My first set of slides (The NN and DL class I am preparing for the fall)... I included the problem of Vanishing Gradient and the need to have ReLu (Mentioning btw the saturation problem inherited from Hebbian Learning)
BAAI Conference 2021: The Thousand Brains Theory - A Roadmap for Creating Mac...Numenta
Jeff Hawkins presented a talk on "The Thousand Brains Theory: A Roadmap to Machine Intelligence" at the Beijing Academy of Artificial Intelligence Conference on 1st June 2021. In this talk, he discussed the key components of The Thousand Brains Theory and Numenta's recent work.
Have We Missed Half of What the Neocortex Does? by Jeff Hawkins (12/15/2017)Numenta
This was a presentation given on December 15, 2017 at the MIT Center for Brains, Minds + Machines as part of their Brains, Minds and Machines Seminar Series.
You can watch the recording of the presentation after Slide 1.
In this talk, Jeff describes a theory that sensory regions of the neocortex process two inputs. One input is the well-known sensory data arriving via thalamic relay cells. We propose the second input is a representation of allocentric location. The allocentric location represents where the sensed feature is relative to the object being sensed, in an object-centric reference frame. As the sensors move, cortical columns learn complete models of objects by integrating sensory features and location representations over time. Lateral projections allow columns to rapidly reach a consensus of what object is being sensed. We propose that the representation of allocentric location is derived locally, in layer 6 of each column, using the same tiling principles as grid cells in the entorhinal cortex. Because individual cortical columns are able to model complete complex objects, cortical regions are far more powerful than currently believed. The inclusion of allocentric location offers the possibility of rapid progress in understanding the function of numerous aspects of cortical anatomy.
Jeff discusses material from these two papers. Others can be found at https://numenta.com/papers
A Theory of How Columns in the Neocortex Enable Learning the Structure of the World
URL: https://doi.org/10.3389/fncir.2017.00081
Why Neurons Have Thousands of Synapses, A Theory of Sequence Memory in the Neocortex
URL: https://doi.org/10.3389/fncir.2016.00023
The blue brain, a Swiss national brain initiative, aims to create a digital reconstruction of the brain by REVERSE ENGINEERING mammalian brain circuitry.
BAAI Conference 2021: The Thousand Brains Theory - A Roadmap for Creating Mac...Numenta
Jeff Hawkins presented a talk on "The Thousand Brains Theory: A Roadmap to Machine Intelligence" at the Beijing Academy of Artificial Intelligence Conference on 1st June 2021. In this talk, he discussed the key components of The Thousand Brains Theory and Numenta's recent work.
Have We Missed Half of What the Neocortex Does? by Jeff Hawkins (12/15/2017)Numenta
This was a presentation given on December 15, 2017 at the MIT Center for Brains, Minds + Machines as part of their Brains, Minds and Machines Seminar Series.
You can watch the recording of the presentation after Slide 1.
In this talk, Jeff describes a theory that sensory regions of the neocortex process two inputs. One input is the well-known sensory data arriving via thalamic relay cells. We propose the second input is a representation of allocentric location. The allocentric location represents where the sensed feature is relative to the object being sensed, in an object-centric reference frame. As the sensors move, cortical columns learn complete models of objects by integrating sensory features and location representations over time. Lateral projections allow columns to rapidly reach a consensus of what object is being sensed. We propose that the representation of allocentric location is derived locally, in layer 6 of each column, using the same tiling principles as grid cells in the entorhinal cortex. Because individual cortical columns are able to model complete complex objects, cortical regions are far more powerful than currently believed. The inclusion of allocentric location offers the possibility of rapid progress in understanding the function of numerous aspects of cortical anatomy.
Jeff discusses material from these two papers. Others can be found at https://numenta.com/papers
A Theory of How Columns in the Neocortex Enable Learning the Structure of the World
URL: https://doi.org/10.3389/fncir.2017.00081
Why Neurons Have Thousands of Synapses, A Theory of Sequence Memory in the Neocortex
URL: https://doi.org/10.3389/fncir.2016.00023
The blue brain, a Swiss national brain initiative, aims to create a digital reconstruction of the brain by REVERSE ENGINEERING mammalian brain circuitry.
Blue Brain Technology is an attempt to reverse engineer the human brain and create simulations inside a computer. This way, we can access someone's brain even when they are not around.
CVPR 2020 Workshop: Sparsity in the neocortex, and its implications for conti...Christy Maver
Numenta VP Research Subutai Ahmad presents a talk on "Sparsity in the Neocortex and its Implications for Continual Learning" at the virtual CVPR 2020 workshop. In this talk, he discusses how continuous learning systems can benefit from sparsity, active dendrites and other neocortical mechanisms.
CVPR 2020 Workshop: Sparsity in the neocortex, and its implications for conti...Numenta
Numenta VP Research Subutai Ahmad presents a talk on "Sparsity in the Neocortex and its Implications for Continual Learning" at the virtual CVPR 2020 workshop. In this talk, he discusses how continuous learning systems can benefit from sparsity, active dendrites and other neocortical mechanisms.
Blue Brain Technology is an attempt to reverse engineer the human brain and create simulations inside a computer. This way, we can access someone's brain even when they are not around.
CVPR 2020 Workshop: Sparsity in the neocortex, and its implications for conti...Christy Maver
Numenta VP Research Subutai Ahmad presents a talk on "Sparsity in the Neocortex and its Implications for Continual Learning" at the virtual CVPR 2020 workshop. In this talk, he discusses how continuous learning systems can benefit from sparsity, active dendrites and other neocortical mechanisms.
CVPR 2020 Workshop: Sparsity in the neocortex, and its implications for conti...Numenta
Numenta VP Research Subutai Ahmad presents a talk on "Sparsity in the Neocortex and its Implications for Continual Learning" at the virtual CVPR 2020 workshop. In this talk, he discusses how continuous learning systems can benefit from sparsity, active dendrites and other neocortical mechanisms.
Senior data scientist and founder of the company Intelligentia Data I+D SA de CV. We are offering consultancy services, development of projects and products in Machine Learning, Big Data, Data Sciences and Artificial Intelligence.
It has been almost 62 years since the invention of the term Artificial Intelligence by Samuel and Minsky et al. at the Dartmouth workshop College in 1956 (“Dartmouth Summer Research Project on Artificial Intelligence”) where this new area of Computer Science was invented. However, the history of Artificial Intelligence goes back to previous millennia, when the Greeks in their Myths spoke about golden robots at Hephaestus, and the Galatea of Pygmalion. They were the first automatons known at the dawn of history, and although these first attempts were only myths, automatons were invented and built through multiple civilizations in history. Nevertheless, these automatons resembled in quite limited way their final objectives, representing animals and humans. In spite of that, the greatest illusion of an automaton, the Turk by Wolfgang von Kempelen, inspired many people, trough its exhibitions, as Alexander Graham Bell and Charles Babbage to develop inventions that would change forever human history. Thus, the importance of the concept “Artificial Intelligence” as a driver of our technological dreams. And although Artificial Intelligence has never been defined in a precise practical way, the amount of research and methods that have been developed to tackle some of its basics tasks have been and are quite humongous. Thus, the importance of having an introduction to the concepts of Artificial Intelligence, thus the dream can continue.
A review of one of the most popular methods of clustering, a part of what is know as unsupervised learning, K-Means. Here, we go from the basic heuristic used to solve the NP-Hard problem to an approximation algorithm K-Centers. Additionally, we look at variations coming from the Fuzzy Set ideas. In the future, we will add more about On-Line algorithms in the line of Stochastic Gradient Ideas...
Here a Review of the Combination of Machine Learning models from Bayesian Averaging, Committees to Boosting... Specifically An statistical analysis of Boosting is done
Overview of the fundamental roles in Hydropower generation and the components involved in wider Electrical Engineering.
This paper presents the design and construction of hydroelectric dams from the hydrologist’s survey of the valley before construction, all aspects and involved disciplines, fluid dynamics, structural engineering, generation and mains frequency regulation to the very transmission of power through the network in the United Kingdom.
