Mixture-of-Experts (MoE) models achieve a favorable trade-off between performance and inference efficiency by activating only a subset of experts. However, the memory overhead of storing all experts remains a major limitation, especially in large-scale MoE models such as DeepSeek-R1 (671B). In this study, we investigate domain specialization and expert redundancy in large-scale MoE models and uncover a consistent behavior we term few-shot expert localization, with only a few in-domain demonstrations, the model consistently activates a sparse and stable subset of experts on tasks within the same domain. Building on this observation, we propose a simple yet effective pruning framework, EASY-EP, that leverages a few domain-specific demonstrations to identify and retain only the most relevant experts. EASY-EP comprises two key components: output-aware expert importance assessment and expert-level token contribution estimation. The former evaluates the importance of each expert for the current token by considering the gating scores and L2 norm of the outputs of activated experts, while the latter assesses the contribution of tokens based on representation similarities before and after routed experts. Experiments on DeepSeek-R1 and DeepSeek-V3-0324 show that our method can achieve comparable performances and 2.99 throughput under the same memory budget as the full model, with only half the experts.

The sparse Mixture-of-Experts (MoE) architecture is increasingly favored for scaling Large Language Models (LLMs) efficiently, but it depends on heterogeneous compute and memory resources. These factors jointly affect system Cost, Accuracy, and Performance (CAP), making trade-offs inevitable. Existing benchmarks often fail to capture these trade-offs accurately, complicating practical deployment decisions. To address this, we introduce MoE-CAP, a benchmark specifically designed for MoE systems. Our analysis reveals that achieving an optimal balance across CAP is difficult with current hardware; MoE systems typically optimize two of the three dimensions at the expense of the third--a dynamic we term the MoE-CAP trade-off. To visualize this, we propose the CAP Radar Diagram. We further introduce sparsity-aware performance metrics--Sparse Memory Bandwidth Utilization (S-MBU) and Sparse Model FLOPS Utilization (S-MFU)--to enable accurate performance benchmarking of MoE systems across diverse hardware platforms and deployment scenarios.

The softmax-contaminated mixture of experts (MoE) model is deployed when a large-scale pre-trained model, which plays the role of a fixed expert, is fine-tuned for learning downstream tasks by including a new contamination part, or prompt, functioning as a new, trainable expert. Despite its popularity and relevance, the theoretical properties of the softmax-contaminated MoE have remained unexplored in the literature. In the paper, we study the convergence rates of the maximum likelihood estimator of gating and prompt parameters in order to gain insights into the statistical properties and potential challenges of fine-tuning with a new prompt. We find that the estimability of these parameters is compromised when the prompt acquires overlapping knowledge with the pre-trained model, in the sense that we make precise by formulating a novel analytic notion of distinguishability. Under distinguishability of the pre-trained and prompt models, we derive minimax optimal estimation rates for all the gating and prompt parameters. By contrast, when the distinguishability condition is violated, these estimation rates become significantly slower due to their dependence on the prompt convergence rate to the pre-trained model. Finally, we empirically corroborate our theoretical findings through several numerical experiments.

Despite the significant breakthrough of Mixture-of-Experts (MoE), the increasing scale of these MoE models presents huge memory and storage challenges. Existing MoE pruning methods, which involve reducing parameter size with a uniform sparsity across all layers, often lead to suboptimal outcomes and performance degradation due to varying expert redundancy in different MoE layers. To address this, we propose a non-uniform pruning strategy, dubbed Differentiable Expert Pruning (DiEP), which adaptively adjusts pruning rates at the layer level while jointly learning inter-layer importance, effectively capturing the varying redundancy across different MoE layers. By transforming the global discrete search space into a continuous one, our method handles exponentially growing non-uniform expert combinations, enabling adaptive gradient-based pruning. Extensive experiments on five advanced MoE models demonstrate the efficacy of our method across various NLP tasks. Notably, \textbf{DiEP} retains around 92\% of original performance on Mixtral 8$\times$7B with only half the experts, outperforming other pruning methods by up to 7.1% on the challenging MMLU dataset.

Feedforward network (FFN) layers account for a large fraction of parameters and nonlinear expressivity in Transformer-based large language models (LLMs). Despite the evolution from ReLU and GELU to gated variants such as SwiGLU, most FFN designs still use a single fixed activation function, applying the same nonlinear transformation to all tokens. In this work, we propose Mixture of Activations (MoA), a token-adaptive FFN design that mixes a dictionary of activation functions using lightweight input-dependent gates while sharing the same linear projections. As an input-independent counterpart, we also introduce learnable activations (LA), which form linear combinations of activation functions for both ReLU-type and SwiGLU-type FFNs. Theoretically, we establish strict finite-width expressive separations among fixed-activation FFNs, LA, and MoA: LA strictly contains fixed-activation FFNs, while MoA strictly contains LA, with the additional expressivity arising from input-dependent nonlinear hybridization. Empirically, we evaluate MoA through extensive pre-training experiments on dense and MoE language models ranging from 0.12B to 2B parameters under different token budgets, optimizers, and learning rate schedules. MoA consistently achieves lower terminal loss and exhibits more favorable scaling behavior than well-tuned baselines, with minimal parameter and computational overhead. These results suggest that token-adaptive activation mixing is a simple and effective mechanism for improving FFN expressivity in LLMs.

