Yi Ma

Tianzhe Chu, Shengbang Tong, Tianjiao Ding et al.

The advent of large pre-trained models has brought about a paradigm shift in both visual representation learning and natural language processing. However, clustering unlabeled images, as a fundamental and classic machine learning problem, still lacks an effective solution, particularly for large-scale datasets. In this paper, we propose a novel image clustering pipeline that leverages the powerful feature representation of large pre-trained models such as CLIP and cluster images effectively and efficiently at scale. We first developed a novel algorithm to estimate the number of clusters in a given dataset. We then show that the pre-trained features are significantly more structured by further optimizing the rate reduction objective. The resulting features may significantly improve the clustering accuracy, e.g., from 57\% to 66\% on ImageNet-1k. Furthermore, by leveraging CLIP's multimodality bridge between image and text, we develop a simple yet effective self-labeling algorithm that produces meaningful captions for the clusters. Through extensive experiments, we show that our pipeline works well on standard datasets such as CIFAR-10, CIFAR-100, and ImageNet-1k. It also extends to datasets that are not curated for clustering, such as LAION-Aesthetics and WikiArts. We released the code in https://github.com/LeslieTrue/CPP.

Haozhi Qi, Brent Yi, Sudharshan Suresh et al. · berkeley

We introduce RotateIt, a system that enables fingertip-based object rotation along multiple axes by leveraging multimodal sensory inputs. Our system is trained in simulation, where it has access to ground-truth object shapes and physical properties. Then we distill it to operate on realistic yet noisy simulated visuotactile and proprioceptive sensory inputs. These multimodal inputs are fused via a visuotactile transformer, enabling online inference of object shapes and physical properties during deployment. We show significant performance improvements over prior methods and the importance of visual and tactile sensing.

Yaodong Yu, Sam Buchanan, Druv Pai et al.

In this paper, we contend that the objective of representation learning is to compress and transform the distribution of the data, say sets of tokens, towards a mixture of low-dimensional Gaussian distributions supported on incoherent subspaces. The quality of the final representation can be measured by a unified objective function called sparse rate reduction. From this perspective, popular deep networks such as transformers can be naturally viewed as realizing iterative schemes to optimize this objective incrementally. Particularly, we show that the standard transformer block can be derived from alternating optimization on complementary parts of this objective: the multi-head self-attention operator can be viewed as a gradient descent step to compress the token sets by minimizing their lossy coding rate, and the subsequent multi-layer perceptron can be viewed as attempting to sparsify the representation of the tokens. This leads to a family of white-box transformer-like deep network architectures which are mathematically fully interpretable. Despite their simplicity, experiments show that these networks indeed learn to optimize the designed objective: they compress and sparsify representations of large-scale real-world vision datasets such as ImageNet, and achieve performance very close to thoroughly engineered transformers such as ViT. Code is at \url{https://github.com/Ma-Lab-Berkeley/CRATE}.

Allen Y. Yang, Zihan Zhou, Arvind Ganesh et al.

L1-minimization refers to finding the minimum L1-norm solution to an underdetermined linear system b=Ax. Under certain conditions as described in compressive sensing theory, the minimum L1-norm solution is also the sparsest solution. In this paper, our study addresses the speed and scalability of its algorithms. In particular, we focus on the numerical implementation of a sparsity-based classification framework in robust face recognition, where sparse representation is sought to recover human identities from very high-dimensional facial images that may be corrupted by illumination, facial disguise, and pose variation. Although the underlying numerical problem is a linear program, traditional algorithms are known to suffer poor scalability for large-scale applications. We investigate a new solution based on a classical convex optimization framework, known as Augmented Lagrangian Methods (ALM). The new convex solvers provide a viable solution to real-world, time-critical applications such as face recognition. We conduct extensive experiments to validate and compare the performance of the ALM algorithms against several popular L1-minimization solvers, including interior-point method, Homotopy, FISTA, SESOP-PCD, approximate message passing (AMP) and TFOCS. To aid peer evaluation, the code for all the algorithms has been made publicly available.

Yaodong Yu, Tianzhe Chu, Shengbang Tong et al.

Transformer-like models for vision tasks have recently proven effective for a wide range of downstream applications such as segmentation and detection. Previous works have shown that segmentation properties emerge in vision transformers (ViTs) trained using self-supervised methods such as DINO, but not in those trained on supervised classification tasks. In this study, we probe whether segmentation emerges in transformer-based models solely as a result of intricate self-supervised learning mechanisms, or if the same emergence can be achieved under much broader conditions through proper design of the model architecture. Through extensive experimental results, we demonstrate that when employing a white-box transformer-like architecture known as CRATE, whose design explicitly models and pursues low-dimensional structures in the data distribution, segmentation properties, at both the whole and parts levels, already emerge with a minimalistic supervised training recipe. Layer-wise finer-grained analysis reveals that the emergent properties strongly corroborate the designed mathematical functions of the white-box network. Our results suggest a path to design white-box foundation models that are simultaneously highly performant and mathematically fully interpretable. Code is at \url{https://github.com/Ma-Lab-Berkeley/CRATE}.

Yaodong Yu, Sam Buchanan, Druv Pai et al.

In this paper, we contend that a natural objective of representation learning is to compress and transform the distribution of the data, say sets of tokens, towards a low-dimensional Gaussian mixture supported on incoherent subspaces. The goodness of such a representation can be evaluated by a principled measure, called sparse rate reduction, that simultaneously maximizes the intrinsic information gain and extrinsic sparsity of the learned representation. From this perspective, popular deep network architectures, including transformers, can be viewed as realizing iterative schemes to optimize this measure. Particularly, we derive a transformer block from alternating optimization on parts of this objective: the multi-head self-attention operator compresses the representation by implementing an approximate gradient descent step on the coding rate of the features, and the subsequent multi-layer perceptron sparsifies the features. This leads to a family of white-box transformer-like deep network architectures, named CRATE, which are mathematically fully interpretable. We show, by way of a novel connection between denoising and compression, that the inverse to the aforementioned compressive encoding can be realized by the same class of CRATE architectures. Thus, the so-derived white-box architectures are universal to both encoders and decoders. Experiments show that these networks, despite their simplicity, indeed learn to compress and sparsify representations of large-scale real-world image and text datasets, and achieve performance very close to highly engineered transformer-based models: ViT, MAE, DINO, BERT, and GPT2. We believe the proposed computational framework demonstrates great potential in bridging the gap between theory and practice of deep learning, from a unified perspective of data compression. Code is available at: https://ma-lab-berkeley.github.io/CRATE .

Brent Yi, Weijia Zeng, Sam Buchanan et al.

Factored feature volumes offer a simple way to build more compact, efficient, and intepretable neural fields, but also introduce biases that are not necessarily beneficial for real-world data. In this work, we (1) characterize the undesirable biases that these architectures have for axis-aligned signals -- they can lead to radiance field reconstruction differences of as high as 2 PSNR -- and (2) explore how learning a set of canonicalizing transformations can improve representations by removing these biases. We prove in a two-dimensional model problem that simultaneously learning these transformations together with scene appearance succeeds with drastically improved efficiency. We validate the resulting architectures, which we call TILTED, using image, signed distance, and radiance field reconstruction tasks, where we observe improvements across quality, robustness, compactness, and runtime. Results demonstrate that TILTED can enable capabilities comparable to baselines that are 2x larger, while highlighting weaknesses of neural field evaluation procedures.

Peng Wang, Huijie Zhang, Zekai Zhang et al.

Recent empirical studies have demonstrated that diffusion models can effectively learn the image distribution and generate new samples. Remarkably, these models can achieve this even with a small number of training samples despite a large image dimension, circumventing the curse of dimensionality. In this work, we provide theoretical insights into this phenomenon by leveraging key empirical observations: (i) the low intrinsic dimensionality of image data, (ii) a union of manifold structure of image data, and (iii) the low-rank property of the denoising autoencoder in trained diffusion models. These observations motivate us to assume the underlying data distribution of image data as a mixture of low-rank Gaussians and to parameterize the denoising autoencoder as a low-rank model according to the score function of the assumed distribution. With these setups, we rigorously show that optimizing the training loss of diffusion models is equivalent to solving the canonical subspace clustering problem over the training samples. Based on this equivalence, we further show that the minimal number of samples required to learn the underlying distribution scales linearly with the intrinsic dimensions under the above data and model assumptions. This insight sheds light on why diffusion models can break the curse of dimensionality and exhibit the phase transition in learning distributions. Moreover, we empirically establish a correspondence between the subspaces and the semantic representations of image data, facilitating image editing. We validate these results with corroborated experimental results on both simulated distributions and image datasets.

Druv Pai, Ziyang Wu, Sam Buchanan et al.

Modern learning frameworks often train deep neural networks with massive amounts of unlabeled data to learn representations by solving simple pretext tasks, then use the representations as foundations for downstream tasks. These networks are empirically designed; as such, they are usually not interpretable, their representations are not structured, and their designs are potentially redundant. White-box deep networks, in which each layer explicitly identifies and transforms structures in the data, present a promising alternative. However, existing white-box architectures have only been shown to work at scale in supervised settings with labeled data, such as classification. In this work, we provide the first instantiation of the white-box design paradigm that can be applied to large-scale unsupervised representation learning. We do this by exploiting a fundamental connection between diffusion, compression, and (masked) completion, deriving a deep transformer-like masked autoencoder architecture, called CRATE-MAE, in which the role of each layer is mathematically fully interpretable: they transform the data distribution to and from a structured representation. Extensive empirical evaluations confirm our analytical insights. CRATE-MAE demonstrates highly promising performance on large-scale imagery datasets while using only ~30% of the parameters compared to the standard masked autoencoder with the same model configuration. The representations learned by CRATE-MAE have explicit structure and also contain semantic meaning. Code is available at https://github.com/Ma-Lab-Berkeley/CRATE .

Xili Dai, Shengbang Tong, Mingyang Li et al.

This work proposes a new computational framework for learning a structured generative model for real-world datasets. In particular, we propose to learn a closed-loop transcription between a multi-class multi-dimensional data distribution and a linear discriminative representation (LDR) in the feature space that consists of multiple independent multi-dimensional linear subspaces. In particular, we argue that the optimal encoding and decoding mappings sought can be formulated as the equilibrium point of a two-player minimax game between the encoder and decoder. A natural utility function for this game is the so-called rate reduction, a simple information-theoretic measure for distances between mixtures of subspace-like Gaussians in the feature space. Our formulation draws inspiration from closed-loop error feedback from control systems and avoids expensive evaluating and minimizing approximated distances between arbitrary distributions in either the data space or the feature space. To a large extent, this new formulation unifies the concepts and benefits of Auto-Encoding and GAN and naturally extends them to the settings of learning a both discriminative and generative representation for multi-class and multi-dimensional real-world data. Our extensive experiments on many benchmark imagery datasets demonstrate tremendous potential of this new closed-loop formulation: under fair comparison, visual quality of the learned decoder and classification performance of the encoder is competitive and often better than existing methods based on GAN, VAE, or a combination of both. Unlike existing generative models, the so learned features of the multiple classes are structured: different classes are explicitly mapped onto corresponding independent principal subspaces in the feature space. Source code can be found at https://github.com/Delay-Xili/LDR.

Yichao Zhou, Shichen Liu, Yi Ma

Recent advances have shown that symmetry, a structural prior that most objects exhibit, can support a variety of single-view 3D understanding tasks. However, detecting 3D symmetry from an image remains a challenging task. Previous works either assume that the symmetry is given or detect the symmetry with a heuristic-based method. In this paper, we present NeRD, a Neural 3D Reflection Symmetry Detector, which combines the strength of learning-based recognition and geometry-based reconstruction to accurately recover the normal direction of objects' mirror planes. Specifically, we first enumerate the symmetry planes with a coarse-to-fine strategy and then find the best ones by building 3D cost volumes to examine the intra-image pixel correspondence from the symmetry. Our experiments show that the symmetry planes detected with our method are significantly more accurate than the planes from direct CNN regression on both synthetic and real-world datasets. We also demonstrate that the detected symmetry can be used to improve the performance of downstream tasks such as pose estimation and depth map regression. The code of this paper has been made public at https://github.com/zhou13/nerd.

Kun Huang, Yifan Wang, Zihan Zhou et al.

In this paper, we propose a learning-based approach to the task of automatically extracting a "wireframe" representation for images of cluttered man-made environments. The wireframe (see Fig. 1) contains all salient straight lines and their junctions of the scene that encode efficiently and accurately large-scale geometry and object shapes. To this end, we have built a very large new dataset of over 5,000 images with wireframes thoroughly labelled by humans. We have proposed two convolutional neural networks that are suitable for extracting junctions and lines with large spatial support, respectively. The networks trained on our dataset have achieved significantly better performance than state-of-the-art methods for junction detection and line segment detection, respectively. We have conducted extensive experiments to evaluate quantitatively and qualitatively the wireframes obtained by our method, and have convincingly shown that effectively and efficiently parsing wireframes for images of man-made environments is a feasible goal within reach. Such wireframes could benefit many important visual tasks such as feature correspondence, 3D reconstruction, vision-based mapping, localization, and navigation. The data and source code are available at https://github.com/huangkuns/wireframe.

Haozhi Qi, Chong You, Xiaolong Wang et al.

Initialization, normalization, and skip connections are believed to be three indispensable techniques for training very deep convolutional neural networks and obtaining state-of-the-art performance. This paper shows that deep vanilla ConvNets without normalization nor skip connections can also be trained to achieve surprisingly good performance on standard image recognition benchmarks. This is achieved by enforcing the convolution kernels to be near isometric during initialization and training, as well as by using a variant of ReLU that is shifted towards being isometric. Further experiments show that if combined with skip connections, such near isometric networks can achieve performances on par with (for ImageNet) and better than (for COCO) the standard ResNet, even without normalization at all. Our code is available at https://github.com/HaozhiQi/ISONet.

Yichao Zhou, Shichen Liu, Yi Ma

3D reconstruction from a single RGB image is a challenging problem in computer vision. Previous methods are usually solely data-driven, which lead to inaccurate 3D shape recovery and limited generalization capability. In this work, we focus on object-level 3D reconstruction and present a geometry-based end-to-end deep learning framework that first detects the mirror plane of reflection symmetry that commonly exists in man-made objects and then predicts depth maps by finding the intra-image pixel-wise correspondence of the symmetry. Our method fully utilizes the geometric cues from symmetry during the test time by building plane-sweep cost volumes, a powerful tool that has been used in multi-view stereopsis. To our knowledge, this is the first work that uses the concept of cost volumes in the setting of single-image 3D reconstruction. We conduct extensive experiments on the ShapeNet dataset and find that our reconstruction method significantly outperforms the previous state-of-the-art single-view 3D reconstruction networks in term of the accuracy of camera poses and depth maps, without requiring objects being completely symmetric. Code is available at https://github.com/zhou13/symmetrynet.

Yichao Zhou, Haozhi Qi, Jingwei Huang et al.

We present a simple yet effective end-to-end trainable deep network with geometry-inspired convolutional operators for detecting vanishing points in images. Traditional convolutional neural networks rely on aggregating edge features and do not have mechanisms to directly exploit the geometric properties of vanishing points as the intersections of parallel lines. In this work, we identify a canonical conic space in which the neural network can effectively compute the global geometric information of vanishing points locally, and we propose a novel operator named conic convolution that can be implemented as regular convolutions in this space. This new operator explicitly enforces feature extractions and aggregations along the structural lines and yet has the same number of parameters as the regular 2D convolution. Our extensive experiments on both synthetic and real-world datasets show that the proposed operator significantly improves the performance of vanishing point detection over traditional methods. The code and dataset have been made publicly available at https://github.com/zhou13/neurvps.

Yichao Zhou, Haozhi Qi, Yuexiang Zhai et al.

In this paper, we propose a method to obtain a compact and accurate 3D wireframe representation from a single image by effectively exploiting global structural regularities. Our method trains a convolutional neural network to simultaneously detect salient junctions and straight lines, as well as predict their 3D depth and vanishing points. Compared with the state-of-the-art learning-based wireframe detection methods, our network is simpler and more unified, leading to better 2D wireframe detection. With global structural priors from parallelism, our method further reconstructs a full 3D wireframe model, a compact vector representation suitable for a variety of high-level vision tasks such as AR and CAD. We conduct extensive evaluations on a large synthetic dataset of urban scenes as well as real images. Our code and datasets have been made public at https://github.com/zhou13/shapeunity.

Yichao Zhou, Haozhi Qi, Yi Ma

We present a conceptually simple yet effective algorithm to detect wireframes in a given image. Compared to the previous methods which first predict an intermediate heat map and then extract straight lines with heuristic algorithms, our method is end-to-end trainable and can directly output a vectorized wireframe that contains semantically meaningful and geometrically salient junctions and lines. To better understand the quality of the outputs, we propose a new metric for wireframe evaluation that penalizes overlapped line segments and incorrect line connectivities. We conduct extensive experiments and show that our method significantly outperforms the previous state-of-the-art wireframe and line extraction algorithms. We hope our simple approach can be served as a baseline for future wireframe parsing studies. Code has been made publicly available at https://github.com/zhou13/lcnn.

Jingwei Xu, Chenyu Wang, Zibo Zhao et al.

This paper aims to design a unified Computer-Aided Design (CAD) generation system that can easily generate CAD models based on the user's inputs in the form of textual description, images, point clouds, or even a combination of them. Towards this goal, we introduce the CAD-MLLM, the first system capable of generating parametric CAD models conditioned on the multimodal input. Specifically, within the CAD-MLLM framework, we leverage the command sequences of CAD models and then employ advanced large language models (LLMs) to align the feature space across these diverse multi-modalities data and CAD models' vectorized representations. To facilitate the model training, we design a comprehensive data construction and annotation pipeline that equips each CAD model with corresponding multimodal data. Our resulting dataset, named Omni-CAD, is the first multimodal CAD dataset that contains textual description, multi-view images, points, and command sequence for each CAD model. It contains approximately 450K instances and their CAD construction sequences. To thoroughly evaluate the quality of our generated CAD models, we go beyond current evaluation metrics that focus on reconstruction quality by introducing additional metrics that assess topology quality and surface enclosure extent. Extensive experimental results demonstrate that CAD-MLLM significantly outperforms existing conditional generative methods and remains highly robust to noises and missing points. The project page and more visualizations can be found at: https://cad-mllm.github.io/

Haozhi Qi, Brent Yi, Mike Lambeta et al.

Learning policies in simulation and transferring them to the real world has become a promising approach in dexterous manipulation. However, bridging the sim-to-real gap for each new task requires substantial human effort, such as careful reward engineering, hyperparameter tuning, and system identification. In this work, we present a system that leverages low-level skills to address these challenges for more complex tasks. Specifically, we introduce a hierarchical policy for in-hand object reorientation based on previously acquired rotation skills. This hierarchical policy learns to select which low-level skill to execute based on feedback from both the environment and the low-level skill policies themselves. Compared to learning from scratch, the hierarchical policy is more robust to out-of-distribution changes and transfers easily from simulation to real-world environments. Additionally, we propose a generalizable object pose estimator that uses proprioceptive information, low-level skill predictions, and control errors as inputs to estimate the object pose over time. We demonstrate that our system can reorient objects, including symmetrical and textureless ones, to a desired pose.

Kwan Ho Ryan Chan, Yaodong Yu, Chong You et al.

This work attempts to provide a plausible theoretical framework that aims to interpret modern deep (convolutional) networks from the principles of data compression and discriminative representation. We argue that for high-dimensional multi-class data, the optimal linear discriminative representation maximizes the coding rate difference between the whole dataset and the average of all the subsets. We show that the basic iterative gradient ascent scheme for optimizing the rate reduction objective naturally leads to a multi-layer deep network, named ReduNet, which shares common characteristics of modern deep networks. The deep layered architectures, linear and nonlinear operators, and even parameters of the network are all explicitly constructed layer-by-layer via forward propagation, although they are amenable to fine-tuning via back propagation. All components of so-obtained "white-box" network have precise optimization, statistical, and geometric interpretation. Moreover, all linear operators of the so-derived network naturally become multi-channel convolutions when we enforce classification to be rigorously shift-invariant. The derivation in the invariant setting suggests a trade-off between sparsity and invariance, and also indicates that such a deep convolution network is significantly more efficient to construct and learn in the spectral domain. Our preliminary simulations and experiments clearly verify the effectiveness of both the rate reduction objective and the associated ReduNet. All code and data are available at \url{https://github.com/Ma-Lab-Berkeley}.

Yaodong Yu, Zitong Yang, Edgar Dobriban et al.

Adversarially trained models exhibit a large generalization gap: they can interpolate the training set even for large perturbation radii, but at the cost of large test error on clean samples. To investigate this gap, we decompose the test risk into its bias and variance components and study their behavior as a function of adversarial training perturbation radii ($\varepsilon$). We find that the bias increases monotonically with $\varepsilon$ and is the dominant term in the risk. Meanwhile, the variance is unimodal as a function of $\varepsilon$, peaking near the interpolation threshold for the training set. This characteristic behavior occurs robustly across different datasets and also for other robust training procedures such as randomized smoothing. It thus provides a test for proposed explanations of the generalization gap. We find that some existing explanations fail this test--for instance, by predicting a monotonically increasing variance curve. This underscores the power of bias-variance decompositions in modern settings-by providing two measurements instead of one, they can rule out more explanations than test accuracy alone. We also show that bias and variance can provide useful guidance for scalably reducing the generalization gap, highlighting pre-training and unlabeled data as promising routes.

Ziyang Wu, Christina Baek, Chong You et al.

Current deep learning architectures suffer from catastrophic forgetting, a failure to retain knowledge of previously learned classes when incrementally trained on new classes. The fundamental roadblock faced by deep learning methods is that deep learning models are optimized as "black boxes," making it difficult to properly adjust the model parameters to preserve knowledge about previously seen data. To overcome the problem of catastrophic forgetting, we propose utilizing an alternative "white box" architecture derived from the principle of rate reduction, where each layer of the network is explicitly computed without back propagation. Under this paradigm, we demonstrate that, given a pre-trained network and new data classes, our approach can provably construct a new network that emulates joint training with all past and new classes. Finally, our experiments show that our proposed learning algorithm observes significantly less decay in classification performance, outperforming state of the art methods on MNIST and CIFAR-10 by a large margin and justifying the use of "white box" algorithms for incremental learning even for sufficiently complex image data.

Kwan Ho Ryan Chan, Yaodong Yu, Chong You et al.

This work attempts to interpret modern deep (convolutional) networks from the principles of rate reduction and (shift) invariant classification. We show that the basic iterative gradient ascent scheme for optimizing the rate reduction of learned features naturally leads to a multi-layer deep network, one iteration per layer. The layered architectures, linear and nonlinear operators, and even parameters of the network are all explicitly constructed layer-by-layer in a forward propagation fashion by emulating the gradient scheme. All components of this "white box" network have precise optimization, statistical, and geometric interpretation. This principled framework also reveals and justifies the role of multi-channel lifting and sparse coding in early stage of deep networks. Moreover, all linear operators of the so-derived network naturally become multi-channel convolutions when we enforce classification to be rigorously shift-invariant. The derivation also indicates that such a convolutional network is significantly more efficient to construct and learn in the spectral domain. Our preliminary simulations and experiments indicate that so constructed deep network can already learn a good discriminative representation even without any back propagation training.

Yichao Zhou, Jingwei Huang, Xili Dai et al.

We present HoliCity, a city-scale 3D dataset with rich structural information. Currently, this dataset has 6,300 real-world panoramas of resolution $13312 \times 6656$ that are accurately aligned with the CAD model of downtown London with an area of more than 20 km$^2$, in which the median reprojection error of the alignment of an average image is less than half a degree. This dataset aims to be an all-in-one data platform for research of learning abstracted high-level holistic 3D structures that can be derived from city CAD models, e.g., corners, lines, wireframes, planes, and cuboids, with the ultimate goal of supporting real-world applications including city-scale reconstruction, localization, mapping, and augmented reality. The accurate alignment of the 3D CAD models and panoramas also benefits low-level 3D vision tasks such as surface normal estimation, as the surface normal extracted from previous LiDAR-based datasets is often noisy. We conduct experiments to demonstrate the applications of HoliCity, such as predicting surface segmentation, normal maps, depth maps, and vanishing points, as well as test the generalizability of methods trained on HoliCity and other related datasets. HoliCity is available at https://holicity.io.

Haozhi Qi, Xiaolong Wang, Deepak Pathak et al.

Learning long-term dynamics models is the key to understanding physical common sense. Most existing approaches on learning dynamics from visual input sidestep long-term predictions by resorting to rapid re-planning with short-term models. This not only requires such models to be super accurate but also limits them only to tasks where an agent can continuously obtain feedback and take action at each step until completion. In this paper, we aim to leverage the ideas from success stories in visual recognition tasks to build object representations that can capture inter-object and object-environment interactions over a long-range. To this end, we propose Region Proposal Interaction Networks (RPIN), which reason about each object's trajectory in a latent region-proposal feature space. Thanks to the simple yet effective object representation, our approach outperforms prior methods by a significant margin both in terms of prediction quality and their ability to plan for downstream tasks, and also generalize well to novel environments. Code, pre-trained models, and more visualization results are available at https://haozhi.io/RPIN.

Chong You, Zhihui Zhu, Qing Qu et al.

Recent advances have shown that implicit bias of gradient descent on over-parameterized models enables the recovery of low-rank matrices from linear measurements, even with no prior knowledge on the intrinsic rank. In contrast, for robust low-rank matrix recovery from grossly corrupted measurements, over-parameterization leads to overfitting without prior knowledge on both the intrinsic rank and sparsity of corruption. This paper shows that with a double over-parameterization for both the low-rank matrix and sparse corruption, gradient descent with discrepant learning rates provably recovers the underlying matrix even without prior knowledge on neither rank of the matrix nor sparsity of the corruption. We further extend our approach for the robust recovery of natural images by over-parameterizing images with deep convolutional networks. Experiments show that our method handles different test images and varying corruption levels with a single learning pipeline where the network width and termination conditions do not need to be adjusted on a case-by-case basis. Underlying the success is again the implicit bias with discrepant learning rates on different over-parameterized parameters, which may bear on broader applications.

Yaodong Yu, Kwan Ho Ryan Chan, Chong You et al.

To learn intrinsic low-dimensional structures from high-dimensional data that most discriminate between classes, we propose the principle of Maximal Coding Rate Reduction ($\text{MCR}^2$), an information-theoretic measure that maximizes the coding rate difference between the whole dataset and the sum of each individual class. We clarify its relationships with most existing frameworks such as cross-entropy, information bottleneck, information gain, contractive and contrastive learning, and provide theoretical guarantees for learning diverse and discriminative features. The coding rate can be accurately computed from finite samples of degenerate subspace-like distributions and can learn intrinsic representations in supervised, self-supervised, and unsupervised settings in a unified manner. Empirically, the representations learned using this principle alone are significantly more robust to label corruptions in classification than those using cross-entropy, and can lead to state-of-the-art results in clustering mixed data from self-learned invariant features.

Zitong Yang, Yaodong Yu, Chong You et al.

The classical bias-variance trade-off predicts that bias decreases and variance increase with model complexity, leading to a U-shaped risk curve. Recent work calls this into question for neural networks and other over-parameterized models, for which it is often observed that larger models generalize better. We provide a simple explanation for this by measuring the bias and variance of neural networks: while the bias is monotonically decreasing as in the classical theory, the variance is unimodal or bell-shaped: it increases then decreases with the width of the network. We vary the network architecture, loss function, and choice of dataset and confirm that variance unimodality occurs robustly for all models we considered. The risk curve is the sum of the bias and variance curves and displays different qualitative shapes depending on the relative scale of bias and variance, with the double descent curve observed in recent literature as a special case. We corroborate these empirical results with a theoretical analysis of two-layer linear networks with random first layer. Finally, evaluation on out-of-distribution data shows that most of the drop in accuracy comes from increased bias while variance increases by a relatively small amount. Moreover, we find that deeper models decrease bias and increase variance for both in-distribution and out-of-distribution data.

Yi Ma, Jianye Hao, Yaodong Yang et al.

Graph convolutional networks(GCNs) have become the most popular approaches for graph data in these days because of their powerful ability to extract features from graph. GCNs approaches are divided into two categories, spectral-based and spatial-based. As the earliest convolutional networks for graph data, spectral-based GCNs have achieved impressive results in many graph related analytics tasks. However, spectral-based models cannot directly work on directed graphs. In this paper, we propose an improved spectral-based GCN for the directed graph by leveraging redefined Laplacians to improve its propagation model. Our approach can work directly on directed graph data in semi-supervised nodes classification tasks. Experiments on a number of directed graph datasets demonstrate that our approach outperforms the state-of-the-art methods.

Yuexiang Zhai, Zitong Yang, Zhenyu Liao et al.

This paper considers the fundamental problem of learning a complete (orthogonal) dictionary from samples of sparsely generated signals. Most existing methods solve the dictionary (and sparse representations) based on heuristic algorithms, usually without theoretical guarantees for either optimality or complexity. The recent $\ell^1$-minimization based methods do provide such guarantees but the associated algorithms recover the dictionary one column at a time. In this work, we propose a new formulation that maximizes the $\ell^4$-norm over the orthogonal group, to learn the entire dictionary. We prove that under a random data model, with nearly minimum sample complexity, the global optima of the $\ell^4$ norm are very close to signed permutations of the ground truth. Inspired by this observation, we give a conceptually simple and yet effective algorithm based on "matching, stretching, and projection" (MSP). The algorithm provably converges locally at a superlinear (cubic) rate and cost per iteration is merely an SVD. In addition to strong theoretical guarantees, experiments show that the new algorithm is significantly more efficient and effective than existing methods, including KSVD and $\ell^1$-based methods. Preliminary experimental results on mixed real imagery data clearly demonstrate advantages of so learned dictionary over classic PCA bases.

Chen Zhu, Xiao Tan, Feng Zhou et al.

For fine-grained categorization tasks, videos could serve as a better source than static images as videos have a higher chance of containing discriminative patterns. Nevertheless, a video sequence could also contain a lot of redundant and irrelevant frames. How to locate critical information of interest is a challenging task. In this paper, we propose a new network structure, known as Redundancy Reduction Attention (RRA), which learns to focus on multiple discriminative patterns by sup- pressing redundant feature channels. Specifically, it firstly summarizes the video by weight-summing all feature vectors in the feature maps of selected frames with a spatio-temporal soft attention, and then predicts which channels to suppress or to enhance according to this summary with a learned non-linear transform. Suppression is achieved by modulating the feature maps and threshing out weak activations. The updated feature maps are then used in the next iteration. Finally, the video is classified based on multiple summaries. The proposed method achieves out- standing performances in multiple video classification datasets. Further- more, we have collected two large-scale video datasets, YouTube-Birds and YouTube-Cars, for future researches on fine-grained video categorization. The datasets are available at http://www.cs.umd.edu/~chenzhu/fgvc.

Qiaosong Wang, Haiting Lin, Yi Ma et al.

We propose a novel approach that jointly removes reflection or translucent layer from a scene and estimates scene depth. The input data are captured via light field imaging. The problem is couched as minimizing the rank of the transmitted scene layer via Robust Principle Component Analysis (RPCA). We also impose regularization based on piecewise smoothness, gradient sparsity, and layer independence to simultaneously recover 3D geometry of the transmitted layer. Experimental results on synthetic and real data show that our technique is robust and reliable, and can handle a broad range of layer separation problems.

Yuting Zhang, Kui Jia, Yueming Wang et al.

Developing a reliable and practical face recognition system is a long-standing goal in computer vision research. Existing literature suggests that pixel-wise face alignment is the key to achieve high-accuracy face recognition. By assuming a human face as piece-wise planar surfaces, where each surface corresponds to a facial part, we develop in this paper a Constrained Part-based Alignment (CPA) algorithm for face recognition across pose and/or expression. Our proposed algorithm is based on a trainable CPA model, which learns appearance evidence of individual parts and a tree-structured shape configuration among different parts. Given a probe face, CPA simultaneously aligns all its parts by fitting them to the appearance evidence with consideration of the constraint from the tree-structured shape configuration. This objective is formulated as a norm minimization problem regularized by graph likelihoods. CPA can be easily integrated with many existing classifiers to perform part-based face recognition. Extensive experiments on benchmark face datasets show that CPA outperforms or is on par with existing methods for robust face recognition across pose, expression, and/or illumination changes.

Kui Jia, Tsung-Han Chan, Zinan Zeng et al.