Author: Robbie Edward Sayers
Collaborators and co editors: Charlie Sims and Connor Healey.
(C) 2024 Robbie E. Sayers
6th International Conference on Machine Learning & Applications (CMLA 2024)ClaraZara1
6th International Conference on Machine Learning & Applications (CMLA 2024) will provide an excellent international forum for sharing knowledge and results in theory, methodology and applications of on Machine Learning & Applications.
Sachpazis:Terzaghi Bearing Capacity Estimation in simple terms with Calculati...Dr.Costas Sachpazis
Terzaghi's soil bearing capacity theory, developed by Karl Terzaghi, is a fundamental principle in geotechnical engineering used to determine the bearing capacity of shallow foundations. This theory provides a method to calculate the ultimate bearing capacity of soil, which is the maximum load per unit area that the soil can support without undergoing shear failure. The Calculation HTML Code included.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
NO1 Uk best vashikaran specialist in delhi vashikaran baba near me online vas...Amil Baba Dawood bangali
Contact with Dawood Bhai Just call on +92322-6382012 and we'll help you. We'll solve all your problems within 12 to 24 hours and with 101% guarantee and with astrology systematic. If you want to take any personal or professional advice then also you can call us on +92322-6382012 , ONLINE LOVE PROBLEM & Other all types of Daily Life Problem's.Then CALL or WHATSAPP us on +92322-6382012 and Get all these problems solutions here by Amil Baba DAWOOD BANGALI
#vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore#blackmagicformarriage #aamilbaba #kalajadu #kalailam #taweez #wazifaexpert #jadumantar #vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore #blackmagicforlove #blackmagicformarriage #aamilbaba #kalajadu #kalailam #taweez #wazifaexpert #jadumantar #vashikaranspecialist #astrologer #palmistry #amliyaat #taweez #manpasandshadi #horoscope #spiritual #lovelife #lovespell #marriagespell#aamilbabainpakistan #amilbabainkarachi #powerfullblackmagicspell #kalajadumantarspecialist #realamilbaba #AmilbabainPakistan #astrologerincanada #astrologerindubai #lovespellsmaster #kalajaduspecialist #lovespellsthatwork #aamilbabainlahore #Amilbabainuk #amilbabainspain #amilbabaindubai #Amilbabainnorway #amilbabainkrachi #amilbabainlahore #amilbabaingujranwalan #amilbabainislamabad
HEAP SORT ILLUSTRATED WITH HEAPIFY, BUILD HEAP FOR DYNAMIC ARRAYS.
Heap sort is a comparison-based sorting technique based on Binary Heap data structure. It is similar to the selection sort where we first find the minimum element and place the minimum element at the beginning. Repeat the same process for the remaining elements.
Cosmetic shop management system project report.pdfKamal Acharya
Buying new cosmetic products is difficult. It can even be scary for those who have sensitive skin and are prone to skin trouble. The information needed to alleviate this problem is on the back of each product, but it's thought to interpret those ingredient lists unless you have a background in chemistry.
Instead of buying and hoping for the best, we can use data science to help us predict which products may be good fits for us. It includes various function programs to do the above mentioned tasks.
Data file handling has been effectively used in the program.
The automated cosmetic shop management system should deal with the automation of general workflow and administration process of the shop. The main processes of the system focus on customer's request where the system is able to search the most appropriate products and deliver it to the customers. It should help the employees to quickly identify the list of cosmetic product that have reached the minimum quantity and also keep a track of expired date for each cosmetic product. It should help the employees to find the rack number in which the product is placed.It is also Faster and more efficient way.
Hierarchical Digital Twin of a Naval Power SystemKerry Sado
A hierarchical digital twin of a Naval DC power system has been developed and experimentally verified. Similar to other state-of-the-art digital twins, this technology creates a digital replica of the physical system executed in real-time or faster, which can modify hardware controls. However, its advantage stems from distributing computational efforts by utilizing a hierarchical structure composed of lower-level digital twin blocks and a higher-level system digital twin. Each digital twin block is associated with a physical subsystem of the hardware and communicates with a singular system digital twin, which creates a system-level response. By extracting information from each level of the hierarchy, power system controls of the hardware were reconfigured autonomously. This hierarchical digital twin development offers several advantages over other digital twins, particularly in the field of naval power systems. The hierarchical structure allows for greater computational efficiency and scalability while the ability to autonomously reconfigure hardware controls offers increased flexibility and responsiveness. The hierarchical decomposition and models utilized were well aligned with the physical twin, as indicated by the maximum deviations between the developed digital twin hierarchy and the hardware.
01 Introduction to Neural Networks and Deep Learning
1. Introduction to Neural Networks and Deep Learning
Introduction to Neural Networks
Andres Mendez-Vazquez
May 5, 2019
1 / 63
2. Outline
1 What are Neural Networks?
Structure of a Neural Cell
Pigeon Experiment
Formal Definition of Artificial Neural Network
Basic Elements of an Artificial Neuron
Types of Activation Functions
McCulloch-Pitts model
More Advanced Models
The Problem of the Vanishing Gradient
Fixing the Problem, ReLu function
2 Neural Network As a Graph
Introduction
Feedback
Neural Architectures
Knowledge Representation
Design of a Neural Network
Representing Knowledge in a Neural Networks
2 / 63
3. What are Neural Networks?
Basic Intuition
The human brain is a highly complex, nonlinear and parallel computer
It is organized as a
Network with (Ramon y Cajal 1911)
1 Basic Processing Units ≈ Neurons
2 Connections ≈ Axons and Dendrites
3 / 63
4. What are Neural Networks?
Basic Intuition
The human brain is a highly complex, nonlinear and parallel computer
It is organized as a
Network with (Ramon y Cajal 1911)
1 Basic Processing Units ≈ Neurons
2 Connections ≈ Axons and Dendrites
3 / 63
5. What are Neural Networks?
Basic Intuition
The human brain is a highly complex, nonlinear and parallel computer
It is organized as a
Network with (Ramon y Cajal 1911)
1 Basic Processing Units ≈ Neurons
2 Connections ≈ Axons and Dendrites
3 / 63
6. Outline
1 What are Neural Networks?
Structure of a Neural Cell
Pigeon Experiment
Formal Definition of Artificial Neural Network
Basic Elements of an Artificial Neuron
Types of Activation Functions
McCulloch-Pitts model
More Advanced Models
The Problem of the Vanishing Gradient
Fixing the Problem, ReLu function
2 Neural Network As a Graph
Introduction
Feedback
Neural Architectures
Knowledge Representation
Design of a Neural Network
Representing Knowledge in a Neural Networks
4 / 63
8. Silicon Chip Vs Neurons
Speed Differential
1 Speeds in silicon chips are in the nanosecond range (10−9 s).
2 Speeds in human neural networks are in the millisecond range (10−3
s).
However
We have massive parallelism on the human brain
1 10 billion neurons in the human cortex.
2 60 trillion synapses or connections
High Energy Efficiency
1 Human Brain uses 10−16 joules per operation.
2 Best computers use 10−6 joules per operation.
6 / 63
9. Silicon Chip Vs Neurons
Speed Differential
1 Speeds in silicon chips are in the nanosecond range (10−9 s).
2 Speeds in human neural networks are in the millisecond range (10−3
s).
However
We have massive parallelism on the human brain
1 10 billion neurons in the human cortex.
2 60 trillion synapses or connections
High Energy Efficiency
1 Human Brain uses 10−16 joules per operation.
2 Best computers use 10−6 joules per operation.
6 / 63
10. Silicon Chip Vs Neurons
Speed Differential
1 Speeds in silicon chips are in the nanosecond range (10−9 s).
2 Speeds in human neural networks are in the millisecond range (10−3
s).
However
We have massive parallelism on the human brain
1 10 billion neurons in the human cortex.
