Early Stage Convergence and Global Convergence of Training Mildly Parameterized Neural Networks

The convergence of GD and SGD when training mildly parameterized neural networks starting from random initialization is studied. For a broad range of models and loss functions, including the most commonly used square loss and cross entropy loss, we prove an ``early stage convergence'' result. We show that the loss is decreased by a significant amount in the early stage of the training, and this decrease is fast. Furthurmore, for exponential type loss functions, and under some assumptions on the training data, we show global convergence of GD. Instead of relying on extreme over-parameterization, our study is based on a microscopic analysis of the activation patterns for the neurons, which helps us derive more powerful lower bounds for the gradient. The results on activation patterns, which we call ``neuron partition'', help build intuitions for understanding the behavior of neural networks' training dynamics, and may be of independent interest.

PillarNet: Real-Time and High-Performance Pillar-based 3D Object Detection

Real-time and high-performance 3D object detection is of critical importance for autonomous driving. Recent top-performing 3D object detectors mainly rely on point-based or 3D voxel-based convolutions, which are both computationally inefficient for onboard deployment. While recent researches focus on point-based or 3D voxel-based convolutions for higher performance, these methods fail to meet latency and power efficiency requirements especially for deployment on embedded devices. In contrast, pillar-based methods use merely 2D convolutions, which consume less computation resources, but they lag far behind their voxel-based counterparts in detection accuracy. However, the superiority of such 3D voxel-based methods over pillar-based methods is still broadly attributed to the effectiveness of 3D convolution neural network (CNN). In this paper, by examining the primary performance gap between pillar- and voxel-based detectors, we develop a real-time and high-performance pillar-based detector, dubbed PillarNet. The proposed PillarNet consists of a powerful encoder network for effective pillar feature learning, a neck network for spatial-semantic feature fusion and the commonly used detect head. Using only 2D convolutions, PillarNet is flexible to an optional pillar size and compatible with classical 2D CNN backbones, such as VGGNet and ResNet. Additionally, PillarNet benefits from our designed orientation-decoupled IoU regression loss along with the IoU-aware prediction branch. Extensive experimental results on large-scale nuScenes Dataset and Waymo Open Dataset demonstrate that the proposed PillarNet performs well over the state-of-the-art 3D detectors in terms of effectiveness and efficiency. Code will be made publicly available.

PillarNet: High-Performance Pillar-based 3D Object Detection

Real-time and high-performance 3D object detection is of critical importance for autonomous driving. Recent top-performing 3D object detectors mainly rely on point-based or 3D voxel-based convolutions, which are both computationally inefficient for onboard deployment. In contrast, pillar-based methods use merely 2D convolutions, which consume less computation resources, but they lag far behind their voxel-based counterparts in detection accuracy. In this paper, by examining the primary performance gap between pillar- and voxel-based detectors, we develop a real-time and high-performance pillar-based detector, dubbed PillarNet. The proposed PillarNet consists of a powerful encoder network for effective pillar feature learning, a neck network for spatial-semantic feature fusion and the commonly used detect head. Using only 2D convolutions, PillarNet is flexible to an optional pillar size and compatible with classical 2D CNN backbones, such as VGGNet and ResNet. Additionally, PillarNet benefits from an orientation-decoupled IoU regression loss along with the IoU-aware prediction branch. Extensive experimental results on the large-scale nuScenes Dataset and Waymo Open Dataset demonstrate that the proposed PillarNet performs well over the state-of-the-art 3D detectors in terms of effectiveness and efficiency.

The Multiscale Structure of Neural Network Loss Functions: The Effect on Optimization and Origin

Local quadratic approximation has been extensively used to study the optimization of neural network loss functions around the minimum. Though, it usually holds in a very small neighborhood of the minimum, and cannot explain many phenomena observed during the optimization process. In this work, we study the structure of neural network loss functions and its implication on optimization in a region beyond the reach of good quadratic approximation. Numerically, we observe that neural network loss functions possesses a multiscale structure, manifested in two ways: (1) in a neighborhood of minima, the loss mixes a continuum of scales and grows subquadratically, and (2) in a larger region, the loss shows several separate scales clearly. Using the subquadratic growth, we are able to explain the Edge of Stability phenomenon[4] observed for gradient descent (GD) method. Using the separate scales, we explain the working mechanism of learning rate decay by simple examples. Finally, we study the origin of the multiscale structure and propose that the non-uniformity of training data is one of its cause. By constructing a two-layer neural network problem we show that training data with different magnitudes give rise to different scales of the loss function, producing subquadratic growth or multiple separate scales.

Exploring Frequency Adversarial Attacks for Face Forgery Detection

Various facial manipulation techniques have drawn serious public concerns in morality, security, and privacy. Although existing face forgery classifiers achieve promising performance on detecting fake images, these methods are vulnerable to adversarial examples with injected imperceptible perturbations on the pixels. Meanwhile, many face forgery detectors always utilize the frequency diversity between real and fake faces as a crucial clue. In this paper, instead of injecting adversarial perturbations into the spatial domain, we propose a frequency adversarial attack method against face forgery detectors. Concretely, we apply discrete cosine transform (DCT) on the input images and introduce a fusion module to capture the salient region of adversary in the frequency domain. Compared with existing adversarial attacks (e.g. FGSM, PGD) in the spatial domain, our method is more imperceptible to human observers and does not degrade the visual quality of the original images. Moreover, inspired by the idea of meta-learning, we also propose a hybrid adversarial attack that performs attacks in both the spatial and frequency domains. Extensive experiments indicate that the proposed method fools not only the spatial-based detectors but also the state-of-the-art frequency-based detectors effectively. In addition, the proposed frequency attack enhances the transferability across face forgery detectors as black-box attacks.

