ReasFlow: Assisting Reasoning-Centric Scientific Discovery in Applied Mathematics via a Knowledge-Based Multi-Agent System

Recent advances in Large Language Models have fueled autonomous AI agents capable of tackling complex scientific tasks, yet existing automated research systems remain predominantly focused on empirically driven domains with quantitative benchmarks, leaving theory-driven discovery, particularly in mathematically grounded disciplines requiring rigorous proofs and synthesis of domain knowledge, largely underexplored. Key challenges include the difficulty of verifying theoretical reasoning at scale, insufficient reasoning ability for autonomous frontier exploration, and a scarcity of procedural heuristics in the literature. We introduce ReasFlow, an end-to-end autonomous agent system for reasoning-centric scientific discovery that operationalizes a collaborative paradigm where the human expert acts as Principal Investigator while the agent executes rigorous derivations as a capable graduate student. ReasFlow incorporates (i) a robust internal verification loop that audits logical coherence and corrects fundamental errors prior to human inspection, and (ii) an automated knowledge retrieval and self-improvement mechanism that proactively surfaces both declarative facts and overlooked procedural heuristics, substantially reducing expert intervention. The system unifies literature synthesis, algorithm design, theorem proving, experimentation, and manuscript preparation in a single system. Deployed to autonomously generate five complete research papers with rigorous theoretical and empirical content from minimal prompts, ReasFlow consistently achieves the highest evaluation scores among state-of-the-art open-access baselines under a curated LLM-based review rubric. ReasFlow is publicly accessible via the ReasLab platform, providing a collaborative workspace for AI-assisted theoretical research. Github repo: https://github.com/ReasLab/ReasFlow.git.

FedSLoP: Memory-Efficient Federated Learning with Low-Rank Gradient Projection

Federated learning enables a population of clients to collaboratively train machine learning models without exchanging their raw data, but standard algorithms such as FedAvg suffer from slow convergence and high communication and memory costs in heterogeneous, resource-constrained environments. We introduce FedSLoP, a federated optimization algorithm that combines stochastic low-rank subspace projections of gradients, thereby reducing the dimension of communicated and stored updates while preserving optimization progress. On the theoretical side, we develop a detailed nonconvex convergence analysis under standard smoothness and bounded-variance assumptions, showing that FedSLoP is guaranteed to converge to a first-order stationary point at a rate of $O(1/\sqrt{NT})$. On the empirical side, we conduct extensive experiments on federated MNIST classification with heterogeneous data partitions, showing that FedSLoP substantially reduces communication volume and client-side memory while achieving competitive or better accuracy compared with FedAvg and representative sparse or low-rank baselines. Together, our results demonstrate that random subspace momentum methods such as FedSLoP provide a principled and effective approach to communication- and memory-efficient federated learning. Codes are available at: https://github.com/pkumelon/FedSLoP.git.