Yikai Wang

Xiao Yang, Chang Liu, Longlong Xu et al. · microsoft-research, tsinghua

Face recognition is a prevailing authentication solution in numerous biometric applications. Physical adversarial attacks, as an important surrogate, can identify the weaknesses of face recognition systems and evaluate their robustness before deployed. However, most existing physical attacks are either detectable readily or ineffective against commercial recognition systems. The goal of this work is to develop a more reliable technique that can carry out an end-to-end evaluation of adversarial robustness for commercial systems. It requires that this technique can simultaneously deceive black-box recognition models and evade defensive mechanisms. To fulfill this, we design adversarial textured 3D meshes (AT3D) with an elaborate topology on a human face, which can be 3D-printed and pasted on the attacker's face to evade the defenses. However, the mesh-based optimization regime calculates gradients in high-dimensional mesh space, and can be trapped into local optima with unsatisfactory transferability. To deviate from the mesh-based space, we propose to perturb the low-dimensional coefficient space based on 3D Morphable Model, which significantly improves black-box transferability meanwhile enjoying faster search efficiency and better visual quality. Extensive experiments in digital and physical scenarios show that our method effectively explores the security vulnerabilities of multiple popular commercial services, including three recognition APIs, four anti-spoofing APIs, two prevailing mobile phones and two automated access control systems.

Yikai Wang, Xinwei Sun, Yanwei Fu

Noisy training set usually leads to the degradation of generalization and robustness of neural networks. In this paper, we propose using a theoretically guaranteed noisy label detection framework to detect and remove noisy data for Learning with Noisy Labels (LNL). Specifically, we design a penalized regression to model the linear relation between network features and one-hot labels, where the noisy data are identified by the non-zero mean shift parameters solved in the regression model. To make the framework scalable to datasets that contain a large number of categories and training data, we propose a split algorithm to divide the whole training set into small pieces that can be solved by the penalized regression in parallel, leading to the Scalable Penalized Regression (SPR) framework. We provide the non-asymptotic probabilistic condition for SPR to correctly identify the noisy data. While SPR can be regarded as a sample selection module for standard supervised training pipeline, we further combine it with semi-supervised algorithm to further exploit the support of noisy data as unlabeled data. Experimental results on several benchmark datasets and real-world noisy datasets show the effectiveness of our framework. Our code and pretrained models are released at https://github.com/Yikai-Wang/SPR-LNL.

Yikai Wang, Yanwei Fu, Xinwei Sun

A noisy training set usually leads to the degradation of the generalization and robustness of neural networks. In this paper, we propose a novel theoretically guaranteed clean sample selection framework for learning with noisy labels. Specifically, we first present a Scalable Penalized Regression (SPR) method, to model the linear relation between network features and one-hot labels. In SPR, the clean data are identified by the zero mean-shift parameters solved in the regression model. We theoretically show that SPR can recover clean data under some conditions. Under general scenarios, the conditions may be no longer satisfied; and some noisy data are falsely selected as clean data. To solve this problem, we propose a data-adaptive method for Scalable Penalized Regression with Knockoff filters (Knockoffs-SPR), which is provable to control the False-Selection-Rate (FSR) in the selected clean data. To improve the efficiency, we further present a split algorithm that divides the whole training set into small pieces that can be solved in parallel to make the framework scalable to large datasets. While Knockoffs-SPR can be regarded as a sample selection module for a standard supervised training pipeline, we further combine it with a semi-supervised algorithm to exploit the support of noisy data as unlabeled data. Experimental results on several benchmark datasets and real-world noisy datasets show the effectiveness of our framework and validate the theoretical results of Knockoffs-SPR. Our code and pre-trained models are available at https://github.com/Yikai-Wang/Knockoffs-SPR.

Yikai Wang, Jianan Wang, Guansong Lu et al.

