United States

We study the convergence rate of gradient-based local search methods for solving low-rank matrix recovery problems with general objectives in both symmetric and asymmetric cases, under the assumption of the restricted isometry property. First, we develop a new technique to verify the Polyak-Lojasiewicz inequality in a neighborhood of the global minimizers, which leads to a local linear convergence region for the gradient descent method. Second, based on the local convergence result and a sharp strict saddle property proven in this paper, we present two new conditions that guarantee the global linear convergence of the perturbed gradient descent method. The developed local and global convergence results provide much stronger theoretical guarantees than the existing results. As a by-product, this work significantly improves the existing bounds on the RIP constant required to guarantee the non-existence of spurious solutions.

AAAI 2022

Local and Global Linear Convergence of General Low-Rank Matrix Recovery Problems

The purpose of the AAAI conference is to promote research in artificial intelligence (AI) and scientific exchange among AI researchers, practitioners, scientists, and engineers in affiliated disciplines. 

technical paper

Recovering detailed facial geometry from a set of calibrated multi-view images is valuable for its wide range of applications. Traditional multi-view stereo (MVS) methods adopt an optimization-based scheme to regularize the matching cost. Recently, learning-based methods integrate all these into an end-to-end neural network and show superiority of efficiency. In this paper, we propose a novel architecture to recover extremely detailed 3D faces within dozens of seconds.  Unlike previous learning-based methods that regularize the cost volume via 3D CNN, we propose to learn an implicit function for regressing the matching cost.  By fitting a 3D morphable model from multi-view images, the features of multiple images are extracted and aggregated in the mesh-attached UV space, which makes the implicit function more effective in recovering detailed facial shape. Our method outperforms SOTA learning-based MVS in accuracy by a large margin on the FaceScape dataset. The code and data are released in https://github.com/zhuhao-nju/mvfr.

Detailed Facial Geometry Recovery from Multi-View Images by Learning an Implicit Function

In many real-world problems, first-order (FO) derivative evaluations are too expensive or even inaccessible. For solving these problems, zeroth-order (ZO) methods that only need function evaluations are often more efficient than FO methods or sometimes the only options. In this paper, we propose a novel zeroth-order inexact augmented Lagrangian method (ZO-iALM) to solve black-box optimization problems, which involve a composite (i.e., smooth+nonsmooth) objective and functional constraints. This appears to be the first work that develops an iALM-based ZO method for functional constrained optimization and meanwhile achieves query complexity results matching the best-known FO complexity results up to a factor of variable dimension. With an extensive experimental study, we show the effectiveness of our method. The applications of our method span from classical optimization problems to practical machine learning examples such as resource allocation in sensor networks and adversarial example generation.

Zeroth-Order Optimization for Composite Problems with Functional Constraints

We consider applications involving a large set of instances of projecting points to polytopes. We develop an intuition guided by theoretical and empirical analysis to show that when these instances follow certain structures, a large majority of the projections lie on vertices of the polytopes. To do these projections efficiently we derive a vertex-oriented incremental algorithm to project a point onto any arbitrary polytope, as well as give specific algorithms to cater to simplex projection and polytopes where the unit box is cut by planes. Such settings are especially useful in web-scale applications such as optimal matching or allocation problems. Several such problems in internet marketplaces (e-commerce, ride-sharing, food delivery, professional services, advertising, etc.), can be formulated as Linear Programs (LP) with such polytope constraints that require a projection step in the overall optimization process. We show that in some of the very recent works, the polytopic projection is the most expensive step and our efficient projection algorithms help in gaining massive improvements in performance.

Efficient Vertex-Oriented Polytopic Projection for Web-Scale Applications

Federated learning (FL) is a training technique that enables client devices to jointly learn a shared model by aggregating locally computed models without exposing their raw data. While most of the existing work focuses on improving the FL model accuracy, in this paper, we focus on the improving the training efficiency, which is often a hurdle for adopting FL in real world applications. Specifically, we design an efficient FL framework which jointly optimizes model accuracy, processing latency and communication efficiency, all of which are primary design considerations for real implementation of FL. Inspired by the recent success of Multi Agent Reinforcement Learning (MARL) in solving complex control problems, we present FedMarl, a federated learning framework that relies on trained MARL agents to perform efficient run-time client selection. Experiments show that FedMarl can significantly improve model accuracy with much lower processing latency and communication cost.

Learning Advanced Client Selection Strategy for Federated Learning

Recent advances in generative adversarial networks (GANs) have led to remarkable achievements in face image synthesis. While methods that use style-based GANs can generate strikingly photorealistic face images, it is often difficult to control the characteristics of the generated faces in a meaningful and disentangled way. Prior approaches aim to achieve such semantic control and disentanglement within the latent space of a previously trained GAN. In contrast, we propose a framework that a priori models physical attributes of the face such as 3D shape, albedo, pose, and lighting explicitly, thus providing disentanglement by design. Our method, MOST-GAN, integrates the expressive power and photorealism of style-based GANs with the physical disentanglement and flexibility of nonlinear 3D morphable models, which we couple with a state-of-the-art 2D hair manipulation network. MOST-GAN achieves photorealistic manipulation of portrait images with fully disentangled 3D control over their physical attributes, enabling extreme manipulation of lighting, facial expression, and pose variations up to full profile view.

