We propose a deep Graph Neural Network (GNN) model that alternates two types of layers. The first type is inspired by Reservoir Computing (RC) and generates new vertex features by iterating a non-linear map until it converges to a fixed point. The second type of layer implements graph pooling operations, that gradually reduce the support graph and the vertex features, and further improve the computational efficiency of the RC-based GNN. The architecture is, therefore, pyramidal. In the last layer, the features of the remaining vertices are combined into a single vector, which represents the graph embedding. Through a mathematical derivation introduced in this paper, we show formally how graph pooling can reduce the computational complexity of the model and speed-up the convergence of the dynamical updates of the vertex features. Our proposed approach to the design of RC-based GNNs offers an advantageous and principled trade-off between accuracy and complexity, which we extensively demonstrate in experiments on a large set of graph datasets.
TU Kaiserslautern（凯泽斯劳滕工业大学）；MPI-MIS（马克斯·普朗克软件系统研究所）；IST Austria（奥地利科学技术研究所）
Recent works have shown that gradient descent can find a global minimum for over-parameterized neural networks where the widths of all the hidden layers scale polynomially with $N$ ($N$ being the number of training samples). In this paper, we prove that, for deep networks, a single layer of width $N$ following the input layer suffices to ensure a similar guarantee. In particular, all the remaining layers are allowed to have constant widths, and form a pyramidal topology. We show an application of our result to the widely used LeCun's initialization and obtain an over-parameterization requireme…
Expressivity plays a fundamental role in evaluating deep neural networks, and it is closely related to understanding the limit of performance improvement. In this paper, we propose a three-pipeline training framework based on critical expressivity, including global model contraction, weight evolution, and link's weight rewiring. Specifically, we propose a pyramidal-like skeleton to overcome the saddle points that affect information transfer. Then we analyze the reason for the modularity (clustering) phenomenon in network topology and use it to rewire potential erroneous weighted links. We cond…
Inception Institute of Artificial Intelligence（起始人工智能研究所）
This work introduces pyramidal convolution (PyConv), which is capable of processing the input at multiple filter scales. PyConv contains a pyramid of kernels, where each level involves different types of filters with varying size and depth, which are able to capture different levels of details in the scene. On top of these improved recognition capabilities, PyConv is also efficient and, with our formulation, it does not increase the computational cost and parameters compared to standard convolution. Moreover, it is very flexible and extensible, providing a large space of potential network arch…
Machine Learning for graphs is nowadays a research topic of consolidated relevance. Common approaches in the field typically resort to complex deep neural network architectures and demanding training algorithms, highlighting the need for more efficient solutions. The class of Reservoir Computing (RC) models can play an important role in this context, enabling to develop fruitful graph embeddings through untrained recursive architectures. In this paper, we study progressive simplifications to the design strategy of RC neural networks for graphs. Our core proposal is based on shaping the organiz…
The implementation of artificial neural networks in hardware substrates is a major interdisciplinary enterprise. Well suited candidates for physical implementations must combine nonlinear neurons with dedicated and efficient hardware solutions for both connectivity and training. Reservoir computing addresses the problems related with the network connectivity and training in an elegant and efficient way. However, important questions regarding impact of reservoir size and learning routines on the convergence-speed during learning remain unaddressed. Here, we study in detail the learning process …
École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；Yerevan State University（埃里温国立大学）
Reservoir Computing is a class of Recurrent Neural Networks with internal weights fixed at random. Stability relates to the sensitivity of the network state to perturbations. It is an important property in Reservoir Computing as it directly impacts performance. In practice, it is desirable to stay in a stable regime, where the effect of perturbations does not explode exponentially, but also close to the chaotic frontier where reservoir dynamics are rich. Open questions remain today regarding input regularization and discontinuous activation functions. In this work, we use the recurrent kernel …
