GAN composed of LSTM encoder, context-pooling module and LSTM decoder

GAN that uses path history and scence information

Uses discrimination-, adversarial- and information loss

GAN for multimodal trajectory predictions

Social GAN: Socially Acceptable Trajectories with Generative Adversarial Networks

Abstract: Understanding human motion behavior is critical for autonomous moving platforms (like self-driving cars and social robots) if they are to navigate human-centric environments. This is challenging because human motion is inherently multimodal: given a history of human motion paths, there are many socially plausible ways that people could move in the future. We tackle this problem by combining tools from sequence prediction and generative adversarial networks: a recurrent sequence-to-sequence model observes motion histories and predicts future behavior, using a novel pooling mechanism to aggregate information across people. We predict socially plausible futures by training adversarially against a recurrent discriminator, and encourage diverse predictions with a novel variety loss. Through experiments on several datasets we demonstrate that our approach outperforms prior work in terms of accuracy, variety, collision avoidance, and computational complexity.

SoPhie: An Attentive GAN for Predicting Paths Compliant to Social and Physical Constraints

Abstract: This paper addresses the problem of path prediction for multiple interacting agents in a scene, which is a crucial step for many autonomous platforms such as self-driving cars and social robots. We present SoPhie; an interpretable framework based on Generative Adversarial Network (GAN), which leverages two sources of information, the path history of all the agents in a scene, and the scene context information, using images of the scene. To predict a future path for an agent, both physical and social information must be leveraged. Previous work has not been successful to jointly model physical and social interactions. Our approach blends a social attention mechanism with physical attention that helps the model to learn where to look in a large scene and extract the most salient parts of the image relevant to the path. Whereas, the social attention component aggregates information across the different agent interactions and extracts the most important trajectory information from the surrounding neighbors. SoPhie also takes advantage of GAN to generates more realistic samples and to capture the uncertain nature of the future paths by modeling its distribution. All these mechanisms enable our approach to predict socially and physically plausible paths for the agents and to achieve state-of-the-art performance on several different trajectory forecasting benchmarks.

Social Ways: Learning Multi-Modal Distributions of Pedestrian Trajectories with GANs

Abstract: This paper proposes a novel approach for predicting the motion of pedestrians interacting with others. It uses a Generative Adversarial Network (GAN) to sample plausible predictions for any agent in the scene. As GANs are very susceptible to mode collapsing and dropping, we show that the recently proposed Info-GAN allows dramatic improvements in multi-modal pedestrian trajectory prediction to avoid these issues. We also left out L2-loss in training the generator, unlike some previous works, because it causes serious mode collapsing though faster convergence. We show through experiments on real and synthetic data that the proposed method leads to generate more diverse samples and to preserve the modes of the predictive distribution. In particular, to prove this claim, we have designed a toy example dataset of trajectories that can be used to assess the performance of different methods in preserving the predictive distribution modes.

Social-BiGAT: Multimodal Trajectory Forecasting using Bicycle-GAN and Graph Attention Networks

Abstract: Predicting the future trajectories of multiple interacting agents in a scene has become an increasingly important problem for many different applications ranging from control of autonomous vehicles and social robots to security and surveillance. This problem is compounded by the presence of social interactions between humans and their physical interactions with the scene. While the existing literature has explored some of these cues, they mainly ignored the multimodal nature of each human's future trajectory. In this paper, we present Social-BiGAT, a graph-based generative adversarial network that generates realistic, multimodal trajectory predictions by better modelling the social interactions of pedestrians in a scene. Our method is based on a graph attention network (GAT) that learns reliable feature representations that encode the social interactions between humans in the scene, and a recurrent encoder-decoder architecture that is trained adversarially to predict, based on the features, the humans' paths. We explicitly account for the multimodal nature of the prediction problem by forming a reversible transformation between each scene and its latent noise vector, as in Bicycle-GAN. We show that our framework achieves state-of-the-art performance comparing it to several baselines on existing trajectory forecasting benchmarks.

Overview of DL pedestrian trajectory prediction algorithms relying on generative adversarial neural networks.

A problem that is inherent with predictions of trajectories is the multimodal nature of future pedestrian trajectories. GANs have a high potential to cope with this problem, because of their capabilities to generate multimodal samples {{cite:d7e03e2}}. With the use of GANs, it is possible to predict a distribution of potential future trajectories and not just the best single trajectory {{cite:b4b7099}}.
The architecture of a GAN consists of two part: a generator and a discriminator. In the DL approach, a neural network is trained to match the desired data distribution and achieve a low error rate. In a non-intuitive way, the generator of a GAN is trained so that the error rate of the discriminator increases at first. The generator takes the training data as input and creates different output samples. In turn, the discriminator takes the generated samples and the training data and tries to distinguish whether a given sample belongs to the true data distribution or is generated by the generator. Both components are engaged in a competition similar to a two-player min-max game where each one tries to outsmart the other one {{cite:7e0b5bc}}, {{cite:51010ed}}. From this process, the generator learns to generate data that resemble the true data distribution. Although the results of the GAN-based methods are promising, there are two main difficulties. First, GANs can be hard to train and second, GAN learning often suffers from mode collapse {{cite:05a14e8}}, {{cite:96cd645}}.
Applied for trajectory prediction, most GANs are combined with LSTM networks. In the social GAN from Gupta et al. {{cite:7e0b5bc}} the generator is composed of an LSTM-based encoder, a context pooling module, and an LSTM-based decoder. The discriminator uses LSTMs as well. The pooling module adopted in the social GAN uses a uniform weight for all surrounding pedestrians. Therefore, it can not distinguish the different effects exerted on a target pedestrian by pedestrians at different distances and traveling at different speeds.
For that reason, many authors added attention mechanisms. Sadegehian et al. {{cite:031c9fe}} add an attention module to assign different soft attention distribution weights to the surrounding pedestrians and the static environment. Using an attention module with a physical and social component and a feature extractor module composed of a CNN and several LSTM network encoder, the model SoPhie learns the interaction information of different agents and extracts the most important information from the neighbors.
Social Ways {{cite:e16ac32}} applies info-GAN {{cite:ef35329}}, which introduces latent code to enhance the multi-modality of prediction and computes the attentive social features to generate a more convincing result. It uses discrimination loss for the discriminator, adversarial loss for the generator and information loss for both. Social-BiGAT {{cite:cd854ae}} relies on BiGAN architecture to help reduce the variance of the predicted trajectory distributions and allow for better generalization. In Lv et al. {{cite:946765c}} the authors propose a GAN combined with transformer networks which generates trajectory distributions to capture the uncertainty of the predictions.
However, these methods focus on the trajectory prediction in homogeneous environment without considering the types of road users. Lai et al. {{cite:6ab9f40}} use an attention module, containing two components, in order to alleviate the issues given by the complexity of a scene with many heterogeneous interacting agents {{cite:6ab9f40}}.
An overview of DL pedestrian trajectory prediction algorithms relying on generative adversarial neural networks is proposed in Table {{table:480b35a5-c3b6-4852-9272-b52056abd5f1}} .


