Yi Zhang

Yi Zhang, Pengliang Ji, Angtian Wang et al.

Regression-based methods for 3D human pose estimation directly predict the 3D pose parameters from a 2D image using deep networks. While achieving state-of-the-art performance on standard benchmarks, their performance degrades under occlusion. In contrast, optimization-based methods fit a parametric body model to 2D features in an iterative manner. The localized reconstruction loss can potentially make them robust to occlusion, but they suffer from the 2D-3D ambiguity. Motivated by the recent success of generative models in rigid object pose estimation, we propose 3D-aware Neural Body Fitting (3DNBF) - an approximate analysis-by-synthesis approach to 3D human pose estimation with SOTA performance and occlusion robustness. In particular, we propose a generative model of deep features based on a volumetric human representation with Gaussian ellipsoidal kernels emitting 3D pose-dependent feature vectors. The neural features are trained with contrastive learning to become 3D-aware and hence to overcome the 2D-3D ambiguity. Experiments show that 3DNBF outperforms other approaches on both occluded and standard benchmarks. Code is available at https://github.com/edz-o/3DNBF

Yu Wang, Yuying Zhao, Yi Zhang et al.

Graph Neural Networks (GNNs) have been successfully adopted in recommender systems by virtue of the message-passing that implicitly captures collaborative effect. Nevertheless, most of the existing message-passing mechanisms for recommendation are directly inherited from GNNs without scrutinizing whether the captured collaborative effect would benefit the prediction of user preferences. In this paper, we first analyze how message-passing captures the collaborative effect and propose a recommendation-oriented topological metric, Common Interacted Ratio (CIR), which measures the level of interaction between a specific neighbor of a node with the rest of its neighbors. After demonstrating the benefits of leveraging collaborations from neighbors with higher CIR, we propose a recommendation-tailored GNN, Collaboration-Aware Graph Convolutional Network (CAGCN), that goes beyond 1-Weisfeiler-Lehman(1-WL) test in distinguishing non-bipartite-subgraph-isomorphic graphs. Experiments on six benchmark datasets show that the best CAGCN variant outperforms the most representative GNN-based recommendation model, LightGCN, by nearly 10% in Recall@20 and also achieves around 80% speedup. Our code is publicly available at https://github.com/YuWVandy/CAGCN.

Yi Zhang, Ce Zhang, Yushun Tang et al. · cmu

Large-scale pre-trained Vision-Language Models (VLMs), such as CLIP, establish the correlation between texts and images, achieving remarkable success on various downstream tasks with fine-tuning. In existing fine-tuning methods, the class-specific text description is matched against the whole image. We recognize that this whole image matching is not effective since images from the same class often contain a set of different semantic objects, and an object further consists of a set of semantic parts or concepts. Individual semantic parts or concepts may appear in image samples from different classes. To address this issue, in this paper, we develop a new method called cross-model concept learning and inference (CCLI). Using the powerful text-image correlation capability of CLIP, our method automatically learns a large set of distinctive visual concepts from images using a set of semantic text concepts. Based on these visual concepts, we construct a discriminative representation of images and learn a concept inference network to perform downstream image classification tasks, such as few-shot learning and domain generalization. Extensive experimental results demonstrate that our CCLI method is able to improve the performance upon the current state-of-the-art methods by large margins, for example, by up to 8.0% improvement on few-shot learning and by up to 1.3% for domain generalization.

Ziyuan Yang, Yingyu Chen, Huijie Huangfu et al.

U-shaped networks are widely used in various medical image tasks, such as segmentation, restoration and reconstruction, but most of them usually rely on centralized learning and thus ignore privacy issues. To address the privacy concerns, federated learning (FL) and split learning (SL) have attracted increasing attention. However, it is hard for both FL and SL to balance the local computational cost, model privacy and parallel training simultaneously. To achieve this goal, in this paper, we propose Robust Split Federated Learning (RoS-FL) for U-shaped medical image networks, which is a novel hybrid learning paradigm of FL and SL. Previous works cannot preserve the data privacy, including the input, model parameters, label and output simultaneously. To effectively deal with all of them, we design a novel splitting method for U-shaped medical image networks, which splits the network into three parts hosted by different parties. Besides, the distributed learning methods usually suffer from a drift between local and global models caused by data heterogeneity. Based on this consideration, we propose a dynamic weight correction strategy (\textbf{DWCS}) to stabilize the training process and avoid model drift. Specifically, a weight correction loss is designed to quantify the drift between the models from two adjacent communication rounds. By minimizing this loss, a correction model is obtained. Then we treat the weighted sum of correction model and final round models as the result. The effectiveness of the proposed RoS-FL is supported by extensive experimental results on different tasks. Related codes will be released at https://github.com/Zi-YuanYang/RoS-FL.

Kwangjun Ahn, Sébastien Bubeck, Sinho Chewi et al.

Existing analyses of neural network training often operate under the unrealistic assumption of an extremely small learning rate. This lies in stark contrast to practical wisdom and empirical studies, such as the work of J. Cohen et al. (ICLR 2021), which exhibit startling new phenomena (the "edge of stability" or "unstable convergence") and potential benefits for generalization in the large learning rate regime. Despite a flurry of recent works on this topic, however, the latter effect is still poorly understood. In this paper, we take a step towards understanding genuinely non-convex training dynamics with large learning rates by performing a detailed analysis of gradient descent for simplified models of two-layer neural networks. For these models, we provably establish the edge of stability phenomenon and discover a sharp phase transition for the step size below which the neural network fails to learn "threshold-like" neurons (i.e., neurons with a non-zero first-layer bias). This elucidates one possible mechanism by which the edge of stability can in fact lead to better generalization, as threshold neurons are basic building blocks with useful inductive bias for many tasks.

Xueting Hu, Ce Zhang, Yi Zhang et al. · cmu

Pre-trained Vision-Language Models (VLMs), such as CLIP, have shown enhanced performance across a range of tasks that involve the integration of visual and linguistic modalities. When CLIP is used for depth estimation tasks, the patches, divided from the input images, can be combined with a series of semantic descriptions of the depth information to obtain similarity results. The coarse estimation of depth is then achieved by weighting and summing the depth values, called depth bins, corresponding to the predefined semantic descriptions. The zero-shot approach circumvents the computational and time-intensive nature of traditional fully-supervised depth estimation methods. However, this method, utilizing fixed depth bins, may not effectively generalize as images from different scenes may exhibit distinct depth distributions. To address this challenge, we propose a few-shot-based method which learns to adapt the VLMs for monocular depth estimation to balance training costs and generalization capabilities. Specifically, it assigns different depth bins for different scenes, which can be selected by the model during inference. Additionally, we incorporate learnable prompts to preprocess the input text to convert the easily human-understood text into easily model-understood vectors and further enhance the performance. With only one image per scene for training, our extensive experiment results on the NYU V2 and KITTI dataset demonstrate that our method outperforms the previous state-of-the-art method by up to 10.6\% in terms of MARE.

Ruoqi Shen, Sébastien Bubeck, Ronen Eldan et al.

Transformers, central to the successes in modern Natural Language Processing, often falter on arithmetic tasks despite their vast capabilities --which paradoxically include remarkable coding abilities. We observe that a crucial challenge is their naive reliance on positional information to solve arithmetic problems with a small number of digits, leading to poor performance on larger numbers. Herein, we delve deeper into the role of positional encoding, and propose several ways to fix the issue, either by modifying the positional encoding directly, or by modifying the representation of the arithmetic task to leverage standard positional encoding differently. We investigate the value of these modifications for three tasks: (i) classical multiplication, (ii) length extrapolation in addition, and (iii) addition in natural language context. For (i) we train a small model on a small dataset (100M parameters and 300k samples) with remarkable aptitude in (direct, no scratchpad) 15 digits multiplication and essentially perfect up to 12 digits, while usual training in this context would give a model failing at 4 digits multiplication. In the experiments on addition, we use a mere 120k samples to demonstrate: for (ii) extrapolation from 10 digits to testing on 12 digits numbers while usual training would have no extrapolation, and for (iii) almost perfect accuracy up to 5 digits while usual training would be correct only up to 3 digits (which is essentially memorization with a training set of 120k samples).

Leheng Sheng, An Zhang, Yi Zhang et al.

Recent studies empirically indicate that language models (LMs) encode rich world knowledge beyond mere semantics, attracting significant attention across various fields. However, in the recommendation domain, it remains uncertain whether LMs implicitly encode user preference information. Contrary to prevailing understanding that LMs and traditional recommenders learn two distinct representation spaces due to the huge gap in language and behavior modeling objectives, this work re-examines such understanding and explores extracting a recommendation space directly from the language representation space. Surprisingly, our findings demonstrate that item representations, when linearly mapped from advanced LM representations, yield superior recommendation performance. This outcome suggests the possible homomorphism between the advanced language representation space and an effective item representation space for recommendation, implying that collaborative signals may be implicitly encoded within LMs. Motivated by these findings, we explore the possibility of designing advanced collaborative filtering (CF) models purely based on language representations without ID-based embeddings. To be specific, we incorporate several crucial components to build a simple yet effective model, with item titles as the input. Empirical results show that such a simple model can outperform leading ID-based CF models, which sheds light on using language representations for better recommendation. Moreover, we systematically analyze this simple model and find several key features for using advanced language representations: a good initialization for item representations, zero-shot recommendation abilities, and being aware of user intention. Our findings highlight the connection between language modeling and behavior modeling, which can inspire both natural language processing and recommender system communities.

Han He, Song Feng, Daniele Bonadiman et al.

DataFlow has been emerging as a new paradigm for building task-oriented chatbots due to its expressive semantic representations of the dialogue tasks. Despite the availability of a large dataset SMCalFlow and a simplified syntax, the development and evaluation of DataFlow-based chatbots remain challenging due to the system complexity and the lack of downstream toolchains. In this demonstration, we present DFEE, an interactive DataFlow Execution and Evaluation toolkit that supports execution, visualization and benchmarking of semantic parsers given dialogue input and backend database. We demonstrate the system via a complex dialog task: event scheduling that involves temporal reasoning. It also supports diagnosing the parsing results via a friendly interface that allows developers to examine dynamic DataFlow and the corresponding execution results. To illustrate how to benchmark SoTA models, we propose a novel benchmark that covers more sophisticated event scheduling scenarios and a new metric on task success evaluation. The codes of DFEE have been released on https://github.com/amazonscience/dataflow-evaluation-toolkit.

Yi-An Lai, Elman Mansimov, Yuqing Xie et al.

When upgrading neural models to a newer version, new errors that were not encountered in the legacy version can be introduced, known as regression errors. This inconsistent behavior during model upgrade often outweighs the benefits of accuracy gain and hinders the adoption of new models. To mitigate regression errors from model upgrade, distillation and ensemble have proven to be viable solutions without significant compromise in performance. Despite the progress, these approaches attained an incremental reduction in regression which is still far from achieving backward-compatible model upgrade. In this work, we propose a novel method, Gated Fusion, that promotes backward compatibility via learning to mix predictions between old and new models. Empirical results on two distinct model upgrade scenarios show that our method reduces the number of regression errors by 62% on average, outperforming the strongest baseline by an average of 25%.

Jun Xia, Yi Zhang, Zhihao Yue et al.

Federated learning (FL) has been recognized as a privacy-preserving distributed machine learning paradigm that enables knowledge sharing among various heterogeneous artificial intelligence (AIoT) devices through centralized global model aggregation. FL suffers from model inaccuracy and slow convergence due to the model heterogeneity of the AIoT devices involved. Although various existing methods try to solve the bottleneck of the model heterogeneity problem, most of them improve the accuracy of heterogeneous models in a coarse-grained manner, which makes it still a great challenge to deploy large-scale AIoT devices. To alleviate the negative impact of this problem and take full advantage of the diversity of each heterogeneous model, we propose an efficient framework named HierarchyFL, which uses a small amount of public data for efficient and scalable knowledge across a variety of differently structured models. By using self-distillation and our proposed ensemble library, each hierarchical model can intelligently learn from each other on cloud servers. Experimental results on various well-known datasets show that HierarchyFL can not only maximize the knowledge sharing among various heterogeneous models in large-scale AIoT systems, but also greatly improve the model performance of each involved heterogeneous AIoT device.

Taha ValizadehAslani, Yiwen Shi, Jing Wang et al.

