An artificial neural network (ANN) is a machine learning approach that models the human brain. It consists of artificial neurons that are connected in a network. Each neuron receives inputs and applies an activation function to produce an output. ANNs can learn from examples through a process of adjusting the weights between neurons. Backpropagation is a common learning algorithm that propagates errors backward from the output to adjust weights and minimize errors. While single-layer perceptrons can only model linearly separable problems, multi-layer feedforward neural networks can handle non-linear problems using hidden layers that allow the network to learn complex patterns from data.
Artificial Intelligence: Artificial Neural NetworksThe Integral Worm
This presentation covers artificial neural networks for artificial intelligence. Topics covered are as follows: artificial neural networks, basic representation, hidden units, exclusive OR problem, backpropagation, advantages of artificial neural networks, properties of artificial neural networks, and disadvantages of artificial neural networks.
Artificial Intelligence: Artificial Neural NetworksThe Integral Worm
This presentation covers artificial neural networks for artificial intelligence. Topics covered are as follows: artificial neural networks, basic representation, hidden units, exclusive OR problem, backpropagation, advantages of artificial neural networks, properties of artificial neural networks, and disadvantages of artificial neural networks.
In machine learning, a convolutional neural network is a class of deep, feed-forward artificial neural networks that have successfully been applied fpr analyzing visual imagery.
This presentation discusses the following ANN concepts:
Introduction
Characteristics
Learning methods
Taxonomy
Evolution of neural networks
Basic models
Important technologies
Applications
Basic definitions, terminologies, and Working of ANN has been explained. This ppt also shows how ANN can be performed in matlab. This material contains the explanation of Feed forward back propagation algorithm in detail.
An artificial neuron network (ANN) is a computational model based on the structure and functions of biological neural networks. It works on real-valued, discrete-valued and vector valued.
In machine learning, a convolutional neural network is a class of deep, feed-forward artificial neural networks that have successfully been applied fpr analyzing visual imagery.
This presentation discusses the following ANN concepts:
Introduction
Characteristics
Learning methods
Taxonomy
Evolution of neural networks
Basic models
Important technologies
Applications
Basic definitions, terminologies, and Working of ANN has been explained. This ppt also shows how ANN can be performed in matlab. This material contains the explanation of Feed forward back propagation algorithm in detail.
An artificial neuron network (ANN) is a computational model based on the structure and functions of biological neural networks. It works on real-valued, discrete-valued and vector valued.
An artificial neuron network (neural network) is a computational model that mimics the way nerve cells work in the human brain. Artificial neural networks (ANNs) use learning algorithms that can independently make adjustments - or learn, in a sense - as they receive new input
Builder.ai Founder Sachin Dev Duggal's Strategic Approach to Create an Innova...Ramesh Iyer
In today's fast-changing business world, Companies that adapt and embrace new ideas often need help to keep up with the competition. However, fostering a culture of innovation takes much work. It takes vision, leadership and willingness to take risks in the right proportion. Sachin Dev Duggal, co-founder of Builder.ai, has perfected the art of this balance, creating a company culture where creativity and growth are nurtured at each stage.
Neuro-symbolic is not enough, we need neuro-*semantic*Frank van Harmelen
Neuro-symbolic (NeSy) AI is on the rise. However, simply machine learning on just any symbolic structure is not sufficient to really harvest the gains of NeSy. These will only be gained when the symbolic structures have an actual semantics. I give an operational definition of semantics as “predictable inference”.
All of this illustrated with link prediction over knowledge graphs, but the argument is general.
Kubernetes & AI - Beauty and the Beast !?! @KCD Istanbul 2024Tobias Schneck
As AI technology is pushing into IT I was wondering myself, as an “infrastructure container kubernetes guy”, how get this fancy AI technology get managed from an infrastructure operational view? Is it possible to apply our lovely cloud native principals as well? What benefit’s both technologies could bring to each other?
