Echo State Networks (ESNs) are a special type of recurrent neural networks (RNNs), in which the input and recurrent connections are traditionally generated randomly, and only the output weights are trained. Despite the recent success of ESNs in various tasks of audio, image and radar recognition, we postulate that a purely random initialization is not the ideal way of initializing ESNs. The aim of this work is to propose an unsupervised initialization of the input connections using the $K$-Means algorithm on the training data. We show that for a large variety of datasets this initialization performs equivalently or superior than a randomly initialized ESN whilst needing significantly less reservoir neurons. Furthermore, we discuss that this approach provides the opportunity to estimate a suitable size of the reservoir based on prior knowledge about the data.
Georgia Institute of Technology（佐治亚理工学院）；JD.COM American Technologies Corporation（京东美国技术公司）
Many neural networks use the tanh activation function, however when given a probability distribution as input, the problem of computing the output distribution in neural networks with tanh activation has not yet been addressed. One important example is the initialization of the echo state network in reservoir computing, where random initialization of the reservoir requires time to wash out the initial conditions, thereby wasting precious data and computational resources. Motivated by this problem, we propose a novel solution utilizing a moment based approach to propagate uncertainty through an…
Minimal Deterministic Echo State Networks Outperform Random Reservoirs in Learning Chaotic Dynamics
Center for Scalable Data Analytics；Artificial Intelligence (ScaDS.AI), Leipzig University, Leipzig, Germany；Institute for Earth System Science \& Remote Sensing, Leipzig University, Leipzig, Germany
A proper initialization of the weights in a neural network is critical to its convergence. Current insights into weight initialization come primarily from linear activation functions. In this paper, I develop a theory for weight initializations with non-linear activations. First, I derive a general weight initialization strategy for any neural network using activation functions differentiable at 0. Next, I derive the weight initialization strategy for the Rectified Linear Unit (RELU), and provide theoretical insights into why the Xavier initialization is a poor choice with RELU activations. My…
Reservoir Computing (RC) provides an efficient way for designing dynamical recurrent neural models. While training is restricted to a simple output component, the recurrent connections are left untrained after initialization, subject to stability constraints specified by the Echo State Property (ESP). Literature conditions for the ESP typically fail to properly account for the effects of driving input signals, often limiting the potentialities of the RC approach. In this paper, we study the fundamental aspect of asymptotic stability of RC models in presence of driving input, introducing an emp…
In artificial neural network, the activation function and the weight initialization method play important roles in training and performance of a neural network. The question arises is what properties of a function are important/necessary for being a well-performing activation function. Also, the most widely used weight initialization methods - Xavier and He normal initialization have fundamental connection with activation function. This survey discusses the important/necessary properties of activation function and the most widely used activation functions (sigmoid, tanh, ReLU, LReLU and PReLU)…
Faculty of Electrical Engineering and Computer Science（电气工程与计算机科学学院）；VŠB-Technical University of Ostrava（俄斯特拉发技术大学）；INRIA Rennes – Bretagne Atlantique（法国国家信息与自动化研究所雷恩-布列塔尼大西洋中心）
The Echo State Network (ESN) is a class of Recurrent Neural Network with a large number of hidden-hidden weights (in the so-called reservoir). Canonical ESN and its variations have recently received significant attention due to their remarkable success in the modeling of non-linear dynamical systems. The reservoir is randomly connected with fixed weights that don't change in the learning process. Only the weights from reservoir to output are trained. Since the reservoir is fixed during the training procedure, we may wonder if the computational power of the recurrent structure is fully harnesse…
The University of Texas at Austin（德克萨斯大学奥斯汀分校）；Cognizant AI Labs（高知特人工智能实验室）
Neural networks require careful weight initialization to prevent signals from exploding or vanishing. Existing initialization schemes solve this problem in specific cases by assuming that the network has a certain activation function or topology. It is difficult to derive such weight initialization strategies, and modern architectures therefore often use these same initialization schemes even though their assumptions do not hold. This paper introduces AutoInit, a weight initialization algorithm that automatically adapts to different neural network architectures. By analytically tracking the me…
Pennsylvania State University（宾夕法尼亚州立大学）；The University of Texas at Austin（德克萨斯大学奥斯汀分校）