Facial Geometric Detail Recovery via Implicit Representation

Learning a dense 3D model with fine-scale details from a single facial image is highly challenging and ill-posed. To address this problem, many approaches fit smooth geometries through facial prior while learning details as additional displacement maps or personalized basis. However, these techniques typically require vast datasets of paired multi-view data or 3D scans, whereas such datasets are scarce and expensive. To alleviate heavy data dependency, we present a robust texture-guided geometric detail recovery approach using only a single in-the-wild facial image. More specifically, our method combines high-quality texture completion with the powerful expressiveness of implicit surfaces. Initially, we inpaint occluded facial parts, generate complete textures, and build an accurate multi-view dataset of the same subject. In order to estimate the detailed geometry, we define an implicit signed distance function and employ a physically-based implicit renderer to reconstruct fine geometric details from the generated multi-view images. Our method not only recovers accurate facial details but also decomposes normals, albedos, and shading parts in a self-supervised way. Finally, we register the implicit shape details to a 3D Morphable Model template, which can be used in traditional modeling and rendering pipelines. Extensive experiments demonstrate that the proposed approach can reconstruct impressive facial details from a single image, especially when compared with state-of-the-art methods trained on large datasets.

Provably convergent quasistatic dynamics for mean-field two-player zero-sum games

In this paper, we study the problem of finding mixed Nash equilibrium for mean-field two-player zero-sum games. Solving this problem requires optimizing over two probability distributions. We consider a quasistatic Wasserstein gradient flow dynamics in which one probability distribution follows the Wasserstein gradient flow, while the other one is always at the equilibrium. Theoretical analysis are conducted on this dynamics, showing its convergence to the mixed Nash equilibrium under mild conditions. Inspired by the continuous dynamics of probability distributions, we derive a quasistatic Langevin gradient descent method with inner-outer iterations, and test the method on different problems, including training mixture of GANs.

Missing Data Imputation and Acquisition with Deep Hierarchical Models and Hamiltonian Monte Carlo

Variational Autoencoders (VAEs) have recently been highly successful at imputing and acquiring heterogeneous missing data and identifying outliers. However, within this specific application domain, existing VAE methods are restricted by using only one layer of latent variables and strictly Gaussian posterior approximations. To address these limitations, we present HH-VAEM, a Hierarchical VAE model for mixed-type incomplete data that uses Hamiltonian Monte Carlo with automatic hyper-parameter tuning for improved approximate inference. Our experiments show that HH-VAEM outperforms existing baselines in the tasks of missing data imputation, supervised learning and outlier identification with missing features. Finally, we also present a sampling-based approach for efficiently computing the information gain when missing features are to be acquired with HH-VAEM. Our experiments show that this sampling-based approach is superior to alternatives based on Gaussian approximations.

Deep End-to-end Causal Inference

Causal inference is essential for data-driven decision making across domains such as business engagement, medical treatment or policy making. However, research on causal discovery and inference has evolved separately, and the combination of the two domains is not trivial. In this work, we develop Deep End-to-end Causal Inference (DECI), a single flow-based method that takes in observational data and can perform both causal discovery and inference, including conditional average treatment effect (CATE) estimation. We provide a theoretical guarantee that DECI can recover the ground truth causal graph under mild assumptions. In addition, our method can handle heterogeneous, real-world, mixed-type data with missing values, allowing for both continuous and discrete treatment decisions. Moreover, the design principle of our method can generalize beyond DECI, providing a general End-to-end Causal Inference (ECI) recipe, which enables different ECI frameworks to be built using existing methods. Our results show the superior performance of DECI when compared to relevant baselines for both causal discovery and (C)ATE estimation in over a thousand experiments on both synthetic datasets and other causal machine learning benchmark datasets.

Identifiable Generative Models for Missing Not at Random Data Imputation

Real-world datasets often have missing values associated with complex generative processes, where the cause of the missingness may not be fully observed. This is known as missing not at random (MNAR) data. However, many imputation methods do not take into account the missingness mechanism, resulting in biased imputation values when MNAR data is present. Although there are a few methods that have considered the MNAR scenario, their model's identifiability under MNAR is generally not guaranteed. That is, model parameters can not be uniquely determined even with infinite data samples, hence the imputation results given by such models can still be biased. This issue is especially overlooked by many modern deep generative models. In this work, we fill in this gap by systematically analyzing the identifiability of generative models under MNAR. Furthermore, we propose a practical deep generative model which can provide identifiability guarantees under mild assumptions, for a wide range of MNAR mechanisms. Our method demonstrates a clear advantage for tasks on both synthetic data and multiple real-world scenarios with MNAR data.