RPROP Resilient Propagation

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RPROPResilient Propagation

• Students Novica Zarvic
• Roxana Grigoras
• Term Winter semester 2003/2004
• Lecture Machine Learning / Neural Networks
• Course Information Engineering
• Date 2004-01-06

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Content

• Part I
• General remarks
• Foundations (MLP, Supervised Learning,
  Backpropagation and its problems)
• Part II
• Description of the RProp Algorithm
• Example cases
• Part III
• Visualization with SNNS
• Discussion

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General remarks
I.

• Basis for this talk
• Rprop Description and Implementation Details
• (Technical report by Martin Riedmiller, January
  1994)
• URL http//lrb.cs.uni-dortmund.de/riedmill/publi
  cations/rprop.details.ps.Z

-03-
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MLPMulti-Layer Perceptron
I.
Output layer
Input layer
Hidden layer(s)
Topology of a typical feed-forward network with
two hidden layers. The external input is
presented to the input layer, propagated forward
through the hidden layers and yields an output
activation vector in the output layer.
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Supervised Learning
I.

• Objective
• Tune the weights in the network such that the
  network performs a desired mapping of input to
  output activations.

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Principleof supervised learning (like BP or one
of its derivatives)
I.

• Presentation of the input pattern through
  activation of the input units. The pattern set
  consists of input activation vector xp and a
  target vector tp.
• Feedforward computation to get the resulting
  output vector sp.
• Compare sp with tp. Distance between the vectors
  is measured by the function E ½ ?p ?n
  tp sp 2 . (n number of units in output
  layer, p
  a pattern pair of the pattern set P)
• Backpropagation of the errors from the output to
  the input changes the weights of the connections.
  This minimizes the error vector.
• Changing the weights of all neurons with the
  previous calculated values.

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Problems of Backpropagation
I.

• ? No information about the complete error
  function. It is difficult to choose a good
  learning rate.
• a. Local Minima of E
• b. Plateaus
• c. Oscillation
• d. Leaving good Minima
• ? It uses only weight-specific information
  (partial derivative) to adapt weight-specific
  parameters.

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RPROPResilient Propagation
II.

• What is the traditional Backpropagation algorithm
  doing?
• ? It modifies the weights of the partial
  derivatives. (?E/ ?wij)
• ? Problem The size of this differential does
  not really represent the size of the necessary
  modification of the weight changes.
• ? Solution RProp does not count on the value of
  the partial derivative. It considers only the
  sign of the derivative to indicate the direction
  of the weight update.

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RPROP-Description-
II.

• Effective learning scheme
• It performs a direct adaption of weight step
  based on local gradient information
• Basic principle of RProp is to eliminate the
  harmful influence of the size of the partial
  derivative on the weight step
• It considers only the sign of the derivative to
  indicate the direction of the weight update.

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RPROPResilient Propagation
II.
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RPROPWhat is ?ij ?
II.

• ?ij is an update value.
• The size of the weight change is exclusively
  determined by this weight-specific update
  value.
• ?ij evolves during the learning process based on
  its local sight on the errorfunction E, according
  to the following learning-rule

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RPROP
II.

• The weight update ?wij follows a simple rule
• If the derivative is positive (increasing
  error), the weight is decreased by its update
  value.
• If the derivative is negative, the update value
  is added.

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RPROPOne exception (Take bad steps back!)
II.

• If the partial derivative changes sign, i.e. the
  previous step was too large and the minimum was
  missed, the previous weight update is reverted.

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RPROP-The pseudo code-
II.
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RPROP-Settings-
II.

• Increasing and decreasing factors
• ?- 0.5 (decrease factor)
• ? 1.2 (increase factor)
• Limits
• ?max 50.0 (upper limit)
• ?min 1e-6 (upper limit)
• Initial value
• ?o 0.1 (default setting)

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RPROPBackprop vs. RProp
III.
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RPROP-Discussion-
III.

• Compared to all other algorithms, only the sign
  of the differential is used to perform learning
  and adaptation.
• The size of the derivative decreases
  exponentially with the distance between the
  weight and the output-layer.
• Using RProp the size of the weight-step is
  dependent only on the sequence of signs ?
  learning is spread equally all over the entire
  network.

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RPROP-Further material-
III.

• Advanced Supervised Learning in Multi-layer
  Perceptrons From Backpropagation to Adaptive
  Learning Algorithms (Martin Riedmiller)
• A Direct Adaptive Method for Faster
  Backpropagation Learning The RPROP Algorithm
  (Martin Riedmiller)
• Rprop Description and Implementation Details
  (Martin Riedmiller)

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RPROPResilient Propagation
III.

• Thank you for listening!
• ?

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