- Artificial neural networks are inspired by biological neural networks and try to mimic their learning mechanisms. Learning can be viewed as an optimization process that modifies synaptic strengths between neurons.
- Neural networks can be used to approximate nonlinear functions by reformulating tasks as function approximation problems and finding the optimal synaptic weights through mathematical optimization techniques that minimize approximation error.
- A single hidden layer neural network is sufficient to learn nonlinear function approximation, allowing general optimization methods to derive weight change rules.
파이콘 한국 2020) 파이썬으로 구현하는 신경세포 기반의 인공 뇌 시뮬레이터Seonghyun Kim
* 파이콘 한국 2020의 발표자료입니다.
현대 인공 신경망의 뿌리가 되었던 뇌 과학!
이 발표에서는 인공 신경망에 대한 뇌 과학적 접근과,
뇌 세포의 발화를 모사하는 파이썬 기반의 뉴로모픽 신경망 모델에 대한 사례를 공유할 예정입니다.
뉴로모픽 신경망은 단순히 기존의 딥러닝에서 셀 구조만을 변경한 것이 아닙니다.
실제로 실험을 수행하기 어려운 생물학적 한계점을 뇌 시뮬레이션을 통해서 극복할 수 있으며,
나아가 뇌의 정보처리 메커니즘을 밝히고, 다양한 뇌 질환 치료제의 타겟을 연구하는데 아주 중요한 역할을 할 수 있습니다.
이번 발표를 통해, 기계학습을 연구하고 있는 많은 연구자 분들에게 새로운 아이디어에 대한 영감이 될 수 있기를 희망합니다.
اسلایدهای درس شبکه عصبی و یادگیری عمیق که در دانشگاه شیراز توسط استاد اقبال منصوری تدریس می شود.
Neural network and deep learning course slide taught by Professor Iqbal Mansouri at Shiraz University.
Boundness of a neural network weights using the notion of a limit of a sequenceIJDKP
feed forward neural network with backpropagation le
arning algorithm is considered as a black box
learning classifier since there is no certain inter
pretation or anticipation of the behavior of a neur
al
network weights. The weights of a neural network ar
e considered as the learning tool of the classifier
, and
the learning task is performed by the repetition mo
dification of those weights. This modification is
performed using the delta rule which is mainly used
in the gradient descent technique. In this article
a
proof is provided that helps to understand and expl
ain the behavior of the weights in a feed forward n
eural
network with backpropagation learning algorithm. Al
so, it illustrates why a feed forward neural networ
k is
not always guaranteed to converge in a global minim
um. Moreover, the proof shows that the weights in t
he
neural network are upper bounded (i.e. they do not
approach infinity). Data Mining, Delta
Lecture for Reinforcement Learning study group held on August 19th, 2017.
Reference book: http://incompleteideas.net/book/the-book.html
Video: https://youtu.be/xv5ZsOSf6ZQ
Initiated by Taiwan AI Group (https://www.facebook.com/groups/Taiwan.AI.Group/permalink/1796526840669749/)
파이콘 한국 2020) 파이썬으로 구현하는 신경세포 기반의 인공 뇌 시뮬레이터Seonghyun Kim
* 파이콘 한국 2020의 발표자료입니다.
현대 인공 신경망의 뿌리가 되었던 뇌 과학!
이 발표에서는 인공 신경망에 대한 뇌 과학적 접근과,
뇌 세포의 발화를 모사하는 파이썬 기반의 뉴로모픽 신경망 모델에 대한 사례를 공유할 예정입니다.
뉴로모픽 신경망은 단순히 기존의 딥러닝에서 셀 구조만을 변경한 것이 아닙니다.
실제로 실험을 수행하기 어려운 생물학적 한계점을 뇌 시뮬레이션을 통해서 극복할 수 있으며,
나아가 뇌의 정보처리 메커니즘을 밝히고, 다양한 뇌 질환 치료제의 타겟을 연구하는데 아주 중요한 역할을 할 수 있습니다.
이번 발표를 통해, 기계학습을 연구하고 있는 많은 연구자 분들에게 새로운 아이디어에 대한 영감이 될 수 있기를 희망합니다.