A Comparison Study of Canonical Correlation Analysis Based Methods for Detecting Steady-State Visual Evoked Potentials

Abstract: Canonical correlation analysis (CCA) has been widely used in the detection of the steady-state visual evoked potentials (SSVEPs) in brain-computer interfaces (BCIs). The standard CCA method, which uses sinusoidal signals as reference signals, was first proposed for SSVEP detection without calibration. However, the detection performance can be deteriorated by the interference from the spontaneous EEG activities. Recently, various extended methods have been developed to incorporate individual EEG calibration data in CCA to improve the detection performance. Although advantages of the extended CCA methods have been demonstrated in separate studies, a comprehensive comparison between these methods is still missing. This study performed a comparison of the existing CCA-based SSVEP detection methods using a 12-class SSVEP dataset recorded from 10 subjects in a simulated online BCI experiment. Classification accuracy and information transfer rate (ITR) were used for performance evaluation. The results suggest that individual calibration data can significantly improve the detection performance. Furthermore, the results showed that the combination method based on the standard CCA and the individual template based CCA (IT-CCA) achieved the highest performance.

A Fully Automated Trial Selection Method for Optimization of Motor Imagery Based Brain-Computer Interface

Abstract: Independent component analysis (ICA) as a promising spatial filtering method can separate motor-related independent components (MRICs) from the multichannel electroencephalogram (EEG) signals. However, the unpredictable burst interferences may significantly degrade the performance of ICA-based brain-computer interface (BCI) system. In this study, we proposed a new algorithm frame to address this issue by combining the single-trial-based ICA filter with zero-training classifier. We developed a two-round data selection method to identify automatically the badly corrupted EEG trials in the training set. The “high quality” training trials were utilized to optimize the ICA filter. In addition, we proposed an accuracy-matrix method to locate the artifact data segments within a single trial and investigated which types of artifacts can influence the performance of the ICA-based MIBCIs. Twenty-six EEG datasets of three-class motor imagery were used to validate the proposed methods, and the classification accuracies were compared with that obtained by frequently used common spatial pattern (CSP) spatial filtering algorithm. The experimental results demonstrated that the proposed optimizing strategy could effectively improve the stability, practicality and classification performance of ICA-based MIBCI. The study revealed that rational use of ICA method may be crucial in building a practical ICA-based MIBCI system.

List of datasets: SSVEP, Motor Imagery and P300 speller.

While MOABB is a powerful tool, it still lacks the support to do cross-subject transfer learning. It is a more global issue as no existing framework allows to fairly evaluate transfer learning algorithms.
This works is a first attempt to improve MOABB with transfer learning support and we will contribute to this open source project.
Our analysis focuses three kinds of paradigms, SSVEP, Motor Imagery (MI) and P300 Speller.
For the MI, the choice was based on two typical paradigms signal, left-hand vs right-hand imagery.
The number of channels and subjects for each paradigm is described in Table {{table:004c2af0-b4ae-4481-914a-2e51b57d9067}} .


IEEE International Conference on Trust, Security and Privacy in Computing and Communications

IEEE International Conference on Internet of Things: Systems, Management and Security

reclaimID: Secure, Self-Sovereign Identities using Name Systems and Attribute-Based Encryption

Abstract: In this paper we present reclaimID: An architecture that allows users to reclaim their digital identities by securely sharing identity attributes without the need for a centralised service provider. We propose a design where user attributes are stored in and shared over a name system under user-owned namespaces. Attributes are encrypted using attribute-based encryption (ABE), allowing the user to selectively authorize and revoke access of requesting parties to subsets of his attributes. We present an implementation based on the decentralised GNU Name System (GNS) in combination with ciphertext-policy ABE using type-1 pairings. To show the practicality of our implementation, we carried out experimental evaluations of selected implementation aspects including attribute resolution performance. Finally, we show that our design can be used as a standard OpenID Connect Identity Provider allowing our implementation to be integrated into standard-compliant services.

Full-text Search for Verifiable Credential Metadata on Distributed Ledgers

Abstract: Self-sovereign Identity (SSI) powered by distributed ledger technologies enables more flexible and faster digital identification workflows, while at the same time limiting the control and influence of central authorities. However, a global identity solution must be able to handle myriad credential types from millions of issuing organizations. As metadata about types of digital credentials is readable by everyone on the public permissioned ledger with Hyperledger Indy, anyone could find relevant and trusted credential types for their use cases by looking at the records on the blockchain. To this date, no efficient full-text search mechanism exists that would allow users to search for credential types in a simple and efficient fashion tightly integrated into their applications. In this work, we propose a full-text search framework based on the publicly available metadata on the Hyperledger Indy ledger for retrieving matching credential types. The proposed solution is able to find credential types based on textual input from the user by using a full-text search engine and maintaining a local copy of the ledger. Thus, we do not need to rely on information about credentials coming from a very large candidate pool of third parties we would need to trust, such as the website of a company displaying its own identifier and a list of issued credentials. We have also proven the feasiblity of the concept by implementing and evaluating a prototype of the full-text credential metadata search service.

Studies published in conferences, symposia or forums.

The conferences selected by authors to publish their works vary widely. Table {{table:3788af75-f478-4e5b-9f8f-ecfeb7e778aa}}  shows in which conferences, symposia, forums, and workshops the mapped articles were published. Although there are thirty articles mapped in this type of venue, only six conferences received two publications. The other eighteen papers are spread across eighteen different conventions. Moreover, the colloquia held by the IEEE are the most popular choice, which received thirteen papers spread across ten conferences. The same trend is true for essays in scientific journals, as shown in Table {{table:c15b8f0a-0355-4558-8b32-501a4975cd85}} . Five of the nine studies were published in IEEE journals.


Deep Stock Trading: A Hierarchical Reinforcement Learning Framework for Portfolio Optimization and Order Execution

Abstract: Portfolio management via reinforcement learning is at the forefront of fintech research, which explores how to optimally reallocate a fund into different financial assets over the long term by trial-and-error. Existing methods are impractical since they usually assume each reallocation can be finished immediately and thus ignoring the price slippage as part of the trading cost. To address these issues, we propose a hierarchical reinforced stock trading system for portfolio management (HRPM). Concretely, we decompose the trading process into a hierarchy of portfolio management over trade execution and train the corresponding policies. The high-level policy gives portfolio weights at a lower frequency to maximize the long term profit and invokes the low-level policy to sell or buy the corresponding shares within a short time window at a higher frequency to minimize the trading cost. We train two levels of policies via pre-training scheme and iterative training scheme for data efficiency. Extensive experimental results in the U.S. market and the China market demonstrate that HRPM achieves significant improvement against many state-of-the-art approaches.