Let me take this questions and provide you a short journey through existing deployment models and use cases for AI software. On practical examples, we discuss what cloud/on-premise strategy we may need for applying it to our own infrastructure to get it to work from an enterprise perspective. I want to give an overview about infrastructure requirements and technologies, what could be beneficial or limiting your AI use cases in an enterprise environment. An interactive Demo will give you some insides, what approaches I got already working for real.
Elevating Tactical DDD Patterns Through Object CalisthenicsDorra BARTAGUIZ
After immersing yourself in the blue book and its red counterpart, attending DDD-focused conferences, and applying tactical patterns, you're left with a crucial question: How do I ensure my design is effective? Tactical patterns within Domain-Driven Design (DDD) serve as guiding principles for creating clear and manageable domain models. However, achieving success with these patterns requires additional guidance. Interestingly, we've observed that a set of constraints initially designed for training purposes remarkably aligns with effective pattern implementation, offering a more ‘mechanical’ approach. Let's explore together how Object Calisthenics can elevate the design of your tactical DDD patterns, offering concrete help for those venturing into DDD for the first time!
UiPath Test Automation using UiPath Test Suite series, part 3DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 3. In this session, we will cover desktop automation along with UI automation.
Topics covered:
UI automation Introduction,
UI automation Sample
Desktop automation flow
Pradeep Chinnala, Senior Consultant Automation Developer @WonderBotz and UiPath MVP
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
Securing your Kubernetes cluster_ a step-by-step guide to success !KatiaHIMEUR1
Today, after several years of existence, an extremely active community and an ultra-dynamic ecosystem, Kubernetes has established itself as the de facto standard in container orchestration. Thanks to a wide range of managed services, it has never been so easy to set up a ready-to-use Kubernetes cluster.
However, this ease of use means that the subject of security in Kubernetes is often left for later, or even neglected. This exposes companies to significant risks.
In this talk, I'll show you step-by-step how to secure your Kubernetes cluster for greater peace of mind and reliability.
DevOps and Testing slides at DASA ConnectKari Kakkonen
My and Rik Marselis slides at 30.5.2024 DASA Connect conference. We discuss about what is testing, then what is agile testing and finally what is Testing in DevOps. Finally we had lovely workshop with the participants trying to find out different ways to think about quality and testing in different parts of the DevOps infinity loop.
Transcript: Selling digital books in 2024: Insights from industry leaders - T...BookNet Canada
The publishing industry has been selling digital audiobooks and ebooks for over a decade and has found its groove. What’s changed? What has stayed the same? Where do we go from here? Join a group of leading sales peers from across the industry for a conversation about the lessons learned since the popularization of digital books, best practices, digital book supply chain management, and more.
Link to video recording: https://bnctechforum.ca/sessions/selling-digital-books-in-2024-insights-from-industry-leaders/
Presented by BookNet Canada on May 28, 2024, with support from the Department of Canadian Heritage.
GraphRAG is All You need? LLM & Knowledge GraphGuy Korland
Guy Korland, CEO and Co-founder of FalkorDB, will review two articles on the integration of language models with knowledge graphs.
1. Unifying Large Language Models and Knowledge Graphs: A Roadmap.
https://arxiv.org/abs/2306.08302
2. Microsoft Research's GraphRAG paper and a review paper on various uses of knowledge graphs:
https://www.microsoft.com/en-us/research/blog/graphrag-unlocking-llm-discovery-on-narrative-private-data/
UiPath Test Automation using UiPath Test Suite series, part 4DianaGray10
Welcome to UiPath Test Automation using UiPath Test Suite series part 4. In this session, we will cover Test Manager overview along with SAP heatmap.
The UiPath Test Manager overview with SAP heatmap webinar offers a concise yet comprehensive exploration of the role of a Test Manager within SAP environments, coupled with the utilization of heatmaps for effective testing strategies.
