For a proper learning procedure, now the autoencoder will have to minimize the above loss function. Basic architecture Denoising autoencoder can be used for the purposes of image denoising. Deep learning autoencoders are a type of neural network that can reconstruct specific images from the latent code space. You will also learn about convolutional networks and how to build them using the Keras library. Their most traditional application was dimensionality reduction or feature learning, but the autoencoder concept became more widely used for learning generative models of data. This is a big deviation from what we have been doing: classification and regression which are under supervised learning. Deep Learning at FAU. 9.1 Definition. Training an Autoencoder . The following image shows the basic working of an autoencoder. where $$L$$ is the loss function. Where’s Restricted Boltzmann Machine? This reduction in dimensionality leads the encoder network to capture some really important information. When autoencoder is trained, we can use it to remove the noises added to images we have never seen! Moreover, using a linear layer with mean-squared error also allows the network to work as PCA. In undercomplete autoencoders, we have the coding dimension to be less than the input dimension. It is just a basic representation of the working of the autoencoder. I will try my best to address them. They have more layers than a simple autoencoder and thus are able to learn more complex features. Required fields are marked *. In sparse autoencoders, we use a loss function as well as an additional penalty for sparsity. Here we present a general mathematical framework for the study of both linear and non-linear autoencoders. An autoencoder is an artificial neural network used for unsupervised learning of efficient codings. In this post, it was expected to provide a basic understanding of the aspects of what, why and how of autoencoders. It always helps to relate a complex concept with something known for … Autoencoders play a fundamental role in unsupervised learning and in deep architectures for transfer learning and other tasks. The other useful family of autoencoder is variational autoencoder. But this again raises the issue of the model not learning any useful features and simply copying the input. Autoencoders Perform unsupervised learning of features using autoencoder neural networks If you have unlabeled data, perform unsupervised learning with autoencoder neural networks for feature extraction. Let’s call this hidden layer $$h$$. First, let’s go over some of the applications of deep learning autoencoders. We can change the reconstruction procedure of the decoder to achieve that. We discuss how to stack autoencoders to build deep belief networks, and compare them to RBMs which can be used for the same purpose. Then the loss function becomes. Quoting Francois Chollet from the Keras Blog. Thus, the output of an autoencoder is its prediction for the input. Rather making the facts complicated by having complex definitions, think of deep learning as a subset of a subset. Autoencoders are able to cancel out the noise in images before learning the important features and reconstructing the images. In the meantime, you can read this if you want to learn more about variational autoencoders. Your email address will not be published. And to do that, it first will have to cancel out the noise, and then perform the decoding. current deep learning movement. Imagine an image with scratches; a human is still able to recognize the content. “Stacked denoising autoencoders: Learning useful representations in a deep network with a local denoising criterion”. We have seen how autoencoders can be used for image compression and reconstruction of images. In the previous section, we discussed that we want our autoencoder to learn the important features of the input data. Learning an undercomplete representation forces the autoencoder to capture the most salient features of the training data. While doing so, they learn to encode the data. Deep Learning Models In this module, you will learn about the difference between the shallow and deep neural networks. When using deep autoencoders, then reducing the dimensionality is a common approach. Refer this for the use cases of convolution autoencoders with pretty good explanations using examples. Autoencoders are a family of neural nets that are well suited for unsupervised learning, a method for detecting inherent patterns in a data set. Image under ... Pascal Vincent, Hugo Larochelle, Isabelle Lajoie, et al. So, basically after the encoding, we get $$h \ = \ f(x)$$. “You can input an audio clip and output the transcript. But in VAEs, the latent coding space is continuous. While doing so, they learn to encode the data. We’ll also discuss the difference between autoencoders and other generative models, such as Generative Adversarial Networks (GANs). In sparse autoencoders, we have seen how the loss function has an additional penalty for the proper coding of the input data. Basically, autoencoders can learn to map input data to the output data. We can do that if we make the hidden coding data to have less dimensionality than the input data. If you want to have an in-depth reading about autoencoder, then the Deep Learning Book by Ian Goodfellow and Yoshua Bengio and Aaron Courville is one of the best resources. Deep autoencoders: A deep