2 60 trillion synapses or connections
High Energy Efficiency
1 Human Brain uses 10−16 joules per operation.
2 Best computers use 10−6 joules per operation.
6 / 63
11. Silicon Chip Vs Neurons
Speed Differential
1 Speeds in silicon chips are in the nanosecond range (10−9 s).
2 Speeds in human neural networks are in the millisecond range (10−3
s).
However
We have massive parallelism on the human brain
1 10 billion neurons in the human cortex.
2 60 trillion synapses or connections
High Energy Efficiency
1 Human Brain uses 10−16 joules per operation.
2 Best computers use 10−6 joules per operation.
6 / 63
12. Silicon Chip Vs Neurons
Speed Differential
1 Speeds in silicon chips are in the nanosecond range (10−9 s).
2 Speeds in human neural networks are in the millisecond range (10−3
s).
However
We have massive parallelism on the human brain
1 10 billion neurons in the human cortex.
2 60 trillion synapses or connections
High Energy Efficiency
1 Human Brain uses 10−16 joules per operation.
2 Best computers use 10−6 joules per operation.
6 / 63
13. Silicon Chip Vs Neurons
Speed Differential
1 Speeds in silicon chips are in the nanosecond range (10−9 s).
2 Speeds in human neural networks are in the millisecond range (10−3
s).
However
We have massive parallelism on the human brain
1 10 billion neurons in the human cortex.
2 60 trillion synapses or connections
High Energy Efficiency
1 Human Brain uses 10−16 joules per operation.
2 Best computers use 10−6 joules per operation.
6 / 63
14. Silicon Chip Vs Neurons
Speed Differential
1 Speeds in silicon chips are in the nanosecond range (10−9 s).
2 Speeds in human neural networks are in the millisecond range (10−3
s).
However
We have massive parallelism on the human brain
1 10 billion neurons in the human cortex.
2 60 trillion synapses or connections
High Energy Efficiency
1 Human Brain uses 10−16 joules per operation.
2 Best computers use 10−6 joules per operation.
6 / 63
15. Outline
1 What are Neural Networks?
Structure of a Neural Cell
Pigeon Experiment
Formal Definition of Artificial Neural Network
Basic Elements of an Artificial Neuron
Types of Activation Functions
McCulloch-Pitts model
More Advanced Models
The Problem of the Vanishing Gradient
Fixing the Problem, ReLu function
2 Neural Network As a Graph
Introduction
Feedback
Neural Architectures
Knowledge Representation
Design of a Neural Network
Representing Knowledge in a Neural Networks
7 / 63
16. Pigeon Experiment
Watanabe et al. 1995
Pigeons as art experts
Experiment
Pigeon is in a Skinner box
Then, paintings of two different artists (e.g. Chagall / Van Gogh) are
presented to it.
A Reward is given for pecking when presented a particular artist (e.g.
Van Gogh).
8 / 63
17. Pigeon Experiment
Watanabe et al. 1995
Pigeons as art experts
Experiment
Pigeon is in a Skinner box
Then, paintings of two different artists (e.g. Chagall / Van Gogh) are
presented to it.
A Reward is given for pecking when presented a particular artist (e.g.
Van Gogh).
8 / 63
18. Pigeon Experiment
Watanabe et al. 1995
Pigeons as art experts
Experiment
Pigeon is in a Skinner box
Then, paintings of two different artists (e.g. Chagall / Van Gogh) are
presented to it.
A Reward is given for pecking when presented a particular artist (e.g.
Van Gogh).
8 / 63
19. The Pigeon in the Skinner Box
Something like this
9 / 63
20. Results
Something Notable
Pigeons were able to discriminate between Van Gogh and Chagall
with 95% accuracy (when presented with pictures they had been
trained on).
Discrimination still 85% successful for previously unseen paintings of
the artists.
Thus
1 Pigeons do not simply memorize the pictures.
2 They can extract and recognize patterns (the ‘style’).
3 They generalize from the already seen to make predictions.
4 This is what neural networks (biological and artificial) are good at
(unlike conventional computer).
10 / 63
21. Results
Something Notable
Pigeons were able to discriminate between Van Gogh and Chagall
with 95% accuracy (when presented with pictures they had been
trained on).
Discrimination still 85% successful for previously unseen paintings of
the artists.
Thus
1 Pigeons do not simply memorize the pictures.
2 They can extract and recognize patterns (the ‘style’).
3 They generalize from the already seen to make predictions.
4 This is what neural networks (biological and artificial) are good at
(unlike conventional computer).
10 / 63
22. Results
Something Notable
Pigeons were able to discriminate between Van Gogh and Chagall
with 95% accuracy (when presented with pictures they had been
trained on).
Discrimination still 85% successful for previously unseen paintings of
the artists.
Thus
1 Pigeons do not simply memorize the pictures.
2 They can extract and recognize patterns (the ‘style’).
3 They generalize from the already seen to make predictions.
4 This is what neural networks (biological and artificial) are good at
(unlike conventional computer).
10 / 63
23. Results
Something Notable
Pigeons were able to discriminate between Van Gogh and Chagall
with 95% accuracy (when presented with pictures they had been
trained on).
Discrimination still 85% successful for previously unseen paintings of
the artists.
Thus
1 Pigeons do not simply memorize the pictures.
2 They can extract and recognize patterns (the ‘style’).
3 They generalize from the already seen to make predictions.
4 This is what neural networks (biological and artificial) are good at
(unlike conventional computer).
10 / 63
24. Results
Something Notable
Pigeons were able to discriminate between Van Gogh and Chagall
with 95% accuracy (when presented with pictures they had been
trained on).
Discrimination still 85% successful for previously unseen paintings of
the artists.
Thus
1 Pigeons do not simply memorize the pictures.
2 They can extract and recognize patterns (the ‘style’).
3 They generalize from the already seen to make predictions.
4 This is what neural networks (biological and artificial) are good at
(unlike conventional computer).
10 / 63
25. Results
Something Notable
Pigeons were able to discriminate between Van Gogh and Chagall
with 95% accuracy (when presented with pictures they had been
trained on).
Discrimination still 85% successful for previously unseen paintings of
the artists.
Thus
1 Pigeons do not simply memorize the pictures.
2 They can extract and recognize patterns (the ‘style’).
3 They generalize from the already seen to make predictions.
4 This is what neural networks (biological and artificial) are good at
(unlike conventional computer).
10 / 63
26. Outline
1 What are Neural Networks?
Structure of a Neural Cell
Pigeon Experiment
Formal Definition of Artificial Neural Network
Basic Elements of an Artificial Neuron
Types of Activation Functions
McCulloch-Pitts model
More Advanced Models
The Problem of the Vanishing Gradient
Fixing the Problem, ReLu function
2 Neural Network As a Graph
Introduction
Feedback
Neural Architectures
Knowledge Representation
Design of a Neural Network
Representing Knowledge in a Neural Networks
11 / 63
27. Formal Definition
Definition
An artificial neural network is a massively parallel distributed processor made up of
simple processing units. It resembles the brain in two respects:
1 Knowledge is acquired by the network from its environment through a learning
process.
2 Inter-neuron connection strengths, known as synaptic weights, are used to store
the acquired knowledge.
12 / 63
28. Formal Definition
Definition
An artificial neural network is a massively parallel distributed processor made up of
simple processing units. It resembles the brain in two respects:
1 Knowledge is acquired by the network from its environment through a learning
process.
2 Inter-neuron connection strengths, known as synaptic weights, are used to store
the acquired knowledge.
12 / 63
29. Formal Definition
Definition
An artificial neural network is a massively parallel distributed processor made up of
simple processing units. It resembles the brain in two respects:
1 Knowledge is acquired by the network from its environment through a learning
process.
2 Inter-neuron connection strengths, known as synaptic weights, are used to store
the acquired knowledge.
12 / 63
30. Inter-neuron connection strengths?
How do the neuron collect this information?
Some way to aggregate information needs to be devised...
A Classic
Use a summation of product of weights by inputs!!!
Something like
m
i=1
wi × xi
Where: wi is the strength given to signal xi
However: We still need a way to regulate this “aggregation”
(Activation function)
13 / 63
31. Inter-neuron connection strengths?
How do the neuron collect this information?