Participants will gain insights into the responsibilities, challenges, and best practices associated with test management in SAP projects. Additionally, the webinar delves into the significance of heatmaps as a visual aid for identifying testing priorities, areas of risk, and resource allocation within SAP landscapes. Through this session, attendees can expect to enhance their understanding of test management principles while learning practical approaches to optimize testing processes in SAP environments using heatmap visualization techniques
What will you get from this session?
1. Insights into SAP testing best practices
2. Heatmap utilization for testing
3. Optimization of testing processes
4. Demo
Topics covered:
Execution from the test manager
Orchestrator execution result
Defect reporting
SAP heatmap example with demo
Speaker:
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
2. A new sort of computer
What are (everyday) computer systems good at... and
not so good at?
Good at Not so good at
Rule-based systems:
doing what the programmer
wants them to do
Dealing with noisy data
Dealing with unknown
environment data
Massive parallelism
Fault tolerance
Adapting to circumstances
3. Neural Networks
● Artificial neural network (ANN) is a machine learning
approach that models human brain and consists of a
number of artificial neurons.
● Neuron in ANNs tend to have fewer connections than
biological neurons.
● Each neuron in ANN receives a number of inputs.
● An activation function is applied to these inputs which
results in activation level of neuron (output value of the
neuron).
● Knowledge about the learning task is given in the form of
examples called training examples.
4. Where can neural network systems help
when we can't formulate an algorithmic solution.
when we can get lots of examples of the behavior we
require.
‘learning from experience’
when we need to pick out the structure from existing
data.
5. Contd..
● An Artificial Neural Network is specified by:
− neuron model: the information processing unit of the NN,
− an architecture: a set of neurons and links connecting
neurons. Each link has a weight,
− a learning algorithm: used for training the NN by modifying
the weights in order to model a particular learning task
correctly on the training examples.
● The aim is to obtain a NN that is trained and
generalizes well.
● It should behaves correctly on new instances of the
learning task.
6. Inspiration from Neurobiology
A neuron: many-inputs /
one-output unit
output can be excited or not
excited
incoming signals from other
neurons determine if the
neuron shall excite ("fire")
Output subject to
attenuation in the synapses,
which are junction parts of
the neuron
7. Synapse concept
The synapse resistance to the incoming signal can be
changed during a "learning" process [1949]
Hebb’s Rule:
If an input of a neuron is repeatedly and persistently
causing the neuron to fire, a metabolic change
happens in the synapse of that particular input to
reduce its resistance
8. Mathematical representation
The neuron calculates a weighted sum of inputs and
compares it to a threshold. If the sum is higher than the
threshold, the output is set to 1, otherwise to -1.
Non-linearity
9. A simple perceptron
It’s a single-unit network
Change the weight by an
amount proportional to the
difference between the desired
output and the actual output.
Δ Wi = η * (D-Y).Ii
Perceptron Learning Rule
Learning rate
Desired output
Input
Actual output
10. Example: A simple single unit adaptive
network
The network has 2
inputs, and one output.
All are binary. The
output is
1 if W0I0 + W1I1 + Wb > 0
0 if W0I0 + W1I1 + Wb ≤ 0
We want it to learn
simple OR: output a 1 if
either I0 or I1 is 1.
Demo
11. Neuron
● The neuron is the basic information processing unit of a
NN. It consists of:
1 A set of links, describing the neuron inputs, with weights W1,
W2, …, Wm
2 An adder function (linear combiner) for computing the
weighted sum of the inputs:
(real numbers)
3 Activation function for limiting the amplitude of the neuron
output. Here ‘b’ denotes bias.
m
1
jjxwu
j
)(uy b
13. Bias of a Neuron
● The bias b has the effect of applying a transformation to
the weighted sum u
v = u + b
● The bias is an external parameter of the neuron. It can
be modeled by adding an extra input.
● v is called induced field of the neuron
bw
xwv j
m
j
j
0
0
14. Neuron Models
● The choice of activation function determines the
neuron model.
