Hall Geometry and Auslander-Reiten Quiver
We show how the geometric information in the motivic Hall algebra and the correspondence of the moduli stack recovers the Auslander-Reiten sequences and the Auslander-Reiten quiver.
math.AG↗
arXiv subjects
Aayush Verma
Publications and source records attributed to Aayush Verma.
Syllabus: Portable Curricula for Reinforcement Learning Agents
Curriculum learning has been a quiet, yet crucial component of many high-profile successes of reinforcement learning. Despite this, it is still a niche topic that is not directly supported by any of the major reinforcement learning libraries. These methods can improve the capabilities and generalization of RL agents, but often require complex changes to training code. We introduce Syllabus, a portable curriculum learning library, as a solution to this problem. Syllabus provides a universal API for curriculum learning, modular implementations of popular automatic curriculum learning methods, and infrastructure that allows them to be easily integrated with asynchronous training code in nearly any RL library. Syllabus provides a minimal API for core curriculum learning components, making it easier to design new algorithms and adapt existing ones to new environments. We demonstrate this by evaluating the algorithms in Syllabus on several new environments, each using agents written in a different RL library. We present the first examples of automatic curriculum learning in NetHack and Neural MMO, two of the most challenging RL benchmarks, and find evidence that existing methods do not directly transfer to complex new environments. Syllabus can be found at https://github.com/RyanNavillus/Syllabus.
cs.AI↗
Local aspects of topological quantization and the Wu-Yang Monopoles
In this paper, we review how local potentials arise in the Wu-Yang topological quantization. We also discuss the isomorphism between the de Rham cohomology classes and Cech cohomology classes in such topological quantization. We also emphasize the importance and application of local and global information in gauge theories.
math-ph↗
The Canvas of Holography in (A)dS/CFT
The dynamic of holography between anti-de Sitter space holography and de Sitter holography is a very fascinating comparison, which provides many key insights into what we expect from holography in general. In this Essay, we highlight this dynamic with three examples: first, when taking Wheeler-DeWitt states to the asymptotic boundary, the dual interpretation is unclear in de Sitter. Second, what we make of bulk reconstruction and subregion duality in AdS/CFT is not trivially reflected in the dS/CFT scenario. Third, a way of formulating emergence and subregion-subalgebra duality in de Sitter space does not yet exist. With these examples, we provide some musings on this canvas of holography in the settings of (A)dS/CFT.
hep-th↗