# Dependencies between the inputs and outputs of the neural network

Is it possible to determine the dependencies between the inputs and outputs of a neural network in the form of a formula or a set of equations?

That is, when the network is already created and trained and the weights are known. Is it possible in some way to simplify the calculations, having determined the dependencies, to bring all this to the dependency equations?

• And why do you even need a neural network if you need equations describing the behavior of an object? Physics tutorial to help - igumnov

A programmed neural network consists of neurons, which are mathematical models of real neurons, so it is theoretically possible to mathematically describe the entire neural network. Theoretically, the solution should be.

But in practice, this is difficult to achieve. The resulting equation will contain three-story fractions, roots, and degrees.

• so what? after can be simplified - slava_evm
• @Vyacheslav1101, here @MuFF tells you everything correctly. Simplify what can happen at the output you most likely will not succeed, since these will not be typical fractions known to you. --- Even in FaceBook, I remember, they tried to implement something similar (the definition of users in the photos and their mark), but it didn’t work for them ... Google Talk managed to implement it but sooo clumsy ... but there is much to develop. I do not think that you will succeed, since the "monsters" did not work out. - Salivan
• is not a fact. money even if it helps, but not the most important! - slava_evm 2:53 pm

Perhaps it all depends on the structure and complexity of the neural network. For a primitive NA is quite real.

``xy z(0-15) 00 0101010101010101 01 0011001100110011 10 0000111100001111 11 0000000011111111` `

Here you have a simple neural network with 2-bit input and 16-bit output, it has 16 different logic output functions! that is, the greater the width at the entrance, the more options at the output. as a rule, we do not use everything, for example, only AND-NO, and this saves us.

Simplification is possible, in the end it’s just “input-output” correspondence, but all input options should be sorted out and for “big data” it is a task comparable to the training of the network.

although no, you already have a configured network. So, we need to start training a new network based on the findings of the configured network. and this NEW network can be optimized. and you understand the principles of construction and optimization.