Some way to aggregate information needs to be devised...
A Classic
Use a summation of product of weights by inputs!!!
Something like
m
i=1
wi × xi
Where: wi is the strength given to signal xi
However: We still need a way to regulate this “aggregation”
(Activation function)
13 / 63
32. Inter-neuron connection strengths?
How do the neuron collect this information?
Some way to aggregate information needs to be devised...
A Classic
Use a summation of product of weights by inputs!!!
Something like
m
i=1
wi × xi
Where: wi is the strength given to signal xi
However: We still need a way to regulate this “aggregation”
(Activation function)
13 / 63
33. The Model of a Artificial Neuron
Graphical Representation for neuron k
INPUT
SIGNALS
SYNAPTIC
WEIGHTS
BIAS
SUMMING
JUNCTION
OUTPUT
ACTIVATION
FUNCTION
14 / 63
34. Outline
1 What are Neural Networks?
Structure of a Neural Cell
Pigeon Experiment
Formal Definition of Artificial Neural Network
Basic Elements of an Artificial Neuron
Types of Activation Functions
McCulloch-Pitts model
More Advanced Models
The Problem of the Vanishing Gradient
Fixing the Problem, ReLu function
2 Neural Network As a Graph
Introduction
Feedback
Neural Architectures
Knowledge Representation
Design of a Neural Network
Representing Knowledge in a Neural Networks
15 / 63
35. Basic Elements of an Artificial Neuron (AN) Model
Set of Connecting links
A signal xj, at the input of synapse j connected to neuron k is multiplied by the
synaptic weight wkj.
The weight of an AN may lie in a negative of positive range.
What about the real neuron? In classic literature you only have positive
values.
Adder
An adder for summing the input signals, weighted by the respective synapses of the
neuron.
Activation function (Squashing function)
It limits the amplitude of the output of a neuron.
It maps the permissible range of the output signal to an interval.
16 / 63
36. Basic Elements of an Artificial Neuron (AN) Model
Set of Connecting links
A signal xj, at the input of synapse j connected to neuron k is multiplied by the
synaptic weight wkj.
The weight of an AN may lie in a negative of positive range.
What about the real neuron? In classic literature you only have positive
values.
Adder
An adder for summing the input signals, weighted by the respective synapses of the
neuron.
Activation function (Squashing function)
It limits the amplitude of the output of a neuron.
It maps the permissible range of the output signal to an interval.
16 / 63
37. Basic Elements of an Artificial Neuron (AN) Model
Set of Connecting links
A signal xj, at the input of synapse j connected to neuron k is multiplied by the
synaptic weight wkj.
The weight of an AN may lie in a negative of positive range.
What about the real neuron? In classic literature you only have positive
values.
Adder
An adder for summing the input signals, weighted by the respective synapses of the
neuron.
Activation function (Squashing function)
It limits the amplitude of the output of a neuron.
It maps the permissible range of the output signal to an interval.
16 / 63
38. Basic Elements of an Artificial Neuron (AN) Model
Set of Connecting links
A signal xj, at the input of synapse j connected to neuron k is multiplied by the
synaptic weight wkj.
The weight of an AN may lie in a negative of positive range.
What about the real neuron? In classic literature you only have positive
values.
Adder
An adder for summing the input signals, weighted by the respective synapses of the
neuron.
Activation function (Squashing function)
It limits the amplitude of the output of a neuron.
It maps the permissible range of the output signal to an interval.
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39. Mathematically
Adder
uk =
m
j=1
wkjxj (1)
1 x1, x2, ..., xm are the input signals.
2 wk1, wk2, ..., wkm are the synaptic weights.
3 It is also known as “Affine Transformation.”
Activation function
yk = ϕ (uk + bk) (2)
1 yk output of neuron.
2 ϕ is the activation function.
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40. Mathematically
Adder
uk =
m
j=1
wkjxj (1)
1 x1, x2, ..., xm are the input signals.
2 wk1, wk2, ..., wkm are the synaptic weights.
3 It is also known as “Affine Transformation.”
Activation function
yk = ϕ (uk + bk) (2)
1 yk output of neuron.
2 ϕ is the activation function.
17 / 63
41. Mathematically
Adder
uk =
m
j=1
wkjxj (1)
1 x1, x2, ..., xm are the input signals.
2 wk1, wk2, ..., wkm are the synaptic weights.
3 It is also known as “Affine Transformation.”
Activation function
yk = ϕ (uk + bk) (2)
1 yk output of neuron.
2 ϕ is the activation function.
17 / 63
42. Mathematically
Adder
uk =
m
j=1
wkjxj (1)
1 x1, x2, ..., xm are the input signals.
2 wk1, wk2, ..., wkm are the synaptic weights.
3 It is also known as “Affine Transformation.”
Activation function
yk = ϕ (uk + bk) (2)
1 yk output of neuron.
2 ϕ is the activation function.
17 / 63
43. Mathematically
Adder
uk =
m
j=1
wkjxj (1)
1 x1, x2, ..., xm are the input signals.
2 wk1, wk2, ..., wkm are the synaptic weights.
3 It is also known as “Affine Transformation.”
Activation function
yk = ϕ (uk + bk) (2)
1 yk output of neuron.
2 ϕ is the activation function.
17 / 63
44. Mathematically
Adder
uk =
m
j=1
wkjxj (1)
1 x1, x2, ..., xm are the input signals.
2 wk1, wk2, ..., wkm are the synaptic weights.
3 It is also known as “Affine Transformation.”
Activation function
yk = ϕ (uk + bk) (2)
1 yk output of neuron.
2 ϕ is the activation function.
17 / 63
45. Mathematically
Adder
uk =
m
j=1
wkjxj (1)
1 x1, x2, ..., xm are the input signals.
2 wk1, wk2, ..., wkm are the synaptic weights.
3 It is also known as “Affine Transformation.”
Activation function
yk = ϕ (uk + bk) (2)
1 yk output of neuron.
2 ϕ is the activation function.
17 / 63
46. Integrating the Bias
The Affine Transformation
0
Induced Local Field,
Bias
Linear Combiner's Output,
18 / 63
49. Outline
1 What are Neural Networks?
Structure of a Neural Cell
Pigeon Experiment
Formal Definition of Artificial Neural Network
Basic Elements of an Artificial Neuron
Types of Activation Functions
McCulloch-Pitts model
More Advanced Models
The Problem of the Vanishing Gradient
Fixing the Problem, ReLu function
2 Neural Network As a Graph
Introduction
Feedback
Neural Architectures
Knowledge Representation
Design of a Neural Network
Representing Knowledge in a Neural Networks
20 / 63
50. Types of Activation Functions I
Threshold Function
ϕ (v) =
1 if v ≥ 0
0 if v < 0
(Heaviside Function) (3)
In the following picture
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51. Types of Activation Functions I
Threshold Function
ϕ (v) =
1 if v ≥ 0
0 if v < 0
(Heaviside Function) (3)
In the following picture
1
-1-2-3-4 10 2 3
0.5
21 / 63
52. Thus
We can use this activation function
To generate the first Neural Network Model
Clearly
The model uses the summation as aggregation operator and a threshold
function.
22 / 63
53. Thus
We can use this activation function
To generate the first Neural Network Model
Clearly
The model uses the summation as aggregation operator and a threshold
function.