Examples:
● step function:
● ramp function:
● sigmoid function with z,x,y parameters
● Gaussian function:
2
2
1
exp
2
1
)(
v
v
)exp(1
1
)(
yxv
zv
otherwise))/())(((
if
if
)(
cdabcva
dvb
cva
v
cvb
cva
v
if
if
)(
18. • The Gaussian function is the probability function of the
normal distribution. Sometimes also called the frequency
curve.
19. Network Architectures
● Three different classes of network architectures
− single-layer feed-forward
− multi-layer feed-forward
− recurrent
● The architecture of a neural network is linked with
the learning algorithm used to train
21. Perceptron: Neuron Model
(Special form of single layer feed forward)
− The perceptron was first proposed by Rosenblatt (1958) is a
simple neuron that is used to classify its input into one of two
categories.
− A perceptron uses a step function that returns +1 if weighted
sum of its input 0 and -1 otherwise
x1
x2
xn
w2
w1
wn
b (bias)
v y
(v)
0if1
0if1
)(
v
v
v
22. Perceptron for Classification
● The perceptron is used for binary classification.
● First train a perceptron for a classification task.
− Find suitable weights in such a way that the training examples are
correctly classified.
− Geometrically try to find a hyper-plane that separates the examples of
the two classes.
● The perceptron can only model linearly separable classes.
● When the two classes are not linearly separable, it may be
desirable to obtain a linear separator that minimizes the mean
squared error.
● Given training examples of classes C1, C2 train the perceptron
in such a way that :
− If the output of the perceptron is +1 then the input is assigned to class C1
− If the output is -1 then the input is assigned to C2
24. Learning Process for Perceptron
● Initially assign random weights to inputs between -0.5 and
+0.5
● Training data is presented to perceptron and its output is
observed.
● If output is incorrect, the weights are adjusted accordingly
using following formula.
wi wi + (a* xi *e), where ‘e’ is error produced
and ‘a’ (-1 a 1) is learning rate
− ‘a’ is defined as 0 if output is correct, it is +ve, if output is too low
and –ve, if output is too high.
− Once the modification to weights has taken place, the next piece of
training data is used in the same way.
− Once all the training data have been applied, the process starts
again until all the weights are correct and all errors are zero.
− Each iteration of this process is known as an epoch.
25. Example: Perceptron to learn OR
function
● Initially consider w1 = -0.2 and w2 = 0.4
● Training data say, x1 = 0 and x2 = 0, output is 0.
● Compute y = Step(w1*x1 + w2*x2) = 0. Output is correct so
weights are not changed.
● For training data x1=0 and x2 = 1, output is 1
● Compute y = Step(w1*x1 + w2*x2) = 0.4 = 1. Output is correct
so weights are not changed.
● Next training data x1=1 and x2 = 0 and output is 1
● Compute y = Step(w1*x1 + w2*x2) = - 0.2 = 0. Output is
incorrect, hence weights are to be changed.
● Assume a = 0.2 and error e=1
wi = wi + (a * xi * e) gives w1 = 0 and w2 =0.4
● With these weights, test the remaining test data.
● Repeat the process till we get stable result.
26. Perceptron: Limitations
● The perceptron can only model linearly separable
functions,
− those functions which can be drawn in 2-dim graph and single
straight line separates values in two part.
● Boolean functions given below are linearly separable:
− AND
− OR
− COMPLEMENT
● It cannot model XOR function as it is non linearly
separable.
− When the two classes are not linearly separable, it may be
desirable to obtain a linear separator that minimizes the mean
squared error.
27. XOR – Non linearly separable function
● A typical example of non-linearly separable function is
the XOR that computes the logical exclusive or..
● This function takes two input arguments with values in
{0,1} and returns one output in {0,1},
● Here 0 and 1 are encoding of the truth values false and
true,
● The output is true if and only if the two inputs have
different truth values.
● XOR is non linearly separable function which can not be
modeled by perceptron.
● For such functions we have to use multi layer feed-
forward network.
