For neural networks, function determines form

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Representing smooth functions as compositions of near-identity functions with implications for deep network optimization (2018, background): “(This was shown for generic parameter values and tanh networks of arbitrary depth by Fefferman (1994), and improved by Albertini and Sontag (1992) for the special case of two-layer networks.)”
Lie Algebra of Recurrent Neural Networks and Identifiability (1993, methodology): “References [1] F. Albertini and E. D. Sontag.”
Processing directed acyclic graphs with recursive neural networks (2001, background): “of a feedforward neural network are uniquely identifiable by the network input–output function [25], thus implies .”
Neural Networks for Control (1993, background): “Then, in [ 1 ], the following result was proved: Assume that is odd and satises property (*).”
Neural networks for pattern recognition (1995, background): “Furthermore, the existence of these symmetries is not a particular property of the ' tanh' function, but applies to a wide range of activation functions (Sussmann, 1992; Chen et ai, 1993; Albertini and Sontag, 1993; Kiirkova and Kainen, 1994).”