Forget MLPs, it’s all about KANs now… or so the hype would have you believe.
Kolmogorov-Arnold networks are a drop-in replacement for multilayer perceptrons that boast 100x better accuracy and 100x fewer parameters for the same network topology. They’re also trivially interpretable. What’s the catch? There is no catch. So then why does the author think all this attention is unwarranted?
In this session we’ll discuss the mathematics that underpin the Kolmogorov-Arnold network, the downsides of the reference implementation, alternate 1-d function approximators that can be used in place of B-splines, scalability of interpretability, and more besides. Let’s come to a nuanced understanding of the KAN as another tool in the ML arsenal.
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.