# Neural Networks - Hopfield Net Dynamics

In the book by K.Du, "Neural Networks and Machine Learning", Springer, 2014, p.159", the Hopfied dynamics equation (in discrete network model) is given as

$$net_{i}(t+1) = \sum_{i=1}^{J}x_{i}(t)w_{ij} + \theta{i}$$

Where: $x_{i}(t + 1) = \theta(net_{i}(t + 1))$,

$net_{i}$ is the weighted net input of the i-th neuron, xi (t) is the output of the i-th neuron and $\theta$ the threshold of the neuron. The above Hopfield net consists of a total of $J$ perceptrons and t notates time-state in the network.

The net input of the perceptron (McCulloch-Pitts model) is given by

$$\sum_{i=1}^{n}x_{i}w_{i} - \theta$$

In this model, it seems perfectly logical to detract the threshold of the nuron from the total collected weight.

However why in the hopfield dynamics equation Du adds the threshold instead of substrating it?

• If you read the text it says that $\theta_i$ is a bias to the neuron. It's not a threshold. – Chantry Cargill Nov 22 '15 at 13:17
• bias $\neq$ threshold ? – Rrjrjtlokrthjji Nov 22 '15 at 13:30
• I'm not familiar with your text and I have only learned about basic neural networks, but I believe threshold indicates when a neuron fires, whereas a bias artificially changes the strength of a neuron. I'm not entirely certain though, which is why I comment. – Chantry Cargill Nov 22 '15 at 13:40
• Threshold : The threshold potential is the critical level to which the membrane potential must be depolarized in order to initiate an action potential. Eg the pain threshold, when you pinch your hand, pain starts to be felt after $f > \theta$, where $\theta$ is the threshold. – Rrjrjtlokrthjji Nov 22 '15 at 14:25
• An answer at SE stackoverflow.com/questions/18353295/… states that threshold and bias are the same concepts. – Rrjrjtlokrthjji Nov 22 '15 at 14:26