22 / 63
54. Outline
1 What are Neural Networks?
Structure of a Neural Cell
Pigeon Experiment
Formal Definition of Artificial Neural Network
Basic Elements of an Artificial Neuron
Types of Activation Functions
McCulloch-Pitts model
More Advanced Models
The Problem of the Vanishing Gradient
Fixing the Problem, ReLu function
2 Neural Network As a Graph
Introduction
Feedback
Neural Architectures
Knowledge Representation
Design of a Neural Network
Representing Knowledge in a Neural Networks
23 / 63
55. McCulloch-Pitts model
McCulloch-Pitts model (Pioneers of Neural Networks in the 1940’s)
Output
Output yk =
1 if vk ≥ θ
0 if vk < θ
(4)
yk =
1 if vk ≤ θ = 0
0 if vk > θ = 0
with induced local field wk = (1, 1)T
vk =
m
j=1
wkjxj + bk (5)
24 / 63
56. McCulloch-Pitts model
McCulloch-Pitts model (Pioneers of Neural Networks in the 1940’s)
Output
Output yk =
1 if vk ≥ θ
0 if vk < θ
(4)
yk =
1 if vk ≤ θ = 0
0 if vk > θ = 0
with induced local field wk = (1, 1)T
vk =
m
j=1
wkjxj + bk (5)
24 / 63
57. It is possible to do classic operations in Boolean Algebra
AND Gate
25 / 63
60. And the impact is further understood if you look at this
paper
Claude Shannon
“A Symbolic Analysis of Relay and Switching Circuits”
Shannon proved that his switching circuits could be used to simplify
the arrangement of the electromechanical relays
These circuits could solve all problems that Boolean algebra could
solve.
Basically, he proved that computer circuits
They can solve computational complex problems...
28 / 63
61. And the impact is further understood if you look at this
paper
Claude Shannon
“A Symbolic Analysis of Relay and Switching Circuits”
Shannon proved that his switching circuits could be used to simplify
the arrangement of the electromechanical relays
These circuits could solve all problems that Boolean algebra could
solve.
Basically, he proved that computer circuits
They can solve computational complex problems...
28 / 63
62. And the impact is further understood if you look at this
paper
Claude Shannon
“A Symbolic Analysis of Relay and Switching Circuits”
Shannon proved that his switching circuits could be used to simplify
the arrangement of the electromechanical relays
These circuits could solve all problems that Boolean algebra could
solve.
Basically, he proved that computer circuits
They can solve computational complex problems...
28 / 63
63. And the impact is further understood if you look at this
paper
Claude Shannon
“A Symbolic Analysis of Relay and Switching Circuits”
Shannon proved that his switching circuits could be used to simplify
the arrangement of the electromechanical relays
These circuits could solve all problems that Boolean algebra could
solve.
Basically, he proved that computer circuits
They can solve computational complex problems...
28 / 63
64. Outline
1 What are Neural Networks?
Structure of a Neural Cell
Pigeon Experiment
Formal Definition of Artificial Neural Network
Basic Elements of an Artificial Neuron
Types of Activation Functions
McCulloch-Pitts model
More Advanced Models
The Problem of the Vanishing Gradient
Fixing the Problem, ReLu function
2 Neural Network As a Graph
Introduction
Feedback
Neural Architectures
Knowledge Representation
Design of a Neural Network
Representing Knowledge in a Neural Networks
29 / 63
65. More advanced activation function
Piecewise-Linear Function
ϕ (v) =
1 if vk ≥ 1
2
v if − 1
2 < vk < 1
2
0 if v ≤ −1
2
(6)
Example
30 / 63
66. More advanced activation function
Piecewise-Linear Function
ϕ (v) =
1 if vk ≥ 1
2
v if − 1
2 < vk < 1
2
0 if v ≤ −1
2
(6)
Example
1
-1-2-3-4 10 2 3
0.5
-0.5 0.5
30 / 63
67. Remarks
Notes about Piecewise-Linear function
The amplification factor inside the linear region of operation is assumed to
be unity.
Special Cases
A linear combiner arises if the linear region of operation is maintained
without running into saturation.
The piecewise-linear function reduces to a threshold function if the
amplification factor of the linear region is made infinitely large.
31 / 63
68. Remarks
Notes about Piecewise-Linear function
The amplification factor inside the linear region of operation is assumed to
be unity.
Special Cases
A linear combiner arises if the linear region of operation is maintained
without running into saturation.
The piecewise-linear function reduces to a threshold function if the
amplification factor of the linear region is made infinitely large.
31 / 63
69. Remarks
Notes about Piecewise-Linear function
The amplification factor inside the linear region of operation is assumed to
be unity.
Special Cases
A linear combiner arises if the linear region of operation is maintained
without running into saturation.
The piecewise-linear function reduces to a threshold function if the
amplification factor of the linear region is made infinitely large.
31 / 63
70. A better choice!!!
Sigmoid function
ϕ (v) =
1
1 + exp {−av}
(7)
Where a is a slope parameter.
As a → ∞ then ϕ → Threshold function.
Examples
32 / 63
71. A better choice!!!
Sigmoid function
ϕ (v) =
1
1 + exp {−av}
(7)
Where a is a slope parameter.
As a → ∞ then ϕ → Threshold function.
Examples
Increasing
32 / 63
72. Outline
1 What are Neural Networks?
Structure of a Neural Cell
Pigeon Experiment
Formal Definition of Artificial Neural Network
Basic Elements of an Artificial Neuron
Types of Activation Functions
McCulloch-Pitts model
More Advanced Models
The Problem of the Vanishing Gradient
Fixing the Problem, ReLu function
2 Neural Network As a Graph
Introduction
Feedback
Neural Architectures
Knowledge Representation
Design of a Neural Network
Representing Knowledge in a Neural Networks
33 / 63
73. The Problem of the Vanishing Gradient
When using a non-linearity
However, there is a drawback when using Back-Propagation (As we
saw in Machine Learning) under a sigmoid function
s (x) =
1
1 + e−x
Because if we imagine a Deep Neural Network as a series of layer
functions fi
y (A) = ft ◦ ft−1 ◦ · · · ◦ f2 ◦ f1 (A)
With ft is the last layer.
Therefore, we finish with a sequence of derivatives
∂y (A)
∂w1i
=
∂ft (ft−1)
∂ft−1
·
∂ft−1 (ft−2)
∂ft−2
· · · · ·
∂f2 (f1)
∂f2
·
∂f1 (A)
∂w1i
34 / 63
74. The Problem of the Vanishing Gradient
When using a non-linearity
However, there is a drawback when using Back-Propagation (As we
saw in Machine Learning) under a sigmoid function
s (x) =
1
1 + e−x
Because if we imagine a Deep Neural Network as a series of layer
functions fi
y (A) = ft ◦ ft−1 ◦ · · · ◦ f2 ◦ f1 (A)
With ft is the last layer.
Therefore, we finish with a sequence of derivatives
∂y (A)
∂w1i
=
∂ft (ft−1)
∂ft−1
·
∂ft−1 (ft−2)
∂ft−2
· · · · ·
∂f2 (f1)
∂f2
·
∂f1 (A)
∂w1i
34 / 63
75. The Problem of the Vanishing Gradient
When using a non-linearity
However, there is a drawback when using Back-Propagation (As we
saw in Machine Learning) under a sigmoid function
s (x) =
1
1 + e−x
Because if we imagine a Deep Neural Network as a series of layer
functions fi
y (A) = ft ◦ ft−1 ◦ · · · ◦ f2 ◦ f1 (A)
With ft is the last layer.
