VGG19 ,
Mobile Net ,Inception ,Xception Inception ResNet v2

VGG19, DenseNet121, ResNetV2, InceptionV3, InceptionResNetV2, Xception, and MobileNetV2

ResNet50, InceptionV3 and Inception-ResNetV2

Classification ,quantification and tracking: Covid-19 patients

Classification: Covid-19,
Model Evaluation

Rapid AI Development Cycle for the Coronavirus (COVID-19) Pandemic: Initial Results for Automated Detection & Patient Monitoring using Deep Learning CT Image Analysis

Abstract: Purpose: Develop AI-based automated CT image analysis tools for detection, quantification, and tracking of Coronavirus; demonstrate they can differentiate coronavirus patients from non-patients. Materials and Methods: Multiple international datasets, including from Chinese disease-infected areas were included. We present a system that utilizes robust 2D and 3D deep learning models, modifying and adapting existing AI models and combining them with clinical understanding. We conducted multiple retrospective experiments to analyze the performance of the system in the detection of suspected COVID-19 thoracic CT features and to evaluate evolution of the disease in each patient over time using a 3D volume review, generating a Corona score. The study includes a testing set of 157 international patients (China and U.S). Results: Classification results for Coronavirus vs Non-coronavirus cases per thoracic CT studies were 0.996 AUC (95%CI: 0.989-1.00) ; on datasets of Chinese control and infected patients. Possible working point: 98.2% sensitivity, 92.2% specificity. For time analysis of Coronavirus patients, the system output enables quantitative measurements for smaller opacities (volume, diameter) and visualization of the larger opacities in a slice-based heat map or a 3D volume display. Our suggested Corona score measures the progression of disease over time. Conclusion: This initial study, which is currently being expanded to a larger population, demonstrated that rapidly developed AI-based image analysis can achieve high accuracy in detection of Coronavirus as well as quantification and tracking of disease burden.

Covid-19: Automatic detection from X-Ray images utilizing Transfer Learning with Convolutional Neural Networks

Abstract: In this study, a dataset of X-Ray images from patients with common pneumonia, Covid-19, and normal incidents was utilized for the automatic detection of the Coronavirus. The aim of the study is to evaluate the performance of state-of-the-art Convolutional Neural Network architectures proposed over recent years for medical image classification. Specifically, the procedure called transfer learning was adopted. With transfer learning, the detection of various abnormalities in small medical image datasets is an achievable target, often yielding remarkable results. The dataset utilized in this experiment is a collection of 1427 X-Ray images. 224 images with confirmed Covid-19, 700 images with confirmed common pneumonia, and 504 images of normal conditions are included. The data was collected from the available X-Ray images on public medical repositories. With transfer learning, an overall accuracy of 97.82% in the detection of Covid-19 is achieved.

COVIDX-Net: A Framework of Deep Learning Classifiers to Diagnose COVID-19 in X-Ray Images

Abstract: Background and Purpose: Coronaviruses (CoV) are perilous viruses that may cause Severe Acute Respiratory Syndrome (SARS-CoV), Middle East Respiratory Syndrome (MERS-CoV). The novel 2019 Coronavirus disease (COVID-19) was discovered as a novel disease pneumonia in the city of Wuhan, China at the end of 2019. Now, it becomes a Coronavirus outbreak around the world, the number of infected people and deaths are increasing rapidly every day according to the updated reports of the World Health Organization (WHO). Therefore, the aim of this article is to introduce a new deep learning framework; namely COVIDX-Net to assist radiologists to automatically diagnose COVID-19 in X-ray images. Materials and Methods: Due to the lack of public COVID-19 datasets, the study is validated on 50 Chest X-ray images with 25 confirmed positive COVID-19 cases. The COVIDX-Net includes seven different architectures of deep convolutional neural network models, such as modified Visual Geometry Group Network (VGG19) and the second version of Google MobileNet. Each deep neural network model is able to analyze the normalized intensities of the X-ray image to classify the patient status either negative or positive COVID-19 case. Results: Experiments and evaluation of the COVIDX-Net have been successfully done based on 80-20% of X-ray images for the model training and testing phases, respectively. The VGG19 and Dense Convolutional Network (DenseNet) models showed a good and similar performance of automated COVID-19 classification with f1-scores of 0.89 and 0.91 for normal and COVID-19, respectively. Conclusions: This study demonstrated the useful application of deep learning models to classify COVID-19 in X-ray images based on the proposed COVIDX-Net framework. Clinical studies are the next milestone of this research work.

Automatic Detection of Coronavirus Disease (COVID-19) Using X-ray Images and Deep Convolutional Neural Networks

Abstract: The 2019 novel coronavirus disease (COVID-19), with a starting point in China, has spread rapidly among people living in other countries, and is approaching approximately 34,986,502 cases worldwide according to the statistics of European Centre for Disease Prevention and Control. There are a limited number of COVID-19 test kits available in hospitals due to the increasing cases daily. Therefore, it is necessary to implement an automatic detection system as a quick alternative diagnosis option to prevent COVID-19 spreading among people. In this study, five pre-trained convolutional neural network based models (ResNet50, ResNet101, ResNet152, InceptionV3 and Inception-ResNetV2) have been proposed for the detection of coronavirus pneumonia infected patient using chest X-ray radiographs. We have implemented three different binary classifications with four classes (COVID-19, normal (healthy), viral pneumonia and bacterial pneumonia) by using 5-fold cross validation. Considering the performance results obtained, it has seen that the pre-trained ResNet50 model provides the highest classification performance (96.1% accuracy for Dataset-1, 99.5% accuracy for Dataset-2 and 99.7% accuracy for Dataset-3) among other four used models.

Summary of papers that used Deep Learning in the field of COVID-19

COVID-19 has put researchers, health professionals at a critical situation due to the lack of timely information and historical data. Intelligent systems cannot work unless they are trained with reliable data. Application of AI and other related techniques: machine learning, deep learning is done based on the previous experiences i.e data and models. Given that very little information related to COVID-19 are available, researchers mostly rely on X-ray images and CT scan images. Although a very small amount of Chest-X Ray (CXR) of COVID-19 is available, CXRs are prescribed as one of the first diagnostic tests by the physician. Most of the earlier research works use CXR images to detect COVID-19 (26.67%) and others use chest CT images (Figure {{figure:896b51d4-4f2f-45af-b605-cfea07ba22e8}} ). The recent development of deep neural networks has opened up a new frontier in image classification. We found most of the research papers (43%) use different architecture of deep neural networks (Figure {{figure:42da3db9-91cc-42fe-b275-3dafa6c8d3f4}} ) to classify images, both CXR and CT scan (Table {{table:505a0852-f4c5-46d6-b674-8d5c22a663c4}} ). When it comes to image data, Convoluted Neural Networks dominated over all other algorithms and techniques(Table {{table:7a7c2f4a-e0dc-435d-ad87-6702c99d392c}} ). Using CNN as a base, several studies come up with their architecture {{cite:dc38c15}}. Our observation finds out among several CNNs, the Res-Net architecture as the most used one (Figure {{figure:3ec127d9-6b19-4525-a67d-8200356c9518}} ). Using the Res-Net architecture as a backbone, the models are different from one another on several parameters i.e. several hidden parameters, epochs and optimizer. Some studies also use a combination of different deep neural architectures. For example, Ezz et al.{{cite:3889aef}} compared six other different models with Red-NetV2 to propose the best one. Some studies, for example, Wang et al. {{cite:82c23c5}} use a combination of Res-Net with other machine learning algorithms. The authors used Res-Net for feature extraction from CXR and leverage SVM and decision trees to develop a new algorithm. Other than classification, Biraja et al.{{cite:7a8c5a1}} use different architectures i.e. bayesian CNN, monte Carlo drop weights along with Res-Net to assess the uncertainty associated with applying deep neural networks to detect COVID-19. Due to the pervasive use of deep learning networks and models, we have used a separate a table, Table {{table:505a0852-f4c5-46d6-b674-8d5c22a663c4}}  to present the deep learning architectures used and their results.

The authors depend on the train-test split method for validation of their models as none of these models is used to test on real patients. As a validation metric, the studies have used accuracy, specificity, sensitivity, f-1 score and area under Receiver Operating Characteristic(ROC) curve (AUC). Among other evaluation matrics authors also used False Positive Rate (FPR), True Positive Rate (TPR), positive and negative predictive values (PPV and NPV respectively). Our finding suggests that deep learning algorithms achieve a higher score in most of the evaluation matrices (see Table {{table:7a7c2f4a-e0dc-435d-ad87-6702c99d392c}} , and {{table:505a0852-f4c5-46d6-b674-8d5c22a663c4}} ).


It can be easily added to any training model.

Has big potential of generalization among different tasks.

Good performance, being the state-of-the-art.

Difficult and complex to estimate the transition matrix in practice.

Requires to be combined with other strategies to be competitive with state-of-the-art.

Not competitive with state-of-the-art because do not use the noisy samples in an unsupervised way.

Usually requires a clean validation set.

Use a set of combined methods that adds complexity to the solution.

