CoopInit: Initializing Generative Adversarial Networks via Cooperative Learning

Numerous research efforts have been made to stabilize the training of the Generative Adversarial Networks (GANs), such as through regularization and architecture design. However, we identify the instability can also arise from the fragile balance at the early stage of adversarial learning. This paper proposes the CoopInit, a simple yet effective cooperative learning-based initialization strategy that can quickly learn a good starting point for GANs, with a very small computation overhead during training. The proposed algorithm consists of two learning stages: (i) Cooperative initialization stage: The discriminator of GAN is treated as an energy-based model (EBM) and is optimized via maximum likelihood estimation (MLE), with the help of the GAN's generator to provide synthetic data to approximate the learning gradients. The EBM also guides the MLE learning of the generator via MCMC teaching; (ii) Adversarial finalization stage: After a few iterations of initialization, the algorithm seamlessly transits to the regular mini-max adversarial training until convergence. The motivation is that the MLE-based initialization stage drives the model towards mode coverage, which is helpful in alleviating the issue of mode dropping during the adversarial learning stage. We demonstrate the effectiveness of the proposed approach on image generation and one-sided unpaired image-to-image translation tasks through extensive experiments.

Sparse Recovery with Shuffled Labels: Statistical Limits and Practical Estimators

This paper considers the sparse recovery with shuffled labels, i.e., $\by = \bPitrue \bX \bbetatrue + \bw$, where $\by \in \RR^n$, $\bPi\in \RR^{n\times n}$, $\bX\in \RR^{n\times p}$, $\bbetatrue\in \RR^p$, $\bw \in \RR^n$ denote the sensing result, the unknown permutation matrix, the design matrix, the sparse signal, and the additive noise, respectively. Our goal is to reconstruct both the permutation matrix $\bPitrue$ and the sparse signal $\bbetatrue$. We investigate this problem from both the statistical and computational aspects. From the statistical aspect, we first establish the minimax lower bounds on the sample number $n$ and the \emph{signal-to-noise ratio} ($\snr$) for the correct recovery of permutation matrix $\bPitrue$ and the support set $\supp(\bbetatrue)$, to be more specific, $n \gtrsim k\log p$ and $\log\snr \gtrsim \log n + \frac{k\log p}{n}$. Then, we confirm the tightness of these minimax lower bounds by presenting an exhaustive-search based estimator whose performance matches the lower bounds thereof up to some multiplicative constants. From the computational aspect, we impose a parsimonious assumption on the number of permuted rows and propose a computationally-efficient estimator accordingly. Moreover, we show that our proposed estimator can obtain the ground-truth $(\bPitrue, \supp(\bbetatrue))$ under mild conditions. Furthermore, we provide numerical experiments to corroborate our claims.

AnimeDiffusion: Anime Face Line Drawing Colorization via Diffusion Models

It is a time-consuming and tedious work for manually colorizing anime line drawing images, which is an essential stage in cartoon animation creation pipeline. Reference-based line drawing colorization is a challenging task that relies on the precise cross-domain long-range dependency modelling between the line drawing and reference image. Existing learning methods still utilize generative adversarial networks (GANs) as one key module of their model architecture. In this paper, we propose a novel method called AnimeDiffusion using diffusion models that performs anime face line drawing colorization automatically. To the best of our knowledge, this is the first diffusion model tailored for anime content creation. In order to solve the huge training consumption problem of diffusion models, we design a hybrid training strategy, first pre-training a diffusion model with classifier-free guidance and then fine-tuning it with image reconstruction guidance. We find that with a few iterations of fine-tuning, the model shows wonderful colorization performance, as illustrated in Fig. 1. For training AnimeDiffusion, we conduct an anime face line drawing colorization benchmark dataset, which contains 31696 training data and 579 testing data. We hope this dataset can fill the gap of no available high resolution anime face dataset for colorization method evaluation. Through multiple quantitative metrics evaluated on our dataset and a user study, we demonstrate AnimeDiffusion outperforms state-of-the-art GANs-based models for anime face line drawing colorization. We also collaborate with professional artists to test and apply our AnimeDiffusion for their creation work. We release our code on https://github.com/xq-meng/AnimeDiffusion.

