Learning Process

1
Learning Process

• CS/CMPE 333 Neural Networks

2
Learning

• Learning?
• Learning is a process by which the free
  parameters of a neural network are adapted
  through a continuing process of stimulation by
  the environment in which the network is embedded
• The type of learning is determined by the manner
  in which the parameter changes take place
• Types of learning
• Error-correction, Hebbian, competitive, Boltzmann
• Supervised, reinforced, unsupervised

3
Learning Process

• Adapting the synaptic weight
• wkj(n 1) wkj(n) ?wkj(n)

4
Learning Algorithms

• Learning algorithm a prescribed set of
  well-defined rules for the solution of a learning
  problem
• In the context of synaptic weight updating, the
  learning algorithm prescribes rules for ?w
• Learning rules
• Error-correction
• Boltzmann
• Hebbian
• Competitive
• Learning paradigms
• Supervised
• Reinforced
• Self-organizing (unsupervised)

5
Error-Correction Learning (1)

• ek(n) dk(n) yk(n)
• The goal of error-correction learning is to
  minimize a cost function based on the error
  function
• Least-mean-square error as cost function
• J E0.5Skek2(n)
• E expectation operator
• Minimizing J with respect to the network
  parameters is the method of gradient descent

6
Error-Correction Learning (2)

• How do we find the expectation of the process?
• We avoid its computation, and use an
  instantaneous value of the sum of squared errors
  as the error function (as an approximation)
• ?(n) 0.5Skek2(n)
• Error correction learning rule (or delta rule)
• ?wkj(n) ?ek(n)xj(n)
• ? learning rate
• A plot of error function and weights is called an
  error surface. The minimization process tries to
  find the minimum point on the surface through an
  iterative procedure.

7
Hebbian Learning (1)

• Hebb, a neuropsychologist, proposed a model of
  neural activation in 1949. Its idealization is
  used as a learning rule in neural network
  learning.
• Hebbs postulate (1949)
• If the axon of cell A is near enough to excite
  cell B and repeatedly or perseistently takes part
  in firing it, some growth process or metabolic
  change occurs in one or both cells such that As
  efficiency as one of the cells firing B is
  increased.

8
Hebbian Learning (2)

• Hebbian learning (model of Hebbian synapse)
• If two neurons on either side of a synapse are
  activated simultaneously, then the strength of
  that synapse is selectively increased
• If two neurons on either side of synapse are
  activated asynchronously, then that synapse is
  selectively weakened or eliminated
• Properties of Hebbian synapse
• Time-dependent mechanism
• Local mechanism
• Interactive mechanism
• Correlational mechanism

9
Mathematical Models of Hebbian Learning (1)

• General form of Hebbian rule
• ?wkj(n) Fyk(n), xj(n)
• F is a function of pre-synaptic and
  post-synaptic activities.
• A specific Hebbian rule (activity product rule)
• ?wkj(n) ?yk(n)xj(n)
• ? learning rate
• Is there a problem with the above rule?
• No bounds on increase (or decrease) of wkj

10
Mathematical Models of Hebbian Learning (2)

• Generalized activity product rule
• ?wkj(n) ?yk(n)xj(n) ayk(n)wkj(n)
• Or
• ?wkj(n) ayk(n)cxk(n) - wkj(n)
• where c ?/ a and a positive constant

11
Mathematical Models of Hebbian Learning (3)
12
Mathematical Models of Hebbian Learning (4)

• Activity covariance rule
• ?wkj(n) ? covyk(n), xj(n)
• ? E(yk(n) y)(xj(n) x)
• where ? proportionality constant and x and y
  are respective means
• After simplification
• ?wkj(n) ? Eyk(n)xj(n) xy

13
Competitive Learning (1)

• The output neurons of a neural network (or a
  group of output neurons) compete among themselves
  for being the one to be active (fired)
• At any given time, only one neuron in the group
  is active
• This behavior naturally leads to identifying
  features in input data (feature detection)
• Neurobiological basis
• Competitive behavior was observed and studied in
  the 1970s
• Early self-organizing and topographic map neural
  networks were also proposed in the 1970s (e.g.
  cognitron by Fukushima)

14
Competitive Learning (2)

• Elements of competitive learning
• A set of neurons
• A limit on the strength of each neuron
• A mechanism that permits the neurons to compete
  for the right to respond to a given input, such
  that only one neuron is active at a time

15
Competitive Learning (3)
16
Competitive Learning (4)

• Standard competitive learning rule
• ?wji ?(xi wji) if neuron j wins the
  competition
• 0 otherwise
• Each neuron is allotted a fixed amount of
  synaptic weight which is distributed among its
  input nodes
• Si wji 1 for all j