Making Deep Neural Networks Robust to Label Noise: a Loss Correction Approach

Abstract: We present a theoretically grounded approach to train deep neural networks, including recurrent networks, subject to class-dependent label noise. We propose two procedures for loss correction that are agnostic to both application domain and network architecture. They simply amount to at most a matrix inversion and multiplication, provided that we know the probability of each class being corrupted into another. We further show how one can estimate these probabilities, adapting a recent technique for noise estimation to the multi-class setting, and thus providing an end-to-end framework. Extensive experiments on MNIST, IMDB, CIFAR-10, CIFAR-100 and a large scale dataset of clothing images employing a diversity of architectures --- stacking dense, convolutional, pooling, dropout, batch normalization, word embedding, LSTM and residual layers --- demonstrate the noise robustness of our proposals. Incidentally, we also prove that, when ReLU is the only non-linearity, the loss curvature is immune to class-dependent label noise.

Noise Tolerance Under Risk Minimization

Abstract: In this paper, we explore noise-tolerant learning of classifiers. We formulate the problem as follows. We assume that there is an unobservable training set that is noise free. The actual training set given to the learning algorithm is obtained from this ideal data set by corrupting the class label of each example. The probability that the class label of an example is corrupted is a function of the feature vector of the example. This would account for most kinds of noisy data one encounters in practice. We say that a learning method is noise tolerant if the classifiers learnt with noise-free data and with noisy data, both have the same classification accuracy on the noise-free data. In this paper, we analyze the noise-tolerance properties of risk minimization (under different loss functions). We show that risk minimization under 0-1 loss function has impressive noise-tolerance properties and that under squared error loss is tolerant only to uniform noise; risk minimization under other loss functions is not noise tolerant. We conclude this paper with some discussion on the implications of these theoretical results.

MentorNet: Learning Data-Driven Curriculum for Very Deep Neural Networks on Corrupted Labels

Abstract: Recent deep networks are capable of memorizing the entire data even when the labels are completely random. To overcome the overfitting on corrupted labels, we propose a novel technique of learning another neural network, called MentorNet, to supervise the training of the base deep networks, namely, StudentNet. During training, MentorNet provides a curriculum (sample weighting scheme) for StudentNet to focus on the sample the label of which is probably correct. Unlike the existing curriculum that is usually predefined by human experts, MentorNet learns a data-driven curriculum dynamically with StudentNet. Experimental results demonstrate that our approach can significantly improve the generalization performance of deep networks trained on corrupted training data. Notably, to the best of our knowledge, we achieve the best-published result on WebVision, a large benchmark containing 2.2 million images of real-world noisy labels. The code are at https://github.com/google/mentornet

Learning to Reweight Examples for Robust Deep Learning

Abstract: Deep neural networks have been shown to be very powerful modeling tools for many supervised learning tasks involving complex input patterns. However, they can also easily overfit to training set biases and label noises. In addition to various regularizers, example reweighting algorithms are popular solutions to these problems, but they require careful tuning of additional hyperparameters, such as example mining schedules and regularization hyperparameters. In contrast to past reweighting methods, which typically consist of functions of the cost value of each example, in this work we propose a novel meta-learning algorithm that learns to assign weights to training examples based on their gradient directions. To determine the example weights, our method performs a meta gradient descent step on the current mini-batch example weights (which are initialized from zero) to minimize the loss on a clean unbiased validation set. Our proposed method can be easily implemented on any type of deep network, does not require any additional hyperparameter tuning, and achieves impressive performance on class imbalance and corrupted label problems where only a small amount of clean validation data is available.

mixup: Beyond Empirical Risk Minimization

Abstract: Large deep neural networks are powerful, but exhibit undesirable behaviors such as memorization and sensitivity to adversarial examples. In this work, we propose mixup, a simple learning principle to alleviate these issues. In essence, mixup trains a neural network on convex combinations of pairs of examples and their labels. By doing so, mixup regularizes the neural network to favor simple linear behavior in-between training examples. Our experiments on the ImageNet-2012, CIFAR-10, CIFAR-100, Google commands and UCI datasets show that mixup improves the generalization of state-of-the-art neural network architectures. We also find that mixup reduces the memorization of corrupt labels, increases the robustness to adversarial examples, and stabilizes the training of generative adversarial networks.

Main approaches in the literature to deal with noisy labels.

The main approaches described in this section are summarized in Table {{table:f99c4b2f-3655-4011-abfe-7706c11e5942}}  that shows the combined strategies used by the methods of the state-of-the-art. Table {{table:51f8f73c-c3dd-4b2a-b293-cbb6fb8cc013}}  shows the main components of the combined techniques in the state-of-the-art and the difference between them.


SMASH: One-Shot Model Architecture Search through HyperNetworks

Abstract: Designing architectures for deep neural networks requires expert knowledge and substantial computation time. We propose a technique to accelerate architecture selection by learning an auxiliary HyperNet that generates the weights of a main model conditioned on that model's architecture. By comparing the relative validation performance of networks with HyperNet-generated weights, we can effectively search over a wide range of architectures at the cost of a single training run. To facilitate this search, we develop a flexible mechanism based on memory read-writes that allows us to define a wide range of network connectivity patterns, with ResNet, DenseNet, and FractalNet blocks as special cases. We validate our method (SMASH) on CIFAR-10 and CIFAR-100, STL-10, ModelNet10, and Imagenet32x32, achieving competitive performance with similarly-sized hand-designed networks. Our code is available at https://github.com/ajbrock/SMASH

DeepSwarm: Optimising Convolutional Neural Networks using Swarm Intelligence

Abstract: In this paper we propose DeepSwarm, a novel neural architecture search (NAS) method based on Swarm Intelligence principles. At its core DeepSwarm uses Ant Colony Optimization (ACO) to generate ant population which uses the pheromone information to collectively search for the best neural architecture. Furthermore, by using local and global pheromone update rules our method ensures the balance between exploitation and exploration. On top of this, to make our method more efficient we combine progressive neural architecture search with weight reusability. Furthermore, due to the nature of ACO our method can incorporate heuristic information which can further speed up the search process. After systematic and extensive evaluation, we discover that on three different datasets (MNIST, Fashion-MNIST, and CIFAR-10) when compared to existing systems our proposed method demonstrates competitive performance. Finally, we open source DeepSwarm as a NAS library and hope it can be used by more deep learning researchers and practitioners.

Path-Level Network Transformation for Efficient Architecture Search

Abstract: We introduce a new function-preserving transformation for efficient neural architecture search. This network transformation allows reusing previously trained networks and existing successful architectures that improves sample efficiency. We aim to address the limitation of current network transformation operations that can only perform layer-level architecture modifications, such as adding (pruning) filters or inserting (removing) a layer, which fails to change the topology of connection paths. Our proposed path-level transformation operations enable the meta-controller to modify the path topology of the given network while keeping the merits of reusing weights, and thus allow efficiently designing effective structures with complex path topologies like Inception models. We further propose a bidirectional tree-structured reinforcement learning meta-controller to explore a simple yet highly expressive tree-structured architecture space that can be viewed as a generalization of multi-branch architectures. We experimented on the image classification datasets with limited computational resources (about 200 GPU-hours), where we observed improved parameter efficiency and better test results (97.70% test accuracy on CIFAR-10 with 14.3M parameters and 74.6% top-1 accuracy on ImageNet in the mobile setting), demonstrating the effectiveness and transferability of our designed architectures.

ProxylessNAS: Direct Neural Architecture Search on Target Task and Hardware

Abstract: Neural architecture search (NAS) has a great impact by automatically designing effective neural network architectures. However, the prohibitive computational demand of conventional NAS algorithms (e.g. $10^4$ GPU hours) makes it difficult to \emph{directly} search the architectures on large-scale tasks (e.g. ImageNet). Differentiable NAS can reduce the cost of GPU hours via a continuous representation of network architecture but suffers from the high GPU memory consumption issue (grow linearly w.r.t. candidate set size). As a result, they need to utilize~\emph{proxy} tasks, such as training on a smaller dataset, or learning with only a few blocks, or training just for a few epochs. These architectures optimized on proxy tasks are not guaranteed to be optimal on the target task. In this paper, we present \emph{ProxylessNAS} that can \emph{directly} learn the architectures for large-scale target tasks and target hardware platforms. We address the high memory consumption issue of differentiable NAS and reduce the computational cost (GPU hours and GPU memory) to the same level of regular training while still allowing a large candidate set. Experiments on CIFAR-10 and ImageNet demonstrate the effectiveness of directness and specialization. On CIFAR-10, our model achieves 2.08\% test error with only 5.7M parameters, better than the previous state-of-the-art architecture AmoebaNet-B, while using 6$\times$ fewer parameters. On ImageNet, our model achieves 3.1\% better top-1 accuracy than MobileNetV2, while being 1.2$\times$ faster with measured GPU latency. We also apply ProxylessNAS to specialize neural architectures for hardware with direct hardware metrics (e.g. latency) and provide insights for efficient CNN architecture design.

Simple And Efficient Architecture Search for Convolutional Neural Networks

Abstract: Neural networks have recently had a lot of success for many tasks. However, neural network architectures that perform well are still typically designed manually by experts in a cumbersome trial-and-error process. We propose a new method to automatically search for well-performing CNN architectures based on a simple hill climbing procedure whose operators apply network morphisms, followed by short optimization runs by cosine annealing. Surprisingly, this simple method yields competitive results, despite only requiring resources in the same order of magnitude as training a single network. E.g., on CIFAR-10, our method designs and trains networks with an error rate below 6% in only 12 hours on a single GPU; training for one day reduces this error further, to almost 5%.

