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Can neural network learn any function?
The Universal Approximation Theorem states that a neural network with 1 hidden layer can approximate any continuous function for inputs within a specific range. If the function jumps around or has large gaps, we won’t be able to approximate it.
Can neural networks learn any non separable problem?
Neural networks are very good at classifying data points into different regions, even in cases when the data are not linearly separable. Neural networks can be represented as, y = W2 phi( W1 x+B1) +B2. The classification problem can be seen as a 2 part problem, one of learning W1 and other of learning W2.
Which is a striking fact about neural networks?
One of the most striking facts about neural networks is that they can compute any function at all. That is, suppose someone hands you some complicated, wiggly function, : No matter what the function, there is guaranteed to be a neural network so that for every possible input, ,…
How are neural networks used in deep learning?
For instance, here’s a network computing a function with m = 3 inputs and n = 2 outputs: This result tells us that neural networks have a kind of universality. No matter what function we want to compute, we know that there is a neural network which can do the job.
How is the output of a neural network guaranteed?
No matter what the function, there is guaranteed to be a neural network so that for every possible input, x, the value f ( x) (or some close approximation) is output from the network, e.g.: This result holds even if the function has many inputs, f = f ( x 1, …, x m), and many outputs.
How are nonlinear functions used in neural networks?
As discussed in the Learn article on Neural Networks, an activation function determines whether a neuron should be activated. The nonlinear functions typically convert the output of a given neuron to a value between 0 and 1 or -1 and 1.