LEC 3 A basic abstract model for a biological neuron

1. Weights of connections

Neuron gets fired if it has received from the presynaptic neurons 突触前神经元 a summary impulse 脉冲, which is above a certain threshold.

Signal from a single synapse突触 may sometime overcome the threshold and push a neuron to fire an action potential, but other synapses can achieve this only by simultaneously delivering their signals: Some inputs are more important!

定义：

Therefore, input from every synapse, or “connection”, to the neuron in the abstract model must be assigned with some value w, called connection strength or weight of connection, to describe the importance of a connection.

2. Model

1. The abstract neuron is excited when weighted sum is above the threshold 0

vs. 

The biological neuron is excited when the signal density (spatial or temporal summation) is above the excitation potential threshold.

2. Output is either 1 or 0. 

vs. 

Only the spikes（峰值）are remembered

LEC 4

Topic 2. The McCulloch-Pitts Neuron (1943) 

1. McCulloch and Pitts demonstrated that 

“...because of the all-or-none character of nervous activity, neural events and the relations among them can be treated by means of the propositional logic”. 

2. The authors modelled the neuron as

      a.  a binary, discrete-time input

       b. discrete-time：

The basic idea was to divide time into units, i.e., steps, and in each time period at most one spike can be initiated in the axon of a given neuron

将时间分成单位和步骤，每个时间一个神经元的轴突最多产生一次峰值

uniform velocity 脉冲基本都以匀速传播

Thus, the McCulloch-Pitts neuron operates on a discrete time scale, 

t = 0,1,2,3, …

        c. binary input:

The types of the input and the output of a MP neuron are thus unified.

        d. with excitatory and inhibitory connections 有着兴奋和抑制之间的联系 and an excitation threshold. 兴奋阙值

The network of such elements was the first model to tie the study of neural networks to the idea of computation in its modern sense.

将神经网络和现代意义上的计算思想联系起来

         e. with excitatory and inhibitory connections 有着兴奋和抑制之间的联系 and an excitation threshold. 兴奋阙值

         f. The network of such elements was the first model to tie the study of neural networks to the idea of computation in its modern sense. 将神经网络和现代意义上的计算思想联系起来

        g. excitatory and inhibitory connections :

The weight of connection wi are:

 +1 for excitatory type connection and 加一促进

Cerebral pyramidal cell：

 -1 for inhibitory type connection. 减一抑制

    h. Threshold

     I. MP Neuron

In the MP neuron, we call the instant total input

St-1: instant state of the neuron

    j. Actication Function