PreprintCC BY 4.0arXiv
On the Information Bottleneck for Stable Variables
Abstract
We consider a generalization of the Gaussian information bottleneck problem to jointly stable variables X and Y. Specifically, for X = Y + A, where A is stable and independent of Y, we find optimal stable linear encoders of the form T = kX + N, with N stable and independent of X. We characterize the linear stable information bottleneck in closed-form and its critical value. Furthermore, we show that, except for the Gaussian case, such stochastic linear encoders are strictly suboptimal, while becoming asymptotically optimal at large compression rates. Our linear solution recovers the Gaussian information bottleneck for jointly Gaussian variables as a special case.
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BibTeX
@misc{park2026information,
title = {{On the Information Bottleneck for Stable Variables}},
author = {Dongmin Park and Jihad Fahs and Mohamad Assaad},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.08007},
eprint = {2610.08007},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.08007},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - On the Information Bottleneck for Stable Variables
AU - Dongmin Park
AU - Jihad Fahs
AU - Mohamad Assaad
PY - 2026
DA - 2026/10/18
PB - arXiv
DO - 10.48550/arxiv.2610.08007
UR - https://arxiv.org/abs/2610.08007
AB - We consider a generalization of the Gaussian information bottleneck problem to jointly stable variables X and Y. Specifically, for X = Y + A, where A is stable and independent of Y, we find optimal stable linear encoders of the form T = kX + N, with N stable and independent of X. We characterize the linear stable information bottleneck in closed-form and its critical value. Furthermore, we show that, except for the Gaussian case, such stochastic linear encoders are strictly suboptimal, while becoming asymptotically optimal at large compression rates. Our linear solution recovers the Gaussian information bottleneck for jointly Gaussian variables as a special case.
ER -