Training large language models with data collected from various domains can improve their performance on downstream tasks. However, given a fixed training budget, the sampling proportions of these different domains significantly impact the model’s performance. How can we determine the domain weights across different data domains to train the best-performing model within constrained computational resources? In this paper, we provide a comprehensive overview of existing data mixture methods. First, we propose a fine-grained categorization of existing methods, extending beyond the previous offline and online classification. Offline methods are further grouped into heuristic-based, algorithm-based, and function fitting-based methods. For online methods, we categorize them into three groups—online min-max optimization, online mixing law, and other approaches—by drawing connections with the optimization frameworks underlying offline methods. Second, we summarize the problem formulations, representative algorithms for each subtype of offline and online methods, and clarify the relationships and distinctions among them. Finally, we discuss the advantages and disadvantages of each method and highlight key challenges in the field of data mixture.

Supervised fine-tuning (SFT) on long chain-of-thought (CoT) trajectories has emerged as a crucial technique for enhancing the reasoning abilities of large language models (LLMs). However, the standard cross-entropy loss treats all tokens equally, ignoring their heterogeneous contributions across a reasoning trajectory. This uniform treatment leads to misallocated supervision and weak generalization, especially in complex, long-form reasoning tasks. To address this, we introduce Variance-Controlled Optimization-based REweighting (VCORE), a principled framework that reformulates CoT supervision as a constrained optimization problem. By adopting an optimization-theoretic perspective, VCORE enables a principled and adaptive allocation of supervision across tokens, thereby aligning the training objective more closely with the goal of robust reasoning generalization. Empirical evaluations demonstrate that VCORE achieves the strongest overall average performance, with especially clear gains on lower-capacity models. Across both in-domain and out-of-domain settings, VCORE achieves substantial performance gains on mathematical and coding benchmarks, using models from the Qwen3 series (4B, 8B, 32B) and LLaMA-3.1-8B-Instruct. Moreover, we show that VCORE serves as a more effective initialization for subsequent reinforcement learning, establishing a stronger foundation for advancing the reasoning capabilities of LLMs.

Privacy-sensitive users require deploying large language models (LLMs) within their own infrastructure (on-premises) to safeguard private data and enable customization. However, vulnerabilities in local environments can lead to unauthorized access and potential model theft. To address this, prior research on small models has explored securing only the output layer within hardware-secured devices to balance model confidentiality and customization. Yet this approach fails to protect LLMs effectively. In this paper, we discover that (1) query-based distillation attacks targeting the secured top layer can produce a functionally equivalent replica of the victim model; (2) securing the same number of layers, bottom layers before a transition layer provide stronger protection against distillation attacks than top layers, with comparable effects on customization performance; and (3) the number of secured layers creates a trade-off between protection and customization flexibility. Based on these insights, we propose SOLID, a novel deployment framework that secures a few bottom layers in a secure environment and introduces an efficient metric to optimize the trade-off by determining the ideal number of hidden layers. Extensive experiments on five models (1.3B to 70B parameters) demonstrate that SOLID outperforms baselines, achieving a better balance between protection and downstream customization.

This paper addresses the critical need for democratizing large language models (LLM) in the Arab world, a region that has seen slower progress in developing models comparable to state-of-the-art offerings like GPT-4 or GPT-3.5, due to a predominant focus on mainstream languages (e.g., English and Chinese). One practical objective for Arabic LLMs is to utilize Arabic-specific vocabulary in the tokenizer to accelerate decoding. However, using a different vocabulary often leads to degradation of the model’s learned knowledge, since many words become out-of-vocabulary (OOV) at the beginning of training. Inspired by the vocabulary learning during Second Language (Arabic) Acquisition for humans, the released AraLLaMA employs progressive vocabulary expansion, which is implemented by a modified BPE algorithm that progressively extends the Arabic subwords in its dynamic vocabulary during training, thereby balancing the OOV ratio at every stage. The ablation study demonstrated the effectiveness of Progressive Vocabulary Expansion.Moreover, AraLLaMA achieves decent performance comparable to the best Arabic LLMs across a variety of Arabic benchmarks. Our model weights are available at: https://github.com/FreedomIntelligence/AraLLaMa.

Prompt optimization emerges as an important technique for adapting Large Language Models (LLMs) to specific tasks. Unfortunately, LLM proprietors often limit access to models’ internal weights, confining users to inference API services. This restriction poses a significant challenge for prompt optimization, as conventional optimization-based algorithms rely heavily on gradient information, which is unavailable via inference APIs. Addressing this challenge, this paper presents the Zeroth-Order Tuning (ZOT) approach, which enables efficient prompt tuning solely via inference APIs. ZOT adopts the zeroth-order optimization framework, utilizing finite differences to approximate gradient information. We further incorporate ZOT with gradient clipping and momentum techniques to enhance the tuning effectiveness. Experimental results show that ZOT outperforms existing black-box prompt tuning methods in terms of both task-specific performance and convergence speed. Furthermore, we provide a theoretical explanation for the unexpectedly strong performance of zeroth-order methods on LLM prompt tuning. By introducing the concept of effective dimension, we establish a strong connection between the inherently low effective dimension of prompt spaces and the superior convergence speed of zeroth-order methods. Our code is available at https://github.com/ZhanHeshen/ZOT.