Randomized Neural Networks explore the behavior of neural systems where the majority of connections are fixed, either in a stochastic or a deterministic fashion. Typical examples of such systems consist of multi-layered neural network architectures where the connections to the hidden layer(s) are left untrained after initialization. Limiting the training algorithms to operate on a reduced set of weights inherently characterizes the class of Randomized Neural Networks with a number of intriguing features. Among them, the extreme efficiency of the resulting learning processes is undoubtedly a striking advantage with respect to fully trained architectures. Besides, despite the involved simplifications, randomized neural systems possess remarkable properties both in practice, achieving state-of-the-art results in multiple domains, and theoretically, allowing to analyze intrinsic properties of neural architectures (e.g. before training of the hidden layers' connections). In recent years, the study of Randomized Neural Networks has been extended towards deep architectures, opening new research directions to the design of effective yet extremely efficient deep learning models in vectorial as well as in more complex data domains. This chapter surveys all the major aspects regarding the design and analysis of Randomized Neural Networks, and some of the key results with respect to their approximation capabilities. In particular, we first introduce the fundamentals of randomized neural models in the context of feed-forward networks (i.e., Random Vector Functional Link and equivalent models) and convolutional filters, before moving to the case of recurrent systems (i.e., Reservoir Computing networks). For both, we focus specifically on recent results in the domain of deep randomized systems, and (for recurrent models) their application to structured domains.
In this work, a method of random parameters generation for randomized learning of a single-hidden-layer feedforward neural network is proposed. The method firstly, randomly selects the slope angles of the hidden neurons activation functions from an interval adjusted to the target function, then randomly rotates the activation functions, and finally distributes them across the input space. For complex target functions the proposed method gives better results than the approach commonly used in practice, where the random parameters are selected from the fixed interval. This is because it introduc…
Randomized methods of neural network learning suffer from a problem with the generation of random parameters as they are difficult to set optimally to obtain a good projection space. The standard method draws the parameters from a fixed interval which is independent of the data scope and activation function type. This does not lead to good results in the approximation of the strongly nonlinear functions. In this work, a method which adjusts the random parameters, representing the slopes and positions of the sigmoids, to the target function features is proposed. The method randomly selects the …
Optimization of randomized neural networks for transfer operator approximation
Maxwell Institute for Mathematical Sciences, University of Edinburgh and Heriot–Watt University（爱丁堡大学麦克斯韦数学科学研究所和赫里奥特-瓦特大学）；School of Mathematical & Computer Sciences, Heriot–Watt University（赫里奥特-瓦特大学数学与计算机科学学院）
In this paper, we propose a novel data-driven operator learning framework referred to as the \textit{Randomized Prior Wavelet Neural Operator} (RP-WNO). The proposed RP-WNO is an extension of the recently proposed wavelet neural operator, which boasts excellent generalizing capabilities but cannot estimate the uncertainty associated with its predictions. RP-WNO, unlike the vanilla WNO, comes with inherent uncertainty quantification module and hence, is expected to be extremely useful for scientists and engineers alike. RP-WNO utilizes randomized prior networks, which can account for prior info…
Deep learning is vulnerable to adversarial examples. Many defenses based on randomized neural networks have been proposed to solve the problem, but fail to achieve robustness against attacks using proxy gradients such as the Expectation over Transformation (EOT) attack. We investigate the effect of the adversarial attacks using proxy gradients on randomized neural networks and demonstrate that it highly relies on the directional distribution of the loss gradients of the randomized neural network. We show in particular that proxy gradients are less effective when the gradients are more scattere…
Current deep learning architectures are growing larger in order to learn from complex datasets. These architectures require giant matrix multiplication operations to train millions of parameters. Conversely, there is another growing trend to bring deep learning to low-power, embedded devices. The matrix operations, associated with both training and testing of deep networks, are very expensive from a computational and energy standpoint. We present a novel hashing based technique to drastically reduce the amount of computation needed to train and test deep networks. Our approach combines recent …
We study the use of randomized value functions to guide deep exploration in reinforcement learning. This offers an elegant means for synthesizing statistically and computationally efficient exploration with common practical approaches to value function learning. We present several reinforcement learning algorithms that leverage randomized value functions and demonstrate their efficacy through computational studies. We also prove a regret bound that establishes statistical efficiency with a tabular representation.
