Information Complexity: Exact Computable Bounds via Convex Optimization — E8 Intelligence Research

FINDING: Information complexity provides exact, computable bounds for communication problems, with a geometric interpretation via the "information cost" of protocols as a convex optimization over distributions. | MATH: Information complexity \(IC(f,μ) = infπ I(X,Y;Π)\) where \(π\) is a protocol, \(I\) is mutual information, \(μ\) is the input distribution; exact bounds via "information complexity is computable" (Braverman) — reduces to a linear programming / convex optimization problem over the space of protocol trees; KRW conjecture: \(L(f∘ g) ≥ L(f) + L(g)\) (compositional lower bounds via information complexity). | CONNECTION: The convex geometry of the space of distributions over protocol transcripts naturally embeds in simplex structures; the infimum over protocols corresponds to finding the minimal "information radius" — analogous to the inradius of a convex polytope. The ratio between worst-case communication and information complexity often approaches const Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com