Classification on long-tailed distributed data is a challenging problem, which suffers from serious class-imbalance and hence poor performance on tail classes with only a few samples. Owing to this paucity of samples, learning on the tail classes is especially challenging for the fine-tuning when transferring a pretrained model to a downstream task. In this work, we present a simple modification of standard fine-tuning to cope with these challenges. Specifically, we propose a two-stage fine-tuning: we first fine-tune the final layer of the pretrained model with class-balanced reweighting loss, and then we perform the standard fine-tuning. Our modification has several benefits: (1) it leverages pretrained representations by only fine-tuning a small portion of the model parameters while keeping the rest untouched; (2) it allows the model to learn an initial representation of the specific task; and importantly (3) it protects the learning of tail classes from being at a disadvantage during the model updating. We conduct extensive experiments on synthetic datasets of both two-class and multi-class tasks of text classification as well as a real-world application to ADME (i.e., absorption, distribution, metabolism, and excretion) semantic labeling. The experimental results show that the proposed two-stage fine-tuning outperforms both fine-tuning with conventional loss and fine-tuning with a reweighting loss on the above datasets.

Yingyu Chen, Ziyuan Yang, Chenyu Shen et al.

Recently, uncertainty-aware methods have attracted increasing attention in semi-supervised medical image segmentation. However, current methods usually suffer from the drawback that it is difficult to balance the computational cost, estimation accuracy, and theoretical support in a unified framework. To alleviate this problem, we introduce the Dempster-Shafer Theory of Evidence (DST) into semi-supervised medical image segmentation, dubbed Evidential Inference Learning (EVIL). EVIL provides a theoretically guaranteed solution to infer accurate uncertainty quantification in a single forward pass. Trustworthy pseudo labels on unlabeled data are generated after uncertainty estimation. The recently proposed consistency regularization-based training paradigm is adopted in our framework, which enforces the consistency on the perturbed predictions to enhance the generalization with few labeled data. Experimental results show that EVIL achieves competitive performance in comparison with several state-of-the-art methods on the public dataset.

Xia Yuan, Jianping Gou, Baosheng Yu et al.

In recent years, deep dictionary learning (DDL)has attracted a great amount of attention due to its effectiveness for representation learning and visual recognition.~However, most existing methods focus on unsupervised deep dictionary learning, failing to further explore the category information.~To make full use of the category information of different samples, we propose a novel deep dictionary learning model with an intra-class constraint (DDLIC) for visual classification. Specifically, we design the intra-class compactness constraint on the intermediate representation at different levels to encourage the intra-class representations to be closer to each other, and eventually the learned representation becomes more discriminative.~Unlike the traditional DDL methods, during the classification stage, our DDLIC performs a layer-wise greedy optimization in a similar way to the training stage. Experimental results on four image datasets show that our method is superior to the state-of-the-art methods.

Leheng Sheng, An Zhang, Zijian Wu et al.

Recent studies empirically reveal that large reasoning models (LRMs) can automatically allocate more reasoning strengths (i.e., the number of reasoning tokens) for harder problems, exhibiting difficulty-awareness for better task performance. While this automatic reasoning strength allocation phenomenon has been widely observed, its underlying mechanism remains largely unexplored. To this end, we provide explanations for this phenomenon from the perspective of model activations. We find evidence that LRMs pre-plan the reasoning strengths in their activations even before generation, with this reasoning strength causally controlled by the magnitude of a pre-allocated directional vector. Specifically, we show that the number of reasoning tokens is predictable solely based on the question activations using linear probes, indicating that LRMs estimate the required reasoning strength in advance. We then uncover that LRMs encode this reasoning strength through a pre-allocated directional vector embedded in the activations of the model, where the vector's magnitude modulates the reasoning strength. Subtracting this vector can lead to reduced reasoning token number and performance, while adding this vector can lead to increased reasoning token number and even improved performance. We further reveal that this direction vector consistently yields positive reasoning length prediction, and it modifies the logits of end-of-reasoning token </think> to affect the reasoning length. Finally, we demonstrate two potential applications of our findings: overthinking behavior detection and enabling efficient reasoning on simple problems. Our work provides new insights into the internal mechanisms of reasoning in LRMs and offers practical tools for controlling their reasoning behaviors. Our code is available at https://github.com/AlphaLab-USTC/LRM-plans-CoT.

Quansong He, Xiaojun Yao, Jun Wu et al.

In recent years, advanced U-like networks have demonstrated remarkable performance in medical image segmentation tasks. However, their drawbacks, including excessive parameters, high computational complexity, and slow inference speed, pose challenges for practical implementation in scenarios with limited computational resources. Existing lightweight U-like networks have alleviated some of these problems, but they often have pre-designed structures and consist of inseparable modules, limiting their application scenarios. In this paper, we propose three plug-and-play decoders by employing different discretization methods of the neural memory Ordinary Differential Equations (nmODEs). These decoders integrate features at various levels of abstraction by processing information from skip connections and performing numerical operations on upward path. Through experiments on the PH2, ISIC2017, and ISIC2018 datasets, we embed these decoders into different U-like networks, demonstrating their effectiveness in significantly reducing the number of parameters and FLOPs while maintaining performance. In summary, the proposed discretized nmODEs decoders are capable of reducing the number of parameters by about 20% ~ 50% and FLOPs by up to 74%, while possessing the potential to adapt to all U-like networks. Our code is available at https://github.com/nayutayuki/Lightweight-nmODE-Decoders-For-U-like-networks.

Yi Zhang, Kosuke Imai

Although there is now a large literature on policy evaluation and learning, much of the prior work assumes that the treatment assignment of one unit does not affect the outcome of another unit. Unfortunately, ignoring interference can lead to biased policy evaluation and ineffective learned policies. For example, treating influential individuals who have many friends can generate positive spillover effects, thereby improving the overall performance of an individualized treatment rule (ITR). We consider the problem of evaluating and learning an optimal ITR under clustered network interference (also known as partial interference), where clusters of units are sampled from a population and units may influence one another within each cluster. Unlike previous methods that impose strong restrictions on spillover effects, such as anonymous interference, the proposed methodology only assumes a semiparametric structural model, where each unit's outcome is an additive function of individual treatments within the cluster. Under this model, we propose an estimator that can be used to evaluate the empirical performance of an ITR. We show that this estimator is substantially more efficient than the standard inverse probability weighting estimator, which does not impose any assumption about spillover effects. We derive the finite-sample regret bound for a learned ITR, showing that the use of our efficient evaluation estimator leads to the improved performance of learned policies. We consider both experimental and observational studies, and for the latter, we develop a doubly robust estimator that is semiparametrically efficient and yields an optimal regret bound. Finally, we conduct simulation and empirical studies to illustrate the advantages of the proposed methodology.

