The (co)limit of metabeliefs

Benjamin Sheller, Patrick Shafto

Primary Area: transfer learning, meta learning, and lifelong learning

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics.

Keywords: Belief, colimit, category theory

Submission Guidelines: I certify that this submission complies with the submission instructions as described on https://iclr.cc/Conferences/2024/AuthorGuide.

TL;DR: We construct the colimit space of infinitely deep beliefs

Abstract: Potentially infinite sequences of beliefs arise when reasoning about the future, one's own beliefs, or others' beliefs. Machine learning researchers are typically content with heuristic truncation, or proofs of asymptotic convergence, of sequences of beliefs; however, such approaches lack insight into the structure of the possible choices. We construct and analyze several (co)limits of meta beliefs to understand the topological and geometric structure of sequences of beliefs. We analyze the relationship between different levels, the relationship between different beliefs at different levels, the encoding of temporal and other indexing structures in belief space, and structures preserved in the colimit. Examples demonstrate the ability to formalize and reason about problems of learning, cooperative and competitive reasoning, and sequential decision making. We conclude by emphasizing insights gained, and future directions for more concrete machine learning models.

Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors' identity.

No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.

Submission Number: 5744