2025/11/06 by Berx, Jonas
#Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.2511.04329
I investigate the generic problem of lossy compression of a fluctuating stochastic signal X into a discrete representation Z through optimal thresholding. The signal modulates transition rates of a two-state system described by a binary variable Y. Optimising the retained mutual information between Z and Y under a constraint on fixed encoding cost of Z reveals Pareto-optimal trade-offs, determined numerically using genetic algorithms. In the small-noise regime, these fronts are either concave or exhibit piecewise convex ``intrusions'' separated by first-order transitions in the optimal protocol. An analytical high-rate expansion shows that the optimal threshold density follows a universal cube-root scaling with the product of the prior distribution and the Fisher information associated with the response, which holds qualitatively even for few discrete states. Extending the analysis to non-Gaussian fluctuations reveals that for some parameters optimal encoders can yield strictly better information-cost trade-offs than Gaussian surrogates, meaning the same information content can often be achieved with fewer discrete readout states.