Then why would you choose to use a CNN over a fully connected neural network for visual data? For the same reason you'd choose a KAN over a traditional neural n

Then why would you choose to use a CNN over a fully connected neural network for visual data? For the same reason you'd choose a KAN over a traditional neural network if you were trying to fit a continuous function that can easily be modeled as a combination of b-splines. Machine learning models aren't magic and their internal function very much determines the kinds of problems to which they are well applied. My intuitions about KANs and visual data comes from an impression that it would be hard for a decision boundary on visual data to behave nicely if it could only be built from b-splines. Judging the usefulness of a machine learning architecture is not a matter of determining which architecture will perform the best in all scenarios.