Geometry and universal scaling of Pareto-optimal signal compression
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915602237489152 |
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| author | Berx, Jonas |
| author_facet | Berx, Jonas |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_04329 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometry and universal scaling of Pareto-optimal signal compression Berx, Jonas Statistical Mechanics Disordered Systems and Neural Networks 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. |
| title | Geometry and universal scaling of Pareto-optimal signal compression |
| topic | Statistical Mechanics Disordered Systems and Neural Networks |
| url | https://arxiv.org/abs/2511.04329 |