Interpretación de las entrevistas e interpretación del mural de

In the previous sections we introduced the fundamental findings we need for developing a computational model. Our goal is to model the underlying circuit of neocortical pro-

3_{”Small protrusions of the dendrite with which an axon terminal forms a synapse.” (Spine (Dendritic)}

Binder et al., 2009)

1.7 DEVELOPING A MODEL SKETCH

cessing. Universal enough to be applicable to other brain areas. Precise enough to have explanatory power on the processes in the early visual system.

Basic elements The core units of the intended network model are the excitatory neu- rons. This is because they are the only units who project to other brain areas and gather and transform the information of preceding areas. To the excitatory neurons, we need a form of inhibition to be able to implement any form of biologically plausible synaptic plasticity. Consequently, we will model inhibitory interneurons as dedicated neuron type.

Circuit While the inhibitory interneurons have to be mainly locally connected, the ex- citatory neurons can have a richer connectivity. The minimal required connectivity would be the feedforward pathway across the brain. That is, a connection from a population of excitatory neurons from the entrance layer of an area (layer 4) to the next downstream layer (layer 2/3) and from the excitatory neurons there to the next area. This circuit seems over idealized. So that a model aiming to allow new insights in the functioning of the brain should implement also the other layers and the recurrent connections between them and between the areas. On the other side, this would potentiate the complexity of the model. Implementing the layers 5 and 6 would make just sense when the cortical feedback cir- cuit including the second order thalamus and its processing are implemented. It seems not promising to start with the complete complexity at once. Thus, we should implement the layers of the feedforward pathway, but include the recurrent connections between the neurons. Therefore, we use as inspiration the findings about the intra connectivity of a typically neocortical area.

Stimuli To measure later neuron responses which are comparable to experimental data we need to stimulate the network with realistic input. The logical consequence from that is using natural scene input for a model of the visual system. This input has to be given as presynaptic activity onto the V1 layer-4 neurons. Of course, in the visual system a cascade of retinal and thalamic processing has taken place until this stage. Albeit, the receptive fields of LGN neurons follow a simple description, which is easy to approximate. This approximation appears standard in computational modeling, thus, we can focus on the cortical processing and use established image preprocessing methods. A neuron layer, which should obviously be named LGN, should transfer the image values into neuron activities.

1 GENERAL INTRODUCTION

Plasticity Now we have a good idea in mind how the processing elements of the net- work should be arranged. But we still have to define the synaptic weights and the neuron functioning. The receptive fields of neurons in the entrance layer are described as Gabor like. Thus, we could define the weights through a mathematical function. However, find- ing a good parametrization for high biological plausibility would be complicated. Even basic properties as receptive field sizes differ between experimental studies and measures (cf. eCRF and pRF Angelucci et al., 2002; Wandell and Winawer, 2015). Moreover, no concrete data are available for inhibitory connections or the recurrent connections, apart from the feedforward pathway, or the connections within deeper layers, which are even more abstract than their receptive field, which is defined in the input space. Thus, hard wiring the neurons would be tough.

A much more appealing strategy is to implement the self-organizing mechanisms of the cortex itself. This means at first, the synaptic plasticity. We will use rate based learning rules, since they have shown to develop proper V1-like receptive fields. Because of the unbound increase of the weights in naive Hebbian rules, we have to combine the learning with a normalization term which applies a multiplicative normalization without violating the Hebbian property of locality. The multiplicative normalization has also been shown to give proper receptive fields shapes. Further, the rule should be able to account for the invariance properties of neurons, like the one in V1 layer-2/3. The plasticity mechanisms determine the neuron model so that we use the simplest, but plausible enough, activation function for the neurons: a rectified linear function. Albeit synaptic plasticity finds the connection strength between the neurons for us, we would have to connect each individual neuron of two connected neuron populations. This is an ill concept considering about 190 million neurons just in the macaque V1. Again, we could define a connection matrix, individual for each neuron, based on a mathematical concept considering the findings on the receptive field size. This network design would have the potential to give us sufficient insights in the brain machinery, but it will be again strongly biased from our modeling decisions, how we fill up the unknown parameters. To overcome the “modeler’s bias”, we will apply structural plasticity to refine an initially defined connectivity. Structural plasticity should be a random process just weight based. To not degenerate to a fully random process, dealing with the enormous amount of potential connections which could exist in the brain, the physiological property that new synapses are just formed where dendrites are should be used. Not required synapses should be removed based on their