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Deep neural networks are widely used prediction algorithms whose performance often improves as the number of weights increases, leading to over-parametrization. We consider a two-layered neural network whose first layer is frozen while the last layer is trainable, known as the random feature model. We study over-parametrization in the context of a student-teacher framework by deriving a set of differential equations for the learning dynamics. For any finite ratio of hidden layer size and input dimension, the student cannot generalize perfectly, and we compute the non-zero asymptotic generalization error. Only when the student's hidden layer size is exponentially larger than the input dimension, an approach to perfect generalization is possible.

We consider stochastic approximations of sampling algorithms, such as Stochastic Gradient Langevin Dynamics (SGLD) and the Random Batch Method (RBM) for Interacting Particle Dynamcs (IPD). We observe that the noise introduced by the stochastic approximation is nearly Gaussian due to the Central Limit Theorem (CLT) while the driving Brownian motion is exactly Gaussian. We harness this structure to absorb the stochastic approximation error inside the diffusion process, and obtain improved convergence guarantees for these algorithms. For SGLD, we prove the first stable convergence rate in KL divergence without requiring uniform warm start, assuming the target density satisfies a Log-Sobolev Inequality. Our result implies superior first-order oracle complexity compared to prior works, under significantly milder assumptions. We also prove the first guarantees for SGLD under even weaker conditions such as H\"{o}lder smoothness and Poincare Inequality, thus bridging the gap between the state-of-the-art guarantees for LMC and SGLD. Our analysis motivates a new algorithm called covariance correction, which corrects for the additional noise introduced by the stochastic approximation by rescaling the strength of the diffusion. Finally, we apply our techniques to analyze RBM, and significantly improve upon the guarantees in prior works (such as removing exponential dependence on horizon), under minimal assumptions.

This paper presents a new adversarial training framework for image inpainting with segmentation confusion adversarial training (SCAT) and contrastive learning. SCAT plays an adversarial game between an inpainting generator and a segmentation network, which provides pixel-level local training signals and can adapt to images with free-form holes. By combining SCAT with standard global adversarial training, the new adversarial training framework exhibits the following three advantages simultaneously: (1) the global consistency of the repaired image, (2) the local fine texture details of the repaired image, and (3) the flexibility of handling images with free-form holes. Moreover, we propose the textural and semantic contrastive learning losses to stabilize and improve our inpainting model's training by exploiting the feature representation space of the discriminator, in which the inpainting images are pulled closer to the ground truth images but pushed farther from the corrupted images. The proposed contrastive losses better guide the repaired images to move from the corrupted image data points to the real image data points in the feature representation space, resulting in more realistic completed images. We conduct extensive experiments on two benchmark datasets, demonstrating our model's effectiveness and superiority both qualitatively and quantitatively.

The conditional moment problem is a powerful formulation for describing structural causal parameters in terms of observables, a prominent example being instrumental variable regression. A standard approach reduces the problem to a finite set of marginal moment conditions and applies the optimally weighted generalized method of moments (OWGMM), but this requires we know a finite set of identifying moments, can still be inefficient even if identifying, or can be theoretically efficient but practically unwieldy if we use a growing sieve of moment conditions. Motivated by a variational minimax reformulation of OWGMM, we define a very general class of estimators for the conditional moment problem, which we term the variational method of moments (VMM) and which naturally enables controlling infinitely-many moments. We provide a detailed theoretical analysis of multiple VMM estimators, including ones based on kernel methods and neural nets, and provide conditions under which these are consistent, asymptotically normal, and semiparametrically efficient in the full conditional moment model. We additionally provide algorithms for valid statistical inference based on the same kind of variational reformulations, both for kernel- and neural-net-based varieties. Finally, we demonstrate the strong performance of our proposed estimation and inference algorithms in a detailed series of synthetic experiments.

When dealing with deep neural network (DNN) applications on edge devices, continuously updating the model is important. Although updating a model with real incoming data is ideal, using all of them is not always feasible due to limits, such as labeling and communication costs. Thus, it is necessary to filter and select the data to use for training (i.e., active learning) on the device. In this paper, we formalize a practical active learning problem for DNNs on edge devices and propose a general task-agnostic framework to tackle this problem, which reduces it to a stream submodular maximization. This framework is light enough to be run with low computational resources, yet provides solutions whose quality is theoretically guaranteed thanks to the submodular property. Through this framework, we can configure data selection criteria flexibly, including using methods proposed in previous active learning studies. We evaluate our approach on both classification and object detection tasks in a practical setting to simulate a real-life scenario. The results of our study show that the proposed framework outperforms all other methods in both tasks, while running at a practical speed on real devices.

