Rational Jacobi Rotations and the Complexity of Approximating Mixed Integer Quadratic Programming

What the math gives to ML

The paper develops rational Jacobi rotations that approximately eliminate off-diagonal entries of a symmetric matrix while preserving exact orthogonality and the matrix inertia, avoiding the irrational coefficients produced by classical eigendecomposition. This suggests a quantization-friendly, Hessian-aware optimizer or preconditioner whose coordinate transforms can be represented exactly with rational numbers and applied as norm-preserving rotations. The most promising transfer is blockwise curvature diagonalization: use a few rational rotations to decouple strongly coupled parameter directions, then apply separate signed diagonal steps. A falsifiable benefit is improved optimization under low precision or restricted arithmetic, especially when curvature is highly anisotropic or indefinite.