Existing text-guided image manipulation methods aim to modify the appearance of the image or to edit a few objects in a virtual or simple scenario, which is far from practical applications. In this work, we study a novel task on text-guided image manipulation on the entity level in the real world (eL-TGIM). The task imposes three basic requirements, (1) to edit the entity consistent with the text descriptions, (2) to preserve the entity-irrelevant regions, and (3) to merge the manipulated entity into the image naturally. To this end, we propose an elegant framework, dubbed as SeMani, forming the Semantic Manipulation of real-world images that can not only edit the appearance of entities but also generate new entities corresponding to the text guidance. To solve eL-TGIM, SeMani decomposes the task into two phases: the semantic alignment phase and the image manipulation phase. In the semantic alignment phase, SeMani incorporates a semantic alignment module to locate the entity-relevant region to be manipulated. In the image manipulation phase, SeMani adopts a generative model to synthesize new images conditioned on the entity-irrelevant regions and target text descriptions. We discuss and propose two popular generation processes that can be utilized in SeMani, the discrete auto-regressive generation with transformers and the continuous denoising generation with diffusion models, yielding SeMani-Trans and SeMani-Diff, respectively. We conduct extensive experiments on the real datasets CUB, Oxford, and COCO datasets to verify that SeMani can distinguish the entity-relevant and -irrelevant regions and achieve more precise and flexible manipulation in a zero-shot manner compared with baseline methods. Our codes and models will be released at https://github.com/Yikai-Wang/SeMani.

Jianxiong Gao, Xuelin Qian, Yikai Wang et al.

Amodal object segmentation is a challenging task that involves segmenting both visible and occluded parts of an object. In this paper, we propose a novel approach, called Coarse-to-Fine Segmentation (C2F-Seg), that addresses this problem by progressively modeling the amodal segmentation. C2F-Seg initially reduces the learning space from the pixel-level image space to the vector-quantized latent space. This enables us to better handle long-range dependencies and learn a coarse-grained amodal segment from visual features and visible segments. However, this latent space lacks detailed information about the object, which makes it difficult to provide a precise segmentation directly. To address this issue, we propose a convolution refine module to inject fine-grained information and provide a more precise amodal object segmentation based on visual features and coarse-predicted segmentation. To help the studies of amodal object segmentation, we create a synthetic amodal dataset, named as MOViD-Amodal (MOViD-A), which can be used for both image and video amodal object segmentation. We extensively evaluate our model on two benchmark datasets: KINS and COCO-A. Our empirical results demonstrate the superiority of C2F-Seg. Moreover, we exhibit the potential of our approach for video amodal object segmentation tasks on FISHBOWL and our proposed MOViD-A. Project page at: http://jianxgao.github.io/C2F-Seg.

Yifan Li, Yikai Wang, Yanwei Fu et al.

Visual-Language Alignment (VLA) has gained a lot of attention since CLIP's groundbreaking work. Although CLIP performs well, the typical direct latent feature alignment lacks clarity in its representation and similarity scores. On the other hand, lexical representation, a vector whose element represents the similarity between the sample and a word from the vocabulary, is a natural sparse representation and interpretable, providing exact matches for individual words. However, lexical representations are difficult to learn due to no ground-truth supervision and false-discovery issues, and thus requires complex design to train effectively. In this paper, we introduce LexVLA, a more interpretable VLA framework by learning a unified lexical representation for both modalities without complex design. We use DINOv2 as our visual model for its local-inclined features and Llama 2, a generative language model, to leverage its in-context lexical prediction ability. To avoid the false discovery, we propose an overuse penalty to refrain the lexical representation from falsely frequently activating meaningless words. We demonstrate that these two pre-trained uni-modal models can be well-aligned by fine-tuning on the modest multi-modal dataset and avoid intricate training configurations. On cross-modal retrieval benchmarks, LexVLA, trained on the CC-12M multi-modal dataset, outperforms baselines fine-tuned on larger datasets (e.g., YFCC15M) and those trained from scratch on even bigger datasets (e.g., 1.1B data, including CC-12M). We conduct extensive experiments to analyze LexVLA. Codes are available at https://github.com/Clementine24/LexVLA.

Xuelin Qian, Yikai Wang, Yanwei Fu et al.

The connection between brain activity and corresponding visual stimuli is crucial in comprehending the human brain. While deep generative models have exhibited advancement in recovering brain recordings by generating images conditioned on fMRI signals, accomplishing high-quality generation with consistent semantics continues to pose challenges. Moreover, the prediction of brain activity from visual stimuli remains a formidable undertaking. In this paper, we introduce a unified framework that addresses both fMRI decoding and encoding. Commencing with the establishment of two latent spaces capable of representing and reconstructing fMRI signals and visual images, respectively, we proceed to align the fMRI signals and visual images within the latent space, thereby enabling a bidirectional transformation between the two domains. Our Latent Embedding Alignment (LEA) model concurrently recovers visual stimuli from fMRI signals and predicts brain activity from images within a unified framework. The performance of LEA surpasses that of existing methods on multiple benchmark fMRI decoding and encoding datasets. By integrating fMRI decoding and encoding, LEA offers a comprehensive solution for modeling the intricate relationship between brain activity and visual stimuli.