Steering Graph Neural Networks with Pinning Control

In the semi-supervised setting where labeled data are largely limited, it remains to be a big challenge for message passing based graph neural networks (GNNs) to learn feature representations for the nodes with the same class label that is distributed discontinuously over the graph. To resolve the discontinuous information transmission problem, we propose a control principle to supervise representation learning by leveraging the prototypes (i.e., class centers) of labeled data. Treating graph learning as a discrete dynamic process and the prototypes of labeled data as "desired" class representations, we borrow the pinning control idea from automatic control theory to design learning feedback controllers for the feature learning process, attempting to minimize the differences between message passing derived features and the class prototypes in every round so as to generate class-relevant features. Specifically, we equip every node with an optimal controller in each round through learning the matching relationships between nodes and the class prototypes, enabling nodes to rectify the aggregated information from incompatible neighbors in a graph with strong heterophily. Our experiments demonstrate that the proposed PCGCN model achieves better performances than deep GNNs and other competitive heterophily-oriented methods, especially when the graph has very few labels and strong heterophily.

Building Shortcuts between Distant Nodes with Biaffine Mapping for Graph Convolutional Networks

Multiple recent studies show a paradox in graph convolutional networks (GCNs), that is, shallow architectures limit the capability of learning information from high-order neighbors, while deep architectures suffer from over-smoothing or over-squashing. To enjoy the simplicity of shallow architectures and overcome their limits of neighborhood extension, in this work, we introduce Biaffine technique to improve the expressiveness of graph convolutional networks with a shallow architecture. The core design of our method is to learn direct dependency on long-distance neighbors for nodes, with which only one-hop message passing is capable of capturing rich information for node representation. Besides, we propose a multi-view contrastive learning method to exploit the representations learned from long-distance dependencies. Extensive experiments on nine graph benchmark datasets suggest that the shallow biaffine graph convolutional networks (BAGCN) significantly outperforms state-of-the-art GCNs (with deep or shallow architectures) on semi-supervised node classification. We further verify the effectiveness of biaffine design in node representation learning and the performance consistency on different sizes of training data.

OPORP: One Permutation + One Random Projection

Consider two $D$-dimensional data vectors (e.g., embeddings): $u, v$. In many embedding-based retrieval (EBR) applications where the vectors are generated from trained models, $D=256\sim 1024$ are common. In this paper, OPORP (one permutation + one random projection) uses a variant of the ``count-sketch'' type of data structures for achieving data reduction/compression. With OPORP, we first apply a permutation on the data vectors. A random vector $r$ is generated i.i.d. with moments: $E(r_i) = 0, E(r_i^2)=1, E(r_i^3) =0, E(r_i^4)=s$. We multiply (as dot product) $r$ with all permuted data vectors. Then we break the $D$ columns into $k$ equal-length bins and aggregate (i.e., sum) the values in each bin to obtain $k$ samples from each data vector. One crucial step is to normalize the $k$ samples to the unit $l_2$ norm. We show that the estimation variance is essentially: $(s-1)A + \frac{D-k}{D-1}\frac{1}{k}\left[ (1-\rho^2)^2 -2A\right]$, where $A\geq 0$ is a function of the data ($u,v$). This formula reveals several key properties: (1) We need $s=1$. (2) The factor $\frac{D-k}{D-1}$ can be highly beneficial in reducing variances. (3) The term $\frac{1}{k}(1-\rho^2)^2$ is actually the asymptotic variance of the classical correlation estimator. We illustrate that by letting the $k$ in OPORP to be $k=1$ and repeat the procedure $m$ times, we exactly recover the work of ``very spars random projections'' (VSRP). This immediately leads to a normalized estimator for VSRP which substantially improves the original estimator of VSRP. In summary, with OPORP, the two key steps: (i) the normalization and (ii) the fixed-length binning scheme, have considerably improved the accuracy in estimating the cosine similarity, which is a routine (and crucial) task in modern embedding-based retrieval (EBR) applications.