اسلایدهای درس شبکه عصبی و یادگیری عمیق که در دانشگاه شیراز توسط استاد اقبال منصوری تدریس می شود.
Neural network and deep learning course slide taught by Professor Iqbal Mansouri at Shiraz University.
Boundness of a neural network weights using the notion of a limit of a sequenceIJDKP
feed forward neural network with backpropagation le
arning algorithm is considered as a black box
learning classifier since there is no certain inter
pretation or anticipation of the behavior of a neur
al
network weights. The weights of a neural network ar
e considered as the learning tool of the classifier
, and
the learning task is performed by the repetition mo
dification of those weights. This modification is
performed using the delta rule which is mainly used
in the gradient descent technique. In this article
a
proof is provided that helps to understand and expl
ain the behavior of the weights in a feed forward n
eural
network with backpropagation learning algorithm. Al
so, it illustrates why a feed forward neural networ
k is
not always guaranteed to converge in a global minim
um. Moreover, the proof shows that the weights in t
he
neural network are upper bounded (i.e. they do not
approach infinity). Data Mining, Delta
Lecture for Reinforcement Learning study group held on August 19th, 2017.
Reference book: http://incompleteideas.net/book/the-book.html
Video: https://youtu.be/xv5ZsOSf6ZQ
Initiated by Taiwan AI Group (https://www.facebook.com/groups/Taiwan.AI.Group/permalink/1796526840669749/)
Introduction to Spiking Neural Networks: From a Computational Neuroscience pe...Jason Tsai
Abstract:
Being the third generation of neural network models, the study of spiking neural networks is an interdisciplinary field among brain science, theoretical neuroscience, and artificial neural networks research. Recently it is gaining attention and momentum, especially in neuromorphic device design for real-time machine learning. Some of you might have heard of it, but its underneath principles probably remain unknown for most of you. In this talk, I will briefly illustrate the basic building blocks of this emerging architecture and technology.
International Journal of Engineering Research and Development (IJERD)IJERD Editor
call for paper 2012, hard copy of journal, research paper publishing, where to publish research paper,
journal publishing, how to publish research paper, Call For research paper, international journal, publishing a paper, IJERD, journal of science and technology, how to get a research paper published, publishing a paper, publishing of journal, publishing of research paper, reserach and review articles, IJERD Journal, How to publish your research paper, publish research paper, open access engineering journal, Engineering journal, Mathemetics journal, Physics journal, Chemistry journal, Computer Engineering, Computer Science journal, how to submit your paper, peer reviw journal, indexed journal, reserach and review articles, engineering journal, www.ijerd.com, research journals,
yahoo journals, bing journals, International Journal of Engineering Research and Development, google journals, hard copy of journal
An ANN depends on an assortment of associated units or hubs called fake neurons, which freely model the neurons in an organic cerebrum. Every association, similar to the neurotransmitters in an organic cerebrum, can send a sign to different neurons. A counterfeit neuron that gets a sign at that point measures it and can flag neurons associated with it.
Introduction to Spiking Neural Networks: From a Computational Neuroscience pe...Jason Tsai
Abstract:
Being the third generation of neural network models, the study of spiking neural networks is an interdisciplinary field among brain science, theoretical neuroscience, and artificial neural networks research. Recently it is gaining attention and momentum, especially in neuromorphic device design for real-time machine learning. Some of you might have heard of it, but its underneath principles probably remain unknown for most of you. In this talk, I will briefly illustrate the basic building blocks of this emerging architecture and technology.
International Journal of Engineering Research and Development (IJERD)IJERD Editor
call for paper 2012, hard copy of journal, research paper publishing, where to publish research paper,
journal publishing, how to publish research paper, Call For research paper, international journal, publishing a paper, IJERD, journal of science and technology, how to get a research paper published, publishing a paper, publishing of journal, publishing of research paper, reserach and review articles, IJERD Journal, How to publish your research paper, publish research paper, open access engineering journal, Engineering journal, Mathemetics journal, Physics journal, Chemistry journal, Computer Engineering, Computer Science journal, how to submit your paper, peer reviw journal, indexed journal, reserach and review articles, engineering journal, www.ijerd.com, research journals,
yahoo journals, bing journals, International Journal of Engineering Research and Development, google journals, hard copy of journal
An ANN depends on an assortment of associated units or hubs called fake neurons, which freely model the neurons in an organic cerebrum. Every association, similar to the neurotransmitters in an organic cerebrum, can send a sign to different neurons. A counterfeit neuron that gets a sign at that point measures it and can flag neurons associated with it.