Feature-based object matching is a fundamental problem for many applications in computer vision, such as object recognition, 3D reconstruction, tracking, and motion segmentation. In this work, we consider simultaneously matching object instances in a set of images, where both inlier and outlier features are extracted. The task is to identify the inlier features and establish their consistent correspondences across the image set. This is a challenging combinatorial problem, and the problem complexity grows exponentially with the image number. To this end, we propose a novel framework, termed ROML, to address this problem. ROML optimizes simultaneously a partial permutation matrix (PPM) for each image, and feature correspondences are established by the obtained PPMs. Two of our key contributions are summarized as follows. (1) We formulate the problem as rank and sparsity minimization for PPM optimization, and treat simultaneous optimization of multiple PPMs as a regularized consensus problem in the context of distributed optimization. (2) We use the ADMM method to solve the thus formulated ROML problem, in which a subproblem associated with a single PPM optimization appears to be a difficult integer quadratic program (IQP). We prove that under wildly applicable conditions, this IQP is equivalent to a linear sum assignment problem (LSAP), which can be efficiently solved to an exact solution. Extensive experiments on rigid/non-rigid object matching, matching instances of a common object category, and common object localization show the efficacy of our proposed method.

Liansheng Zhuang, Tsung-Han Chan, Allen Y. Yang et al.

Single-sample face recognition is one of the most challenging problems in face recognition. We propose a novel algorithm to address this problem based on a sparse representation based classification (SRC) framework. The new algorithm is robust to image misalignment and pixel corruption, and is able to reduce required gallery images to one sample per class. To compensate for the missing illumination information traditionally provided by multiple gallery images, a sparse illumination learning and transfer (SILT) technique is introduced. The illumination in SILT is learned by fitting illumination examples of auxiliary face images from one or more additional subjects with a sparsely-used illumination dictionary. By enforcing a sparse representation of the query image in the illumination dictionary, the SILT can effectively recover and transfer the illumination and pose information from the alignment stage to the recognition stage. Our extensive experiments have demonstrated that the new algorithms significantly outperform the state of the art in the single-sample regime and with less restrictions. In particular, the single-sample face alignment accuracy is comparable to that of the well-known Deformable SRC algorithm using multiple gallery images per class. Furthermore, the face recognition accuracy exceeds those of the SRC and Extended SRC algorithms using hand labeled alignment initialization.

Guangcan Liu, Shiyu Chang, Yi Ma

In this paper, we study the problem of recovering a sharp version of a given blurry image when the blur kernel is unknown. Previous methods often introduce an image-independent regularizer (such as Gaussian or sparse priors) on the desired blur kernel. We shall show that the blurry image itself encodes rich information about the blur kernel. Such information can be found through analyzing and comparing how the spectrum of an image as a convolution operator changes before and after blurring. Our analysis leads to an effective convex regularizer on the blur kernel which depends only on the given blurry image. We show that the minimizer of this regularizer guarantees to give good approximation to the blur kernel if the original image is sharp enough. By combining this powerful regularizer with conventional image deblurring techniques, we show how we could significantly improve the deblurring results through simulations and experiments on real images. In addition, our analysis and experiments help explaining a widely accepted doctrine; that is, the edges are good features for deblurring.

Lei Zhang, Meng Yang, Xiangchu Feng et al.

By coding a query sample as a sparse linear combination of all training samples and then classifying it by evaluating which class leads to the minimal coding residual, sparse representation based classification (SRC) leads to interesting results for robust face recognition. It is widely believed that the l1- norm sparsity constraint on coding coefficients plays a key role in the success of SRC, while its use of all training samples to collaboratively represent the query sample is rather ignored. In this paper we discuss how SRC works, and show that the collaborative representation mechanism used in SRC is much more crucial to its success of face classification. The SRC is a special case of collaborative representation based classification (CRC), which has various instantiations by applying different norms to the coding residual and coding coefficient. More specifically, the l1 or l2 norm characterization of coding residual is related to the robustness of CRC to outlier facial pixels, while the l1 or l2 norm characterization of coding coefficient is related to the degree of discrimination of facial features. Extensive experiments were conducted to verify the face recognition accuracy and efficiency of CRC with different instantiations.

Rene Vidal, Yi Ma, Shankar Sastry

This paper presents an algebro-geometric solution to the problem of segmenting an unknown number of subspaces of unknown and varying dimensions from sample data points. We represent the subspaces with a set of homogeneous polynomials whose degree is the number of subspaces and whose derivatives at a data point give normal vectors to the subspace passing through the point. When the number of subspaces is known, we show that these polynomials can be estimated linearly from data; hence, subspace segmentation is reduced to classifying one point per subspace. We select these points optimally from the data set by minimizing certain distance function, thus dealing automatically with moderate noise in the data. A basis for the complement of each subspace is then recovered by applying standard PCA to the collection of derivatives (normal vectors). Extensions of GPCA that deal with data in a high- dimensional space and with an unknown number of subspaces are also presented. Our experiments on low-dimensional data show that GPCA outperforms existing algebraic algorithms based on polynomial factorization and provides a good initialization to iterative techniques such as K-subspaces and Expectation Maximization. We also present applications of GPCA to computer vision problems such as face clustering, temporal video segmentation, and 3D motion segmentation from point correspondences in multiple affine views.