Weight initialization plays an important role in training neural networks and also affects tremendous deep learning applications. Various weight initialization strategies have already been developed for different activation functions with different neural networks. These initialization algorithms are based on minimizing the variance of the parameters between layers and might still fail when neural networks are deep, e.g., dying ReLU. To address this challenge, we study neural networks from a nonlinear computation point of view and propose a novel weight initialization strategy that is based on…
We report an improvement to the conventional Echo State Network (ESN) across three benchmark chaotic time-series prediction tasks using fruit fly connectome data alone. We also investigate the impact of key connectome-derived structural features on prediction performance -- uniquely bridging neurobiological structure and machine learning function; and find that both increasing the global average clustering coefficient and modifying the position of weights -- by permuting their synapse-synapse partners -- can lead to increased model variance and (in some cases) degraded performance. In all we c…
We present neural machine translation (NMT) models inspired by echo state network (ESN), named Echo State NMT (ESNMT), in which the encoder and decoder layer weights are randomly generated then fixed throughout training. We show that even with this extremely simple model construction and training procedure, ESNMT can already reach 70-80% quality of fully trainable baselines. We examine how spectral radius of the reservoir, a key quantity that characterizes the model, determines the model behavior. Our findings indicate that randomized networks can work well even for complicated sequence-to-seq…
University of British Columbia（不列颠哥伦比亚大学）；Microsoft Research（微软研究院）
Echo State Networks (ESNs) are a special type of the temporally deep network model, the Recurrent Neural Network (RNN), where the recurrent matrix is carefully designed and both the recurrent and input matrices are fixed. An ESN uses the linearity of the activation function of the output units to simplify the learning of the output matrix. In this paper, we devise a special technique that take advantage of this linearity in the output units of an ESN, to learn the input and recurrent matrices. This has not been done in earlier ESNs due to their well known difficulty in learning those matrices.…
Language Technologies Institute, School of Computer Science, Carnegie Mellon University（卡内基梅隆大学计算机科学学院语言技术研究所）；Allen Institute for Artificial Intelligence（艾伦人工智能研究所）；Paul G. Allen School of Computer Science and Engineering, University of Washington（华盛顿大学保罗·G·艾伦计算机科学与工程学院）
Fine-tuning pretrained contextual word embedding models to supervised downstream tasks has become commonplace in natural language processing. This process, however, is often brittle: even with the same hyperparameter values, distinct random seeds can lead to substantially different results. To better understand this phenomenon, we experiment with four datasets from the GLUE benchmark, fine-tuning BERT hundreds of times on each while varying only the random seeds. We find substantial performance increases compared to previously reported results, and we quantify how the performance of the best-f…
University of Technology Sydney（悉尼科技大学）；Northwestern University（西北大学）
The prevailing thinking is that orthogonal weights are crucial to enforcing dynamical isometry and speeding up training. The increase in learning speed that results from orthogonal initialization in linear networks has been well-proven. However, while the same is believed to also hold for nonlinear networks when the dynamical isometry condition is satisfied, the training dynamics behind this contention have not been thoroughly explored. In this work, we study the dynamics of ultra-wide networks across a range of architectures, including Fully Connected Networks (FCNs) and Convolutional Neural …
Air Force Research Laboratory Information Directorate（空军研究实验室信息局）
This work introduces a tensor-based method to perform supervised classification on spatiotemporal data processed in an echo state network. Typically when performing supervised classification tasks on data processed in an echo state network, the entire collection of hidden layer node states from the training dataset is shaped into a matrix, allowing one to use standard linear algebra techniques to train the output layer. However, the collection of hidden layer states is multidimensional in nature, and representing it as a matrix may lead to undesirable numerical conditions or loss of spatial an…
Echo State Networks (ESNs) are a class of single-layer recurrent neural networks with randomly generated internal weights, and a single layer of tuneable outer weights, which are usually trained by regularised linear least squares regression. Remarkably, ESNs still enjoy the universal approximation property despite the training procedure being entirely linear. In this paper, we prove that an ESN trained on a sequence of observations from an ergodic dynamical system (with invariant measure $μ$) using Tikhonov least squares regression against a set of targets, will approximate the target functio…