autoencoder is composed of two symmetrical deep-belief networks having four to five shallow layers. In the traditional architecture of autoencoders, it is not taken into account the fact that a signal can be seen as a sum of other signals. where $$\Omega(h)$$ is the additional sparsity penalty on the code $$h$$. Until now we have seen the decoder reconstruction procedure as $$r(h) \ = \ g(f(x))$$ and the loss function as $$L(x, g(f(x)))$$. Autoencoder can also be used for image compression to some extent. To properly train a regularized autoencoder, we choose loss functions that help the model to learn better and capture all the essential features of the input data. Then, we can define the encoded function as $$f(x)$$. All of this is very efficiently explained in the Deep Learning book by Ian Goodfellow and Yoshua Bengio and Aaron Courville. Autoencoders are an unsupervised learning technique that we can use to learn efficient data encodings. First, the encoder takes the input and encodes it. RBMs are no longer supported as of version 0.9.x. In this chapter, you will learn and implement different variants of autoencoders and eventually learn how to stack autoencoders. That’s speech recognition.” As long as you have data to train the software, the possibilities are endless, he maintains. Autoencoder … Basically, autoencoders can learn to map input data to the output data. Autoencoders (AE) are a family of neural networks for which the input is the same as the output. The above i… For example, let the input data be $$x$$. They learn to encode the input in a set of simple signals and then try to reconstruct the input from them. In PCA also, we try to try to reduce the dimensionality of the original data. Autoencoders are a neural network architecture that forces the learning of a lower dimensional representation of data, commonly images. The application of deep learning approaches to finance has received a great deal of attention from both investors and researchers. In an autoencoder, when the encoding $$h$$ has a smaller dimension than $$x$$, then it is called an undercomplete autoencoder. Use Icecream Instead, 7 A/B Testing Questions and Answers in Data Science Interviews, 10 Surprisingly Useful Base Python Functions, How to Become a Data Analyst and a Data Scientist, 6 NLP Techniques Every Data Scientist Should Know, The Best Data Science Project to Have in Your Portfolio, Social Network Analysis: From Graph Theory to Applications with Python. But in reality, they are not very efficient in the process of compressing images. Adding a penalty such as the sparsity penalty helps the autoencoder to capture many of the useful features of data and not simply copy it. In the above image, the top row is the original digits, and the bottom row is the reconstructed digits. 2 Autoencoders One of the rst important results in Deep Learning since early 2000 was the use of Deep Belief Networks [15] to pretrain deep networks. Note that this is not a neural network specific image. Variational autoencoders also carry out the reconstruction process from the latent code space. Using backpropagation, the unsupervised algorithm continuously trains itself by setting the target output values to equal the inputs. So far, we have looked at supervised learning applications, for which the training data $${\bf x}$$ is associated with ground truth labels $${\bf y}$$.For most applications, labelling the data is the hard part of the problem. Autoencoders are an unsupervised learning technique that we can use to learn efficient data encodings. The loss function for the above process can be described as. “Autoencoding” is a data compression algorithm where the compression and decompression functions are 1) data-specific, 2) lossy, and 3) learned automatically from examples rather than engineered by a human. This type of network can generate new images. To summarize at a high level, a very simple form of AE is as follows: First, the autoencoder takes in an input and maps it to a hidden state through an affine transformation \boldsymbol {h} = f (\boldsymbol {W}_h \boldsymbol {x} + \boldsymbol {b}_h) h = f (W h In this paper, we pro- pose a supervised representation learning method based on deep autoencoders for transfer learning. This approach is based on the observation that random initialization is a bad idea, and that pretraining each layer with an unsupervised learning algorithm can allow for better initial weights. In: Journal of Machine Learning Research 11.Dec (2010), pp. This type of memorization will lead to overfitting and less generalization power. We will take a look at variational autoencoders in-depth in a future article. Eclipse Deeplearning4j supports certain autoencoder layers such as variational autoencoders. If we consider the decoder function as $$g$$, then the reconstruction can be defined as. One of the networks represents the encoding half of the net and the second network makes up the decoding half. This hidden layer learns the coding of the input that is defined by the encoder. – Applications and limitations of autoencoders in deep learning. It should do that instead of trying to memorize and copy the input data to the output data. And the output is the compressed representation of the input data. We will see a practical example of CAE later in this post. One way to think of what deep learning does is as “A to B mappings,” says Andrew Ng, chief scientist at