What is the Hopfield model of neural network ? Explain its algorithm and differentiate discrete and continuous Hopfield model in terms of energy landscape and stable state.
1 Answer


Hopfield model:

Fig: Hopfield model with four node

Distinguishing features*:*

  1. Fully connected networks of neuron
  2. Bi-directional connections
  3. Symmetric weights {Wij=Wji}
  4. Neurons are linear threshold elements
  5. Asynchronous (most common) / Synchronous Operation
  6. Computes by Energy Minimization (unlike error reduction as in Back Propagation)
  7. Mostly used as Content Addressable Memory (CAM) and in optimization
  8. The network oscillates duw to feedback connections
  9. The feed-forward network is a mapping device whereas the Hopfield Net is a CAM
  10. The Hopfield Net Oscillates due to feedback connections but reached some stable state due to energy minimization
  11. Hopfield Net behaves as an N-stable multivibrator.
  • "The state of neuron does not depend on its previous state but on the previous states of other neurons in the network". This makes the design of Hopfield Net difficult to conceptualize (OTR).
  • The neurons at any part of the network at any point in time lok at the rest of the network and the input arriving from it and fire or inhibit.

Modes of operation:

  • Asynchronous Mode: In the asynchronous operation, one single neuron (randomly selected) will examine its net input and assume +1 -1 state depending upon the inputs weights and equality.
  • Synchronous Mode: In the synchronous mode all neurons fire together and assume +1 -1 state accordingly. The central concern is to stabilize a pattern in the network.

Hardware realization of Hopfield Net with switching devices:

  • Individual neurons may be treated as binary switching devices.
  • In addition to their network connections, each neuron will have provisions to set and read the activation state of that neuron at any point t in time.
  • Collection of all the inputs of each neuron in the Net forms the imposed state patterns.
  • Collection of all the outputs of each neuron in the Net forms the state of the Hopfield Net.

Software realization of Hopfield Net with variables:

  • The activation of each neuron may be treated as a memory variable which can be set and sensed.
  • By setting some value for all the inputs to each neuron in the net can be pattern in the Hopfield Net can be sensed.
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