The identification of black-box nonlinear state-space models requires a flexible representation of the state and output equation. Artificial neural networks have proven to provide such a representation. However, as in many identification problems, a nonlinear optimization problem needs to be solved to obtain the model parameters (layer weights and biases). A well-thought initialization of these model parameters can often avoid that the nonlinear optimization algorithm converges to a poorly performing local minimum of the considered cost function. This paper introduces an improved initializatio…
Researchers have proposed various activation functions. These activation functions help the deep network to learn non-linear behavior with a significant effect on training dynamics and task performance. The performance of these activations also depends on the initial state of the weight parameters, i.e., different initial state leads to a difference in the performance of a network. In this paper, we have proposed a cooperative initialization for training the deep network using ReLU activation function to improve the network performance. Our approach uses multiple activation functions in the in…
The interpretability of neural networks (NNs) is a challenging but essential topic for transparency in the decision-making process using machine learning. One of the reasons for the lack of interpretability is random weight initialization, where the input is randomly embedded into a different feature space in each layer. In this paper, we propose an interpretation method for a deep multilayer perceptron, which is the most general architecture of NNs, based on identity initialization (namely, initialization using identity matrices). The proposed method allows us to analyze the contribution of e…
Department of EECS, Oregon State University（俄勒冈州立大学电子工程与计算机科学系）
Training a neural network (NN) depends on multiple factors, including but not limited to the initial weights. In this paper, we focus on initializing deep NN parameters such that it performs better, comparing to random or zero initialization. We do this by reducing the process of initialization into an SMT solver. Previous works consider certain activation functions on small NNs, however the studied NN is a deep network with different activation functions. Our experiments show that the proposed approach for parameter initialization achieves better performance comparing to randomly initialized …
Echo state networks are powerful recurrent neural networks. However, they are often unstable and shaky, making the process of finding an good ESN for a specific dataset quite hard. Obtaining a superb accuracy by using the Echo State Network is a challenging task. We create, develop and implement a family of predictably optimal robust and stable ensemble of Echo State Networks via regularizing the training and perturbing the input. Furthermore, several distributions of weights have been tried based on the shape to see if the shape of the distribution has the impact for reducing the error. We fo…
Laboratoire Kastler Brossel（卡斯特勒布罗塞尔实验室）；CNRS（法国国家科学研究中心）；PSL Research University（巴黎文理研究大学）；Laboratoire de Physique Statistique（统计物理实验室）；LightOn（LightOn公司）
Echo-State Networks and Reservoir Computing have been studied for more than a decade. They provide a simpler yet powerful alternative to Recurrent Neural Networks, every internal weight is fixed and only the last linear layer is trained. They involve many multiplications by dense random matrices. Very large networks are difficult to obtain, as the complexity scales quadratically both in time and memory. Here, we present a novel optical implementation of Echo-State Networks using light-scattering media and a Digital Micromirror Device. As a proof of concept, binary networks have been successful…
University of Manouba（马努巴大学）；Taibah University（塔伊巴大学）；Al-Baha University（巴哈大学）；University of Sfax（斯法克斯大学）
During the last decade, several research works have focused on providing novel deep learning methods in many application fields. However, few of them have investigated the weight initialization process for deep learning, although its importance is revealed in improving deep learning performance. This can be justified by the technical difficulties in proposing new techniques for this promising research field. In this paper, a survey related to weight initialization techniques for deep algorithms in remote sensing is conducted. This survey will help practitioners to drive further research in thi…
A new initialization method for hidden parameters in a neural network is proposed. Derived from the integral representation of the neural network, a nonparametric probability distribution of hidden parameters is introduced. In this proposal, hidden parameters are initialized by samples drawn from this distribution, and output parameters are fitted by ordinary linear regression. Numerical experiments show that backpropagation with proposed initialization converges faster than uniformly random initialization. Also it is shown that the proposed method achieves enough accuracy by itself without ba…
University of Chicago（芝加哥大学）；Toyota Technological Institute at Chicago（芝加哥丰田工业大学）
We show how to adjust for the variance introduced by dropout with corrections to weight initialization and Batch Normalization, yielding higher accuracy. Though dropout can preserve the expected input to a neuron between train and test, the variance of the input differs. We thus propose a new weight initialization by correcting for the influence of dropout rates and an arbitrary nonlinearity's influence on variance through simple corrective scalars. Since Batch Normalization trained with dropout estimates the variance of a layer's incoming distribution with some inputs dropped, the variance al…
Harbin Institute of Technology Shenzhen（哈尔滨工业大学（深圳））；University of Electronic Science and Technology of China（电子科技大学）；Tokyo Institute of Technology（东京工业大学）；Institute of Automation, Chinese Academy of Sciences（中国科学院自动化研究所）；University of Chinese Academy of Sciences（中国科学院大学）；Pengcheng Laboratory（鹏城实验室）
Tensorial Convolutional Neural Networks (TCNNs) have attracted much research attention for their power in reducing model parameters or enhancing the generalization ability. However, exploration of TCNNs is hindered even from weight initialization methods. To be specific, general initialization methods, such as Xavier or Kaiming initialization, usually fail to generate appropriate weights for TCNNs. Meanwhile, although there are ad-hoc approaches for specific architectures (e.g., Tensor Ring Nets), they are not applicable to TCNNs with other tensor decomposition methods (e.g., CP or Tucker deco…
Ulm University（乌尔姆大学）；University College London（伦敦大学学院）
Appropriate weight initialization has been of key importance to successfully train neural networks. Recently, batch normalization has diminished the role of weight initialization by simply normalizing each layer based on batch statistics. Unfortunately, batch normalization has several drawbacks when applied to small batch sizes, as they are required to cope with memory limitations when learning on point clouds. While well-founded weight initialization strategies can render batch normalization unnecessary and thus avoid these drawbacks, no such approaches have been proposed for point convolutio…
Convergence rate of training algorithms for neural networks is heavily affected by initialization of weights. In this paper, an original algorithm for initialization of weights in backpropagation neural net is presented with application to character recognition. The initialization method is mainly based on a customization of the Kalman filter, translating it into Bayesian statistics terms. A metrological approach is used in this context considering weights as measurements modeled by mutually dependent normal random variables. The algorithm performance is demonstrated by reporting and discussin…
Recent studies assessing the efficacy of pruning neural networks methods uncovered a surprising finding: when conducting ablation studies on existing pruning-at-initialization methods, namely SNIP, GraSP, SynFlow, and magnitude pruning, performances of these methods remain unchanged and sometimes even improve when randomly shuffling the mask positions within each layer (Layerwise Shuffling) or sampling new initial weight values (Reinit), while keeping pruning masks the same. We attempt to understand the reason behind such network immunity towards weight/mask modifications, by studying layer-wi…
Residual Network (ResNet) is the state-of-the-art architecture that realizes successful training of really deep neural network. It is also known that good weight initialization of neural network avoids problem of vanishing/exploding gradients. In this paper, simplified models of ResNets are analyzed. We argue that goodness of ResNet is correlated with the fact that ResNets are relatively insensitive to choice of initial weights. We also demonstrate how batch normalization improves backpropagation of deep ResNets without tuning initial values of weights.
In recent years significant progress has been made in successfully training recurrent neural networks (RNNs) on sequence learning problems involving long range temporal dependencies. The progress has been made on three fronts: (a) Algorithmic improvements involving sophisticated optimization techniques, (b) network design involving complex hidden layer nodes and specialized recurrent layer connections and (c) weight initialization methods. In this paper, we focus on recently proposed weight initialization with identity matrix for the recurrent weights in a RNN. This initialization is specifica…
Salesforce Research（赛富时研究院）；Barcelona Supercomputing Center（巴塞罗那超级计算中心）；Montréal Institute for Learning Algorithms（蒙特利尔学习算法研究所）；Université de Montréal（蒙特利尔大学）
Residual networks (ResNet) and weight normalization play an important role in various deep learning applications. However, parameter initialization strategies have not been studied previously for weight normalized networks and, in practice, initialization methods designed for un-normalized networks are used as a proxy. Similarly, initialization for ResNets have also been studied for un-normalized networks and often under simplified settings ignoring the shortcut connection. To address these issues, we propose a novel parameter initialization strategy that avoids explosion/vanishment of informa…
