Many previous proposals for adversarial training of deep neural nets have included di- rectly modifying the gradient, training on a mix of original and adversarial examples, using contractive penalties, and approximately optimizing constrained adversarial ob- jective functions. In this paper, we show these proposals are actually all instances of optimizing a general, regularized objective we call DataGrad. Our proposed DataGrad framework, which can be viewed as a deep extension of the layerwise contractive au- toencoder penalty, cleanly simplifies prior work and easily allows extensions such as adversarial training with multi-task cues. In our experiments, we find that the deep gra- dient regularization of DataGrad (which also has L1 and L2 flavors of regularization) outperforms alternative forms of regularization, including classical L1, L2, and multi- task, both on the original dataset as well as on adversarial sets. Furthermore, we find that combining multi-task optimization with DataGrad adversarial training results in the most robust performance.
Hangzhou Innovation Institute, Beihang University（北京航空航天大学杭州创新研究院）；Beihang University（北京航空航天大学）；University of Ottawa（渥太华大学）
Recent researches have suggested that the predictive accuracy of neural network may contend with its adversarial robustness. This presents challenges in designing effective regularization schemes that also provide strong adversarial robustness. Revisiting Vicinal Risk Minimization (VRM) as a unifying regularization principle, we propose Adversarial Labelling of Perturbed Samples (ALPS) as a regularization scheme that aims at improving the generalization ability and adversarial robustness of the trained model. ALPS trains neural networks with synthetic samples formed by perturbing each authenti…
École polytechnique fédérale de Lausanne (EPFL)（洛桑联邦理工学院）
The minimization of a data-fidelity term and an additive regularization functional gives rise to a powerful framework for supervised learning. In this paper, we present a unifying regularization functional that depends on an operator and on a generic Radon-domain norm. We establish the existence of a minimizer and give the parametric form of the solution(s) under very mild assumptions. When the norm is Hilbertian, the proposed formulation yields a solution that involves radial-basis functions and is compatible with the classical methods of machine learning. By contrast, for the total-variation…
Monash University（莫纳什大学）；La Trobe University（乐卓博大学）；University of Chinese Academy of Sciences（中国科学院大学）；Nanjing University of Science and Technology（南京理工大学）；Griffith University（格里菲斯大学）
Graph contrastive learning (GCL) has recently emerged as an effective learning paradigm to alleviate the reliance on labelling information for graph representation learning. The core of GCL is to maximise the mutual information between the representation of a node and its contextual representation (i.e., the corresponding instance with similar semantic information) summarised from the contextual scope (e.g., the whole graph or 1-hop neighbourhood). This scheme distils valuable self-supervision signals for GCL training. However, existing GCL methods still suffer from limitations, such as the in…
University of Chicago（芝加哥大学）；Simons Institute, University of California at Berkeley（加州大学伯克利分校西蒙斯研究所）；University of British Columbia（不列颠哥伦比亚大学）；Alberta Machine Intelligence Institute（阿尔伯塔机器智能研究所）；Toyota Technological Institute at Chicago（芝加哥丰田技术研究所）
We study a localized notion of uniform convergence known as an "optimistic rate" (Panchenko 2002; Srebro et al. 2010) for linear regression with Gaussian data. Our refined analysis avoids the hidden constant and logarithmic factor in existing results, which are known to be crucial in high-dimensional settings, especially for understanding interpolation learning. As a special case, our analysis recovers the guarantee from Koehler et al. (2021), which tightly characterizes the population risk of low-norm interpolators under the benign overfitting conditions. Our optimistic rate bound, though, al…
Unifying Entropy Regularization in Optimal Control: From and Back to Classical Objectives via Iterated Soft Policies and Path Integral Solutions
Department of Electromechanical, Systems and Metal Engineering, Ghent University, Ghent, Belgium（电子机械、系统与金属工程系，根特大学，根特，比利时）；Core lab MIRO, Flanders Make, Belgium（Flanders Make核心实验室，比利时）
Stony Brook University（石溪大学）；Tencent AI Lab（腾讯人工智能实验室）
