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arXiv:2607. 18930v1 Announce Type: cross Abstract: The Universal Approximation Theorem states that a neural network with a single hidden layer is sufficient to approximate any continuous univariate function on a compact domain to arbitrary error.
arXiv:2607. 08843v1 Announce Type: new Abstract: In artificial and biological neural networks, concepts are often encoded as consistent linear directions in representation space.
The Universal Approximation Theorem states that a neural network with a single hidden layer is sufficient to approximate any continuous univariate function on a compact domain to arbitrary error. However, the uniqueness of such neural network representations is not guaranteed, raising questions about practical identifiability.
arXiv:2607. 05546v1 Announce Type: cross Abstract: We develop a unified function space theory of deep fully connected neural networks.
arXiv:2512. 11000v2 Announce Type: replace-cross Abstract: Representations pervade our daily experience, from letters representing sounds to bit strings encoding digital files.
arXiv:2606. 04754v1 Announce Type: new Abstract: Many striking phenomena in deep learning, such as linear mode connectivity and the structured behavior of training dynamics, are closely tied to parameter symmetries: transformations that leave the realized function unchanged.