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When a neural network solved a problem, it means it found the algebraic function it needs to solve the problem.

> Once it found the algebraic function, there is no need to run the problem to the neural network. We can sideload the problem to a simple program that takes input and gives an output. This strategy can help to free up the GPU for next set of problem.

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How would one extract an algebraic function from the network’s weights? Why would the function the network approximates necessarily be algebraic?

The function would simply be a chain of multiplications and (typically) non-linear transformations.

For classification problems, there is often a final non-linear transformation, like a softmax.

Example with ReLu activation:

Output_i = max((input_i * weight_i),0)

I don't understand. The example you gave is not an algebraic function.

You are correct. It is possible to construct a linear neural network, where an algebraic function could be extracted, but in practice, almost all networks use non-linear activation functions.

In the case of a linear network, the function would be a dot product between the input and the weights: 𝑥1𝑤1+𝑥2𝑤2+𝑥3𝑤3 ... for all inputs (xi) and weights (wi)

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