Therefore, we finish with a sequence of derivatives
∂y (A)
∂w1i
=
∂ft (ft−1)
∂ft−1
·
∂ft−1 (ft−2)
∂ft−2
· · · · ·
∂f2 (f1)
∂f2
·
∂f1 (A)
∂w1i
34 / 63
76. Therefore
Given the commutativity of the product
You could put together the derivative of the sigmoid’s
f (x) =
ds (x)
dx
=
e−x
(1 + e−x)2
Therefore, deriving again
df (x)
dx
= −
e−x
(1 + e−x)2 +
2 (e−x)
2
(1 + e−x)3
After making df(x)
dx
= 0
We have the maximum is at x = 0
35 / 63
77. Therefore
Given the commutativity of the product
You could put together the derivative of the sigmoid’s
f (x) =
ds (x)
dx
=
e−x
(1 + e−x)2
Therefore, deriving again
df (x)
dx
= −
e−x
(1 + e−x)2 +
2 (e−x)
2
(1 + e−x)3
After making df(x)
dx
= 0
We have the maximum is at x = 0
35 / 63
78. Therefore
Given the commutativity of the product
You could put together the derivative of the sigmoid’s
f (x) =
ds (x)
dx
=
e−x
(1 + e−x)2
Therefore, deriving again
df (x)
dx
= −
e−x
(1 + e−x)2 +
2 (e−x)
2
(1 + e−x)3
After making df(x)
dx
= 0
We have the maximum is at x = 0
35 / 63
79. Therefore
The maximum for the derivative of the sigmoid
f (0) = 0.25
Therefore, Given a Deep Convolutional Network
We could finish with
lim
k→∞
ds (x)
dx
k
= lim
k→∞
(0.25)k
→ 0
A Vanishing Derivative or Vanishing Gradient
Making quite difficult to do train a deeper network using this
activation function for Deep Learning and even in Shallow Learning
36 / 63
80. Therefore
The maximum for the derivative of the sigmoid
f (0) = 0.25
Therefore, Given a Deep Convolutional Network
We could finish with
lim
k→∞
ds (x)
dx
k
= lim
k→∞
(0.25)k
→ 0
A Vanishing Derivative or Vanishing Gradient
Making quite difficult to do train a deeper network using this
activation function for Deep Learning and even in Shallow Learning
36 / 63
81. Therefore
The maximum for the derivative of the sigmoid
f (0) = 0.25
Therefore, Given a Deep Convolutional Network
We could finish with
lim
k→∞
ds (x)
dx
k
= lim
k→∞
(0.25)k
→ 0
A Vanishing Derivative or Vanishing Gradient
Making quite difficult to do train a deeper network using this
activation function for Deep Learning and even in Shallow Learning
36 / 63
82. Outline
1 What are Neural Networks?
Structure of a Neural Cell
Pigeon Experiment
Formal Definition of Artificial Neural Network
Basic Elements of an Artificial Neuron
Types of Activation Functions
McCulloch-Pitts model
More Advanced Models
The Problem of the Vanishing Gradient
Fixing the Problem, ReLu function
2 Neural Network As a Graph
Introduction
Feedback
Neural Architectures
Knowledge Representation
Design of a Neural Network
Representing Knowledge in a Neural Networks
37 / 63
83. Thus
The need to introduce a new function
f (x) = x+
= max (0, x)
It is called ReLu or Rectifier
With a smooth approximation (Softplus function)
f (x) =
ln 1 + ekx
k
38 / 63
84. Thus
The need to introduce a new function
f (x) = x+
= max (0, x)
It is called ReLu or Rectifier
With a smooth approximation (Softplus function)
f (x) =
ln 1 + ekx
k
38 / 63
85. We have
When k = 1
+0.4 +1.0 +1.6 +2.2−0.4−1.0−1.6−2.2−2.8
−0.5
+0.5
+1.0
+1.5
+2.0
+2.5
+3.0
+3.5
Softplus
ReLu
39 / 63
86. Increase k
When k = 104
+0.0006 +0.0012 +0.0018 +0.0024−0.0004−0.001−0.0016−0.0022
−0.001
+0.001
+0.002
+0.003
+0.004
Softplus
ReLu
40 / 63
87. Final Remarks
Although, ReLu functions
They can handle the problem of vanishing problem
However, as we will see, saturation starts to appear as a problem
As in Hebbian Learning!!!
41 / 63
88. Final Remarks
Although, ReLu functions
They can handle the problem of vanishing problem
However, as we will see, saturation starts to appear as a problem
As in Hebbian Learning!!!
41 / 63
89. Outline
1 What are Neural Networks?
Structure of a Neural Cell
Pigeon Experiment
Formal Definition of Artificial Neural Network
Basic Elements of an Artificial Neuron
Types of Activation Functions
McCulloch-Pitts model
More Advanced Models
The Problem of the Vanishing Gradient
Fixing the Problem, ReLu function
2 Neural Network As a Graph
Introduction
Feedback
Neural Architectures
Knowledge Representation
Design of a Neural Network
Representing Knowledge in a Neural Networks
42 / 63
90. Neural Network As a Graph
Definition
A neural network is a directed graph consisting of nodes with
interconnecting synaptic and activation links.
Properties
1 Each neuron is represented by a set of linear synaptic links, an
externally applied bias, and a possibly nonlinear activation link.
2 The synaptic to links of a neuron weight their respective input signals.
3 The weighted sum of the input signals defines the induced local field
of the neuron.
4 The activation link squashes the induced local field of the neuron to
produce an output.
43 / 63
91. Neural Network As a Graph
Definition
A neural network is a directed graph consisting of nodes with
interconnecting synaptic and activation links.
Properties
1 Each neuron is represented by a set of linear synaptic links, an
externally applied bias, and a possibly nonlinear activation link.
2 The synaptic to links of a neuron weight their respective input signals.
3 The weighted sum of the input signals defines the induced local field
of the neuron.
4 The activation link squashes the induced local field of the neuron to
produce an output.
43 / 63
92. Neural Network As a Graph
Definition
A neural network is a directed graph consisting of nodes with
interconnecting synaptic and activation links.
Properties
1 Each neuron is represented by a set of linear synaptic links, an
externally applied bias, and a possibly nonlinear activation link.
2 The synaptic to links of a neuron weight their respective input signals.
3 The weighted sum of the input signals defines the induced local field
of the neuron.
4 The activation link squashes the induced local field of the neuron to
produce an output.
43 / 63
93. Neural Network As a Graph
Definition
A neural network is a directed graph consisting of nodes with
interconnecting synaptic and activation links.
Properties
1 Each neuron is represented by a set of linear synaptic links, an
externally applied bias, and a possibly nonlinear activation link.
2 The synaptic to links of a neuron weight their respective input signals.
3 The weighted sum of the input signals defines the induced local field
of the neuron.
4 The activation link squashes the induced local field of the neuron to
produce an output.
43 / 63
94. Neural Network As a Graph
Definition
A neural network is a directed graph consisting of nodes with
interconnecting synaptic and activation links.
Properties
1 Each neuron is represented by a set of linear synaptic links, an
externally applied bias, and a possibly nonlinear activation link.
2 The synaptic to links of a neuron weight their respective input signals.
3 The weighted sum of the input signals defines the induced local field
of the neuron.
4 The activation link squashes the induced local field of the neuron to
produce an output.
43 / 63
96. Some Observations
Observation
A partially complete graph describing a neural architecture has the following
characteristics:
Source nodes supply input signals to the graph.
Each neuron is represented by a single node called a computation node.
The communication links provide directions of signal flow in the graph.
However
Other Representations exist!!!
Three main representations ones
Block diagram, providing a functional description of the network.
Signal-flow graph, providing a complete description of signal flow in the
network.
Then one we plan to use.
Architectural graph, describing the network layout.
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97. Some Observations
Observation
A partially complete graph describing a neural architecture has the following
characteristics:
Source nodes supply input signals to the graph.
Each neuron is represented by a single node called a computation node.
The communication links provide directions of signal flow in the graph.
However
Other Representations exist!!!
Three main representations ones
Block diagram, providing a functional description of the network.
Signal-flow graph, providing a complete description of signal flow in the
network.
Then one we plan to use.
Architectural graph, describing the network layout.
45 / 63
98. Some Observations
Observation
A partially complete graph describing a neural architecture has the following
characteristics:
Source nodes supply input signals to the graph.
Each neuron is represented by a single node called a computation node.
The communication links provide directions of signal flow in the graph.
However
Other Representations exist!!!
Three main representations ones
Block diagram, providing a functional description of the network.
Signal-flow graph, providing a complete description of signal flow in the
network.
Then one we plan to use.
Architectural graph, describing the network layout.
45 / 63
99. Some Observations
Observation
A partially complete graph describing a neural architecture has the following
characteristics:
Source nodes supply input signals to the graph.
Each neuron is represented by a single node called a computation node.
The communication links provide directions of signal flow in the graph.
However
Other Representations exist!!!
Three main representations ones
Block diagram, providing a functional description of the network.
Signal-flow graph, providing a complete description of signal flow in the
network.
Then one we plan to use.
Architectural graph, describing the network layout.
