the first to introduce MoE mechanism into DIR tasks.

Accurate univariate forecasting remains a pressing need in real-world systems, such as energy markets, hydrology, retail demand, and IoT monitoring, where signals are often intermittent and horizons span both short- and long-term. While transformers and Mixture-of-Experts (MoE) architectures are increasingly favored for time-series forecasting, a key gap persists: MoE models typically require complicated training with both the main forecasting loss and auxiliary load-balancing losses, along with careful routing/temperature tuning, which hinders practical adoption. In this paper, we propose a model architecture that simplifies the training process for univariate time series forecasting and effectively addresses both long- and short-term horizons, including intermittent patterns. Our approach combines sparse MoE computation with a novel attention-inspired gating mechanism that replaces the traditional one-layer softmax router. Through extensive empirical evaluation, we demonstrate that our gating design naturally promotes balanced expert utilization and achieves superior predictive accuracy without requiring the auxiliary load-balancing losses typically used in classical MoE implementations. The model achieves better performance while utilizing only a fraction of the parameters required by state-of-the-art transformer models, such as PatchTST. Furthermore, experiments across diverse datasets confirm that our MoE architecture with the proposed gating mechanism is more computationally efficient than LSTM for both long- and short-term forecasting, enabling cost-effective inference. These results highlight the potential of our approach for practical time-series forecasting applications where both accuracy and computational efficiency are critical.

Amodal segmentation aims to predict complete object masks covering both visible and occluded regions, serving as a critical foundation for robust multimedia scene understanding and interactive media editing. This task poses significant challenges in complex visual media due to severe occlusions and extreme shape variation, ranging from rigid furniture to highly deformable clothing. Existing one-size-fits-all approaches struggle to reason about diverse amodal shapes in multimedia content due to limited representation capacity. While a mixture-of-experts framework is a natural solution, naively applying it without considering the underlying shape distribution leads to mismatched routing and redundant experts. To address these issues, we introduce ShapeMoE, a shape-specific sparse mixture-of-experts framework designed for complex visual scene parsing. The key idea is to learn a latent shape distribution space and dynamically route each object to a lightweight expert tailored to its geometric characteristics. Specifically, ShapeMoE encodes each object into a compact Gaussian embedding that captures key shape features. A Shape-Aware Sparse Router then maps the object to the most suitable expert, enabling precise shape-aware routing. Each expert is lightweight and specializes in recovering occluded regions for specific shape patterns. ShapeMoE is designed for shape-specific expert specialization while maintaining computational efficiency. Extensive experiments on three challenging benchmarks demonstrate that ShapeMoE consistently outperforms state-of-the-art methods. Beyond advancing fundamental visual reasoning, ShapeMoE provides a robust and efficient visual prior for downstream multimedia applications, particularly in occlusion-heavy immersive environments.

Graph-based multi-task learning at billion-scale presents a significant challenge, as different tasks correspond to distinct billion-scale graphs. Traditional multi-task learning methods often neglect these graph structures, relying solely on individual user and item embeddings. However, disregarding graph structures overlooks substantial potential for improving performance. In this paper, we introduce the Macro Graph of Experts (MGOE) framework, the first approach capable of leveraging macro graph embeddings to capture task-specific macro features while modeling the correlations between task-specific experts. Specifically, we propose the concept of a Macro Graph Bottom, which, for the first time, enables multi-task learning models to incorporate graph information effectively. We design the Macro Prediction Tower to dynamically integrate macro knowledge across tasks. MGOE has been deployed at scale, powering multi-task learning for a leading billion-scale recommender system, Alibaba. Extensive offline experiments conducted on three public benchmark datasets demonstrate its superiority over state-of-the-art multi-task learning methods, establishing MGOE as a breakthrough in multi-task graph-based recommendation. Furthermore, online A/B tests confirm the superiority of MGOE in billion-scale recommender systems.

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.

This paper considers the setting in which local Mixture-of-experts (MoE) models are fitted independently on distributed datasets and must be combined into a single global MoE model. Weighted averaging the local mixtures, whose experts are not aligned across machines, often yields a large mixture with many experts instead of $K$ and does not provide an estimator of the true model parameters. We propose to reduce this large mixture to a $K$-expert MoE by minimizing an expected transportation divergence, in which the transport plan depends on the covariates. A relaxation of this problem separates the experts from the gating network: the experts are computed by a majorization--minimization algorithm, which decreases the objective monotonically, and the gating network is then fitted to the gates implied by the optimal plan, with an explicit bound on the resulting loss. We show that the aggregated estimator is consistent whenever the local estimators are, without requiring the local models to have the same labeling across machines. The procedure only needs a single one-way communication round. Experiments on simulated and real data show accuracy close to centralized estimation at a fraction of its computation time. Our source code is available at https://github.com/nhat-thien/Distributed-Mixture-Of-Experts.