Auto-Keras: An Efficient Neural Architecture Search System

Abstract: Neural architecture search (NAS) has been proposed to automatically tune deep neural networks, but existing search algorithms, e.g., NASNet, PNAS, usually suffer from expensive computational cost. Network morphism, which keeps the functionality of a neural network while changing its neural architecture, could be helpful for NAS by enabling more efficient training during the search. In this paper, we propose a novel framework enabling Bayesian optimization to guide the network morphism for efficient neural architecture search. The framework develops a neural network kernel and a tree-structured acquisition function optimization algorithm to efficiently explores the search space. Extensive experiments on real-world benchmark datasets have been done to demonstrate the superior performance of the developed framework over the state-of-the-art methods. Moreover, we build an open-source AutoML system based on our method, namely Auto-Keras. The code and documentation are available at https://autokeras.com. The system runs in parallel on CPU and GPU, with an adaptive search strategy for different GPU memory limits.

Neural Architecture Search with Bayesian Optimisation and Optimal Transport

Abstract: Bayesian Optimisation (BO) refers to a class of methods for global optimisation of a function $f$ which is only accessible via point evaluations. It is typically used in settings where $f$ is expensive to evaluate. A common use case for BO in machine learning is model selection, where it is not possible to analytically model the generalisation performance of a statistical model, and we resort to noisy and expensive training and validation procedures to choose the best model. Conventional BO methods have focused on Euclidean and categorical domains, which, in the context of model selection, only permits tuning scalar hyper-parameters of machine learning algorithms. However, with the surge of interest in deep learning, there is an increasing demand to tune neural network \emph{architectures}. In this work, we develop NASBOT, a Gaussian process based BO framework for neural architecture search. To accomplish this, we develop a distance metric in the space of neural network architectures which can be computed efficiently via an optimal transport program. This distance might be of independent interest to the deep learning community as it may find applications outside of BO. We demonstrate that NASBOT outperforms other alternatives for architecture search in several cross validation based model selection tasks on multi-layer perceptrons and convolutional neural networks.

Evolutionary architecture search for deep multitask networks

Abstract: Multitask learning, i.e. learning several tasks at once with the same neural network, can improve performance in each of the tasks. Designing deep neural network architectures for multitask learning is a challenge: There are many ways to tie the tasks together, and the design choices matter. The size and complexity of this problem exceeds human design ability, making it a compelling domain for evolutionary optimization. Using the existing state of the art soft ordering architecture as the starting point, methods for evolving the modules of this architecture and for evolving the overall topology or routing between modules are evaluated in this paper. A synergetic approach of evolving custom routings with evolved, shared modules for each task is found to be very powerful, significantly improving the state of the art in the Omniglot multitask, multialphabet character recognition domain. This result demonstrates how evolution can be instrumental in advancing deep neural network and complex system design in general.

Progressive Neural Architecture Search

Abstract: We propose a new method for learning the structure of convolutional neural networks (CNNs) that is more efficient than recent state-of-the-art methods based on reinforcement learning and evolutionary algorithms. Our approach uses a sequential model-based optimization (SMBO) strategy, in which we search for structures in order of increasing complexity, while simultaneously learning a surrogate model to guide the search through structure space. Direct comparison under the same search space shows that our method is up to 5 times more efficient than the RL method of Zoph et al. (2018) in terms of number of models evaluated, and 8 times faster in terms of total compute. The structures we discover in this way achieve state of the art classification accuracies on CIFAR-10 and ImageNet.

DARTS: Differentiable Architecture Search

Abstract: This paper addresses the scalability challenge of architecture search by formulating the task in a differentiable manner. Unlike conventional approaches of applying evolution or reinforcement learning over a discrete and non-differentiable search space, our method is based on the continuous relaxation of the architecture representation, allowing efficient search of the architecture using gradient descent. Extensive experiments on CIFAR-10, ImageNet, Penn Treebank and WikiText-2 show that our algorithm excels in discovering high-performance convolutional architectures for image classification and recurrent architectures for language modeling, while being orders of magnitude faster than state-of-the-art non-differentiable techniques. Our implementation has been made publicly available to facilitate further research on efficient architecture search algorithms.

Hierarchical Representations for Efficient Architecture Search

Abstract: We explore efficient neural architecture search methods and show that a simple yet powerful evolutionary algorithm can discover new architectures with excellent performance. Our approach combines a novel hierarchical genetic representation scheme that imitates the modularized design pattern commonly adopted by human experts, and an expressive search space that supports complex topologies. Our algorithm efficiently discovers architectures that outperform a large number of manually designed models for image classification, obtaining top-1 error of 3.6% on CIFAR-10 and 20.3% when transferred to ImageNet, which is competitive with the best existing neural architecture search approaches. We also present results using random search, achieving 0.3% less top-1 accuracy on CIFAR-10 and 0.1% less on ImageNet whilst reducing the search time from 36 hours down to 1 hour.

Neural Architecture Optimization

Abstract: Automatic neural architecture design has shown its potential in discovering powerful neural network architectures. Existing methods, no matter based on reinforcement learning or evolutionary algorithms (EA), conduct architecture search in a discrete space, which is highly inefficient. In this paper, we propose a simple and efficient method to automatic neural architecture design based on continuous optimization. We call this new approach neural architecture optimization (NAO). There are three key components in our proposed approach: (1) An encoder embeds/maps neural network architectures into a continuous space. (2) A predictor takes the continuous representation of a network as input and predicts its accuracy. (3) A decoder maps a continuous representation of a network back to its architecture. The performance predictor and the encoder enable us to perform gradient based optimization in the continuous space to find the embedding of a new architecture with potentially better accuracy. Such a better embedding is then decoded to a network by the decoder. Experiments show that the architecture discovered by our method is very competitive for image classification task on CIFAR-10 and language modeling task on PTB, outperforming or on par with the best results of previous architecture search methods with a significantly reduction of computational resources. Specifically we obtain 1.93% test set error rate for CIFAR-10 image classification task and 56.0 test set perplexity of PTB language modeling task. Furthermore, combined with the recent proposed weight sharing mechanism, we discover powerful architecture on CIFAR-10 (with error rate 2.93%) and on PTB (with test set perplexity 56.6), with very limited computational resources (less than 10 GPU hours) for both tasks.

Efficient Neural Architecture Search via Parameter Sharing

Abstract: We propose Efficient Neural Architecture Search (ENAS), a fast and inexpensive approach for automatic model design. In ENAS, a controller learns to discover neural network architectures by searching for an optimal subgraph within a large computational graph. The controller is trained with policy gradient to select a subgraph that maximizes the expected reward on the validation set. Meanwhile the model corresponding to the selected subgraph is trained to minimize a canonical cross entropy loss. Thanks to parameter sharing between child models, ENAS is fast: it delivers strong empirical performances using much fewer GPU-hours than all existing automatic model design approaches, and notably, 1000x less expensive than standard Neural Architecture Search. On the Penn Treebank dataset, ENAS discovers a novel architecture that achieves a test perplexity of 55.8, establishing a new state-of-the-art among all methods without post-training processing. On the CIFAR-10 dataset, ENAS designs novel architectures that achieve a test error of 2.89%, which is on par with NASNet (Zoph et al., 2018), whose test error is 2.65%.

Regularized Evolution for Image Classifier Architecture Search

Abstract: The effort devoted to hand-crafting neural network image classifiers has motivated the use of architecture search to discover them automatically. Although evolutionary algorithms have been repeatedly applied to neural network topologies, the image classifiers thus discovered have remained inferior to human-crafted ones. Here, we evolve an image classifier— AmoebaNet-A—that surpasses hand-designs for the first time. To do this, we modify the tournament selection evolutionary algorithm by introducing an age property to favor the younger genotypes. Matching size, AmoebaNet-A has comparable accuracy to current state-of-the-art ImageNet models discovered with more complex architecture-search methods. Scaled to larger size, AmoebaNet-A sets a new state-of-theart 83.9% top-1 / 96.6% top-5 ImageNet accuracy. In a controlled comparison against a well known reinforcement learning algorithm, we give evidence that evolution can obtain results faster with the same hardware, especially at the earlier stages of the search. This is relevant when fewer compute resources are available. Evolution is, thus, a simple method to effectively discover high-quality architectures.

MnasNet: Platform-Aware Neural Architecture Search for Mobile

Abstract: Designing convolutional neural networks (CNN) for mobile devices is challenging because mobile models need to be small and fast, yet still accurate. Although significant efforts have been dedicated to design and improve mobile CNNs on all dimensions, it is very difficult to manually balance these trade-offs when there are so many architectural possibilities to consider. In this paper, we propose an automated mobile neural architecture search (MNAS) approach, which explicitly incorporate model latency into the main objective so that the search can identify a model that achieves a good trade-off between accuracy and latency. Unlike previous work, where latency is considered via another, often inaccurate proxy (e.g., FLOPS), our approach directly measures real-world inference latency by executing the model on mobile phones. To further strike the right balance between flexibility and search space size, we propose a novel factorized hierarchical search space that encourages layer diversity throughout the network. Experimental results show that our approach consistently outperforms state-of-the-art mobile CNN models across multiple vision tasks. On the ImageNet classification task, our MnasNet achieves 75.2% top-1 accuracy with 78ms latency on a Pixel phone, which is 1.8× faster than MobileNetV2 with 0.5% higher accuracy and 2.3× faster than NASNet with 1.2% higher accuracy. Our MnasNet also achieves better mAP quality than MobileNets for COCO object detection. Code is at https://github.com/tensorflow/tpu/tree/master/models/official/mnasnet.

