Regularization in Deep Learning: L1, L2 & Dropout

August 24, 2022

If you are developing a deep learning model, overfitting is the most prevalent word that comes to mind, whether you are a beginner or an expert in the area. Overfitting revolves around the perfectly fitting training data on the model and when this happens the algorithm fails to achieve its objective. This is where we need regularization techniques to deal with the overfitting problems.

This blog discusses the problem of overfitting and how regularization aids in the accomplishment of the goal of deep learning models.

The blog's structure is intended to focus on the following topics:

  1. What is overfitting?
  2. What is Regularization?
  3. Why Regularization?
  4. How does Regularization work? 
  5. Techniques of Regularization
  6. L1 Regularization 
  7. L2 Regularization
  8. The Key differences between L1 and L2 Regularization
  9. Dropout regularization
  10. Takeaways

What is Overfitting? 

Simply put, when a model trains on sample data for an excessively long time or becomes very complicated, it may begin to learn "noise," or unimportant information, from the dataset. The model becomes "overfitted" and unable to generalize successfully to new data when it memorizes the noise and fits the training set too closely. A model won't be able to carry out the classification or prediction tasks that it was designed for if it can't generalize successfully to new data.

What is Regularization? 

When completely new data from the problem domain is fed as an input into deep learning models, regularization is a collection of strategies that can assist prevent overfitting in neural networks and improve their accuracy by modifying the learning procedure slightly such that the model generalizes more successfully. The model then performs better on the unobserved data as a result.

Why Regularization? 

Through Regularization the bigger coefficient input parameters receive a "penalty", which ultimately reduces the variance of the model, and particularly in deep learning the nodes' weight matrices are penalized. With regularization, a more optimized and better accurate model for better output is achieved. 

How does Regularization work? 

When modeling the data, a low bias and high variance scenario is referred to as overfitting. To handle this, regularization techniques trade more bias for less variance. Effective regularization is one that strikes the optimal balance between bias and variation, with the final result being a notable decrease in variance at the least possible cost to bias. This would imply low variation without significantly raising the bias value, to put it another way.

Additionally, Regularization orders possible models from weakest overfit to biggest and adds penalties to more complicated models. Regularization makes the assumption that the least weights could result in simpler models and help prevent overfitting.

Techniques of Regularization 

So as we now have a better understanding of what overfitting is and how regularization helps in making deep learning models better and more effective, now let's shift our focus to the techniques that we need to use for regularization in deep learning.

L1 Regularization 

Essentially, the L1 regularizer searches for parameter vectors that minimize the parameter vector's norm (the length of the vector). The main issue here is how to best optimize the parameters of a single neuron, a single layer neural network generally, and a single layer feed-forward neural network specifically.

Since L1 regularization offers sparse solutions, it is the favored method when there are many features. Even so, we benefit from the computational advantage since it is possible to omit features with zero coefficients.

The mathematical representation for the L1 regularization is:

Here the lambda is the regularization parameter. Here we penalize the absolute value of the weights and weights may be reduced to zero. Hence L1 regularization techniques come very handily when we are trying to compress the deep learning model.

L2 Regularization 

By limiting the coefficient and maintaining all the variables, L2 regularization helps solve problems with multicollinearity (highly correlated independent variables). The importance of predictors may be estimated using L2 regression, and based on that, the unimportant predictors can be penalized.

The mathematical representation for the L2 regularization is:

The regularization parameter, in this case, is lambda. The value of this hyperparameter is generally tweaked for better outcomes. Since L2 regularization leads the weights to decay towards zero(but not exactly zero ), it is also known as weight decay.


The key differences between L1 and L2 Regularization

A regression model is referred to as Lasso Regression if the L1 Regularization method is used and Ridge Regression is the term used if the L2 regularization method is employed.

The penalty for L1 regularization is equal to the amount of the coefficient in absolute terms. With this form of regularization, sparse models with few coefficients may be produced. It's possible that certain coefficients will go to zero and be dropped from the model. Coefficient values are closer to zero when the penalties are higher (ideal for producing simpler models). 

