Original Contribution: Uniqueness of the weights for minimal feedforward nets with a given input-output map

By Héctor J. Sussmann. 1992

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In Statistical Learning Theory

Citations in the corpus

Overcoming catastrophic forgetting in neural networks (2016, background): “Many conﬁgurations of θ will result in the same performance [Nielsen, 1989, Sussmann, 1992]; this is relevant for EWC: over-parameterization makes it likely that there is a solution for task B, θ ∗ B , that is close to the previously found solution for task A, θ ∗ A .”
Incremental Learning for Semantic Segmentation of Large-Scale Remote Sensing Data (2018, background): “It has been proven that many configurations of the network parameters may produce the same result [27].”
Deep Learning for Mortgage Risk* (2016, neutral): “Sussmann (1992) and Albertini & Sontag (1993) study identifiability.”
Recurrent neural networks (2013, unknown): “On the other hand, it is useful in approximating functions, and some theory has been developed around it (see, e.g., [3, 4, 6, 7, 15, 16, 20, 37 , 36]).”
Neural Networks for Control (1993, methodology): “ever, the most interesting activation for neural network applications is (x) = tanh(x), or equivalently after a linear transformation, the standard sigmoid 1 1+e x . In this case, Sussmann showed in [ 37 ] that the ip property, and hence the desired uniqueness statement, hold.”
For neural networks, function determines form (1992, methodology): “The question was partially answered (for so-called "single-hidden layer" nets, and using a particular activation function) by Sussmann (1992), who established a uniqueness result that, in our setting, would apply to systems of the special type x = li(Bu), y = ex, with a = tanh(x).”
Local minima and plateaus in hierarchical structures of multilayer perceptrons (2000, background): “The G set is a line in the v1v2-plane, defined by v1 1 v2 z2: It is known that all the other components in Vu H21 are obtained as the transforms of L , J and G by g [ GH (Kůrkova & Kainen, 1994; Sussmann, 1992).”
Dynamics of Learning Near Singularities in Layered Networks (2008, background): “The geometric structure of the parameter space of a hierarchical model has been studied from the point of view of unidentifiability by many researchers (Sussmann, 1992; Chen et al., 1993; Kurková & Kainen, 1994; Fukumizu, 1996).”
MODELING MULTIPLE REGIMES IN FINANCIAL VOLATILITY WITH A FLEXIBLE COEFFICIENT GARCH(1,1) MODEL (2009, methodology): “In the spirit of the results stated in Sussman (1992) and Hwang and Ding (1997), we show that, if the model is irreducible, properties (P.”
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).”
VC dimension of neural networks (1998, background): “Pick a sequence f v k g of points where g is analytic, Theorem 2 is from Sussmann (1992) The proof given here is from Alber-tini, Sontag and Maillot (1993); in addition to simplicity, has the advantage of generalizing, with no changes, to other typical choices of sigmoids, such as (1 + e − x ) − 1…”