Deep Reinforcement Learning for Trading

Abstract: In this article, the authors adopt deep reinforcement learning algorithms to design trading strategies for continuous futures contracts. Both discrete and continuous action spaces are considered, and volatility scaling is incorporated to create reward functions that scale trade positions based on market volatility. They test their algorithms on 50 very liquid futures contracts from 2011 to 2019 and investigate how performance varies across different asset classes, including commodities, equity indexes, fixed income, and foreign exchange markets. They compare their algorithms against classical time-series momentum strategies and show that their method outperforms such baseline models, delivering positive profits despite heavy transaction costs. The experiments show that the proposed algorithms can follow large market trends without changing positions and can also scale down, or hold, through consolidation periods. TOPICS: Futures and forward contracts, exchanges/markets/clearinghouses, statistical methods, simulations Key Findings • In this article, the authors introduce reinforcement learning algorithms to design trading strategies for futures contracts. They investigate both discrete and continuous action spaces and improve reward functions by using volatility scaling to scale trade positions based on market volatility. • The authors discuss the connection between modern portfolio theory and the reinforcement learning reward hypothesis and show that they are equivalent if a linear utility function is used. • The authors back test their methods on 50 very liquid futures contracts from 2011 to 2019, and their algorithms deliver positive profits despite heavy transaction costs.

Option Hedging with Risk Averse Reinforcement Learning

Abstract: In this paper we show how risk-averse reinforcement learning can be used to hedge options. We apply a state-of-the-art risk-averse algorithm: Trust Region Volatility Optimization (TRVO) to a vanilla option hedging environment, considering realistic factors such as discrete time and transaction costs. Realism makes the problem twofold: the agent must both minimize volatility and contain transaction costs, these tasks usually being in competition. We use the algorithm to train a sheaf of agents each characterized by a different risk aversion, so to be able to span an efficient frontier on the volatility-p\&l space. The results show that the derived hedging strategy not only outperforms the Black \& Scholes delta hedge, but is also extremely robust and flexible, as it can efficiently hedge options with different characteristics and work on markets with different behaviors than what was used in training.

Practical Deep Reinforcement Learning Approach for Stock Trading

Abstract: Stock trading strategy plays a crucial role in investment companies. However, it is challenging to obtain optimal strategy in the complex and dynamic stock market. We explore the potential of deep reinforcement learning to optimize stock trading strategy and thus maximize investment return. 30 stocks are selected as our trading stocks and their daily prices are used as the training and trading market environment. We train a deep reinforcement learning agent and obtain an adaptive trading strategy. The agent's performance is evaluated and compared with Dow Jones Industrial Average and the traditional min-variance portfolio allocation strategy. The proposed deep reinforcement learning approach is shown to outperform the two baselines in terms of both the Sharpe ratio and cumulative returns.

Using Data Augmentation Based Reinforcement Learning for Daily Stock Trading

Abstract: In algorithmic trading, adequate training data set is key to making profits. However, stock trading data in units of a day can not meet the great demand for reinforcement learning. To address this problem, we proposed a framework named data augmentation based reinforcement learning (DARL) which uses minute-candle data (open, high, low, close) to train the agent. The agent is then used to guide daily stock trading. In this way, we can increase the instances of data available for training in hundreds of folds, which can substantially improve the reinforcement learning effect. But not all stocks are suitable for this kind of trading. Therefore, we propose an access mechanism based on skewness and kurtosis to select stocks that can be traded properly using this algorithm. In our experiment, we find proximal policy optimization (PPO) is the most stable algorithm to achieve high risk-adjusted returns. Deep Q-learning (DQN) and soft actor critic (SAC) can beat the market in Sharp Ratio.

Deep Reinforcement Learning for Trading

Publications Based on Different Reinforcement Learning Algorithms

In order to provide a bird-eye's view of this field, existing works are classified from different perspectives. Table {{table:a826b4f0-3841-4c90-99e2-dae2f546765c}}  summarizes existing works from the RL algorithm perspective. Q-learning and recurrent RL are the most popular RL algorithms for QT. Recent trend indicates DRL methods such as DQN, DDPG and PPO outperform traditional RL methods. In addition, we use three pie charts to provide taxonomies of existing works based on financial markets, financial assets and data frequencies. The percentage numbers shown in the pie charts are calculated by dividing the number of papers belonging to each type with the total number of papers. We classify existing works based on financial markets (illustrated in Figure. {{figure:bcae320d-556f-4bbc-81df-2271df535d92}} ). The US market is the most studied market in the literature. Chinese market is getting popular in recent years. The study of European market is mainly in the early era. We classify existing works based on financial assets (illustrated in Figure. {{figure:bcae320d-556f-4bbc-81df-2271df535d92}} ). Stock data is used for more than 40% of publications. Stock index is the second popular additional option. There are also some works focusing on cryptocurrency in recent years. We classify existing works based on data frequencies (illustrated in Figure. {{figure:bcae320d-556f-4bbc-81df-2271df535d92}} ). About half of papers use day-level data since it is easy to access. For order execution and market making, fine-grained data (e.g., second-level and minute-level) are often used to simulate the micro-level financial market.


Frustum ConvNet: Sliding Frustums to Aggregate Local Point-Wise Features for Amodal

Abstract: In this work, we propose a novel method termed Frustum ConvNet (F-ConvNet) for amodal 3D object detection from point clouds. Given 2D region proposals in an RGB image, our method first generates a sequence of frustums for each region proposal, and uses the obtained frustums to group local points. F-ConvNet aggregates point-wise features as frustum-level feature vectors, and arrays these feature vectors as a feature map for use of its subsequent component of fully convolutional network (FCN), which spatially fuses frustum-level features and supports an end-to-end and continuous estimation of oriented boxes in the 3D space. We also propose component variants of F-ConvNet, including an FCN variant that extracts multi-resolution frustum features, and a refined use of F-ConvNet over a reduced 3D space. Careful ablation studies verify the efficacy of these component variants. F-ConvNet assumes no prior knowledge of the working 3D environment and is thus dataset-agnostic. We present experiments on both the indoor SUN-RGBD and outdoor KITTI datasets. F-ConvNet outperforms all existing methods on SUN-RGBD, and at the time of submission it outperforms all published works on the KITTI benchmark. Code has been made available at: https://github.com/zhixinwang/frustum-convnet.

CLOCs: Camera-LiDAR Object Candidates Fusion for 3D Object Detection

Abstract: There have been significant advances in neural networks for both 3D object detection using LiDAR and 2D object detection using video. However, it has been surprisingly difficult to train networks to effectively use both modalities in a way that demonstrates gain over single-modality networks. In this paper, we propose a novel Camera-LiDAR Object Candidates (CLOCs) fusion network. CLOCs fusion provides a low-complexity multi-modal fusion framework that significantly improves the performance of single-modality detectors. CLOCs operates on the combined output candidates before Non-Maximum Suppression (NMS) of any 2D and any 3D detector, and is trained to leverage their geometric and semantic consistencies to produce more accurate final 3D and 2D detection results. Our experimental evaluation on the challenging KITTI object detection benchmark, including 3D and bird's eye view metrics, shows significant improvements, especially at long distance, over the state-of-the-art fusion based methods. At time of submission, CLOCs ranks the highest among all the fusion-based methods in the official KITTI leaderboard. We will release our code upon acceptance.

