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Triangles
Although the targets in benchmark dataset are computed by algebraic formula, the AI training is challenging in terms of performance and accuracy.
The target is the area of triangle and features are positions of random points in 100 * 100 square. The dataset has 10 000 records. It may look simple, but
ordinary MLPs are failing. Typical training time is near a minute and usual errors for predicted targets are 10 to 15%.
We compare KAN to Neural Designer application, downloaded from their site.
Accuracy and performance of Neural Designer look better than some other MLPs, I tried to use for this dataset. After some experimenting with configuration for
network, training algorithm, activation functions and some other options the best result was 0.87 for Pearson correlation
coefficient for predicted and actual targets for unseen (not used in training) records. Below is the chart of network and the fragment
of report. The activation functions were hyperbolic tangent, the training algorithm was stochastic gradient descent.
The execution time was about 8 seconds.
KAN piecewise linear version accuracy was 96% for Pearson correlation coefficient and it took near 5 seconds for training.
The code has a big room for runtime optimization. Here is one version which needs only one second for the same accuracy model.
The optimization is achieved by excluding records with low residual errors during training and keeping only those that did not achieve wanted accuracy.


