A two-point approach to the inverse problem in information geometry

What the math gives to ML

The paper develops an explicit two-point construction that reconstructs metric-affine geometry from a local parallelism induced by parallel transport, without assuming a Levi-Civita connection or imposing curvature or torsion constraints. The transferable asset is an asymmetric, connection-aware contrast on pairs of representations: a metric measures local displacement while an affine connection transports that displacement between endpoints. A practical neural adaptation is to replace ordinary squared embedding distances with a learned metric-affine contrast for retrieval, representation alignment, and directional robustness.