Joint Multi-Object Detection and Tracking with Camera-LiDAR Fusion for Autonomous Driving

Abstract: Multi-object tracking (MOT) with camera-LiDAR fusion demands accurate results of object detection, affinity computation and data association in real time. This paper presents an efficient multi-modal MOT framework with online joint detection and tracking schemes and robust data association for autonomous driving applications. The novelty of this work includes: (1) development of an end-to-end deep neural network for joint object detection and correlation using 2D and 3D measurements; (2) development of a robust affinity computation module to compute occlusion-aware appearance and motion affinities in 3D space; (3) development of a comprehensive data association module for joint optimization among detection confidences, affinities and start-end probabilities. The experiment results on the KITTI tracking benchmark demonstrate the superior performance of the proposed method in terms of both tracking accuracy and processing speed.

DeepFusionMOT: A 3D Multi-Object Tracking Framework Based on Camera-LiDAR Fusion With Deep Association

Abstract: In the recent literature, on the one hand, many 3D multi-object tracking (MOT) works have focused on tracking accuracy and neglected computation speed, commonly by designing rather complex cost functions and feature extractors. On the other hand, some methods have focused too much on computation speed at the expense of tracking accuracy. In view of these issues, this paper proposes a robust and fast camera-LiDAR fusion-based MOT method that achieves a good trade-off between accuracy and speed. Relying on the characteristics of camera and LiDAR sensors, an effective deep association mechanism is designed and embedded in the proposed MOT method. This association mechanism realizes tracking of an object in a 2D domain when the object is far away and only detected by the camera, and updating of the 2D trajectory with 3D information obtained when the object appears in the LiDAR field of view to achieve a smooth fusion of 2D and 3D trajectories. Extensive experiments based on the typical datasets indicate that our proposed method presents obvious advantages over the state-of-the-art MOT methods in terms of both tracking accuracy and processing speed. Our code is made publicly available for the benefit of the community.

Depth Completion with Twin Surface Extrapolation at Occlusion Boundaries

Abstract: Depth completion starts from a sparse set of known depth values and estimates the unknown depths for the remaining image pixels. Most methods model this as depth interpolation and erroneously interpolate depth pixels into the empty space between spatially distinct objects, resulting in depth-smearing across occlusion boundaries. Here we propose a multi-hypothesis depth representation that explicitly models both foreground and background depths in the difficult occlusion-boundary regions. Our method can be thought of as performing twin-surface extrapolation, rather than interpolation, in these regions. Next our method fuses these extrapolated surfaces into a single depth image leveraging the image data. Key to our method is the use of an asymmetric loss function that operates on a novel twin-surface representation. This enables us to train a network to simultaneously do surface extrapolation and surface fusion. We characterize our loss function and compare with other common losses. Finally, we validate our method on three different datasets; KITTI, an outdoor real-world dataset, NYU2, indoor real-world depth dataset and Virtual KITTI, a photo-realistic synthetic dataset with dense groundtruth, and demonstrate improvement over the state of the art.

The collected MSF systems. Performance of each system is evaluated by task-specific metrics (detailed in Sec. ).

Table {{table:f3280b24-6009-450a-8c7c-f80147982fe5}}  summarizes the seven MSF systems selected in our benchmark.
These seven systems cover three different tasks and three different fusion mechanisms. Due to the page limit, we refer audiences to our supplementary website {{cite:acb4419}} for details of each MSF system.

In experiments, we use
Second {{cite:60cc32d}} as the LiDAR branch for CLOCs and DFMOT, Cascade-RCNN {{cite:761d465}} as the camera branch for CLOCs, DFMOT, and FConv.
We implement all MSF systems with PyTorch 1.8 and Python 3.7. For each system, we use default configurations to ensure a consistent runtime environment.
Table {{table:f3280b24-6009-450a-8c7c-f80147982fe5}}  shows the performance of each reproduced system.
The detailed settings of each system can be found in supplementary website {{cite:acb4419}}.
All experiments are conducted on a server with an Intel i7-10700K CPU (3.80 GHz), 48 GB RAM, and an NVIDIA RTX 3070 GPU (8 GB VRAM).


What is Gab? A Bastion of Free Speech or an Alt-Right Echo Chamber?

Endogenetic Structure of Filter Bubble in Social Networks

Measuring Political Polarization: Twitter shows the two sides of Venezuela

Abstract: We say that a population is perfectly polarized when divided in two groups of the same size and opposite opinions. In this paper, we propose a methodology to study and measure the emergence of polarization from social interactions. We begin by proposing a model to estimate opinions in which a minority of influential individuals propagate their opinions through a social network. The result of the model is an opinion probability density function. Next, we propose an index to quantify the extent to which the resulting distribution is polarized. Finally, we apply the proposed methodology to a Twitter conversation about the late Venezuelan president, Hugo Chávez, finding a good agreement between our results and offline data. Hence, we show that our methodology can detect different degrees of polarization, depending on the structure of the network.

What is Gab: A Bastion of Free Speech or an Alt-Right Echo Chamber

Abstract: Over the past few years, a number of new "fringe" communities, like 4chan or certain subreddits, have gained traction on the Web at a rapid pace. However, more often than not, little is known about how they evolve or what kind of activities they attract, despite recent research has shown that they influence how false information reaches mainstream communities. This motivates the need to monitor these communities and analyze their impact on the Web's information ecosystem. In August 2016, a new social network called Gab was created as an alternative to Twitter. It positions itself as putting "people and free speech first", welcoming users banned or suspended from other social networks. In this paper, we provide, to the best of our knowledge, the first characterization of Gab. We collect and analyze 22M posts produced by 336K users between August 2016 and January 2018, finding that Gab is predominantly used for the dissemination and discussion of news and world events, and that it attracts alt-right users, conspiracy theorists, and other trolls. We also measure the prevalence of hate speech on the platform, finding it to be much higher than Twitter, but lower than 4chan's Politically Incorrect board.

Endogenetic structure of filter bubble in social networks

Abstract: The filter bubble is an intermediate structure to provoke polarization and echo chambers in social networks, and it has become one of today's most urgent issues for social media. Previous studies usually equated filter bubbles with community structures and emphasized this exogenous isolation effect, but there is a lack of full discussion of the internal organization of filter bubbles. Here, we design an experiment for analysing filter bubbles taking advantage of social bots. We deployed 128 bots to Weibo (the largest microblogging network in China), and each bot consumed a specific topic (entertainment or sci-tech) and ran for at least two months. In total, we recorded about 1.3 million messages exposed to these bots and their social networks. By analysing the text received by the bots and motifs in their social networks, we found that a filter bubble is not only a dense community of users with the same preferences but also presents an endogenetic unidirectional star-like structure. The structure could spontaneously exclude non-preferred information and cause polarization. Moreover, our work proved that the felicitous use of artificial intelligence technology could provide a useful experimental approach that combines privacy protection and controllability in studying social media.