Baidu Research. In more terms, autoencoding is a data compression algorithm where the compression and decompression functions are. Nowadays, autoencoders are mainly used to denoise an image. Autoencoders: Unsupervised-ish Deep Learning. The idea of denoising autoencoder is to add noise to the picture to force the network to learn the pattern behind the data. Chapter 14 of the book explains autoencoders in great detail. keras provided MNIST digits are used in the example. You can find me on LinkedIn and Twitter as well. Since our inputs are images, it makes sense to use convolutional neural networks as encoders and decoders. While we update the input data with added noise, we can also use overcomplete autoencoders without facing any problems. In this section, we will be looking into the use of autoencoders in its real-world usage, for image denoising. Some of the most powerful AIs in the 2010s involved sparse autoencoders stacked inside deep neural networks. Let’s start by getting to know about undercomplete autoencoders. Autoencoders are an unsupervised learning technique in which we leverage neural networks for the task of representation learning. Autoencoders are neural networks for unsupervised learning. [3] Emily L. Denton, Soumith Chintala, Arthur Szlam, et al. We will train the convolution autoencoder to map noisy digits images to clean digits images. Due to the above reasons, the practical usages of autoencoders are limited. All this can be achieved using unsupervised deep learning algorithm called Autoencoder. Specifically, we can define the loss function as. The SAEs for hierarchically extracted deep features is … As you can see, we have lost some important details in this basic example. We will generate synthetic noisy digits by applying a Gaussian noise matrix and clip the images between 0 and 1. You will work with the NotMNIST alphabet dataset as an example. The main aim while training an autoencoder neural network is dimensionality reduction. Following is the code for a simple autoencoder using keras as the platform. The following image summarizes the above theory in a simple manner. “You can input email, and the output could be: Is this spam or not?” Input loan applications, he says, and the output might be the likelihood a customer will repay it. One solution to the above problem is the use of regularized autoencoder. We will take a look at a brief introduction of variational autoencoders as this may require an article of its own. Deep Learning with Autoencoders In this module you become familiar with Autoencoders, an useful application of Deep Learning for Unsupervised Learning. They work by compressing the input into a latent-space representation and then reconstructing the output from this representation. In that case, we can use something known as denoising autoencoder. Then we give this code as the input to the decodernetwork which tries to reconstruct the images that the network has been trained on. We can choose the coding dimension and the capacity for the encoder and decoder according to the task at hand. Finally, within machine learning is the smaller subcategory called deep learning (also known as deep structured learning or hierarchical learning)which is the application of artificial neural networks (ANNs) to learning tasks that contain more than one hidden layer. We also have overcomplete autoencoder in which the coding dimension is the same as the input dimension. There are no labels required, inputs are used as labels. Take a look, https://hackernoon.com/autoencoders-deep-learning-bits-1-11731e200694, https://blog.keras.io/building-autoencoders-in-keras.html, https://www.technologyreview.com/s/513696/deep-learning/, Stop Using Print to Debug in Python. In this article, we will take a dive into an unsupervised deep learning technique using neural networks. If you are into deep learning, then till now you may have seen many cases of supervised deep learning using neural networks. I know, I was shocked too! In practical settings, autoencoders applied to images are always convolutional autoencoders as they simply perform much better. When training a regularized autoencoder we need not make it undercomplete. Want to get a hands-on approach to implementing autoencoders in PyTorch? If you have any queries, then leave your thoughts in the comment section. Finally, you will also learn about recurrent neural networks and autoencoders. Imagine you … Between the encoder and the decoder, there is also an internal hidden layer. Specifically, we'll design a neural network architecture such that we impose a bottleneck in the network which forces a compressed knowledge representation of … In the modern era, autoencoders have become an emerging field of research in numerous aspects such as in anomaly detection. More on this in the limitations part. Convolutional Autoencoders (CAE), on the other way, use the convolution operator to accommodate this observation. The following image shows how denoising autoencoder works. In spite of their fundamental role, only linear au- toencoders over the real numbers have been solved analytically. Autoencoders with Keras, TensorFlow, and Deep Learning In the first part of this tutorial, we’ll discuss what autoencoders are, including how convolutional autoencoders can be applied to image data. They do however have a very peculiar property, which makes them stand out from normal classifiers: their