Learning Process CS/CMPE 537 – Neural Networks

CS/CMPE Neural Networks (Sp 2004/2005) - Asim LUMS2 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

CS/CMPE Neural Networks (Sp 2004/2005) - Asim LUMS3 Learning Process Adapting the synaptic weight w kj (n + 1) = w kj (n) + Δw kj (n)

CS/CMPE Neural Networks (Sp 2004/2005) - Asim LUMS4 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)

CS/CMPE Neural Networks (Sp 2004/2005) - Asim LUMS5 Error-Correction Learning (1) e k (n) = d k (n) – y k (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[0.5Σ k e k 2 (n)] E = expectation operator  Minimizing J with respect to the network parameters is the method of gradient descent

CS/CMPE Neural Networks (Sp 2004/2005) - Asim LUMS6 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) = 0.5Σ k e k 2 (n) Error correction learning rule (or delta rule) Δw kj (n) = ηe k (n)x j (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.

CS/CMPE Neural Networks (Sp 2004/2005) - Asim LUMS7 Memory-based Learning (1) All (or most) of the past experiences are stored explicitly in memory of correctly classified input- output examples: {(x i, d i )}i = 1, N Given a test vector x test, the algorithm retrieves the classification of the x i ‘closest’ to x test 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

CS/CMPE Neural Networks (Sp 2004/2005) - Asim LUMS8 Memory-based Learning (2) Nearest neigbor rule K-nearest neighbor rule Radial-basis function rule (network)

CS/CMPE Neural Networks (Sp 2004/2005) - Asim LUMS9 Hebbian Learning (1) Hebb, a neuropsychologist, proposed a model of neural activation in 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.

CS/CMPE Neural Networks (Sp 2004/2005) - Asim LUMS10 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

CS/CMPE Neural Networks (Sp 2004/2005) - Asim LUMS11 Mathematical Models of Hebbian Learning (1) General form of Hebbian rule Δw kj (n) = F[y k (n), x j (n)] F is a function of pre-synaptic and post-synaptic activities. A specific Hebbian rule (activity product rule) Δw kj (n) = ηy k (n)x j (n) η = learning rate Is there a problem with the above rule?  No bounds on increase (or decrease) of w kj

CS/CMPE Neural Networks (Sp 2004/2005) - Asim LUMS12 Mathematical Models of Hebbian Learning (2) Generalized activity product rule Δw kj (n) = ηy k (n)x j (n) – αy k (n)w kj (n) Or Δw kj (n) = αy k (n)[cx k (n) - w kj (n)] where c = η/ α and α = positive constant

CS/CMPE Neural Networks (Sp 2004/2005) - Asim LUMS13 Mathematical Models of Hebbian Learning (3)

CS/CMPE Neural Networks (Sp 2004/2005) - Asim LUMS14 Mathematical Models of Hebbian Learning (4) Activity covariance rule Δw kj (n) = η cov[y k (n), x j (n)] = η E[(y k (n) – y’)(x j (n) – x’)] where η = proportionality constant and x’ and y’ are respective means After simplification Δw kj (n) = η {E[y k (n)x j (n)] – x’y’}

CS/CMPE Neural Networks (Sp 2004/2005) - Asim LUMS15 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)

CS/CMPE Neural Networks (Sp 2004/2005) - Asim LUMS16 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

CS/CMPE Neural Networks (Sp 2004/2005) - Asim LUMS17 Competitive Learning (3)

CS/CMPE Neural Networks (Sp 2004/2005) - Asim LUMS18 Competitive Learning (4) Standard competitive learning rule Δw ji = η(x i – w ji ) 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 Σ i w ji = 1 for all j

CS/CMPE Neural Networks (Sp 2004/2005) - Asim LUMS19 Competitive Learning (5)

CS/CMPE Neural Networks (Sp 2004/2005) - Asim LUMS20 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 Σ k Σ j w kj s i s k where s j = 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 s k (to - s k ) by the following probability w(s k -> -s k ) = (1 + exp(-ΔE k /T)] -1  The state evolves until thermal equilibrium is achieved

CS/CMPE Neural Networks (Sp 2004/2005) - Asim LUMS21 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

CS/CMPE Neural Networks (Sp 2004/2005) - Asim LUMS22 Supervised Learning (1)

CS/CMPE Neural Networks (Sp 2004/2005) - Asim LUMS23 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

CS/CMPE Neural Networks (Sp 2004/2005) - Asim LUMS24 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

CS/CMPE Neural Networks (Sp 2004/2005) - Asim LUMS25 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.

CS/CMPE Neural Networks (Sp 2004/2005) - Asim LUMS26 Supervised Vs Reinforcement Learning Supervised learningReinforcement learning Teacher – detailed information available Critic – only reward information available Instructive feedback systemEvaluative 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 trainingSlower training

CS/CMPE Neural Networks (Sp 2004/2005) - Asim LUMS27 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

CS/CMPE Neural Networks (Sp 2004/2005) - Asim LUMS28 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

CS/CMPE Neural Networks (Sp 2004/2005) - Asim LUMS29 Supervised Vs Unsupervised Learning Supervised learningUnsupervised learning Teacher – detailed information available No specific information available Instructive feedback systemTask-independent feedback system Poor scalabilityBetter scalability

CS/CMPE Neural Networks (Sp 2004/2005) - Asim LUMS30 Learning Tasks Pattern association Pattern recognition Function approximation Control Filtering Beamforming

CS/CMPE Neural Networks (Sp 2004/2005) - Asim LUMS31 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

CS/CMPE Neural Networks (Sp 2004/2005) - Asim LUMS32 Adaptation and Learning (2)

CS/CMPE Neural Networks (Sp 2004/2005) - Asim LUMS33 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)

CS/CMPE Neural Networks (Sp 2004/2005) - Asim LUMS34 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