7 papers
Measuring and Reducing Unusable Replies of LLM Agents
Yilin Jiang, Fei Tan, Xuanyu Yin +3
People delegate multi-step work to LLM agents and read only the reply that the agent hands back. Current evaluation scores task completion and the faithfulness of reports, and it l…
The Discrete Minkowski Problem for Negative
Junjie Shan
In this paper, we establish a homological existence criterion for the discrete Minkowski problem for all , where corresponds to the celebrated centro-affine case.…
The Dual Minkowski Problem under Group Actions
Junjie Shan
In this paper, we study the dual Minkowski problem under group symmetry. For , we give a complete existence characterization in the framework of -invariant convex bodi…
The Dual Minkowski Problem for Group-Invariant Convex Bodies
Junjie Shan
In this paper, we study the dual Minkowski problem for all from an algebraic perspective. We establish the existence of solutions for group-invariant co…
The Gaussian Minkowski problem for -pseudo-cones
Junjie Shan, Wenchuan Hu
The Gaussian Minkowski problem for -pseudo-cones is studied in this paper, and the existence and uniqueness results are established. This extends our previous work on th…
The Gaussian log-Minkowski problem for C-pseudo-cones
Junjie Shan, Wenchuan Hu
The existence of solutions to the Gaussian logarithmic Minkowski problem for C-pseudo-cones is established in this paper. In addition, the non-uniqueness of solutions to the proble…
The Gaussian Minkowski-type problems for -pseudo-cones
Junjie Shan, Wenchuan Hu, Wenxue Xu
The Gaussian surface area measure and the Gaussian cone measure for -pseudo-cones are introduced and their corresponding Gaussian Minkowski problem and Gaussian log-Minkowski pr…