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### Problem Set 5 (2.6 - 16.6.08)

#### Exercise 1

In this exercise we want to implement a standard Hopfield net (see lecture) and analyze it's memory capabilities.

- Implement a Hopfield network that can be trained with the standard learning rule (either asynchronous or synchronous).
- Find a sensible way to plot the reconstruction capabilites of the network as a function of L (the number of trained patterns) and N (the number of nodes).
- Try to verify the theoretical result that the memory capacity of a Hopfield net is limited by L/N < 0.138 (i.e. reconstruction only works well if the number of stored patterns does not exceed approximately 14 percent of the number of nodes). Of course you do not have to reach this level of precission.