Ke Fan, Yikai Wang, Qian Yu et al.

Neural networks are known to produce over-confident predictions on input images, even when these images are out-of-distribution (OOD) samples. This limits the applications of neural network models in real-world scenarios, where OOD samples exist. Many existing approaches identify the OOD instances via exploiting various cues, such as finding irregular patterns in the feature space, logits space, gradient space or the raw space of images. In contrast, this paper proposes a simple Test-time Linear Training (ETLT) method for OOD detection. Empirically, we find that the probabilities of input images being out-of-distribution are surprisingly linearly correlated to the features extracted by neural networks. To be specific, many state-of-the-art OOD algorithms, although designed to measure reliability in different ways, actually lead to OOD scores mostly linearly related to their image features. Thus, by simply learning a linear regression model trained from the paired image features and inferred OOD scores at test-time, we can make a more precise OOD prediction for the test instances. We further propose an online variant of the proposed method, which achieves promising performance and is more practical in real-world applications. Remarkably, we improve FPR95 from $51.37\%$ to $12.30\%$ on CIFAR-10 datasets with maximum softmax probability as the base OOD detector. Extensive experiments on several benchmark datasets show the efficacy of ETLT for OOD detection task.

Pengkun Liu, Yikai Wang, Fuchun Sun et al.

Encouraged by the growing availability of pre-trained 2D diffusion models, image-to-3D generation by leveraging Score Distillation Sampling (SDS) is making remarkable progress. Most existing methods combine novel-view lifting from 2D diffusion models which usually take the reference image as a condition while applying hard L2 image supervision at the reference view. Yet heavily adhering to the image is prone to corrupting the inductive knowledge of the 2D diffusion model leading to flat or distorted 3D generation frequently. In this work, we reexamine image-to-3D in a novel perspective and present Isotropic3D, an image-to-3D generation pipeline that takes only an image CLIP embedding as input. Isotropic3D allows the optimization to be isotropic w.r.t. the azimuth angle by solely resting on the SDS loss. The core of our framework lies in a two-stage diffusion model fine-tuning. Firstly, we fine-tune a text-to-3D diffusion model by substituting its text encoder with an image encoder, by which the model preliminarily acquires image-to-image capabilities. Secondly, we perform fine-tuning using our Explicit Multi-view Attention (EMA) which combines noisy multi-view images with the noise-free reference image as an explicit condition. CLIP embedding is sent to the diffusion model throughout the whole process while reference images are discarded once after fine-tuning. As a result, with a single image CLIP embedding, Isotropic3D is capable of generating multi-view mutually consistent images and also a 3D model with more symmetrical and neat content, well-proportioned geometry, rich colored texture, and less distortion compared with existing image-to-3D methods while still preserving the similarity to the reference image to a large extent. The project page is available at https://isotropic3d.github.io/. The code and models are available at https://github.com/pkunliu/Isotropic3D.

Chenjie Cao, Yunuo Cai, Qiaole Dong et al.

This paper introduces LeftRefill, an innovative approach to efficiently harness large Text-to-Image (T2I) diffusion models for reference-guided image synthesis. As the name implies, LeftRefill horizontally stitches reference and target views together as a whole input. The reference image occupies the left side, while the target canvas is positioned on the right. Then, LeftRefill paints the right-side target canvas based on the left-side reference and specific task instructions. Such a task formulation shares some similarities with contextual inpainting, akin to the actions of a human painter. This novel formulation efficiently learns both structural and textured correspondence between reference and target without other image encoders or adapters. We inject task and view information through cross-attention modules in T2I models, and further exhibit multi-view reference ability via the re-arranged self-attention modules. These enable LeftRefill to perform consistent generation as a generalized model without requiring test-time fine-tuning or model modifications. Thus, LeftRefill can be seen as a simple yet unified framework to address reference-guided synthesis. As an exemplar, we leverage LeftRefill to address two different challenges: reference-guided inpainting and novel view synthesis, based on the pre-trained StableDiffusion. Codes and models are released at https://github.com/ewrfcas/LeftRefill.

