Glassy materials, like polycrystalline metals, have a mutable internal structural state that affects stress-strain response and functional properties. The internal structural state of polycrystalline metals is well-represented by grain sizes, dislocation densities, and so forth. However, a concise set of physically real, broadly applicable structural descriptors remains enigmatic for many glasses. This gap hobbles the development of multi-scale and continuum models with engineering relevance for these materials. We report a dimensionality reduction method based on diffusion maps that parameterizes the low-dimensional manifold of local structural states found in the glass. Distributions of these machine-learned parameters constitute a computationally convenient structural description of the glass. We show how the machine-learned structural description can be linked to fracture behavior in silica glass, and to plasticity in metallic glass. SNL is managed and operated by NTESS under DOE NNSA contract DE-NA0003525 (SAND2022-16339 A).