Learning Process CS/CMPE 537 – Neural Networks. CS/CMPE 537 - Neural Networks (Sp 2004/2005) -...

Learning Process

CS/CMPE 537 – Neural Networks

CS/CMPE 537 - Neural Networks (Sp 2004/2005) - Asim Karim @ LUMS 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, memory-based, Hebbian, competitive,

Boltzmann Supervised, reinforced, unsupervised


Learning Process

Adapting the synaptic weight

wkj(n + 1) = wkj(n) + Δwkj(n)


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 Δw

Learning rules Error-correction Memory based Boltzmann Hebbian Competitive

Learning paradigms Supervised Reinforced Self-organizing (unsupervised)


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 = E[0.5Σkek2(n)]

E = expectation operator Minimizing J with respect to the network parameters is the

method of gradient descent


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)

ξ(n) = 0.5Σkek2(n)

Error correction learning rule (or delta rule)

Δwkj(n) = ηek(n)xj(n)η = 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.


Memory-based Learning (1)

All (or most) of the past experiences are stored explicitly in memory of correctly classified input-output examples: {(xi, di)}i = 1, N

Given a test vector xtest , the algorithm retrieves the classification of the xi ‘closest’ to xtest in the training examples (and memory)

Ingredients Definition of what is ‘closest’ or ‘local neighborhood’ Learning rule applied to the training examples in the local

neigborhood


Memory-based Learning (2)

Nearest neigbor rule K-nearest neighbor rule Radial-basis function rule (network)


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.

Hebb’s 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 A’s efficiency as one of the cells firing B is increased.


Hebbian Learning (2)

Hebbian learning (model of Hebbian synapse)1. If two neurons on either side of a synapse are activated

simultaneously, then the strength of that synapse is selectively increased

2. 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


Mathematical Models of Hebbian Learning (1)

General form of Hebbian rule

Δwkj(n) = F[yk(n), xj(n)]

F is a function of pre-synaptic and post-synaptic activities.

A specific Hebbian rule (activity product rule)

Δwkj(n) = ηyk(n)xj(n)

η = learning rate Is there a problem with the above rule?

No bounds on increase (or decrease) of wkj



Generalized activity product rule

Δwkj(n) = ηyk(n)xj(n) – αyk(n)wkj(n)

Or

Δwkj(n) = αyk(n)[cxk(n) - wkj(n)]

where c = η/ α and α = positive constant



Activity covariance rule

Δwkj(n) = η cov[yk(n), xj(n)]

= η E[(yk(n) – y’)(xj(n) – x’)]

where η = proportionality constant and x’ and y’ are respective means

After simplification

Δwkj(n) = η {E[yk(n)xj(n)] – x’y’}


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)



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



Standard competitive learning rule

Δwji = η(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

Σi wji = 1 for all j


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 Σk Σj wkjsisk

where sj = state of neuron j [0, 1] (i.e. binary state)

Learning process At each step, choose a neuron at random (say kj) and flip its

state sk (to - sk ) by the following probability

w(sk -> -sk) = (1 + exp(-ΔEk/T)]-1 The state evolves until thermal equilibrium is achieved


Credit-Assignment Problem

How to assign credit and blame for a neural network’s 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 component’s behavior should be

modified and by how much


Supervised Learning (1)


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


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


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.


Supervised Vs Reinforcement Learning

Supervised learning Reinforcement learning

Teacher – detailed information available

Critic – only reward information available

Instructive feedback system Evaluative feedback system

Instantaneous and local information

Delayed and general information

Directed information – how system should adapt

Undirected info – system has to probe with trial and error

Faster training Slower training


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


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


Supervised Vs Unsupervised Learning

Supervised learning Unsupervised learning

Teacher – detailed information available

No specific information available

Instructive feedback system Task-independent feedback system

Poor scalability Better scalability


Learning Tasks

Pattern association Pattern recognition Function approximation Control Filtering Beamforming


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



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)


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) + ε

where g(x) = actual model; ε = statistical estimate of error

Learning Process CS/CMPE 537 – Neural Networks. CS/CMPE 537 - Neural Networks (Sp 2004/2005) -...

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