Journey LLM: MP Neuron Model

McCulloch-Pitts Neuron: The first computational model of a neuron was proposed by Warren McCulloch and Walter Pitts in 1943. This model imitates the functionality of a biological neuron , thus also known as Artificial Neuron. An artificial neuron accepts binary inputs and produces a binary output based on a certain threshold value which can be adjusted.

Characteristics of MP Model can be understood from seven topics namely Data, Model, Task, Loss, Learning, Evaluation and Geometric Interpretation. Lets dig further into them.

1. Data: Inputs belong to discrete set of values {0,1}. Hence input data will always contain binary values 0 or 1. If our input features contain non-binary features then we need to convert them to Boolean.

mobile_rating_prediction_PerceptronNeuron/data_mp_neuron.csv at…

2. Model:

Ahh !!! This is where it all get started with

g, aggregates the inputs and function f takes a decision based on these aggregations. These inputs can be excitatory or inhibitory.

y=0 if inputs are inhibitory ( think like an override functionality)

b is a threshold value, it is adjusted with aim of maximizing the number of correct predictions

3. Task: We need to identify the relationship between output variable (y) and inputs

4. Loss: Loss can also be calculated as yi — yi(hat) , however this will result cancelling the values between each other . Hence, Loss Function will be defined as

5. Learning : In this case we have only one parameter to learn i.e. b, so we can perform brut force search. Lets say we have n features, then b can vary from 0 to n . b will always have discrete value, as inputs are also discrete values {0,1}

6. Evaluation: The model can be evaluated by accuracy score.

Accuracy = Number of correct predictions/ Total number of predictions

7. Geometric Interpretation:

In order to understand geometric interpretation for this model, lets understand some basics about line

2D: General Form of line is defined as

Consider a=2 , b=1 , c=-2 , the intercepts are 1 and 2, plugging into the equation gives us the value 2

This model is a very restrictive model due to availability of only one parameter.

Conclusion:

This model has various downsides as mentioned below

1. Boolean inputs and outputs
2. Model is linear
3. Model has fixed slope
4. Model has few possible intercepts (b’s)

As we have seen that MP Neuron Model have various disadvantages, we will try to overcome those limitations by introducing Perceptron Model. Perceptron Model was developed by Frank Rosenblatt in 1957. This is tweaked version of artificial neuron and also called as Linear Threshold Unit. This model can work on non boolean values where each input connection gets associated with weight. Here the function calculates the weighted sum and based on threshold value provided, it gives binary output.

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