Neural networks are normally displayed in 'computational graph' form, because it's a more logical and simple display. But there's no reason we couldn't write it in standard, simplified form. Even though it would be ugly, what does the function look like in simplified form (say 3 inputs, 2 hidden layers of 3 inputs each, logistic activation, 1 output). Weights can be marked as $w_1,w_2,w_3$, etc. So $$f(x_1,x_2,x_3) = …$$
What does the hypothesis function for a simple neural network (MLP with logistic activation, single output) look like in simplified form?
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machine-learning
neural-networks
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0You can't write a neural network in the form $f( g(x_1,x_2),h(x_3,\ldots),\ldots)$ because a neural network is a **graph, not a tree**. – 2017-02-19
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0thanks but I don't think that's accurate. It's clearly possible to do it with 0 hidden layers, and I can't see why you could't do it with more. It would just be ugly and have a lot of repeated terms – 2017-02-19
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0Come on http://cs231n.github.io/assets/nn1/neural_net2.jpeg ... A neural network is a graph, not a tree. You can represent it by such a diagram, or by listing how each neuron output depends on the other neurons. – 2017-02-19
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0Thanks, but in the end of the day you are just summing, multiplying, and doing sigmoid a lot. So you COULD write it in that form, which is the point of this question. – 2017-02-19
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0The output of the $i$th neuron is $x_i = h(\sum_j w_{ij} x_j)$ where $h$ is the sigmoid function. So all we need is the weights – 2017-02-19