9h ago

Divergences Induce Distinct Geometries of Sample Dependence in Probability Simplex

——0——
Original post
OPPedro A. Ortega#1258Pedro A. Ortega@ADAPTIVEAGENTS

This cost induces a geometry of sample dependence. KL gives the Shannon mutual-information geometry; other regularizers give other native coordinates. In practice, architecture and optimization determine the effective response law.

8:23 AM · May 19, 2026 View on X
REPLYPedro A. Ortega#1258Pedro A. Ortega@ADAPTIVEAGENTS

Varying the operating level (=rationality/regularization parameter) traces a lower frontier: the best empirical loss attainable for a given amount of native sample dependence. This is the learner’s native rate-distortion curve.

Pedro A. OrtegaPedro A. Ortega@AdaptiveAgents

This cost induces a geometry of sample dependence. KL gives the Shannon mutual-information geometry; other regularizers give other native coordinates. In practice, architecture and optimization determine the effective response law.

3:23 PM · May 19, 2026 · 131 Views
3:23 PM · May 19, 2026 · 127 Views