Notorietatea organizatiilor neguvernamentale in RomaniaAsociatia React
Notorietatea organizatiilor neguvernamentale in Romania - studiu cantitativ
Cercetare realizata de Centrul de Marketig si Prognoza Sociala la solicitarea Asociatiei React, pe un esantion reprezentativ la nivel national pentru populatia cu varsta de 15 ani si peste.
Let’s get straight to the point: SEO-unfriendly web development can cost you your business.
It goes without saying that this is bad news for marketing managers. As web builds become more and more complex, technical SEO is becoming increasingly important – and even small technical slip-ups can have catastrophic effects on your search engine performance and bottom line.
What is insight on the Indonesia Infrastructure Dilemma. Land acquisition? Law supremacy? Finance? Engineering? or is that any unspoken word that we never know
final Year Projects, Final Year Projects in Chennai, Software Projects, Embedded Projects, Microcontrollers Projects, DSP Projects, VLSI Projects, Matlab Projects, Java Projects, .NET Projects, IEEE Projects, IEEE 2009 Projects, IEEE 2009 Projects, Software, IEEE 2009 Projects, Embedded, Software IEEE 2009 Projects, Embedded IEEE 2009 Projects, Final Year Project Titles, Final Year Project Reports, Final Year Project Review, Robotics Projects, Mechanical Projects, Electrical Projects, Power Electronics Projects, Power System Projects, Model Projects, Java Projects, J2EE Projects, Engineering Projects, Student Projects, Engineering College Projects, MCA Projects, BE Projects, BTech Projects, ME Projects, MTech Projects, Wireless Networks Projects, Network Security Projects, Networking Projects, final year projects, ieee projects, student projects, college projects, ieee projects in chennai, java projects, software ieee projects, embedded ieee projects, "ieee2009projects", "final year projects", "ieee projects", "Engineering Projects", "Final Year Projects in Chennai", "Final year Projects at Chennai", Java Projects, ASP.NET Projects, VB.NET Projects, C# Projects, Visual C++ Projects, Matlab Projects, NS2 Projects, C Projects, Microcontroller Projects, ATMEL Projects, PIC Projects, ARM Projects, DSP Projects, VLSI Projects, FPGA Projects, CPLD Projects, Power Electronics Projects, Electrical Projects, Robotics Projects, Solor Projects, MEMS Projects, J2EE Projects, J2ME Projects, AJAX Projects, Structs Projects, EJB Projects, Real Time Projects, Live Projects, Student Projects, Engineering Projects, MCA Projects, MBA Projects, College Projects, BE Projects, BTech Projects, ME Projects, MTech Projects, M.Sc Projects, Final Year Java Projects, Final Year ASP.NET Projects, Final Year VB.NET Projects, Final Year C# Projects, Final Year Visual C++ Projects, Final Year Matlab Projects, Final Year NS2 Projects, Final Year C Projects, Final Year Microcontroller Projects, Final Year ATMEL Projects, Final Year PIC Projects, Final Year ARM Projects, Final Year DSP Projects, Final Year VLSI Projects, Final Year FPGA Projects, Final Year CPLD Projects, Final Year Power Electronics Projects, Final Year Electrical Projects, Final Year Robotics Projects, Final Year Solor Projects, Final Year MEMS Projects, Final Year J2EE Projects, Final Year J2ME Projects, Final Year AJAX Projects, Final Year Structs Projects, Final Year EJB Projects, Final Year Real Time Projects, Final Year Live Projects, Final Year Student Projects, Final Year Engineering Projects, Final Year MCA Projects, Final Year MBA Projects, Final Year College Projects, Final Year BE Projects, Final Year BTech Projects, Final Year ME Projects, Final Year MTech Projects, Final Year M.Sc Projects, IEEE Java Projects, ASP.NET Projects, VB.NET Projects, C# Projects, Visual C++ Projects, Matlab Projects, NS2 Projects, C Projects, Microcontroller Projects, ATMEL Projects, PIC Projects, ARM Projects, DSP Projects, VLSI Projects, FPGA Projects, CPLD Projects, Power Electronics Projects, Electrical Projects, Robotics Projects, Solor Projects, MEMS Projects, J2EE Projects, J2ME Projects, AJAX Projects, Structs