17
Competitive Learning (5)
18
Boltzmann Learning

• Stochastic learning algorithm based on
  information-theoretic and thermodynamic
  principles
• The state of the network is captured by an energy
  function, E
• E -1/2 Si Sj wjisisj
• where si state of neuron i 0, 1 (i.e. binary
  state)
• Learning process
• At each step, choose a neuron at random (say j)
  and flip its state sj by the following
  probability
• w(sj -gt -sj) (1 exp(-?Ej/T)-1
• The state evolves until thermal equilibrium is
  achieved

19
Credit-Assignment Problem

• How to assign credit and blame for a neural
  networks output to its internal (free)
  parameters ?
• This is basically the credit-assignment problem
• The learning system (rule) must distribute credit
  or blame in such a way that the network evolves
  to the correct outcomes
• Temporal credit-assignment problem
• Determining which actions, among a sequence of
  actions, are responsible for certain outcomes of
  the network
• Structural credit-assignment problem
• Determining which internal components behavior
  should be modified and by how much

20
Supervised Learning (1)
21
Supervised Learning (2)

• Conceptually, supervised learning involves a
  teacher who has knowledge of the environment and
  guides the training of the network
• In practice, knowledge of the environment is in
  the form of input-output examples
• When viewed as a intelligent agent, this
  knowledge is current knowledge obtained from
  sensors
• How is supervised learning applied?
• Error-correction learning
• Examples of supervised learning algorithms
• LMS algorithm
• Back-propagation algorithm

22
Reinforcement Learning (1)

• Reinforcement learing is supervised learning in
  which limited information of the desired outputs
  is known
• Complete knowledge of the environment is not
  available only basic benefit or reward
  information
• In other words, a critic rather than a teacher
  guides the learning process
• Reinforcement learning has roots in experimental
  studies of animal learning
• Training a dog by positive (good dog, something
  to eat) and negative (bad dog, nothing to eat)
  reinforcement

23
Reinforcement Learning (2)

• Reinforcement learning is the online learning of
  an input-output mapping through a process of
  trail and error designed to maximize a scalar
  performance index called reinforcement signal
• Types of reinforcement learning
• Non-associative selecting one action instead of
  associating actions with stimuli. The only input
  received from the environment is reinforcement
  information. Examples include genetic algorithms
  and simulated annealing.
• Associative associating action and stimuli. In
  other words, developing a action-stimuli mapping
  from reinforcement information received from the
  environment. This type is more closely related to
  neural network learning.

24
Supervised Vs Reinforcement Learning
25
Unsupervised Learning (1)

• There is no teacher or critic in unsupervised
  learning
• No specific example of the function/model to be
  learned
• A task-independent measure is used to guide the
  internal representation of knowledge
• The free parameters of the network are optimized
  with respect to this measure

26
Unsupervised Learning (2)

• Also known as self-organizing when used in the
  context of neural networks
• The neural network develops an internal
  representation of the inputs without any specific
  information
• Once it is trained it can identify features in
  the input, based on the task-independent (or
  general) criterion

27
Supervised Vs Unsupervised Learning
28
Learning Tasks

• Approximation
• Association
• Auto-association
• Hetero-association
• Pattern classification
• Prediction
• Control

29
Adaptation and Learning (1)

• Learning, as we know it in biological systems, is
  a spatiotemporal process
• Space and time dimensions are equally significant
• Is supervised error-correcting learning
  spatiotemporal?
• Yes and no (trick question ?)
• Stationary environment
• Learning one time procedure in which
  environment knowledge is built-in (memory) and
  later recalled for use
• Non-stationary environment
• Adaptation continually update the free
  parameters to reflect the changing environment

30
Adaptation and Learning (2)
31
Adaptation and Learning (3)

• e(n) x(n) - x(n)
• where e error x actual input x model
  output
• Adaptation needed when e not equal to zero
• This means that the knowledge encoded in the
  neural network has become outdated requiring
  modification to reflect the new environment
• How to perform adaptation?
• As an adaptive control system
• As an adaptive filter (adaptive error-correcting
  supervised learning)

32
Statistical Nature of Learning

• Learning can be viewed as a stochastic process
• Stochastic process? when there is some element
  of randomness (e.g. neural network encoding is
  not unique for the same environment that is
  temporal)
• Also, in general, neural network represent just
  one form of representation. Other representation
  forms are also possible.
• Regression model
• d g(x) e
• where g(x) actual model e statistical
  estimate of error