Feedforward neural networks are widely used as universal predictive models to fit data distribution. Common gradient-based learning, however, suffers from many drawbacks making the training process ineffective and time-consuming. Alternative randomized learning does not use gradients but selects hidden node parameters randomly. This makes the training process extremely fast. However, the problem in randomized learning is how to determine the random parameters. A recently proposed method uses autoencoders for unsupervised parameter learning. This method showed superior performance on classifica…
PSL, Université Paris-Dauphine, Miles Team（PSL，巴黎 Dauphine 大学，Miles 团队）；Wavestone；Facebook AI Research（Facebook 人工智能研究）；CEA, Université Paris-Saclay（法国原子能委员会，巴黎萨克雷大学）
This paper tackles the problem of defending a neural network against adversarial attacks crafted with different norms (in particular $\ell_\infty$ and $\ell_2$ bounded adversarial examples). It has been observed that defense mechanisms designed to protect against one type of attacks often offer poor performance against the other. We show that $\ell_\infty$ defense mechanisms cannot offer good protection against $\ell_2$ attacks and vice-versa, and we provide both theoretical and empirical insights on this phenomenon. Then, we discuss various ways of combining existing defense mechanisms in ord…
This work contributes to the development of neural forecasting models with novel randomization-based learning methods. These methods improve the fitting abilities of the neural model, in comparison to the standard method, by generating network parameters in accordance with the data and target function features. A pattern-based representation of time series makes the proposed approach useful for forecasting time series with multiple seasonality. In the simulation study, we evaluate the performance of the proposed models and find that they can compete in terms of forecasting accuracy with fully-…
We present a simple and effective approach for posterior uncertainty quantification in deep operator networks (DeepONets); an emerging paradigm for supervised learning in function spaces. We adopt a frequentist approach based on randomized prior ensembles, and put forth an efficient vectorized implementation for fast parallel inference on accelerated hardware. Through a collection of representative examples in computational mechanics and climate modeling, we show that the merits of the proposed approach are fourfold. (1) It can provide more robust and accurate predictions when compared against…
Dealing with uncertainty is essential for efficient reinforcement learning. There is a growing literature on uncertainty estimation for deep learning from fixed datasets, but many of the most popular approaches are poorly-suited to sequential decision problems. Other methods, such as bootstrap sampling, have no mechanism for uncertainty that does not come from the observed data. We highlight why this can be a crucial shortcoming and propose a simple remedy through addition of a randomized untrainable `prior' network to each ensemble member. We prove that this approach is efficient with linear …
Institut de Recherche Technologique SystemX（SystemX技术研究院）；Univ. Bordeaux（波尔多大学）；CNRS（法国国家科学研究中心）；Bordeaux INP（波尔多国立理工学院）；IMB（波尔多数学研究所）
Certification of neural networks is an important and challenging problem that has been attracting the attention of the machine learning community since few years. In this paper, we focus on randomized smoothing (RS) which is considered as the state-of-the-art method to obtain certifiably robust neural networks. In particular, a new data-dependent RS technique called ANCER introduced recently can be used to certify ellipses with orthogonal axis near each input data of the neural network. In this work, we remark that ANCER is not invariant under rotation of input data and propose a new rotationa…
São Carlos Institute of Physics, University of São Paulo（圣保罗大学圣卡洛斯物理研究所）；Universidade Federal do Ceará（塞阿拉联邦大学）；Institute of Mathematics and Computer Science, University of São Paulo（圣保罗大学数学与计算机科学研究所）
This paper presents a high discriminative texture analysis method based on the fusion of complex networks and randomized neural networks. In this approach, the input image is modeled as a complex networks and its topological properties as well as the image pixels are used to train randomized neural networks in order to create a signature that represents the deep characteristics of the texture. The results obtained surpassed the accuracies of many methods available in the literature. This performance demonstrates that our proposed approach opens a promising source of research, which consists of…
University of Rome “La Sapienza”（罗马“萨皮恩扎”大学）；UC Berkeley（加州大学伯克利分校）；Research Institutes of Sweden（瑞典研究院）
In the supervised learning domain, considering the recent prevalence of algorithms with high computational cost, the attention is steering towards simpler, lighter, and less computationally extensive training and inference approaches. In particular, randomized algorithms are currently having a resurgence, given their generalized elementary approach. By using randomized neural networks, we study distributed classification, which can be employed in situations were data cannot be stored at a central location nor shared. We propose a more efficient solution for distributed classification by making…