Projects, EJB Projects, Real Time Projects, Live Projects, Student Projects, Engineering Projects, MCA Projects, MBA Projects, College Projects, BE Projects, BTech Projects, ME Projects, MTech Projects, M.Sc Projects, IEEE 2009 Java Projects, IEEE 2009 ASP.NET Projects, IEEE 2009 VB.NET Projects, IEEE 2009 C# Projects, IEEE 2009 Visual C++ Projects, IEEE 2009 Matlab Projects, IEEE 2009 NS2 Projects, IEEE 2009 C Projects, IEEE 2009 Microcontroller Projects, IEEE 2009 ATMEL Projects, IEEE 2009 PIC Projects, IEEE 2009 ARM Projects, IEEE 2009 DSP Projects, IEEE 2009 VLSI Projects, IEEE 2009 FPGA Projects, IEEE 2009 CPLD Projects, IEEE 2009 Power Electronics Projects, IEEE 2009 Electrical Projects, IEEE 2009 Robotics Projects, IEEE 2009 Solor Projects, IEEE 2009 MEMS Projects, IEEE 2009 J2EE P
Levelwise PageRank with Loop-Based Dead End Handling Strategy : SHORT REPORT ...Subhajit Sahu
Abstract — Levelwise PageRank is an alternative method of PageRank computation which decomposes the input graph into a directed acyclic block-graph of strongly connected components, and processes them in topological order, one level at a time. This enables calculation for ranks in a distributed fashion without per-iteration communication, unlike the standard method where all vertices are processed in each iteration. It however comes with a precondition of the absence of dead ends in the input graph. Here, the native non-distributed performance of Levelwise PageRank was compared against Monolithic PageRank on a CPU as well as a GPU. To ensure a fair comparison, Monolithic PageRank was also performed on a graph where vertices were split by components. Results indicate that Levelwise PageRank is about as fast as Monolithic PageRank on the CPU, but quite a bit slower on the GPU. Slowdown on the GPU is likely caused by a large submission of small workloads, and expected to be non-issue when the computation is performed on massive graphs.
Data Centers - Striving Within A Narrow Range - Research Report - MCG - May 2...pchutichetpong
M Capital Group (“MCG”) expects to see demand and the changing evolution of supply, facilitated through institutional investment rotation out of offices and into work from home (“WFH”), while the ever-expanding need for data storage as global internet usage expands, with experts predicting 5.3 billion users by 2023. These market factors will be underpinned by technological changes, such as progressing cloud services and edge sites, allowing the industry to see strong expected annual growth of 13% over the next 4 years.
Whilst competitive headwinds remain, represented through the recent second bankruptcy filing of Sungard, which blames “COVID-19 and other macroeconomic trends including delayed customer spending decisions, insourcing and reductions in IT spending, energy inflation and reduction in demand for certain services”, the industry has seen key adjustments, where MCG believes that engineering cost management and technological innovation will be paramount to success.
MCG reports that the more favorable market conditions expected over the next few years, helped by the winding down of pandemic restrictions and a hybrid working environment will be driving market momentum forward. The continuous injection of capital by alternative investment firms, as well as the growing infrastructural investment from cloud service providers and social media companies, whose revenues are expected to grow over 3.6x larger by value in 2026, will likely help propel center provision and innovation. These factors paint a promising picture for the industry players that offset rising input costs and adapt to new technologies.
According to M Capital Group: “Specifically, the long-term cost-saving opportunities available from the rise of remote managing will likely aid value growth for the industry. Through margin optimization and further availability of capital for reinvestment, strong players will maintain their competitive foothold, while weaker players exit the market to balance supply and demand.”
