Table 1.
Mathematical symbols used in the definition of the learning module
| Symbols related to the RVs of the inputs and the outputs | |
| x | Vector of all multinomial RVs 
corresponding to the inputs |
| xi | i-th multinomial RV from the vector x |
| z | RV corresponding to the output neurons |
| M( . . . ) | Operator that gives the maximum integer value of the RV given as an argument; for example M(xi ) and M(z) denote the maximum values of xi and z, respectively. |
| Target probability distribution learned by the learning module |
| The output and input neurons in the learning module | |
| Population of input neurons that together encode the value of the RV xi through population coding |
| χim | Input neuron in 
whose firing signals the value m of the RV xi
|
| xim | Binary RV that assumes value 1 if and only if xi = m; it corresponds to the coding property of the input neuron χim . |
| ζ | Population of output neurons that encode the value of the RV z |
| ζl | Output neuron in ζ whose firing signals the value l of the RV z |
| The WTA populations of neurons in the learning module and their associated RVs | |
| α | The whole WTA population of neurons that represent the auxiliary RVs a |
| Subpopulation of neurons in α that connects to the output neuron ζl |
| Jl | Number of neurons in 
|
| A neuron from the subpopulation 
|
| Binary RV which value corresponds to the coding property of the neuron 
|
| Vector of all RVs 
(for all 
) that corresponds to the subpopulation of neurons 
|
| a | Vector of the union of the RVs in the vectors 
for all 
; corresponds to the WTA population α
|
| Synaptic weights and biases and their corresponding parameters in the generative model | |
| Bias (intrinsic excitability) of the neuron 
|
| Synaptic weight of the synaptic connection that connects the input neuron χim
to the neuron 
|
| Probability distribution of the generative model implicitly represented in the module |
| Parameter in the generative model 
; every such parameter, except for l = 0, is represented in the learning module by the bias 
through the relation 
. |
| Parameter in the mixture generative model 
; every such parameter, except the ones with l = 0 or m = 0, is represented in the network by the synaptic weight 
through the relation 
. |
| θ | Vector of all parameters of the generative model of the module; it includes all 
(for all l and j) and all 
(for all l, i, m and j) as components. |
| Indices used throughout all symbols | |
| l | Index that iterates through the output neurons ζl, and through their corresponding WTA subpopulations 
as well as through the binary RVs zl
|
| j | Index that enumerates the individual neurons in the subpopulation 
|
| i | Index that iterates through the RVs xi, and also through their corresponding populations of input neurons 
|
| m | Index that enumerates the binary RVs xim that represent individual values of the input RV xi, and their corresponding input neurons χim in the population 
|