Towards Automated Deep Learning: Efficient Joint Neural Architecture and Hyperparameter Search

Abstract: While existing work on neural architecture search (NAS) tunes hyperparameters in a separate post-processing step, we demonstrate that architectural choices and other hyperparameter settings interact in a way that can render this separation suboptimal. Likewise, we demonstrate that the common practice of using very few epochs during the main NAS and much larger numbers of epochs during a post-processing step is inefficient due to little correlation in the relative rankings for these two training regimes. To combat both of these problems, we propose to use a recent combination of Bayesian optimization and Hyperband for efficient joint neural architecture and hyperparameter search.

Graph HyperNetworks for Neural Architecture Search

Abstract: Neural architecture search (NAS) automatically finds the best task-specific neural network topology, outperforming many manual architecture designs. However, it can be prohibitively expensive as the search requires training thousands of different networks, while each can last for hours. In this work, we propose the Graph HyperNetwork (GHN) to amortize the search cost: given an architecture, it directly generates the weights by running inference on a graph neural network. GHNs model the topology of an architecture and therefore can predict network performance more accurately than regular hypernetworks and premature early stopping. To perform NAS, we randomly sample architectures and use the validation accuracy of networks with GHN generated weights as the surrogate search signal. GHNs are fast -- they can search nearly 10 times faster than other random search methods on CIFAR-10 and ImageNet. GHNs can be further extended to the anytime prediction setting, where they have found networks with better speed-accuracy tradeoff than the state-of-the-art manual designs.

Neural Architecture Search with Reinforcement Learning

Abstract: Neural networks are powerful and flexible models that work well for many difficult learning tasks in image, speech and natural language understanding. Despite their success, neural networks are still hard to design. In this paper, we use a recurrent network to generate the model descriptions of neural networks and train this RNN with reinforcement learning to maximize the expected accuracy of the generated architectures on a validation set. On the CIFAR-10 dataset, our method, starting from scratch, can design a novel network architecture that rivals the best human-invented architecture in terms of test set accuracy. Our CIFAR-10 model achieves a test error rate of 3.65, which is 0.09 percent better and 1.05x faster than the previous state-of-the-art model that used a similar architectural scheme. On the Penn Treebank dataset, our model can compose a novel recurrent cell that outperforms the widely-used LSTM cell, and other state-of-the-art baselines. Our cell achieves a test set perplexity of 62.4 on the Penn Treebank, which is 3.6 perplexity better than the previous state-of-the-art model. The cell can also be transferred to the character language modeling task on PTB and achieves a state-of-the-art perplexity of 1.214.

Learning Transferable Architectures for Scalable Image Recognition

Abstract: Developing neural network image classification models often requires significant architecture engineering. In this paper, we study a method to learn the model architectures directly on the dataset of interest. As this approach is expensive when the dataset is large, we propose to search for an architectural building block on a small dataset and then transfer the block to a larger dataset. The key contribution of this work is the design of a new search space (which we call the "NASNet search space") which enables transferability. In our experiments, we search for the best convolutional layer (or "cell") on the CIFAR-10 dataset and then apply this cell to the ImageNet dataset by stacking together more copies of this cell, each with their own parameters to design a convolutional architecture, which we name a "NASNet architecture". We also introduce a new regularization technique called ScheduledDropPath that significantly improves generalization in the NASNet models. On CIFAR-10 itself, a NASNet found by our method achieves 2.4% error rate, which is state-of-the-art. Although the cell is not searched for directly on ImageNet, a NASNet constructed from the best cell achieves, among the published works, state-of-the-art accuracy of 82.7% top-1 and 96.2% top-5 on ImageNet. Our model is 1.2% better in top-1 accuracy than the best human-invented architectures while having 9 billion fewer FLOPS - a reduction of 28% in computational demand from the previous state-of-the-art model. When evaluated at different levels of computational cost, accuracies of NASNets exceed those of the state-of-the-art human-designed models. For instance, a small version of NASNet also achieves 74% top-1 accuracy, which is 3.1% better than equivalently-sized, state-of-the-art models for mobile platforms. Finally, the image features learned from image classification are generically useful and can be transferred to other computer vision problems. On the task of object detection, the learned features by NASNet used with the Faster-RCNN framework surpass state-of-the-art by 4.0% achieving 43.1% mAP on the COCO dataset.

Overview of various algorithms.

Finally, as shown in {{cite:e49ee71}}, weight-sharing amongst candidate architectures has been demonstrated to provide positive ranking correlation to architectures trained from scartch. This has been leveraged by the one-shot and weight-sharing family of methods, where either a hyper-graph is trained with gradient descent {{cite:be2a65c}} or individual paths are chosen and the corresponding weights are updated {{cite:168ab29}}, {{cite:47982d0}}, {{cite:e49ee71}}. Concluding the algorithm presentation sections, Table {{table:fc00a1dd-f0c8-4121-a764-f20028b0fb34}}  contains an overview of the algorithms presented in this work. Table {{table:ca664042-dd73-486c-a8f8-4f0c881c10d7}}  contains an explanation of the abbreviations used.


Variable Rate Image Compression with Recurrent Neural Networks

End-to-End Optimization of Nonlinear Transform Codes for Perceptual Quality

Full Resolution Image Compression with Recurrent Neural Networks

Soft-to-Hard Vector Quantization for End-to-End Learning Compressible Representations

Lossy Image Compression with Compressive Autoencoder

Learning to Inpaint for Image Compression

Spatially Adaptive Image Compression Using a Tiled Deep Network

Variational Image Compression with a Scale Hyperprior

Image-Dependent Local Entropy Models for Learned Image Compression

Conditional Probability Models for Deep Image Compression

Improved Lossy Image Compression with Priming and Spatially Adaptive Bit Rates for Recurrent Networks

Learning Convolutional Networks for Content-Weighted Image Compression

Deep Generative Models for Distribution-Preserving Lossy Compression

Context Adaptive Entropy Model for End-To-End Optimized Image Compression

Learning Image and Video Compression through Spatial-Temporal Energy Compaction

The first work to utilize a convolutional LSTM network for variable-bit-rate end-to-end learned image compression.

Introduces GDN, a trainable decorrelation nonlinear normalization that shows a great capability for image compression.

The first practical recurrent model for variable-bit-rate full-resolution image compression.

Introduces vector quantization for learned compression and proposes using soft-to-hard annealing techniques to improve the performance of networks with quantization.

Residual network is first employed for CNN-based image compression models. A Laplace-smoothed histogram is used as the entropy model.

Introduces the multilayer nonpartitioning end-to-end architecture with GDN for image compression.

Utilizes image inpainting techniques in a recurrent framework to improve compression performance.

The first method to adopt a multiscale framework with adversarial loss for learned real-time image compression.

Introduces explicit intraprediction with a tiled structure in the network.

The first work to propose a hyperprior for image compression, which greatly advances the compression performance.

Aims to better encode latent representations with an offline dictionary.

3D-CNN is used for learning a conditional probability model for a multiresidual-block-based network.

The recurrent compression model is improved with a proposed priming technique and spatial contextual entropy model.

Proposes using a learned importance map to guide the allocation of bits for latent code.

GAN is first used for extremely low bit-rate image compression.

Proposes a multiscale model and corresponding contextual entropy estimation to improve compression efficiency.

Introduces a different approach to combine a hyperprior and the context model for image compression.

Introduces a subband coding energy compaction technique for CNN-based image compression.

Abstract: A large fraction of Internet traffic is now driven by requests from mobile devices with relatively small screens and often stringent bandwidth requirements. Due to these factors, it has become the norm for modern graphics-heavy websites to transmit low-resolution, low-bytecount image previews (thumbnails) as part of the initial page load process to improve apparent page responsiveness. Increasing thumbnail compression beyond the capabilities of existing codecs is therefore a current research focus, as any byte savings will significantly enhance the experience of mobile device users. Toward this end, we propose a general framework for variable-rate image compression and a novel architecture based on convolutional and deconvolutional LSTM recurrent networks. Our models address the main issues that have prevented autoencoder neural networks from competing with existing image compression algorithms: (1) our networks only need to be trained once (not per-image), regardless of input image dimensions and the desired compression rate; (2) our networks are progressive, meaning that the more bits are sent, the more accurate the image reconstruction; and (3) the proposed architecture is at least as efficient as a standard purpose-trained autoencoder for a given number of bits. On a large-scale benchmark of 32$\times$32 thumbnails, our LSTM-based approaches provide better visual quality than (headerless) JPEG, JPEG2000 and WebP, with a storage size that is reduced by 10% or more.

End-to-end optimization of nonlinear transform codes for perceptual quality

Abstract: We introduce a general framework for end-to-end optimization of the rate--distortion performance of nonlinear transform codes assuming scalar quantization. The framework can be used to optimize any differentiable pair of analysis and synthesis transforms in combination with any differentiable perceptual metric. As an example, we consider a code built from a linear transform followed by a form of multi-dimensional local gain control. Distortion is measured with a state-of-the-art perceptual metric. When optimized over a large database of images, this representation offers substantial improvements in bitrate and perceptual appearance over fixed (DCT) codes, and over linear transform codes optimized for mean squared error.