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Empowering the Data Analytics Ecosystem: A Laser Focus on Value
The data analytics ecosystem thrives when every component functions at its peak, unlocking the true potential of data. Here's a laser focus on key areas for an empowered ecosystem:
1. Democratize Access, Not Data:
Granular Access Controls: Provide users with self-service tools tailored to their specific needs, preventing data overload and misuse.
Data Catalogs: Implement robust data catalogs for easy discovery and understanding of available data sources.
2. Foster Collaboration with Clear Roles:
Data Mesh Architecture: Break down data silos by creating a distributed data ownership model with clear ownership and responsibilities.
Collaborative Workspaces: Utilize interactive platforms where data scientists, analysts, and domain experts can work seamlessly together.
3. Leverage Advanced Analytics Strategically:
AI-powered Automation: Automate repetitive tasks like data cleaning and feature engineering, freeing up data talent for higher-level analysis.
Right-Tool Selection: Strategically choose the most effective advanced analytics techniques (e.g., AI, ML) based on specific business problems.
4. Prioritize Data Quality with Automation:
Automated Data Validation: Implement automated data quality checks to identify and rectify errors at the source, minimizing downstream issues.
Data Lineage Tracking: Track the flow of data throughout the ecosystem, ensuring transparency and facilitating root cause analysis for errors.
5. Cultivate a Data-Driven Mindset:
Metrics-Driven Performance Management: Align KPIs and performance metrics with data-driven insights to ensure actionable decision making.
Data Storytelling Workshops: Equip stakeholders with the skills to translate complex data findings into compelling narratives that drive action.
Benefits of a Precise Ecosystem:
Sharpened Focus: Precise access and clear roles ensure everyone works with the most relevant data, maximizing efficiency.
Actionable Insights: Strategic analytics and automated quality checks lead to more reliable and actionable data insights.
Continuous Improvement: Data-driven performance management fosters a culture of learning and continuous improvement.
Sustainable Growth: Empowered by data, organizations can make informed decisions to drive sustainable growth and innovation.
By focusing on these precise actions, organizations can create an empowered data analytics ecosystem that delivers real value by driving data-driven decisions and maximizing the return on their data investment.
06-04-2024 - NYC Tech Week - Discussion on Vector Databases, Unstructured Data and AI
Round table discussion of vector databases, unstructured data, ai, big data, real-time, robots and Milvus.
A lively discussion with NJ Gen AI Meetup Lead, Prasad and Procure.FYI's Co-Found
Opendatabay - Open Data Marketplace.pptxOpendatabay
Opendatabay.com unlocks the power of data for everyone. Open Data Marketplace fosters a collaborative hub for data enthusiasts to explore, share, and contribute to a vast collection of datasets.
First ever open hub for data enthusiasts to collaborate and innovate. A platform to explore, share, and contribute to a vast collection of datasets. Through robust quality control and innovative technologies like blockchain verification, opendatabay ensures the authenticity and reliability of datasets, empowering users to make data-driven decisions with confidence. Leverage cutting-edge AI technologies to enhance the data exploration, analysis, and discovery experience.
From intelligent search and recommendations to automated data productisation and quotation, Opendatabay AI-driven features streamline the data workflow. Finding the data you need shouldn't be a complex. Opendatabay simplifies the data acquisition process with an intuitive interface and robust search tools. Effortlessly explore, discover, and access the data you need, allowing you to focus on extracting valuable insights. Opendatabay breaks new ground with a dedicated, AI-generated, synthetic datasets.
Leverage these privacy-preserving datasets for training and testing AI models without compromising sensitive information. Opendatabay prioritizes transparency by providing detailed metadata, provenance information, and usage guidelines for each dataset, ensuring users have a comprehensive understanding of the data they're working with. By leveraging a powerful combination of distributed ledger technology and rigorous third-party audits Opendatabay ensures the authenticity and reliability of every dataset. Security is at the core of Opendatabay. Marketplace implements stringent security measures, including encryption, access controls, and regular vulnerability assessments, to safeguard your data and protect your privacy.
3. Biological inspiration
Animals are able to react adaptively to changes in their
external and internal environment, and they use their nervous
system to perform these behaviours.
An appropriate model/simulation of the nervous system
should be able to produce similar responses and behaviours in
artificial systems.
