Diffusion models are typically trained using pointwise reconstruction objectives that are agnostic to the spectral and multi-scale structure of natural signals. We propose a loss-level spectral regularization framework that augments standard diffusion training with differentiable Fourier- and wavelet-domain losses, without modifying the diffusion process, model architecture, or sampling procedure. The proposed regularizers act as soft inductive biases that encourage appropriate frequency balance and coherent multi-scale structure in generated samples. Our approach is compatible with DDPM, DDIM, and EDM formulations and introduces negligible computational overhead. Experiments on image and audio generation demonstrate consistent improvements in sample quality, with the largest gains observed on higher-resolution, unconditional datasets where fine-scale structure is most challenging to model.
RED-DiffEq: Regularization by denoising diffusion models for solving inverse PDE problems with application to full waveform inversion
Department of Statistics and Data Science, Yale University（耶鲁大学统计与数据科学系）；School of Data Science and Society, University of North Carolina at Chapel Hill（北卡罗来纳大学夏洛特分校数据科学与社会学院）
Shenzhen University（深圳大学）；University of Nottingham（诺丁汉大学）
Despite excellent progress in recent years, mode collapse remains a major unsolved problem in generative adversarial networks (GANs).In this paper, we present spectral regularization for GANs (SR-GANs), a new and robust method for combating the mode collapse problem in GANs. Theoretical analysis shows that the optimal solution to the discriminator has a strong relationship to the spectral distributions of the weight matrix.Therefore, we monitor the spectral distribution in the discriminator of spectral normalized GANs (SN-GANs), and discover a phenomenon which we refer to as spectral collapse,…
UiT The Arctic University of Norway（挪威北极大学UiT）；NORCE Norwegian Research Centre（NORCE挪威研究中心）
Full characterization of the spectral behavior of generative models based on neural networks remains an open issue. Recent research has focused heavily on generative adversarial networks and the high-frequency discrepancies between real and generated images. The current solution to avoid this is to either replace transposed convolutions with bilinear up-sampling or add a spectral regularization term in the generator. It is well known that Variational Autoencoders (VAEs) also suffer from these issues. In this work, we propose a simple 2D Fourier transform-based spectral regularization loss for …
An Analysis of Regularization and Fokker-Planck Residuals in Diffusion Models for Image Generation
MCIN/ AEI / 10.13039/501100011033 / FEDER, UE（MCIN/ AEI / 10.残补10.13039/501100011033 / FEDER, UE）；Autonomous Community of Madrid（马德里自治区）；ELLIS Unit Madrid（马德里ELLIS单位）；Centro de Computación Científica-Universidad Autónoma de Madrid (CCC-UAM)（马德里自治大学计算中心（CCC-UAM））
University of California, Los Angeles（加利福尼亚大学洛杉矶分校）；University of Minnesota Twin Cities（明尼苏达大学双城分校）；Chinese University of Hong Kong, Shenzhen（香港中文大学（深圳））
Perceptually Regularized Diffusion Model for Image Super-Resolution
University of North Carolina（北卡罗来纳大学）；Texas Tech University（德克萨斯理工大学）；Case Western Reserve University（凯斯西储大学）；University of Houston（休斯顿大学）；University of Kentucky（肯塔基大学）
Indian Institute of Science（印度科学学院）；Google Research（谷歌研究院）
Deep long-tailed learning aims to train useful deep networks on practical, real-world imbalanced distributions, wherein most labels of the tail classes are associated with a few samples. There has been a large body of work to train discriminative models for visual recognition on long-tailed distribution. In contrast, we aim to train conditional Generative Adversarial Networks, a class of image generation models on long-tailed distributions. We find that similar to recognition, state-of-the-art methods for image generation also suffer from performance degradation on tail classes. The performanc…
Generative Adversarial Networks (GANs) are known to be difficult to train, despite considerable research effort. Several regularization techniques for stabilizing training have been proposed, but they introduce non-trivial computational overheads and interact poorly with existing techniques like spectral normalization. In this work, we propose a simple, effective training stabilizer based on the notion of consistency regularization---a popular technique in the semi-supervised learning literature. In particular, we augment data passing into the GAN discriminator and penalize the sensitivity of …
University of California（加利福尼亚大学）；INRIA（法国国家信息与自动化研究所）；Laboratoire d’Informatique de l’Ecole Normale Supérieure（巴黎高等师范学院计算机科学实验室）；INSEAD（欧洲工商管理学院）；Mines ParisTech（巴黎高等矿业学院）；Institut Curie（居里研究所）；Inserm（法国国家健康与医学研究院）
We present a general approach for collaborative filtering (CF) using spectral regularization to learn linear operators from "users" to the "objects" they rate. Recent low-rank type matrix completion approaches to CF are shown to be special cases. However, unlike existing regularization based CF methods, our approach can be used to also incorporate information such as attributes of the users or the objects -- a limitation of existing regularization based CF methods. We then provide novel representer theorems that we use to develop new estimation methods. We provide learning algorithms based on …
GIPSA-lab（GIPSA实验室）；CNRS（法国国家科学研究中心）；Grenoble INP（格勒诺布尔国立理工学院）；L2S（L2S实验室）；University of Paris Saclay（巴黎萨克雷大学）
Regularization of the classical Laplacian matrices was empirically shown to improve spectral clustering in sparse networks. It was observed that small regularizations are preferable, but this point was left as a heuristic argument. In this paper we formally determine a proper regularization which is intimately related to alternative state-of-the-art spectral techniques for sparse graphs.