Abstract: This paper presents a set of full-resolution lossy image compression methods based on neural networks. Each of the architectures we describe can provide variable compression rates during deployment without requiring retraining of the network: each network need only be trained once. All of our architectures consist of a recurrent neural network (RNN)-based encoder and decoder, a binarizer, and a neural network for entropy coding. We compare RNN types (LSTM, associative LSTM) and introduce a new hybrid of GRU and ResNet. We also study "one-shot" versus additive reconstruction architectures and introduce a new scaled-additive framework. We compare to previous work, showing improvements of 4.3%-8.8% AUC (area under the rate-distortion curve), depending on the perceptual metric used. As far as we know, this is the first neural network architecture that is able to outperform JPEG at image compression across most bitrates on the rate-distortion curve on the Kodak dataset images, with and without the aid of entropy coding.

Abstract: We present a new approach to learn compressible representations in deep architectures with an end-to-end training strategy. Our method is based on a soft (continuous) relaxation of quantization and entropy, which we anneal to their discrete counterparts throughout training. We showcase this method for two challenging applications: Image compression and neural network compression. While these tasks have typically been approached with different methods, our soft-to-hard quantization approach gives results competitive with the state-of-the-art for both.

Lossy Image Compression with Compressive Autoencoders

Abstract: We propose a new approach to the problem of optimizing autoencoders for lossy image compression. New media formats, changing hardware technology, as well as diverse requirements and content types create a need for compression algorithms which are more flexible than existing codecs. Autoencoders have the potential to address this need, but are difficult to optimize directly due to the inherent non-differentiabilty of the compression loss. We here show that minimal changes to the loss are sufficient to train deep autoencoders competitive with JPEG 2000 and outperforming recently proposed approaches based on RNNs. Our network is furthermore computationally efficient thanks to a sub-pixel architecture, which makes it suitable for high-resolution images. This is in contrast to previous work on autoencoders for compression using coarser approximations, shallower architectures, computationally expensive methods, or focusing on small images.

End-to-end Optimized Image Compression

Abstract: We describe an image compression method, consisting of a nonlinear analysis transformation, a uniform quantizer, and a nonlinear synthesis transformation. The transforms are constructed in three successive stages of convolutional linear filters and nonlinear activation functions. Unlike most convolutional neural networks, the joint nonlinearity is chosen to implement a form of local gain control, inspired by those used to model biological neurons. Using a variant of stochastic gradient descent, we jointly optimize the entire model for rate-distortion performance over a database of training images, introducing a continuous proxy for the discontinuous loss function arising from the quantizer. Under certain conditions, the relaxed loss function may be interpreted as the log likelihood of a generative model, as implemented by a variational autoencoder. Unlike these models, however, the compression model must operate at any given point along the rate-distortion curve, as specified by a trade-off parameter. Across an independent set of test images, we find that the optimized method generally exhibits better rate-distortion performance than the standard JPEG and JPEG 2000 compression methods. More importantly, we observe a dramatic improvement in visual quality for all images at all bit rates, which is supported by objective quality estimates using MS-SSIM.

Learning to Inpaint for Image Compression

Abstract: We study the design of deep architectures for lossy image compression. We present two architectural recipes in the context of multi-stage progressive encoders and empirically demonstrate their importance on compression performance. Specifically, we show that: (a) predicting the original image data from residuals in a multi-stage progressive architecture facilitates learning and leads to improved performance at approximating the original content and (b) learning to inpaint (from neighboring image pixels) before performing compression reduces the amount of information that must be stored to achieve a high-quality approximation. Incorporating these design choices in a baseline progressive encoder yields an average reduction of over $60\%$ in file size with similar quality compared to the original residual encoder.

Real-Time Adaptive Image Compression

Abstract: We present a machine learning-based approach to lossy image compression which outperforms all existing codecs, while running in real-time. Our algorithm typically produces files 2.5 times smaller than JPEG and JPEG 2000, 2 times smaller than WebP, and 1.7 times smaller than BPG on datasets of generic images across all quality levels. At the same time, our codec is designed to be lightweight and deployable: for example, it can encode or decode the Kodak dataset in around 10ms per image on GPU. Our architecture is an autoencoder featuring pyramidal analysis, an adaptive coding module, and regularization of the expected codelength. We also supplement our approach with adversarial training specialized towards use in a compression setting: this enables us to produce visually pleasing reconstructions for very low bitrates.

Spatially adaptive image compression using a tiled deep network

Abstract: Deep neural networks represent a powerful class of function approximators that can learn to compress and reconstruct images. Existing image compression algorithms based on neural networks learn quantized representations with a constant spatial bit rate across each image. While entropy coding introduces some spatial variation, traditional codecs have benefited significantly by explicitly adapting the bit rate based on local image complexity and visual saliency. This paper introduces an algorithm that combines deep neural networks with quality-sensitive bit rate adaptation using a tiled network. We demonstrate the importance of spatial context prediction and show improved quantitative (PSNR) and qualitative (subjective rater assessment) results compared to a non-adaptive baseline and a recently published image compression model based on fully-convolutional neural networks.

Variational image compression with a scale hyperprior

Abstract: We describe an end-to-end trainable model for image compression based on variational autoencoders. The model incorporates a hyperprior to effectively capture spatial dependencies in the latent representation. This hyperprior relates to side information, a concept universal to virtually all modern image codecs, but largely unexplored in image compression using artificial neural networks (ANNs). Unlike existing autoencoder compression methods, our model trains a complex prior jointly with the underlying autoencoder. We demonstrate that this model leads to state-of-the-art image compression when measuring visual quality using the popular MS-SSIM index, and yields rate-distortion performance surpassing published ANN-based methods when evaluated using a more traditional metric based on squared error (PSNR). Furthermore, we provide a qualitative comparison of models trained for different distortion metrics.

Abstract: The leading approach for image compression with artificial neural networks (ANNs) is to learn a nonlinear transform and a fixed entropy model that are optimized for rate-distortion performance. We show that this approach can be significantly improved by incorporating spatially local, image-dependent entropy models. The key insight is that existing ANN-based methods learn an entropy model that is shared between the encoder and decoder, but they do not transmit any side information that would allow the model to adapt to the structure of a specific image. We present a method for augmenting ANN-based image coders with image-dependent side information that leads to a 17.8% rate reduction over a state-of-the-art ANN-based baseline model on a standard evaluation set, and 70-98% reductions on images with low visual complexity that are poorly captured by a fixed, global entropy model.

Abstract: Deep Neural Networks trained as image auto-encoders have recently emerged as a promising direction for advancing the state-of-the-art in image compression. The key challenge in learning such networks is twofold: To deal with quantization, and to control the trade-off between reconstruction error (distortion) and entropy (rate) of the latent image representation. In this paper, we focus on the latter challenge and propose a new technique to navigate the rate-distortion trade-off for an image compression auto-encoder. The main idea is to directly model the entropy of the latent representation by using a context model: A 3D-CNN which learns a conditional probability model of the latent distribution of the auto-encoder. During training, the auto-encoder makes use of the context model to estimate the entropy of its representation, and the context model is concurrently updated to learn the dependencies between the symbols in the latent representation. Our experiments show that this approach, when measured in MS-SSIM, yields a state-of-the-art image compression system based on a simple convolutional auto-encoder.

Abstract: We propose a method for lossy image compression based on recurrent, convolutional neural networks that outperforms BPG (4:2:0 ), WebP, JPEG2000, and JPEG as measured by MS-SSIM. We introduce three improvements over previous research that lead to this state-of-the-art result. First, we show that training with a pixel-wise loss weighted by SSIM increases reconstruction quality according to several metrics. Second, we modify the recurrent architecture to improve spatial diffusion, which allows the network to more effectively capture and propagate image information through the network's hidden state. Finally, in addition to lossless entropy coding, we use a spatially adaptive bit allocation algorithm to more efficiently use the limited number of bits to encode visually complex image regions. We evaluate our method on the Kodak and Tecnick image sets and compare against standard codecs as well recently published methods based on deep neural networks.

Learning Convolutional Networks for Content-weighted Image Compression

Abstract: Lossy image compression is generally formulated as a joint rate-distortion optimization to learn encoder, quantizer, and decoder. However, the quantizer is non-differentiable, and discrete entropy estimation usually is required for rate control. These make it very challenging to develop a convolutional network (CNN)-based image compression system. In this paper, motivated by that the local information content is spatially variant in an image, we suggest that the bit rate of the different parts of the image should be adapted to local content. And the content aware bit rate is allocated under the guidance of a content-weighted importance map. Thus, the sum of the importance map can serve as a continuous alternative of discrete entropy estimation to control compression rate. And binarizer is adopted to quantize the output of encoder due to the binarization scheme is also directly defined by the importance map. Furthermore, a proxy function is introduced for binary operation in backward propagation to make it differentiable. Therefore, the encoder, decoder, binarizer and importance map can be jointly optimized in an end-to-end manner by using a subset of the ImageNet database. In low bit rate image compression, experiments show that our system significantly outperforms JPEG and JPEG 2000 by structural similarity (SSIM) index, and can produce the much better visual result with sharp edges, rich textures, and fewer artifacts.