28. These two classes (true and false) cannot be separated using a
line. Hence XOR is non linearly separable.
Input Output
X1 X2 X1 XOR X2
0 0 0
0 1 1
1 0 1
1 1 0
X1
1 true false
false true
0 1 X2
29. Multi layer feed-forward NN (FFNN)
● FFNN is a more general network architecture, where there
are hidden layers between input and output layers.
● Hidden nodes do not directly receive inputs nor send
outputs to the external environment.
● FFNNs overcome the limitation of single-layer NN.
● They can handle non-linearly separable learning tasks.
Input
layer
Output
layer
Hidden Layer
3-4-2 Network
30. FFNN for XOR
● The ANN for XOR has two hidden nodes that realizes this non-linear
separation and uses the sign (step) activation function.
● Arrows from input nodes to two hidden nodes indicate the directions
of the weight vectors (1,-1) and (-1,1).
● The output node is used to combine the outputs of the two hidden
nodes.
Input nodes Hidden layer Output layer Output
H1 –0.5
X1 1
–1 1
Y
–1 H2
X2 1 1
31. Inputs Output of Hidden Nodes Output
Node
X1 XOR X2
X1 X2 H1 H2
0 0 0 0 –0.5 0 0
0 1 –1 0 1 0.5 1 1
1 0 1 –1 0 0.5 1 1
1 1 0 0 –0.5 0 0
Since we are representing two states by 0 (false) and 1 (true), we
will map negative outputs (–1, –0.5) of hidden and output layers
to 0 and positive output (0.5) to 1.
32. Learning
From experience: examples / training data
Strength of connection between the neurons is stored
as a weight-value for the specific connection
Learning the solution to a problem = changing the
connection weights
33. Operation mode
Fix weights (unless in online learning)
Network simulation = input signals flow through
network to outputs
Output is often a binary decision
Inherently parallel
Simple operations and threshold:
fast decisions and real-time response
34. Artificial Neural Networks
Adaptive interaction between individual neurons
Power: collective behavior of interconnected neurons
The hidden layer learns to
recode (or to provide a
representation of) the
inputs: associative mapping
35. Evolving networks
Continuous process of:
Evaluate output
Adapt weights
Take new inputs
ANN evolving causes stable state of the weights, but
neurons continue working: network has ‘learned’
dealing with the problem
“Learning”
37. Unsupervised learning
No help from the outside
No training data, no information available on the
desired output
Learning by doing
Used to pick out structure in the input:
Clustering
Reduction of dimensionality compression
Example: Kohonen’s Learning Law
38. Competitive learning: example
Example: Kohonen network
Winner takes all
only update weights of winning neuron
Network topology
Training patterns
Activation rule
Neighbourhood
Learning
39. Reinforcement learning
Teacher: training data
The teacher scores the performance of the training
examples
Use performance score to shuffle weights ‘randomly’
Relatively slow learning due to ‘randomness’
40. FFNN NEURON MODEL
● The classical learning algorithm of FFNN is based on the
gradient descent method.
● For this reason the activation function used in FFNN are
continuous functions of the weights, differentiable
everywhere.
● The activation function for node i may be defined as a
simple form of the sigmoid function in the following
manner:
where A > 0, Vi = Wij * Yj , such that Wij is a weight of the
link from node i to node j and Yj is the output of node j.
)*(
1
1
)( ViA
e
Vi
41. Training Algorithm: Backpropagation
● The Backpropagation algorithm learns in the same way as
single perceptron.
● It searches for weight values that minimize the total error
of the network over the set of training examples (training
set).
● Backpropagation consists of the repeated application of
the following two passes:
− Forward pass: In this step, the network is activated on one
example and the error of (each neuron of) the output layer is
computed.
− Backward pass: in this step the network error is used for
updating the weights. The error is propagated backwards from the
output layer through the network layer by layer. This is done by
recursively computing the local gradient of each neuron.
