Answer
See the explanation
Work Step by Step
To design an artificial neural network for associative memory with a rectangular array of neurons aiming to stabilize a single vertical column of excited neurons, we can use a Hopfield network architecture.
Here's a basic outline of the design:
1. **Neuron Activation**: Each neuron in the rectangular array can be represented as a node. The activation of each neuron can be binary (0 or 1), indicating whether it's excited or not.
2. **Weight Matrix**: Create a weight matrix \( W \) where \( W_{ij} \) represents the weight between neuron \( i \) and neuron \( j \). Initialize the weight matrix with appropriate values. For associative memory, the weight matrix can be calculated using Hebb's rule or other learning algorithms.
3. **Activation Dynamics**: Update the activation of neurons iteratively based on the activation of neighboring neurons and the weight matrix. This can be done using synchronous or asynchronous updating schemes until the network reaches a stable state.
4. **Stable State**: The network is considered to have reached a stable state when the activation of neurons no longer changes with further iterations. At this point, ideally, only one vertical column of neurons should be excited.
5. **Pattern Retrieval**: To retrieve a pattern, initialize the activation of neurons with the desired pattern and let the network evolve until it stabilizes.
By following these steps, the artificial neural network can serve as an associative memory system where stable patterns with a single vertical column of excited neurons can be achieved.