Echo chamber datasets

In table {{table:7abe59b9-2269-46fc-ad7b-de957865640b}} , we list some of the datasets that could be used in any future work related to echo chambers or any related topic, such as political polarization and filter bubbles.


StarGAN: Unified Generative Adversarial Networks for Multi-domain Image-to-Image Translation

Abstract: Recent studies have shown remarkable success in image-to-image translation for two domains. However, existing approaches have limited scalability and robustness in handling more than two domains, since different models should be built independently for every pair of image domains. To address this limitation, we propose StarGAN, a novel and scalable approach that can perform image-to-image translations for multiple domains using only a single model. Such a unified model architecture of StarGAN allows simultaneous training of multiple datasets with different domains within a single network. This leads to StarGAN's superior quality of translated images compared to existing models as well as the novel capability of flexibly translating an input image to any desired target domain. We empirically demonstrate the effectiveness of our approach on a facial attribute transfer and a facial expression synthesis tasks.

A Style-Based Generator Architecture for Generative Adversarial Networks

Abstract: We propose an alternative generator architecture for generative adversarial networks, borrowing from style transfer literature. The new architecture leads to an automatically learned, unsupervised separation of high-level attributes (e.g., pose and identity when trained on human faces) and stochastic variation in the generated images (e.g., freckles, hair), and it enables intuitive, scale-specific control of the synthesis. The new generator improves the state-of-the-art in terms of traditional distribution quality metrics, leads to demonstrably better interpolation properties, and also better disentangles the latent factors of variation. To quantify interpolation quality and disentanglement, we propose two new, automated methods that are applicable to any generator architecture. Finally, we introduce a new, highly varied and high-quality dataset of human faces.

Large Scale GAN Training for High Fidelity Natural Image Synthesis

Abstract: Despite recent progress in generative image modeling, successfully generating high-resolution, diverse samples from complex datasets such as ImageNet remains an elusive goal. To this end, we train Generative Adversarial Networks at the largest scale yet attempted, and study the instabilities specific to such scale. We find that applying orthogonal regularization to the generator renders it amenable to a simple "truncation trick," allowing fine control over the trade-off between sample fidelity and variety by reducing the variance of the Generator's input. Our modifications lead to models which set the new state of the art in class-conditional image synthesis. When trained on ImageNet at 128x128 resolution, our models (BigGANs) achieve an Inception Score (IS) of 166.5 and Frechet Inception Distance (FID) of 7.4, improving over the previous best IS of 52.52 and FID of 18.6.

Analyzing and Improving the Image Quality of StyleGAN

Abstract: The style-based GAN architecture (StyleGAN) yields state-of-the-art results in data-driven unconditional generative image modeling. We expose and analyze several of its characteristic artifacts, and propose changes in both model architecture and training methods to address them. In particular, we redesign the generator normalization, revisit progressive growing, and regularize the generator to encourage good conditioning in the mapping from latent codes to images. In addition to improving image quality, this path length regularizer yields the additional benefit that the generator becomes significantly easier to invert. This makes it possible to reliably attribute a generated image to a particular network. We furthermore visualize how well the generator utilizes its output resolution, and identify a capacity problem, motivating us to train larger models for additional quality improvements. Overall, our improved model redefines the state of the art in unconditional image modeling, both in terms of existing distribution quality metrics as well as perceived image quality.

Photographic Image Synthesis with Cascaded Refinement Networks

Abstract: We present an approach to synthesizing photographic images conditioned on semantic layouts. Given a semantic label map, our approach produces an image with photographic appearance that conforms to the input layout. The approach thus functions as a rendering engine that takes a two-dimensional semantic specification of the scene and produces a corresponding photographic image. Unlike recent and contemporaneous work, our approach does not rely on adversarial training. We show that photographic images can be synthesized from semantic layouts by a single feedforward network with appropriate structure, trained end-to-end with a direct regression objective. The presented approach scales seamlessly to high resolutions; we demonstrate this by synthesizing photographic images at 2-megapixel resolution, the full resolution of our training data. Extensive perceptual experiments on datasets of outdoor and indoor scenes demonstrate that images synthesized by the presented approach are considerably more realistic than alternative approaches.

Diverse Image Synthesis From Semantic Layouts via Conditional IMLE

Abstract: Most existing methods for conditional image synthesis are only able to generate a single plausible image for any given input, or at best a fixed number of plausible images. In this paper, we focus on the problem of generating images from semantic segmentation maps and present a simple new method that can generate an arbitrary number of images with diverse appearance for the same semantic layout. Unlike most existing approaches which adopt the GAN framework, our method is based on the recently introduced Implicit Maximum Likelihood Estimation (IMLE) framework. Compared to the leading approach, our method is able to generate more diverse images while producing fewer artifacts despite using the same architecture. The learned latent space also has sensible structure despite the lack of supervision that encourages such behaviour.

Details of the testing dataset

Testing Dataset: Testing dataset contains images which were generated using completely unseen generators as described in Table {{table:c473db42-77fd-48b5-8460-c8fe549460a3}} . To remain consistent with the current state of the art, the same generators are selected as that of {{cite:51cf46e}}. The real images for testing purposes are obtained from the repository for each generator.


A ConvNet for the 2020s

Abstract: The “Roaring 20s” of visual recognition began with the introduction of Vision Transformers (ViTs), which quickly superseded ConvNets as the state-of-the-art image classification model. A vanilla ViT, on the other hand, faces difficulties when applied to general computer vision tasks such as object detection and semantic segmentation. It is the hierarchical Transformers (e.g., Swin Transformers) that reintroduced several ConvNet priors, making Transformers practically viable as a generic vision backbone and demonstrating remarkable performance on a wide variety of vision tasks. However, the effectiveness of such hybrid approaches is still largely credited to the intrinsic superiority of Transformers, rather than the inherent inductive biases of convolutions. In this work, we reexamine the design spaces and test the limits of what a pure ConvNet can achieve. We gradually “modernize” a standard ResNet toward the design of a vision Transformer, and discover several key components that contribute to the performance difference along the way. The outcome of this exploration is a family of pure ConvNet models dubbed ConvNeXt. Constructed entirely from standard ConvNet modules, ConvNeXts compete favorably with Transformers in terms of accuracy and scalability, achieving 87.8% ImageNet top-1 accuracy and outperforming Swin Transformers on COCO detection and ADE20K segmentation, while maintaining the simplicity and efficiency of standard ConvNets.