42. Backpropagation
● Back-propagation training algorithm
● Backpropagation adjusts the weights of the NN in order
to minimize the network total mean squared error.
Network activation
Forward Step
Error propagation
Backward Step
43. Contd..
● Consider a network of three layers.
● Let us use i to represent nodes in input layer, j to
represent nodes in hidden layer and k represent nodes in
output layer.
● wij refers to weight of connection between a node in input
layer and node in hidden layer.
● The following equation is used to derive the output value
Yj of node j
where, Xj = xi . wij - j , 1 i n; n is the number of inputs to node
j, and j is threshold for node j
jX
e
1
1
Yj
44. Total Mean Squared Error
● The error of output neuron k after the activation of the
network on the n-th training example (x(n), d(n)) is:
ek(n) = dk(n) – yk(n)
● The network error is the sum of the squared errors of the
output neurons:
● The total mean squared error is the average of the network
errors of the training examples.
(n)eE(n) 2
k
N
1n
N
1
AV (n)EE
45. Weight Update Rule
● The Backprop weight update rule is based on the
gradient descent method:
− It takes a step in the direction yielding the maximum decrease of
the network error E.
− This direction is the opposite of the gradient of E.
● Iteration of the Backprop algorithm is usually
terminated when the sum of squares of errors of the
output values for all training data in an epoch is less
than some threshold such as 0.01
ijijij www
ij
ij
w
-w
E
46. Backprop learning algorithm
(incremental-mode)
n=1;
initialize weights randomly;
while (stopping criterion not satisfied or n <max_iterations)
for each example (x,d)
- run the network with input x and compute the output y
- update the weights in backward order starting from those
of the output layer:
with computed using the (generalized) Delta rule
end-for
n = n+1;
end-while;
jijiji www
jiw
47. Stopping criterions
● Total mean squared error change:
− Back-prop is considered to have converged when the absolute
rate of change in the average squared error per epoch is
sufficiently small (in the range [0.1, 0.01]).
● Generalization based criterion:
− After each epoch, the NN is tested for generalization.
− If the generalization performance is adequate then stop.
− If this stopping criterion is used then the part of the training set
used for testing the network generalization will not used for
updating the weights.
48. ● Data representation
● Network Topology
● Network Parameters
● Training
● Validation
NN DESIGN ISSUES
49. ● Data representation depends on the problem.
● In general ANNs work on continuous (real valued) attributes.
Therefore symbolic attributes are encoded into continuous ones.
● Attributes of different types may have different ranges of values
which affect the training process.
● Normalization may be used, like the following one which scales
each attribute to assume values between 0 and 1.
for each value xi of ith attribute, mini and maxi are the minimum and
maximum value of that attribute over the training set.
Data Representation
i
i
minmax
min
i
i
i
x
x
50. ● The number of layers and neurons depend on the specific
task.
● In practice this issue is solved by trial and error.
● Two types of adaptive algorithms can be used:
− start from a large network and successively remove some neurons
and links until network performance degrades.
− begin with a small network and introduce new neurons until
performance is satisfactory.
Network Topology
51. ● How are the weights initialized?
● How is the learning rate chosen?
● How many hidden layers and how many neurons?
● How many examples in the training set?
Network parameters
52. Initialization of weights
● In general, initial weights are randomly chosen, with
typical values between -1.0 and 1.0 or -0.5 and 0.5.
● If some inputs are much larger than others, random
initialization may bias the network to give much more
importance to larger inputs.
● In such a case, weights can be initialized as follows:
Ni
N
,...,1
|x|
1
2
1
ij i
w For weights from the input to the first layer
For weights from the first to the second layer
Ni
N
i
,...,1
)xw(
1
2
1
jk ij
w
53. ● The right value of depends on the application.
● Values between 0.1 and 0.9 have been used in many
applications.
● Other heuristics is that adapt during the training as
described in previous slides.
Choice of learning rate
54. Training
● Rule of thumb:
− the number of training examples should be at least five to ten
times the number of weights of the network.