The University of Sydney（悉尼大学）；Humboldt-University of Berlin（柏林洪堡大学）；Bielefeld University（比勒费尔德大学）；National Research Council of Canada（加拿大国家研究委员会）
Differentiable neural computers extend artificial neural networks with an explicit memory without interference, thus enabling the model to perform classic computation tasks such as graph traversal. However, such models are difficult to train, requiring long training times and large datasets. In this work, we achieve some of the computational capabilities of differentiable neural computers with a model that can be trained very efficiently, namely an echo state network with an explicit memory without interference. This extension enables echo state networks to recognize all regular languages, inc…
In recent years, Neural Turing Machines have gathered attention by joining the flexibility of neural networks with the computational capabilities of Turing machines. However, Neural Turing Machines are notoriously hard to train, which limits their applicability. We propose reservoir memory machines, which are still able to solve some of the benchmark tests for Neural Turing Machines, but are much faster to train, requiring only an alignment algorithm and linear regression. Our model can also be seen as an extension of echo state networks with an external memory, enabling arbitrarily long stora…
Reservoir Computing (RC) is a well-known strategy for designing Recurrent Neural Networks featured by striking efficiency of training. The crucial aspect of RC is to properly instantiate the hidden recurrent layer that serves as dynamical memory to the system. In this respect, the common recipe is to create a pool of randomly and sparsely connected recurrent neurons. While the aspect of sparsity in the design of RC systems has been debated in the literature, it is nowadays understood mainly as a way to enhance the efficiency of computation, exploiting sparse matrix operations. In this paper, w…
Università Degli Studi Di Pavia（帕维亚大学）；STMicroelectronics（意法半导体）
Echo State Networks (ESN) are a class of Recurrent Neural Networks (RNN) that has gained substantial popularity due to their effectiveness, ease of use and potential for compact hardware implementation. An ESN contains the three network layers input, reservoir and readout where the reservoir is the truly recurrent network. The input and reservoir layers of an ESN are initialized at random and never trained afterwards and the training of the ESN is applied to the readout layer only. The alternative of Recursive Neural Gas (RNG) is one of the many proposals of fully-trainable reservoirs that can…
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究院）；Gazpromneft Science and Technology Centre（俄罗斯天然气工业石油公司科技中心）
We present a novel technique for assessing the dynamics of multiphase fluid flow in the oil reservoir. We demonstrate an efficient workflow for handling the 3D reservoir simulation data in a way which is orders of magnitude faster than the conventional routine. The workflow (we call it "Metamodel") is based on a projection of the system dynamics into a latent variable space, using Variational Autoencoder model, where Recurrent Neural Network predicts the dynamics. We show that being trained on multiple results of the conventional reservoir modelling, the Metamodel does not compromise the accur…
University of Sheffield（谢菲尔德大学）；The University of Sheffield（谢菲尔德大学）
"Sparse" neural networks, in which relatively few neurons or connections are active, are common in both machine learning and neuroscience. Whereas in machine learning, "sparsity" is related to a penalty term that leads to some connecting weights becoming small or zero, in biological brains, sparsity is often created when high spiking thresholds prevent neuronal activity. Here we introduce sparsity into a reservoir computing network via neuron-specific learnable thresholds of activity, allowing neurons with low thresholds to contribute to decision-making but suppressing information from neurons…
Recently, reinforcement learning models have achieved great success, completing complex tasks such as mastering Go and other games with higher scores than human players. Many of these models collect considerable data on the tasks and improve accuracy by extracting visual and time-series features using convolutional neural networks (CNNs) and recurrent neural networks, respectively. However, these networks have very high computational costs because they need to be trained by repeatedly using a large volume of past playing data. In this study, we propose a novel practical approach called reinfor…
We develop a proxy model based on deep learning methods to accelerate the simulations of oil reservoirs--by three orders of magnitude--compared to industry-strength physics-based PDE solvers. This paper describes a new architectural approach to this task, accompanied by a thorough experimental evaluation on a publicly available reservoir model. We demonstrate that in a practical setting a speedup of more than 2000X can be achieved with an average sequence error of about 10\% relative to the oil-field simulator. The proxy model is contrasted with a high-quality physics-based acceleration baseli…
