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.

Latest Blogs
This is a decorative image for: A Complete Guide To Customer Acquisition For Startups
October 18, 2022

A Complete Guide To Customer Acquisition For Startups

Any business is enlivened by its customers. Therefore, a strategy to constantly bring in new clients is an ongoing requirement. In this regard, having a proper customer acquisition strategy can be of great importance.

So, if you are just starting your business, or planning to expand it, read on to learn more about this concept.

The problem with customer acquisition

As an organization, when working in a diverse and competitive market like India, you need to have a well-defined customer acquisition strategy to attain success. However, this is where most startups struggle. Now, you may have a great product or service, but if you are not in the right place targeting the right demographic, you are not likely to get the results you want.

To resolve this, typically, companies invest, but if that is not channelized properly, it will be futile.

So, the best way out of this dilemma is to have a clear customer acquisition strategy in place.

How can you create the ideal customer acquisition strategy for your business?

  • Define what your goals are

You need to define your goals so that you can meet the revenue expectations you have for the current fiscal year. You need to find a value for the metrics –

  • MRR – Monthly recurring revenue, which tells you all the income that can be generated from all your income channels.
  • CLV – Customer lifetime value tells you how much a customer is willing to spend on your business during your mutual relationship duration.  
  • CAC – Customer acquisition costs, which tells how much your organization needs to spend to acquire customers constantly.
  • Churn rate – It tells you the rate at which customers stop doing business.

All these metrics tell you how well you will be able to grow your business and revenue.

  • Identify your ideal customers

You need to understand who your current customers are and who your target customers are. Once you are aware of your customer base, you can focus your energies in that direction and get the maximum sale of your products or services. You can also understand what your customers require through various analytics and markers and address them to leverage your products/services towards them.

  • Choose your channels for customer acquisition

How will you acquire customers who will eventually tell at what scale and at what rate you need to expand your business? You could market and sell your products on social media channels like Instagram, Facebook and YouTube, or invest in paid marketing like Google Ads. You need to develop a unique strategy for each of these channels. 

  • Communicate with your customers

If you know exactly what your customers have in mind, then you will be able to develop your customer strategy with a clear perspective in mind. You can do it through surveys or customer opinion forms, email contact forms, blog posts and social media posts. After that, you just need to measure the analytics, clearly understand the insights, and improve your strategy accordingly.

Combining these strategies with your long-term business plan will bring results. However, there will be challenges on the way, where you need to adapt as per the requirements to make the most of it. At the same time, introducing new technologies like AI and ML can also solve such issues easily. To learn more about the use of AI and ML and how they are transforming businesses, keep referring to the blog section of E2E Networks.

Reference Links

This is a decorative image for: Constructing 3D objects through Deep Learning
October 18, 2022

Image-based 3D Object Reconstruction State-of-the-Art and trends in the Deep Learning Era

3D reconstruction is one of the most complex issues of deep learning systems. There have been multiple types of research in this field, and almost everything has been tried on it — computer vision, computer graphics and machine learning, but to no avail. However, that has resulted in CNN or convolutional neural networks foraying into this field, which has yielded some success.

The Main Objective of the 3D Object Reconstruction

Developing this deep learning technology aims to infer the shape of 3D objects from 2D images. So, to conduct the experiment, you need the following:

  • Highly calibrated cameras that take a photograph of the image from various angles.
  • Large training datasets can predict the geometry of the object whose 3D image reconstruction needs to be done. These datasets can be collected from a database of images, or they can be collected and sampled from a video.

By using the apparatus and datasets, you will be able to proceed with the 3D reconstruction from 2D datasets.

State-of-the-art Technology Used by the Datasets for the Reconstruction of 3D Objects

The technology used for this purpose needs to stick to the following parameters:

  • Input

Training with the help of one or multiple RGB images, where the segmentation of the 3D ground truth needs to be done. It could be one image, multiple images or even a video stream.

The testing will also be done on the same parameters, which will also help to create a uniform, cluttered background, or both.

