Update README.md

README.md

@@ -3,7 +3,7 @@ neural network  built on a scalar engine rather than regular tensor engine
 
 ## scalar.py
 
-This is a simple Python class named `Scalar` which represents scalar values and supports basic arithmetic operations and some elementary mathematical functions along with automatic differentiation for gradient computation.
+This is a simple Python class named `Scalar` which represents scalar values and helps in implementing backpropagation on small neural networks representing arithmetic expressions.
 
 ### Features
 
@@ -13,6 +13,66 @@ This is a simple Python class named `Scalar` which represents scalar values and
 - Automatic differentiation for gradient computation using backpropagation.
 - Support for building computational graphs and computing gradients for scalar-valued expressions.
 
+### Comparison between pytorch and Scalar usage
+
+- Implementing \[
+w_1 \cdot x_1 + w_2 \cdot x_2 + b
+\]
+where \( w_1 \), \( w_2 \) are weights, \( x_1 \), \( x_2 \) are inputs, and \( b \) is the bias and a backward pass to evaluate gradients in pytorch
+
+```python
+import torch
+
+x1 = torch.Tensor([2.0]).double()
+x2 = torch.Tensor([0.0]).double()
+w1 = torch.Tensor([-3.0]).double()
+w2 = torch.Tensor([1.0]).double()
+b = torch.Tensor([6.8813735870195432]).double()
+
+x1.requires_grad = True
+x2.requires_grad = True
+w1.requires_grad = True
+w2.requires_grad = True
+b.requires_grad = True
+
+n = x1*w1 + x2*w2 + b
+o = torch.tanh(n)
+
+print('o: ',o.item())
+
+o.backward()
+
+print('x2',x2.grad.item())
+print('x1',x1.grad.item())
+print('w1',w1.grad.item())
+print('w2',w2.grad.item())
+```
+Now implementing the same in Scalar :
+
+```python
+x1 = Scalar(2.0,label='x1')
+x2 = Scalar(0.0,label='x2')
+
+w1 = Scalar(-3.0,label='w1')
+w2 = Scalar(1.0,label='w2')
+
+b = Scalar(6.8813735870195432,label='b')
+
+x1w1 = x1*w1
+x1w1.label='x1*w1'
+x2w2 = x2*w2 
+x2w2.label = 'x2*w2'
+
+x1w1x2w2 = x1w1 + x2w2
+x1w1x2w2.label = 'x1w1+x2w2'
+
+n = x1w1x2w2 + b
+n.label = 'n'
+o = n.tanh()
+o.label = 'o'
+o.backward()
+```
+
 ### Usage
 
 You can use the `Scalar` class to perform arithmetic operations, compute mathematical functions, and automatically calculate gradients. Here's a brief overview of how to use it: