Non-symmetric vector dyson equations

What the math gives to ML

The paper provides a nonlinear diagonal scaling for arbitrary nonnegative, non-symmetric interaction matrices, obtained from the vector Dyson equation. In the purely imaginary specialization, the complex equation becomes a positive fixed-point system whose solution transforms a directed matrix into a strictly substochastic diagonally scaled matrix, without requiring symmetry or reversible graph structure. This suggests a graph-neural-network propagation normalization that controls amplification on directed graphs more robustly than degree normalization, with the damping parameter providing an explicit stability knob.