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  UUSSAAGGEE

        polarity [reset | update | report]  <group-list>

  DDEESSCCRRIIPPTTIIOONN

  Polarity is a measure of the degree to which the units in a group are
  adopting outputs close to the minimum or maximum possible output value. In
  a logistic group, the minimum output is 0 and the maximum is 1, but other
  types of units may have a different range. In order to compute the polarity
  of a unit, its output is first normalized to the range [0,1]. The polarity
  of a unit whose normalized output is x is given by the following formula:

        polarity = x log2(x) + (1-x) log2(1-x) + 1
  This is a U-shaped function. If the normalized output is 0.5, the polarity
  is 0. As the output increases towards 1 or decreases towards 0, the
  polarity grows towards 1.

  The average polarity of the units in a group, across several training or
  testing examples, is a useful measure. A high polarity, close to 1,
  indicates that the units are adopting binary states. A low polarity can
  indicate that there are too few units to solve the given task and the
  network is forced to make use of intermediate activation values. In the
  absence of noise, it is also possible for a network to find a low-polariity
  solution when it has too many units.

  Various techniques can be used to encourage a network to adopt more
  polarized output values. Indirectly this can be done by adding noise to the
  unit inputs. Units with non-polarized values will be more susceptible to
  this kind of noise and the network will be more successful with a solution
  that uses binary activations. An output cost function, such as
  LOGISTIC_COST, can also be used to directly encourage polarized output
  values. In fact, the LOGISTIC_COST function uses a cost function that is
  simply the inverse of polarity.

  The polarity command takes an action and a list of groups on which to
  perform that action. If the first argument is reset, the groups will erase
  all of the stored polarity information. If the first argument is update,
  the current polarity of each of the units in the group will be computed and
  these observations are recorded in the group structure using the
  polaritySum and polarityNum fields. It is common to add a call to "polarity
  update" to the postEventProc or postExampleProc so that the polarity is
  tracked following each event or example. Finally, if the first argument is
  report, the command will return the average polarity, since the last reset,
  of each of the listed groups (along with the group name).

  EEXXAAMMPPLLEE

  Here is one way to compute the polarity of all of the groups during a
  testing session. First we reset the polarity and set the postExampleProc to
  update the polarity after each example. Then we test and check the average
  polarities. Finally, the postExampleProc is cleared to speed things up
  during further training.

        lens> polarity reset *
        lens> setObject postExampleProc {polarity update *}
        lens> test
        lens> polarity report *
        {"bias" 1} {"input" 1} {"hidden" 0.670024} {"output" 0.797647}
        lens> setObject postExampleProc {}

  SSEEEE AALLSSOO

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    Last modified: Mon Jun 8.33:59:51 EDT 1998