On the other hand, sparse models or coefficients are not eliminated by L2 regularization. As a result, as compared to the Ridge, Lasso Regression is simpler to understand.

Apart from this, there are a few other factors where the L1 regularization technique differs from the L1 regularization. These factors are as follows:

  1. L1 regularization can add the penalty term to the cost function by taking the absolute value of the weight parameters into account. On the other hand, the squared value of the weights in the cost function is added via L2 regularization.
  2. In order to avoid overfitting, L2 regularization makes estimates for the data mean instead of the median as is done by L1 regularization.
  3. Since L2 is a square of weight, it has a closed-form solution; however, L1, which is a non-differentiable function and includes an absolute value, does not. Due to this, L1 regularization requires more approximations, is computationally more costly, and cannot be done within the framework of matrix measurement.

Dropout Regularization

Dropout is a regularization method in which certain neurons are disregarded at random. They "drop out" at random. This means that any weight changes are not applied to the neuron on the backward trip and that their effect on the activation of downstream neurons is temporally erased on the forward pass. Neuron weights inside a neural network find their place in the network as it learns. 

Neuronal weights are customized for particular characteristics, resulting in some specialization. Neighboring neurons start to depend on this specialization, which, if it goes too far, might produce a fragile model that is overly dependent on the training data, which can be dangerous. 

In the dropout regularization technique, complex co-adaptations are used to describe how a neuron becomes dependent on circumstances during training.


Regularization plays a crucial role in Deep Neural Network training. All of the aforementioned tactics may be divided into two broad groups. At some point throughout the training lifespan, they either penalize the trainable parameters or the introduced noise. Whether this is on the target labels, the trainable parameters, the network design, or the training data. 

L1 regularization is used to reduce the number of features in a massive, dimensional dataset by producing output for the model's features as binary weights ranging from 0 to 1. 

L2 regularization disperses the error terms among all weights, resulting in more precise final models that are specifically tailored. 

And, dropout is a regularization technique that produces a "thinned" network with distinct combinations of the hidden layer units being deleted at random intervals throughout the training process.

Just to mention, you can not have a high accuracy working model without the use of regularization techniques. And apart from L1, L2, and Dropout regularization techniques, there are a few other regularization techniques that are out of the scope of this article, we might try to cover them for you in a different article. 

As of now, our quest toward regularization comes to an end. If you have any inquiries, please do not hesitate to contact us. As always, feel free to share it if you find it useful.

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Cloud GPUs: Cloud GPUs are remote data centers where you can rent unused GPU resources. This allows you to run your models on a massive scale, without having to install and manage a local machine learning cluster.

Lower TCO: Cloud GPUs require no upfront investment, making them ideal for companies that are looking to reduce their overall capital expenses. Furthermore, the cost of maintenance and upgrades is also low since it takes place in the cloud rather than on-premises.

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Impact of the Strong Dollar: Cloud Costs Increasing, Be Indian Buy Indian

Indian SMEs and startups are feeling the effects of the high dollar. These businesses use hyperscalers(MNC Cloud) who cannot modify their rates to account for the changing exchange rate. For certain companies, even a little shift in the currency rate may have a significant effect on their bottom line. Did you know, when the INR-USD exchange rate moved from 60 to 70 in December 2015, it had an impact of around 20% on Digital Innovation?

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What is a Strong Dollar?

A strong US dollar($) is a term used to describe a situation where a US’s currency has appreciated in value compared to other major currencies. This can be due to a variety of factors, including interest rate changes, a country’s current account deficit, and investor sentiment. When a currency appreciates, it means that it is worth more. A strong dollar makes imports more expensive, while making exports cheaper. Strong dollars have been a growing trend in the past couple of years. As the US Federal Reserve continues to hike interest rates, the dollar strengthens further. The rising value of the dollar means that the cost of cloud services, especially from hyperscalers based in the US, will rise as well. 

Increase in Cloud Costs Due to Strong Dollar

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Why are Cloud Services Becoming More Expensive?

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Possible Indian Alternatives to Cloud Services

If you're looking for a cost-effective substitute for services provided by the U.S.-based suppliers, consider E2E Cloud, an Indian cloud service provider. When it comes to cloud services, E2E Cloud provides everything that startups and SMEs could possibly need.

