Information Compression at Criticality

What the math gives to ML

The paper identifies a constructive compression mechanism at criticality: a vanishing fraction of Hamiltonian eigenlevels, selected in energy space, preserves the mid-time power-law decay of the survival probability. The retained spectrum is fractal, with heavy-tailed level spacings and a spectral form factor sharing the same asymptotic decay exponent. A transferable neural-network version is spectral compression of linear recurrent or state-space dynamics: retain a small set of weighted modes whose pairwise frequency differences reproduce the target long-time autocorrelation, rather than pruning parameters or states uniformly.