{"ID":2836534,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.21626","arxiv_id":"2511.21626","title":"Scale-Agnostic Kolmogorov-Arnold Geometry in Neural Networks","abstract":"Recent work by Freedman and Mulligan demonstrated that shallow multilayer perceptrons spontaneously develop Kolmogorov-Arnold geometric (KAG) structure during training on synthetic three-dimensional tasks. However, it remained unclear whether this phenomenon persists in realistic high-dimensional settings and what spatial properties this geometry exhibits. We extend KAG analysis to MNIST digit classification (784 dimensions) using 2-layer MLPs with systematic spatial analysis at multiple scales. We find that KAG emerges during training and appears consistently across spatial scales, from local 7-pixel neighborhoods to the full 28x28 image. This scale-agnostic property holds across different training procedures: both standard training and training with spatial augmentation produce the same qualitative pattern. These findings reveal that neural networks spontaneously develop organized, scale-invariant geometric structure during learning on realistic high-dimensional data.","short_abstract":"Recent work by Freedman and Mulligan demonstrated that shallow multilayer perceptrons spontaneously develop Kolmogorov-Arnold geometric (KAG) structure during training on synthetic three-dimensional tasks. However, it remained unclear whether this phenomenon persists in realistic high-dimensional settings and what spat...","url_abs":"https://arxiv.org/abs/2511.21626","url_pdf":"https://arxiv.org/pdf/2511.21626v3","authors":"[\"Mathew Vanherreweghe\",\"Michael H. Freedman\",\"Keith M. Adams\"]","published":"2025-11-26T17:52:05Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.AI\"]","methods":"[\"Generative Adversarial Network\"]","has_code":false}