The nervous system is build by relatively simple units, the
neurons, so copying their behavior and functionality should be
the solution.
6. Biological inspiration
The spikes travelling along the axon of the pre-synaptic
neuron trigger the release of neurotransmitter substances
at the synapse.
The neurotransmitters cause excitation or inhibition in the
dendrite of the post-synaptic neuron.
The integration of the excitatory and inhibitory signals
may produce spikes in the post-synaptic neuron.
The contribution of the signals depends on the strength of
the synaptic connection.
7. Artificial neurons
Neurons work by processing information. They receive and
provide information in form of spikes.
The McCullogh-Pitts model
Inputs
Output
w2
w1
w3
wn
wn-1
.
.
.
x1
x2
x3
…
xn-1
xn
y
)(;
1
zHyxwz
n
i
ii == ∑=
8. Artificial neurons
The McCullogh-Pitts model:
• spikes are interpreted as spike rates;
• synaptic strength are translated as synaptic weights;
• excitation means positive product between the
incoming spike rate and the corresponding synaptic
weight;
• inhibition means negative product between the
incoming spike rate and the corresponding synaptic
weight;
9. Artificial neurons
Nonlinear generalization of the McCullogh-Pitts
neuron:
),( wxfy =
y is the neuron’s output, x is the vector of inputs, and w
is the vector of synaptic weights.
Examples:
2
2
2
||||
1
1
a
wx
axw
ey
e
y T
−
−
−−
=
+
= sigmoidal neuron
Gaussian neuron
10. Artificial neural networksInputs
Output
An artificial neural network is composed of many artificial
neurons that are linked together according to a specific
network architecture. The objective of the neural network
is to transform the inputs into meaningful outputs.
11. Artificial neural networks
Tasks to be solved by artificial neural networks:
• controlling the movements of a robot based on self-
perception and other information (e.g., visual
information);
• deciding the category of potential food items (e.g.,
edible or non-edible) in an artificial world;
• recognizing a visual object (e.g., a familiar face);
• predicting where a moving object goes, when a robot
wants to catch it.
12. Learning in biological systems
Learning = learning by adaptation
The young animal learns that the green fruits are sour,
while the yellowish/reddish ones are sweet. The learning
happens by adapting the fruit picking behavior.
At the neural level the learning happens by changing of the
synaptic strengths, eliminating some synapses, and
building new ones.
13. Learning as optimisation
The objective of adapting the responses on the basis of the
information received from the environment is to achieve a
better state. E.g., the animal likes to eat many energy rich,
juicy fruits that make its stomach full, and makes it feel
happy.
In other words, the objective of learning in biological
organisms is to optimise the amount of available resources,
happiness, or in general to achieve a closer to optimal state.
14. Learning in biological neural
networks
The learning rules of Hebb:
• synchronous activation increases the synaptic strength;
• asynchronous activation decreases the synaptic
strength.
These rules fit with energy minimization principles.
Maintaining synaptic strength needs energy, it should be
maintained at those places where it is needed, and it
shouldn’t be maintained at places where it’s not needed.
15. Learning principle for
artificial neural networks
ENERGY MINIMIZATION
We need an appropriate definition of energy for artificial
neural networks, and having that we can use
mathematical optimisation techniques to find how to
change the weights of the synaptic connections between
neurons.
ENERGY = measure of task performance error
18. MLP neural networks
MLP = multi-layer perceptron
Perceptron:
MLP neural network:
xwy T
out = x yout
x yout
23
2
1
23
2
2
2
1
2
2
1
3
1
2
1
1
1
1
),(
2,1,
1
1
),,(
3,2,1,
1
1
212
11
ywywy
yyy
k
e
y
yyyy
k
e
y
T
k
kkout
T
aywk
T
axwk
k
kT
k
kT
==
=
=
+
=
=
=
+
=
∑
=
−−
−−
19. RBF neural networks
RBF = radial basis function
2
2
2
||||
)(
||)(||)(
a
wx
exf
cxrxr
−
−
=
−=
Example: Gaussian RBF
x
yout
∑
=
−
−
⋅=
4
1
)(2
||||
2 2
2,1
k
a
wx
kout
k
k
ewy
20. Neural network tasks
• control
• classification
• prediction
• approximation
These can be reformulated
in general as
FUNCTION
APPROXIMATION
tasks.
