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Researchers confirmed that Kolmogorov-Arnold Geometry (KAG) spontaneously emerges in standard multilayer perceptrons trained on high-dimensional MNIST image data, exhibiting a scale-agnostic organization from local to global input regions. The study found that spatial data augmentation moderates the intensity of KAG while preserving its qualitative patterns, suggesting a connection between data diversity and learned geometric structure.

Researchers from Logical Intelligence, Harvard, and UC Riverside investigated whether Kolmogorov-Arnold-like geometric structures naturally form in conventional shallow neural networks during optimization. They found that these geometries spontaneously emerge when models learn complex, nonlinear functions, and their presence correlates with improved learning performance.