Fluctuation-dissipation violations in mean-field non-reciprocal spin glasses

What the math gives to ML

The paper identifies a transferable mechanism in which non-reciprocal couplings split dynamics into dissipative and rotational components. Stable time-translationally invariant states can relax exponentially while violating fluctuation-dissipation, and sufficiently strong antisymmetric coupling creates damped oscillations rather than monotone relaxation. A neural-network optimizer can use a controlled skew component in its update Jacobian, with its strength limited by a spectral stability condition and monitored through response-covariance mismatch.