We propose a novel adaptive Mixture-of-Experts (MoE) framework for time series forecasting that enhances expert specialization by incorporating expert-specific loss information directly into the training process. Notably, the overall objective comprises the base forecasting loss and expert-specific losses, allowing expert-level prediction errors to jointly shape training alongside the global forecasting loss. This framework is further combined with a partial online learning strategy, enabling incremental updates of both the gating mechanism and expert parameters. This approach significantly reduces computational cost by eliminating the need for repeated full model retraining. By integrating expert-level loss awareness with efficient online optimization, the proposed method achieves improved learning efficiency while maintaining strong predictive performance. Empirical results across economic, tourism, and energy datasets with varying frequencies demonstrate that the proposed approach generally outperforms both statistical methods and state-of-the-art neural network models, such as Transformers and WaveNet, in forecasting accuracy and computational efficiency. Furthermore, ablation studies confirm the effectiveness of the expert-specific loss integration strategy, highlighting its contribution to enhancing predictive performance.

Larger transformer models perform better on various downstream tasks but require more cost to scale up the model size. To efficiently enlarge models, the Mixture-of-Expert (MoE) architecture is widely adopted, which consists of a gate network and a series of experts and keep the training cost constant by routing the input data to a fixed number of experts instead of all.In existing large-scale MoE training systems, experts would be distributed among different GPUs for parallelization, and thus input data requires additional all-to-all communication to access the target expert and conduct corresponding computation. However, upon evaluating the training process of three mainstream MoE models on commonly used GPU clusters, we found that the all-to-all communication ratio averaged around 45\%, which significantly hinders the training efficiency and scalability of MoE models.In this paper, we propose LSH-MoE, a communication-efficient MoE training framework using locality-sensitive hashing (LSH). We first present the problems of scaling MoE training in existing systems and highlight the potential of exploiting token similarity to facilitate data compression.Then, we introduce an efficient LSH-based compression technique, which utilizes the cross-polytope hashing for rapid clustering and implements a residual-based error compensation scheme to alleviate the adverse impact of compression. To verify the effectiveness of our methods, we conduct experiments on both language models (e.g., RoBERTa, GPT, and T5) and vision models (e.g., Swin) for both pre-training and fine-tuning tasks. The results demonstrate that our method substantially outperforms its counterparts across different tasks by 1.28-2.2$\times$ of speedup.

Our 8BMoE model achieves stronger pre-training perplexity than its dense counterpart. However, a better perplexity does not always directly translate to downstream performance as demonstrated in Section 4.4. To this end, we compare fine-tuning performance of the 8B dense model and MoE model in Table 1. As shown in the table, our MoE model using expert choice routing consistently outperforms the dense model across the 11 tasks in GLUE and SuperGLUE. We evaluate the downstream task fine-tuning performance by varying the capacity factors.

Mixture of Experts (MoE) models based on Transformer architecture are pushing the boundaries of language and vision tasks. The allure of these models lies in their ability to substantially increase the parameter count without a corresponding increase in FLOPs. Most widely adopted MoE models are discontinuous with respect to their parameters - often referred to as . At the same time, existing continuous MoE designs either lag behind their sparse counterparts or are incompatible with autoregressive decoding. Motivated by the observation that the adaptation of fully continuous methods has been an overarching trend in Deep Learning, we develop Mixture of Tokens (MoT), a simple, continuous architecture that is capable of scaling the number of parameters similarly to sparse MoE models. Unlike conventional methods, MoT assigns mixtures of tokens from different examples to each expert. This architecture is fully compatible with autoregressive training and generation. Our best models not only achieve a 3x increase in training speed over dense Transformer models in language pretraining but also match the performance of state-of-the-art MoE architectures. Additionally, a close connection between MoT and MoE is demonstrated through a novel technique we call .

The sparsely activated mixture of experts (MoE) model presents an effective alternative to densely activated (dense) models, combining improved accuracy with computational efficiency. However, training MoE models from scratch requires extensive data and computational resources, a challenge that limits their widespread adoption. To address this, we introduce MoE Jetpack, a framework designed to fine-tune the abundant and easily accessible dense checkpoints into MoE models.