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One of my friends found the paper An Empirical Analysis of Feature Engineering for Predictive Modeling. We were discussing the models the author wrote about. He wrote:

If the machine-learning model can learn to reproduce that feature, with a low error, it means that that particular model could have learned that engineered feature without assistance.

Now he listed ten types of transformation; they are:

•Counts • Differences • Logarithms • Polynomials • Powers • Ratios • Rational Differences • Rational Polynomials • Root Distance • Square Roots

and generated a data set based on the above ten transformations. However, he didn't explicitly mention what his machine learning models predict after using those ten data sets in training.

Now my question is, what does the author's model predict? Are his machine-learning models predicting above transformations? for example, if we give a number $x$, is author's model predict the square roots of $x$?

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