Beyond Accuracy: Evaluating Strategy Diversity in LLM Mathematical Reasoning

Large language models now achieve high final-answer accuracy on mathematical reasoning benchmarks, but accuracy alone does not capture reasoning flexibility. We introduce a strategy-level evaluation framework instantiated on 80 AMC 10/12 and AIME problems with 217 AoPS-derived reference strategy families. Model outputs are annotated for strategy identity, validity, and correctness using dual-AI coding with human adjudication. Across four frontier models, we find a pronounced decoupling between answer accuracy and strategy diversity. Under a single-solution prompt, all models achieve high accuracy (95%-100%), but under a multiple-strategy prompt they recover substantially fewer strategies than the human reference set. Gemini, DeepSeek, GPT, and Claude generate 184, 152, 151, and 110 distinct valid strategies, respectively, with the largest gaps in Geometry and Number Theory. The models collectively produce 50 benchmark-novel valid strategies, indicating both incomplete coverage of human strategies and some capacity for alternative reasoning. A repeated-run robustness check on 20 problems shows diminishing gains in discovered strategies, with the strongest model recovering only 39 of 55 AoPS-reference strategies (71%) after three runs. These findings position strategy diversity as a complementary dimension for evaluating mathematical reasoning beyond answer correctness.

Open World Knowledge Aided Single-Cell Foundation Model with Robust Cross-Modal Cell-Language Pre-training

Recent advancements in single-cell multi-omics, particularly RNA-seq, have provided profound insights into cellular heterogeneity and gene regulation. While pre-trained language model (PLM) paradigm based single-cell foundation models have shown promise, they remain constrained by insufficient integration of in-depth individual profiles and neglecting the influence of noise within multi-modal data. To address both issues, we propose an Open-world Language Knowledge-Aided Robust Single-Cell Foundation Model (OKR-CELL). It is built based on a cross-modal Cell-Language pre-training framework, which comprises two key innovations: (1) leveraging Large Language Models (LLMs) based workflow with retrieval-augmented generation (RAG) enriches cell textual descriptions using open-world knowledge; (2) devising a Cross-modal Robust Alignment (CRA) objective that incorporates sample reliability assessment, curriculum learning, and coupled momentum contrastive learning to strengthen the model's resistance to noisy data. After pretraining on 32M cell-text pairs, OKR-CELL obtains cutting-edge results across 6 evaluation tasks. Beyond standard benchmarks such as cell clustering, cell-type annotation, batch-effect correction, and few-shot annotation, the model also demonstrates superior performance in broader multi-modal applications, including zero-shot cell-type annotation and bidirectional cell-text retrieval.