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.

Multimodal Large Language Models (MLLMs) are known to hallucinate, which limits their practical applications. Recent works have attempted to apply Direct Preference Optimization (DPO) to enhance the performance of MLLMs, but have shown inconsistent improvements in mitigating hallucinations. To address this issue more effectively, we introduce Hallucination-targeted Direct Preference Optimization (HDPO) to reduce hallucinations in MLLMs. Unlike previous approaches, our method tackles hallucinations from their diverse forms and causes. Specifically, we develop three types of preference pair data targeting the following causes of MLLM hallucinations: (1) insufficient visual capabilities, (2) long context generation, and (3) multimodal conflicts. Experimental results demonstrate that our method achieves superior performance across multiple hallucination evaluation datasets, surpassing most state-of-the-art (SOTA) methods and highlighting the potential of our approach. Ablation studies and in-depth analyses further confirm the effectiveness of our method and suggest the potential for further improvements through scaling up.