Yi Zhang, Lu Zhang, Kang Wang et al.

Salient human detection (SHD) in dynamic 360° immersive videos is of great importance for various applications such as robotics, inter-human and human-object interaction in augmented reality. However, 360° video SHD has been seldom discussed in the computer vision community due to a lack of datasets with large-scale omnidirectional videos and rich annotations. To this end, we propose SHD360, the first 360° video SHD dataset which contains various real-life daily scenes. Since so far there is no method proposed for 360° image/video SHD, we systematically benchmark 11 representative state-of-the-art salient object detection (SOD) approaches on our SHD360, and explore key issues derived from extensive experimenting results. We hope our proposed dataset and benchmark could serve as a good starting point for advancing human-centric researches towards 360° panoramic data. The dataset is available at https://github.com/PanoAsh/SHD360.

Bowei Zhang, Yi Zhang

Vision Transformer (ViT) has demonstrated significant potential in various vision tasks due to its strong ability in modelling long-range dependencies. However, such success is largely fueled by training on massive samples. In real applications, the large-scale datasets are not always available, and ViT performs worse than Convolutional Neural Networks (CNNs) if it is only trained on small scale dataset (called tiny dataset), since it requires large amount of training data to ensure its representational capacity. In this paper, a small-size ViT architecture with multi-scale self-attention mechanism and convolution blocks is presented (dubbed MSCViT) to model different scales of attention at each layer. Firstly, we introduced wavelet convolution, which selectively combines the high-frequency components obtained by frequency division with our convolution channel to extract local features. Then, a lightweight multi-head attention module is developed to reduce the number of tokens and computational costs. Finally, the positional encoding (PE) in the backbone is replaced by a local feature extraction module. Compared with the original ViT, it is parameter-efficient and is particularly suitable for tiny datasets. Extensive experiments have been conducted on tiny datasets, in which our model achieves an accuracy of 84.68% on CIFAR-100 with 14.0M parameters and 2.5 GFLOPs, without pre-training on large datasets.

Han Zhang, Zhuo Zhang, Yi Zhang et al.

Recent advancements in AI alignment techniques have significantly improved the alignment of large language models (LLMs) with static human preferences. However, the dynamic nature of human preferences can render some prior training data outdated or even erroneous, ultimately causing LLMs to deviate from contemporary human preferences and societal norms. Existing methodologies, whether they involve the curation of new data for continual alignment or the manual correction of outdated data for re-alignment, demand costly human resources. To address this challenge, we propose a novel approach, Large Language Model Behavior Correction with Influence Function Recall and Post-Training (LANCET), which requires no human involvement. LANCET consists of two phases: (1) using influence functions to identify the training data that significantly impact undesirable model outputs, and (2) applying an Influence function-driven Bregman Optimization (IBO) technique to adjust the model's behavior based on these influence distributions. Our experiments demonstrate that LANCET effectively and efficiently correct inappropriate behaviors of LLMs. Furthermore, LANCET can outperform methods that rely on collecting human preferences, and it enhances the interpretability of learning human preferences within LLMs.

Yi Zhang, Yi Wang, Yawen Cui et al.

This paper proposes 3DGeoDet, a novel geometry-aware 3D object detection approach that effectively handles single- and multi-view RGB images in indoor and outdoor environments, showcasing its general-purpose applicability. The key challenge for image-based 3D object detection tasks is the lack of 3D geometric cues, which leads to ambiguity in establishing correspondences between images and 3D representations. To tackle this problem, 3DGeoDet generates efficient 3D geometric representations in both explicit and implicit manners based on predicted depth information. Specifically, we utilize the predicted depth to learn voxel occupancy and optimize the voxelized 3D feature volume explicitly through the proposed voxel occupancy attention. To further enhance 3D awareness, the feature volume is integrated with an implicit 3D representation, the truncated signed distance function (TSDF). Without requiring supervision from 3D signals, we significantly improve the model's comprehension of 3D geometry by leveraging intermediate 3D representations and achieve end-to-end training. Our approach surpasses the performance of state-of-the-art image-based methods on both single- and multi-view benchmark datasets across diverse environments, achieving a 9.3 mAP@0.5 improvement on the SUN RGB-D dataset, a 3.3 mAP@0.5 improvement on the ScanNetV2 dataset, and a 0.19 AP3D@0.7 improvement on the KITTI dataset. The project page is available at: https://cindy0725.github.io/3DGeoDet/.

Dechen Zhang, Zhenmei Shi, Yi Zhang et al.

Kernel ridge regression (KRR) is a foundational tool in machine learning, with recent work emphasizing its connections to neural networks. However, existing theory primarily addresses the i.i.d. setting, while real-world data often exhibits structured dependencies - particularly in applications like denoising score learning where multiple noisy observations derive from shared underlying signals. We present the first systematic study of KRR generalization for non-i.i.d. data with signal-noise causal structure, where observations represent different noisy views of common signals. By developing a novel blockwise decomposition method that enables precise concentration analysis for dependent data, we derive excess risk bounds for KRR that explicitly depend on: (1) the kernel spectrum, (2) causal structure parameters, and (3) sampling mechanisms (including relative sample sizes for signals and noises). We further apply our results to denoising score learning, establishing generalization guarantees and providing principled guidance for sampling noisy data points. This work advances KRR theory while providing practical tools for analyzing dependent data in modern machine learning applications.

Yi Zhang, Xiaoyang Huang, Yishun Dou et al.

We present InstantSticker, a disentangled reconstruction pipeline based on Image-Based Lighting (IBL), which focuses on highly realistic decal blending, simulates stickers attached to the reconstructed surface, and allows for instant editing and real-time rendering. To achieve stereoscopic impression of the decal, we introduce shadow factor into IBL, which can be adaptively optimized during training. This allows the shadow brightness of surfaces to be accurately decomposed rather than baked into the diffuse color, ensuring that the edited texture exhibits authentic shading. To address the issues of warping and blurriness in previous methods, we apply As-Rigid-As-Possible (ARAP) parameterization to pre-unfold a specified area of the mesh and use the local UV mapping combined with a neural texture map to enhance the ability to express high-frequency details in that area. For instant editing, we utilize the Disney BRDF model, explicitly defining material colors with 3-channel diffuse albedo. This enables instant replacement of albedo RGB values during the editing process, avoiding the prolonged optimization required in previous approaches. In our experiment, we introduce the Ratio Variance Warping (RVW) metric to evaluate the local geometric warping of the decal area. Extensive experimental results demonstrate that our method surpasses previous decal blending methods in terms of editing quality, editing speed and rendering speed, achieving the state-of-the-art.

Wang Lituan, Zhang Lei, Wang Yan et al.

Weakly-supervised medical image segmentation is gaining traction as it requires only rough annotations rather than accurate pixel-to-pixel labels, thereby reducing the workload for specialists. Although some progress has been made, there is still a considerable performance gap between the label-efficient methods and fully-supervised one, which can be attributed to the uncertainty nature of these weak labels. To address this issue, we propose a novel weak annotation method coupled with its learning framework EAUWSeg to eliminate the annotation uncertainty. Specifically, we first propose the Bounded Polygon Annotation (BPAnno) by simply labeling two polygons for a lesion. Then, the tailored learning mechanism that explicitly treat bounded polygons as two separated annotations is proposed to learn invariant feature by providing adversarial supervision signal for model training. Subsequently, a confidence-auxiliary consistency learner incorporates with a classification-guided confidence generator is designed to provide reliable supervision signal for pixels in uncertain region by leveraging the feature presentation consistency across pixels within the same category as well as class-specific information encapsulated in bounded polygons annotation. Experimental results demonstrate that EAUWSeg outperforms existing weakly-supervised segmentation methods. Furthermore, compared to fully-supervised counterparts, the proposed method not only delivers superior performance but also costs much less annotation workload. This underscores the superiority and effectiveness of our approach.

Yushun Tang, Shuoshuo Chen, Zhehan Kan et al.

Fully test-time adaptation aims to adapt the network model based on sequential analysis of input samples during the inference stage to address the cross-domain performance degradation problem of deep neural networks. This work is based on the following interesting finding: in transformer-based image classification, the class token at the first transformer encoder layer can be learned to capture the domain-specific characteristics of target samples during test-time adaptation. This learned token, when combined with input image patch embeddings, is able to gradually remove the domain-specific information from the feature representations of input samples during the transformer encoding process, thereby significantly improving the test-time adaptation performance of the source model across different domains. We refer to this class token as visual conditioning token (VCT). To successfully learn the VCT, we propose a bi-level learning approach to capture the long-term variations of domain-specific characteristics while accommodating local variations of instance-specific characteristics. Experimental results on the benchmark datasets demonstrate that our proposed bi-level visual conditioning token learning method is able to achieve significantly improved test-time adaptation performance by up to 1.9%.

Yi Zhang, Xiaoyu Shi, Dasong Li et al.

Diffusion Probabilistic Models (DPMs) have recently shown remarkable performance in image generation tasks, which are capable of generating highly realistic images. When adopting DPMs for image restoration tasks, the crucial aspect lies in how to integrate the conditional information to guide the DPMs to generate accurate and natural output, which has been largely overlooked in existing works. In this paper, we present a unified conditional framework based on diffusion models for image restoration. We leverage a lightweight UNet to predict initial guidance and the diffusion model to learn the residual of the guidance. By carefully designing the basic module and integration module for the diffusion model block, we integrate the guidance and other auxiliary conditional information into every block of the diffusion model to achieve spatially-adaptive generation conditioning. To handle high-resolution images, we propose a simple yet effective inter-step patch-splitting strategy to produce arbitrary-resolution images without grid artifacts. We evaluate our conditional framework on three challenging tasks: extreme low-light denoising, deblurring, and JPEG restoration, demonstrating its significant improvements in perceptual quality and the generalization to restoration tasks.

Mujeen Sung, James Gung, Elman Mansimov et al.

Intent classification (IC) plays an important role in task-oriented dialogue systems. However, IC models often generalize poorly when training without sufficient annotated examples for each user intent. We propose a novel pre-training method for text encoders that uses contrastive learning with intent psuedo-labels to produce embeddings that are well-suited for IC tasks, reducing the need for manual annotations. By applying this pre-training strategy, we also introduce Pre-trained Intent-aware Encoder (PIE), which is designed to align encodings of utterances with their intent names. Specifically, we first train a tagger to identify key phrases within utterances that are crucial for interpreting intents. We then use these extracted phrases to create examples for pre-training a text encoder in a contrastive manner. As a result, our PIE model achieves up to 5.4% and 4.0% higher accuracy than the previous state-of-the-art text encoder for the N-way zero- and one-shot settings on four IC datasets.

Shangxi Wu, Qiuyang He, Yi Zhang et al.

Backdoor attack is a new AI security risk that has emerged in recent years. Drawing on the previous research of adversarial attack, we argue that the backdoor attack has the potential to tap into the model learning process and improve model performance. Based on Clean Accuracy Drop (CAD) in backdoor attack, we found that CAD came out of the effect of pseudo-deletion of data. We provided a preliminary explanation of this phenomenon from the perspective of model classification boundaries and observed that this pseudo-deletion had advantages over direct deletion in the data debiasing problem. Based on the above findings, we proposed Debiasing Backdoor Attack (DBA). It achieves SOTA in the debiasing task and has a broader application scenario than undersampling.

Deng Cai, Elman Mansimov, Yi-An Lai et al.

Recent advance in deep learning has led to the rapid adoption of machine learning-based NLP models in a wide range of applications. Despite the continuous gain in accuracy, backward compatibility is also an important aspect for industrial applications, yet it received little research attention. Backward compatibility requires that the new model does not regress on cases that were correctly handled by its predecessor. This work studies model update regression in structured prediction tasks. We choose syntactic dependency parsing and conversational semantic parsing as representative examples of structured prediction tasks in NLP. First, we measure and analyze model update regression in different model update settings. Next, we explore and benchmark existing techniques for reducing model update regression including model ensemble and knowledge distillation. We further propose a simple and effective method, Backward-Congruent Re-ranking (BCR), by taking into account the characteristics of structured prediction. Experiments show that BCR can better mitigate model update regression than model ensemble and knowledge distillation approaches.

Yi Zhang, Arushi Gupta, Nikunj Saunshi et al.

Research on generalization bounds for deep networks seeks to give ways to predict test error using just the training dataset and the network parameters. While generalization bounds can give many insights about architecture design, training algorithms, etc., what they do not currently do is yield good predictions for actual test error. A recently introduced Predicting Generalization in Deep Learning competition~\citep{jiang2020neurips} aims to encourage discovery of methods to better predict test error. The current paper investigates a simple idea: can test error be predicted using {\em synthetic data,} produced using a Generative Adversarial Network (GAN) that was trained on the same training dataset? Upon investigating several GAN models and architectures, we find that this turns out to be the case. In fact, using GANs pre-trained on standard datasets, the test error can be predicted without requiring any additional hyper-parameter tuning. This result is surprising because GANs have well-known limitations (e.g. mode collapse) and are known to not learn the data distribution accurately. Yet the generated samples are good enough to substitute for test data. Several additional experiments are presented to explore reasons why GANs do well at this task. In addition to a new approach for predicting generalization, the counter-intuitive phenomena presented in our work may also call for a better understanding of GANs' strengths and limitations.

Xinyue Wei, Weichao Qiu, Yi Zhang et al.

In this paper, we present a Nuisance-label Supervision (NLS) module, which can make models more robust to nuisance factor variations. Nuisance factors are those irrelevant to a task, and an ideal model should be invariant to them. For example, an activity recognition model should perform consistently regardless of the change of clothes and background. But our experiments show existing models are far from this capability. So we explicitly supervise a model with nuisance labels to make extracted features less dependent on nuisance factors. Although the values of nuisance factors are rarely annotated, we demonstrate that besides existing annotations, nuisance labels can be acquired freely from data augmentation and synthetic data. Experiments show consistent improvement in robustness towards image corruption and appearance change in action recognition.

Sawsan Alqahtani, Garima Lalwani, Yi Zhang et al.

Recent studies have proposed different methods to improve multilingual word representations in contextualized settings including techniques that align between source and target embedding spaces. For contextualized embeddings, alignment becomes more complex as we additionally take context into consideration. In this work, we propose using Optimal Transport (OT) as an alignment objective during fine-tuning to further improve multilingual contextualized representations for downstream cross-lingual transfer. This approach does not require word-alignment pairs prior to fine-tuning that may lead to sub-optimal matching and instead learns the word alignments within context in an unsupervised manner. It also allows different types of mappings due to soft matching between source and target sentences. We benchmark our proposed method on two tasks (XNLI and XQuAD) and achieve improvements over baselines as well as competitive results compared to similar recent works.

Elman Mansimov, Yi Zhang

We introduce a Recursive INsertion-based Encoder (RINE), a novel approach for semantic parsing in task-oriented dialog. Our model consists of an encoder network that incrementally builds the semantic parse tree by predicting the non-terminal label and its positions in the linearized tree. At the generation time, the model constructs the semantic parse tree by recursively inserting the predicted non-terminal labels at the predicted positions until termination. RINE achieves state-of-the-art exact match accuracy on low- and high-resource versions of the conversational semantic parsing benchmark TOP (Gupta et al., 2018; Chen et al., 2020), outperforming strong sequence-to-sequence models and transition-based parsers. We also show that our model design is applicable to nested named entity recognition task, where it performs on par with state-of-the-art approach designed for that task. Finally, we demonstrate that our approach is 2-3.5 times faster than the sequence-to-sequence model at inference time.

Haoyi Niu, Jianming Hu, Zheyu Cui et al.

How to explore corner cases as efficiently and thoroughly as possible has long been one of the top concerns in the context of deep reinforcement learning (DeepRL) autonomous driving. Training with simulated data is less costly and dangerous than utilizing real-world data, but the inconsistency of parameter distribution and the incorrect system modeling in simulators always lead to an inevitable Sim2real gap, which probably accounts for the underperformance in novel, anomalous and risky cases that simulators can hardly generate. Domain Randomization(DR) is a methodology that can bridge this gap with little or no real-world data. Consequently, in this research, an adversarial model is put forward to robustify DeepRL-based autonomous vehicles trained in simulation to gradually surfacing harder events, so that the models could readily transfer to the real world.

Chengwei Chen, Yuan Xie, Shaohui Lin et al.

Novelty detection is the process of determining whether a query example differs from the learned training distribution. Previous methods attempt to learn the representation of the normal samples via generative adversarial networks (GANs). However, they will suffer from instability training, mode dropping, and low discriminative ability. Recently, various pretext tasks (e.g. rotation prediction and clustering) have been proposed for self-supervised learning in novelty detection. However, the learned latent features are still low discriminative. We overcome such problems by introducing a novel decoder-encoder framework. Firstly, a generative network (a.k.a. decoder) learns the representation by mapping the initialized latent vector to an image. In particular, this vector is initialized by considering the entire distribution of training data to avoid the problem of mode-dropping. Secondly, a contrastive network (a.k.a. encoder) aims to ``learn to compare'' through mutual information estimation, which directly helps the generative network to obtain a more discriminative representation by using a negative data augmentation strategy. Extensive experiments show that our model has significant superiority over cutting-edge novelty detectors and achieves new state-of-the-art results on some novelty detection benchmarks, e.g. CIFAR10 and DCASE. Moreover, our model is more stable for training in a non-adversarial manner, compared to other adversarial based novelty detection methods.

Sanjeev Arora, Yi Zhang

Traditional statistics forbids use of test data (a.k.a. holdout data) during training. Dwork et al. 2015 pointed out that current practices in machine learning, whereby researchers build upon each other's models, copying hyperparameters and even computer code -- amounts to implicitly training on the test set. Thus error rate on test data may not reflect the true population error. This observation initiated {\em adaptive data analysis}, which provides evaluation mechanisms with guaranteed upper bounds on this difference. With statistical query (i.e. test accuracy) feedbacks, the best upper bound is fairly pessimistic: the deviation can hit a practically vacuous value if the number of models tested is quadratic in the size of the test set. In this work, we present a simple new estimate, {\em Rip van Winkle's Razor}. It relies upon a new notion of \textquotedblleft information content\textquotedblright\ of a model: the amount of information that would have to be provided to an expert referee who is intimately familiar with the field and relevant science/math, and who has been just been woken up after falling asleep at the moment of the creation of the test data (like \textquotedblleft Rip van Winkle\textquotedblright\ of the famous fairy tale). This notion of information content is used to provide an estimate of the above deviation which is shown to be non-vacuous in many modern settings.

Jason Krone, Yi Zhang, Mona Diab

Intent classification (IC) and slot filling (SF) are core components in most goal-oriented dialogue systems. Current IC/SF models perform poorly when the number of training examples per class is small. We propose a new few-shot learning task, few-shot IC/SF, to study and improve the performance of IC and SF models on classes not seen at training time in ultra low resource scenarios. We establish a few-shot IC/SF benchmark by defining few-shot splits for three public IC/SF datasets, ATIS, TOP, and Snips. We show that two popular few-shot learning algorithms, model agnostic meta learning (MAML) and prototypical networks, outperform a fine-tuning baseline on this benchmark. Prototypical networks achieves significant gains in IC performance on the ATIS and TOP datasets, while both prototypical networks and MAML outperform the baseline with respect to SF on all three datasets. In addition, we demonstrate that joint training as well as the use of pre-trained language models, ELMo and BERT in our case, are complementary to these few-shot learning methods and yield further gains.

Yi Zhang, Orestis Plevrakis, Simon S. Du et al.

Adversarial training is a popular method to give neural nets robustness against adversarial perturbations. In practice adversarial training leads to low robust training loss. However, a rigorous explanation for why this happens under natural conditions is still missing. Recently a convergence theory for standard (non-adversarial) supervised training was developed by various groups for {\em very overparametrized} nets. It is unclear how to extend these results to adversarial training because of the min-max objective. Recently, a first step towards this direction was made by Gao et al. using tools from online learning, but they require the width of the net to be \emph{exponential} in input dimension $d$, and with an unnatural activation function. Our work proves convergence to low robust training loss for \emph{polynomial} width instead of exponential, under natural assumptions and with the ReLU activation. Key element of our proof is showing that ReLU networks near initialization can approximate the step function, which may be of independent interest.

Sanjeev Arora, Andrej Risteski, Yi Zhang

Encoder-decoder GANs architectures (e.g., BiGAN and ALI) seek to add an inference mechanism to the GANs setup, consisting of a small encoder deep net that maps data-points to their succinct encodings. The intuition is that being forced to train an encoder alongside the usual generator forces the system to learn meaningful mappings from the code to the data-point and vice-versa, which should improve the learning of the target distribution and ameliorate mode-collapse. It should also yield meaningful codes that are useful as features for downstream tasks. The current paper shows rigorously that even on real-life distributions of images, the encode-decoder GAN training objectives (a) cannot prevent mode collapse; i.e. the objective can be near-optimal even when the generated distribution has low and finite support (b) cannot prevent learning meaningless codes for data -- essentially white noise. Thus if encoder-decoder GANs do indeed work then it must be due to reasons as yet not understood, since the training objective can be low even for meaningless solutions.

Brian Bullins, Cyril Zhang, Yi Zhang

We propose a principled method for kernel learning, which relies on a Fourier-analytic characterization of translation-invariant or rotation-invariant kernels. Our method produces a sequence of feature maps, iteratively refining the SVM margin. We provide rigorous guarantees for optimality and generalization, interpreting our algorithm as online equilibrium-finding dynamics in a certain two-player min-max game. Evaluations on synthetic and real-world datasets demonstrate scalability and consistent improvements over related random features-based methods.

Xi Peng, Jiashi Feng, Shijie Xiao et al.

In this paper, we present a deep extension of Sparse Subspace Clustering, termed Deep Sparse Subspace Clustering (DSSC). Regularized by the unit sphere distribution assumption for the learned deep features, DSSC can infer a new data affinity matrix by simultaneously satisfying the sparsity principle of SSC and the nonlinearity given by neural networks. One of the appealing advantages brought by DSSC is: when original real-world data do not meet the class-specific linear subspace distribution assumption, DSSC can employ neural networks to make the assumption valid with its hierarchical nonlinear transformations. To the best of our knowledge, this is among the first deep learning based subspace clustering methods. Extensive experiments are conducted on four real-world datasets to show the proposed DSSC is significantly superior to 12 existing methods for subspace clustering.

Jie Zhu, Ying Shan, JC Mao et al.

Deep Neural Networks (DNN) have demonstrated superior ability to extract high level embedding vectors from low level features. Despite the success, the serving time is still the bottleneck due to expensive run-time computation of multiple layers of dense matrices. GPGPU, FPGA, or ASIC-based serving systems require additional hardware that are not in the mainstream design of most commercial applications. In contrast, tree or forest-based models are widely adopted because of low serving cost, but heavily depend on carefully engineered features. This work proposes a Deep Embedding Forest model that benefits from the best of both worlds. The model consists of a number of embedding layers and a forest/tree layer. The former maps high dimensional (hundreds of thousands to millions) and heterogeneous low-level features to the lower dimensional (thousands) vectors, and the latter ensures fast serving. Built on top of a representative DNN model called Deep Crossing, and two forest/tree-based models including XGBoost and LightGBM, a two-step Deep Embedding Forest algorithm is demonstrated to achieve on-par or slightly better performance as compared with the DNN counterpart, with only a fraction of serving time on conventional hardware. After comparing with a joint optimization algorithm called partial fuzzification, also proposed in this paper, it is concluded that the two-step Deep Embedding Forest has achieved near optimal performance. Experiments based on large scale data sets (up to 1 billion samples) from a major sponsored search engine proves the efficacy of the proposed model.

Sanjeev Arora, Rong Ge, Yingyu Liang et al.

We show that training of generative adversarial network (GAN) may not have good generalization properties; e.g., training may appear successful but the trained distribution may be far from target distribution in standard metrics. However, generalization does occur for a weaker metric called neural net distance. It is also shown that an approximate pure equilibrium exists in the discriminator/generator game for a special class of generators with natural training objectives when generator capacity and training set sizes are moderate. This existence of equilibrium inspires MIX+GAN protocol, which can be combined with any existing GAN training, and empirically shown to improve some of them.

Xi Peng, Canyi Lu, Zhang Yi et al.

A lot of works have shown that frobenius-norm based representation (FNR) is competitive to sparse representation and nuclear-norm based representation (NNR) in numerous tasks such as subspace clustering. Despite the success of FNR in experimental studies, less theoretical analysis is provided to understand its working mechanism. In this paper, we fill this gap by building the theoretical connections between FNR and NNR. More specially, we prove that: 1) when the dictionary can provide enough representative capacity, FNR is exactly NNR even though the data set contains the Gaussian noise, Laplacian noise, or sample-specified corruption, 2) otherwise, FNR and NNR are two solutions on the column space of the dictionary.

Xi Peng, Jiwen Lu, Zhang Yi et al.

