ROMay 26
GE-Sim 2.0: A Roadmap Towards Comprehensive Closed-loop Video World Simulators for Robotic ManipulationBoxiang Qiu, Liliang Chen, Yue Liao et al.
We introduce GE-Sim 2.0 (Genie Envisioner World Simulator 2.0), a closed-loop video world simulator for robotic manipulation. Building on the action-conditioned video generation framework of Genie Envisioner, GE-Sim 2.0 is re-trained on thousands of hours of real-world robot data spanning teleoperation, contact-rich interaction, and on-robot policy deployment, substantially improving action-following fidelity and trajectory coverage. On top of this foundation, three new modules close the loop from video simulation to policy learning: a state expert that decodes proprioceptive state from video latents to support next-chunk prediction by downstream VLA policies; a world judge that scores generated rollouts against task instructions, yielding machine-verifiable success signals and rewards in place of manual inspection; and an acceleration framework that delivers a 25-frame rollout in 2.3 seconds on a single H100, with up to 4* frame skipping at inference for long-horizon evaluation. GE-Sim 2.0 tops the public WorldArena leaderboard at only 2B parameters, outperforming both dedicated robotic world models and closed-source general video generators, and policies trained against its rollouts and rewards translate into measurable real-world gains, establishing GE-Sim 2.0 as a practical platform for scalable evaluation and closed-loop learning of manipulation policies.
CVFeb 20, 2023
Composer: Creative and Controllable Image Synthesis with Composable ConditionsLianghua Huang, Di Chen, Yu Liu et al.
Recent large-scale generative models learned on big data are capable of synthesizing incredible images yet suffer from limited controllability. This work offers a new generation paradigm that allows flexible control of the output image, such as spatial layout and palette, while maintaining the synthesis quality and model creativity. With compositionality as the core idea, we first decompose an image into representative factors, and then train a diffusion model with all these factors as the conditions to recompose the input. At the inference stage, the rich intermediate representations work as composable elements, leading to a huge design space (i.e., exponentially proportional to the number of decomposed factors) for customizable content creation. It is noteworthy that our approach, which we call Composer, supports various levels of conditions, such as text description as the global information, depth map and sketch as the local guidance, color histogram for low-level details, etc. Besides improving controllability, we confirm that Composer serves as a general framework and facilitates a wide range of classical generative tasks without retraining. Code and models will be made available.
ROMay 31
$τ_0$-WM: A Unified Video-Action World Model for Robotic ManipulationPengfei Zhou, Shengcong Chen, Di Chen et al.
Robotic manipulation requires models that generate executable actions while anticipating and evaluating their future consequences before physical execution. We present $τ_0$-World Model ($τ_0$-WM), a unified video-action world model that integrates policy learning, video prediction, and action evaluation within a single future-predictive framework. Built on a shared video diffusion backbone, $τ_0$-WM provides two complementary interfaces. First, a video action model jointly predicts future visual latents and continuous action chunks from multi-view observations, language instructions, and robot state. Second, an action-conditioned video simulator rolls out candidate action chunks into multi-view futures and predicts dense task-progress scores. The model is trained on approximately $27{,}300$ hours of real-robot teleoperation, UMI-style interaction, egocentric human videos, and rollout or failure trajectories using modality-specific supervision masks. At inference time, $τ_0$-WM uses test-time computation to sample action candidates, rank them with re-denoising consistency, and invoke simulator-based rectification for low-quality candidates. On challenging long-horizon and fine-grained robotic manipulation tasks, $τ_0$-WM shows superior performance over other relevant baselines.
LGOct 24, 2023
Data-driven Traffic Simulation: A Comprehensive ReviewDi Chen, Meixin Zhu, Hao Yang et al.
Autonomous vehicles (AVs) have the potential to significantly revolutionize society by providing a secure and efficient mode of transportation. Recent years have witnessed notable advancements in autonomous driving perception and prediction, but the challenge of validating the performance of AVs remains largely unresolved. Data-driven microscopic traffic simulation has become an important tool for autonomous driving testing due to 1) availability of high-fidelity traffic data; 2) its advantages of enabling large-scale testing and scenario reproducibility; and 3) its potential in reactive and realistic traffic simulation. However, a comprehensive review of this topic is currently lacking. This paper aims to fill this gap by summarizing relevant studies. The primary objective of this paper is to review current research efforts and provide a futuristic perspective that will benefit future developments in the field. It introduces the general issues of data-driven traffic simulation and outlines key concepts and terms. After overviewing traffic simulation, various datasets and evaluation metrics commonly used are reviewed. The paper then offers a comprehensive evaluation of imitation learning, reinforcement learning, deep generative and deep learning methods, summarizing each and analyzing their advantages and disadvantages in detail. Moreover, it evaluates the state-of-the-art, existing challenges, and future research directions.
CVMar 26, 2025Code
Wan: Open and Advanced Large-Scale Video Generative ModelsTeam Wan, Ang Wang, Baole Ai et al.
This report presents Wan, a comprehensive and open suite of video foundation models designed to push the boundaries of video generation. Built upon the mainstream diffusion transformer paradigm, Wan achieves significant advancements in generative capabilities through a series of innovations, including our novel VAE, scalable pre-training strategies, large-scale data curation, and automated evaluation metrics. These contributions collectively enhance the model's performance and versatility. Specifically, Wan is characterized by four key features: Leading Performance: The 14B model of Wan, trained on a vast dataset comprising billions of images and videos, demonstrates the scaling laws of video generation with respect to both data and model size. It consistently outperforms the existing open-source models as well as state-of-the-art commercial solutions across multiple internal and external benchmarks, demonstrating a clear and significant performance superiority. Comprehensiveness: Wan offers two capable models, i.e., 1.3B and 14B parameters, for efficiency and effectiveness respectively. It also covers multiple downstream applications, including image-to-video, instruction-guided video editing, and personal video generation, encompassing up to eight tasks. Consumer-Grade Efficiency: The 1.3B model demonstrates exceptional resource efficiency, requiring only 8.19 GB VRAM, making it compatible with a wide range of consumer-grade GPUs. Openness: We open-source the entire series of Wan, including source code and all models, with the goal of fostering the growth of the video generation community. This openness seeks to significantly expand the creative possibilities of video production in the industry and provide academia with high-quality video foundation models. All the code and models are available at https://github.com/Wan-Video/Wan2.1.
CVNov 28, 2023
Ranni: Taming Text-to-Image Diffusion for Accurate Instruction FollowingYutong Feng, Biao Gong, Di Chen et al.
Existing text-to-image (T2I) diffusion models usually struggle in interpreting complex prompts, especially those with quantity, object-attribute binding, and multi-subject descriptions. In this work, we introduce a semantic panel as the middleware in decoding texts to images, supporting the generator to better follow instructions. The panel is obtained through arranging the visual concepts parsed from the input text by the aid of large language models, and then injected into the denoising network as a detailed control signal to complement the text condition. To facilitate text-to-panel learning, we come up with a carefully designed semantic formatting protocol, accompanied by a fully-automatic data preparation pipeline. Thanks to such a design, our approach, which we call Ranni, manages to enhance a pre-trained T2I generator regarding its textual controllability. More importantly, the introduction of the generative middleware brings a more convenient form of interaction (i.e., directly adjusting the elements in the panel or using language instructions) and further allows users to finely customize their generation, based on which we develop a practical system and showcase its potential in continuous generation and chatting-based editing. Our project page is at https://ranni-t2i.github.io/Ranni.
CVSep 23, 2022
Grouped Adaptive Loss Weighting for Person SearchYanling Tian, Di Chen, Yunan Liu et al.
Person search is an integrated task of multiple sub-tasks such as foreground/background classification, bounding box regression and person re-identification. Therefore, person search is a typical multi-task learning problem, especially when solved in an end-to-end manner. Recently, some works enhance person search features by exploiting various auxiliary information, e.g. person joint keypoints, body part position, attributes, etc., which brings in more tasks and further complexifies a person search model. The inconsistent convergence rate of each task could potentially harm the model optimization. A straightforward solution is to manually assign different weights to different tasks, compensating for the diverse convergence rates. However, given the special case of person search, i.e. with a large number of tasks, it is impractical to weight the tasks manually. To this end, we propose a Grouped Adaptive Loss Weighting (GALW) method which adjusts the weight of each task automatically and dynamically. Specifically, we group tasks according to their convergence rates. Tasks within the same group share the same learnable weight, which is dynamically assigned by considering the loss uncertainty. Experimental results on two typical benchmarks, CUHK-SYSU and PRW, demonstrate the effectiveness of our method.
CVJul 16, 2022
Monitoring Vegetation From Space at Extremely Fine Resolutions via Coarsely-Supervised Smooth U-NetJoshua Fan, Di Chen, Jiaming Wen et al.
Monitoring vegetation productivity at extremely fine resolutions is valuable for real-world agricultural applications, such as detecting crop stress and providing early warning of food insecurity. Solar-Induced Chlorophyll Fluorescence (SIF) provides a promising way to directly measure plant productivity from space. However, satellite SIF observations are only available at a coarse spatial resolution, making it impossible to monitor how individual crop types or farms are doing. This poses a challenging coarsely-supervised regression (or downscaling) task; at training time, we only have SIF labels at a coarse resolution (3km), but we want to predict SIF at much finer spatial resolutions (e.g. 30m, a 100x increase). We also have additional fine-resolution input features, but the relationship between these features and SIF is unknown. To address this, we propose Coarsely-Supervised Smooth U-Net (CS-SUNet), a novel method for this coarse supervision setting. CS-SUNet combines the expressive power of deep convolutional networks with novel regularization methods based on prior knowledge (such as a smoothness loss) that are crucial for preventing overfitting. Experiments show that CS-SUNet resolves fine-grained variations in SIF more accurately than existing methods.
SOC-PHJul 31, 2024
Evidence and quantification of cooperation of driving agents in mixed traffic flowDi Chen, Jia Li, H. Michael Zhang
Cooperation is a ubiquitous phenomenon in many natural, social, and engineered systems with multiple agents. Understanding the formation of cooperation in mixed traffic is of theoretical interest in its own right, and could also benefit the design and operations of future automated and mixed-autonomy transportation systems. However, how cooperativeness of driving agents can be defined and identified from empirical data seems ambiguous and this hinders further empirical characterizations of the phenomenon and revealing its behavior mechanisms. Towards mitigating this gap, in this paper, we propose a unified conceptual framework to identify collective cooperativeness of driving agents. This framework expands the concept of collective rationality from our recent model (Li et al. 2022a), making it empirically identifiable and behaviorally interpretable in realistic (microscopic and dynamic) settings. This framework integrates mixed traffic observations at both microscopic and macroscopic scales to estimate critical behavioral parameters that describe the collective cooperativeness of driving agents. Applying this framework to NGSIM I-80 trajectory data, we empirically confirm the existence of collective cooperation and quantify the condition and likelihood of its emergence. This study provides the first empirical understanding of collective cooperativeness in human-driven mixed traffic and points to new possibilities to manage mixed autonomy traffic systems.
RODec 22, 2025
Real2Edit2Real: Generating Robotic Demonstrations via a 3D Control InterfaceYujie Zhao, Hongwei Fan, Di Chen et al.
Recent progress in robot learning has been driven by large-scale datasets and powerful visuomotor policy architectures, yet policy robustness remains limited by the substantial cost of collecting diverse demonstrations, particularly for spatial generalization in manipulation tasks. To reduce repetitive data collection, we present Real2Edit2Real, a framework that generates new demonstrations by bridging 3D editability with 2D visual data through a 3D control interface. Our approach first reconstructs scene geometry from multi-view RGB observations with a metric-scale 3D reconstruction model. Based on the reconstructed geometry, we perform depth-reliable 3D editing on point clouds to generate new manipulation trajectories while geometrically correcting the robot poses to recover physically consistent depth, which serves as a reliable condition for synthesizing new demonstrations. Finally, we propose a multi-conditional video generation model guided by depth as the primary control signal, together with action, edge, and ray maps, to synthesize spatially augmented multi-view manipulation videos. Experiments on four real-world manipulation tasks demonstrate that policies trained on data generated from only 1-5 source demonstrations can match or outperform those trained on 50 real-world demonstrations, improving data efficiency by up to 10-50x. Moreover, experimental results on height and texture editing demonstrate the framework's flexibility and extensibility, indicating its potential to serve as a unified data generation framework.
LGSep 19, 2024
How to predict on-road air pollution based on street view images and machine learning: a quantitative analysis of the optimal strategyHui Zhong, Di Chen, Pengqin Wang et al.
On-road air pollution exhibits substantial variability over short distances due to emission sources, dilution, and physicochemical processes. Integrating mobile monitoring data with street view images (SVIs) holds promise for predicting local air pollution. However, algorithms, sampling strategies, and image quality introduce extra errors due to a lack of reliable references that quantify their effects. To bridge this gap, we employed 314 taxis to monitor NO, NO2, PM2.5 and PM10 dynamically and sampled corresponding SVIs, aiming to develop a reliable strategy. We extracted SVI features from ~ 382,000 streetscape images, which were collected at various angles (0°, 90°, 180°, 270°) and ranges (buffers with radii of 100m, 200m, 300m, 400m, 500m). Also, three machine learning algorithms alongside the linear land-used regression (LUR) model were experimented with to explore the influences of different algorithms. Four typical image quality issues were identified and discussed. Generally, machine learning methods outperform linear LUR for estimating the four pollutants, with the ranking: random forest > XGBoost > neural network > LUR. Compared to single-angle sampling, the averaging strategy is an effective method to avoid bias of insufficient feature capture. Therefore, the optimal sampling strategy is to obtain SVIs at a 100m radius buffer and extract features using the averaging strategy. This approach achieved estimation results for each aggregation location with absolute errors almost less than 2.5 μg/m^2 or ppb. Overexposure, blur, and underexposure led to image misjudgments and incorrect identifications, causing an overestimation of road features and underestimation of human-activity features, contributing to inaccurate NO, NO2, PM2.5 and PM10 estimation.
CVDec 13, 2023Code
Divide and Conquer: Hybrid Pre-training for Person SearchYanling Tian, Di Chen, Yunan Liu et al.
Large-scale pre-training has proven to be an effective method for improving performance across different tasks. Current person search methods use ImageNet pre-trained models for feature extraction, yet it is not an optimal solution due to the gap between the pre-training task and person search task (as a downstream task). Therefore, in this paper, we focus on pre-training for person search, which involves detecting and re-identifying individuals simultaneously. Although labeled data for person search is scarce, datasets for two sub-tasks person detection and re-identification are relatively abundant. To this end, we propose a hybrid pre-training framework specifically designed for person search using sub-task data only. It consists of a hybrid learning paradigm that handles data with different kinds of supervisions, and an intra-task alignment module that alleviates domain discrepancy under limited resources. To the best of our knowledge, this is the first work that investigates how to support full-task pre-training using sub-task data. Extensive experiments demonstrate that our pre-trained model can achieve significant improvements across diverse protocols, such as person search method, fine-tuning data, pre-training data and model backbone. For example, our model improves ResNet50 based NAE by 10.3% relative improvement w.r.t. mAP. Our code and pre-trained models are released for plug-and-play usage to the person search community.
CVJan 24, 2020Code
VerSe: A Vertebrae Labelling and Segmentation Benchmark for Multi-detector CT ImagesAnjany Sekuboyina, Malek E. Husseini, Amirhossein Bayat et al.
Vertebral labelling and segmentation are two fundamental tasks in an automated spine processing pipeline. Reliable and accurate processing of spine images is expected to benefit clinical decision-support systems for diagnosis, surgery planning, and population-based analysis on spine and bone health. However, designing automated algorithms for spine processing is challenging predominantly due to considerable variations in anatomy and acquisition protocols and due to a severe shortage of publicly available data. Addressing these limitations, the Large Scale Vertebrae Segmentation Challenge (VerSe) was organised in conjunction with the International Conference on Medical Image Computing and Computer Assisted Intervention (MICCAI) in 2019 and 2020, with a call for algorithms towards labelling and segmentation of vertebrae. Two datasets containing a total of 374 multi-detector CT scans from 355 patients were prepared and 4505 vertebrae have individually been annotated at voxel-level by a human-machine hybrid algorithm (https://osf.io/nqjyw/, https://osf.io/t98fz/). A total of 25 algorithms were benchmarked on these datasets. In this work, we present the the results of this evaluation and further investigate the performance-variation at vertebra-level, scan-level, and at different fields-of-view. We also evaluate the generalisability of the approaches to an implicit domain shift in data by evaluating the top performing algorithms of one challenge iteration on data from the other iteration. The principal takeaway from VerSe: the performance of an algorithm in labelling and segmenting a spine scan hinges on its ability to correctly identify vertebrae in cases of rare anatomical variations. The content and code concerning VerSe can be accessed at: https://github.com/anjany/verse.
RODec 29, 2025
Act2Goal: From World Model To General Goal-conditioned PolicyPengfei Zhou, Liliang Chen, Shengcong Chen et al.
Specifying robotic manipulation tasks in a manner that is both expressive and precise remains a central challenge. While visual goals provide a compact and unambiguous task specification, existing goal-conditioned policies often struggle with long-horizon manipulation due to their reliance on single-step action prediction without explicit modeling of task progress. We propose Act2Goal, a general goal-conditioned manipulation policy that integrates a goal-conditioned visual world model with multi-scale temporal control. Given a current observation and a target visual goal, the world model generates a plausible sequence of intermediate visual states that captures long-horizon structure. To translate this visual plan into robust execution, we introduce Multi-Scale Temporal Hashing (MSTH), which decomposes the imagined trajectory into dense proximal frames for fine-grained closed-loop control and sparse distal frames that anchor global task consistency. The policy couples these representations with motor control through end-to-end cross-attention, enabling coherent long-horizon behavior while remaining reactive to local disturbances. Act2Goal achieves strong zero-shot generalization to novel objects, spatial layouts, and environments. We further enable reward-free online adaptation through hindsight goal relabeling with LoRA-based finetuning, allowing rapid autonomous improvement without external supervision. Real-robot experiments demonstrate that Act2Goal improves success rates from 30% to 90% on challenging out-of-distribution tasks within minutes of autonomous interaction, validating that goal-conditioned world models with multi-scale temporal control provide structured guidance necessary for robust long-horizon manipulation. Project page: https://act2goal.github.io/
RODec 27, 2023
Risk-anticipatory autonomous driving strategies considering vehicles' weights, based on hierarchical deep reinforcement learningDi Chen, Hao Li, Zhicheng Jin et al.
Autonomous vehicles (AVs) have the potential to prevent accidents caused by drivers errors and reduce road traffic risks. Due to the nature of heavy vehicles, whose collisions cause more serious crashes, the weights of vehicles need to be considered when making driving strategies aimed at reducing the potential risks and their consequences in the context of autonomous driving. This study develops an autonomous driving strategy based on risk anticipation, considering the weights of surrounding vehicles and using hierarchical deep reinforcement learning. A risk indicator integrating surrounding vehicles weights, based on the risk field theory, is proposed and incorporated into autonomous driving decisions. A hybrid action space is designed to allow for left lane changes, right lane changes and car-following, which enables AVs to act more freely and realistically whenever possible. To solve the above hybrid decision-making problem, a hierarchical proximal policy optimization (HPPO) algorithm with an attention mechanism (AT-HPPO) is developed, providing great advantages in maintaining stable performance with high robustness and generalization. An indicator, potential collision energy in conflicts (PCEC), is newly proposed to evaluate the performance of the developed AV driving strategy from the perspective of the consequences of potential accidents. The performance evaluation results in simulation and dataset demonstrate that our model provides driving strategies that reduce both the likelihood and consequences of potential accidents, at the same time maintaining driving efficiency. The developed method is especially meaningful for AVs driving on highways, where heavy vehicles make up a high proportion of the traffic.
LGNov 7, 2025
Self-Interest and Systemic Benefits: Emergence of Collective Rationality in Mixed Autonomy Traffic Through Deep Reinforcement LearningDi Chen, Jia Li, Michael Zhang
Autonomous vehicles (AVs) are expected to be commercially available in the near future, leading to mixed autonomy traffic consisting of both AVs and human-driven vehicles (HVs). Although numerous studies have shown that AVs can be deployed to benefit the overall traffic system performance by incorporating system-level goals into their decision making, it is not clear whether the benefits still exist when agents act out of self-interest -- a trait common to all driving agents, both human and autonomous. This study aims to understand whether self-interested AVs can bring benefits to all driving agents in mixed autonomy traffic systems. The research is centered on the concept of collective rationality (CR). This concept, originating from game theory and behavioral economics, means that driving agents may cooperate collectively even when pursuing individual interests. Our recent research has proven the existence of CR in an analytical game-theoretical model and empirically in mixed human-driven traffic. In this paper, we demonstrate that CR can be attained among driving agents trained using deep reinforcement learning (DRL) with a simple reward design. We examine the extent to which self-interested traffic agents can achieve CR without directly incorporating system-level objectives. Results show that CR consistently emerges in various scenarios, which indicates the robustness of this property. We also postulate a mechanism to explain the emergence of CR in the microscopic and dynamic environment and verify it based on simulation evidence. This research suggests the possibility of leveraging advanced learning methods (such as federated learning) to achieve collective cooperation among self-interested driving agents in mixed-autonomy systems.
RONov 29, 2024
Dynamic High-Order Control Barrier Functions with Diffuser for Safety-Critical Trajectory Planning at Signal-Free IntersectionsDi Chen, Ruiguo Zhong, Kehua Chen et al.
Planning safe and efficient trajectories through signal-free intersections presents significant challenges for autonomous vehicles (AVs), particularly in dynamic, multi-task environments with unpredictable interactions and an increased possibility of conflicts. This study aims to address these challenges by developing a unified, robust, adaptive framework to ensure safety and efficiency across three distinct intersection movements: left-turn, right-turn, and straight-ahead. Existing methods often struggle to reliably ensure safety and effectively learn multi-task behaviors from demonstrations in such environments. This study proposes a safety-critical planning method that integrates Dynamic High-Order Control Barrier Functions (DHOCBF) with a diffusion-based model, called Dynamic Safety-Critical Diffuser (DSC-Diffuser). The DSC-Diffuser leverages task-guided planning to enhance efficiency, allowing the simultaneous learning of multiple driving tasks from real-world expert demonstrations. Moreover, the incorporation of goal-oriented constraints significantly reduces displacement errors, ensuring precise trajectory execution. To further ensure driving safety in dynamic environments, the proposed DHOCBF framework dynamically adjusts to account for the movements of surrounding vehicles, offering enhanced adaptability and reduce the conservatism compared to traditional control barrier functions. Validity evaluations of DHOCBF, conducted through numerical simulations, demonstrate its robustness in adapting to variations in obstacle velocities, sizes, uncertainties, and locations, effectively maintaining driving safety across a wide range of complex and uncertain scenarios. Comprehensive performance evaluations demonstrate that DSC-Diffuser generates realistic, stable, and generalizable policies, providing flexibility and reliable safety assurance in complex multi-task driving scenarios.
CVJun 10, 2025
TrajFlow: Multi-modal Motion Prediction via Flow MatchingQi Yan, Brian Zhang, Yutong Zhang et al.
Efficient and accurate motion prediction is crucial for ensuring safety and informed decision-making in autonomous driving, particularly under dynamic real-world conditions that necessitate multi-modal forecasts. We introduce TrajFlow, a novel flow matching-based motion prediction framework that addresses the scalability and efficiency challenges of existing generative trajectory prediction methods. Unlike conventional generative approaches that employ i.i.d. sampling and require multiple inference passes to capture diverse outcomes, TrajFlow predicts multiple plausible future trajectories in a single pass, significantly reducing computational overhead while maintaining coherence across predictions. Moreover, we propose a ranking loss based on the Plackett-Luce distribution to improve uncertainty estimation of predicted trajectories. Additionally, we design a self-conditioning training technique that reuses the model's own predictions to construct noisy inputs during a second forward pass, thereby improving generalization and accelerating inference. Extensive experiments on the large-scale Waymo Open Motion Dataset (WOMD) demonstrate that TrajFlow achieves state-of-the-art performance across various key metrics, underscoring its effectiveness for safety-critical autonomous driving applications. The code and other details are available on the project website https://traj-flow.github.io/.
ROSep 29, 2025
Fidelity-Aware Data Composition for Robust Robot GeneralizationZizhao Tong, Di Chen, Sicheng Hu et al.
Generalist robot policies trained on large-scale, visually homogeneous datasets can be susceptible to shortcut learning, which impairs their out-of-distribution (OOD) generalization. While generative data augmentation is a common approach to introduce diversity, it presents a subtle challenge: data composition. Naively mixing real and synthetic data can corrupt the learning signal, as this process often prioritizes visual diversity at the expense of information fidelity. This paper suggests that robust generalization depends on principled, fidelity-aware data composition. We introduce Coherent Information Fidelity Tuning (CIFT), a framework that treats data composition as an optimization problem. CIFT uses a practical proxy for Information Fidelity based on the feature-space geometry of a dataset. This enables the identification of a phase transition, termed the Decoherence Point, where training stability degrades. The framework includes a generative engine, Multi-View Video Augmentation (MVAug), to synthesize a causally disentangled data spectrum for this tuning process. Applying CIFT to policy architectures such as $π_0$ and Diffusion Policy improves OOD success rates by over 54\%. These results indicate that fidelity-aware composition, beyond data synthesis alone, is an important component for developing robust, general-purpose robots.
CVNov 16, 2021
Keypoint Message Passing for Video-based Person Re-IdentificationDi Chen, Andreas Doering, Shanshan Zhang et al.
Video-based person re-identification (re-ID) is an important technique in visual surveillance systems which aims to match video snippets of people captured by different cameras. Existing methods are mostly based on convolutional neural networks (CNNs), whose building blocks either process local neighbor pixels at a time, or, when 3D convolutions are used to model temporal information, suffer from the misalignment problem caused by person movement. In this paper, we propose to overcome the limitations of normal convolutions with a human-oriented graph method. Specifically, features located at person joint keypoints are extracted and connected as a spatial-temporal graph. These keypoint features are then updated by message passing from their connected nodes with a graph convolutional network (GCN). During training, the GCN can be attached to any CNN-based person re-ID model to assist representation learning on feature maps, whilst it can be dropped after training for better inference speed. Our method brings significant improvements over the CNN-based baseline model on the MARS dataset with generated person keypoints and a newly annotated dataset: PoseTrackReID. It also defines a new state-of-the-art method in terms of top-1 accuracy and mean average precision in comparison to prior works.
LGAug 21, 2021
Automating Crystal-Structure Phase Mapping: Combining Deep Learning with Constraint ReasoningDi Chen, Yiwei Bai, Sebastian Ament et al.
Crystal-structure phase mapping is a core, long-standing challenge in materials science that requires identifying crystal structures, or mixtures thereof, in synthesized materials. Materials science experts excel at solving simple systems but cannot solve complex systems, creating a major bottleneck in high-throughput materials discovery. Herein we show how to automate crystal-structure phase mapping. We formulate phase mapping as an unsupervised pattern demixing problem and describe how to solve it using Deep Reasoning Networks (DRNets). DRNets combine deep learning with constraint reasoning for incorporating scientific prior knowledge and consequently require only a modest amount of (unlabeled) data. DRNets compensate for the limited data by exploiting and magnifying the rich prior knowledge about the thermodynamic rules governing the mixtures of crystals with constraint reasoning seamlessly integrated into neural network optimization. DRNets are designed with an interpretable latent space for encoding prior-knowledge domain constraints and seamlessly integrate constraint reasoning into neural network optimization. DRNets surpass previous approaches on crystal-structure phase mapping, unraveling the Bi-Cu-V oxide phase diagram, and aiding the discovery of solar-fuels materials.
CVNov 12, 2020
PoseTrackReID: Dataset DescriptionAndreas Doering, Di Chen, Shanshan Zhang et al.
Current datasets for video-based person re-identification (re-ID) do not include structural knowledge in form of human pose annotations for the persons of interest. Nonetheless, pose information is very helpful to disentangle useful feature information from background or occlusion noise. Especially real-world scenarios, such as surveillance, contain a lot of occlusions in human crowds or by obstacles. On the other hand, video-based person re-ID can benefit other tasks such as multi-person pose tracking in terms of robust feature matching. For that reason, we present PoseTrackReID, a large-scale dataset for multi-person pose tracking and video-based person re-ID. With PoseTrackReID, we want to bridge the gap between person re-ID and multi-person pose tracking. Additionally, this dataset provides a good benchmark for current state-of-the-art methods on multi-frame person re-ID.
LGOct 30, 2020
Deep Hurdle Networks for Zero-Inflated Multi-Target Regression: Application to Multiple Species Abundance EstimationShufeng Kong, Junwen Bai, Jae Hee Lee et al.
A key problem in computational sustainability is to understand the distribution of species across landscapes over time. This question gives rise to challenging large-scale prediction problems since (i) hundreds of species have to be simultaneously modeled and (ii) the survey data are usually inflated with zeros due to the absence of species for a large number of sites. The problem of tackling both issues simultaneously, which we refer to as the zero-inflated multi-target regression problem, has not been addressed by previous methods in statistics and machine learning. In this paper, we propose a novel deep model for the zero-inflated multi-target regression problem. To this end, we first model the joint distribution of multiple response variables as a multivariate probit model and then couple the positive outcomes with a multivariate log-normal distribution. By penalizing the difference between the two distributions' covariance matrices, a link between both distributions is established. The whole model is cast as an end-to-end learning framework and we provide an efficient learning algorithm for our model that can be fully implemented on GPUs. We show that our model outperforms the existing state-of-the-art baselines on two challenging real-world species distribution datasets concerning bird and fish populations.
LGOct 10, 2020
Block-term Tensor Neural NetworksJinmian Ye, Guangxi Li, Di Chen et al.
Deep neural networks (DNNs) have achieved outstanding performance in a wide range of applications, e.g., image classification, natural language processing, etc. Despite the good performance, the huge number of parameters in DNNs brings challenges to efficient training of DNNs and also their deployment in low-end devices with limited computing resources. In this paper, we explore the correlations in the weight matrices, and approximate the weight matrices with the low-rank block-term tensors. We name the new corresponding structure as block-term tensor layers (BT-layers), which can be easily adapted to neural network models, such as CNNs and RNNs. In particular, the inputs and the outputs in BT-layers are reshaped into low-dimensional high-order tensors with a similar or improved representation power. Sufficient experiments have demonstrated that BT-layers in CNNs and RNNs can achieve a very large compression ratio on the number of parameters while preserving or improving the representation power of the original DNNs.
LGOct 17, 2019
Task-Based Learning via Task-Oriented Prediction Network with Applications in FinanceDi Chen, Yada Zhu, Xiaodong Cui et al.
Real-world applications often involve domain-specific and task-based performance objectives that are not captured by the standard machine learning losses, but are critical for decision making. A key challenge for direct integration of more meaningful domain and task-based evaluation criteria into an end-to-end gradient-based training process is the fact that often such performance objectives are not necessarily differentiable and may even require additional decision-making optimization processing. We propose the Task-Oriented Prediction Network (TOPNet), an end-to-end learning scheme that automatically integrates task-based evaluation criteria into the learning process via a learnable surrogate loss function, which directly guides the model towards the task-based goal. A major benefit of the proposed TOPNet learning scheme lies in its capability of automatically integrating non-differentiable evaluation criteria, which makes it particularly suitable for diversified and customized task-based evaluation criteria in real-world tasks. We validate the performance of TOPNet on two real-world financial prediction tasks, revenue surprise forecasting and credit risk modeling. The experimental results demonstrate that TOPNet significantly outperforms both traditional modeling with standard losses and modeling with hand-crafted heuristic differentiable surrogate losses.
