Learning Process in an Asymmetric Threshold Network

  • Yann Le Cun
Conference paper
Part of the NATO ASI Series book series (volume 20)


Threshold functions and related operators are widely used as basic elements of adaptive and associative networks [Nakano 72, Amari 72, Hopfield 82]. There exist numerous learning rules for finding a set of weights to achieve a particular correspondence between input-output pairs. But early works in the field have shown that the number of threshold functions (or linearly separable functions) in N binary variables is small compared to the number of all possible boolean mappings in N variables, especially if N is large. This problem is one of the main limitations of most neural networks models where the state is fully specified by the environment during learning: they can only learn linearly separable functions of their inputs. Moreover, a learning procedure which requires the outside world to specify the state of every neuron during the learning session can hardly be considered as a general learning rule because in real-world conditions, only a partial information on the “ideal” network state for each task is available from the environment. It is possible to use a set of so-called “hidden units” [Hinton,Sejnowski,Ackley. 84], without direct interaction with the environment, which can compute intermediate predicates. Unfortunately, the global response depends on the output of a particular hidden unit in a highly non-linear way, moreover the nature of this dependence is influenced by the states of the other cells.


Learning Rule Associative Memory Hide Unit Threshold Function Separable Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Yann Le Cun
    • 1
    • 2
  1. 1.Ecole Supérieure d’Ingénieurs en Electrotechnique et ElectroniqueParisFrance
  2. 2.Laboratoire de dynamique des réseauxParisFrance

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