Human brain theory
ISBN
978-3-00-068559-0
Monograph of Dr. rer. nat. Andreas Heinrich Malczan
The convergence module with lateral signal overlay
The convergence module with vertical signal mixing can approximately recover the input of a divergence module with vertical signal mixing from its output. Whereby it is only about the firing rate ratios, i.e. the extreme value coding - a constant factor has no influence on extreme values and is omitted when differentiating!
This is also the case with a convergence module with lateral or with spatial signal propagation. Such convergence modules produce a convergence error that can be very small in many cases, but increases with the increase of the firing rate ratios.
We need to discuss this case by example. We choose a convergence module with lateral signal superposition. The corresponding divergence module was discussed in chapter 4.2.1. Its output is now to be converted back to the original signals as far as possible in a convergence circuit.
Figure 42: Linking divergence modulus and convergence modulus with lateral signal superposition
In the figure above, the divergence module receives 4 input signals. The supplied neuronal excitation spreads throughout the square by means of interneurons. One neuron - here located at point PD - exhibits the excitation maximum, which occurs by default in this divergence module. The position of the point PD codes the parameters of the input signals (e.g. brightness, colour, muscle tension, ...).
In front of the many output neurons, only the neuron in the point PD is drawn, the many hundreds or thousands that are evenly distributed in the square have been omitted for the sake of clarity.
Each output neuron now projects into an input neuron of the convergence module, which has (almost) the same coordinates and is located at point PK. Note, however, the mirroring of the modules. They are shown in the view from above. In nature, they are folded into the plane of the cortex. All the output neurons of the divergence module must send their axons downwards on semi-circular paths into the motor module next to it. So that the axons do not mix wildly and the order is totally lost, the receiving module is mirrored by 180 degrees with respect to the y-axis. This means that the x-axis in the convergence module runs in the opposite direction to the x-axis in the divergence module. The correct positioning of the neurons involved is certainly controlled by the gradients of directional markers.
We now look at the firing rate ratios in both modules and remember the distance-dependent attenuation. The greater the signal path travelled, the more the signal is attenuated.
Thus, in the divergence module, the input neuron that has the strongest firing rate will also have the shortest distance to the common extreme point PD. The further an input neuron is from the extreme point PD, the weaker its firing rate will be. If it increases, the extreme point PD is shifted to the neuron whose firing rate is currently increasing.
This allows us to estimate the strength of the four fire rates involved in the divergence module:
The closer an input neuron NiD is to the common extreme point PD in the divergence module, the stronger its input firing rate.
The output firing rate fD of the divergence module feeds the convergence module as input. The projection is done while preserving the topology. And the distance-dependent damping also applies here. Therefore, we can also estimate the strength of the four involved firing rates of the in the convergence module:
The closer an input neuron NiK is to the common extreme point PK in the convergence module, the stronger its input firing rate.
Thus, the relation of the firing rates at the transition from the divergence modulus to the convergence modulus is preserved, even if a non-linear convergence error arises here, which we will not examine in more detail here.
In any case, this restores the original output on the motor side, even if only approximately. The signal transformation is only completely error-free if all four firing rates are completely equal.
The convergence module with spatial signal propagation has in principle the same output properties, because it is derived from the convergence module with vertical signal superposition and delivers - except for the height factor - the same results.