Institute of Statistics, RWTH Aachen University（亚琛工业大学统计研究所）；Forschungszentrum Jülich, Institut für Energie- und Klimaforschung, IEK-5（于利希研究中心能源与气候研究所 IEK-5）
Randomized artificial neural networks such as extreme learning machines provide an attractive and efficient method for supervised learning under limited computing ressources and green machine learning. This especially applies when equipping mobile devices (sensors) with weak artificial intelligence. Results are discussed about supervised learning with such networks and regression methods in terms of consistency and bounds for the generalization and prediction error. Especially, some recent results are reviewed addressing learning with data sampled by moving sensors leading to non-stationary an…
University of Rome “La Sapienza”（罗马“萨皮恩扎”大学）；Luleå University of Technology（吕勒奥理工大学）；Research Institutes of Sweden（瑞典研究院）；University of California, Berkeley（加州大学伯克利分校）
A change of the prevalent supervised learning techniques is foreseeable in the near future: from the complex, computational expensive algorithms to more flexible and elementary training ones. The strong revitalization of randomized algorithms can be framed in this prospect steering. We recently proposed a model for distributed classification based on randomized neural networks and hyperdimensional computing, which takes into account cost of information exchange between agents using compression. The use of compression is important as it addresses the issues related to the communication bottlene…
Deep reinforcement learning methods have achieved state-of-the-art results in a variety of challenging, high-dimensional domains ranging from video games to locomotion. The key to success has been the use of deep neural networks used to approximate the policy and value function. Yet, substantial tuning of weights is required for good results. We instead use randomized function approximation. Such networks are not only cheaper than training fully connected networks but also improve the numerical performance. We present \texttt{RANDPOL}, a generalized policy iteration algorithm for MDPs with con…
This paper addresses distributed parameter estimation in randomized one-hidden-layer neural networks. A group of agents sequentially receive measurements of an unknown parameter that is only partially observable to them. In this paper, we present a fully distributed estimation algorithm where agents exchange local estimates with their neighbors to collectively identify the true value of the parameter. We prove that this distributed update provides an asymptotically unbiased estimator of the unknown parameter, i.e., the first moment of the expected global error converges to zero asymptotically.…
New York University（纽约大学）；University of British Columbia（不列颠哥伦比亚大学）；Microsoft Research（微软研究院）
We develop a new, principled algorithm for estimating the contribution of training data points to the behavior of a deep learning model, such as a specific prediction it makes. Our algorithm estimates the AME, a quantity that measures the expected (average) marginal effect of adding a data point to a subset of the training data, sampled from a given distribution. When subsets are sampled from the uniform distribution, the AME reduces to the well-known Shapley value. Our approach is inspired by causal inference and randomized experiments: we sample different subsets of the training data to trai…
ETH Z\"urich, D-Math, R\"amistrasse 101, CH-8092 Z\"urich, Switzerland
Randomized neural networks (randomized NNs), where only the terminal layer's weights are optimized constitute a powerful model class to reduce computational time in training the neural network model. At the same time, these models generalize surprisingly well in various regression and classification tasks. In this paper, we give an exact macroscopic characterization (i.e., a characterization in function space) of the generalization behavior of randomized, shallow NNs with ReLU activation (RSNs). We show that RSNs correspond to a generalized additive model (GAM)-typed regression in which infini…
Feedforward neural networks with random hidden nodes suffer from a problem with the generation of random weights and biases as these are difficult to set optimally to obtain a good projection space. Typically, random parameters are drawn from an interval which is fixed before or adapted during the learning process. Due to the different functions of the weights and biases, selecting them both from the same interval is not a good idea. Recently more sophisticated methods of random parameters generation have been developed, such as the data-driven method proposed in \cite{Anon19}, where the sigmo…
Tsinghua University（清华大学）；Harvard University（哈佛大学）；University of California, Berkeley（加州大学伯克利分校）；Huazhong University of Science and Technology（华中科技大学）；Virginia Tech（弗吉尼亚理工大学）
Deep learning techniques have achieved remarkable performance in wide-ranging tasks. However, when trained on privacy-sensitive datasets, the model parameters may expose private information in training data. Prior attempts for differentially private training, although offering rigorous privacy guarantees, lead to much lower model performance than the non-private ones. Besides, different runs of the same training algorithm produce models with large performance variance. To address these issues, we propose DPlis--Differentially Private Learning wIth Smoothing. The core idea of DPlis is to constr…