Swin Transformer: Hierarchical Vision Transformer using Shifted Windows

Abstract: This paper presents a new vision Transformer, called Swin Transformer, that capably serves as a general-purpose backbone for computer vision. Challenges in adapting Transformer from language to vision arise from differences between the two domains, such as large variations in the scale of visual entities and the high resolution of pixels in images compared to words in text. To address these differences, we propose a hierarchical Transformer whose representation is computed with Shifted windows. The shifted windowing scheme brings greater efficiency by limiting self-attention computation to non-overlapping local windows while also allowing for cross-window connection. This hierarchical architecture has the flexibility to model at various scales and has linear computational complexity with respect to image size. These qualities of Swin Transformer make it compatible with a broad range of vision tasks, including image classification (87.3 top-1 accuracy on ImageNet-1K) and dense prediction tasks such as object detection (58.7 box AP and 51.1 mask AP on COCO test-dev) and semantic segmentation (53.5 mIoU on ADE20K val). Its performance surpasses the previous state-of-the-art by a large margin of +2.7 box AP and +2.6 mask AP on COCO, and +3.2 mIoU on ADE20K, demonstrating the potential of Transformer-based models as vision backbones. The hierarchical design and the shifted window approach also prove beneficial for all-MLP architectures. The code and models are publicly available at https://github.com/microsoft/Swin-Transformer.

ResNet50 {{cite:5b0d8e1}}, ConvNeXt-T {{cite:051b22a}}, Swin-T {{cite:d9c069c}}, Swin-S, Swin-B, and Swin-L's parameters. FLOPs stands for floating point of operations and it's a measure of model complexity.

We choose ResNet50 {{cite:5b0d8e1}}, Swin-Transformer-Tiny (Swin-T) {{cite:d9c069c}}, ConvNeXt-Tiny (ConvNeXt-T) {{cite:051b22a}} as RoI Transformer's {{cite:acd5326}} backbone and test their performance on clean DOTA-v1.0 {{cite:a9fce49}} test set and corrupted one respectively. All models are trained on clean DOTA-v1.0 for 12 epochs. It's worth emphasizing that all the three backbones are pre-trained on ImageNet-1K {{cite:7f930c1}} and their parameters can be seen in Table {{table:59170874-d062-4bf7-a3c1-a14c7020c7f9}} .

On the basis of Swin-Transformer {{cite:d9c069c}} as the backbone of RoI Transformer, we conduct a series of experiments to investigate the impact of different backbone capacities on the model's performance. All models were trained on clean DOTA-v1.0 for 12 epochs. Specifically, we evaluate the performance of RoI Transformer using Swin-Transformer-Tiny (Swin-T), Swin-Transformer-Small (Swin-S), Swin-Transformer-Base (Swin-B), and Swin-Transformer-Large (Swin-L), all of which were pre-trained on ImageNet-1K except for Swin-L (which was pre-trained on ImageNet-22K and then finetuned to ImageNet-1K). The parameters for each of the backbones are provided in Table {{table:59170874-d062-4bf7-a3c1-a14c7020c7f9}} .


A Prerecognition Model for Hot Topic Discovery Based on Microblogging Data

Abstract: The microblogging is prevailing since its easy and anonymous information sharing at Internet, which also brings the issue of dispersing negative topics, or even rumors. Many researchers have focused on how to find and trace emerging topics for analysis. When adopting topic detection and tracking techniques to find hot topics with streamed microblogging data, it will meet obstacles like streamed microblogging data clustering, topic hotness definition, and emerging hot topic discovery. This paper schemes a novel prerecognition model for hot topic discovery. In this model, the concepts of the topic life cycle, the hot velocity, and the hot acceleration are promoted to calculate the change of topic hotness, which aims to discover those emerging hot topics before they boost and break out. Our experiments show that this new model would help to discover potential hot topics efficiently and achieve considerable performance.

A Latent Source Model for Nonparametric Time Series Classification

Abstract: For classifying time series, a nearest-neighbor approach is widely used in practice with performance often competitive with or better than more elaborate methods such as neural networks, decision trees, and support vector machines. We develop theoretical justification for the effectiveness of nearest-neighbor-like classification of time series. Our guiding hypothesis is that in many applications, such as forecasting which topics will become trends on Twitter, there aren't actually that many prototypical time series to begin with, relative to the number of time series we have access to, e.g., topics become trends on Twitter only in a few distinct manners whereas we can collect massive amounts of Twitter data. To operationalize this hypothesis, we propose a latent source model for time series, which naturally leads to a "weighted majority voting" classification rule that can be approximated by a nearest-neighbor classifier. We establish nonasymptotic performance guarantees of both weighted majority voting and nearest-neighbor classification under our model accounting for how much of the time series we observe and the model complexity. Experimental results on synthetic data show weighted majority voting achieving the same misclassification rate as nearest-neighbor classification while observing less of the time series. We then use weighted majority to forecast which news topics on Twitter become trends, where we are able to detect such "trending topics" in advance of Twitter 79% of the time, with a mean early advantage of 1 hour and 26 minutes, a true positive rate of 95%, and a false positive rate of 4%.

Qualitative Evaluation of Relation Based Methods

The evaluation results are listed in Table {{table:3cfcc913-d427-466d-aa47-127d85929a90}} . The chosen metrics in the evaluation platform can be described as follows:


Online Human-Bot Interactions: Detection, Estimation, and Characterization

Abstract: Increasing evidence suggests that a growing amount of social media content is generated by autonomous entities known as social bots. In this work we present a framework to detect such entities on Twitter. We leverage more than a thousand features extracted from public data and meta-data about users: friends, tweet content and sentiment, network patterns, and activity time series. We benchmark the classification framework by using a publicly available dataset of Twitter bots. This training data is enriched by a manually annotated collection of active Twitter users that include both humans and bots of varying sophistication. Our models yield high accuracy and agreement with each other and can detect bots of different nature. Our estimates suggest that between 9% and 15% of active Twitter accounts are bots. Characterizing ties among accounts, we observe that simple bots tend to interact with bots that exhibit more human-like behaviors. Analysis of content flows reveals retweet and mention strategies adopted by bots to interact with different target groups. Using clustering analysis, we characterize several subclasses of accounts, including spammers, self promoters, and accounts that post content from connected applications.

The paradigm-shift of social spambots: Evidence, theories, and tools for the arms race

Abstract: Recent studies in social media spam and automation provide anecdotal argumentation of the rise of a new generation of spambots, so-called social spambots. Here, for the first time, we extensively study this novel phenomenon on Twitter and we provide quantitative evidence that a paradigm-shift exists in spambot design. First, we measure current Twitter's capabilities of detecting the new social spambots. Later, we assess the human performance in discriminating between genuine accounts, social spambots, and traditional spambots. Then, we benchmark several state-of-the-art techniques proposed by the academic literature. Results show that neither Twitter, nor humans, nor cutting-edge applications are currently capable of accurately detecting the new social spambots. Our results call for new approaches capable of turning the tide in the fight against this raising phenomenon. We conclude by reviewing the latest literature on spambots detection and we highlight an emerging common research trend based on the analysis of collective behaviors. Insights derived from both our extensive experimental campaign and survey shed light on the most promising directions of research and lay the foundations for the arms race against the novel social spambots. Finally, to foster research on this novel phenomenon, we make publicly available to the scientific community all the datasets used in this study.

