Methods · Interpretability-by-Design Methods for Intrinsic Interpretability

Kolmogorov–Arnold Networks (KANs)

Survey sections: §6.10.5 Kolmogorov–Arnold Networks

Inspired by the Kolmogorov–Arnold representation theorem, KANs place learnable nonlinear functions, typically parameterised using B-splines, on edges rather than using fixed nonlinear activation functions at nodes.
Survey §6.10.5 Kolmogorov–Arnold Networks

Intended applications

As the nonlinearities are univariate and can be visualised directly on individual edges, researchers can use techniques like symbolic regression to approximate and inspect the learned analytical expressions, such as rediscovering known physical equations.

Limitations

Although KAN training is currently more computationally expensive than training standard MLPs and has not yet been convincingly demonstrated at the scale of large language models, this architectural innovation points to an ambitious direction towards interpretable neural networks in which parameters correspond to mathematically meaningful functions.

Key papers

Cited in §6.10.5.

Ziming Liu, Yixuan Wang, Sachin Vaidya, Fabian Ruehle, James Halverson, Marin Soljacic, Thomas Y. Hou, and Max Tegmark. KAN: Kolmogorovarnold networks. In The Thirteenth International Conference on Learning Representations, 2025b. URL https://openreview.net/forum?id=Ozo7qJ5vZi.

Also discussed in: §5.2 Architectural Responses to Superposition · §6.10.4 Modifications of Computational Primitives: MOLT · §15.2 The Road Ahead

Other methods in Interpretability-by-Design Methods for Intrinsic Interpretability

Weight-Sparse Training (Weight-Sparse Transformer) · Attention-Sparse Training (SPARTAN) · Softmax Linear Units (SoLU) · Sparse Mixture of Linear Transforms (MOLT)