On pooling networks and fluctuation in suboptimal detection framework

Motivated by biological neural networks and distributed sensing networks, we study how pooling networks – or quantizers – with random thresholds can be used in detection tasks. We provide a brief overview of the use of deterministic quantizers in detection by presenting how quantizers can be optimally designed for detection purposes. We study the behavior of these networks when they are used in a problem for which they are not optimal (mismatching). We show that adding random fluctuations to the thresholds of the networks can then enhance the performance of the quantizers, thus helping in the recovery of "a kind of" optimality. We also show that (for a small number of thresholds) it suffices to use random uniform quantizers, for which we provide a study of the behavior as a function of several parameters (size, fluctuation nature, observation noise nature). The conclusion to these studies are the robustness of the uniform quantizer used as a detector with respect to fluctuations added on its thresholds.