Domain adaptation (DA) is the task of classifying an unlabeled dataset (target) using a labeled dataset (source) from a related domain. The majority of successful DA methods try to directly match the distributions of the source and target data by transforming the feature space. Despite their success, state of the art methods based on this approach are either involved or unable to directly scale to data with many features. This article shows that domain adaptation can be successfully performed by using a very simple randomized expectation maximization (EM) method. We consider two instances of t…
Adaptive Randomized Neural Networks for PDEs: Structure-Aware Feature Redistribution and Residual-Driven Block Enrichment
School of Mathematics and Statistics, Xi’an Jiaotong University（西安交通大学数学与统计学院）；School of Mathematics and Statistics & State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University（西安交通大学数学与统计学院）
Space exploration missions have seen use of increasingly sophisticated robotic systems with ever more autonomy. Deep learning promises to take this even a step further, and has applications for high-level tasks, like path planning, as well as low-level tasks, like motion control, which are critical components for mission efficiency and success. Using deep reinforcement end-to-end learning with randomized reward function parameters during training, we teach a simulated 8 degree-of-freedom quadruped ant-like robot to travel anywhere within a perimeter, conducting path plan and motion control on …
University of Maryland, College Park（马里兰大学帕克分校）；Adobe Research（Adobe研究院）
Watermarking is a commonly used strategy to protect creators' rights to digital images, videos and audio. Recently, watermarking methods have been extended to deep learning models -- in principle, the watermark should be preserved when an adversary tries to copy the model. However, in practice, watermarks can often be removed by an intelligent adversary. Several papers have proposed watermarking methods that claim to be empirically resistant to different types of removal attacks, but these new techniques often fail in the face of new or better-tuned adversaries. In this paper, we propose a cer…
In recent years, neural networks have become the default choice for image classification and many other learning tasks, even though they are vulnerable to so-called adversarial attacks. To increase their robustness against these attacks, there have emerged numerous detection mechanisms that aim to automatically determine if an input is adversarial. However, state-of-the-art detection mechanisms either rely on being tuned for each type of attack, or they do not generalize across different attack types. To alleviate these issues, we propose a novel technique for adversarial-image detection, RAID…
Randomized Matrix Sketching for Neural Network Training and Gradient Monitoring
Department of Mathematical Sciences（数学科学系）；Center for Mathematics（数学中心）；Artificial Intelligence (CMAI), George Mason University. Fairfax, VA 22030.（人工智能（CMAI），乔治·马歇尔大学，弗吉尼亚州 Fairfax，22030）；School of Mathematical（数学系）；Statistical Sciences, Clemson University, Clemson, SC 29634.（统计科学系，克莱姆森大学，SC州 Clemson，29634）
New Jersey Institute of Technology（新泽西理工学院）；Qatar Computing Research Institute（卡塔尔计算研究所）；University of Florida（佛罗里达大学）；University of Arkansas（阿肯色大学）
Graph neural networks (GNNs) are susceptible to privacy inference attacks (PIAs), given their ability to learn joint representation from features and edges among nodes in graph data. To prevent privacy leakages in GNNs, we propose a novel heterogeneous randomized response (HeteroRR) mechanism to protect nodes' features and edges against PIAs under differential privacy (DP) guarantees without an undue cost of data and model utility in training GNNs. Our idea is to balance the importance and sensitivity of nodes' features and edges in redistributing the privacy budgets since some features and ed…
University of Salzburg（萨尔茨堡大学）；Purdue University（普渡大学）
Expressive text encoders such as RNNs and Transformer Networks have been at the center of NLP models in recent work. Most of the effort has focused on sentence-level tasks, capturing the dependencies between words in a single sentence, or pairs of sentences. However, certain tasks, such as argumentation mining, require accounting for longer texts and complicated structural dependencies between them. Deep structured prediction is a general framework to combine the complementary strengths of expressive neural encoders and structured inference for highly structured domains. Nevertheless, when the…
King Abdullah University of Science and Technology (KAUST)（阿卜杜拉国王科技大学）；University of Oxford（牛津大学）
Deep neural networks are vulnerable to input deformations in the form of vector fields of pixel displacements and to other parameterized geometric deformations e.g. translations, rotations, etc. Current input deformation certification methods either 1. do not scale to deep networks on large input datasets, or 2. can only certify a specific class of deformations, e.g. only rotations. We reformulate certification in randomized smoothing setting for both general vector field and parameterized deformations and propose DeformRS-VF and DeformRS-Par, respectively. Our new formulation scales to large …
