Mathematical reasoning poses significant challenges for Large Language Models (LLMs) due to its demand for multi-step reasoning and abstract conceptual integration. While recent test-time scaling techniques rely heavily on high-quality, challenging problems, the scarcity of Olympiad-level math problems remains a bottleneck. We introduce CogAtom, a novel cognitive atom-based framework for synthesizing mathematically rigorous and cognitively diverse problems. Unlike prior approaches, CogAtom models problem construction as a process of selecting and recombining fundamental reasoning units, cognitive atoms, extracted from human-authored solutions. A diversity-promoting random walk algorithm enables exploration of the cognitive atom space, while a constraint-based recombination mechanism ensures logical soundness and structural validity. The combinatorial nature of the graph structure provides a near-infinite space of reasoning paths, and the walk algorithm systematically explores this space to achieve large-scale synthesis of high-quality problems; meanwhile, by controlling the number of cognitive atoms, we can precisely adjust problem difficulty, ensuring diversity, scalability, and controllability of the generated problems. Experimental results demonstrate that CogAtom outperforms existing methods in accuracy, reasoning depth, and diversity, generating problems that closely match the difficulty of AIME while exceeding it in structural variation. Our work offers a cognitively grounded pathway toward scalable, high-quality math problem generation.Our code is publicly available at https://github.com/Icarus-1111/CogAtom.

Text ranking has witnessed significant advancements, attributed to the utilization of dual-encoder enhanced by Pre-trained Language Models (PLMs). Given the proliferation of available PLMs, selecting the most effective one for a given dataset has become a non-trivial challenge. As a promising alternative to human intuition and brute-force fine-tuning, Transferability Estimation (TE) has emerged as an effective approach to model selection. However, current TE methods are primarily designed for classification tasks, and their estimated transferability may not align well with the objectives of text ranking. To address this challenge, we propose to compute the expected rank as transferability, explicitly reflecting the model’s ranking capability. Furthermore, to mitigate anisotropy and incorporate training dynamics, we adaptively scale isotropic sentence embeddings to yield an accurate expected rank score. Our resulting method, Adaptive Ranking Transferability (AiRTran), can effectively capture subtle differences between models. On challenging model selection scenarios across various text ranking datasets, it demonstrates significant improvements over previous classification-oriented TE methods, human intuition, and ChatGPT with minor time consumption.