  • Output

The volumetric output will be done in both high and low resolution, and the surface output will be generated through parameterisation, template deformation and point cloud. Moreover, the direct and intermediate outputs will be calculated this way.

  • Network architecture used

The architecture used in training is 3D-VAE-GAN, which has an encoder and a decoder, with TL-Net and conditional GAN. At the same time, the testing architecture is 3D-VAE, which has an encoder and a decoder.

  • Training used

The degree of supervision used in 2D vs 3D supervision, weak supervision along with loss functions have to be included in this system. The training procedure is adversarial training with joint 2D and 3D embeddings. Also, the network architecture is extremely important for the speed and processing quality of the output images.

  • Practical applications and use cases

Volumetric representations and surface representations can do the reconstruction. Powerful computer systems need to be used for reconstruction.

Given below are some of the places where 3D Object Reconstruction Deep Learning Systems are used:

  • 3D reconstruction technology can be used in the Police Department for drawing the faces of criminals whose images have been procured from a crime site where their faces are not completely revealed.
  • It can be used for re-modelling ruins at ancient architectural sites. The rubble or the debris stubs of structures can be used to recreate the entire building structure and get an idea of how it looked in the past.
  • They can be used in plastic surgery where the organs, face, limbs or any other portion of the body has been damaged and needs to be rebuilt.
  • It can be used in airport security, where concealed shapes can be used for guessing whether a person is armed or is carrying explosives or not.
  • It can also help in completing DNA sequences.

So, if you are planning to implement this technology, then you can rent the required infrastructure from E2E Networks and avoid investing in it. And if you plan to learn more about such topics, then keep a tab on the blog section of the website

Reference Links

This is a decorative image for: Comprehensive Guide to Deep Q-Learning for Data Science Enthusiasts
October 18, 2022

A Comprehensive Guide To Deep Q-Learning For Data Science Enthusiasts

For all data science enthusiasts who would love to dig deep, we have composed a write-up about Q-Learning specifically for you all. Deep Q-Learning and Reinforcement learning (RL) are extremely popular these days. These two data science methodologies use Python libraries like TensorFlow 2 and openAI’s Gym environment.

So, read on to know more.

What is Deep Q-Learning?

Deep Q-Learning utilizes the principles of Q-learning, but instead of using the Q-table, it uses the neural network. The algorithm of deep Q-Learning uses the states as input and the optimal Q-value of every action possible as the output. The agent gathers and stores all the previous experiences in the memory of the trained tuple in the following order:

State> Next state> Action> Reward

The neural network training stability increases using a random batch of previous data by using the experience replay. Experience replay also means the previous experiences stocking, and the target network uses it for training and calculation of the Q-network and the predicted Q-Value. This neural network uses openAI Gym, which is provided by taxi-v3 environments.

Now, any understanding of Deep Q-Learning   is incomplete without talking about Reinforcement Learning.

What is Reinforcement Learning?

Reinforcement is a subsection of ML. This part of ML is related to the action in which an environmental agent participates in a reward-based system and uses Reinforcement Learning to maximize the rewards. Reinforcement Learning is a different technique from unsupervised learning or supervised learning because it does not require a supervised input/output pair. The number of corrections is also less, so it is a highly efficient technique.

Now, the understanding of reinforcement learning is incomplete without knowing about Markov Decision Process (MDP). MDP is involved with each state that has been presented in the results of the environment, derived from the state previously there. The information which composes both states is gathered and transferred to the decision process. The task of the chosen agent is to maximize the awards. The MDP optimizes the actions and helps construct the optimal policy.

For developing the MDP, you need to follow the Q-Learning Algorithm, which is an extremely important part of data science and machine learning.

What is Q-Learning Algorithm?

The process of Q-Learning is important for understanding the data from scratch. It involves defining the parameters, choosing the actions from the current state and also choosing the actions from the previous state and then developing a Q-table for maximizing the results or output rewards.

