All the data science practitioners and machine learning developers are starving for higher accuracy and faster convergence of their neural networks. Building a neural is a combination of different processes. like pushing optimal data, pushing optimal layers in the networks are the tasks that define the upcoming convergence of neural networks. By applying some changes we can make our neural network converge faster. In this article, we are going to discuss what these methods are. The major points to be discussed in the article are listed below.

Table of content 

1. What is converge in neural network 
2. How can we make neural networks converge faster?    
   1. Learning type 
   2. Input normalization 
   3. Activation function  
   4. Learning rate 

Let’s first discuss convergence in neural network

What is convergence in neural networks?

In general, we can define convergence as the meeting points of two or more people or things that are already moving toward each other. When it comes to machine learning and deep learning we can consider people or things as the layer of the models and decision about any sample as the meeting point. Most of the time we want to make neural networks converge faster and In the field of machine learning, there can be various senses of word converge but we mainly focus on two senses 

• Adaptive converge: this sense of converge word represents the weights of the network during the training of the neural network. For example, as the neural network starts to find the values needed to produce means that converge is on.
• Reactive converge: this sense of converge word represents the propagation of signals within the network that consists of network feedback. We can also call it reactive feedback and there is no connection between reactive and adaptive converge. 

In a simple sense, we can say that the adaptive type represents the convergence of weights and the reactive type represents the convergence of signal values. convergence of a neural network can be of two types and we want them to make it faster. Various techniques can help us in making it faster. In the next section, we will look at some of these techniques.     

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How can we make neural networks converge faster?

From the above discussion we can understand that to process faster with the network it is required to converge it faster and to do so there are various techniques that we need to follow while building or training neural networks. Before going on deep into this section, we need to know that there is no guarantee that the network will converge to a better solution. Some of  the techniques to make the neural network converge faster are as follows:

Learning type 

Talking about the learning type, we mainly find the implementation of stochastic and batch learning scenarios. Both of them help train our neural networks. Let’s discuss a general introduction of both of these learning methods.

Stochastic gradient descent:  this type of learning sometimes can also be referred to as online gradient descent or online learning and we normally estimate the error gradient in it where a single sample from the training data is selected and after calculation of the error we update the weights of the model we also call weights as a parameter. More details about this training can be found here.

Batch learning: We also call this learning batch learning. In this type of learning, we train the models in a batch manner and push the model into production at regular intervals based on the performance of the model with batch data or new data. More details about this type of training can be found here. 

Both of these learning methods have different convergence rates. We can differentiate between these learning using the following points:

• Stochastic gradient descent is considered to be faster than batch learning.
• The accuracy of a model trained with SGD learning is better than batch learning.
• SGD is more convenient in tracking the changes in weights and signals.
• Batch learning has better conditions of convergence.
• Most of the acceleration mechanism works with batch learning.
• Convergence rates are simpler in batch learning.

It is suggested to prefer SGD learning over batch learning because it makes our neural network converge faster with the large datasets.

Input normalization 

This method is also one of the most helpful methods to make neural networks converge faster. In many of the learning processes, we experience faster training when the training data sum to zero. We can normalize the input data by subtracting the mean value from each input variable. We can also call this process centring.  Normalization also affects the speed of convergence for example convergence of a neural network can be faster if the average input variable values are near zero. 

In the processes of modelling, we can also observe the effect of centring when the input data is transferred to the hidden layer from the prior layers. One more thing which is noticeable here is that normalization mostly works properly with batch training. So if batch training is applied in the neural networks we can make it converge faster using the input normalization and the whole process can be called batch normalization. 

In input normalization, we also find the usage of principal component analysis for decorrelating the data. Decorrelating is the process of removing linear dependencies between the variables and here it should only work with input variables to remove the linear dependencies between input variables. 

Input normalization consists of three transformations of the data 

• Centring 
• Scaling 
• Decorrelating

These transformations are very helpful in making neural network convergence faster.

Activation function 

Information about different activation functions can be found here. In this section, we are going to compare these activation functions in terms of making neural network convergence faster. 

One of the very basic things about the sigmoid function is that it makes the neural network capable of dealing better with nonlinear input and it is the most common form of the activation function. In the list of sigmoid functions, we see that hyperbolic tangent sigmoid makes neural networks converge faster than the standard logistic sigmoid function. If not using these standard functions we can use ReLU activation to converge faster.

Learning rate 

Learning rate is also one of the major factors that work for the speed of convergence of the neural network. We can also consider the learning rate as the update in the weights of parameters of neural networks. Convergence and accuracy of the model can be considered inversely proportional. It means if the learning rate is higher there can be a faster convergence but less optimal accuracy while with a small learning rate we can expect that the accuracy will be higher but the convergence will be slower. 

By looking at the above situation we can say that we need to fix the learning rate in a dynamic nature so that when the parameter vector oscillates, the learning rate should be slower and when it is steady then the learning rate should be higher.

One more method to adjust the optimal learning rate is to use an adaptive learning rate. This kind of learning rate can also be considered as applying different learning rates at each parameter of the neural network. The adaptive learning rate has proven the faster convergence of neural networks by making the convergence of weights at the same speed.

Final words 

In the article, we have seen some techniques to make the neural network converge faster. We can say that these techniques are smaller changes in the network of data. Along with this we also see what can be the difference in our network by applying these technologies.