Discrete Hopfield Network

Duration: 5 min

This video lesson is available to enrolled students.

Return to /learn/MPPSC-ASSISTANT-PROFESSOR-COMPUTER-SCIENCE-PAPER-2/current-trends-technologies/artificial-intelligence-artificial-neural-networks/training-of-hopfield-networks/asset-discrete-hopfield-network after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. About Course: About the Course
  2. Paper 1 | General Studies: State Wise GK
  3. Paper 1 | Information and Communication Technology: Role of Internet and Web Services, Security in Mobile and Wireless Computing
  4. Paper 1 | Current Affairs: GK- Current Affairs
  5. Paper 2 | Discrete Mathematical Structure: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic, Probability
  6. Paper 2 | Digital Computer Organization And Architecture: Number System, Number Representation, Sequential Circuits, Combinational Circuit, Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Register Transfer and Microoperations, Control Unit Design, Programming the Basic Computer
  7. Paper 2 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  8. Paper 2 | Programming Languages & Object-Oriented Programming Concepts: Java, OOPS with C++, Java Fundamentals, Array, String, IO & References
  9. Paper 2 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  10. Paper 2 | Data Structure And Algorithms: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Minimum Spanning Trees, Advanced Algorithms
  11. Paper 2 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Unix OS
  12. Paper 2 | Theory Of Computation: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Complexity Theory
  13. Paper 2 | Compiler Design: Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization, Run Time Environment
  14. Paper 2 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, Relational Algebra, SQL, Transaction Management, Concurrency Control, Database Recovery, Database Security & Authorization, Enhanced Data Models
  15. Paper 2 | Computer Network And Information Security: Introduction to CN, Data Communication, Application Layer, Hardware basics, Cyber Threats and Malware Attacks, Network Security, DLL: Access Control, DLL: Flow Control, DLL: Error Control, DLL: Framing, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP
  16. Paper 2 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  17. Paper 2 | Current Trends & Technologies: Emerging Tech Trends, Approaches to AI, Search Algorithms, Game Playing, Knowledge Representation, Planning, Multi Agent Systems, Fuzzy Sets, Natural Language Processing, Artificial Neural Networks, Genetic Algorithms, Artificial Intelligence, Data Warehousing & Mining, Electronic Data Interchange and E-Commerce, Terms & Abbreviations
  18. Paper 2 | Full Length Mock Tests:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

This lecture provides a comprehensive introduction to the Hopfield Network, a type of recurrent neural network. The instructor begins by defining the architectural constraints, emphasizing that neurons are fully interconnected without self-loops and that weights must be symmetric. The session covers the network's history, noting its invention by Dr. John J. Hopfield in 1982, and its key property of being auto-associative, capable of reconstructing data from corrupted inputs. The lecture then delves into the mathematical formulation for discrete Hopfield networks, defining the activation function and the structure of the weight matrix. Finally, it presents the training algorithm, specifically deriving the weight update rule for binary input patterns.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor starts by detailing the fundamental architecture of the Hopfield network using a slide with bullet points. She highlights that the output of each neuron serves as input to other neurons but explicitly excludes self-input. To illustrate this, she draws a diagram on the right side of the screen representing a single layer of neurons labeled Y1 through Yn. She writes 'one layer of neurons' and draws lines connecting them to show full connectivity. She annotates the connections with 'wij' and 'wji' to visually demonstrate the requirement that weights must be symmetrical, meaning the connection strength from neuron i to j is identical to j to i.

  2. 2:00 – 5:00 02:00-05:00

    The lecture shifts to the theoretical background and mathematical definitions. A slide appears stating the network was invented by Dr. John J. Hopfield in 1982 and possesses 'auto-associative properties,' allowing it to reconstruct data from corrupt versions. The instructor writes the discrete activation function on the board: yi equals +1 if the sum of weighted inputs is greater than or equal to zero, and -1 otherwise. She displays the weight matrix W, noting the zeros on the diagonal, and the input matrix X. The segment concludes by introducing the 'Training Algorithm' for binary input patterns, showing the formula for calculating the weight matrix based on stored patterns s(p).

  3. 5:00 – 5:06 05:00-05:06

    The video concludes with a close-up of the 'Training Algorithm' slide. The visible text displays the specific formula for the weight matrix when dealing with binary input patterns: the summation from p=1 to P of [2si(p) - 1][2sj(p) - 1], valid for i not equal to j. This formula represents the Hebbian learning rule adapted for this specific network type.

The lesson progresses logically from structural constraints to mathematical implementation. By first establishing that weights are symmetric and self-connections are zero, the instructor sets the stage for the energy function minimization inherent in Hopfield networks. The transition to the training algorithm shows how these structural rules are applied to store patterns. The specific formula for binary inputs converts the binary values (0, 1) into bipolar values (-1, 1) via the term [2si(p) - 1], ensuring the network operates correctly with the defined activation function. This connects the abstract architecture to the concrete mathematical operations required for training.

Loading lesson…