[ag2718]

Ah I see, that's an interesting point about higher depth potentially having other benefits. For our work on smaller models (e.g. generally <5 layers), this might not have been as relevant but I would definitely be interested to see implications for much deeper networks. As to your point about KANs performing better or worse depending on the specific task, we definitely did notice this to some extent (symbolic tasks were the best, non-symbolic tasks such as image recognition were the worst).

[Lerc]

>symbolic tasks were the best, non-symbolic tasks such as image recognition were the worst

I wonder how much of that is not so much the overall task but the need to build up to a complex state where KANs can excel. If you consider the classic neuralnet edge detector example, it's hard to imagine a KAN doing the task more efficiently, it seems like a necessary task as part of the overall process but delegating a more capable system to a menial task is probably wasting resources.

One layer of conv2d might be enough to turn pixels into something that KANs manage better.

[ag2718]

This is definitely true: one could imagine a model with a mix of the two layers or a simple linear / MLP-like kernel doing "preprocessing" before KAN layers. Other work that explores task performances for KANs and MLPs generally finds KANs are worse at non-symbolic tasks, but it would be interesting to see if hybrid architectures could improve on this failure mode.