Dirk Bergemann

Shuche Wang, Fengzhuo Zhang, Jiaxiang Li et al.

Muon improves training efficiency over Adam in large language-model training by about two times, but the local geometric source of this advantage remains unclear. Our work takes a first step toward demystifying Muon's superiority over Adam from a curvature perspective. First, we apply a second-order Taylor approximation to the training landscape and show that Muon achieves a larger one-step loss decrease than Adam at matched validation loss. The two optimizers have comparable first-order gains, but Muon consistently incurs a smaller second-order curvature penalty. Second, we decompose this curvature penalty into the squared update norm and Normalized Directional Sharpness (NDS). We find that Muon and Adam have comparable update norms, so Muon's smaller curvature penalty is driven by lower NDS, not update scale. Third, we study how training data and model structure shape Muon's NDS advantage. Using Zipf-Probabilistic Context-Free Grammar (PCFG) data with controlled imbalance, we show that data imbalance amplifies Muon's NDS advantage over Adam. A within-/cross-layer decomposition further shows that, in the middle and late stages of training, Muon's lower NDS is mainly sustained by smaller within-layer curvature. Beyond empirical evidence, we analyze stylized quadratic problems with heterogeneous curvature and gradient alignment toward high-curvature modes. We prove that Muon attains a smaller average NDS than GD by balancing update energy across curvature groups; when curvature heterogeneity is sufficiently strong, this also yields lower local quadratic loss after the same number of steps.

Dirk Bergemann, Soheil Ghili, Xinyang Hu et al.

Bilateral bargaining under incomplete information provides a controlled testbed for evaluating large language model (LLM) agent capabilities. Bilateral trade demands individual rationality, strategic surplus maximization, and cooperation to realize gains from trade. We develop a structured bargaining environment where LLMs negotiate via tool calls within an event-driven simulator, separating binding offers from natural-language messages to enable automated evaluation. The environment serves two purposes: as a benchmark for frontier models and as a training environment for open-weight models via reinforcement learning. In benchmark experiments, a round-robin tournament among five frontier models (15,000 negotiations) reveals that effective strategies implement price discrimination through sequential offers. Aggressive anchoring, calibrated concession, and temporal patience correlate with the highest surplus share and deal rate. Accommodating strategies that concede quickly disable price discrimination in the buyer role, yielding the lowest surplus capture and deal completion. Stronger models scale their behavior proportionally to item value, maintaining performance across price tiers; weaker models perform well only when wide zones of possible agreement offset suboptimal strategies. In training experiments, we fine-tune Qwen3 (8B, 14B) via supervised fine-tuning (SFT) followed by Group Relative Policy Optimization (GRPO) against a fixed frontier opponent. These stages optimize competing objectives: SFT approximately doubles surplus share but reduces deal rates, while RL recovers deal rates but erodes surplus gains, reflecting the reward structure. SFT also compresses surplus variation across price tiers, which generalizes to unseen opponents, suggesting that behavioral cloning instills proportional strategies rather than memorized price points.

Ed Li, Junyu Ren, Xintian Pan et al.

The automation of scientific discovery represents a critical milestone in Artificial Intelligence (AI) research. However, existing agentic systems for science suffer from two fundamental limitations: rigid, pre-programmed workflows that cannot adapt to intermediate findings, and inadequate context management that hinders long-horizon research. We present \texttt{freephdlabor}, an open-source multiagent framework featuring \textit{fully dynamic workflows} determined by real-time agent reasoning and a \coloremph{\textit{modular architecture}} enabling seamless customization -- users can modify, add, or remove agents to address domain-specific requirements. The framework provides comprehensive infrastructure including \textit{automatic context compaction}, \textit{workspace-based communication} to prevent information degradation, \textit{memory persistence} across sessions, and \textit{non-blocking human intervention} mechanisms. These features collectively transform automated research from isolated, single-run attempts into \textit{continual research programs} that build systematically on prior explorations and incorporate human feedback. By providing both the architectural principles and practical implementation for building customizable co-scientist systems, this work aims to facilitate broader adoption of automated research across scientific domains, enabling practitioners to deploy interactive multiagent systems that autonomously conduct end-to-end research -- from ideation through experimentation to publication-ready manuscripts.