Variable decoupling and the Kolmogorov Superposition Theorem for rational functions
Provides a theoretical simplification for variable decoupling in rational functions, with potential applications in approximation theory.
The authors prove that for rational multivariate functions, the Kolmogorov Superposition Theorem yields explicit single-variable functions by inspection, eliminating computation for variable decoupling. This enables low-complexity approximation of non-rational functions.
This work shows that for rational multivariate functions, the Kolmogorov Superposition Theorem (KST) involves several single-variable functions, which can be written down by inspection. In other words, no computation is required for decoupling the variables of multivariate rational functions. The key tool for this development is the Loewner Framework for multivariate functions. Applications of this result involve approximating multivariate non-rational functions by low-complexity multivariate rational and polynomial functions.