W. M. Keck Science Department of Pitzer, Scripps, and Claremont McKenna College（皮泽学院、斯克里普斯学院和克莱蒙特·麦肯纳学院W.M.凯克科学系）；Nanyang Technological University（南洋理工大学）；University of California at Davis（加州大学戴维斯分校）
Recurrent neural networks are used to forecast time series in finance, climate, language, and from many other domains. Reservoir computers are a particularly easily trainable form of recurrent neural network. Recently, a "next-generation" reservoir computer was introduced in which the memory trace involves only a finite number of previous symbols. We explore the inherent limitations of finite-past memory traces in this intriguing proposal. A lower bound from Fano's inequality shows that, on highly non-Markovian processes generated by large probabilistic state machines, next-generation reservoi…
Beckman Institute for Advanced Science and Technology, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校贝克曼先进科学技术研究所）；Mechanical Science and Engineering, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校机械科学与工程学院）；National Center for Supercomputing Applications, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校国家超级计算应用中心）；The Grainger College of Engineering, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校格兰杰工程学院）；Carl R. Woese Institute for Genomic Biology, University of Illinois Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校卡尔·R·沃斯基因组生物学研究所）
Reservoir computing is a neural network approach for processing time-dependent signals that has seen rapid development in recent years. Physical implementations of the technique using optical reservoirs have demonstrated remarkable accuracy and processing speed at benchmark tasks. However, these approaches require an electronic output layer to maintain high performance, which limits their use in tasks such as time-series prediction, where the output is fed back into the reservoir. We present here a reservoir computing scheme that has rapid processing speed both by the reservoir and the output …
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究所）；Gazprom Neft, Science and Technology Center（俄罗斯天然气工业石油公司科技中心）
We develop a data-driven model, introducing recent advances in machine learning to reservoir simulation. We use a conventional reservoir modeling tool to generate training set and a special ensemble of artificial neural networks (ANNs) to build a predictive model. The ANN-based model allows to reproduce the time dependence of fluids and pressure distribution within the computational cells of the reservoir model. We compare the performance of the ANN-based model with conventional reservoir modeling and illustrate that ANN-based model (1) is able to capture all the output parameters of the conve…
Petrozavodsk State University（彼得罗扎沃茨克国立大学）；K-SkAI LLC（K-SkAI有限责任公司）
The presented compact algorithm for recognizing handwritten digits of the MNIST database, created on the LogNNet reservoir neural network, reaches the recognition accuracy of 82%. The algorithm was tested on a low-memory Arduino board with 2 Kb static RAM low-power microcontroller. The dependences of the accuracy and time of image recognition on the number of neurons in the reservoir have been investigated. The memory allocation demonstrates that the algorithm stores all the necessary information in RAM without using additional data storage, and operates with original images without preliminar…
Skolkovo Institute of Science and Technology（斯科尔科沃科学技术研究院）；TOTAL Research and Development（道达尔研发中心）
Reservoir simulation and adaptation (also known as history matching) are typically considered as separate problems. While a set of models are aimed at the solution of the forward simulation problem assuming all initial geological parameters are known, the other set of models adjust geological parameters under the fixed forward simulation model to fit production data. This results in many difficulties for both reservoir engineers and developers of new efficient computation schemes. We present a unified approach to reservoir simulation and adaptation problems. A single neural network model allow…
Spatiotemporal information processing is fundamental to brain functions. The present study investigates a canonic neural network model for spatiotemporal pattern recognition. Specifically, the model consists of two modules, a reservoir subnetwork and a decision-making subnetwork. The former projects complex spatiotemporal patterns into spatially separated neural representations, and the latter reads out these neural representations via integrating information over time; the two modules are combined together via supervised-learning using known examples. We elucidate the working mechanism of the…