National Institute of Informatics（国立信息学研究所）；Preferred Networks, Inc.（Preferred Networks公司）
We investigate the generalizability of deep learning based on the sensitivity to input perturbation. We hypothesize that the high sensitivity to the perturbation of data degrades the performance on it. To reduce the sensitivity to perturbation, we propose a simple and effective regularization method, referred to as spectral norm regularization, which penalizes the high spectral norm of weight matrices in neural networks. We provide supportive evidence for the abovementioned hypothesis by experimentally confirming that the models trained using spectral norm regularization exhibit better general…
We pursue a line of research that seeks to regularize the spectral norm of the Jacobian of the input-output mapping for deep neural networks. While previous work rely on upper bounding techniques, we provide a scheme that targets the exact spectral norm. We showcase that our algorithm achieves an improved generalization performance compared to previous spectral regularization techniques while simultaneously maintaining a strong safeguard against natural and adversarial noise. Moreover, we further explore some previous reasoning concerning the strong adversarial protection that Jacobian regular…
UCLA（加州大学洛杉矶分校）；Max Planck Institute for Mathematics in the Sciences（马克斯·普朗克数学科学研究所）
We propose regularization strategies for learning discriminative models that are robust to in-class variations of the input data. We use the Wasserstein-2 geometry to capture semantically meaningful neighborhoods in the space of images, and define a corresponding input-dependent additive noise data augmentation model. Expanding and integrating the augmented loss yields an effective Tikhonov-type Wasserstein diffusion smoothness regularizer. This approach allows us to apply high levels of regularization and train functions that have low variability within classes but remain flexible across clas…
Non-Convex Optimization with Spectral Radius Regularization
Engineering Sciences and Applied Mathematics, Northwestern University（西北大学工程科学与应用数学系）；Industrial Engineering and Management Sciences, Northwestern University（西北大学工业工程与管理科学系）；Preventive Medicine (Health and Biomedical Informatics), Northwestern University（西北大学预防医学（健康与生物医学信息学））
Indian Institute of Space Science and Technology（印度空间科学与技术研究所）
Graph convolutional neural networks (GCNNs) have been widely used in graph learning. It has been observed that the smoothness functional on graphs can be defined in terms of the graph Laplacian. This fact points out in the direction of using Laplacian in deriving regularization operators on graphs and its consequent use with spectral GCNN filter designs. In this work, we explore the regularization properties of graph Laplacian and proposed a generalized framework for regularized filter designs in spectral GCNNs. We found that the filters used in many state-of-the-art GCNNs can be derived as a …
Tsinghua University（清华大学）；Mila（米拉研究所）；Université de Montréal（蒙特利尔大学）；CIFAR AI Chair（CIFAR人工智能讲席）
Various forms of regularization in learning tasks strive for different notions of simplicity. This paper presents a spectral regularization technique, which attaches a unique inductive bias to sequence modeling based on an intuitive concept of simplicity defined in the Chomsky hierarchy. From fundamental connections between Hankel matrices and regular grammars, we propose to use the trace norm of the Hankel matrix, the tightest convex relaxation of its rank, as the spectral regularizer. To cope with the fact that the Hankel matrix is bi-infinite, we propose an unbiased stochastic estimator for…
Spectral embedding is a popular technique for the representation of graph data. Several regularization techniques have been proposed to improve the quality of the embedding with respect to downstream tasks like clustering. In this paper, we explain on a simple block model the impact of the complete graph regularization, whereby a constant is added to all entries of the adjacency matrix. Specifically, we show that the regularization forces the spectral embedding to focus on the largest blocks, making the representation less sensitive to noise or outliers. We illustrate these results on both on …
Toulouse Mathematics Institute（图卢兹数学研究所）；University of Toulouse（图卢兹大学）；Metabolic and Cardiovascular Diseases Institute（代谢与心血管疾病研究所）；CNRS（法国国家科学研究中心）