Multi-task learning (MTL) is a common paradigm that seeks to improve the generalization performance of task learning by training related tasks simultaneously. However, it is still a challenging problem to search the flexible and accurate architecture that can be shared among multiple tasks. In this paper, we propose a novel deep learning model called Task Adaptive Activation Network (TAAN) that can automatically learn the optimal network architecture for MTL. The main principle of TAAN is to derive flexible activation functions for different tasks from the data with other parameters of the net…
Regularization is one of the crucial ingredients of deep learning, yet the term regularization has various definitions, and regularization methods are often studied separately from each other. In our work we present a systematic, unifying taxonomy to categorize existing methods. We distinguish methods that affect data, network architectures, error terms, regularization terms, and optimization procedures. We do not provide all details about the listed methods; instead, we present an overview of how the methods can be sorted into meaningful categories and sub-categories. This helps revealing lin…
Konica Minolta Laboratory Europe（柯尼卡美能达欧洲实验室）；Technical University of Munich（慕尼黑工业大学）
Variational methods for revealing visual concepts learned by convolutional neural networks have gained significant attention during the last years. Being based on noisy gradients obtained via back-propagation such methods require the application of regularization strategies. We present a mathematical framework unifying previously employed regularization methods. Within this framework, we propose a novel technique based on Sobolev gradients which can be implemented via convolutions and does not require specialized numerical treatment, such as total variation regularization. The experiments perf…
Gaussian processes (GPs) are flexible distributions over functions that enable high-level assumptions about unknown functions to be encoded in a parsimonious, flexible and general way. Although elegant, the application of GPs is limited by computational and analytical intractabilities that arise when data are sufficiently numerous or when employing non-Gaussian models. Consequently, a wealth of GP approximation schemes have been developed over the last 15 years to address these key limitations. Many of these schemes employ a small set of pseudo data points to summarise the actual data. In this…
Google（谷歌）；DeepMind（深度思维）；University College London（伦敦大学学院）
In many contexts, simpler models are preferable to more complex models and the control of this model complexity is the goal for many methods in machine learning such as regularization, hyperparameter tuning and architecture design. In deep learning, it has been difficult to understand the underlying mechanisms of complexity control, since many traditional measures are not naturally suitable for deep neural networks. Here we develop the notion of geometric complexity, which is a measure of the variability of the model function, computed using a discrete Dirichlet energy. Using a combination of …
Amazon Alexa AI Search（亚马逊Alexa AI搜索）；Department of Computer Sciences（计算机科学系）；University of Wisconsin-Madison（威斯康星大学麦迪逊分校）；Manhattan Beach, CA, USA（美国加利福尼亚州曼哈顿海滩（此处为地址，按要求不提取））
Unsupervised and self-supervised learning approaches have become a crucial tool to learn representations for downstream prediction tasks. While these approaches are widely used in practice and achieve impressive empirical gains, their theoretical understanding largely lags behind. Towards bridging this gap, we present a unifying perspective where several such approaches can be viewed as imposing a regularization on the representation via a learnable function using unlabeled data. We propose a discriminative theoretical framework for analyzing the sample complexity of these approaches, which ge…
Flatiron Institute, a division of the Simons Foundation Center for Cosmology and Particle Physics, Department of Physics, New York University（纽约大学纽约大学西蒙斯基金会宇宙学与粒子物理中心分属的Flatiron研究所，物理系）；Center for Data Science, New York University（纽约大学数据科学中心）；Max-Planck-Institut für Astronomie, Heidelberg（海德堡马克斯-普朗克天文研究所）；Department of Applied Mathematics & Statistics, Johns Hopkins University（约翰斯·霍普金斯大学应用数学与统计系）；Mathematical Institute for Data Science, Johns Hopkins University（约翰斯·霍普金斯大学数据科学数学研究所）
There are many uses for linear fitting; the context here is interpolation and denoising of data, as when you have calibration data and you want to fit a smooth, flexible function to those data. Or you want to fit a flexible function to de-trend a time series or normalize a spectrum. In these contexts, investigators often choose a polynomial basis, or a Fourier basis, or wavelets, or something equally general. They also choose an order, or number of basis functions to fit, and (often) some kind of regularization. We discuss how this basis-function fitting is done, with ordinary least squares an…