Yikai Wang, Yi Yang, Fuchun Sun et al.

In the low-bit quantization field, training Binary Neural Networks (BNNs) is the extreme solution to ease the deployment of deep models on resource-constrained devices, having the lowest storage cost and significantly cheaper bit-wise operations compared to 32-bit floating-point counterparts. In this paper, we introduce Sub-bit Neural Networks (SNNs), a new type of binary quantization design tailored to compress and accelerate BNNs. SNNs are inspired by an empirical observation, showing that binary kernels learnt at convolutional layers of a BNN model are likely to be distributed over kernel subsets. As a result, unlike existing methods that binarize weights one by one, SNNs are trained with a kernel-aware optimization framework, which exploits binary quantization in the fine-grained convolutional kernel space. Specifically, our method includes a random sampling step generating layer-specific subsets of the kernel space, and a refinement step learning to adjust these subsets of binary kernels via optimization. Experiments on visual recognition benchmarks and the hardware deployment on FPGA validate the great potentials of SNNs. For instance, on ImageNet, SNNs of ResNet-18/ResNet-34 with 0.56-bit weights achieve 3.13/3.33 times runtime speed-up and 1.8 times compression over conventional BNNs with moderate drops in recognition accuracy. Promising results are also obtained when applying SNNs to binarize both weights and activations. Our code is available at https://github.com/yikaiw/SNN.

Yikai Wang, Chengming Xu, Chen Liu et al.

Few-shot learning (FSL) aims to recognize new objects with extremely limited training data for each category. Previous efforts are made by either leveraging meta-learning paradigm or novel principles in data augmentation to alleviate this extremely data-scarce problem. In contrast, this paper presents a simple statistical approach, dubbed Instance Credibility Inference (ICI) to exploit the distribution support of unlabeled instances for few-shot learning. Specifically, we first train a linear classifier with the labeled few-shot examples and use it to infer the pseudo-labels for the unlabeled data. To measure the credibility of each pseudo-labeled instance, we then propose to solve another linear regression hypothesis by increasing the sparsity of the incidental parameters and rank the pseudo-labeled instances with their sparsity degree. We select the most trustworthy pseudo-labeled instances alongside the labeled examples to re-train the linear classifier. This process is iterated until all the unlabeled samples are included in the expanded training set, i.e. the pseudo-label is converged for unlabeled data pool. Extensive experiments under two few-shot settings show that our simple approach can establish new state-of-the-arts on four widely used few-shot learning benchmark datasets including miniImageNet, tieredImageNet, CIFAR-FS, and CUB. Our code is available at: https://github.com/Yikai-Wang/ICI-FSL

Ruowen Zhao, Junliang Ye, Zhengyi Wang et al.

Triangle meshes play a crucial role in 3D applications for efficient manipulation and rendering. While auto-regressive methods generate structured meshes by predicting discrete vertex tokens, they are often constrained by limited face counts and mesh incompleteness. To address these challenges, we propose DeepMesh, a framework that optimizes mesh generation through two key innovations: (1) an efficient pre-training strategy incorporating a novel tokenization algorithm, along with improvements in data curation and processing, and (2) the introduction of Reinforcement Learning (RL) into 3D mesh generation to achieve human preference alignment via Direct Preference Optimization (DPO). We design a scoring standard that combines human evaluation with 3D metrics to collect preference pairs for DPO, ensuring both visual appeal and geometric accuracy. Conditioned on point clouds and images, DeepMesh generates meshes with intricate details and precise topology, outperforming state-of-the-art methods in both precision and quality. Project page: https://zhaorw02.github.io/DeepMesh/

Chengming Xu, Chen Liu, Yikai Wang et al.

Visual In-Context Learning (VICL) is a prevailing way to transfer visual foundation models to new tasks by leveraging contextual information contained in in-context examples to enhance learning and prediction of query sample. The fundamental problem in VICL is how to select the best prompt to activate its power as much as possible, which is equivalent to the ranking problem to test the in-context behavior of each candidate in the alternative set and select the best one. To utilize more appropriate ranking metric and leverage more comprehensive information among the alternative set, we propose a novel in-context example selection framework to approximately identify the global optimal prompt, i.e. choosing the best performing in-context examples from all alternatives for each query sample. Our method, dubbed Partial2Global, adopts a transformer-based list-wise ranker to provide a more comprehensive comparison within several alternatives, and a consistency-aware ranking aggregator to generate globally consistent ranking. The effectiveness of Partial2Global is validated through experiments on foreground segmentation, single object detection and image colorization, demonstrating that Partial2Global selects consistently better in-context examples compared with other methods, and thus establish the new state-of-the-arts.

