Networks of the Pooling Type and Optimal Quantization

We study the link between networks of the pooling type and the problem of quantification. Pooling networks consist in parallel processors that are summed after having processed the same information. If the processors are simple threshold model of noisy neurons, the behavior of the network has the behavior of a quantizer. Using the compander approach to quantizers as well as the notion of density of levels, we study these networks and show that they are asymptotically equivalent to quantizers. Furthermore, we show how these devices can be infomax processors