Kolmogorov-Arnold Networks (KANs) are a new kind of neural network, which were proposed in the paper KAN: Kolmogorov-Arnold Networks. From the abstract:

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.

If KANs are truly better than MLPs, we should expect that AI labs will start using them when they try to train SOTA models. If this is confirmed to happen by 2029, this market resolves YES, otherwise NO.

Qualifying models

Uses KANs

A model must use Kolmogorov-Arnold Networks to qualify, or some other kind of neural network that clearly descends from KANs. If the resolution date comes around and we don't know whether or not a SOTA model uses KANs, the market will resolve NO.

State-of-the-art

If the model is close to the state-of-the-art on a commonly-used eval, that's good enough to count. For instance, Gemini Ultra supposedly got a state-of-the-art, 90.0% score on MMLU, but some argued that they were gaming the eval. Rather than getting into the weeds figuring out whether or not a model counts as SOTA, I'll err on the side of counting it, since the important thing is that a serious attempt was made at achieving SOTA using KANs.

If the model focuses on a new domain that doesn't yet have commonly-used evals and it is clearly better than anything that came before, that also counts as state-of-the-art.

Past examples of AI models that qualify as "state-of-the-art" would include AlexNet, AlphaZero, GPT-3, DALL-E 2, Sora, Gemini Ultra, Suno, Udio, and Claude 3 Opus.

KAN: Kolmogorov-Arnold Networks

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.