Model merging has emerged as an effective approach for integrating multiple task-specific fine-tuned models into a single unified model without requiring additional data-intensive training. A central challenge in model merging is to reduce task interference while preserving the task-specific capabilities of the original models. In this work, we propose PRIME, an ultra-low-rank principal-residual model merging framework that decomposes task vector merging into two complementary stages. First, ultra-low-rank principal task vector merging retains only a small fraction of singular vectors, effectively reducing task interference while preserving most of the task-specific performance. Second, orthogonal residual task vector merging incorporates the remaining components by projecting them onto the null space of the principal subspace, thereby avoiding interference while recovering additional task-relevant information. Extensive experiments on eight natural language processing tasks demonstrate that PRIME consistently outperforms existing model merging methods, achieving improvements of up to 1.18% on T5 and 1.9% on LLaMA-3.2-3B.

Finding the right north-star metrics is highly critical for advancing mathematical reasoning capabilities of foundation models, especially given that existing evaluations are either too easy or only focusing on getting correct short answers. To address these issues, we present IMO-Bench, a suite of advanced reasoning benchmarks that specifically targets the level of the International Mathematical Olympiad (IMO), the most prestigious venue for young mathematicians. IMOAnswerBench first tests models on 400 diverse Olympiad problems with verifiable short answers. IMO-ProofBench is the next-level evaluation for proof-writing capabilities, which includes both basic and advanced IMO problems as well as detailed grading guidelines to facilitate automatic grading. These benchmarks played a crucial role in our historic achievement of the gold-level performance at IMO 2025 with Gemini Deep Think (Luong and Lockhart, 2025). Our model achieved 80.0% on IMO-AnswerBench and 65.7% on the advanced IMO-ProofBench, surpassing the best non-Gemini models by large margins of 6.9% and 42.4% respectively. We also showed that autograders built with Gemini reasoning correlate well with human evaluations and construct IMO-GradingBench, with 1000 human gradings on proofs, to enable further progress in automatic evaluation of long-form answers. We hope that IMO-Bench will help the community towards advancing robust mathematical reasoning and release it at https://github.com/google-deepmind/superhuman/imobench.