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
|