Interpolation and Extrapolation in High-Dimensional Datasets

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Learning in High Dimension Always Amounts to Extrapolation

State-of-the-art algorithms work so well because of their ability to correctly interpolate training data.

We empirically and theoretically argue against those two points and demonstrate that on any high-dimensional dataset, interpolation almost surely never happens.

Those results challenge the validity of our current interpolation/extrapolation definition as an indicator of generalization performances.

Authors

Randall Balestriero, Jerome Pesenti, Yann LeCun

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