Cluster structure detection is a fundamental task for the analysis of graphs, in order to understand and to visualize their functional characteristics. Among the different cluster structure detection methods, spectral clustering is currently one of the most widely used due to its speed and simplicity. Yet, there are few theoretical guarantee to recover the underlying partitions of the graph for general models. This paper therefore presents a variant of spectral clustering, called 1-spectral clustering, performed on a new random model closely related to stochastic block model. Its goal is to pr…
Beyond Penalization: Diffusion-based Out-of-Distribution Detection and Selective Regularization in Offline Reinforcement Learning
School of Computer Science and Technology, Tongji University, Shanghai, China（同济大学计算机科学与技术学院，上海，中国）；MOE Key Lab of Embedded System and Service Computing, Tongji University, Shanghai, China（教育部嵌入式系统与服务计算重点实验室，同济大学，上海，中国）；Shanghai Innovation Institute（上海创新研究院）
Georgia Institute of Technology（佐治亚理工学院）；University of California, Berkeley（加州大学伯克利分校）
Data-driven machine learning models are being increasingly employed in several important inference problems in biology, chemistry, and physics which require learning over combinatorial spaces. Recent empirical evidence (see, e.g., [1], [2], [3]) suggests that regularizing the spectral representation of such models improves their generalization power when labeled data is scarce. However, despite these empirical studies, the theoretical underpinning of when and how spectral regularization enables improved generalization is poorly understood. In this paper, we focus on learning pseudo-Boolean fun…
Institute of Theoretical Physics, Chinese Academy of Sciences（中国科学院理论物理研究所）
Spectral methods are popular in detecting global structures in the given data that can be represented as a matrix. However when the data matrix is sparse or noisy, classic spectral methods usually fail to work, due to localization of eigenvectors (or singular vectors) induced by the sparsity or noise. In this work, we propose a general method to solve the localization problem by learning a regularization matrix from the localized eigenvectors. Using matrix perturbation analysis, we demonstrate that the learned regularizations suppress down the eigenvalues associated with localized eigenvectors…
Qingdao University（青岛大学）；Harbin Institute of Technology（哈尔滨工业大学）；University of Electronic Science and Technology of China（电子科技大学）；University of Kentucky（肯塔基大学）；University of California, Santa Barbara（加州大学圣巴巴拉分校）
In this paper, we propose a novel nonconvex approach to robust principal component analysis for HSI denoising, which focuses on simultaneously developing more accurate approximations to both rank and column-wise sparsity for the low-rank and sparse components, respectively. In particular, the new method adopts the log-determinant rank approximation and a novel $\ell_{2,\log}$ norm, to restrict the local low-rank or column-wisely sparse properties for the component matrices, respectively. For the $\ell_{2,\log}$-regularized shrinkage problem, we develop an efficient, closed-form solution, which…
Spectral regularization for adversarially-robust representation learning
John A. Paulson School of Engineering and Applied Sciences, Harvard University（哈佛大学约翰·保尔森工程与应用科学学院）；Center for Brain Science, Harvard University（哈佛大学脑科学中心）；Kempner Institute for the Study of Natural and Artificial Intelligence, Harvard University（哈佛大学肯普ner自然与人工智能研究所）
Sapienza University of Rome（罗马大学）；University of California, Los Angeles（加州大学洛杉矶分校）
This article proposes diffusion LMS strategies for distributed estimation over adaptive networks that are able to exploit sparsity in the underlying system model. The approach relies on convex regularization, common in compressive sensing, to enhance the detection of sparsity via a diffusive process over the network. The resulting algorithms endow networks with learning abilities and allow them to learn the sparse structure from the incoming data in real-time, and also to track variations in the sparsity of the model. We provide convergence and mean-square performance analysis of the proposed …
Guided Deep Generative Model-based Spatial Regularization for Multiband Imaging Inverse Problems
Northwestern Polytechnical University（西北工业大学）；University of Toulouse（图卢兹大学）；IRIT/INPENSEEIHT（图卢兹计算机研究所/国立图卢兹应用科学学院国立高等电力技术、电子学、计算机、水力学与电信学院）；CNRS（法国国家科学研究中心）；Institut Universitaire de France (IUF)（法国大学研究院）