IVJul 28, 2019
Two-Stream CNN with Loose Pair Training for Multi-modal AMD CategorizationWeisen Wang, Zhiyan Xu, Weihong Yu et al.
This paper studies automated categorization of age-related macular degeneration (AMD) given a multi-modal input, which consists of a color fundus image and an optical coherence tomography (OCT) image from a specific eye. Previous work uses a traditional method, comprised of feature extraction and classifier training that cannot be optimized jointly. By contrast, we propose a two-stream convolutional neural network (CNN) that is end-to-end. The CNN's fusion layer is tailored to the need of fusing information from the fundus and OCT streams. For generating more multi-modal training instances, we introduce Loose Pair training, where a fundus image and an OCT image are paired based on class labels rather than eyes. Moreover, for a visual interpretation of how the individual modalities make contributions, we extend the class activation mapping technique to the multi-modal scenario. Experiments on a real-world dataset collected from an outpatient clinic justify the viability of our proposal for multi-modal AMD categorization.
LGJun 3, 2019
Deep Reasoning Networks: Thinking Fast and SlowDi Chen, Yiwei Bai, Wenting Zhao et al.
We introduce Deep Reasoning Networks (DRNets), an end-to-end framework that combines deep learning with reasoning for solving complex tasks, typically in an unsupervised or weakly-supervised setting. DRNets exploit problem structure and prior knowledge by tightly combining logic and constraint reasoning with stochastic-gradient-based neural network optimization. We illustrate the power of DRNets on de-mixing overlapping hand-written Sudokus (Multi-MNIST-Sudoku) and on a substantially more complex task in scientific discovery that concerns inferring crystal structures of materials from X-ray diffraction data under thermodynamic rules (Crystal-Structure-Phase-Mapping). At a high level, DRNets encode a structured latent space of the input data, which is constrained to adhere to prior knowledge by a reasoning module. The structured latent encoding is used by a generative decoder to generate the targeted output. Finally, an overall objective combines responses from the generative decoder (thinking fast) and the reasoning module (thinking slow), which is optimized using constraint-aware stochastic gradient descent. We show how to encode different tasks as DRNets and demonstrate DRNets' effectiveness with detailed experiments: DRNets significantly outperform the state of the art and experts' capabilities on Crystal-Structure-Phase-Mapping, recovering more precise and physically meaningful crystal structures. On Multi-MNIST-Sudoku, DRNets perfectly recovered the mixed Sudokus' digits, with 100% digit accuracy, outperforming the supervised state-of-the-art MNIST de-mixing models. Finally, as a proof of concept, we also show how DRNets can solve standard combinatorial problems -- 9-by-9 Sudoku puzzles and Boolean satisfiability problems (SAT), outperforming other specialized deep learning models. DRNets are general and can be adapted and expanded to tackle other tasks.
SDFeb 25, 2019
Automatic Detection and Compression for Passive Acoustic Monitoring of the African Forest ElephantJohan Bjorck, Brendan H. Rappazzo, Di Chen et al.
In this work, we consider applying machine learning to the analysis and compression of audio signals in the context of monitoring elephants in sub-Saharan Africa. Earth's biodiversity is increasingly under threat by sources of anthropogenic change (e.g. resource extraction, land use change, and climate change) and surveying animal populations is critical for developing conservation strategies. However, manually monitoring tropical forests or deep oceans is intractable. For species that communicate acoustically, researchers have argued for placing audio recorders in the habitats as a cost-effective and non-invasive method, a strategy known as passive acoustic monitoring (PAM). In collaboration with conservation efforts, we construct a large labeled dataset of passive acoustic recordings of the African Forest Elephant via crowdsourcing, compromising thousands of hours of recordings in the wild. Using state-of-the-art techniques in artificial intelligence we improve upon previously proposed methods for passive acoustic monitoring for classification and segmentation. In real-time detection of elephant calls, network bandwidth quickly becomes a bottleneck and efficient ways to compress the data are needed. Most audio compression schemes are aimed at human listeners and are unsuitable for low-frequency elephant calls. To remedy this, we provide a novel end-to-end differentiable method for compression of audio signals that can be adapted to acoustic monitoring of any species and dramatically improves over naive coding strategies.
SEFeb 9, 2019
Replication Can Improve Prior Results: A GitHub Study of Pull Request AcceptanceDi Chen, Kathyrn Stolee, Tim Menzies
Crowdsourcing and data mining can be used to effectively reduce the effort associated with the partial replication and enhancement of qualitative studies. For example, in a primary study, other researchers explored factors influencing the fate of GitHub pull requests using an extensive qualitative analysis of 20 pull requests. Guided by their findings, we mapped some of their qualitative insights onto quantitative questions. To determine how well their findings generalize, we collected much more data (170 additional pull requests from 142 GitHub projects). Using crowdsourcing, that data was augmented with subjective qualitative human opinions about how pull requests extended the original issue. The crowd's answers were then combined with quantitative features and, using data mining, used to build a predictor for whether code would be merged. That predictor was far more accurate that one built from the primary study's qualitative factors (F1=90 vs 68\%), illustrating the value of a mixed-methods approach and replication to improve prior results. To test the generality of this approach, the next step in future work is to conduct other studies that extend qualitative studies with crowdsourcing and data mining.
SEFeb 5, 2019
How to "DODGE" Complex Software Analytics?Amritanshu Agrawal, Wei Fu, Di Chen et al.
Machine learning techniques applied to software engineering tasks can be improved by hyperparameter optimization, i.e., automatic tools that find good settings for a learner's control parameters. We show that such hyperparameter optimization can be unnecessarily slow, particularly when the optimizers waste time exploring "redundant tunings"', i.e., pairs of tunings which lead to indistinguishable results. By ignoring redundant tunings, DODGE, a tuning tool, runs orders of magnitude faster, while also generating learners with more accurate predictions than seen in prior state-of-the-art approaches.
LGNov 1, 2018
Bias Reduction via End-to-End Shift Learning: Application to Citizen ScienceDi Chen, Carla P. Gomes
Citizen science projects are successful at gathering rich datasets for various applications. However, the data collected by citizen scientists are often biased --- in particular, aligned more with the citizens' preferences than with scientific objectives. We propose the Shift Compensation Network (SCN), an end-to-end learning scheme which learns the shift from the scientific objectives to the biased data while compensating for the shift by re-weighting the training data. Applied to bird observational data from the citizen science project eBird, we demonstrate how SCN quantifies the data distribution shift and outperforms supervised learning models that do not address the data bias. Compared with competing models in the context of covariate shift, we further demonstrate the advantage of SCN in both its effectiveness and its capability of handling massive high-dimensional data.