Zhenyang Liu, Yikai Wang, Sixiao Zheng et al.

Open-vocabulary 3D visual grounding and reasoning aim to localize objects in a scene based on implicit language descriptions, even when they are occluded. This ability is crucial for tasks such as vision-language navigation and autonomous robotics. However, current methods struggle because they rely heavily on fine-tuning with 3D annotations and mask proposals, which limits their ability to handle diverse semantics and common knowledge required for effective reasoning. In this work, we propose ReasonGrounder, an LVLM-guided framework that uses hierarchical 3D feature Gaussian fields for adaptive grouping based on physical scale, enabling open-vocabulary 3D grounding and reasoning. ReasonGrounder interprets implicit instructions using large vision-language models (LVLM) and localizes occluded objects through 3D Gaussian splatting. By incorporating 2D segmentation masks from the SAM and multi-view CLIP embeddings, ReasonGrounder selects Gaussian groups based on object scale, enabling accurate localization through both explicit and implicit language understanding, even in novel, occluded views. We also contribute ReasoningGD, a new dataset containing over 10K scenes and 2 million annotations for evaluating open-vocabulary 3D grounding and amodal perception under occlusion. Experiments show that ReasonGrounder significantly improves 3D grounding accuracy in real-world scenarios.

Yikai Wang, Chenjie Cao, Ke Fan et al.

Current image manipulation primarily centers on static manipulation, such as replacing specific regions within an image or altering its overall style. In this paper, we introduce an innovative dynamic manipulation task, subject repositioning. This task involves relocating a user-specified subject to a desired position while preserving the image's fidelity. Our research reveals that the fundamental sub-tasks of subject repositioning, which include filling the void left by the repositioned subject, reconstructing obscured portions of the subject and blending the subject to be consistent with surrounding areas, can be effectively reformulated as a unified, prompt-guided inpainting task. Consequently, we can employ a single diffusion generative model to address these sub-tasks using various task prompts learned through our proposed task inversion technique. Additionally, we integrate pre-processing and post-processing techniques to further enhance the quality of subject repositioning. These elements together form our SEgment-gEnerate-and-bLEnd (SEELE) framework. To assess SEELE's effectiveness in subject repositioning, we assemble a real-world subject repositioning dataset called ReS. Results of SEELE on ReS demonstrate its efficacy. Code and ReS dataset are available at https://yikai-wang.github.io/seele/.

Zhengyi Wang, Cheng Lu, Yikai Wang et al.

Score distillation sampling (SDS) has shown great promise in text-to-3D generation by distilling pretrained large-scale text-to-image diffusion models, but suffers from over-saturation, over-smoothing, and low-diversity problems. In this work, we propose to model the 3D parameter as a random variable instead of a constant as in SDS and present variational score distillation (VSD), a principled particle-based variational framework to explain and address the aforementioned issues in text-to-3D generation. We show that SDS is a special case of VSD and leads to poor samples with both small and large CFG weights. In comparison, VSD works well with various CFG weights as ancestral sampling from diffusion models and simultaneously improves the diversity and sample quality with a common CFG weight (i.e., $7.5$). We further present various improvements in the design space for text-to-3D such as distillation time schedule and density initialization, which are orthogonal to the distillation algorithm yet not well explored. Our overall approach, dubbed ProlificDreamer, can generate high rendering resolution (i.e., $512\times512$) and high-fidelity NeRF with rich structure and complex effects (e.g., smoke and drops). Further, initialized from NeRF, meshes fine-tuned by VSD are meticulously detailed and photo-realistic. Project page and codes: https://ml.cs.tsinghua.edu.cn/prolificdreamer/

Zihao Wang, Le Ma, Chen Zhang et al.