This book develops an effective theory approach to understanding deep neural networks of practical relevance. Beginning from a first-principles component-level picture of networks, we explain how to determine an accurate description of the output of trained networks by solving layer-to-layer iteration equations and nonlinear learning dynamics. A main result is that the predictions of networks are described by nearly-Gaussian distributions, with the depth-to-width aspect ratio of the network controlling the deviations from the infinite-width Gaussian description. We explain how these effectively-deep networks learn nontrivial representations from training and more broadly analyze the mechanism of representation learning for nonlinear models. From a nearly-kernel-methods perspective, we find that the dependence of such models' predictions on the underlying learning algorithm can be expressed in a simple and universal way. To obtain these results, we develop the notion of representation group flow (RG flow) to characterize the propagation of signals through the network. By tuning networks to criticality, we give a practical solution to the exploding and vanishing gradient problem. We further explain how RG flow leads to near-universal behavior and lets us categorize networks built from different activation functions into universality classes. Altogether, we show that the depth-to-width ratio governs the effective model complexity of the ensemble of trained networks. By using information-theoretic techniques, we estimate the optimal aspect ratio at which we expect the network to be practically most useful and show how residual connections can be used to push this scale to arbitrary depths. With these tools, we can learn in detail about the inductive bias of architectures, hyperparameters, and optimizers.

Recent advances in maximizing mutual information (MI) between the source and target have demonstrated its effectiveness in text generation. However, previous works paid little attention to modeling the backward network of MI (i.e., dependency from the target to the source), which is crucial to the tightness of the variational information maximization lower bound. In this paper, we propose Adversarial Mutual Information (AMI): a text generation framework which is formed as a novel saddle point (min-max) optimization aiming to identify joint interactions between the source and target. Within this framework, the forward and backward networks are able to iteratively promote or demote each other's generated instances by comparing the real and synthetic data distributions. We also develop a latent noise sampling strategy that leverages random variations at the high-level semantic space to enhance the long term dependency in the generation process. Extensive experiments based on different text generation tasks demonstrate that the proposed AMI framework can significantly outperform several strong baselines, and we also show that AMI has potential to lead to a tighter lower bound of maximum mutual information for the variational information maximization problem.

We present a new method to learn video representations from large-scale unlabeled video data. Ideally, this representation will be generic and transferable, directly usable for new tasks such as action recognition and zero or few-shot learning. We formulate unsupervised representation learning as a multi-modal, multi-task learning problem, where the representations are shared across different modalities via distillation. Further, we introduce the concept of loss function evolution by using an evolutionary search algorithm to automatically find optimal combination of loss functions capturing many (self-supervised) tasks and modalities. Thirdly, we propose an unsupervised representation evaluation metric using distribution matching to a large unlabeled dataset as a prior constraint, based on Zipf's law. This unsupervised constraint, which is not guided by any labeling, produces similar results to weakly-supervised, task-specific ones. The proposed unsupervised representation learning results in a single RGB network and outperforms previous methods. Notably, it is also more effective than several label-based methods (e.g., ImageNet), with the exception of large, fully labeled video datasets.

When and why can a neural network be successfully trained? This article provides an overview of optimization algorithms and theory for training neural networks. First, we discuss the issue of gradient explosion/vanishing and the more general issue of undesirable spectrum, and then discuss practical solutions including careful initialization and normalization methods. Second, we review generic optimization methods used in training neural networks, such as SGD, adaptive gradient methods and distributed methods, and theoretical results for these algorithms. Third, we review existing research on the global issues of neural network training, including results on bad local minima, mode connectivity, lottery ticket hypothesis and infinite-width analysis.

With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of long-tailed data distribution (i.e., a few classes account for most of the data, while most classes are under-represented). Existing solutions typically adopt class re-balancing strategies such as re-sampling and re-weighting based on the number of observations for each class. In this work, we argue that as the number of samples increases, the additional benefit of a newly added data point will diminish. We introduce a novel theoretical framework to measure data overlap by associating with each sample a small neighboring region rather than a single point. The effective number of samples is defined as the volume of samples and can be calculated by a simple formula $(1-\beta^{n})/(1-\beta)$, where $n$ is the number of samples and $\beta \in [0,1)$ is a hyperparameter. We design a re-weighting scheme that uses the effective number of samples for each class to re-balance the loss, thereby yielding a class-balanced loss. Comprehensive experiments are conducted on artificially induced long-tailed CIFAR datasets and large-scale datasets including ImageNet and iNaturalist. Our results show that when trained with the proposed class-balanced loss, the network is able to achieve significant performance gains on long-tailed datasets.