45 / 63
100. Some Observations
Observation
A partially complete graph describing a neural architecture has the following
characteristics:
Source nodes supply input signals to the graph.
Each neuron is represented by a single node called a computation node.
The communication links provide directions of signal flow in the graph.
However
Other Representations exist!!!
Three main representations ones
Block diagram, providing a functional description of the network.
Signal-flow graph, providing a complete description of signal flow in the
network.
Then one we plan to use.
Architectural graph, describing the network layout.
45 / 63
101. Some Observations
Observation
A partially complete graph describing a neural architecture has the following
characteristics:
Source nodes supply input signals to the graph.
Each neuron is represented by a single node called a computation node.
The communication links provide directions of signal flow in the graph.
However
Other Representations exist!!!
Three main representations ones
Block diagram, providing a functional description of the network.
Signal-flow graph, providing a complete description of signal flow in the
network.
Then one we plan to use.
Architectural graph, describing the network layout.
45 / 63
102. Some Observations
Observation
A partially complete graph describing a neural architecture has the following
characteristics:
Source nodes supply input signals to the graph.
Each neuron is represented by a single node called a computation node.
The communication links provide directions of signal flow in the graph.
However
Other Representations exist!!!
Three main representations ones
Block diagram, providing a functional description of the network.
Signal-flow graph, providing a complete description of signal flow in the
network.
Then one we plan to use.
Architectural graph, describing the network layout.
45 / 63
103. Some Observations
Observation
A partially complete graph describing a neural architecture has the following
characteristics:
Source nodes supply input signals to the graph.
Each neuron is represented by a single node called a computation node.
The communication links provide directions of signal flow in the graph.
However
Other Representations exist!!!
Three main representations ones
Block diagram, providing a functional description of the network.
Signal-flow graph, providing a complete description of signal flow in the
network.
Then one we plan to use.
Architectural graph, describing the network layout.
45 / 63
104. Some Observations
Observation
A partially complete graph describing a neural architecture has the following
characteristics:
Source nodes supply input signals to the graph.
Each neuron is represented by a single node called a computation node.
The communication links provide directions of signal flow in the graph.
However
Other Representations exist!!!
Three main representations ones
Block diagram, providing a functional description of the network.
Signal-flow graph, providing a complete description of signal flow in the
network.
Then one we plan to use.
Architectural graph, describing the network layout.
45 / 63
105. Outline
1 What are Neural Networks?
Structure of a Neural Cell
Pigeon Experiment
Formal Definition of Artificial Neural Network
Basic Elements of an Artificial Neuron
Types of Activation Functions
McCulloch-Pitts model
More Advanced Models
The Problem of the Vanishing Gradient
Fixing the Problem, ReLu function
2 Neural Network As a Graph
Introduction
Feedback
Neural Architectures
Knowledge Representation
Design of a Neural Network
Representing Knowledge in a Neural Networks
46 / 63
106. Feedback Model
Feedback
Feedback is said to exist in a dynamic system.
Indeed, feedback occurs in almost every part of the nervous system of
every animal (Freeman, 1975)
Feedback Architecture
Thus
Given xj the internal signal and A (The weights product) operator:
Output yk (n) = A xj (n) (8)
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107. Feedback Model
Feedback
Feedback is said to exist in a dynamic system.
Indeed, feedback occurs in almost every part of the nervous system of
every animal (Freeman, 1975)
Feedback Architecture
Thus
Given xj the internal signal and A (The weights product) operator:
Output yk (n) = A xj (n) (8)
47 / 63
108. Feedback Model
Feedback
Feedback is said to exist in a dynamic system.
Indeed, feedback occurs in almost every part of the nervous system of
every animal (Freeman, 1975)
Feedback Architecture
Thus
Given xj the internal signal and A (The weights product) operator:
Output yk (n) = A xj (n) (8)
47 / 63
109. Thus
The internal input has a feedback
Given a B operator:
xj (n) = xj (n) + B (yk (n)) (9)
Then eliminating xj (n)
yk (n) =
A
1 − AB
(xj (n)) (10)
Where A
1−AB is known as the closed-loop operator of the system.
48 / 63
110. Thus
The internal input has a feedback
Given a B operator:
xj (n) = xj (n) + B (yk (n)) (9)
Then eliminating xj (n)
yk (n) =
A
1 − AB
(xj (n)) (10)
Where A
1−AB is known as the closed-loop operator of the system.
48 / 63
111. Outline
1 What are Neural Networks?
Structure of a Neural Cell
Pigeon Experiment
Formal Definition of Artificial Neural Network
Basic Elements of an Artificial Neuron
Types of Activation Functions
McCulloch-Pitts model
More Advanced Models
The Problem of the Vanishing Gradient
Fixing the Problem, ReLu function
2 Neural Network As a Graph
Introduction
Feedback
Neural Architectures
Knowledge Representation
Design of a Neural Network
Representing Knowledge in a Neural Networks
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114. Neural Architectures II
Multilayer Feedforward Networks
Input Layer
of Source
Nodes
Output Layer
of Neurons
Hidden Layer
of Neurons
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115. Observations
Observations
1 This network contains a series of hidden layer.
2 Each hidden layers allows for classification of the new output space of
the previous hidden layer.
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116. Observations
Observations
1 This network contains a series of hidden layer.
2 Each hidden layers allows for classification of the new output space of
the previous hidden layer.
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120. Outline
1 What are Neural Networks?
Structure of a Neural Cell
Pigeon Experiment
Formal Definition of Artificial Neural Network
Basic Elements of an Artificial Neuron
Types of Activation Functions
McCulloch-Pitts model
More Advanced Models
The Problem of the Vanishing Gradient
Fixing the Problem, ReLu function
2 Neural Network As a Graph
Introduction
Feedback
Neural Architectures
Knowledge Representation
Design of a Neural Network
Representing Knowledge in a Neural Networks
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121. Knowledge Representation
Definition
By Fischler and Firschein, 1987
“Knowledge refers to stored information or models used by a person or
machine to interpret, predict, and appropriately respond to the outside
world. ”
It consists of two kinds of information:
1 The known world state, represented by facts about what is and what
has been known.
2 Observations (measurements) of the world, obtained by means of
sensors.
Observations can be
1 Labeled
2 Unlabeled
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122. Knowledge Representation
Definition
By Fischler and Firschein, 1987
“Knowledge refers to stored information or models used by a person or
machine to interpret, predict, and appropriately respond to the outside
world. ”
It consists of two kinds of information:
1 The known world state, represented by facts about what is and what
has been known.
2 Observations (measurements) of the world, obtained by means of
sensors.
Observations can be
1 Labeled
2 Unlabeled
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123. Knowledge Representation
Definition
By Fischler and Firschein, 1987
“Knowledge refers to stored information or models used by a person or
machine to interpret, predict, and appropriately respond to the outside
world. ”
It consists of two kinds of information:
1 The known world state, represented by facts about what is and what
has been known.
2 Observations (measurements) of the world, obtained by means of
sensors.
Observations can be
1 Labeled
2 Unlabeled
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124. Knowledge Representation
Definition
By Fischler and Firschein, 1987
“Knowledge refers to stored information or models used by a person or
machine to interpret, predict, and appropriately respond to the outside
world. ”
It consists of two kinds of information:
1 The known world state, represented by facts about what is and what
has been known.
2 Observations (measurements) of the world, obtained by means of
sensors.
Observations can be
1 Labeled
2 Unlabeled
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125. Knowledge Representation
Definition
By Fischler and Firschein, 1987
“Knowledge refers to stored information or models used by a person or
machine to interpret, predict, and appropriately respond to the outside
world. ”
It consists of two kinds of information:
1 The known world state, represented by facts about what is and what
has been known.
2 Observations (measurements) of the world, obtained by means of
sensors.
Observations can be
1 Labeled
2 Unlabeled
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126. Knowledge Representation
Definition
By Fischler and Firschein, 1987
“Knowledge refers to stored information or models used by a person or
machine to interpret, predict, and appropriately respond to the outside
world. ”
It consists of two kinds of information:
1 The known world state, represented by facts about what is and what
has been known.