MOST-GAN: 3D Morphable StyleGAN for Disentangled Face Image Manipulation

Training neural networks with discrete stochastic variables presents a unique challenge. Backpropagation is not directly applicable, nor are the reparameterization tricks used in networks with continuous stochastic variables. To address this challenge, we present Hindsight Network Credit Assignment (HNCA), a novel gradient estimation algorithm for networks of discrete stochastic units. HNCA works by assigning credit to each unit based on the degree to which its output influences its immediate children in the network. We prove that HNCA produces unbiased gradient estimates with reduced variance compared to the REINFORCE estimator, while the computational cost is similar to that of backpropagation. We first apply HNCA in a contextual bandit setting to optimize a reward function that is unknown to the agent. In this setting, we empirically demonstrate that HNCA significantly outperforms REINFORCE, indicating that the variance reduction implied by our theoretical analysis is significant and impactful. We then show how HNCA can be extended to optimize a more general function of the outputs of a network of stochastic units, where the function is known to the agent. We apply this extended version of HNCA to train a discrete variational auto-encoder and empirically show it compares favourably to other strong methods. We believe that the ideas underlying HNCA can help stimulate new ways of thinking about efficient credit assignment in stochastic compute graphs.

Hindsight Network Credit Assignment: Efficient Credit Assignment in Networks of Discrete Stochastic Units

How deep neural networks (DNNs) learn from noisy labels has been studied extensively in image classification but much less in image segmentation. So far, our understanding of the learning behavior of DNNs trained by noisy segmentation labels remains limited. In this study, we address this deficiency in both binary segmentation of biological microscopy images and multi-class segmentation of natural images. We generate extremely noisy labels by randomly sampling a small fraction (e.g., 10%) or flipping a large fraction (e.g., 90%) of the ground truth labels. When trained with these noisy labels, DNNs provide largely the same segmentation performance as trained by the original ground truth. This indicates that DNNs learn structures hidden in labels rather than pixel-level labels per se in their supervised training for semantic segmentation. We refer to these hidden structures in labels as meta-structures. When DNNs are trained by labels with different perturbations to the meta-structure, we find consistent degradation in their segmentation performance. In contrast, incorporation of meta-structure information substantially improves performance of an unsupervised segmentation model developed for binary semantic segmentation. We define meta-structures mathematically as spatial density distributions and show both theoretically and experimentally how this formulation explains key observed learning behavior of DNNs.

Deep Neural Networks Learn Meta-Structures from Noisy Labels in Semantic Segmentation

Adversarial examples causing evasive predictions are widely used to evaluate and improve the robustness of machine learning models. However, current studies focus on supervised learning tasks, relying on the ground truth data label, a targeted objective, or supervision from a trained classifier. In this paper, we propose a framework of generating adversarial examples for unsupervised models and demonstrate novel applications to data augmentation. Our framework exploits a mutual information neural estimator as an information theoretic similarity measure to generate adversarial examples without supervision. We propose a new MinMax algorithm with provable convergence guarantees for the efficient generation of unsupervised adversarial examples. Our framework can also be extended to supervised adversarial examples. When using unsupervised adversarial examples as a simple plugin data augmentation tool for model retraining, significant improvements are consistently observed across different unsupervised tasks and datasets, including data reconstruction, representation learning, and contrastive learning. Our results show novel methods and considerable advantages in studying and improving unsupervised machine learning via adversarial examples.

Adversarial Examples can be Effective Data Augmentation for Unsupervised Machine Learning

In this paper, we propose two new definitions of local differential privacy for belief functions. One is based on Shafer's semantics of randomly coded messages and the other from the perspective of imprecise probabilities. We show that such basic properties as composition and post-processing also hold for our new definitions. Moreover, we provide a hypothesis testing framework for these definitions and study the effect of "don't know" in the trade-off between privacy and utility in discrete distribution estimation.

Local Differential Privacy for Belief Functions

We study algorithms for approximating pairwise similarity matrices that arise in natural language processing. Generally, computing a similarity matrix for n data points requires Omega(n^2) similarity computations.
This quadratic scaling is a significant bottleneck, especially when similarities are computed via expensive functions, e.g., via transformer models.  Approximation methods reduce this quadratic complexity, often by using a small subset of exactly computed similarities to approximate the remainder of the complete pairwise similarity matrix.

Significant  work focuses on the efficient approximation of positive semidefinite (PSD) similarity matrices, which arise e.g., in kernel methods. However, much less is understood about indefinite (non-PSD) similarity matrices, which often  arise in  NLP. Motivated by the observation that many of these matrices are still somewhat close to PSD, we introduce a generalization of the popular Nystrom method to the indefinite setting. Our algorithm can be applied to any similarity matrix and runs in sublinear time in the size of the matrix, producing a rank-s approximation with just O(ns) similarity computations.

We show that our method, along with a simple variant of CUR decomposition, performs very well in approximating a variety of similarity matrices arising in NLP tasks. We demonstrate high accuracy of the approximated similarity matrices in tasks of document classification, sentence similarity, and cross-document coreference.

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Detailed Facial Geometry Recovery from Multi-View Images by Learning an Implicit Function

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Sharp Restricted Isometry Property Bounds for Low-Rank Matrix Recovery Problems with Corrupted Measurements

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Next from AAAI 2022

Detailed Facial Geometry Recovery from Multi-View Images by Learning an Implicit Function

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Sharp Restricted Isometry Property Bounds for Low-Rank Matrix Recovery Problems with Corrupted Measurements

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