Contents

- 1 What role does the back-propagation error have in training a neural network?
- 2 How is the training algorithm performed in back-propagation neural networks?
- 3 How to train a neural network using back propagation?
- 4 What is the time complexity of backpropagation algorithm for training?
- 5 Why do we separate training and inference phases of neural networks?
- 6 How is the time complexity of a neural network calculated?

## What role does the back-propagation error have in training a neural network?

Back-propagation is just a way of propagating the total loss back into the neural network to know how much of the loss every node is responsible for, and subsequently updating the weights in such a way that minimizes the loss by giving the nodes with higher error rates lower weights and vice versa.

## How is the training algorithm performed in back-propagation neural networks?

The algorithm is used to effectively train a neural network through a method called chain rule. In simple terms, after each forward pass through a network, backpropagation performs a backward pass while adjusting the model’s parameters (weights and biases).

## How to train a neural network using back propagation?

The back-propagation algorithm proceeds as follows. Starting from the output layer l → k, we compute the error signal, E l t, a matrix containing the error signals for nodes at layer l where ⊙ means element-wise multiplication. Note that E l t has l rows and t columns: it simply means each column is the error signal for training example t.

## What is the time complexity of backpropagation algorithm for training?

In a single layer with input dimension n and output dimension m, the forward and reverse propagations will always be O ( n m d) assuming a naive matrix product algorithm. Sum this over all layers to get the time for a single backprop computation. The time complexity of a single iteration depends on the network’s structure.

## Why do we separate training and inference phases of neural networks?

In order to motivate why we separate the training and inference phases of neural networks, it can be useful to analyse the computational complexity. This essay assumes familiarity with analytical complexity analysis of algorithms, and hereunder big-O notation.

## How is the time complexity of a neural network calculated?

First thing to remember is time-complexity is calculated for an algorithm. An algorithm takes an input and produces an output. Now in case of neural networks, your time complexity depends on what you are taking as input. Case 1: Input is just the dataset. Architecture and hyperparameters are fixed in the algorithm.