McCulloch-Pitts Neuron Model (1943)

In 1943, Warren McCulloch and Walter Pitts published the paper "A Logical Calculus of the Ideas Immanent in Nervous Activity" in the Bulletin of Mathematical Biophysics. This work created the first mathematical model of a biological neuron.

The Original Model

The McCulloch-Pitts (M-P) neuron was a simplified computational model that captured the essential behavior of biological neurons:

Mathematical Formulation

Output = 1, if Σ(wᵢ × xᵢ) >= θ
Output = 0, otherwise

Where:

• xᵢ = input signals (binary: 0 or 1)
• wᵢ = weights (can be positive or negative)
• θ (theta) = threshold value
• Σ = summation of all weighted inputs

Visual Representation

Key Characteristics

1. Binary Inputs and Outputs

• All inputs are either 0 (inactive) or 1 (active)
• Output is also binary: 0 or 1

2. Weighted Connections

• Each input has an associated weight
• Positive weights = excitatory (promote firing)
• Negative weights = inhibitory (prevent firing)

3. Threshold Mechanism

• The neuron only fires if the weighted sum meets or exceeds the threshold
• This mimics the "all-or-nothing" behavior of real neurons

4. Fixed Weights

• Original model had fixed weights (not learnable)
• Learning came later with the Perceptron (Rosenblatt, 1958)

Example: AND Logic Gate

Example: OR Logic Gate

Inhibitory Inputs

The M-P neuron supported inhibitory inputs — if any inhibitory input is 1, the neuron cannot fire:

Output = 1, if Σ(excitatory inputs) >= θ AND (no inhibitory input = 1)
Output = 0, otherwise

This mimics how some synapses can prevent a neuron from firing.

Limitations of the Original Model

1. No Learning: Weights were manually set, not learned
2. Binary Only: Cannot process continuous values
3. No Temporal Dynamics: Doesn't model timing of signals
4. Simplified Activation: Only threshold function used