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Beyond Gain: Measuring Skill Internalization for Agent Skill Retirement

arXiv:2610.32322v1 Announce Type: new Abstract: LLM agents retrieve skills from public hubs that hold up to about 100,000 entries and serve many models. As models improve, a hub must find the skills a given model has internalized, meaning it can do without them, and retire them for that model, yet internalization has not been measured with known reliability. Published rules that compare runs with and without a skill retire on the gain alone. The gain is near zero both for an internalized skill and when neither the model nor the skill delivers the capability, a state we call uncovered. We instead withhold the skill, score the model on a task synthesized from it, and trust a high unaided score only when another model gains from the skill, since nearly half of high scores come from tasks no m

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When and How Does Muon Precondition? The Role of Structured Gradient Noise

arXiv:2610.31728v1 Announce Type: new Abstract: Muon has become a popular optimizer for large language model training, yet its theoretical foundations remain poorly understood. In this work, we study how gradient noise geometry shapes Muon's preconditioning benefits. We first show, theoretically and empirically, that under the classical isotropic noise assumption, Muon offers no acceleration beyond a rescaling of the learning rate. This motivates us to investigate structured noise arising from mini-batch sampling in associative memory with heterogeneous task frequencies. We establish an exact balancing threshold for two tasks and extend the analysis to multiple tasks, revealing how task coverage and gradient reliability jointly shape learning. Our analysis shows that Muon can soften the de

When and How Does Muon Precondition? The Role of Structured Gradient Noise
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