Domain-Decomposed Randomized Neural Networks for Partial Differential Equations in Unbounded Domains
School of Mathematics and Statistics, Xi’an Jiaotong University（西安交通大学数学与统计学院）；State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University（西安交通大学动力工程多相流国家重点实验室）
In spite of several notable efforts, explaining the generalization of deterministic non-smooth deep nets, e.g., ReLU-nets, has remained challenging. Existing approaches for deterministic non-smooth deep nets typically need to bound the Lipschitz constant of such deep nets but such bounds are quite large, may even increase with the training set size yielding vacuous generalization bounds. In this paper, we present a new family of de-randomized PAC-Bayes margin bounds for deterministic non-convex and non-smooth predictors, e.g., ReLU-nets. Unlike PAC-Bayes, which applies to Bayesian predictors, …
In recent years, Deep Neural Networks (DNNs) have had a dramatic impact on a variety of problems that were long considered very difficult, e. g., image classification and automatic language translation to name just a few. The accuracy of modern DNNs in classification tasks is remarkable indeed. At the same time, attackers have devised powerful methods to construct specially-crafted malicious inputs (often referred to as adversarial examples) that can trick DNNs into mis-classifying them. What is worse is that despite the many defense mechanisms proposed to protect DNNs against adversarial atta…
Rice University（莱斯大学）；UC Berkeley（加州大学伯克利分校）；Research Institutes of Sweden（瑞典研究院）
Machine learning algorithms deployed on edge devices must meet certain resource constraints and efficiency requirements. Random Vector Functional Link (RVFL) networks are favored for such applications due to their simple design and training efficiency. We propose a modified RVFL network that avoids computationally expensive matrix operations during training, thus expanding the network's range of potential applications. Our modification replaces the least-squares classifier with the Generalized Learning Vector Quantization (GLVQ) classifier, which only employs simple vector and distance calcula…
In this work, we propose an ensemble forecasting approach based on randomized neural networks. Improved randomized learning streamlines the fitting abilities of individual learners by generating network parameters in accordance with the data and target function features. A pattern-based representation of time series makes the proposed approach suitable for forecasting time series with multiple seasonality. We propose six strategies for controlling the diversity of ensemble members. Case studies conducted on four real-world forecasting problems verified the effectiveness and superior performanc…
Randomized Neural Networks for Partial Differential Equation on Static and Evolving Surfaces
School of Mathematics and Statistics, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, P.R. China（西安交通大学数学与统计学院）；School of Mathematics and Statistics & State Key Laboratory of Multiphase Flow in Power Engineering, Xi’an Jiaotong University, Xi’an, Shaanxi 710049, China（西安交通大学数学与统计学院）
La Trobe University（拉筹伯大学）；Department of Computer Science and Information Technology（计算机科学与信息技术系）
This paper develops a randomized approach for incrementally building deep neural networks, where a supervisory mechanism is proposed to constrain the random assignment of the weights and biases, and all the hidden layers have direct links to the output layer. A fundamental result on the universal approximation property is established for such a class of randomized leaner models, namely deep stochastic configuration networks (DeepSCNs). A learning algorithm is presented to implement DeepSCNs with either specific architecture or self-organization. The read-out weights attached with all direct li…
MIT-IBM Watson AI Lab（MIT-IBM沃森人工智能实验室）；IBM Research（IBM研究院）
The fragility of modern machine learning models has drawn a considerable amount of attention from both academia and the public. While immense interests were in either crafting adversarial attacks as a way to measure the robustness of neural networks or devising worst-case analytical robustness verification with guarantees, few methods could enjoy both scalability and robustness guarantees at the same time. As an alternative to these attempts, randomized smoothing adopts a different prediction rule that enables statistical robustness arguments which easily scale to large networks. However, in t…
KAIST（韩国科学技术院）；University of Michigan（密歇根大学）；Google Brain（谷歌大脑）
Deep reinforcement learning (RL) agents often fail to generalize to unseen environments (yet semantically similar to trained agents), particularly when they are trained on high-dimensional state spaces, such as images. In this paper, we propose a simple technique to improve a generalization ability of deep RL agents by introducing a randomized (convolutional) neural network that randomly perturbs input observations. It enables trained agents to adapt to new domains by learning robust features invariant across varied and randomized environments. Furthermore, we consider an inference method base…