Arming the public with artificial intelligence to counter social bots

Abstract: The increased relevance of social media in our daily life has been accompanied by efforts to manipulate online conversations and opinions. Deceptive social bots -- automated or semi-automated accounts designed to impersonate humans -- have been successfully exploited for these kinds of abuse. Researchers have responded by developing AI tools to arm the public in the fight against social bots. Here we review the literature on different types of bots, their impact, and detection methods. We use the case study of Botometer, a popular bot detection tool developed at Indiana University, to illustrate how people interact with AI countermeasures. A user experience survey suggests that bot detection has become an integral part of the social media experience for many users. However, barriers in interpreting the output of AI tools can lead to fundamental misunderstandings. The arms race between machine learning methods to develop sophisticated bots and effective countermeasures makes it necessary to update the training data and features of detection tools. We again use the Botometer case to illustrate both algorithmic and interpretability improvements of bot scores, designed to meet user expectations. We conclude by discussing how future AI developments may affect the fight between malicious bots and the public.

RTbust: Exploiting Temporal Patterns for Botnet Detection on Twitter

Abstract: Within OSNs, many of our supposedly online friends may instead be fake accounts called social bots, part of large groups that purposely re-share targeted content. Here, we study retweeting behaviors on Twitter, with the ultimate goal of detecting retweeting social bots. We collect a dataset of 10M retweets. We design a novel visualization that we leverage to highlight benign and malicious patterns of retweeting activity. In this way, we uncover a 'normal' retweeting pattern that is peculiar of human-operated accounts, and 3 suspicious patterns related to bot activities. Then, we propose a bot detection technique that stems from the previous exploration of retweeting behaviors. Our technique, called Retweet-Buster (RTbust), leverages unsupervised feature extraction and clustering. An LSTM autoencoder converts the retweet time series into compact and informative latent feature vectors, which are then clustered with a hierarchical density-based algorithm. Accounts belonging to large clusters characterized by malicious retweeting patterns are labeled as bots. RTbust obtains excellent detection results, with F1 = 0.87, whereas competitors achieve F1 < 0.76. Finally, we apply RTbust to a large dataset of retweets, uncovering 2 previously unknown active botnets with hundreds of accounts.

Scalable and Generalizable Social Bot Detection through Data Selection

Abstract: Efficient and reliable social bot classification is crucial for detecting information manipulation on social media. Despite rapid development, state-of-the-art bot detection models still face generalization and scalability challenges, which greatly limit their applications. In this paper we propose a framework that uses minimal account metadata, enabling efficient analysis that scales up to handle the full stream of public tweets of Twitter in real time. To ensure model accuracy, we build a rich collection of labeled datasets for training and validation. We deploy a strict validation system so that model performance on unseen datasets is also optimized, in addition to traditional cross-validation. We find that strategically selecting a subset of training data yields better model accuracy and generalization than exhaustively training on all available data. Thanks to the simplicity of the proposed model, its logic can be interpreted to provide insights into social bot characteristics.

Detection of Novel Social Bots by Ensembles of Specialized Classifiers

Abstract: Malicious actors create inauthentic social media accounts controlled in part by algorithms, known as social bots, to disseminate misinformation and agitate online discussion. While researchers have developed sophisticated methods to detect abuse, novel bots with diverse behaviors evade detection. We show that different types of bots are characterized by different behavioral features. As a result, supervised learning techniques suffer severe performance deterioration when attempting to detect behaviors not observed in the training data. Moreover, tuning these models to recognize novel bots requires retraining with a significant amount of new annotations, which are expensive to obtain. To address these issues, we propose a new supervised learning method that trains classifiers specialized for each class of bots and combines their decisions through the maximum rule. The ensemble of specialized classifiers (ESC) can better generalize, leading to an average improvement of 56% in F1 score for unseen accounts across datasets. Furthermore, novel bot behaviors are learned with fewer labeled examples during retraining. We deployed ESC in the newest version of Botometer, a popular tool to detect social bots in the wild, with a cross-validation AUC of 0.99.

Annotated datasets of human and bot accounts used to train Botometer.

Supervised machine learning for bot detection

Creating a working classifier also requires samples of accounts labeled as bot or human, i.e., the training datasets.
Botometer-V4 is trained on a variety of datasets shown in Table {{table:41872692-3f53-4a13-9ae2-65fb2c1a7532}} , which are publicly available.botometer.osome.iu.edu/bot-repository
With all training accounts being represented as feature vectors, a classifier can learn the characteristics of bot and human accounts.
Botometer uses a classification model called Random Forest, which consists of many rules learned from the training data.

The accuracy of the model is evaluated through 5-fold cross-validation on the annotated datasets shown in Table {{table:41872692-3f53-4a13-9ae2-65fb2c1a7532}} .
Simply speaking, the classifier is trained on part of the annotated datasets and tested on the rest to provide a sense of its accuracy.
In the experimental environment, Botometer works really well. V4 has an AUC (area under the receiver operating characteristic curve) of 0.99, suggesting that the model can distinguish bot and human accounts in Table {{table:41872692-3f53-4a13-9ae2-65fb2c1a7532}}  — as well as accounts in the wild that resemble those in the training datasets — with very high accuracy.


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.

Learning Fast Samplers for Diffusion Models by Differentiating Through Sample Quality

Abstract: Diffusion models have emerged as an expressive family of generative models rivaling GANs in sample quality and autoregressive models in likelihood scores. Standard diffusion models typically require hundreds of forward passes through the model to generate a single high-fidelity sample. We introduce Differentiable Diffusion Sampler Search (DDSS): a method that optimizes fast samplers for any pre-trained diffusion model by differentiating through sample quality scores. We also present Generalized Gaussian Diffusion Models (GGDM), a family of flexible non-Markovian samplers for diffusion models. We show that optimizing the degrees of freedom of GGDM samplers by maximizing sample quality scores via gradient descent leads to improved sample quality. Our optimization procedure backpropagates through the sampling process using the reparametrization trick and gradient rematerialization. DDSS achieves strong results on unconditional image generation across various datasets (e.g., FID scores on LSUN church 128x128 of 11.6 with only 10 inference steps, and 4.82 with 20 steps, compared to 51.1 and 14.9 with strongest DDPM/DDIM baselines). Our method is compatible with any pre-trained diffusion model without fine-tuning or re-training required.

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

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

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.

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.

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

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.