Abstract: We propose and study the problem of distribution-preserving lossy compression. Motivated by recent advances in extreme image compression which allow to maintain artifact-free reconstructions even at very low bitrates, we propose to optimize the rate-distortion tradeoff under the constraint that the reconstructed samples follow the distribution of the training data. The resulting compression system recovers both ends of the spectrum: On one hand, at zero bitrate it learns a generative model of the data, and at high enough bitrates it achieves perfect reconstruction. Furthermore, for intermediate bitrates it smoothly interpolates between learning a generative model of the training data and perfectly reconstructing the training samples. We study several methods to approximately solve the proposed optimization problem, including a novel combination of Wasserstein GAN and Wasserstein Autoencoder, and present an extensive theoretical and empirical characterization of the proposed compression systems.

Neural Multi-scale Image Compression

Abstract: This study presents a new lossy image compression method that utilizes the multi-scale features of natural images. Our model consists of two networks: multi-scale lossy autoencoder and parallel multi-scale lossless coder. The multi-scale lossy autoencoder extracts the multi-scale image features to quantized variables and the parallel multi-scale lossless coder enables rapid and accurate lossless coding of the quantized variables via encoding/decoding the variables in parallel. Our proposed model achieves comparable performance to the state-of-the-art model on Kodak and RAISE-1k dataset images, and it encodes a PNG image of size $768 \times 512$ in 70 ms with a single GPU and a single CPU process and decodes it into a high-fidelity image in approximately 200 ms.

Context-adaptive Entropy Model for End-to-end Optimized Image Compression

Abstract: We propose a context-adaptive entropy model for use in end-to-end optimized image compression. Our model exploits two types of contexts, bit-consuming contexts and bit-free contexts, distinguished based upon whether additional bit allocation is required. Based on these contexts, we allow the model to more accurately estimate the distribution of each latent representation with a more generalized form of the approximation models, which accordingly leads to an enhanced compression performance. Based on the experimental results, the proposed method outperforms the traditional image codecs, such as BPG and JPEG2000, as well as other previous artificial-neural-network (ANN) based approaches, in terms of the peak signal-to-noise ratio (PSNR) and multi-scale structural similarity (MS-SSIM) index.

Learning Image and Video Compression Through Spatial-Temporal Energy Compaction

Abstract: Compression has been an important research topic for many decades, to produce a significant impact on data transmission and storage. Recent advances have shown a great potential of learning based image and video compression. Inspired from related works, in this paper, we present an image compression architecture using a convolutional autoencoder, and then generalize image compression to video compression, by adding an interpolation loop into both encoder and decoder sides. Our basic idea is to realize spatial-temporal energy compaction in learning image and video compression. Thereby, we propose to add a spatial energy compaction-based penalty into loss function, to achieve higher image compression performance. Furthermore, based on temporal energy distribution, we propose to select the number of frames in one interpolation loop, adapting to the motion characteristics of video contents. Experimental results demonstrate that our proposed image compression outperforms the latest image compression standard with MS-SSIM quality metric, and provides higher performance compared with state-of-the-art learning compression methods at high bit rates, which benefits from our spatial energy compaction approach. Meanwhile, our proposed video compression approach with temporal energy compaction can significantly outperform MPEG-4, and is competitive with commonly used H.264. Both our image and video compression can produce more visually pleasant results than traditional standards.

Summary of important contributions of image compression in recent years.

Since the pioneering work of Toderici et al. {{cite:f9ad8cc}} in 2015 exploited recurrent neural networks for learned image compression, much progress has been made.
Benefiting from the strong modeling capacity of deep networks, the performance of learned image compression has exceeded that of JPEG to BPG (HEVC Intra), and the performance gap is widening further.
The milestones of learned image compression are summarized in Table {{table:ccb3eefe-9508-4243-a137-1c9506e3d00f}} . Early works aim to search for possible architectures to apply transform coding with neural networks and propose end-to-end trainable solutions.
Ballé et al. {{cite:9420356}}, {{cite:c8aeb4c}}, {{cite:a213688}} proposes a learning-based framework with GDN nonlinearity embedded analysis and synthesis transforms for learned image compression, while Toderici  et al. utilize recurrent models for variable-rate learned compression {{cite:f9ad8cc}}, {{cite:a1196d5}}.


Score-Based Generative Modeling through Stochastic Differential Equations

Abstract: Creating noise from data is easy; creating data from noise is generative modeling. We present a stochastic differential equation (SDE) that smoothly transforms a complex data distribution to a known prior distribution by slowly injecting noise, and a corresponding reverse-time SDE that transforms the prior distribution back into the data distribution by slowly removing the noise. Crucially, the reverse-time SDE depends only on the time-dependent gradient field (\aka, score) of the perturbed data distribution. By leveraging advances in score-based generative modeling, we can accurately estimate these scores with neural networks, and use numerical SDE solvers to generate samples. We show that this framework encapsulates previous approaches in score-based generative modeling and diffusion probabilistic modeling, allowing for new sampling procedures and new modeling capabilities. In particular, we introduce a predictor-corrector framework to correct errors in the evolution of the discretized reverse-time SDE. We also derive an equivalent neural ODE that samples from the same distribution as the SDE, but additionally enables exact likelihood computation, and improved sampling efficiency. In addition, we provide a new way to solve inverse problems with score-based models, as demonstrated with experiments on class-conditional generation, image inpainting, and colorization. Combined with multiple architectural improvements, we achieve record-breaking performance for unconditional image generation on CIFAR-10 with an Inception score of 9.89 and FID of 2.20, a competitive likelihood of 2.99 bits/dim, and demonstrate high fidelity generation of 1024 x 1024 images for the first time from a score-based generative model.

Gotta Go Fast When Generating Data with Score-Based Models

Abstract: Score-based (denoising diffusion) generative models have recently gained a lot of success in generating realistic and diverse data. These approaches define a forward diffusion process for transforming data to noise and generate data by reversing it (thereby going from noise to data). Unfortunately, current score-based models generate data very slowly due to the sheer number of score network evaluations required by numerical SDE solvers. In this work, we aim to accelerate this process by devising a more efficient SDE solver. Existing approaches rely on the Euler-Maruyama (EM) solver, which uses a fixed step size. We found that naively replacing it with other SDE solvers fares poorly - they either result in low-quality samples or become slower than EM. To get around this issue, we carefully devise an SDE solver with adaptive step sizes tailored to score-based generative models piece by piece. Our solver requires only two score function evaluations, rarely rejects samples, and leads to high-quality samples. Our approach generates data 2 to 10 times faster than EM while achieving better or equal sample quality. For high-resolution images, our method leads to significantly higher quality samples than all other methods tested. Our SDE solver has the benefit of requiring no step size tuning.

Come-Closer-Diffuse-Faster: Accelerating Conditional Diffusion Models for Inverse Problems through Stochastic Contraction

Abstract: Diffusion models have recently attained significant interest within the community owing to their strong performance as generative models. Furthermore, its application to inverse problems have demonstrated state-of-the-art performance. Unfortunately, diffusion models have a critical downside - they are inherently slow to sample from, needing few thousand steps of iteration to generate images from pure Gaussian noise. In this work, we show that starting from Gaussian noise is unnecessary. Instead, starting from a single forward diffusion with better initialization significantly reduces the number of sampling steps in the reverse conditional diffusion. This phenomenon is formally explained by the contraction theory of the stochastic difference equations like our conditional diffusion strategy - the alternating applications of reverse diffusion followed by a non-expansive data consistency step. The new sampling strategy, dubbed Come-Closer-Diffuse-Faster (CCDF), also reveals a new insight on how the existing feed-forward neural network approaches for inverse problems can be synergistically combined with the diffusion models. Experimental results with super-resolution, image inpainting, and compressed sensing MRI demonstrate that our method can achieve state-of-the-art reconstruction performance at significantly reduced sampling steps.

Generative Modeling by Estimating Gradients of the Data Distribution

Abstract: We introduce a new generative model where samples are produced via Langevin dynamics using gradients of the data distribution estimated with score matching. Because gradients can be ill-defined and hard to estimate when the data resides on low-dimensional manifolds, we perturb the data with different levels of Gaussian noise, and jointly estimate the corresponding scores, i.e., the vector fields of gradients of the perturbed data distribution for all noise levels. For sampling, we propose an annealed Langevin dynamics where we use gradients corresponding to gradually decreasing noise levels as the sampling process gets closer to the data manifold. Our framework allows flexible model architectures, requires no sampling during training or the use of adversarial methods, and provides a learning objective that can be used for principled model comparisons. Our models produce samples comparable to GANs on MNIST, CelebA and CIFAR-10 datasets, achieving a new state-of-the-art inception score of 8.87 on CIFAR-10. Additionally, we demonstrate that our models learn effective representations via image inpainting experiments.

