Can a Lightweight Automated AI Pipeline Solve Research-Level Mathematical Problems?

Large language models (LLMs) have recently achieved remarkable success in generating rigorous mathematical proofs, with "AI for Math" emerging as a vibrant field of research. While these models have mastered competition-level benchmarks like the International Mathematical Olympiad and show promise in research applications through auto-formalization, their deployment via lightweight, natural-language pipelines for research problems remains underexplored. In this work, we demonstrate that next-generation models (e.g., Gemini 3 Pro, GPT-5.2 Pro), when integrated into a streamlined automated pipeline optimized for citation-based verification, can solve sophisticated research-grade problems. We evaluate our pipeline on two novel datasets: (1) the ICCM problem sets (comparable to the S.-T. Yau College Student Mathematics Contest) proposed by leading mathematicians, and (2) the "First Proof" problem set, consisting of previously unpublished research questions. Our pipeline generated candidate proofs for all problems in the first two ICCM sets and the "First Proof" set. The solutions for the first two ICCM sets and Problem 4 of the "First Proof" set have been fully verified by our team. All generated proofs have been submitted to the official organization, and our generated results are publicly available. We plan to open-source the complete pipeline methodology in due course.

One Tool Is Enough: Reinforcement Learning for Repository-Level LLM Agents

Locating the files and functions requiring modification in large open-source software (OSS) repositories is challenging due to their scale and structural complexity. Existing large language model (LLM)-based methods typically treat this as a repository-level retrieval task and rely on multiple auxiliary tools, which overlook code execution logic and complicate model control. We propose RepoNavigator, an LLM agent equipped with a single execution-aware tool-jumping to the definition of an invoked symbol. This unified design reflects the actual flow of code execution while simplifying tool manipulation. RepoNavigator is trained end-to-end via Reinforcement Learning (RL) directly from a pretrained model, without any closed-source distillation. Experiments demonstrate that RL-trained RepoNavigator achieves state-of-the-art performance, with the 7B model outperforming 14B baselines, the 14B model surpassing 32B competitors, and even the 32B model exceeding closed-source models such as Claude-3.7. These results confirm that integrating a single, structurally grounded tool with RL training provides an efficient and scalable solution for repository-level issue localization.

Population-Evolve: a Parallel Sampling and Evolutionary Method for LLM Math Reasoning

Test-time scaling has emerged as a promising direction for enhancing the reasoning capabilities of Large Language Models in last few years. In this work, we propose Population-Evolve, a training-free method inspired by Genetic Algorithms to optimize LLM reasoning. Our approach maintains a dynamic population of candidate solutions for each problem via parallel reasoning. By incorporating an evolve prompt, the LLM self-evolves its population in all iterations. Upon convergence, the final answer is derived via majority voting. Furthermore, we establish a unification framework that interprets existing test-time scaling strategies through the lens of genetic algorithms. Empirical results demonstrate that Population-Evolve achieves superior accuracy with low performance variance and computational efficiency. Our findings highlight the potential of evolutionary strategies to unlock the reasoning power of LLMs during inference.

Discretization-independent multifidelity operator learning for partial differential equations

We develop a new and general encode-approximate-reconstruct operator learning model that leverages learned neural representations of bases for input and output function distributions. We introduce the concepts of \textit{numerical operator learning} and \textit{discretization independence}, which clarify the relationship between theoretical formulations and practical realizations of operator learning models. Our model is discretization-independent, making it particularly effective for multifidelity learning. We establish theoretical approximation guarantees, demonstrating uniform universal approximation under strong assumptions on the input functions and statistical approximation under weaker conditions. To our knowledge, this is the first comprehensive study that investigates how discretization independence enables robust and efficient multifidelity operator learning. We validate our method through extensive numerical experiments involving both local and nonlocal PDEs, including time-independent and time-dependent problems. The results show that multifidelity training significantly improves accuracy and computational efficiency. Moreover, multifidelity training further enhances empirical discretization independence.