Neural networks vs calculations by eye

    Today I learned that people can estimate the rank of a matrix by eye!
    (recall, rank is the number of linearly independent rows or columns)


    image


    Like, they look at this and say that the rank is


    Well! Well!

    3


    How to resist and not try to teach it how to do a neural network, we thought cocks students from Carnegie Mellon?


    That is, here we take the matrix, translate it into such a picture and give CNN to the input so that it predicts the rank or whether the matrix is ​​degenerate.


    image


    Look at the bold. Here it is, the future of algorithm optimization.


    The article here and in it is magnificent and the syllable, and the questions raised, and the list of authors, and in general everything.


    For example, then they apply the same approach to matrix multiplication and finding the inverse:


    We then use this data to train the network with
    stochastic gradient descent on a mean square error
    (MSE) loss for 100 epochs. Some qualitative predictions
    on unseen data are shown in Figures 7 and 8.
    We found the multiplication task to be easily solved
    by our network architecture, but the inversion task
    proved much more challenging, as shown by the
    higher MSE values. We note that this is analogous to
    humans taking Linear Algebra 101
    .

    Rzhu nimagu.
    For dessert - slides .


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