Biological motivation and connections

The basic computational unit of our brains is called a neuron, and we have approximately 86 billion neurons in our nervous system, which are connected with approximately to synapses.

Figure 1 shows a biological neuron. Figure 2 shows the corresponding mathematical model. In the drawing of the biological neuron, each neuron receives incoming signals from its dendrites and then produces output signals along its axon, where the axon gets split out and connects via synapses to other neurons.

In the corresponding mathematical computational model of a neuron, the signals that travel along the axons interact with a multiplication operation with the dendrites of the other neuron in the system based on the synaptic strength at that synapse, which is represented by . The idea is that the synaptic weights/strength  gets learned by the network and they're the ones that control the influence of a specific neuron on another.

Also, in the basic computational model in Figure 2, the dendrites carry the signal to the main cell body where it sums them all. If the final result is above a certain threshold, the neuron can fire in the computational model.

Also, it is worth mentioning that we need to control the frequency of the output spikes along the axon, so we use something called an activation function. Practically, a common choice of activation function is the sigmoid function σ, since it takes a real-valued input (the signal strength after the sum) and squashes it to be between 0 and 1. We will see the details of these activation functions later in the following section:

       
Figure 1: Computational unit of the brain (http://cs231n.github.io/assets/nn1/neuron.png)

There is the corresponding basic mathematical model for the biological one:

 
Figure 2: Mathematical modeling of the Brain's computational unit (http://cs231n.github.io/assets/nn1/neuron_model.jpeg)

The basic unit of computation in a neural network is the neuron, often called a node or unit. It receives input from some other nodes or from an external source and computes an output. Each input has an associated weight (w), which is assigned on the basis of its importance relative to other inputs. The node applies a function f (we've defined it later) to the weighted sum of its inputs.

So, the basic computational unit of neural networks in general is called neuron/node/unit.

This neuron receives its input from previous neurons or even an external source and then it does some processing on this input to produce a so-called activation. Each input to this neuron is associated with its own weight , which represents the strength of this connection and hence the importance of this input.

So, the final output of this basic building block of the neural network is a summed version of the inputs weighted by their importance w, and then the neuron passes the summed output through an activation function.

Figure 3: A single neuron
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