Approximation: given a set of values of a function g(x)
build a neural network that approximates the g(x) values
for any input x.
21. Neural network approximation
Task specification:
Data: set of value pairs: (xt
, yt), yt=g(xt
) + zt; zt is random
measurement noise.
Objective: find a neural network that represents the input /
output transformation (a function) F(x,W) such that
F(x,W) approximates g(x) for every x
22. Learning to approximate
Error measure:
∑
=
−=
N
t
tt yWxF
N
E
1
2
));((
1
Rule for changing the synaptic weights:
j
i
j
i
newj
i
j
i
j
i
www
W
w
E
cw
∆+=
∂
∂
⋅−=∆
,
)(
c is the learning parameter (usually a constant)
23. Learning with a perceptron
Perceptron: xwy T
out =
Data: ),(),...,,(),,( 2
2
1
1
N
N
yxyxyx
Error:
22
))(())(()( t
tT
tout yxtwytytE −=−=
Learning:
t
j
m
j
j
T
t
it
tT
ii
i
t
tT
i
i
ii
xtwxtw
xyxtwctwtw
w
yxtw
ctw
w
tE
ctwtw
⋅=
⋅−⋅−=+
∂
−∂
⋅−=
∂
∂
⋅−=+
∑
=1
2
)()(
))(()()1(
))((
)(
)(
)()1(
A perceptron is able to learn a linear function.
24. Learning with RBF neural
networks
RBF neural network:
Data: ),(),...,,(),,( 2
2
1
1
N
N
yxyxyx
Error: 2
1
)(2
||||
22
))(())(()(
2
2,1
t
M
k
a
wx
ktout yetwytytE k
kt
−⋅=−= ∑
=
−
−
Learning:
2
2,1
)(2
||||
2
2
22
)))(,((2
)(
)(
)()1(
i
it
a
wx
t
t
i
i
ii
eytWxF
w
tE
w
tE
ctwtw
−
−
⋅−⋅=
∂
∂
∂
∂
⋅−=+
Only the synaptic weights of the output neuron are modified.
An RBF neural network learns a nonlinear function.
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25. Learning with MLP neural
networks
MLP neural network:
with p layers
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It is very complicated to calculate the weight changes.
x
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1 2 … p-1 p
26. Learning with backpropagation
Solution of the complicated learning:
• calculate first the changes for the synaptic weights
of the output neuron;
• calculate the changes backward starting from layer
p-1, and propagate backward the local error terms.
The method is still relatively complicated but it
is much simpler than the original optimisation
problem.
27. Learning with general optimisation
In general it is enough to have a single layer of nonlinear
neurons in a neural network in order to learn to
approximate a nonlinear function.
In such case general optimisation may be applied without
too much difficulty.
Example: an MLP neural network with a single hidden layer:
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28. Learning with general optimisation
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Synaptic weight change rules for the neurons of the
hidden layer:
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−−
−−
−−
−−
−−
−−
29. New methods for learning with
neural networks
Bayesian learning:
the distribution of the neural network
parameters is learnt
Support vector learning:
the minimal representative subset of the
available data is used to calculate the synaptic
weights of the neurons
30. Summary
• Artificial neural networks are inspired by the learning
processes that take place in biological systems.
• Artificial neurons and neural networks try to imitate the
working mechanisms of their biological counterparts.
• Learning can be perceived as an optimisation process.
• Biological neural learning happens by the modification
of the synaptic strength. Artificial neural networks learn
in the same way.
• The synapse strength modification rules for artificial
neural networks can be derived by applying
mathematical optimisation methods.
31. Summary
• Learning tasks of artificial neural networks can be
reformulated as function approximation tasks.
• Neural networks can be considered as nonlinear function
approximating tools (i.e., linear combinations of nonlinear
basis functions), where the parameters of the networks
should be found by applying optimisation methods.
• The optimisation is done with respect to the approximation
error measure.
• In general it is enough to have a single hidden layer neural
network (MLP, RBF or other) to learn the approximation of
a nonlinear function. In such cases general optimisation can
be applied to find the change rules for the synaptic weights.