Kolmogorov GAM Networks Are All You Need!

Kolmogorov GAM (K-GAM) networks have been shown to be an efficient architecture for both training and inference. They are additive models with embeddings that are independent of the target function of interest. They provide an alternative to Transformer architectures. They are the machine learning version of Kolmogorov's superposition theorem (KST), which provides an efficient representation of multivariate functions. Such representations are useful in machine learning for encoding dictionaries (a.k.a. "look-up" tables). KST theory also provides a representation based on translates of the Köppen function. The goal of our paper is to interpret this representation in a machine learning context for applications in artificial intelligence (AI). Our architecture is equivalent to a topological embedding, which is independent of the function, together with an additive layer that uses a generalized additive model (GAM). This provides a class of learning procedures with far fewer parameters than current deep learning algorithms. Implementation can be parallelizable, which makes our algorithms computationally attractive. To illustrate our methodology, we use the iris data from statistical learning. We also show that our additive model with non-linear embedding provides an alternative to Transformer architectures, which, from a statistical viewpoint, are kernel smoothers. Additive KAN models, therefore, provide a natural alternative to Transformers. Finally, we conclude with directions for future research.