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Actions CEOs can take to get the value in Cloud Computing

It is not a new thing to say that a major transition is on the way. The transition in which businesses will rely heavily on cloud infrastructure rather than having their own physical IT structure. All of this is due to the cost savings and increased productivity that cloud technology brings to these businesses. Each technological advancement comes with a certain level of risk. Which must be handled carefully in order to ensure the long-term viability of the technology and the benefits it provides.

And CEOs are the primary motivators and decision-makers in any major shift or technological migration in the organization. In the twenty-first century, which is a data-driven century, it is up to the company's leader to decide what and how his/her organization will perform, overcome the risk and succeed in the coming days.

In this blog, we are going to address a few of the actions that CEOs can take to get value in cloud Computing.

  1. A Coordinated Effort

As the saying goes, the more you avoid the risk, the closer it gets. So, if CEOs and their management teams have yet to take an active part or give the necessary attention that their migration journey to the cloud requires, now is the best time to start top-team support for the cloud enablement required to expedite digital strategy, digitalization of the organization, 

The CEO's position is critical because no one else can mediate between the many stakeholders involved, including the CIO, CTO, CFO, chief human-resources officer (CHRO), chief information security officer (CISO), and business-unit leaders.

The move to cloud computing is a collective-action challenge, requiring a coordinated effort throughout an organization's leadership staff. In other words, it's a question of orchestration, and only CEOs can wield the baton. To accelerate the transition to the cloud, CEOs should ask their CIO and CTO what assistance they require to guide the business on the path.

     2. Enhancing business interactions 

To achieve the speed and agility that cloud platforms offer, regular engagement is required between IT managers and their counterparts in business units and functions, particularly those who control products and competence areas. CEOs must encourage company executives to choose qualified decision-makers to serve as product owners for each business capability.

  1. Be Agile

If your organization wants to benefit from the cloud, your IT department, if it isn't already, must become more agile. This entails more than simply transitioning development teams to agile product models. Agile IT also entails bringing agility to your IT infrastructure and operations by transitioning infrastructure and security teams from reactive, "ticket-driven" operations to proactive models in which scrum teams create application programme interfaces (APIs) that service businesses and developers can consume.

  1. Recruiting new employees 

CIOs and CTOs are currently in the lead due to their outstanding efforts in the aftermath of the epidemic. The CEOs must ensure that these executives maintain their momentum while they conduct the cloud transformation. 

Also, Cloud technology necessitates the hire of a highly skilled team of engineers, who are few in number but extremely expensive. As a result, it is envisaged that the CHRO's normal hiring procedures will need to be adjusted in order to attract the proper expertise. Company CEOs may facilitate this by appropriate involvement since this will be critical in deciding the success of the cloud transition.

  1. Model of Business Sustainability 

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  1. Taking risks into consideration 

Risk is inherent in all aspects of corporate technology. Companies must be aware of the risks associated with cloud adoption in order to reduce security, resilience, and compliance problems. This includes, among other things, engaging in comprehensive talks about the appropriate procedures for matching risk appetite with technological environment decisions. Getting the business to take the correct risk tone will necessitate special attention from the CEO.

It's easy to allow concerns about security, resilience, and compliance to stall a cloud operation. Instead of allowing risks to derail progress, CEOs should insist on a realistic risk appetite that represents the company plan, while situating cloud computing risks within the context of current on-premises computing risks and demanding choices for risk mitigation in the cloud.


In conclusion, the benefits of cloud computing may be obtained through a high-level approach. A smooth collaboration between the CEO, CIO, and CTO may transform a digital transformation journey into a profitable avenue for the company.

CEOs must consider long-term cloud computing strategy and ensure that the organization is provided with the funding and resources for cloud adoption. The right communication is critical in cloud migration: employees should get these communications from C-suite executives in order to build confidence and guarantee adherence to governance requirements. Simply installing the cloud will not provide value for a company. Higher-level executives (particularly the CEO) must take the lead in the digital transformation path.

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