The 4 steps that are involved in Q-Learning:

  1. Initializing parameters – The RL (reinforcement learning) model learns the set of actions that the agent requires in the state, environment and time.
  2. Identifying current state – The model stores the prior records for optimal action definition for maximizing the results. For acting in the present state, the state needs to be identified and perform an action combination for it.
  3. Choosing the optimal action set and gaining the relevant experience – A Q-table is generated from the data with a set of specific states and actions, and the weight of this data is calculated for updating the Q-Table to the following step.
  4. Updating Q-table rewards and next state determination – After the relevant experience is gained and agents start getting environmental records. The reward amplitude helps to present the subsequent step.  

In case the Q-table size is huge, then the generation of the model is a time-consuming process. This situation requires Deep Q-learning.

Hopefully, this write-up has provided an outline of Deep Q-Learning and its related concepts. If you wish to learn more about such topics, then keep a tab on the blog section of the E2E Networks website.

Reference Links

This is a decorative image for: GAUDI: A Neural Architect for Immersive 3D Scene Generation
October 13, 2022

GAUDI: A Neural Architect for Immersive 3D Scene Generation

The evolution of artificial intelligence in the past decade has been staggering, and now the focus is shifting towards AI and ML systems to understand and generate 3D spaces. As a result, there has been extensive research on manipulating 3D generative models. In this regard, Apple’s AI and ML scientists have developed GAUDI, a method specifically for this job.

An introduction to GAUDI

The GAUDI 3D immersive technique founders named it after the famous architect Antoni Gaudi. This AI model takes the help of a camera pose decoder, which enables it to guess the possible camera angles of a scene. Hence, the decoder then makes it possible to predict the 3D canvas from almost every angle.

What does GAUDI do?

GAUDI can perform multiple functions –

  • The extensions of these generative models have a tremendous effect on ML and computer vision. Pragmatically, such models are highly useful. They are applied in model-based reinforcement learning and planning world models, SLAM is s, or 3D content creation.
  • Generative modelling for 3D objects has been used for generating scenes using graf, pigan, and gsn, which incorporate a GAN (Generative Adversarial Network). The generator codes radiance fields exclusively. Using the 3D space in the scene along with the camera pose generates the 3D image from that point. This point has a density scalar and RGB value for that specific point in 3D space. This can be done from a 2D camera view. It does this by imposing 3D datasets on those 2D shots. It isolates various objects and scenes and combines them to render a new scene altogether.
  • GAUDI also removes GANs pathologies like mode collapse and improved GAN.
  • GAUDI also uses this to train data on a canonical coordinate system. You can compare it by looking at the trajectory of the scenes.

How is GAUDI applied to the content?

The steps of application for GAUDI have been given below:

  • Each trajectory is created, which consists of a sequence of posed images (These images are from a 3D scene) encoded into a latent representation. This representation which has a radiance field or what we refer to as the 3D scene and the camera path is created in a disentangled way. The results are interpreted as free parameters. The problem is optimized by and formulation of a reconstruction objective.
  • This simple training process is then scaled to trajectories, thousands of them creating a large number of views. The model samples the radiance fields totally from the previous distribution that the model has learned.
  • The scenes are thus synthesized by interpolation within the hidden space.
  • The scaling of 3D scenes generates many scenes that contain thousands of images. During training, there is no issue related to canonical orientation or mode collapse.
  • A novel de-noising optimization technique is used to find hidden representations that collaborate in modelling the camera poses and the radiance field to create multiple datasets with state-of-the-art performance in generating 3D scenes by building a setup that uses images and text.

To conclude, GAUDI has more capabilities and can also be used for sampling various images and video datasets. Furthermore, this will make a foray into AR (augmented reality) and VR (virtual reality). With GAUDI in hand, the sky is only the limit in the field of media creation. So, if you enjoy reading about the latest development in the field of AI and ML, then keep a tab on the blog section of the E2E Networks website.

Reference Links

Build on the most powerful infrastructure cloud

A vector illustration of a tech city using latest cloud technologies & infrastructure