In this paper, we address two challenging problems in unsupervised subspace learning: 1) how to automatically identify the feature dimension of the learned subspace (i.e., automatic subspace learning), and 2) how to learn the underlying subspace in the presence of Gaussian noise (i.e., robust subspace learning). We show that these two problems can be simultaneously solved by proposing a new method (called principal coefficients embedding, PCE). For a given data set $\mathbf{D}\in \mathds{R}^{m\times n}$, PCE recovers a clean data set $\mathbf{D}_{0}\in \mathds{R}^{m\times n}$ from $\mathbf{D}$ and simultaneously learns a global reconstruction relation $\mathbf{C}\in \mathbf{R}^{n\times n}$ of $\mathbf{D}_{0}$. By preserving $\mathbf{C}$ into an $m^{\prime}$-dimensional space, the proposed method obtains a projection matrix that can capture the latent manifold structure of $\mathbf{D}_{0}$, where $m^{\prime}\ll m$ is automatically determined by the rank of $\mathbf{C}$ with theoretical guarantees. PCE has three advantages: 1) it can automatically determine the feature dimension even though data are sampled from a union of multiple linear subspaces in presence of the Gaussian noise, 2) Although the objective function of PCE only considers the Gaussian noise, experimental results show that it is robust to the non-Gaussian noise (\textit{e.g.}, random pixel corruption) and real disguises, 3) Our method has a closed-form solution and can be calculated very fast. Extensive experimental results show the superiority of PCE on a range of databases with respect to the classification accuracy, robustness and efficiency.

Jie Chen, Haixian Zhang, Hua Mao et al.

We propose a symmetric low-rank representation (SLRR) method for subspace clustering, which assumes that a data set is approximately drawn from the union of multiple subspaces. The proposed technique can reveal the membership of multiple subspaces through the self-expressiveness property of the data. In particular, the SLRR method considers a collaborative representation combined with low-rank matrix recovery techniques as a low-rank representation to learn a symmetric low-rank representation, which preserves the subspace structures of high-dimensional data. In contrast to performing iterative singular value decomposition in some existing low-rank representation based algorithms, the symmetric low-rank representation in the SLRR method can be calculated as a closed form solution by solving the symmetric low-rank optimization problem. By making use of the angular information of the principal directions of the symmetric low-rank representation, an affinity graph matrix is constructed for spectral clustering. Extensive experimental results show that it outperforms state-of-the-art subspace clustering algorithms.

Xi Peng, Rui Yan, Bo Zhao et al.

Spatial Pyramid Matching (SPM) and its variants have achieved a lot of success in image classification. The main difference among them is their encoding schemes. For example, ScSPM incorporates Sparse Code (SC) instead of Vector Quantization (VQ) into the framework of SPM. Although the methods achieve a higher recognition rate than the traditional SPM, they consume more time to encode the local descriptors extracted from the image. In this paper, we propose using Low Rank Representation (LRR) to encode the descriptors under the framework of SPM. Different from SC, LRR considers the group effect among data points instead of sparsity. Benefiting from this property, the proposed method (i.e., LrrSPM) can offer a better performance. To further improve the generalizability and robustness, we reformulate the rank-minimization problem as a truncated projection problem. Extensive experimental studies show that LrrSPM is more efficient than its counterparts (e.g., ScSPM) while achieving competitive recognition rates on nine image data sets.

Jie Chen, Hua Mao, Yongsheng Sang et al.

In this paper, we propose a low-rank representation with symmetric constraint (LRRSC) method for robust subspace clustering. Given a collection of data points approximately drawn from multiple subspaces, the proposed technique can simultaneously recover the dimension and members of each subspace. LRRSC extends the original low-rank representation algorithm by integrating a symmetric constraint into the low-rankness property of high-dimensional data representation. The symmetric low-rank representation, which preserves the subspace structures of high-dimensional data, guarantees weight consistency for each pair of data points so that highly correlated data points of subspaces are represented together. Moreover, it can be efficiently calculated by solving a convex optimization problem. We provide a rigorous proof for minimizing the nuclear-norm regularized least square problem with a symmetric constraint. The affinity matrix for spectral clustering can be obtained by further exploiting the angular information of the principal directions of the symmetric low-rank representation. This is a critical step towards evaluating the memberships between data points. Experimental results on benchmark databases demonstrate the effectiveness and robustness of LRRSC compared with several state-of-the-art subspace clustering algorithms.

Xi Peng, Huajin Tang, Lei Zhang et al.

Under the framework of spectral clustering, the key of subspace clustering is building a similarity graph which describes the neighborhood relations among data points. Some recent works build the graph using sparse, low-rank, and $\ell_2$-norm-based representation, and have achieved state-of-the-art performance. However, these methods have suffered from the following two limitations. First, the time complexities of these methods are at least proportional to the cube of the data size, which make those methods inefficient for solving large-scale problems. Second, they cannot cope with out-of-sample data that are not used to construct the similarity graph. To cluster each out-of-sample datum, the methods have to recalculate the similarity graph and the cluster membership of the whole data set. In this paper, we propose a unified framework which makes representation-based subspace clustering algorithms feasible to cluster both out-of-sample and large-scale data. Under our framework, the large-scale problem is tackled by converting it as out-of-sample problem in the manner of "sampling, clustering, coding, and classifying". Furthermore, we give an estimation for the error bounds by treating each subspace as a point in a hyperspace. Extensive experimental results on various benchmark data sets show that our methods outperform several recently-proposed scalable methods in clustering large-scale data set.

Liangli Zhen, Zhang Yi, Xi Peng et al.

It is a key to construct a similarity graph in graph-oriented subspace learning and clustering. In a similarity graph, each vertex denotes a data point and the edge weight represents the similarity between two points. There are two popular schemes to construct a similarity graph, i.e., pairwise distance based scheme and linear representation based scheme. Most existing works have only involved one of the above schemes and suffered from some limitations. Specifically, pairwise distance based methods are sensitive to the noises and outliers compared with linear representation based methods. On the other hand, there is the possibility that linear representation based algorithms wrongly select inter-subspaces points to represent a point, which will degrade the performance. In this paper, we propose an algorithm, called Locally Linear Representation (LLR), which integrates pairwise distance with linear representation together to address the problems. The proposed algorithm can automatically encode each data point over a set of points that not only could denote the objective point with less residual error, but also are close to the point in Euclidean space. The experimental results show that our approach is promising in subspace learning and subspace clustering.