Clustering single-cell RNA sequence (scRNA-seq) data poses statistical and computational challenges due to their high-dimensionality and data-sparsity, also known as `dropout' events. Recently, Regularized Auto-Encoder (RAE) based deep neural network models have achieved remarkable success in learning robust low-dimensional representations. The basic idea in RAEs is to learn a non-linear mapping from the high-dimensional data space to a low-dimensional latent space and vice-versa, simultaneously imposing a distributional prior on the latent space, which brings in a regularization effect. This …
Recent interest in the external validity of prediction models (i.e., the problem of different train and test distributions, known as dataset shift) has produced many methods for finding predictive distributions that are invariant to dataset shifts and can be used for prediction in new, unseen environments. However, these methods consider different types of shifts and have been developed under disparate frameworks, making it difficult to theoretically analyze how solutions differ with respect to stability and accuracy. Taking a causal graphical view, we use a flexible graphical representation t…
Institute for Data, Systems, and Society, MIT（麻省理工学院数据、系统与社会研究所）
The COVID-19 pandemic has emphasized the need for a robust understanding of epidemic models. Current models of epidemics are classified as either mechanistic or non-mechanistic: mechanistic models make explicit assumptions on the dynamics of disease, whereas non-mechanistic models make assumptions on the form of observed time series. Here, we introduce a simple mixture-based model which bridges the two approaches while retaining benefits of both. The model represents time series of cases and fatalities as a mixture of Gaussian curves, providing a flexible function class to learn from data comp…
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…
Robust quantization improves the tolerance of networks for various implementations, allowing reliable output in different bit-widths or fragmented low-precision arithmetic. In this work, we perform extensive analyses to identify the sources of quantization error and present three insights to robustify a network against quantization: reduction of error propagation, range clamping for error minimization, and inherited robustness against quantization. Based on these insights, we propose two novel methods called symmetry regularization (SymReg) and saturating nonlinearity (SatNL). Applying the pro…
A Unifying Variational Framework for Gaussian Process Motion Planning
University College London（伦敦大学学院）；ETH Zürich（苏黎世联邦理工学院）；Imperial College London（帝国理工学院）；University of Cambridge（剑桥大学）；Cornell University（康奈尔大学）；TU Delft（代尔夫特理工大学）；Chalmers University of Technology（查尔姆斯理工大学）
Geometric Meta-Learning via Coupled Ricci Flow: Unifying Knowledge Representation and Quantum Entanglement
School of Aeronautics and Astronautics, Shanghai Jiao Tong University（上海交通大学航空航天学院）；Météo-France（法国气象局）；CNRS（法国国家科学研究中心）；Mathematical Institute of Toulouse（图卢兹数学研究所）
Pennsylvania State University（宾夕法尼亚州立大学）；Sant’Anna School of Advanced Studies（圣安娜高等研究院）
In this paper we propose $ε$-Consistent Mixup ($ε$mu). $ε$mu is a data-based structural regularization technique that combines Mixup's linear interpolation with consistency regularization in the Mixup direction, by compelling a simple adaptive tradeoff between the two. This learnable combination of consistency and interpolation induces a more flexible structure on the evolution of the response across the feature space and is shown to improve semi-supervised classification accuracy on the SVHN and CIFAR10 benchmark datasets, yielding the largest gains in the most challenging low label-availabil…
Transfer learning methods address the situation where little labeled training data from the "target" problem exists, but much training data from a related "source" domain is available. However, the overwhelming majority of transfer learning methods are designed for simple settings where the source and target predictive functions are almost identical, limiting the applicability of transfer learning methods to real world data. We propose a novel, weaker, property of the source domain that can be transferred even when the source and target predictive functions diverge. Our method assumes the sour…
MedM2G: Unifying Medical Multi-Modal Generation via Cross-Guided Diffusion with Visual Invariant
College of Computer Science and Technology, Zhejiang University（浙江大学计算机科学与技术学院）；ZIU-UIUC Institute, Zhejiang University（浙江大学ZIU-UIUC研究院）；School of Public Health, Zhejiang University（浙江大学公共卫生学院）
Huazhong University of Science and Technology（华中科技大学）
