Table 1 Number of trainable parameters (or degrees of freedom, DoFs) of full interpolation, Tucker decomposition, and CP decomposition for an I-input single output (L = 1) relationship

From: Unifying machine learning and interpolation theory via interpolating neural networks

 

Full interpolation

Tucker decomposition

CP decomposition

Trainable parameters

\({\prod }_{i}^{I}{J}_{i}\)

\(\mathop{\prod }_{i}^{I}{M}_{i}+\mathop{\sum }_{i}^{I}{M}_{i}{J}_{i}\)

\(M{\sum }_{i}^{I}{J}_{i}\)

  1. The input domain is discretized with a regular grid of J1 × J2 × ⋯ × JI discretization. We assume that the nodal coordinates (x(j)) are fixed.
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