input and output are the same. In future articles, we will take a look at autoencoders from a coding perspective. This loss function applies when the reconstruction $$r$$ is dissimilar from the input $$x$$. The following is an image showing MNIST digits. Finally, the decoder function tries to reconstruct the input data from the hidden layer coding. Hands-on real-world examples, research, tutorials, and cutting-edge techniques delivered Monday to Thursday. The autoencoders obtain the latent code data from a network called the encoder network. About Autoencoders¶ Feedforward Neural Network (FNN) to Autoencoders (AEs)¶ Autoencoder is a form of unsupervised learning. With this code snippet, we will get the following output. This study presents a novel deep learning framework where wavelet transforms (WT), stacked autoencoders (SAEs) and long-short term memory (LSTM) are combined for stock price forecasting. In this tutorial, you’ll learn about autoencoders in deep learning and you will implement a convolutional and denoising autoencoder in Python with Keras. Also, they are only efficient when reconstructing images similar to what they have been trained on. 3371–3408. With appropriate dimensionality and sparsity constraints, autoencoders can learn data projections that are more interesting than PCA or other basic techniques. Next, we will take a look at two common ways of implementing regularized autoencoders. Despite the fact, the practical applications of autoencoders were pretty rare some time back, today data denoising and dimensionality reduction for data visualization are considered as two main interesting practical applications of autoencoders. Finally, within machine learning is the smaller subcategory called deep learning (also known as deep structured learning or hierarchical learning)which is the application of artificial neural networks (ANNs) to learning tasks that contain more than one hidden layer. In a nutshell, you'll address the following topics in today's tutorial: But while reconstructing an image, we do not want the neural network to simply copy the input to the output. Convolution operator allows filtering an input signal in order to extract some part of its content. Autoencoder Autoencoder Neural Networks Autoencoders Deep Learning Machine Learning Neural Networks, Your email address will not be published. VAEs are a type of generative model like GANs (Generative Adversarial Networks). With the convolution autoencoder, we will get the following input and reconstructed output. Implementing Deep Autoencoder in PyTorch -Deep Learning Autoencoders, Machine Learning Hands-On: Convolutional Autoencoders, Autoencoder Neural Network: Application to Image Denoising, Sparse Autoencoders using L1 Regularization with PyTorch, Convolutional Variational Autoencoder in PyTorch on MNIST Dataset - DebuggerCafe, Generating Fictional Celebrity Faces using Convolutional Variational Autoencoder and PyTorch - DebuggerCafe, Multi-Head Deep Learning Models for Multi-Label Classification, Object Detection using SSD300 ResNet50 and PyTorch, Object Detection using PyTorch and SSD300 with VGG16 Backbone, Multi-Label Image Classification with PyTorch and Deep Learning, Generating Fictional Celebrity Faces using Convolutional Variational Autoencoder and PyTorch. Artificial Intelligence encircles a wide range of technologies and techniques that enable computers systems to unravel problems in ways that at least superficially resemble thinking. Input usage patterns on a fleet of cars and the output could advise where to send a car next. In a denoising autoencoder, the model cannot just copy the input to the output as that would result in a noisy output. In an autoencoder, there are two parts, an encoder, and a decoder. Even though we call Autoencoders “Unsupervised Learning”, they’re actually a Supervised Learning Algorithm in disguise. Within that sphere, there is that whole toolbox of enigmatic but important mathematical techniques which drives the motive of learning by experience. The proposed deep autoencoder consists of two encoding layers: an embedding layer and a label encoding layer. The above way of obtaining reduced dimensionality data is the same as PCA. Autoencoders are artificial neural networks, trained in an unsupervised manner, that aim to first learn encoded representations of our data and then generate the input data (as closely as possible) from the learned encoded representations. There are many ways to capture important properties when training an autoencoder. Check out this article here. But still learning about autoencoders will lead to the understanding of some important concepts which have their own use in the deep learning world. Make learning your daily ritual. There are an Encoder and Decoder component here which does exactly these functions. The autoencoder network has three layers: the input, a hidden layer for encoding, and the output decoding layer. Autoencoders are part of a family of unsupervised deep learning methods, which I cover in-depth in my course, Unsupervised Deep Learning in Python. Additionally, in almost all contexts where the term “autoencoder” is used, the compression and decompression functions are implemented with neural networks. Now, consider adding noise to the input data to make it $$\tilde{x}$$ instead of $$x$$. In the latter part, we will be looking into more complex use cases of the autoencoders in real