Discussion
Hopfield networks have the "energy", E, associated with them. Thus for Hopfield network with symmetric weights, this energy, E at each state may ................. .
Answer: C
The energy may decrease or remain same.
For a Hopfield network with symmetric weights and no self-connections, the energy is
\[ \begin{aligned} E = &-\tfrac{1}{2} \sum_{i} \sum_{j} w_{ij} s_i s_j \\ &+ \sum_{i} \theta_i s_i \end{aligned} \]
Each asynchronous update of a neuron either leaves its state unchanged or changes it in the direction that lowers E, so \(\Delta E \le 0\). The energy never increases, which is why the network settles into a stable state at a local minimum.
'Increase' and 'decrease or increase' contradict this, and 'decrease' alone ignores updates that leave the state, and so the energy, unchanged.
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