Mixture of Experts (MoE) pretraining is more scalable than dense Transformer pretraining, because MoEs learn to route inputs to a sparse set of their feedforward parameters. However, this means that MoEs only receive a sparse backward update, leading to training instability and suboptimal performance. We present a lightweight approximation method that gives the MoE router a dense gradient update while continuing to sparsely activate its parameters. Our method, which we refer to as Default MoE, substitutes missing expert activations with default outputs consisting of an exponential moving average of expert outputs previously seen over the course of training. This allows the router to receive signals from every expert for each token, leading to significant improvements in training performance. Our Default MoE outperforms standard TopK routing in a variety of settings without requiring significant computational overhead.

Mixture of Experts (MoE) pretraining is more scalable than dense Transformer pretraining, because MoEs learn to route inputs to a sparse set of their feedforward parameters. However, this means that MoEs only receive a sparse backward update, leading to training instability and suboptimal performance. We present a lightweight approximation method that gives the MoE router a dense gradient update while continuing to sparsely activate its parameters. Our method, which we refer to as Default MoE, substitutes missing expert activations with default outputs consisting of an exponential moving average of expert outputs previously seen over the course of training. This allows the router to receive signals from every expert for each token, leading to significant improvements in training performance. Our Default MoE outperforms standard TopK routing in a variety of settings without requiring significant computational overhead. Code: https://github.com/vatsal0/default-moe.

Test-time scaling (TTS) techniques can improve the performance of large language models (LLMs) at the expense of additional computation and latency. While TTS has proven effective in formal domains such as mathematics and programming, its value in argumentative domains such as law remains underexplored. We present an empirical study of verifier-based TTS methods for legal multiple-choice QA (MCQA) across five benchmarks. Using a family of 7 reward models, we evaluate both outcome-level (Best-of-$N$) and process-level (tree search) verification under realistic low-$N$ budgets. Our analysis systematically investigates how verifier utility is affected by key properties such as domain specialization, model size, and supervision type (process-supervised PRMs vs. outcome-only ORMs), even when applied across different roles.

General-purpose large language models, despite their broad capabilities, often struggle with specialized domain knowledge, a limitation particularly pronounced in more accessible, lower-parameter versions. This gap hinders their deployment as effective agents in demanding fields such as astronomy. Building on our prior work with AstroSage-8B, this study introduces AstroSage-70B, a significantly larger and more advanced domain-specialized natural-language AI assistant. It is designed for research and education across astronomy, astrophysics, space science, astroparticle physics, cosmology, and astronomical instrumentation. Developed from the Llama-3.1-70B foundation, AstroSage-70B underwent extensive continued pre-training on a vast corpus of astronomical literature, followed by supervised fine-tuning and model merging. Beyond its 70-billion parameter scale, this model incorporates refined datasets, judiciously chosen learning hyperparameters, and improved training procedures, achieving state-of-the-art performance on complex astronomical tasks. Notably, we integrated reasoning chains into the SFT dataset, enabling AstroSage-70B to either answer the user query immediately, or first emit a human-readable thought process. Evaluated on the AstroMLab-1 benchmark -- comprising 4,425 questions from literature withheld during training -- AstroSage-70B achieves state-of-the-art performance. It surpasses all other tested open-weight and proprietary models, including leading systems like o3, Gemini-2.5-Pro, Claude-3.7-Sonnet, Deepseek-R1, and Qwen-3-235B, even those with API costs two orders of magnitude higher. This work demonstrates that domain specialization, when applied to large-scale models, can enable them to outperform generalist counterparts in specialized knowledge areas like astronomy, thereby advancing the frontier of AI capabilities in the field.

Scaling laws for language models so far focused on finding the compute-optimal model size and token count for training from scratch. However, achieving this optimal balance requires significant compute resources due to the extensive data demands when training models from randomly-initialized weights. Continual pre-training offers a cost-effective alternative, leveraging the compute investment from pre-trained models to incorporate new knowledge without requiring extensive new data. Recent findings suggest that data quality influences constants in scaling laws, thereby altering the optimal parameter-token allocation ratio. Building on this insight, we investigate the interplay between domain specialization and model size during continual pre-training under compute-constrained scenarios. Our goal is to identify a compute-efficient training regime for this scenario and, potentially, detect patterns in this interplay that can be generalized across different model sizes and domains. To compare general and specialized training, we filtered a web-based dataset to extract legal domain data. We pre-trained models with 1.5B, 3B, 7B and 14B parameters on both the unfiltered and filtered datasets, then evaluated their performance on legal exams. Results show that as model size increases, the compute-effectiveness gap between specialized and general models widens.

The high computational cost associated with pretraining large language models limits their research. Two strategies have emerged to address this issue: domain specialization and pretraining with high-quality data. To explore these strategies, we specialized the Sabi\'a-2 Small model with 1.9 billion unique tokens from reputable Brazilian legal sources and conducted few-shot evaluations on legal and general knowledge exams. Our model, Juru, demonstrates the benefits of domain specialization with a reduced amount of pretraining data. However, this specialization comes at the expense of degrading performance in other knowledge areas within the same language. This study contributes to the growing body of scientific evidence showing that pretraining data selection may enhance the performance of large language models, enabling the exploration of these models at a lower cost.

Large language models (LLMs) have significantly advanced the field of natural language processing (NLP), providing a highly useful, task-agnostic foundation for a wide range of applications. However, directly applying LLMs to solve sophisticated problems in specific domains meets many hurdles, caused by the heterogeneity of domain data, the sophistication of domain knowledge, the uniqueness of domain objectives, and the diversity of the constraints (e.g., various social norms, cultural conformity, religious beliefs, and ethical standards in the domain applications). Domain specification techniques are key to make large language models disruptive in many applications. Specifically, to solve these hurdles, there has been a notable increase in research and practices conducted in recent years on the domain specialization of LLMs. This emerging field of study, with its substantial potential for impact, necessitates a comprehensive and systematic review to better summarize and guide ongoing work in this area. In this article, we present a comprehensive survey on domain specification techniques for large language models, an emerging direction critical for large language model applications. First, we propose a systematic taxonomy that categorizes the LLM domain-specialization techniques based on the accessibility to LLMs and summarizes the framework for all the subcategories as well as their relations and differences to each other. Second, we present an extensive taxonomy of critical application domains that can benefit dramatically from specialized LLMs, discussing their practical significance and open challenges. Last, we offer our insights into the current research status and future trends in this area.