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We establish a matching lower bound for the sextic large sieve over the Eisenstein integers in an unbalanced range, with both indices restricted to squarefree ideals. Let $\Xi_6(A,B)$ denote the squared operator norm of the sextic residue-character matrix with row and column norms at most $A$ and $B$, respectively, out...
Language-model agents revise their working context as information becomes obsolete, but deleting text does not erase its influence on cached computation. Later key-value (KV) states remain conditioned on the deleted content, while recomputing the entire retained suffix can be costly. We introduce budgeted KV-cache repa...
Hierarchical reinforcement learning improves long-horizon control by organizing primitive actions around persistent subgoals and assigning credit at multiple temporal scales. Recent hierarchical language agents bring these benefits to interactive tasks by explicitly separating subgoal planning from action execution. We...
MatrAIx is introduced, a population-scale simulated-user evaluation infrastructure for testing AI systems and digital products with heterogeneous users and provides an end-to-end infrastructure for evaluating AI systems and digital products with diverse simulated human users.
TREK (Teacher-Routed Exploration via Forward KL), a simple staged procedure that uses distillation not for imitation but for exploration support expansion, achieves high success rates early in training while unaided GRPO requires substantially more optimization steps to reach comparable levels.
Autonomous computer-use agents are increasingly applied to long-horizon tasks requiring coordinated application calls, persistent state tracking, and verifier-sensitive writes, yet they remain prone to procedural failures: misreading application state, tool semantics, or task progress. Procedural memory promises more c...
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