Likelihood Training of Schr\"odinger Bridge using Forward-Backward SDEs Theory

Abstract: Schr\"odinger Bridge (SB) is an entropy-regularized optimal transport problem that has received increasing attention in deep generative modeling for its mathematical flexibility compared to the Scored-based Generative Model (SGM). However, it remains unclear whether the optimization principle of SB relates to the modern training of deep generative models, which often rely on constructing log-likelihood objectives.This raises questions on the suitability of SB models as a principled alternative for generative applications. In this work, we present a novel computational framework for likelihood training of SB models grounded on Forward-Backward Stochastic Differential Equations Theory - a mathematical methodology appeared in stochastic optimal control that transforms the optimality condition of SB into a set of SDEs. Crucially, these SDEs can be used to construct the likelihood objectives for SB that, surprisingly, generalizes the ones for SGM as special cases. This leads to a new optimization principle that inherits the same SB optimality yet without losing applications of modern generative training techniques, and we show that the resulting training algorithm achieves comparable results on generating realistic images on MNIST, CelebA, and CIFAR10. Our code is available at https://github.com/ghliu/SB-FBSDE.

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.

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.

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.

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.

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.

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 advanced diffusion models into three categories: sampling acceleration, 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:2b729977-f97f-471e-bdf0-d02fb1d278e0}} , we list the three types of diffusion models with corresponding articles and years, under continuous and discrete settings.


Average of multi-transformed segmentation results

Filtered by the difficulty level obtained from hierarchical distillation, including data distillation and model distillation

Update pseudo labels with training iterations

Data Augmentation Using Learned Transformations for One-Shot Medical Image Segmentation

Abstract: Image segmentation is an important task in many medical applications. Methods based on convolutional neural networks attain state-of-the-art accuracy; however, they typically rely on supervised training with large labeled datasets. Labeling medical images requires significant expertise and time, and typical hand-tuned approaches for data augmentation fail to capture the complex variations in such images. We present an automated data augmentation method for synthesizing labeled medical images. We demonstrate our method on the task of segmenting magnetic resonance imaging (MRI) brain scans. Our method requires only a single segmented scan, and leverages other unlabeled scans in a semi-supervised approach. We learn a model of transformations from the images, and use the model along with the labeled example to synthesize additional labeled examples. Each transformation is comprised of a spatial deformation field and an intensity change, enabling the synthesis of complex effects such as variations in anatomy and image acquisition procedures. We show that training a supervised segmenter with these new examples provides significant improvements over state-of-the-art methods for one-shot biomedical image segmentation.

A Two-Stream Mutual Attention Network for Semi-supervised Biomedical Segmentation with Noisy Labels

Abstract: \begin{abstract} Learning-based methods suffer from a deficiency of clean annotations, especially in biomedical segmentation. Although many semi-supervised methods have been proposed to provide extra training data, automatically generated labels are usually too noisy to retrain models effectively. In this paper, we propose a Two-Stream Mutual Attention Network (TSMAN) that weakens the influence of back-propagated gradients caused by incorrect labels, thereby rendering the network robust to unclean data. The proposed TSMAN consists of two sub-networks that are connected by three types of attention models in different layers. The target of each attention model is to indicate potentially incorrect gradients in a certain layer for both sub-networks by analyzing their inferred features using the same input. In order to achieve this purpose, the attention models are designed based on the propagation analysis of noisy gradients at different layers. This allows the attention models to effectively discover incorrect labels and weaken their influence during the parameter updating process. By exchanging multi-level features within the two-stream architecture, the effects of noisy labels in each sub-network are reduced by decreasing the updating gradients. Furthermore, a hierarchical distillation is developed to provide more reliable pseudo labels for unlabelded data, which further boosts the performance of our retrained TSMAN. The experiments using both the HVSMR 2016 and BRATS 2015 benchmarks demonstrate that our semi-supervised learning framework surpasses the state-of-the-art fully-supervised results.

Uncertainty-aware multi-view co-training for semi-supervised medical image segmentation and domain adaptation

Abstract: Although having achieved great success in medical image segmentation, deep learning-based approaches usually require large amounts of well-annotated data, which can be extremely expensive in the field of medical image analysis. Unlabeled data, on the other hand, is much easier to acquire. Semi-supervised learning and unsupervised domain adaptation both take the advantage of unlabeled data, and they are closely related to each other. In this paper, we propose uncertainty-aware multi-view co-training (UMCT), a unified framework that addresses these two tasks for volumetric medical image segmentation. Our framework is capable of efficiently utilizing unlabeled data for better performance. We firstly rotate and permute the 3D volumes into multiple views and train a 3D deep network on each view. We then apply co-training by enforcing multi-view consistency on unlabeled data, where an uncertainty estimation of each view is utilized to achieve accurate labeling. Experiments on the NIH pancreas segmentation dataset and a multi-organ segmentation dataset show state-of-the-art performance of the proposed framework on semi-supervised medical image segmentation. Under unsupervised domain adaptation settings, we validate the effectiveness of this work by adapting our multi-organ segmentation model to two pathological organs from the Medical Segmentation Decathlon Datasets. Additionally, we show that our UMCT-DA model can even effectively handle the challenging situation where labeled source data is inaccessible, demonstrating strong potentials for real-world applications.

AbdomenCT-1K: Is Abdominal Organ Segmentation A Solved Problem?

Abstract: With the unprecedented developments in deep learning, automatic segmentation of main abdominal organs seems to be a solved problem as state-of-the-art (SOTA) methods have achieved comparable results with inter-rater variability on many benchmark datasets. However, most of the existing abdominal datasets only contain single-center, single-phase, single-vendor, or single-disease cases, and it is unclear whether the excellent performance can generalize on diverse datasets. This paper presents a large and diverse abdominal CT organ segmentation dataset, termed AbdomenCT-1K, with more than 1000 (1K) CT scans from 12 medical centers, including multi-phase, multi-vendor, and multi-disease cases. Furthermore, we conduct a large-scale study for liver, kidney, spleen, and pancreas segmentation and reveal the unsolved segmentation problems of the SOTA methods, such as the limited generalization ability on distinct medical centers, phases, and unseen diseases. To advance the unsolved problems, we further build four organ segmentation benchmarks for fully supervised, semi-supervised, weakly supervised, and continual learning, which are currently challenging and active research topics. Accordingly, we develop a simple and effective method for each benchmark, which can be used as out-of-the-box methods and strong baselines. We believe the AbdomenCT-1K dataset will promote future in-depth research towards clinical applicable abdominal organ segmentation methods. The datasets, codes, and trained models are publicly available at https://github.com/JunMa11/AbdomenCT-1K.

Summary of semi-supervised medical segmentation methods using pseudo labels.

The semi-supervised method using pseudo labels was first proposed by Lee et al. {{cite:8f81da0}} and has been developed as a classical algorithm for semi-supervised for its simple idea and effective performance. As shown in Figure {{figure:a26e610e-72eb-4b23-bb11-51a9f1f60720}}  (a) the model trained by labeled data can be used to predict the pseudo label of unlabeled data, which is fed together with labeled data to co-train the model in an iterative manner, and make the model achieves promising results on validation set outperforming the training using only labeled data. The such a pseudo-labeling approach has a high universality, but its effectiveness is restricted by the quality of the pseudo labels generated from the unlabeled data. And the related works mentioned below differ in the way of pseudo label generation and the treatment of noisy labels and are listed in Table {{table:d5a3df1e-5d3a-4b99-a037-60c34d3b19eb}} .