Fitting a best-fit neural network to a model goes through various kinds of optimization processes. These processes help in determining and defining the accuracy, reliability, functionality and capability of the model. Convergence of the neural network helps in defining how many iterations of training a neural network will require to produce minimum errors. Sometimes we find that a neural network fails to converge. In this article, we are going to discuss what happens and what should we do when a neural network fails to converge. The major points to be discussed in the article are listed below.

**Table of contents**

- Working of deep learning models
- Convergence in deep learning models
- The causes which fail the model to converge
- Why does a NN fail to converge?
- Remedies of convergence failure

Let’s start by understanding the working of neural networks.

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**Working of deep learning models **

In general deep learning modelling, we formulate a problem using the neuron and layers of the network and expect the problem to come up with a loss function. At the same time, the training of models includes weights as parameters. When including backpropagation with the model, the process of backpropagation starts when the errors defined by the loss function reach a defined point.

Every iteration in the training tries to reach closer to that point and at this point, the error value gets minimized by updating the weights. This model includes a set of weights associated with the loss function. The main goal of modelling is to find the minimum value loss at every iteration and overall operation.

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**Convergence in deep learning **

In simple words, we can say that convergence of neural networks is a point of training a model after which changes in the learning rate become lower and the errors produced by the model in training comes to a minimum. We can also say that a deep learning model is in convergence when the loss given by the model reaches its minimum. The convergence can be of two types either global or local. One thing that is noticeable here is that convergence should happen with a decreasing trend. However, In a variety of modelling procedures, it is very rare to see a model converge very strictly but it is common to see the model converge in a convex manner.

Mathematically we can consider convergence as a study of series and sequence. A model can be considered to be in convergence when the series is a converging series. As given below.

Lets say s(n)=lossWn(y^,y) is a converging series.

Where,

- Wn = set of weights after nth iteration
- s(n) = nth term of the series.

If we say that the loss = 0 then we can say the series we are calling converging is an infinite series. But loss = 0 is an ideal condition that can not be achieved but after convergence, the learning rate can keep getting smaller.

The above image is a representation of the convergence where we can see that the training of the model after the 20th iteration becomes converged and the errors after the 20th iteration are lower, decremental and within a smaller range.

By the above, we can say that the convergence in the model is important while training makes us decide whether to proceed with the model or not. One of our articles consists of information about how to converge the neural network faster. This article is focused on the information when the neural network fails to converge. Let’s take a look at what fails to converge means.

**The cause which fails the model to converge **

In simple words, we can think of failure in convergence as a condition where we can’t find the convergence point in the learning curve of a neural network. It directly means there is no such point in the curve which can be represented as the starting point of getting lower and decremental error. We can understand the failure in the convergence by looking at the below image.

In the above image, we can see that the errors are decremental as the count of iteration is increasing but one different thing is we can not tell from which point the error is varying within a smaller range. For what are the global or local minima of the errors? In such a situation, we can say that the neural network is failed to converge. Let’s see why it happens.

**Why does a neural net fail to converge?**

Most of the neural network fails to converge because of an error in the modelling. Let us say the data is required to transform within the network and the nodes we have provided in the networks are way smaller in number. In such a situation how can we expect the network to work properly? So in the majority of the cases when the network fails to converge, it comes into the picture because of inaccurate modelling. Some of the reasons behind this thing are as follows:

- Implementation of not enough nodes may be a reason behind this issue because models with fewer nodes need to change their architecture drastically to model the data better and fail to converge.
- The amount of the training data is low or the data we are pushing on the model is corrupted or not collected with the data integrity.
- The activation function we are using with the network often leads to good results from the model but if complexity is higher then the model can fail to converge.
- Inappropriate weight application in the network can also cause a failure in convergence. The weights we are applying to the network should be well calculated according to the activation function.
- The learning rate parameter we have given in the network should be moderate which means it should not be much larger or much lower.

**Remedies for convergence failure **

In the above section, we have discussed the reason that can cause failure in the convergence of the neural networks. There are various things to do that can help in avoiding this failure. Let’s take a look at some points that can help us in preventing the failure in the convergence of the neural networks.

- Implementing momentum: sometimes convergence depends on the data and if the data is making a model producing errors like a hair comb. The implementation of neural network momentum can help in avoiding convergence and also helps in boosting the accuracy and speed of the model.
- Reinitialization of the weights of the network can help in avoiding the failure of convergence.
- If the training is stuck in the local minima and subsequent sessions have exceeded max iteration, this means the session has failed and we will get a higher error. In such a situation starting another session can be helpful.
- Change in the activation function can be helpful. For example, we are using a ReLU activation and the neurons of the nodes become biased and this can cause the neuron to never be activated. In such a situation changing the activation function to another activation can be helpful.
- While performing classification using neural networks, then we can use the shuffling of the training data to avoid the failure in convergence.
- The learning rate and the number of epochs should be proportional while modelling a network. Applying a lower number of epochs causes the convergence to happen in smaller steps and a bigger number of epochs there will mean a long wait in the appearance of the convergence. A higher learning rate or the number of epochs should be avoided to make the neural network converge faster.

**Final words**

In this article, we have discussed the convergence in a neural network whose appearance makes us decide whether to use the network further or not and need to change some of the things. Along with this, we have discussed the reasons behind a neural network failing to converge and how we can avoid this failure.