Two Curves

Data for the benchmarking of machine learning models taken from Better than classical? The subtle art of benchmarking quantum machine learning models. This classification task is inspired by Buchanan et al. [1] who show that the difficulty of distinguishing between two 1-d curves embedded into a high-dimensional space depends on the curvature and distance between the curves.

Description of the dataset

For each class, 1-d data is sampled from the interval [0,1] and embedded into a $d$-dimensional space by $d$ different functions – one for each dimension. The functions are the same for data from both classes, with the exception of a shift $\Delta$ that controls the distance between the curves. The functions are implemented by low-degree Fourier series, where the degree controls the curvature of the embedding. Gaussian noise is added to the final $d$-dimensional input vectors.

There are two different dataset collections in this task:

• two_curves fixes the degree to $D = 5$, offset to $\Delta = 0.1$ and varies the input vector dimension between $d=2,\ldots,20$.
• two_curves_diff fixes the dimension $d=10$ and varies the degree $D$ of the polynomial between $D=2,\ldots,20$ while adapting the offset $\Delta=1/2D$ between the two curves

Additional details

• The class labels are defined as -1, 1.
• For each dataset, 240 labeled points are provided for training and 60 for testing.
• The datasets are balanced, meaning that they contain the same number of samples for each class.
• Please see the Source code tab to check how the data was generated.

Example usage

[ds] = qml.data.load("other", name="two-curves")

ds.train['4']['inputs'] # points in 4-dimensional space
ds.train['4']['labels'] # labels for the points above

ds.diff_train['5']['inputs'] # points in 10-dimensional space, polynomials of degree 5
ds.diff_train['5']['labels'] # labels for the points above

[1] S. Buchanan, D. Gilboa, and J. Wright, Deep networks and the multiple manifold problem, in International Conference on Learning Representations (2021)

version 0.1 : initial public release