Takagi-Sugeno-Kang (TSK) fuzzy systems are flexible and interpretable machine learning models; however, they may not be easily optimized when the data size is large, and/or the data dimensionality is high. This paper proposes a mini-batch gradient descent (MBGD) based algorithm to efficiently and effectively train TSK fuzzy classifiers. It integrates two novel techniques: 1) uniform regularization (UR), which forces the rules to have similar average contributions to the output, and hence to increase the generalization performance of the TSK classifier; and, 2) batch normalization (BN), which e…
Huawei Noah’s Ark Lab（华为诺亚方舟实验室）；University of Montreal（蒙特利尔大学）
Deep neural networks (DNNs) have demonstrated success for many supervised learning tasks, ranging from voice recognition, object detection, to image classification. However, their increasing complexity might yield poor generalization error that make them hard to be deployed on edge devices. Quantization is an effective approach to compress DNNs in order to meet these constraints. Using a quasiconvex base function in order to construct a binary quantizer helps training binary neural networks (BNNs) and adding noise to the input data or using a concrete regularization function helps to improve g…
ASML（阿斯麦尔）；Eindhoven University of Technology（埃因霍温理工大学）
Performance of model-based feedforward controllers is typically limited by the accuracy of the inverse system dynamics model. Physics-guided neural networks (PGNN), where a known physical model cooperates in parallel with a neural network, were recently proposed as a method to achieve high accuracy of the identified inverse dynamics. However, the flexible nature of neural networks can create overparameterization when employed in parallel with a physical model, which results in a parameter drift during training. This drift may result in parameters of the physical model not corresponding to thei…
Probabilistic Forecast Reconciliation with Kullback-Leibler Divergence Regularization
AI Lab Lenovo Research（联想研究院AI实验室）；School of Statistics and Mathematics Central University of Finance and Economics（中央财经大学统计与数学学院）；School of Economics and Management Beihang University（北京航空航天大学经济管理学院）
Automatic Differentiation-based Full Waveform Inversion with Flexible Workflows
Shanghai Jiao Tong University（上海交通大学）；University of Science and Technology of China（中国科学技术大学）；Stanford University（斯坦福大学）；CAS Center for Excellence in Comparative Planetology（中国科学院比较行星学卓越中心）
Simula Metropolitan Center for Digital Engineering（Simula城市数字工程中心）；Oslo Metropolitan University（奥斯陆城市大学）；CNRS（法国国家科学研究中心）；Université de Rennes（雷恩大学）；Inria（法国国家信息与自动化研究所）；IRISA（IRISA研究所）
Coupled matrix and tensor factorizations (CMTF) are frequently used to jointly analyze data from multiple sources, also called data fusion. However, different characteristics of datasets stemming from multiple sources pose many challenges in data fusion and require to employ various regularizations, constraints, loss functions and different types of coupling structures between datasets. In this paper, we propose a flexible algorithmic framework for coupled matrix and tensor factorizations which utilizes Alternating Optimization (AO) and the Alternating Direction Method of Multipliers (ADMM). T…
Laboratory for Computational and Statistical Learning（计算与统计学习实验室）；Istituto Italiano di Tecnologia（意大利理工学院）；Massachusetts Institute of Technology（麻省理工学院）；DIBRIS, Università di Genova（热那亚大学DIBRIS（信息学、生物信息学与系统生物学系））；Università di Genova（热那亚大学）
We analyze the learning properties of the stochastic gradient method when multiple passes over the data and mini-batches are allowed. We study how regularization properties are controlled by the step-size, the number of passes and the mini-batch size. In particular, we consider the square loss and show that for a universal step-size choice, the number of passes acts as a regularization parameter, and optimal finite sample bounds can be achieved by early-stopping. Moreover, we show that larger step-sizes are allowed when considering mini-batches. Our analysis is based on a unifying approach, en…
Deep matrix factorizations (deep MFs) are recent unsupervised data mining techniques inspired by constrained low-rank approximations. They aim to extract complex hierarchies of features within high-dimensional datasets. Most of the loss functions proposed in the literature to evaluate the quality of deep MF models and the underlying optimization frameworks are not consistent because different losses are used at different layers. In this paper, we introduce two meaningful loss functions for deep MF and present a generic framework to solve the corresponding optimization problems. We illustrate t…
