machine learning - Neural network feature combinatorics -


suppose have neural network sufficiently high number of hidden layers, hidden units per layer, , iterations, such these parameters not affect network's predictions.

given features x1, x2, ..., xn, possible (to prove) whether or not range of potential features redundant given subset of features (x1 through xn). is, given these features (x1 through xn), can neural network discern other features such as:

  • differences or additions (x1-x49, or x17+xn)?
  • products , ratios (x1*x1, or x47/xn)
  • higher order polynomials (or products of sequences ∏(x1 through xn))
  • trigonometric functions based upon original features (sin(x1*xn) + x17)
  • logarithmic functions (ln(x2*x4)/x6)

it in line of inquiry wondering if there situations using neural network need add higher order, or different, functions network predict accurately.

in general, given adequate number of features, possible network model any graph, , if not functional domains can neural networks not predict?

furthermore, there research point out references topic?

thanks!

given features x1, x2, ..., xn, possible (to prove) whether or not range of potential features redundant given subset of features (x1 through xn). is, given these features (x1 through xn), can neural network discern other features

it seems if looking dimensionality reduction neural networks. autoencoders can that:

  • you have inputs x1, x2, ..., xn.
  • you create network gets inputs (n input nodes). has hidden layers, bottleneck (k nodes, k < n) , output layer (n nodes).
  • the target recreate input.

when trained, discard layers after output. if network able restore inputs bottleneck, later layers not necessary.

in general, given adequate number of features, possible network model graph, , if not functional domains can neural networks not predict?

i guess looking universal approximation theorem. in short: neural networks can approximate continuous functions on compact subsets of r^n arbitrary close long give them enough nodes , @ least 1 hidden layer


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