Weiyu Li
Publications
Semi-Autonomous Mathematics Discovery with Gemini: A Case Study on the Erdős Problems
We present a case study in semi-autonomous mathematics discovery, using Gemini to systematically evaluate 700 conjectures labeled 'Open' in Bloom's Erdős Problems database. We employ a hybrid methodology: AI-driven natural language verification to narrow the search space, followed by human expert evaluation to gauge correctness and novelty. We address 13 problems that were marked 'Open' in the database: 5 through seemingly novel autonomous solutions, and 8 through identification of previous solutions in the existing literature. Our findings suggest that the 'Open' status of the problems was through obscurity rather than difficulty. We also identify and discuss issues arising in applying AI to math conjectures at scale, highlighting the difficulty of literature identification and the risk of ''subconscious plagiarism'' by AI. We reflect on the takeaways from AI-assisted efforts on the Erdős Problems.
Topology-Independent Robustness of the Weighted Mean under Label Poisoning Attacks in Heterogeneous Decentralized Learning
Robustness to malicious attacks is crucial for practical decentralized signal processing and machine learning systems. A typical example of such attacks is label poisoning, meaning that some agents possess corrupted local labels and share models trained on these poisoned data. To defend against malicious attacks, existing works often focus on designing robust aggregators; meanwhile, the weighted mean aggregator is typically considered a simple, vulnerable baseline. This paper analyzes the robustness of decentralized gradient descent under label poisoning attacks, considering both robust and weighted mean aggregators. Theoretical results reveal that the learning errors of robust aggregators depend on the network topology, whereas the performance of weighted mean aggregator is topology-independent. Remarkably, the weighted mean aggregator, although often considered vulnerable, can outperform robust aggregators under sufficient heterogeneity, particularly when: (i) the global contamination rate (i.e., the fraction of poisoned agents for the entire network) is smaller than the local contamination rate (i.e., the maximal fraction of poisoned neighbors for the regular agents); (ii) the network of regular agents is disconnected; or (iii) the network of regular agents is sparse and the local contamination rate is high. Empirical results support our theoretical findings, highlighting the important role of network topology in the robustness to label poisoning attacks.