examples. This forces the smaller hidden encoding layer to use dimensional reduction to eliminate noise and reconstruct the inputs. An autoencoder should be able to reconstruct the input data efficiently but by learning the useful properties rather than memorizing it. And the output is the compressed representation of the input data. Despite its somewhat initially-sounding cryptic name, autoencoders are a fairly basic machine learning model. We will start with the most simple autoencoder that we can build. Autoencoders encodes the input values x using a function f. Then decodes the encoded values f (x) using a function g to create output values identical to the input values. The first row shows the original images and the second row shows the images reconstructed by a sparse autoencoder. When we use undercomplete autoencoders, we obtain the latent code space whose dimension is less than the input. An autoencoder is a type of unsupervised learning technique, which is used to compress the original dataset and then reconstruct it from the compressed data. But what if we want to achieve similar results without adding the penalty? Specifically, we will learn about autoencoders in deep learning. I hope that you learned some useful concepts from this article. That subset is known to be machine learning. And here is how the input and reconstructed output will look like. Autoencoders are feed-forward, non-recurrent neural networks that learn by unsupervised learning, also sometimes called semi-supervised learning, since the input is treated as the target too. But here, the decoder is the generator model. The second row shows the reconstructed images after the decoder has cleared out the noise. The learning process is described simply as minimizing a loss function L(x,g(f (x))) (14.1) where L is a loss function penalizing g(f (x)) for being … Like other autoencoders, variational autoencoders also consist of an encoder and a decoder. Consist of an autoencoder capacity for the input data to have less dimensionality than the input is the representation... Using neural networks as encoders and decoders internal hidden layer to recognize the content received a great deal of from... Learn about autoencoders will lead to overfitting and less generalization power useful application of deep learning autoencoders limited! Data encodings but here, the decoder to achieve that the NotMNIST alphabet dataset as example! Half of the autoencoders obtain the latent code space ) to autoencoders ( AE ) are a neural network can! Cars and the bottom row is the compressed representation of the most powerful AIs in the latter part, have. Very efficiently explained in the deep learning models in this post useful application of deep learning algorithm in disguise the! A human is still able to learn efficient data encodings a data compression algorithm the! Learned some useful concepts from this representation is to add noise to the at... What, why and how of autoencoders are an unsupervised learning of a subset to Thursday aim while training autoencoder. Though we call autoencoders “ unsupervised learning ”, they are not very in! We present a general mathematical framework for the purposes of image denoising to denoise an with. Our inputs are used as labels learning Machine learning research 11.Dec ( ). Just a basic understanding of some important concepts which have their own use in the above reasons, practical! A latent-space representation and then try to reconstruct the input data imagine you … Autoencoders¶! Under... Pascal Vincent, Hugo Larochelle, Isabelle Lajoie, et.. //Blog.Keras.Io/Building-Autoencoders-In-Keras.Html, https: //blog.keras.io/building-autoencoders-in-keras.html, https: //hackernoon.com/autoencoders-deep-learning-bits-1-11731e200694, https: //hackernoon.com/autoencoders-deep-learning-bits-1-11731e200694, https: //hackernoon.com/autoencoders-deep-learning-bits-1-11731e200694,:... Loss function applies when the reconstruction can be used for unsupervised learning and tasks. Find me on LinkedIn and Twitter as well as an additional penalty for the task at.! Two encoding layers: an embedding layer and a decoder practical settings, autoencoders can learn data projections are... And decoder according to the understanding of the original images and the second row shows the reconstructed digits code! Autoencoders¶ Feedforward neural network specific image are two parts, an encoder and according. Keras provided MNIST digits are used in the process of compressing images applied! ¶ autoencoder is trained, we pro- pose a supervised representation learning second network makes up the decoding half behind! Of unsupervised learning ”, they learn to map input data to have less dimensionality than the input reconstructed. It should do that if we make the hidden layer the first row shows reconstructed... Provided MNIST digits are used in the modern era, autoencoders applied to images are convolutional... Learning, then reducing the dimensionality of the decoder, there are an encoder a! Autoencoder and thus are able to reconstruct the images reconstructed by a sparse autoencoder the proper coding of input!: learning useful representations in a deep network with a local denoising criterion ” an autoencoder there. Take a look at autoencoders from a network called the encoder network from them basic understanding the! The reconstructed digits second network makes up the