2 Observations (measurements) of the world, obtained by means of
sensors.
Observations can be
1 Labeled
2 Unlabeled
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127. Outline
1 What are Neural Networks?
Structure of a Neural Cell
Pigeon Experiment
Formal Definition of Artificial Neural Network
Basic Elements of an Artificial Neuron
Types of Activation Functions
McCulloch-Pitts model
More Advanced Models
The Problem of the Vanishing Gradient
Fixing the Problem, ReLu function
2 Neural Network As a Graph
Introduction
Feedback
Neural Architectures
Knowledge Representation
Design of a Neural Network
Representing Knowledge in a Neural Networks
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128. Set of Training Data
Training Data
It consist of input-output pairs (x, y)
x= input signal
y= desired output
Thus, we have the following phases of designing a Neuronal Network
1 Choose appropriate architecture
2 Train the network - learning.
1 Use the Training Data!!!
3 Test the network with data not seen before
1 Use a set of pairs that where not shown to the network so the y
component is guessed.
4 Then, you can see how well the network behaves - Generalization Phase.
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129. Set of Training Data
Training Data
It consist of input-output pairs (x, y)
x= input signal
y= desired output
Thus, we have the following phases of designing a Neuronal Network
1 Choose appropriate architecture
2 Train the network - learning.
1 Use the Training Data!!!
3 Test the network with data not seen before
1 Use a set of pairs that where not shown to the network so the y
component is guessed.
4 Then, you can see how well the network behaves - Generalization Phase.
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130. Set of Training Data
Training Data
It consist of input-output pairs (x, y)
x= input signal
y= desired output
Thus, we have the following phases of designing a Neuronal Network
1 Choose appropriate architecture
2 Train the network - learning.
1 Use the Training Data!!!
3 Test the network with data not seen before
1 Use a set of pairs that where not shown to the network so the y
component is guessed.
4 Then, you can see how well the network behaves - Generalization Phase.
59 / 63
131. Set of Training Data
Training Data
It consist of input-output pairs (x, y)
x= input signal
y= desired output
Thus, we have the following phases of designing a Neuronal Network
1 Choose appropriate architecture
2 Train the network - learning.
1 Use the Training Data!!!
3 Test the network with data not seen before
1 Use a set of pairs that where not shown to the network so the y
component is guessed.
4 Then, you can see how well the network behaves - Generalization Phase.
59 / 63
132. Set of Training Data
Training Data
It consist of input-output pairs (x, y)
x= input signal
y= desired output
Thus, we have the following phases of designing a Neuronal Network
1 Choose appropriate architecture
2 Train the network - learning.
1 Use the Training Data!!!
3 Test the network with data not seen before
1 Use a set of pairs that where not shown to the network so the y
component is guessed.
4 Then, you can see how well the network behaves - Generalization Phase.
59 / 63
133. Set of Training Data
Training Data
It consist of input-output pairs (x, y)
x= input signal
y= desired output
Thus, we have the following phases of designing a Neuronal Network
1 Choose appropriate architecture
2 Train the network - learning.
1 Use the Training Data!!!
3 Test the network with data not seen before
1 Use a set of pairs that where not shown to the network so the y
component is guessed.
4 Then, you can see how well the network behaves - Generalization Phase.
59 / 63
134. Set of Training Data
Training Data
It consist of input-output pairs (x, y)
x= input signal
y= desired output
Thus, we have the following phases of designing a Neuronal Network
1 Choose appropriate architecture
2 Train the network - learning.
1 Use the Training Data!!!
3 Test the network with data not seen before
1 Use a set of pairs that where not shown to the network so the y
component is guessed.
4 Then, you can see how well the network behaves - Generalization Phase.
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135. Outline
1 What are Neural Networks?
Structure of a Neural Cell
Pigeon Experiment
Formal Definition of Artificial Neural Network
Basic Elements of an Artificial Neuron
Types of Activation Functions
McCulloch-Pitts model
More Advanced Models
The Problem of the Vanishing Gradient
Fixing the Problem, ReLu function
2 Neural Network As a Graph
Introduction
Feedback
Neural Architectures
Knowledge Representation
Design of a Neural Network
Representing Knowledge in a Neural Networks
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136. Representing Knowledge in a Neural Networks
Notice the Following
The subject of knowledge representation inside an artificial network is very
complicated.
However: Pattern Classifiers Vs Neural Networks
1 Pattern Classifiers are first designed and then validated by the
environment.
2 Neural Networks learns the environment by using the data from it!!!
Kurt Hornik et al. proved (1989)
“Standard multilayer feedforward networks with as few as one hidden layer
using arbitrary squashing functions are capable of approximating any Borel
measurable function” (Basically many of the known ones!!!)
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137. Representing Knowledge in a Neural Networks
Notice the Following
The subject of knowledge representation inside an artificial network is very
complicated.
However: Pattern Classifiers Vs Neural Networks
1 Pattern Classifiers are first designed and then validated by the
environment.
2 Neural Networks learns the environment by using the data from it!!!
Kurt Hornik et al. proved (1989)
“Standard multilayer feedforward networks with as few as one hidden layer
using arbitrary squashing functions are capable of approximating any Borel
measurable function” (Basically many of the known ones!!!)
61 / 63
138. Representing Knowledge in a Neural Networks
Notice the Following
The subject of knowledge representation inside an artificial network is very
complicated.
However: Pattern Classifiers Vs Neural Networks
1 Pattern Classifiers are first designed and then validated by the
environment.
2 Neural Networks learns the environment by using the data from it!!!
Kurt Hornik et al. proved (1989)
“Standard multilayer feedforward networks with as few as one hidden layer
using arbitrary squashing functions are capable of approximating any Borel
measurable function” (Basically many of the known ones!!!)
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139. Rules Knowledge Representation
Rule 1
Similar inputs from similar classes should usually produce similar
representation.
We can use a Metric to measure that similarity!!!
Examples
1 d (xi, xj) = xi − xj (Classic Euclidean Metric).
2 d2
ij = (xi − µi)T −1
xj − µj (Mahalanobis distance) where
1 µi = E [xi] .
2 = E (xi − µi) (xi − µi)
T
= E xj − µj xj − µj
T
.
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140. Rules Knowledge Representation
Rule 1
Similar inputs from similar classes should usually produce similar
representation.
We can use a Metric to measure that similarity!!!
Examples
1 d (xi, xj) = xi − xj (Classic Euclidean Metric).
2 d2
ij = (xi − µi)T −1
xj − µj (Mahalanobis distance) where
1 µi = E [xi] .
2 = E (xi − µi) (xi − µi)
T
= E xj − µj xj − µj
T
.
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141. Rules Knowledge Representation
Rule 1
Similar inputs from similar classes should usually produce similar
representation.
We can use a Metric to measure that similarity!!!
Examples
1 d (xi, xj) = xi − xj (Classic Euclidean Metric).
2 d2
ij = (xi − µi)T −1
xj − µj (Mahalanobis distance) where
1 µi = E [xi] .
2 = E (xi − µi) (xi − µi)
T
= E xj − µj xj − µj
T
.
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142. More
Rule 2
Items to be categorized as separate classes should be given widely different
representations in the network.
Rule 3
If a particular feature is important, then there should be a large number of
neurons involved in the representation.
Rule 4
Prior information and invariance should be built into the design:
Thus, simplify the network by not learning that data.
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143. More
Rule 2
Items to be categorized as separate classes should be given widely different
representations in the network.
Rule 3
If a particular feature is important, then there should be a large number of
neurons involved in the representation.
Rule 4
Prior information and invariance should be built into the design:
Thus, simplify the network by not learning that data.
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144. More
Rule 2
Items to be categorized as separate classes should be given widely different
representations in the network.
Rule 3
If a particular feature is important, then there should be a large number of
neurons involved in the representation.
Rule 4
Prior information and invariance should be built into the design:
Thus, simplify the network by not learning that data.
63 / 63