Inspired by the Kolmogorov-Arnold representation theorem, we propose Kolmogorov-Arnold Networks (KANs) as promising alternatives to Multi-Layer Perceptrons (MLPs). While MLPs have fixed activation functions on nodes ("neurons"), KANs have learnable activation functions on edges ("weights"). KANs have no linear weights at all -- every weight parameter is replaced by a univariate function parametrized as a spline. We show that this seemingly simple change makes KANs outperform MLPs in terms of accuracy and interpretability. For accuracy, much smaller KANs can achieve comparable or better accuracy than much larger MLPs in data fitting and PDE solving. Theoretically and empirically, KANs possess faster neural scaling laws than MLPs. For interpretability, KANs can be intuitively visualized and can easily interact with human users. Through two examples in mathematics and physics, KANs are shown to be useful collaborators helping scientists (re)discover mathematical and physical laws. In summary, KANs are promising alternatives for MLPs, opening opportunities for further improving today's deep learning models which rely heavily on MLPs.
I know this sounds fantastic but can someone please dumb down what KANs are for me, why they're so revolutionary (in practice, not in theory) that all the big labs would wanna switch to them?
Or is it the case that having MLPs is still a better thing for GPUs and in practice that will not change?
And how are KANs different from what SAEs attempt to do
MLP or KAN doesn't make much difference for the GPUs as it is lots of matrix multiplications anyway. It might make some difference in how the data is routed to all the GPU cores as the structure (width, depth) of the matrixes might be different, but I don't know the details of that.
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Abstract: