Yi Zhou

Qingyang Tan, Yi Zhou, Tuanfeng Wang et al.

Despite recent success, deep learning-based methods for predicting 3D garment deformation under body motion suffer from interpenetration problems between the garment and the body. To address this problem, we propose a novel collision handling neural network layer called Repulsive Force Unit (ReFU). Based on the signed distance function (SDF) of the underlying body and the current garment vertex positions, ReFU predicts the per-vertex offsets that push any interpenetrating vertex to a collision-free configuration while preserving the fine geometric details. We show that ReFU is differentiable with trainable parameters and can be integrated into different network backbones that predict 3D garment deformations. Our experiments show that ReFU significantly reduces the number of collisions between the body and the garment and better preserves geometric details compared to prior methods based on collision loss or post-processing optimization.

Chengan He, Jun Saito, James Zachary et al.

We present an implicit neural representation to learn the spatio-temporal space of kinematic motions. Unlike previous work that represents motion as discrete sequential samples, we propose to express the vast motion space as a continuous function over time, hence the name Neural Motion Fields (NeMF). Specifically, we use a neural network to learn this function for miscellaneous sets of motions, which is designed to be a generative model conditioned on a temporal coordinate $t$ and a random vector $z$ for controlling the style. The model is then trained as a Variational Autoencoder (VAE) with motion encoders to sample the latent space. We train our model with a diverse human motion dataset and quadruped dataset to prove its versatility, and finally deploy it as a generic motion prior to solve task-agnostic problems and show its superiority in different motion generation and editing applications, such as motion interpolation, in-betweening, and re-navigating. More details can be found on our project page: https://cs.yale.edu/homes/che/projects/nemf/.

Yasamin Jafarian, Tuanfeng Y. Wang, Duygu Ceylan et al.

Clothes undergo complex geometric deformations, which lead to appearance changes. To edit human videos in a physically plausible way, a texture map must take into account not only the garment transformation induced by the body movements and clothes fitting, but also its 3D fine-grained surface geometry. This poses, however, a new challenge of 3D reconstruction of dynamic clothes from an image or a video. In this paper, we show that it is possible to edit dressed human images and videos without 3D reconstruction. We estimate a geometry aware texture map between the garment region in an image and the texture space, a.k.a, UV map. Our UV map is designed to preserve isometry with respect to the underlying 3D surface by making use of the 3D surface normals predicted from the image. Our approach captures the underlying geometry of the garment in a self-supervised way, requiring no ground truth annotation of UV maps and can be readily extended to predict temporally coherent UV maps. We demonstrate that our method outperforms the state-of-the-art human UV map estimation approaches on both real and synthetic data.

Shuangping Jin, Bingbing Yu, Minhao Jing et al.

RGB-NIR fusion is a promising method for low-light imaging. However, high-intensity noise in low-light images amplifies the effect of structure inconsistency between RGB-NIR images, which fails existing algorithms. To handle this, we propose a new RGB-NIR fusion algorithm called Dark Vision Net (DVN) with two technical novelties: Deep Structure and Deep Inconsistency Prior (DIP). The Deep Structure extracts clear structure details in deep multiscale feature space rather than raw input space, which is more robust to noisy inputs. Based on the deep structures from both RGB and NIR domains, we introduce the DIP to leverage the structure inconsistency to guide the fusion of RGB-NIR. Benefiting from this, the proposed DVN obtains high-quality lowlight images without the visual artifacts. We also propose a new dataset called Dark Vision Dataset (DVD), consisting of aligned RGB-NIR image pairs, as the first public RGBNIR fusion benchmark. Quantitative and qualitative results on the proposed benchmark show that DVN significantly outperforms other comparison algorithms in PSNR and SSIM, especially in extremely low light conditions.

Yue Wang, Yi Zhou, Shaofeng Zou

Greedy-GQ with linear function approximation, originally proposed in \cite{maei2010toward}, is a value-based off-policy algorithm for optimal control in reinforcement learning, and it has a non-linear two timescale structure with the non-convex objective function. This paper develops its tightest finite-time error bounds. We show that the Greedy-GQ algorithm converges as fast as $\mathcal{O}({1}/{\sqrt{T}})$ under the i.i.d.\ setting and $\mathcal{O}({\log T}/{\sqrt{T}})$ under the Markovian setting. We further design a variant of the vanilla Greedy-GQ algorithm using the nested-loop approach, and show that its sample complexity is $\mathcal{O}({\log(1/ε)ε^{-2}})$, which matches with the one of the vanilla Greedy-GQ. Our finite-time error bounds match with one of the stochastic gradient descent algorithms for general smooth non-convex optimization problems, despite its additonal challenge in the two time-scale updates. Our finite-sample analysis provides theoretical guidance on choosing step-sizes for faster convergence in practice, and suggests the trade-off between the convergence rate and the quality of the obtained policy. Our techniques provide a general approach for finite-sample analysis of non-convex two timescale value-based reinforcement learning algorithms.

Shaocong Ma, Ziyi Chen, Yi Zhou et al.

Conventional machine learning applications typically assume that data samples are independently and identically distributed (i.i.d.). However, practical scenarios often involve a data-generating process that produces highly dependent data samples, which are known to heavily bias the stochastic optimization process and slow down the convergence of learning. In this paper, we conduct a fundamental study on how different stochastic data sampling schemes affect the sample complexity of online stochastic gradient descent (SGD) over highly dependent data. Specifically, with a $φ$-mixing model of data dependence, we show that online SGD with proper periodic data-subsampling achieves an improved sample complexity over the standard online SGD in the full spectrum of the data dependence level. Interestingly, even subsampling a subset of data samples can accelerate the convergence of online SGD over highly dependent data. Moreover, we show that online SGD with mini-batch sampling can further substantially improve the sample complexity over online SGD with periodic data-subsampling over highly dependent data. Numerical experiments validate our theoretical results.

Ziyi Chen, Bhavya Kailkhura, Yi Zhou

Many important machine learning applications involve regularized nonconvex bi-level optimization. However, the existing gradient-based bi-level optimization algorithms cannot handle nonconvex or nonsmooth regularizers, and they suffer from a high computation complexity in nonconvex bi-level optimization. In this work, we study a proximal gradient-type algorithm that adopts the approximate implicit differentiation (AID) scheme for nonconvex bi-level optimization with possibly nonconvex and nonsmooth regularizers. In particular, the algorithm applies the Nesterov's momentum to accelerate the computation of the implicit gradient involved in AID. We provide a comprehensive analysis of the global convergence properties of this algorithm through identifying its intrinsic potential function. In particular, we formally establish the convergence of the model parameters to a critical point of the bi-level problem, and obtain an improved computation complexity $\mathcal{O}(κ^{3.5}ε^{-2})$ over the state-of-the-art result. Moreover, we analyze the asymptotic convergence rates of this algorithm under a class of local nonconvex geometries characterized by a Łojasiewicz-type gradient inequality. Experiment on hyper-parameter optimization demonstrates the effectiveness of our algorithm.

Quang Minh Nguyen, Hoang H. Nguyen, Yi Zhou et al.

We study the Unbalanced Optimal Transport (UOT) between two measures of possibly different masses with at most $n$ components, where the marginal constraints of standard Optimal Transport (OT) are relaxed via Kullback-Leibler divergence with regularization factor $τ$. Although only Sinkhorn-based UOT solvers have been analyzed in the literature with the iteration complexity of ${O}\big(\tfrac{τ\log(n)}{\varepsilon} \log\big(\tfrac{\log(n)}{\varepsilon}\big)\big)$ and per-iteration cost of $O(n^2)$ for achieving the desired error $\varepsilon$, their positively dense output transportation plans strongly hinder the practicality. On the other hand, while being vastly used as heuristics for computing UOT in modern deep learning applications and having shown success in sparse OT problem, gradient methods applied to UOT have not been formally studied. In this paper, we propose a novel algorithm based on Gradient Extrapolation Method (GEM-UOT) to find an $\varepsilon$-approximate solution to the UOT problem in $O\big( κ\log\big(\frac{τn}{\varepsilon}\big) \big)$ iterations with $\widetilde{O}(n^2)$ per-iteration cost, where $κ$ is the condition number depending on only the two input measures. Our proof technique is based on a novel dual formulation of the squared $\ell_2$-norm UOT objective, which fills the lack of sparse UOT literature and also leads to a new characterization of approximation error between UOT and OT. To this end, we further present a novel approach of OT retrieval from UOT, which is based on GEM-UOT with fine tuned $τ$ and a post-process projection step. Extensive experiments on synthetic and real datasets validate our theories and demonstrate the favorable performance of our methods in practice.