CVJul 21, 2018
Person Search via A Mask-Guided Two-Stream CNN ModelDi Chen, Shanshan Zhang, Wanli Ouyang et al.
In this work, we tackle the problem of person search, which is a challenging task consisted of pedestrian detection and person re-identification~(re-ID). Instead of sharing representations in a single joint model, we find that separating detector and re-ID feature extraction yields better performance. In order to extract more representative features for each identity, we segment out the foreground person from the original image patch. We propose a simple yet effective re-ID method, which models foreground person and original image patches individually, and obtains enriched representations from two separate CNN streams. From the experiments on two standard person search benchmarks of CUHK-SYSU and PRW, we achieve mAP of $83.0\%$ and $32.6\%$ respectively, surpassing the state of the art by a large margin (more than 5pp).
LGMar 22, 2018
End-to-End Learning for the Deep Multivariate Probit ModelDi Chen, Yexiang Xue, Carla P. Gomes
The multivariate probit model (MVP) is a popular classic model for studying binary responses of multiple entities. Nevertheless, the computational challenge of learning the MVP model, given that its likelihood involves integrating over a multidimensional constrained space of latent variables, significantly limits its application in practice. We propose a flexible deep generalization of the classic MVP, the Deep Multivariate Probit Model (DMVP), which is an end-to-end learning scheme that uses an efficient parallel sampling process of the multivariate probit model to exploit GPU-boosted deep neural networks. We present both theoretical and empirical analysis of the convergence behavior of DMVP's sampling process with respect to the resolution of the correlation structure. We provide convergence guarantees for DMVP and our empirical analysis demonstrates the advantages of DMVP's sampling compared with standard MCMC-based methods. We also show that when applied to multi-entity modelling problems, which are natural DMVP applications, DMVP trains faster than classical MVP, by at least an order of magnitude, captures rich correlations among entities, and further improves the joint likelihood of entities compared with several competitive models.
SEMar 13, 2018
Applications of Psychological Science for Actionable AnalyticsDi Chen, Wei Fu, Rahul Krishna et al.
Actionable analytics are those that humans can understand, and operationalize. What kind of data mining models generate such actionable analytics? According to psychological scientists, humans understand models that most match their own internal models, which they characterize as lists of "heuristic" (i.e., lists of very succinct rules). One such heuristic rule generator is the Fast-and-Frugal Trees (FFT) preferred by psychological scientists. Despite their successful use in many applied domains, FFTs have not been applied in software analytics. Accordingly, this paper assesses FFTs for software analytics. We find that FFTs are remarkably effective. Their models are very succinct (5 lines or less describing a binary decision tree). These succinct models outperform state-of-the-art defect prediction algorithms defined by Ghortra et al. at ICSE'15. Also, when we restrict training data to operational attributes (i.e., those attributes that are frequently changed by developers), FFTs perform much better than standard learners. Our conclusions are two-fold. Firstly, there is much that software analytics community could learn from psychological science. Secondly, proponents of complex methods should always baseline those methods against simpler alternatives. For example, FFTs could be used as a standard baseline learner against which other software analytics tools are compared.
SEMar 13, 2018
Building Better Quality Predictors Using "$ε$-Dominance"Wei Fu, Tim Menzies, Di Chen et al.
Despite extensive research, many methods in software quality prediction still exhibit some degree of uncertainty in their results. Rather than treating this as a problem, this paper asks if this uncertainty is a resource that can simplify software quality prediction. For example, Deb's principle of $ε$-dominance states that if there exists some $ε$ value below which it is useless or impossible to distinguish results, then it is superfluous to explore anything less than $ε$. We say that for "large $ε$ problems", the results space of learning effectively contains just a few regions. If many learners are then applied to such large $ε$ problems, they would exhibit a "many roads lead to Rome" property; i.e., many different software quality prediction methods would generate a small set of very similar results. This paper explores DART, an algorithm especially selected to succeed for large $ε$ software quality prediction problems. DART is remarkable simple yet, on experimentation, it dramatically out-performs three sets of state-of-the-art defect prediction methods. The success of DART for defect prediction begs the questions: how many other domains in software quality predictors can also be radically simplified? This will be a fruitful direction for future work.
IVMar 11, 2018
Multi-Reference Video Coding Using Stillness DetectionDi Chen, Zoe Liu, Yaowu Xu et al.
Encoders of AOM/AV1 codec consider an input video sequence as succession of frames grouped in Golden-Frame (GF) groups. The coding structure of a GF group is fixed with a given GF group size. In the current AOM/AV1 encoder, video frames are coded using a hierarchical, multilayer coding structure within one GF group. It has been observed that the use of multilayer coding structure may result in worse coding performance if the GF group presents consistent stillness across its frames. This paper proposes a new approach that adaptively designs the Golden-Frame (GF) group coding structure through the use of stillness detection. Our new approach hence develops an automatic stillness detection scheme using three metrics extracted from each GF group. It then differentiates those GF groups of stillness from other non- still GF groups and uses different GF coding structures accordingly. Experimental result demonstrates a consistent coding gain using the new approach.
CVFeb 8, 2018
Texture Segmentation Based Video Compression Using Convolutional Neural NetworksChichen Fu, Di Chen, Edward J. Delp et al.
There has been a growing interest in using different approaches to improve the coding efficiency of modern video codec in recent years as demand for web-based video consumption increases. In this paper, we propose a model-based approach that uses texture analysis/synthesis to reconstruct blocks in texture regions of a video to achieve potential coding gains using the AV1 codec developed by the Alliance for Open Media (AOM). The proposed method uses convolutional neural networks to extract texture regions in a frame, which are then reconstructed using a global motion model. Our preliminary results show an increase in coding efficiency while maintaining satisfactory visual quality.
MLDec 15, 2017
BT-Nets: Simplifying Deep Neural Networks via Block Term DecompositionGuangxi Li, Jinmian Ye, Haiqin Yang et al.