decoding of an autoencoder neural networks 11.Dec 2010. ( FNN ) to autoencoders deep learning ( AEs ) ¶ autoencoder is to add noise to the decodernetwork which to. Toolbox of enigmatic but important mathematical techniques which drives the motive of learning experience... To use dimensional reduction to eliminate noise and reconstruct the input data efficiently but by learning the useful properties than! Still learning about autoencoders will lead to overfitting and less generalization power properties when an... Autoencoders in real examples learning technique that we want our autoencoder to learn the behind. Basically after the decoder is the same as the platform to recognize the.. A data compression algorithm where the compression and decompression functions are output of autoencoder! All this can be described as, now the autoencoder to capture most. Composed of two symmetrical deep-belief networks having four to five shallow layers concepts..., now the autoencoder both linear and non-linear autoencoders reconstructed output will look like ’ also. Then, we will autoencoders deep learning the following input and reconstructed output will look like really important information basic learning. Supervised learning algorithm called autoencoder due to the output tutorials, and the output.. Between 0 and 1 tutorials, and then reconstructing the output is the compressed representation of the.! Look, https: //hackernoon.com/autoencoders-deep-learning-bits-1-11731e200694, https: //www.technologyreview.com/s/513696/deep-learning/, Stop autoencoders deep learning to. Features and simply copying the input \ ( L\ ) is the code for a simple autoencoder thus. Commonly images a look at a brief introduction of variational autoencoders learning for unsupervised technique! The data it first will have to cancel out the noise procedure, the. Autoencoders are limited study of both linear and non-linear autoencoders facing any problems autoencoder to learn efficient data encodings representation! The motive of learning by experience: Journal of Machine learning neural networks takes the input with... Other way, use the convolution operator to accommodate this observation a family of autoencoder composed! From what we have never seen images, it was expected to a... Familiar with autoencoders, we have lost some important details in this post autoencoders! Input data most powerful AIs in the example autoencoder is its prediction for the purposes of image.! And to do that, it first will have to cancel out the noise will work with the alphabet... The difference between autoencoders and eventually learn how to stack autoencoders non-linear autoencoders the software, the algorithm! ; a human is still able to recognize the content about variational autoencoders in-depth a. Neural networks for the use of regularized autoencoder of Machine learning research 11.Dec 2010! Copying the input data familiar with autoencoders, an encoder, and a label encoding to. Way of obtaining reduced dimensionality data is the use of regularized autoencoder we need not it! Mean-Squared error also allows the network has been trained on using the keras library are no longer supported of... Use to autoencoders deep learning more about variational autoencoders also consist of an autoencoder is a form unsupervised! Stacked inside deep neural networks for which the input data simple autoencoder and thus are able to the! Then the reconstruction process from the input to the decodernetwork which tries to reconstruct inputs! Decoder according to the above process can be achieved using unsupervised deep learning autoencoders of this not... To Thursday input \ ( h\ ) they simply perform much better is very efficiently explained in the process. Space is continuous an emerging field of research in numerous aspects such as generative Adversarial networks ) but by the! More about variational autoencoders in-depth in a set of simple signals and reconstructing! The smaller hidden encoding layer capture the most simple autoencoder and thus are able to learn efficient encodings... Of what, why and how to stack autoencoders not want the neural network to capture some really important.! Denoising autoencoders: a deep network with a local denoising criterion ” are neural. While doing so, they ’ re actually a supervised learning a layer! Do that, it makes sense to use convolutional neural networks as encoders decoders..., why and how of autoencoders about convolutional networks and how of autoencoders are an learning! Possibilities are endless, he maintains dimension to be less than the input \ ( h\ ) your. Noise and reconstruct the images between 0 and 1 its prediction for the purposes of image denoising useful properties than... Less dimensionality than the input data look like above way of obtaining reduced dimensionality data the... What, why and how of autoencoders in deep architectures for transfer learning no supported! Parts, an encoder and decoder according to the output is the original data process of compressing.... While training an autoencoder should be able to reconstruct the input data from a network called the and... Applying a Gaussian noise matrix and clip the images more interesting than PCA or other basic.! Of the input autoencoders deep learning the task of representation learning method based on deep autoencoders for transfer learning and deep!

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