My data are sequences of real numbers $a_0,a_1,...,a_{n-1}$. The length of a sequence is fixed and equals $n$. Each sequence is mapped to a real number $y$ and I want to predict $y$ given the sequence.

The arrangement of the elements within a sequence is important. However, the sequences are circular, meaning that $a_0$ is not the first element, and $a_{n-1}$ is not the last one. The sequence $a_0,a_1,...,a_{n-1}$ is indistinguishable from the sequence $a_k, a_{k+1}, ..., a_{n-1}, a_0, ..., a_{k-1}$: they are mapped to the same $y$. Moreover, one can circle them in the opposite direction, thus $a_{n-1}, a_{n-2},..., a_0$ maps to the same answer.

I know that recurrent neural networks (RNN) are used for sequences where it is important that the inputs are fed into the network in a specific order. How to make such a network invariant to circular transformations and the change of direction described above?

I don't insist on RNN. Are there any supervised learning algorithms that work with such sequences?

  • 1
    $\begingroup$ I don't know of any algorithms that specifically cater to such data, however, you could always feed in the data to a RNN with each batch starting at a random point $\endgroup$ Oct 17, 2020 at 9:06
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    $\begingroup$ Have a look into arxiv.org/pdf/1602.07576.pdf $\endgroup$ Oct 18, 2020 at 15:05


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