Denoising Diffusion Implicit Models

Abstract: Denoising diffusion probabilistic models (DDPMs) have achieved high quality image generation without adversarial training, yet they require simulating a Markov chain for many steps to produce a sample. To accelerate sampling, we present denoising diffusion implicit models (DDIMs), a more efficient class of iterative implicit probabilistic models with the same training procedure as DDPMs. In DDPMs, the generative process is defined as the reverse of a Markovian diffusion process. We construct a class of non-Markovian diffusion processes that lead to the same training objective, but whose reverse process can be much faster to sample from. We empirically demonstrate that DDIMs can produce high quality samples $10 \times$ to $50 \times$ faster in terms of wall-clock time compared to DDPMs, allow us to trade off computation for sample quality, and can perform semantically meaningful image interpolation directly in the latent space.

gDDIM: Generalized denoising diffusion implicit models

Abstract: Our goal is to extend the denoising diffusion implicit model (DDIM) to general diffusion models~(DMs) besides isotropic diffusions. Instead of constructing a non-Markov noising process as in the original DDIM, we examine the mechanism of DDIM from a numerical perspective. We discover that the DDIM can be obtained by using some specific approximations of the score when solving the corresponding stochastic differential equation. We present an interpretation of the accelerating effects of DDIM that also explains the advantages of a deterministic sampling scheme over the stochastic one for fast sampling. Building on this insight, we extend DDIM to general DMs, coined generalized DDIM (gDDIM), with a small but delicate modification in parameterizing the score network. We validate gDDIM in two non-isotropic DMs: Blurring diffusion model (BDM) and Critically-damped Langevin diffusion model (CLD). We observe more than 20 times acceleration in BDM. In the CLD, a diffusion model by augmenting the diffusion process with velocity, our algorithm achieves an FID score of 2.26, on CIFAR10, with only 50 number of score function evaluations~(NFEs) and an FID score of 2.86 with only 27 NFEs. Code is available at https://github.com/qsh-zh/gDDIM

DPM-Solver: A Fast ODE Solver for Diffusion Probabilistic Model Sampling in Around 10 Steps

Abstract: Diffusion probabilistic models (DPMs) are emerging powerful generative models. Despite their high-quality generation performance, DPMs still suffer from their slow sampling as they generally need hundreds or thousands of sequential function evaluations (steps) of large neural networks to draw a sample. Sampling from DPMs can be viewed alternatively as solving the corresponding diffusion ordinary differential equations (ODEs). In this work, we propose an exact formulation of the solution of diffusion ODEs. The formulation analytically computes the linear part of the solution, rather than leaving all terms to black-box ODE solvers as adopted in previous works. By applying change-of-variable, the solution can be equivalently simplified to an exponentially weighted integral of the neural network. Based on our formulation, we propose DPM-Solver, a fast dedicated high-order solver for diffusion ODEs with the convergence order guarantee. DPM-Solver is suitable for both discrete-time and continuous-time DPMs without any further training. Experimental results show that DPM-Solver can generate high-quality samples in only 10 to 20 function evaluations on various datasets. We achieve 4.70 FID in 10 function evaluations and 2.87 FID in 20 function evaluations on the CIFAR10 dataset, and a $4\sim 16\times$ speedup compared with previous state-of-the-art training-free samplers on various datasets.

Fast Sampling of Diffusion Models with Exponential Integrator

Abstract: The past few years have witnessed the great success of Diffusion models~(DMs) in generating high-fidelity samples in generative modeling tasks. A major limitation of the DM is its notoriously slow sampling procedure which normally requires hundreds to thousands of time discretization steps of the learned diffusion process to reach the desired accuracy. Our goal is to develop a fast sampling method for DMs with a much less number of steps while retaining high sample quality. To this end, we systematically analyze the sampling procedure in DMs and identify key factors that affect the sample quality, among which the method of discretization is most crucial. By carefully examining the learned diffusion process, we propose Diffusion Exponential Integrator Sampler~(DEIS). It is based on the Exponential Integrator designed for discretizing ordinary differential equations (ODEs) and leverages a semilinear structure of the learned diffusion process to reduce the discretization error. The proposed method can be applied to any DMs and can generate high-fidelity samples in as few as 10 steps. In our experiments, it takes about 3 minutes on one A6000 GPU to generate $50k$ images from CIFAR10. Moreover, by directly using pre-trained DMs, we achieve the state-of-art sampling performance when the number of score function evaluation~(NFE) is limited, e.g., 4.17 FID with 10 NFEs, 3.37 FID, and 9.74 IS with only 15 NFEs on CIFAR10. Code is available at https://github.com/qsh-zh/deis

Learning to Efficiently Sample from Diffusion Probabilistic Models

Abstract: Denoising Diffusion Probabilistic Models (DDPMs) have emerged as a powerful family of generative models that can yield high-fidelity samples and competitive log-likelihoods across a range of domains, including image and speech synthesis. Key advantages of DDPMs include ease of training, in contrast to generative adversarial networks, and speed of generation, in contrast to autoregressive models. However, DDPMs typically require hundreds-to-thousands of steps to generate a high fidelity sample, making them prohibitively expensive for high dimensional problems. Fortunately, DDPMs allow trading generation speed for sample quality through adjusting the number of refinement steps as a post process. Prior work has been successful in improving generation speed through handcrafting the time schedule by trial and error. We instead view the selection of the inference time schedules as an optimization problem, and introduce an exact dynamic programming algorithm that finds the optimal discrete time schedules for any pre-trained DDPM. Our method exploits the fact that ELBO can be decomposed into separate KL terms, and given any computation budget, discovers the time schedule that maximizes the training ELBO exactly. Our method is efficient, has no hyper-parameters of its own, and can be applied to any pre-trained DDPM with no retraining. We discover inference time schedules requiring as few as 32 refinement steps, while sacrificing less than 0.1 bits per dimension compared to the default 4,000 steps used on ImageNet 64x64 [Ho et al., 2020; Nichol and Dhariwal, 2021].

Knowledge Distillation in Iterative Generative Models for Improved Sampling Speed

Abstract: Iterative generative models, such as noise conditional score networks and denoising diffusion probabilistic models, produce high quality samples by gradually denoising an initial noise vector. However, their denoising process has many steps, making them 2-3 orders of magnitude slower than other generative models such as GANs and VAEs. In this paper, we establish a novel connection between knowledge distillation and image generation with a technique that distills a multi-step denoising process into a single step, resulting in a sampling speed similar to other single-step generative models. Our Denoising Student generates high quality samples comparable to GANs on the CIFAR-10 and CelebA datasets, without adversarial training. We demonstrate that our method scales to higher resolutions through experiments on 256 x 256 LSUN. Code and checkpoints are available at https://github.com/tcl9876/Denoising_Student

Truncated Diffusion Probabilistic Models

Abstract: Employing a forward diffusion chain to gradually map the data to a noise distribution, diffusion-based generative models learn how to generate the data by inferring a reverse diffusion chain. However, this approach is slow and costly because it needs many forward and reverse steps. We propose a faster and cheaper approach that adds noise not until the data become pure random noise, but until they reach a hidden noisy data distribution that we can confidently learn. Then, we use fewer reverse steps to generate data by starting from this hidden distribution that is made similar to the noisy data. We reveal that the proposed model can be cast as an adversarial auto-encoder empowered by both the diffusion process and a learnable implicit prior. Experimental results show even with a significantly smaller number of reverse diffusion steps, the proposed truncated diffusion probabilistic models can provide consistent improvements over the non-truncated ones in terms of performance in both unconditional and text-guided image generations.

Improved Denoising Diffusion Probabilistic Models

Abstract: Denoising diffusion probabilistic models (DDPM) are a class of generative models which have recently been shown to produce excellent samples. We show that with a few simple modifications, DDPMs can also achieve competitive log-likelihoods while maintaining high sample quality. Additionally, we find that learning variances of the reverse diffusion process allows sampling with an order of magnitude fewer forward passes with a negligible difference in sample quality, which is important for the practical deployment of these models. We additionally use precision and recall to compare how well DDPMs and GANs cover the target distribution. Finally, we show that the sample quality and likelihood of these models scale smoothly with model capacity and training compute, making them easily scalable. We release our code at https://github.com/openai/improved-diffusion

Variational Diffusion Models

Abstract: Diffusion-based generative models have demonstrated a capacity for perceptually impressive synthesis, but can they also be great likelihood-based models? We answer this in the affirmative, and introduce a family of diffusion-based generative models that obtain state-of-the-art likelihoods on standard image density estimation benchmarks. Unlike other diffusion-based models, our method allows for efficient optimization of the noise schedule jointly with the rest of the model. We show that the variational lower bound (VLB) simplifies to a remarkably short expression in terms of the signal-to-noise ratio of the diffused data, thereby improving our theoretical understanding of this model class. Using this insight, we prove an equivalence between several models proposed in the literature. In addition, we show that the continuous-time VLB is invariant to the noise schedule, except for the signal-to-noise ratio at its endpoints. This enables us to learn a noise schedule that minimizes the variance of the resulting VLB estimator, leading to faster optimization. Combining these advances with architectural improvements, we obtain state-of-the-art likelihoods on image density estimation benchmarks, outperforming autoregressive models that have dominated these benchmarks for many years, with often significantly faster optimization. In addition, we show how to use the model as part of a bits-back compression scheme, and demonstrate lossless compression rates close to the theoretical optimum. Code is available at https://github.com/google-research/vdm .

Analytic-DPM: an Analytic Estimate of the Optimal Reverse Variance in Diffusion Probabilistic Models

Abstract: Diffusion probabilistic models (DPMs) represent a class of powerful generative models. Despite their success, the inference of DPMs is expensive since it generally needs to iterate over thousands of timesteps. A key problem in the inference is to estimate the variance in each timestep of the reverse process. In this work, we present a surprising result that both the optimal reverse variance and the corresponding optimal KL divergence of a DPM have analytic forms w.r.t. its score function. Building upon it, we propose Analytic-DPM, a training-free inference framework that estimates the analytic forms of the variance and KL divergence using the Monte Carlo method and a pretrained score-based model. Further, to correct the potential bias caused by the score-based model, we derive both lower and upper bounds of the optimal variance and clip the estimate for a better result. Empirically, our analytic-DPM improves the log-likelihood of various DPMs, produces high-quality samples, and meanwhile enjoys a 20x to 80x speed up.