● Other rule:
|W|= number of weights
a=expected accuracy on test seta)-(1
|W|
N
55. Recurrent Network
● FFNN is acyclic where data passes from input to the
output nodes and not vice versa.
− Once the FFNN is trained, its state is fixed and does not alter as
new data is presented to it. It does not have memory.
● Recurrent network can have connections that go
backward from output to input nodes and models dynamic
systems.
− In this way, a recurrent network’s internal state can be altered as
sets of input data are presented. It can be said to have memory.
− It is useful in solving problems where the solution depends not just
on the current inputs but on all previous inputs.
● Applications
− predict stock market price,
− weather forecast
56. ● Recurrent Network with hidden neuron: unit delay
operator d is used to model a dynamic system
d
d
d
Recurrent Network Architecture
input
hidden
output
57. Learning and Training
● During learning phase,
− a recurrent network feeds its inputs through the network,
including feeding data back from outputs to inputs
− process is repeated until the values of the outputs do not change.
● This state is called equilibrium or stability
● Recurrent networks can be trained by using back-
propagation algorithm.
● In this method, at each step, the activation of the output
is compared with the desired activation and errors are
propagated backward through the network.
● Once this training process is completed, the network
becomes capable of performing a sequence of actions.
58. Hopfield Network
● A Hopfield network is a kind of recurrent network as
output values are fed back to input in an undirected way.
− It consists of a set of N connected neurons with weights which are
symmetric and no unit is connected to itself.
− There are no special input and output neurons.
− The activation of a neuron is binary value decided by the sign of
the weighted sum of the connections to it.
− A threshold value for each neuron determines if it is a firing
neuron.
− A firing neuron is one that activates all neurons that are
connected to it with a positive weight.
− The input is simultaneously applied to all neurons, which then
output to each other.
− This process continues until a stable state is reached.
59. Activation Algorithm
Active unit represented by 1 and inactive by 0.
● Repeat
− Choose any unit randomly. The chosen unit may be active
or inactive.
− For the chosen unit, compute the sum of the weights on
the connection to the active neighbours only, if any.
▪ If sum > 0 (threshold is assumed to be 0), then the chosen
unit becomes active, otherwise it becomes inactive.
− If chosen unit has no active neighbours then ignore it,
and status remains same.
● Until the network reaches to a stable state
60. Current State Selected Unit from
current state
Corresponding New State
-2 3
-2
3 1
-2
-2 3
-2
3 1
-2
Sum = 3 – 2 = 1 > 0;
activated
-2 3
-2
3 1
-2
Here, the sum of weights of
active neighbours of a
selected unit is calculated. -2 3
-2
3 1
-2
-2 3
-2
3 1
-2
Sum = –2 < 0; deactivated
62. Weight Computation Method
● Weights are determined using training examples.
● Here
− W is weight matrix
− Xi is an input example represented by a vector of N values from
the set {–1, 1}.
− Here, N is the number of units in the network; 1 and -1
represent active and inactive units respectively.
− (Xi)T is the transpose of the input Xi ,
− M denotes the number of training input vectors,
− I is an N × N identity matrix.
W = Xi . (Xi)T
– M.I, for 1 i M
63. Example
● Let us now consider a Hopfield network with four units
and three training input vectors that are to be learned by
the network.
● Consider three input examples, namely, X1, X2, and X3
defined as follows:
1 1 –1
X1 = –1 X2 = 1 X3 = 1
–1 –1 1
1 1 –1
W = X1 . (X1)T
+ X2 . (X2)T
+ X3 . (X3)T
– 3.I
65. Contd..
● The networks generated using these weights and
input vectors are stable, except X2.
● X2 stabilizes to X1 (which is at hamming distance
1).
● Finally, with the obtained weights and stable states
(X1 and X3), we can stabilize any new (partial)
pattern to one of those
66. Radial-Basis Function Networks
● A function is said to be a radial basis function (RBF) if
its output depends on the distance of the input from a
given stored vector.
