Mixture-of-Experts (MoE) has emerged as the dominant paradigm for parameter-efficient scaling and cost-effective deployment of Large Language Models (LLMs). However, scaling laws developed for dense models are fundamentally inapplicable to MoE architectures, owing to three critical challenges: the multiplicity of governing factors, their intricate interdependencies, and the non-monotonic nature of their effects on model performance. These challenges collectively demand a rigorous and fine-grained investigation into MoE-specific scaling laws. In this work, we present a systematic decomposition of MoE configurations, identifying five key factors that influence model performance from both size and structural perspectives: data size (D), total model size (N), activated model size (N_a), number of active experts (G), and ratio of shared experts (S). We conduct 450 controlled experiments to characterize the marginal effects of each factor, culminating in a comprehensive and precise joint MoE scaling law. Building on this foundation, we derive the theoretically optimal and practically efficiency-aware optimal configurations for G, S and N_a/N with detailed analyses. Our findings reveal that the optimal settings for G and S are invariant to model and data size, while the optimal activation ratio N_a/N grows sparser as N increases. Our proposed MoE scaling law provides accurate and insightful guidance for future MoE model design and training.

The Transformer architecture has long dominated the development of large language models, but its quadratic complexity in sequence length presents scalability challenges. Recent advances in State Space Models, particularly Mamba series, offer a promising alternative with linear-time inference and competitive performance. While scaling model capacity via sparsification, exemplified by Mixture-of-Experts, has proven effective in reducing computation while expanding knowledge capacity, the integration of sparsification with Mamba remains largely unexplored. Existing attempts typically apply naive block-level stacking, failing to leverage Mamba’s internal structure for fine-grained sparsification. In this work, we mainly explore how to sparsify the parameters inside Mamba. We found that the effects of using sparsification strategies on parameters related to various mechanisms inside mamba are significantly different. Our proposed Mamba-MoZ framework introduces a flexible and effective sparsification mechanism inside Mamba, which can independently achieve parameter scalability and has stronger performance.

Mixture of Experts (MoE) offers remarkable performance and computational efficiency by selectively activating subsets of model parameters. Traditionally, MoE models use homogeneous experts, each with identical capacity. However, varying complexity in input data necessitates experts with diverse capabilities, while homogeneous MoE hinders effective expert specialization and efficient parameter utilization. In this study, we propose a novel Heterogeneous Mixture of Experts (HMoE) framework, where experts differ in size and thus possess diverse capacities. This heterogeneity allows for more specialized experts to handle varying token complexities more effectively. To address the imbalance in expert activation, we propose a novel training objective that encourages the frequent activation of smaller experts, so as to improve computational efficiency and parameter utilization. Extensive experiments demonstrate that HMoE achieves a lower loss rate with fewer activated parameters and outperforms conventional homogeneous MoE models on various pre-training evaluation benchmarks. Codes will be released upon acceptance.

Formality style transfer (FST) is a task that involves paraphrasing an informal sentence into a formal one without altering its meaning. To address the data-scarcity problem of existing parallel datasets, previous studies tend to adopt a cycle-reconstruction scheme to utilize additional unlabeled data, where the FST model mainly benefits from target-side unlabeled sentences. In this work, we propose a simple yet effective semi-supervised framework to better utilize source-side unlabeled sentences based on consistency training. Specifically, our approach augments pseudo-parallel data obtained from a source-side informal sentence by enforcing the model to generate similar outputs for its perturbed version. Moreover, we empirically examined the effects of various data perturbation methods and propose effective data filtering strategies to improve our framework. Experimental results on the GYAFC benchmark demonstrate that our approach can achieve state-of-the-art results, even with less than 40% of the parallel data.