Maximum Likelihood Training of Score-Based Diffusion Models

Abstract: Score-based diffusion models synthesize samples by reversing a stochastic process that diffuses data to noise, and are trained by minimizing a weighted combination of score matching losses. The log-likelihood of score-based diffusion models can be tractably computed through a connection to continuous normalizing flows, but log-likelihood is not directly optimized by the weighted combination of score matching losses. We show that for a specific weighting scheme, the objective upper bounds the negative log-likelihood, thus enabling approximate maximum likelihood training of score-based diffusion models. We empirically observe that maximum likelihood training consistently improves the likelihood of score-based diffusion models across multiple datasets, stochastic processes, and model architectures. Our best models achieve negative log-likelihoods of 2.83 and 3.76 bits/dim on CIFAR-10 and ImageNet 32x32 without any data augmentation, on a par with state-of-the-art autoregressive models on these tasks.

A Variational Perspective on Diffusion-Based Generative Models and Score Matching

Abstract: Discrete-time diffusion-based generative models and score matching methods have shown promising results in modeling high-dimensional image data. Recently, Song et al. (2021) show that diffusion processes that transform data into noise can be reversed via learning the score function, i.e. the gradient of the log-density of the perturbed data. They propose to plug the learned score function into an inverse formula to define a generative diffusion process. Despite the empirical success, a theoretical underpinning of this procedure is still lacking. In this work, we approach the (continuous-time) generative diffusion directly and derive a variational framework for likelihood estimation, which includes continuous-time normalizing flows as a special case, and can be seen as an infinitely deep variational autoencoder. Under this framework, we show that minimizing the score-matching loss is equivalent to maximizing a lower bound of the likelihood of the plug-in reverse SDE proposed by Song et al. (2021), bridging the theoretical gap.

Maximum Likelihood Training for Score-Based Diffusion ODEs by High-Order Denoising Score Matching

Abstract: Score-based generative models have excellent performance in terms of generation quality and likelihood. They model the data distribution by matching a parameterized score network with first-order data score functions. The score network can be used to define an ODE ("score-based diffusion ODE") for exact likelihood evaluation. However, the relationship between the likelihood of the ODE and the score matching objective is unclear. In this work, we prove that matching the first-order score is not sufficient to maximize the likelihood of the ODE, by showing a gap between the maximum likelihood and score matching objectives. To fill up this gap, we show that the negative likelihood of the ODE can be bounded by controlling the first, second, and third-order score matching errors; and we further present a novel high-order denoising score matching method to enable maximum likelihood training of score-based diffusion ODEs. Our algorithm guarantees that the higher-order matching error is bounded by the training error and the lower-order errors. We empirically observe that by high-order score matching, score-based diffusion ODEs achieve better likelihood on both synthetic data and CIFAR-10, while retaining the high generation quality.

Score-based Generative Modeling in Latent Space

Abstract: Score-based generative models (SGMs) have recently demonstrated impressive results in terms of both sample quality and distribution coverage. However, they are usually applied directly in data space and often require thousands of network evaluations for sampling. Here, we propose the Latent Score-based Generative Model (LSGM), a novel approach that trains SGMs in a latent space, relying on the variational autoencoder framework. Moving from data to latent space allows us to train more expressive generative models, apply SGMs to non-continuous data, and learn smoother SGMs in a smaller space, resulting in fewer network evaluations and faster sampling. To enable training LSGMs end-to-end in a scalable and stable manner, we (i) introduce a new score-matching objective suitable to the LSGM setting, (ii) propose a novel parameterization of the score function that allows SGM to focus on the mismatch of the target distribution with respect to a simple Normal one, and (iii) analytically derive multiple techniques for variance reduction of the training objective. LSGM obtains a state-of-the-art FID score of 2.10 on CIFAR-10, outperforming all existing generative results on this dataset. On CelebA-HQ-256, LSGM is on a par with previous SGMs in sample quality while outperforming them in sampling time by two orders of magnitude. In modeling binary images, LSGM achieves state-of-the-art likelihood on the binarized OMNIGLOT dataset. Our project page and code can be found at https://nvlabs.github.io/LSGM .

Diffusion Priors In Variational Autoencoders

Abstract: Among likelihood-based approaches for deep generative modelling, variational autoencoders (VAEs) offer scalable amortized posterior inference and fast sampling. However, VAEs are also more and more outperformed by competing models such as normalizing flows (NFs), deep-energy models, or the new denoising diffusion probabilistic models (DDPMs). In this preliminary work, we improve VAEs by demonstrating how DDPMs can be used for modelling the prior distribution of the latent variables. The diffusion prior model improves upon Gaussian priors of classical VAEs and is competitive with NF-based priors. Finally, we hypothesize that hierarchical VAEs could similarly benefit from the enhanced capacity of diffusion priors.

Permutation Invariant Graph Generation via Score-Based Generative Modeling

Abstract: Learning generative models for graph-structured data is challenging because graphs are discrete, combinatorial, and the underlying data distribution is invariant to the ordering of nodes. However, most of the existing generative models for graphs are not invariant to the chosen ordering, which might lead to an undesirable bias in the learned distribution. To address this difficulty, we propose a permutation invariant approach to modeling graphs, using the recent framework of score-based generative modeling. In particular, we design a permutation equivariant, multi-channel graph neural network to model the gradient of the data distribution at the input graph (a.k.a., the score function). This permutation equivariant model of gradients implicitly defines a permutation invariant distribution for graphs. We train this graph neural network with score matching and sample from it with annealed Langevin dynamics. In our experiments, we first demonstrate the capacity of this new architecture in learning discrete graph algorithms. For graph generation, we find that our learning approach achieves better or comparable results to existing models on benchmark datasets.

GeoDiff: a Geometric Diffusion Model for Molecular Conformation Generation

Abstract: Predicting molecular conformations from molecular graphs is a fundamental problem in cheminformatics and drug discovery. Recently, significant progress has been achieved with machine learning approaches, especially with deep generative models. Inspired by the diffusion process in classical non-equilibrium thermodynamics where heated particles will diffuse from original states to a noise distribution, in this paper, we propose a novel generative model named GeoDiff for molecular conformation prediction. GeoDiff treats each atom as a particle and learns to directly reverse the diffusion process (i.e., transforming from a noise distribution to stable conformations) as a Markov chain. Modeling such a generation process is however very challenging as the likelihood of conformations should be roto-translational invariant. We theoretically show that Markov chains evolving with equivariant Markov kernels can induce an invariant distribution by design, and further propose building blocks for the Markov kernels to preserve the desirable equivariance property. The whole framework can be efficiently trained in an end-to-end fashion by optimizing a weighted variational lower bound to the (conditional) likelihood. Experiments on multiple benchmarks show that GeoDiff is superior or comparable to existing state-of-the-art approaches, especially on large molecules.

Structured Denoising Diffusion Models in Discrete State-Spaces

Abstract: Denoising diffusion probabilistic models (DDPMs) (Ho et al. 2020) have shown impressive results on image and waveform generation in continuous state spaces. Here, we introduce Discrete Denoising Diffusion Probabilistic Models (D3PMs), diffusion-like generative models for discrete data that generalize the multinomial diffusion model of Hoogeboom et al. 2021, by going beyond corruption processes with uniform transition probabilities. This includes corruption with transition matrices that mimic Gaussian kernels in continuous space, matrices based on nearest neighbors in embedding space, and matrices that introduce absorbing states. The third allows us to draw a connection between diffusion models and autoregressive and mask-based generative models. We show that the choice of transition matrix is an important design decision that leads to improved results in image and text domains. We also introduce a new loss function that combines the variational lower bound with an auxiliary cross entropy loss. For text, this model class achieves strong results on character-level text generation while scaling to large vocabularies on LM1B. On the image dataset CIFAR-10, our models approach the sample quality and exceed the log-likelihood of the continuous-space DDPM model.

Deep Unsupervised Learning using Nonequilibrium Thermodynamics

Abstract: A central problem in machine learning involves modeling complex data-sets using highly flexible families of probability distributions in which learning, sampling, inference, and evaluation are still analytically or computationally tractable. Here, we develop an approach that simultaneously achieves both flexibility and tractability. The essential idea, inspired by non-equilibrium statistical physics, is to systematically and slowly destroy structure in a data distribution through an iterative forward diffusion process. We then learn a reverse diffusion process that restores structure in data, yielding a highly flexible and tractable generative model of the data. This approach allows us to rapidly learn, sample from, and evaluate probabilities in deep generative models with thousands of layers or time steps, as well as to compute conditional and posterior probabilities under the learned model. We additionally release an open source reference implementation of the algorithm.

Three types of diffusion models are listed with corresponding articles and years, under continuous and discrete settings.

Classical diffusion models have three major shortcomings: inefficient sampling procedure, sub-optimal likelihood estimation and poor data generalization ability.
Significant efforts have been made to address these shortcomings in recent years.
We categorize the advancements of diffusion models into three categories: sampling efficiency, likelihood maximization, and data generalization, with respect to the model enhancement.
In the next three sections (Section -), we introduce three main enhancements on diffusion models with corresponding works in detail. In Table {{table:dc9310ea-e270-4a36-8f4d-2de9ef8e1bbf}} , we list the three types of diffusion models with more detailed categorization, corresponding articles and years, under continuous and discrete time settings.