Isospectral majorization and isoperimetric inequalities for coherent states on the Bloch sphere

What the math gives to ML

The paper supplies a constructive majorization principle for finite-dimensional coherent-state representations: among density matrices with the same eigenvalues, arranging eigenvalues in decreasing order in the monomial basis maximizes every convex functional of the associated Husimi response. This provides a family of spectral concentration inequalities rather than only an entropy statement. A practical neural-network transfer is a Bloch-sphere attention or routing layer whose states are positive trace-one matrices and whose response is evaluated through SU(2) coherent states, together with a differentiable convex Husimi concentration regularizer. The transfer is most credible for bounded-dimensional attention, mixture-of-experts routing, and spherical representation learning.