A Tale of Two Latent Flows: Learning Latent Space Normalizing Flow with Short-run Langevin Flow for Approximate Inference

We study a normalizing flow in the latent space of a top-down generator model, in which the normalizing flow model plays the role of the informative prior model of the generator. We propose to jointly learn the latent space normalizing flow prior model and the top-down generator model by a Markov chain Monte Carlo (MCMC)-based maximum likelihood algorithm, where a short-run Langevin sampling from the intractable posterior distribution is performed to infer the latent variables for each observed example, so that the parameters of the normalizing flow prior and the generator can be updated with the inferred latent variables. We show that, under the scenario of non-convergent short-run MCMC, the finite step Langevin dynamics is a flow-like approximate inference model and the learning objective actually follows the perturbation of the maximum likelihood estimation (MLE). We further point out that the learning framework seeks to (i) match the latent space normalizing flow and the aggregated posterior produced by the short-run Langevin flow, and (ii) bias the model from MLE such that the short-run Langevin flow inference is close to the true posterior. Empirical results of extensive experiments validate the effectiveness of the proposed latent space normalizing flow model in the tasks of image generation, image reconstruction, anomaly detection, supervised image inpainting and unsupervised image recovery.

Sharper Analysis for Minibatch Stochastic Proximal Point Methods: Stability, Smoothness, and Deviation

The stochastic proximal point (SPP) methods have gained recent attention for stochastic optimization, with strong convergence guarantees and superior robustness to the classic stochastic gradient descent (SGD) methods showcased at little to no cost of computational overhead added. In this article, we study a minibatch variant of SPP, namely M-SPP, for solving convex composite risk minimization problems. The core contribution is a set of novel excess risk bounds of M-SPP derived through the lens of algorithmic stability theory. Particularly under smoothness and quadratic growth conditions, we show that M-SPP with minibatch-size $n$ and iteration count $T$ enjoys an in-expectation fast rate of convergence consisting of an $\mathcal{O}\left(\frac{1}{T^2}\right)$ bias decaying term and an $\mathcal{O}\left(\frac{1}{nT}\right)$ variance decaying term. In the small-$n$-large-$T$ setting, this result substantially improves the best known results of SPP-type approaches by revealing the impact of noise level of model on convergence rate. In the complementary small-$T$-large-$n$ regime, we provide a two-phase extension of M-SPP to achieve comparable convergence rates. Moreover, we derive a near-tight high probability (over the randomness of data) bound on the parameter estimation error of a sampling-without-replacement variant of M-SPP. Numerical evidences are provided to support our theoretical predictions when substantialized to Lasso and logistic regression models.

Exploration in Model-based Reinforcement Learning with Randomized Reward

Model-based Reinforcement Learning (MBRL) has been widely adapted due to its sample efficiency. However, existing worst-case regret analysis typically requires optimistic planning, which is not realistic in general. In contrast, motivated by the theory, empirical study utilizes ensemble of models, which achieve state-of-the-art performance on various testing environments. Such deviation between theory and empirical study leads us to question whether randomized model ensemble guarantee optimism, and hence the optimal worst-case regret? This paper partially answers such question from the perspective of reward randomization, a scarcely explored direction of exploration with MBRL. We show that under the kernelized linear regulator (KNR) model, reward randomization guarantees a partial optimism, which further yields a near-optimal worst-case regret in terms of the number of interactions. We further extend our theory to generalized function approximation and identified conditions for reward randomization to attain provably efficient exploration. Correspondingly, we propose concrete examples of efficient reward randomization. To the best of our knowledge, our analysis establishes the first worst-case regret analysis on randomized MBRL with function approximation.

Rethinking the Structure of Stochastic Gradients: Empirical and Statistical Evidence

Stochastic gradients closely relate to both optimization and generalization of deep neural networks (DNNs). Some works attempted to explain the success of stochastic optimization for deep learning by the arguably heavy-tail properties of gradient noise, while other works presented theoretical and empirical evidence against the heavy-tail hypothesis on gradient noise. Unfortunately, formal statistical tests for analyzing the structure and heavy tails of stochastic gradients in deep learning are still under-explored. In this paper, we mainly make two contributions. First, we conduct formal statistical tests on the distribution of stochastic gradients and gradient noise across both parameters and iterations. Our statistical tests reveal that dimension-wise gradients usually exhibit power-law heavy tails, while iteration-wise gradients and stochastic gradient noise caused by minibatch training usually do not exhibit power-law heavy tails. Second, we further discover that the covariance spectra of stochastic gradients have the power-law structures in deep learning. While previous papers believed that the anisotropic structure of stochastic gradients matters to deep learning, they did not expect the gradient covariance can have such an elegant mathematical structure. Our work challenges the existing belief and provides novel insights on the structure of stochastic gradients in deep learning.