nD-RoPE: A Generalized RoPE for n-Dimensional Position Embedding

Rotary Position Embedding (RoPE) is widely adopted in Transformer models, yet its extension to high-dimensional domains lacks a unified theoretical formulation. Most existing approaches either apply rotations independently along each axis or empirically mix frequencies, which limits cross-dimensional interactions and yields direction-dependent representations. To address these limitations, we propose nD-RoPE, a decomposition-free generalization of RoPE to arbitrary dimensions. From a translation-invariant formulation in continuous Hilbert space, we derive a spectral condition for isotropy that requires treating positions and frequencies as coupled \(n\)-dimensional vectors. We instantiate this formulation with a multi-scale regular-simplex wave-vector design, which provides non-degenerate spatial coverage and a symmetric, directionally balanced second-order response. Experiments across images, videos, and point clouds demonstrate consistent performance gains and improved generalization in high-dimensional settings.

Knowledge-to-Verification: Exploring RLVR for LLMs in Knowledge-Intensive Domains

Reinforcement learning with verifiable rewards (RLVR) has demonstrated promising potential to enhance the reasoning capabilities of large language models (LLMs) in domains such as mathematics and coding. However, its applications on knowledge-intensive domains have not been effectively explored due to the scarcity of high-quality verifiable data. Furthermore, current RLVR focuses solely on the correctness of final answers, leading to the limitations of flawed reasoning and sparse reward signals. In this work, we propose Knowledge-to-Verification (K2V), a framework that extends RLVR to knowledge-intensive domains through automated verifiable data synthesis, while enabling verification of the LLM's reasoning process. Extensive experiments demonstrate that K2V enhances the reasoning of LLM in knowledge-intensive domains without significantly compromising the model's general capabilities. This study also suggests that integrating automated data synthesis with reasoning verification is a promising direction to enhance model capabilities in these broader domains. Code is available at https://github.com/SeedScientist/K2V.

GraphGen: Enhancing Supervised Fine-Tuning for LLMs with Knowledge-Driven Synthetic Data Generation

Fine-tuning for large language models (LLMs) typically requires substantial amounts of high-quality supervised data, which is both costly and labor-intensive to acquire. While synthetic data generation has emerged as a promising solution, existing approaches frequently suffer from factual inaccuracies, insufficient long-tail coverage, simplistic knowledge structures, and homogenized outputs. To address these challenges, we introduce GraphGen, a knowledge graph-guided framework designed for three key question-answering (QA) scenarios: atomic QA, aggregated QA, and multi-hop QA. It begins by constructing a fine-grained knowledge graph from the source text. It then identifies knowledge gaps in LLMs using the expected calibration error metric, prioritizing the generation of QA pairs that target high-value, long-tail knowledge. Furthermore, GraphGen incorporates multi-hop neighborhood sampling to capture complex relational information and employs style-controlled generation to diversify the resulting QA data. Experimental results on knowledge-intensive tasks under closed-book settings demonstrate that GraphGen outperforms conventional synthetic data methods, offering a more reliable and comprehensive solution to the data scarcity challenge in supervised fine-tuning. The code and data are publicly available at https://github.com/open-sciencelab/GraphGen.

SeedBench: A Multi-task Benchmark for Evaluating Large Language Models in Seed Science

Seed science is essential for modern agriculture, directly influencing crop yields and global food security. However, challenges such as interdisciplinary complexity and high costs with limited returns hinder progress, leading to a shortage of experts and insufficient technological support. While large language models (LLMs) have shown promise across various fields, their application in seed science remains limited due to the scarcity of digital resources, complex gene-trait relationships, and the lack of standardized benchmarks. To address this gap, we introduce SeedBench -- the first multi-task benchmark specifically designed for seed science. Developed in collaboration with domain experts, SeedBench focuses on seed breeding and simulates key aspects of modern breeding processes. We conduct a comprehensive evaluation of 26 leading LLMs, encompassing proprietary, open-source, and domain-specific fine-tuned models. Our findings not only highlight the substantial gaps between the power of LLMs and the real-world seed science problems, but also make a foundational step for research on LLMs for seed design.