Good morning dear followers,

are you tired of scraping on the surface only? Okay let’s get a little bit
deeper in neuronal networks. Today it’s gonna be a bit mathematical. If there is
something not clear or you don’t understand it, do not hesitate to ask me or the
other Communitymembers an Comment this or the other Posts.

If you are new to my blog or you want to skip back lessons you can find all
previous posts in this list:
(I’ll do my best to Update any old posts as long as i am able to do it with the
Links of new Parts)

Part	Headline	Steemit Link:
I	Introduction	https://steemit.com/neuronalnetwork/@haggy2k3/neuronal-networks-part-1-introduction
II	Units	https://steemit.com/science/@haggy2k3/neuronal-networks-part-ii-units
III	Connections	https://steemit.com/science/@haggy2k3/neuronal-networks-part-iii-connections
IV	Inputs	Current Document
V	Activities and Outputs
VI	Training and Test
VII	Metrics
VIII	Learning Rules
IX	Types of NN
X	Features of NN
XI	Use Cases
XII	Bonus: Getting started with Membrain

Input and network input

The input that a neuron receives from another unit depends on two values, which
are mostly multiplicatively linked:

• Output (or activity level) of the sending unit

• Weight between the two neurons

Thus, the stronger the activity level of the sending unit and the higher the
weight between the two units, the greater the influence (input) on the receiving
unit. If one of the two terms equals zero, then there is no influence.

The total input of a unit is called network input (also: net input, network
input). This is determined by the so-called propagation function. The most
common propagation function is a linear combination in which the net input is
additively composed of all the individual inputs that the neuron receives from
other neurons.

Formula Presentation

Input and network input of a unit can also be represented as two formulas.

1. Input of the unit i:
   

2. Network input of the unit i:
   
   *where "i" refers to the receiving unit, while "j" means the sending units.
   Convention:
   The first index always identifies the receiving unit, the second index refers to the sending unit.
   a_j= Activity level of the sending unit j
   w_ij= Weight between the sending (j) and the receiving (i) unit

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Haggy2k3