Large Language Models (LLMs) have recently achieved remarkable progress in mathematical reasoning. To enable such capabilities, many existing works distill strong reasoning models into long chains of thought or design algorithms to construct high-quality math question-answer (QA) data for training. However, these efforts primarily focus on generating correct reasoning paths and answers, while largely overlooking the correctness of the questions themselves. In this work, we present ValiMath, a benchmark consisting of 2147 human-verified mathematical questions covering a wide range of domains such as arithmetic, algebra, and geometry, which are synthesized and curated from the NuminaMath dataset. Each question is annotated with its logical structure, domain coverage, and question correctness, enabling fine-grained evaluation of question quality. ValiMath serves as a high-quality gold-standard test set for validating mathematical questions in LLM training corpora. Building upon this benchmark, we further propose MathQ-Verify, a pipeline that performs fine-grained parsing of mathematical questions into atomic assumptions and conclusions, and evaluates their semantic soundness through consistency checks. This pipeline achieves high precision in detecting flawed questions and provides a reliable foundation for cleaning noisy mathematical datasets. Experiments show that MathQ-Verify achieves state-of-the-art performance across multiple benchmarks, improving the F1 score by up to 25 percentage points over the direct verification baseline. MathQ-Verify offers a scalable and accurate solution for curating reliable mathematical datasets, reducing label noise and avoiding unnecessary computation on invalid questions. Our code and data are available at the repository https://github.com/OpenDCAI/MathQ-Verify.

Efficient data selection is crucial to accelerate the pretraining of language model (LMs). While various methods have been proposed to enhance data efficiency, limited research has addressed the inherent conflicts between these approaches to achieve optimal data selection for LM pretraining. To tackle this problem, we propose a multi-actor collaborative data selection mechanism: each data selection method independently prioritizes data based on its criterion and updates its prioritization rules using the current state of the model, functioning as an independent actor for data selection; and a console is designed to adjust the impacts of different actors at various stages and dynamically integrate information from all actors throughout the LM pretraining process. We conduct extensive empirical studies to evaluate our multi-actor framework. The experimental results demonstrate that our approach significantly improves data efficiency, accelerates convergence in LM pretraining, and achieves an average relative performance gain up to 10.5% across multiple language model benchmarks compared to the state-of-the-art methods. Code and checkpoints are publicly released at https://github.com/Relaxed-System-Lab/multi-actor-data-selection.