Most important factor for learning rate in neural network, in this article, will be diligently outlined for your consumption and enrichment of your overall understanding of the field. What is a neural network and where do we use it often?

**Neural Network**

A neural network is a model inspired by the neuronal organization found in the biological neural networks in animal brains.

It is also a method in artificial intelligence that teaches computers to process data in a way that is inspired by the human brain. The element that is made of connected units or nodes called artificial neurons, which loosely model the neurons in a brain, is identified as an ANN. An artificial neuron receives signals from connected neurons, then processes them and sends a signal to other connected neurons.

The said signal is oftentimes a real number, and the output of each neuron is computed by some non-linear function of the sum of its inputs, called the activation function. This artificial neural networks are used for predictive modeling, adaptive control, and other applications where they can be trained via a dataset.

They are also used to solve **problems** in artificial intelligence. Networks can learn from experience, and can derive conclusions from a complex and seemingly unrelated set of information.

How are neural networks trained? They are typically trained through empirical risk minimization. This method is based on the idea of optimizing the network’s parameters to minimize the difference, or empirical risk, between the predicted output and the actual target values in a given dataset.

**Most Important Factor for Learning Rate in Neural Network**

First of all, it is simply the most important hyperparameter in a neural network. It can be found in any optimization algorithm such as RMSprop, Adam, Gradient descent, etc. Choosing this rate is challenging as a value too small may result in a long training process that could get stuck, whereas a value too large may result in learning a sub-optimal set of weights too fast or an unstable training process.

The definition given of the neural network learning rate will bring us to the most important factor for learning it wisely and more effectively.

**Factor: Problem**

There are multiple ways to select a good starting point for the learning rate. A naive approach is to try a few different values and see which one gives you the best loss without sacrificing speed of training. We might start with a large value like 0.1, then try exponentially lower values: 0.01, 0.001, etc.

When we start training with a large learning rate, the loss doesn’t improve and probably even grows while we run the first few iterations of training. When training with a smaller learning rate, at some point the value of the loss function starts decreasing in the first few iterations.

This learning rate is the maximum we can use, any higher value doesn’t let the training converge. Even this value is too high: it won’t be good enough to train for multiple epochs because over time the network will require more fine-grained weight updates. Therefore, a reasonable learning rate to start training from will be probably 1–2 orders of magnitude lower.

Selecting a starting value for it is just one part of the problem. Another thing to optimize is the learning schedule: how to change it during training. The conventional wisdom is that it should decrease over time, and there are multiple ways to set this up: step-wise learning rate annealing when the loss stops improving, exponential learning rate decay, cosine annealing, etc.

**WHY IS LEARNING RATE IMPORTANT?**

The learning rate has a significant impact on the quality and speed of the training process. If the learning rate is too high, the network may overshoot the minimum of the loss function and diverge, resulting in unstable and inaccurate predictions.

If the learning rate is too low, the network may take too long to converge or get stuck in a local minimum, resulting in suboptimal and slow performance. Therefore, the learning rate should be neither too high nor too low, but just right for the network to learn effectively and efficiently.

### Role of the Neural Network in Optimization

**1. Gradient Descent**

In gradient descent, the learning rate determines the size of the steps taken in the direction opposite to the gradient.

**2. Stochastic Gradient Descent (SGD)**

In stochastic gradient descent, the rate influences the step size for each mini-batch.

**3. Optimization Algorithms**

Various **optimization** algorithms, like Adam and RMSprop, adaptively adjust the learning rate during training.

**Effects of the Learning Rate on Optimization**

1. With a large learning rate (on the right), the algorithm learns fast, but it may also cause the algorithm to oscillate around or even jump over the minima. Even worse, a high learning rate equals large weight updates, which might cause the weights to overflow;

2. On the contrary, with a small learning rate (on the left), updates to the weights are small, which will guide the optimizer gradually towards the minima. However, the optimizer may take too long to converge or get stuck in a plateau or undesirable local minima;

3. A good rate is a tradeoff between the coverage rate and overshooting (in the middle). It’s not too small so that our algorithm can converge swiftly, and it’s not too large so that our algorithm won’t jump back and forth without reaching the minima.

**Choosing Learning Rates**

One simple way to choose the learning rate is to try different values and observe their effects on the training process. You can start with a small value, such as 0.01, and increase or decrease it by a factor of 10 until you find a value that works well for your network.

You can monitor the learning curves, which plot the loss and accuracy values against the number of epochs or iterations, to see how the network behaves with different learning rates. You can also check the gradients and weights of the network to see if they are converging or exploding.

Another way to choose the learning rate is to use a learning rate decay method, which reduces the rate over time as the network gets closer to the minimum of the loss function. This way, you can start with a relatively high learning rate to speed up the initial learning, and then gradually lower it to avoid overshooting and oscillating around the minimum.

There are different types of its decay methods, such as step decay, exponential decay, inverse time decay, and adaptive decay. You can use a predefined schedule or a dynamic rule to adjust the learning rate according to the progress of the training.

A more advanced way to choose the learning rate is to use its finder method, which uses a heuristic to find a range of good learning rates for your network. The idea is to start with a very low learning rate and increase it exponentially until the loss starts to increase rapidly.

Then, you can plot the loss against the rate and look for the point where the loss decreases the most. This point is usually a good estimate of the optimal rate of learning, or at least a lower bound for it. You can also use a slightly higher value as an upper bound for the learning rate range.