− The RBF neural network has an input layer, a hidden layer and an
output layer.
− In such RBF networks, the hidden layer uses neurons with RBFs as
activation functions.
− The outputs of all these hidden neurons are combined linearly at
the output node.
● These networks have a wide variety of applications such as
− function approximation,
− time series prediction,
− control and regression,
− pattern classification tasks for performing complex (non-linear).
67. RBF Architecture
● One hidden layer with RBF activation functions
● Output layer with linear activation function.
x2
xm
x1
y
wm1
w1
1
1m
11... m
||)(||...||)(|| 111111 mmm txwtxwy
txxxtx m centerfrom),...,(ofdistance|||| 1
68. Cont...
● Here we require weights, wi from the hidden layer to the
output layer only.
● The weights wi can be determined with the help of any of
the standard iterative methods described earlier for neural
networks.
● However, since the approximating function given below is
linear w. r. t. wi, it can be directly calculated using the
matrix methods of linear least squares without having to
explicitly determine wi iteratively.
● It should be noted that the approximate function f(X) is
differentiable with respect to wi.
)()(
1
N
i
iii tXwXfY
69. RBF NN FF NN
Non-linear layered feed-forward
networks.
Non-linear layered feed-forward
networks
Hidden layer of RBF is non-linear,
the output layer of RBF is linear.
Hidden and output layers of
FFNN are usually non-linear.
One single hidden layer May have more hidden layers.
Neuron model of the hidden neurons
is different from the one of the
output nodes.
Hidden and output neurons
share a common neuron model.
Activation function of each hidden
neuron in a RBF NN computes the
Euclidean distance between input
vector and the center of that unit.
Activation function of each
hidden neuron in a FFNN
computes the inner product of
input vector and the synaptic
weight vector of that neuron
Comparison
70. Generalization vs. specialization
Optimal number of hidden neurons
Too many hidden neurons : you get an over fit, training
set is memorized, thus making the network useless on
new data sets
Not enough hidden neurons:
network is unable to learn problem concept
~ conceptually: the network’s language isn’t able to
express the problem solution
71. Generalization vs. specialization
Overtraining:
Too much examples, the ANN memorizes the examples
instead of the general idea
Generalization vs. specialization trade-off:
# hidden nodes & training samples
MATLAB DEMO
72. Where are NN used?
Recognizing and matching complicated, vague, or
incomplete patterns
Data is unreliable
Problems with noisy data
Prediction
Classification
Data association
Data conceptualization
Filtering
Planning
73. Applications
Prediction: learning from past experience
pick the best stocks in the market
predict weather
identify people with cancer risk
Classification
Image processing
Predict bankruptcy for credit card companies
Risk assessment
74. Applications
Recognition
Pattern recognition: SNOOPE (bomb detector in U.S.
airports)
Character recognition
Handwriting: processing checks
Data association
Not only identify the characters that were scanned but
identify when the scanner is not working properly
75. Applications
Data Conceptualization
infer grouping relationships
e.g. extract from a database the names of those most likely to
buy a particular product.
Data Filtering
e.g. take the noise out of a telephone signal, signal smoothing
Planning
Unknown environments
Sensor data is noisy
Fairly new approach to planning
76. Strengths of a Neural Network
Power: Model complex functions, nonlinearity built
into the network
Ease of use:
Learn by example
Very little user domain-specific expertise needed
Intuitively appealing: based on model of biology,
will it lead to genuinely intelligent computers/robots?
Neural networks cannot do anything that cannot be
done using traditional computing techniques, BUT
they can do some things which would otherwise be
very difficult.
77. General Advantages
Advantages
Adapt to unknown situations
Robustness: fault tolerance due to network redundancy
Autonomous learning and generalization
Disadvantages
Not exact
Large complexity of the network structure
For motion planning?
78. Status of Neural Networks
Most of the reported applications are
still in research stage
No formal proofs, but they seem to
have useful applications that work