Music as an emotional intervention medium has important applications in scenarios such as music therapy, games, and movies. However, music needs real-time arrangement according to changing emotions, bringing challenges to balance emotion real-time fit and soft emotion transition due to the fine-grained and mutable nature of the target emotion. Existing studies mainly focus on achieving emotion real-time fit, while the issue of smooth transition remains understudied, affecting the overall emotional coherence of the music. In this paper, we propose REMAST to address this trade-off. Specifically, we recognize the last timestep's music emotion and fuse it with the current timestep's input emotion. The fused emotion then guides REMAST to generate the music based on the input melody. To adjust music similarity and emotion real-time fit flexibly, we downsample the original melody and feed it into the generation model. Furthermore, we design four music theory features by domain knowledge to enhance emotion information and employ semi-supervised learning to mitigate the subjective bias introduced by manual dataset annotation. According to the evaluation results, REMAST surpasses the state-of-the-art methods in objective and subjective metrics. These results demonstrate that REMAST achieves real-time fit and smooth transition simultaneously, enhancing the coherence of the generated music.

Yikai Wang, Wenbing Huang, Bin Fang et al.

Tactile sensing plays an important role in robotic perception and manipulation tasks. To overcome the real-world limitations of data collection, simulating tactile response in a virtual environment comes as a desirable direction of robotic research. In this paper, we propose Elastic Interaction of Particles (EIP) for tactile simulation. Most existing works model the tactile sensor as a rigid multi-body, which is incapable of reflecting the elastic property of the tactile sensor as well as characterizing the fine-grained physical interaction between the two objects. By contrast, EIP models the tactile sensor as a group of coordinated particles, and the elastic property is applied to regulate the deformation of particles during contact. With the tactile simulation by EIP, we further propose a tactile-visual perception network that enables information fusion between tactile data and visual images. The perception network is based on a global-to-local fusion mechanism where multi-scale tactile features are aggregated to the corresponding local region of the visual modality with the guidance of tactile positions and directions. The fusion method exhibits superiority regarding the 3D geometric reconstruction task.

Yikai Wang, Weijian Li

In recent years, natural language processing (NLP) has become one of the most important areas with various applications in human's life. As the most fundamental task, the field of word embedding still requires more attention and research. Currently, existing works about word embedding are focusing on proposing novel embedding algorithms and dimension reduction techniques on well-trained word embeddings. In this paper, we propose to use a novel joint signal separation method - JIVE to jointly decompose various trained word embeddings into joint and individual components. Through this decomposition framework, we can easily investigate the similarity and difference among different word embeddings. We conducted extensive empirical study on word2vec, FastText and GLoVE trained on different corpus and with different dimensions. We compared the performance of different decomposed components based on sentiment analysis on Twitter and Stanford sentiment treebank. We found that by mapping different word embeddings into the joint component, sentiment performance can be greatly improved for the original word embeddings with lower performance. Moreover, we found that by concatenating different components together, the same model can achieve better performance. These findings provide great insights into the word embeddings and our work offer a new of generating word embeddings by fusing.

Yikai Wang, Li Zhang, Yuan Yao et al.

Deep learning based models have excelled in many computer vision tasks and appear to surpass humans' performance. However, these models require an avalanche of expensive human labeled training data and many iterations to train their large number of parameters. This severely limits their scalability to the real-world long-tail distributed categories, some of which are with a large number of instances, but with only a few manually annotated. Learning from such extremely limited labeled examples is known as Few-shot learning (FSL). Different to prior arts that leverage meta-learning or data augmentation strategies to alleviate this extremely data-scarce problem, this paper presents a statistical approach, dubbed Instance Credibility Inference (ICI) to exploit the support of unlabeled instances for few-shot visual recognition. Typically, we repurpose the self-taught learning paradigm to predict pseudo-labels of unlabeled instances with an initial classifier trained from the few shot and then select the most confident ones to augment the training set to re-train the classifier. This is achieved by constructing a (Generalized) Linear Model (LM/GLM) with incidental parameters to model the mapping from (un-)labeled features to their (pseudo-)labels, in which the sparsity of the incidental parameters indicates the credibility of the corresponding pseudo-labeled instance. We rank the credibility of pseudo-labeled instances along the regularization path of their corresponding incidental parameters, and the most trustworthy pseudo-labeled examples are preserved as the augmented labeled instances. Theoretically, under mild conditions of restricted eigenvalue, irrepresentability, and large error, our approach is guaranteed to collect all the correctly-predicted instances from the noisy pseudo-labeled set.