arXiv:2604.03782v1 Announce Type: cross Abstract: We analyze the last-iterate convergence of the Anchored Gradient Descent Ascent algorithm for smooth convex-concave min-max problems. While previous work established a last-iterate rate of $\mathcal{O}(1/t^{2-2p})$ for the squared gradient norm, where $p \in (1/2, 1)$, it remained an open problem whether the improved exact $\mathcal{O}(1/t)$ rate is achievable. In this work, we resolve this question in the affirmative. This result was discovered autonomously by an AI system capable of writing formal proofs in Lean. The Lean proof can be accessed at https://github.com/google-deepmind/formal-conjectures/pull/3675/commits/a13226b49fd3b897f4c409194f3bcbeb96a08515

arXiv:2603.08448v1 Announce Type: cross Abstract: Large language model (LLM)-based AI systems have shown promise for patient-facing diagnostic and management conversations in simulated settings. Translating these systems into clinical practice requires assessment in real-world workflows with rigorous safety oversight. We report a prospective, single-arm feasibility study of an LLM-based conversational AI, the Articulate Medical Intelligence Explorer (AMIE), conducting clinical history taking and presentation of potential diagnoses for patients to discuss with their provider at urgent care appointments at a leading academic medical center. 100 adult patients completed an AMIE text-chat interaction up to 5 days before their appointment. We sought to assess the conversational safety and quality, patient and clinician experience, and clinical reasoning capabilities compared to primary care providers (PCPs). Human safety supervisors monitored all patient-AMIE interactions in real time and did not need to intervene to stop any consultations based on pre-defined criteria. Patients reported high satisfaction and their attitudes towards AI improved after interacting with AMIE (p