Ziyi Chen, Shaocong Ma, Yi Zhou

Alternating gradient-descent-ascent (AltGDA) is an optimization algorithm that has been widely used for model training in various machine learning applications, which aims to solve a nonconvex minimax optimization problem. However, the existing studies show that it suffers from a high computation complexity in nonconvex minimax optimization. In this paper, we develop a single-loop and fast AltGDA-type algorithm that leverages proximal gradient updates and momentum acceleration to solve regularized nonconvex minimax optimization problems. By leveraging the momentum acceleration technique, we prove that the algorithm converges to a critical point in nonconvex minimax optimization and achieves a computation complexity in the order of $\mathcal{O}(κ^{\frac{11}{6}}ε^{-2})$, where $ε$ is the desired level of accuracy and $κ$ is the problem's condition number. {Such a computation complexity improves the state-of-the-art complexities of single-loop GDA and AltGDA algorithms (see the summary of comparison in \Cref{table1})}. We demonstrate the effectiveness of our algorithm via an experiment on adversarial deep learning.

Xiuyuan Lu, Yi Zhou, Shaojie Shen

Among prerequisites for a synthetic agent to interact with dynamic scenes, the ability to identify independently moving objects is specifically important. From an application perspective, nevertheless, standard cameras may deteriorate remarkably under aggressive motion and challenging illumination conditions. In contrast, event-based cameras, as a category of novel biologically inspired sensors, deliver advantages to deal with these challenges. Its rapid response and asynchronous nature enables it to capture visual stimuli at exactly the same rate of the scene dynamics. In this paper, we present a cascaded two-level multi-model fitting method for identifying independently moving objects (i.e., the motion segmentation problem) with a monocular event camera. The first level leverages tracking of event features and solves the feature clustering problem under a progressive multi-model fitting scheme. Initialized with the resulting motion model instances, the second level further addresses the event clustering problem using a spatio-temporal graph-cut method. This combination leads to efficient and accurate event-wise motion segmentation that cannot be achieved by any of them alone. Experiments demonstrate the effectiveness and versatility of our method in real-world scenes with different motion patterns and an unknown number of independently moving objects.

Ziyi Chen, Zhengyang Hu, Qunwei Li et al.

Gradient descent-ascent (GDA) is a widely used algorithm for minimax optimization. However, GDA has been proved to converge to stationary points for nonconvex minimax optimization, which are suboptimal compared with local minimax points. In this work, we develop cubic regularization (CR) type algorithms that globally converge to local minimax points in nonconvex-strongly-concave minimax optimization. We first show that local minimax points are equivalent to second-order stationary points of a certain envelope function. Then, inspired by the classic cubic regularization algorithm, we propose an algorithm named Cubic-LocalMinimax for finding local minimax points, and provide a comprehensive convergence analysis by leveraging its intrinsic potential function. Specifically, we establish the global convergence of Cubic-LocalMinimax to a local minimax point at a sublinear convergence rate and characterize its iteration complexity. Also, we propose a GDA-based solver for solving the cubic subproblem involved in Cubic-LocalMinimax up to certain pre-defined accuracy, and analyze the overall gradient and Hessian-vector product computation complexities of such an inexact Cubic-LocalMinimax algorithm. Moreover, we propose a stochastic variant of Cubic-LocalMinimax for large-scale minimax optimization, and characterize its sample complexity under stochastic sub-sampling. Experimental results demonstrate faster convergence of our stochastic Cubic-LocalMinimax than some existing algorithms.

Pengtao Xie, Jin Kyu Kim, Yi Zhou et al.

Matrix-parametrized models, including multiclass logistic regression and sparse coding, are used in machine learning (ML) applications ranging from computer vision to computational biology. When these models are applied to large-scale ML problems starting at millions of samples and tens of thousands of classes, their parameter matrix can grow at an unexpected rate, resulting in high parameter synchronization costs that greatly slow down distributed learning. To address this issue, we propose a Sufficient Factor Broadcasting (SFB) computation model for efficient distributed learning of a large family of matrix-parameterized models, which share the following property: the parameter update computed on each data sample is a rank-1 matrix, i.e., the outer product of two "sufficient factors" (SFs). By broadcasting the SFs among worker machines and reconstructing the update matrices locally at each worker, SFB improves communication efficiency --- communication costs are linear in the parameter matrix's dimensions, rather than quadratic --- without affecting computational correctness. We present a theoretical convergence analysis of SFB, and empirically corroborate its efficiency on four different matrix-parametrized ML models.