From Hilbert Explosion to Moduli Compression A practical blueprint for many-electron learning with attention on moduli space Diagnosis. The exponential wall comes from representing states in raw Hilbert space: every electron configuration is distinct, so the search grows combinatorially. But most of those “different” states are the same up to symmetry (permutations, spin rotations, gauge/phases, molecular point-groups, orbital reparameterizations, basis changes, etc.). If we quotient by those...

From Hilbert Explosion to Moduli Compression A practical blueprint for many-electron learning with attention on moduli space Diagnosis. The exponential wall comes from representing states in raw Hilbert space: every electron configuration is distinct, so the search grows combinatorially. But most of those “different” states are the same up to symmetry (permutations, spin rotations, gauge/phases, molecular point-groups, orbital reparameterizations, basis changes, etc.). If we quotient by those...