2000 character limit reached
Homotopical Entropy (2501.10672v1)
Published 18 Jan 2025 in math.CT, cs.IT, math-ph, math.IT, and math.MP
Abstract: We present a "homotopification" of fundamental concepts from information theory. Using homotopy type theory, we define homotopy types that behave analogously to probability spaces, random variables, and the exponentials of Shannon entropy and relative entropy. The original analytic theories emerge through homotopy cardinality, which maps homotopy types to real numbers and generalizes the cardinality of sets.
Paper Prompts
Sign up for free to create and run prompts on this paper using GPT-5.
Top Community Prompts
Collections
Sign up for free to add this paper to one or more collections.