Hopfield Network

The Hopfield networks are constructed from artificial neurons. These artificial neurons have 'N' number of inputs. With each input 'i' there is a weight associated which is wi. They also have an output. The state of the output is maintained till the neuron is updated. A Hopfield network is a network of N artificial neurons which are fully connected. There are two ways of updating the neurons and they are asynchronous random updating and synchronous updating. One of them picks one neuron then calculates the weighted input sum and updates immediately. This can be done in a fixed order or the neurons can be picked at random which is called asynchronous random updating. The weighted input sums of all the neurons are calculated without updating the neurons. Then all neurons are set to their new value according to the value of their weighted input sum.

Summary

The Hopfield networks are constructed from artificial neurons. These artificial neurons have 'N' number of inputs. With each input 'i' there is a weight associated which is wi. They also have an output. The state of the output is maintained till the neuron is updated. A Hopfield network is a network of N artificial neurons which are fully connected. There are two ways of updating the neurons and they are asynchronous random updating and synchronous updating. One of them picks one neuron then calculates the weighted input sum and updates immediately. This can be done in a fixed order or the neurons can be picked at random which is called asynchronous random updating. The weighted input sums of all the neurons are calculated without updating the neurons. Then all neurons are set to their new value according to the value of their weighted input sum.

Things to Remember

  • The hopfield networks are constructed from artificial neurons.
  • These artificial neurons have 'N' number of inputs. With each input 'i' there is a weight associated which is wi.
  • The state of the output is maintained til the neuron is updated.
  • A Hopfield network is a network of N artificial neurons which are fully connected. 
  • There are two ways of updating the neurons and they are asynchronous random updating and synchronous updating.
  • One of them picks one neuron then calculates the weighted input sum and updates immediately. This can be done in a fixed order or the neurons can be picked at random which is called asynchronous random updating.
  • The weighted input sums of all the neurons are calculated without updating the neurons. Then all neurons are set to their new value according to the value of their weighted input sum.

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Subjective Questions

Q1:

  1. What is the role of rendering engines in web browsers?
  2. How browser renders contents like text and images?

Type: Short Difficulty: Easy

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Hopfield Network

Hopfield Network

Hopfield Network

The Hopfield networks are constructed from artificial neurons as shown in the figure below. These artificial neurons have 'N' number of inputs. With each input 'i' there is a weight associated which is wi. They also have an output. The state of the output is maintained till the neuron is updated.

.

Updating the neuron entails the following operations:

  • The value of each input that is xi is determined and the weighted sum of all inputs Σi wixi is calculated.
  • The output state of the neuron is set to +1, if the weighted input sum is larger or equal to 0. It is set to -1, if the weighted input sum is smaller than 0.
  • A neuron retains the output state until it is updated again.
    Written as a formula:
    .

A Hopfield network is a network of N artificial neurons which are fully connected. The connection weight from neuron 'j' to neuron 'i' is given by a number wij . The collection of all such numbers is represented by the weight matrix 'W' whose components are wij . Now for the given weight matrix and the updating rule for neurons, the dynamics of the network is defined if the order is defined in which the neurons are updated. There are two ways of updating them:

  • Asynchronous: One of them picks one neuron then calculates the weighted input sum and updates immediately. This can be done in a fixed order or the neurons can be picked at random which is called asynchronous random updating.
  • Synchronous: The weighted input sums of all the neurons are calculated without updating the neurons. Then all neurons are set to their new value according to the value of their weighted input sum.

References:

  1. Elaine Rich, Kevin Knight 1991, "Artificial Intelligence".
  2. Nilsson, Nils J. Principles of Artificial Intelligence, Narosa Publishing House New Delhi, 1998.
  3. Norvig, Peter & Russel, Stuart Artificial Intelligence: A modern Approach, Prentice Hall, NJ, 1995
  4. Patterson, Dan W. Introduction to Artificial Intelligence and Expert Systems, Prentice Hall of India Private Limited New Delhi, 1998.

Lesson

Applications of AI

Subject

Computer Engineering

Grade

Engineering

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