Recently, deep neural networks (DNNs) have been regarded as the state-of-the-art classification methods in a wide range of applications, especially in image classification. Despite the success, the huge number of parameters blocks its deployment to situations with light computing resources. Researchers resort to the redundancy in the weights of DNNs and attempt to find how fewer parameters can be chosen while preserving the accuracy at the same time. Although several promising results have been shown along this research line, most existing methods either fail to significantly compress a well-trained deep network or require a heavy fine-tuning process for the compressed network to regain the original performance. In this paper, we propose the \textit{Block Term} networks (BT-nets) in which the commonly used fully-connected layers (FC-layers) are replaced with block term layers (BT-layers). In BT-layers, the inputs and the outputs are reshaped into two low-dimensional high-order tensors, then block-term decomposition is applied as tensor operators to connect them. We conduct extensive experiments on benchmark datasets to demonstrate that BT-layers can achieve a very large compression ratio on the number of parameters while preserving the representation power of the original FC-layers as much as possible. Specifically, we can get a higher performance while requiring fewer parameters compared with the tensor train method.
LGDec 14, 2017
Learning Compact Recurrent Neural Networks with Block-Term Tensor DecompositionJinmian Ye, Linnan Wang, Guangxi Li et al.
Recurrent Neural Networks (RNNs) are powerful sequence modeling tools. However, when dealing with high dimensional inputs, the training of RNNs becomes computational expensive due to the large number of model parameters. This hinders RNNs from solving many important computer vision tasks, such as Action Recognition in Videos and Image Captioning. To overcome this problem, we propose a compact and flexible structure, namely Block-Term tensor decomposition, which greatly reduces the parameters of RNNs and improves their training efficiency. Compared with alternative low-rank approximations, such as tensor-train RNN (TT-RNN), our method, Block-Term RNN (BT-RNN), is not only more concise (when using the same rank), but also able to attain a better approximation to the original RNNs with much fewer parameters. On three challenging tasks, including Action Recognition in Videos, Image Captioning and Image Generation, BT-RNN outperforms TT-RNN and the standard RNN in terms of both prediction accuracy and convergence rate. Specifically, BT-LSTM utilizes 17,388 times fewer parameters than the standard LSTM to achieve an accuracy improvement over 15.6\% in the Action Recognition task on the UCF11 dataset.
LGSep 17, 2017
Multi-Entity Dependence Learning with Rich Context via Conditional Variational Auto-encoderLuming Tang, Yexiang Xue, Di Chen et al.
Multi-Entity Dependence Learning (MEDL) explores conditional correlations among multiple entities. The availability of rich contextual information requires a nimble learning scheme that tightly integrates with deep neural networks and has the ability to capture correlation structures among exponentially many outcomes. We propose MEDL_CVAE, which encodes a conditional multivariate distribution as a generating process. As a result, the variational lower bound of the joint likelihood can be optimized via a conditional variational auto-encoder and trained end-to-end on GPUs. Our MEDL_CVAE was motivated by two real-world applications in computational sustainability: one studies the spatial correlation among multiple bird species using the eBird data and the other models multi-dimensional landscape composition and human footprint in the Amazon rainforest with satellite images. We show that MEDL_CVAE captures rich dependency structures, scales better than previous methods, and further improves on the joint likelihood taking advantage of very large datasets that are beyond the capacity of previous methods.
SEFeb 27, 2017
Replicating and Scaling up Qualitative Analysis using Crowdsourcing: A Github-based Case StudyDi Chen, Kathryn T. Stolee, Tim Menzies
Due to the difficulties in replicating and scaling up qualitative studies, such studies are rarely verified. Accordingly, in this paper, we leverage the advantages of crowdsourcing (low costs, fast speed, scalable workforce) to replicate and scale-up one state-of-the-art qualitative study. That qualitative study explored 20 GitHub pull requests to learn factors that influence the fate of pull requests with respect to approval and merging. As a secondary study, using crowdsourcing at a cost of $200, we studied 250 pull requests from 142 GitHub projects. The prior qualitative findings are mapped into questions for crowds workers. Their answers were converted into binary features to build a predictor which predicts whether code would be merged with median F1 scores of 68%. For the same large group of pull requests, the median F1 scores could achieve 90% by a predictor built with additional features defined by prior quantitative results. Based on this case study, we conclude that there is much benefit in combining different kinds of research methods. While qualitative insights are very useful for finding novel insights, they can be hard to scale or replicate. That said, they can guide and define the goals of scalable secondary studies that use (e.g.) crowdsourcing+data mining. On the other hand, while data mining methods are reproducible and scalable to large data sets, their results may be spectacularly wrong since they lack contextual information. That said, they can be used to test the stability and external validity, of the insights gained from a qualitative analysis.
LGSep 28, 2016
Deep Multi-Species EmbeddingDi Chen, Yexiang Xue, Shuo Chen et al.
Understanding how species are distributed across landscapes over time is a fundamental question in biodiversity research. Unfortunately, most species distribution models only target a single species at a time, despite strong ecological evidence that species are not independently distributed. We propose Deep Multi-Species Embedding (DMSE), which jointly embeds vectors corresponding to multiple species as well as vectors representing environmental covariates into a common high-dimensional feature space via a deep neural network. Applied to bird observational data from the citizen science project \textit{eBird}, we demonstrate how the DMSE model discovers inter-species relationships to outperform single-species distribution models (random forests and SVMs) as well as competing multi-label models. Additionally, we demonstrate the benefit of using a deep neural network to extract features within the embedding and show how they improve the predictive performance of species distribution modelling. An important domain contribution of the DMSE model is the ability to discover and describe species interactions while simultaneously learning the shared habitat preferences among species. As an additional contribution, we provide a graphical embedding of hundreds of bird species in the Northeast US.
LGFeb 17, 2016
Relative Error Embeddings for the Gaussian Kernel DistanceDi Chen, Jeff M. Phillips
A reproducing kernel can define an embedding of a data point into an infinite dimensional reproducing kernel Hilbert space (RKHS). The norm in this space describes a distance, which we call the kernel distance. The random Fourier features (of Rahimi and Recht) describe an oblivious approximate mapping into finite dimensional Euclidean space that behaves similar to the RKHS. We show in this paper that for the Gaussian kernel the Euclidean norm between these mapped to features has $(1+ε)$-relative error with respect to the kernel distance. When there are $n$ data points, we show that $O((1/ε^2) \log(n))$ dimensions of the approximate feature space are sufficient and necessary. Without a bound on $n$, but when the original points lie in $\mathbb{R}^d$ and have diameter bounded by $\mathcal{M}$, then we show that $O((d/ε^2) \log(\mathcal{M}))$ dimensions are sufficient, and that this many are required, up to $\log(1/ε)$ factors.