📚Common Concepts

Basic Concepts of ANN

🍭 Basic Neural Network

Convention: The NN in the image called to be a 2-layers NN since input layer is not being counted 📢❗

📚 Common Terms

Term	Description
🌚 Input Layer	A layer that contains the inputs to the NN
🌜 Hidden Layer	The layer(s) where computational operations are being done
🌝 Output Layer	The final layer of the NN and it is responsible for generating the predicted value ŷ
🧠 Neuron	A placeholder for a mathematical function, it applies a function on inputs and provides an output
💥 Activation Function	A function that converts an input signal of a node to an output signal by applying some transformation
👶 Shallow NN	NN with few number of hidden layers (one or two)
💪 Deep NN	NN with large number of hidden layers
$n^{[l]}$	Number of units in l layer

🧠 What does an artificial neuron do?

It calculates a weighted sum of its input, adds a bias and then decides whether it should be fired or not due to an activaiton function

My detailed notes on activation functions are here 👩‍🏫

👩‍🔧 Parameters Dimension Control

Parameter	Dimension
$w^{[l]}$	$(n^{[l]},n^{[l-1]})$
$b^{[l]}$	$(n^{[l]},1)$
$dw^{[l]}$	$(n^{[l]},n^{[l-1]})$
$db^{[l]}$	$(n^{[l]},1)$

Making sure that these dimensions are true help us to write better and bug-free :bug: codes

🎈 Summary of Forward Propagation Process

Input:	$a^{[l-1]}$
Output:	$a^{[l]}, chache (z^{[l]})$

👩‍🔧 Vectorized Equations

$Z^{[l]} =W^{[l]}A^{[l-1]}+b^{[l]}$ $A^{[l]} = g^{[l]}(Z^{[l]})$

🎈 Summary of Back Propagation Process

Input:	$da^{[l]}$
Output:	$da^{[l-1]}, dW^{[l]}, db^{[l]}$

👩‍🔧 Vectorized Equations

$dZ^{[l]}=dA^{[l]} * {g^{[l]}}'(Z^{[l]})$

$dW^{[l]}=\frac{1}{m}dZ^{[l]}A^{[l-1]T}$

$db^{[l]}=\frac{1}{m}np.sum(dZ^{[l]}, axis=1, keepdims=True)$

$dA^{[l-1]}=W^{[l]T}dZ^{[l]}$

➰➰ To Put Forward Prop. and Back Prop. Together

😵🤕

✨ Parameters vs Hyperparameters

👩‍🏫 Parameters

• $W^{[1]}, W^{[2]}, W^{[3]}$

• $b^{[1]}, b^{[2]}$

• ......

👩‍🔧 Hyperparameters

• Learning rate

• Number of iterations

• Number of hidden layers

• Number of hidden units

• Choice of activation function

• ......

We can say that hyperparameters control parameters 🤔