1-Lipschitz Network Initialization for Certifiably Robust Classification Applications: A Decay Problem
The Grainger College of Engineering, Industrial and Enterprise Systems Engineering Department（格拉inger工程学院，工业与企业系统工程系）；Construction Engineering Research Laboratory（建设工程研究实验室）；U.S. Army Corps of Engineers Engineering Research and Development Center（美国陆军工程兵团工程研究与发展中心）
IDInit: A Universal and Stable Initialization Method for Neural Network Training
Harbin Institute of Technology, Shenzhen（哈尔滨工业大学（深圳））；The Chinese University of Hong Kong（香港中文大学）；The Hong Kong Polytechnic University（香港理工大学）；MetaAI（元宇宙人工智能实验室）；Fudan University（复旦大学）；Shanghai Academy of AI for Science（上海人工智能科学研究院）
With the proliferation of deep convolutional neural network (CNN) algorithms for mobile processing, limited precision quantization has become an essential tool for CNN efficiency. Consequently, various works have sought to design fixed precision quantization algorithms and quantization-focused optimization techniques that minimize quantization induced performance degradation. However, there is little concrete understanding of how various CNN design decisions/best practices affect quantized inference behaviour. Weight initialization strategies are often associated with solving issues such as va…
In this work, we propose a data-driven scheme to initialize the parameters of a deep neural network. This is in contrast to traditional approaches which randomly initialize parameters by sampling from transformed standard distributions. Such methods do not use the training data to produce a more informed initialization. Our method uses a sequential layer-wise approach where each layer is initialized using its input activations. The initialization is cast as an optimization problem where we minimize a combination of encoding and decoding losses of the input activations, which is further constra…
Institute of Information Systems, University of Liechtenstein（列支敦士登大学信息系统研究所）
Spatial data exhibits the property that nearby points are correlated. This also holds for learnt representations across layers, but not for commonly used weight initialization methods. Our theoretical analysis quantifies the learning behavior of weights of a single spatial filter. It is thus in contrast to a large body of work that discusses statistical properties of weights. It shows that uncorrelated initialization (i) might lead to poor convergence behavior and (ii) training of (some) parameters is likely subject to slow convergence. Empirical analysis shows that these findings for a single…
We propose a new way of incorporating temporal information present in videos into Spatial Convolutional Neural Networks (ConvNets) trained on images, that avoids training Spatio-Temporal ConvNets from scratch. We describe several initializations of weights in 3D Convolutional Layers of Spatio-Temporal ConvNet using 2D Convolutional Weights learned from ImageNet. We show that it is important to initialize 3D Convolutional Weights judiciously in order to learn temporal representations of videos. We evaluate our methods on the UCF-101 dataset and demonstrate improvement over Spatial ConvNets.
University of Leicester（莱斯特大学）；Siberian Federal University（西伯利亚联邦大学）
The performance of the Self-Organizing Map (SOM) algorithm is dependent on the initial weights of the map. The different initialization methods can broadly be classified into random and data analysis based initialization approach. In this paper, the performance of random initialization (RI) approach is compared to that of principal component initialization (PCI) in which the initial map weights are chosen from the space of the principal component. Performance is evaluated by the fraction of variance unexplained (FVU). Datasets were classified into quasi-linear and non-linear and it was observe…
California Institute of Technology（加州理工学院）；Georgia Institute of Technology（佐治亚理工学院）；NVIDIA（英伟达）
Deep neural networks are usually initialized with random weights, with adequately selected initial variance to ensure stable signal propagation during training. However, selecting the appropriate variance becomes challenging especially as the number of layers grows. In this work, we replace random weight initialization with a fully deterministic initialization scheme, viz., ZerO, which initializes the weights of networks with only zeros and ones (up to a normalization factor), based on identity and Hadamard transforms. Through both theoretical and empirical studies, we demonstrate that ZerO is…
Department of Electrical Engineering Indian Institute of Technology Bombay（印度理工学院孟买分校电气工程系）
Deep neural networks (DNNs) form the backbone of almost every state-of-the-art technique in the fields such as computer vision, speech processing, and text analysis. The recent advances in computational technology have made the use of DNNs more practical. Despite the overwhelming performances by DNN and the advances in computational technology, it is seen that very few researchers try to train their models from the scratch. Training of DNNs still remains a difficult and tedious job. The main challenges that researchers face during training of DNNs are the vanishing/exploding gradient problem a…
