---
license: apache-2.0
library_name: pytorch
---

# a-and-not-b

A neuron that performs the A AND (NOT B) logical computation. It generates the following truth table:

| A | B | C |
| - | - | - |
| 0 | 0 | 0 |
| 0 | 1 | 0 |
| 1 | 0 | 1 |
| 1 | 1 | 0 |

It is inspired by McCulloch & Pitts' 1943 paper 'A Logical Calculus of the Ideas Immanent in Nervous Activity'.

It doesn't contain any parameters.

It takes as input two column vectors of zeros and ones. It outputs a single column vector of zeros and ones.

Its mechanism is outlined in Figure 10-3 of Aurelien Geron's book 'Hands-On Machine Learning with Scikit-Learn, Keras, and TensorFlow'.

![](https://raw.githubusercontent.com/sambitmukherjee/handson-ml3-pytorch/main/chapter10/Figure_10-3.png)

Like all the other neurons in Figure 10-3, it is activated when at least two of its input connections are active.

Code: https://github.com/sambitmukherjee/handson-ml3-pytorch/blob/main/chapter10/logical_computations_with_neurons.ipynb

## Usage

```
import torch
import torch.nn as nn
from huggingface_hub import PyTorchModelHubMixin

# Let's create two column vectors containing `0`s and `1`s.
batch = {'a': torch.tensor([[0], [0], [1], [1]]), 'b': torch.tensor([[0], [1], [0], [1]])}

class A_AND_NOT_B(nn.Module, PyTorchModelHubMixin):
    def __init__(self):
        super().__init__()
        self.operation = "C = A AND (NOT B)"

    def forward(self, x):
        a = x['a']
        b = x['b']
        b = -1 * b
        inputs = torch.cat([a, a, b], axis=1)
        column_sum = torch.sum(inputs, dim=1, keepdim=True)
        output = (column_sum >= 2).long()
        return output

# Instantiate:
a_and_not_b = A_AND_NOT_B.from_pretrained("sadhaklal/a-and-not-b")

# Forward pass:
output = a_and_not_b(batch)
print(output)
```