Input permutations in feedback neural networks

Given a feedback network, like:

  • Make sure it is independent of input order? for example, filing [0.2, 0.3] will give the same result as [0.3, 0.2];
  • Make sure it is independent of the order of input groups? for example, submitting [0.2, 0.3, 0.4, 0.5] will give the same result as [0.4, 0.5, 0.2, 0.3], but not [0 5, 0.4, 0.3, 0.2];
  • Make sure that the permutation on the input sequence gives the permutation in the output sequence. for example, if [0.2, 0.3] gives [0.8, 0.7] as the output, then [0.3, 0.2] gives [0.7, 0.8] as the output.

Given the foregoing:

  • Is there any other solution, besides the fact that the train set covers all possible permutations?
  • Is the hidden layer parity somehow limited (i.e. the number of neurons in the hidden layer must be odd or even)?
  • Does it also make sense to look for some kind of symmetry in the weight matrix?
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2 answers

ok, this looks like hard work for NN, but 1. I would do some preprocessing and maybe a post-process script that took care of all your permutations, make sure NN is the easiest possible input. I think that preprocessing will be much easier to achieve your goal than setting up NN (adding one or more hidden layers).

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