| Mathematician George Polya is attributed the quote: "If you can't solve a problem, there is an easier problem you can solve: find it". The present work is built around this intuition. Learning piecewise continuous functions is a challenging task for Artificial Neural Networks. While past attempts obtained a high degree of accuracy, we identify important speed, model engineering, reproducibility and generalizability limitations. In order to provide a solution we reimagine the problem of learning piecewise continuous functions as a classification task instead of a regression. We use the ability of neural networks to learn complex non-linear data separations and employ it to model 2 piecewise continuous functions: one described by the modulo operation and one described by a data subset of a variation of the ZX81 Linear Congruential Pseudorandom Number Generator. We use a simple approximation algorithm to revert the problem back to its original regression form and report the quality of the results. We evaluate the accuracy vs. speed vs. model complexity vs. reproducibility vs. generalizability trade-off that ensues and compare our method to other approaches in the literature. |
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