Faculty of Information Technology, Monash University（莫纳什大学信息技术学院）；Monash University（莫纳什大学）
Previous work has questioned the conditions under which the decision regions of a neural network are connected and further showed the implications of the corresponding theory to the problem of adversarial manipulation of classifiers. It has been proven that for a class of activation functions including leaky ReLU, neural networks having a pyramidal structure, that is no layer has more hidden units than the input dimension, produce necessarily connected decision regions. In this paper, we advance this important result by further developing the sufficient and necessary conditions under which the…
University of Maryland（马里兰大学）；Institute for Adv. Computer Studies（高级计算机研究所）
Deep Reservoir Computing has emerged as a new paradigm for deep learning, which is based around the reservoir computing principle of maintaining random pools of neurons combined with hierarchical deep learning. The reservoir paradigm reflects and respects the high degree of recurrence in biological brains, and the role that neuronal dynamics play in learning. However, one issue hampering deep reservoir network development is that one cannot backpropagate through the reservoir layers. Recent deep reservoir architectures do not learn hidden or hierarchical representations in the same manner as d…
University College Cork（科克大学）；Raytheon Technologies Research Center Ireland（雷神技术爱尔兰研究中心）
Multifunctionality is a well observed phenomenological feature of biological neural networks and considered to be of fundamental importance to the survival of certain species over time. These multifunctional neural networks are capable of performing more than one task without changing any network connections. In this paper we investigate how this neurological idiosyncrasy can be achieved in an artificial setting with a modern machine learning paradigm known as `Reservoir Computing'. A training technique is designed to enable a Reservoir Computer to perform tasks of a multifunctional nature. We…
Reservoir computing (RC) offers efficient temporal data processing with a low training cost by separating recurrent neural networks into a fixed network with recurrent connections and a trainable linear network. The quality of the fixed network, called reservoir, is the most important factor that determines the performance of the RC system. In this paper, we investigate the influence of the hierarchical reservoir structure on the properties of the reservoir and the performance of the RC system. Analogous to deep neural networks, stacking sub-reservoirs in series is an efficient way to enhance …
Ecole Normale Supérieure（巴黎高等师范学院）；Université PSL（巴黎文理研究大学）；CNRS（法国国家科学研究中心）；Sorbonne Université（索邦大学）；Université de Paris（巴黎大学）；Collège de France（法兰西公学院）；LightOn（LightOn公司）；Ecole Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）
Reservoir Computing is a class of simple yet efficient Recurrent Neural Networks where internal weights are fixed at random and only a linear output layer is trained. In the large size limit, such random neural networks have a deep connection with kernel methods. Our contributions are threefold: a) We rigorously establish the recurrent kernel limit of Reservoir Computing and prove its convergence. b) We test our models on chaotic time series prediction, a classic but challenging benchmark in Reservoir Computing, and show how the Recurrent Kernel is competitive and computationally efficient whe…
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…
The use of electroencephalogram (EEG) as the main input signal in brain-machine interfaces has been widely proposed due to the non-invasive nature of the EEG. Here we are specifically interested in interfaces that extract information from the auditory system and more specifically in the task of classifying heard speech from EEGs. To do so, we propose to limit the preprocessing of the EEGs and use machine learning approaches to automatically extract their meaningful characteristics. More specifically, we use a regulated recurrent neural network (RNN) reservoir, which has been shown to outperfor…
Faculty of Engineering（工学院）；University of Tsukuba（筑波大学）；Toyota Motor Corporation（丰田汽车公司）
Reservoir computing derived from recurrent neural networks is more applicable to real world systems than deep learning because of its low computational cost and potential for physical implementation. Specifically, physical reservoir computing, which replaces the dynamics of reservoir units with physical phenomena, has recently received considerable attention. In this study, we propose a method of exploiting the dynamics of road traffic as a reservoir, and numerically confirm its feasibility by applying several prediction tasks based on a simple mathematical model of the traffic flow.
Recurrent neural network (RNN) based reinforcement learning (RL) is used for learning context-dependent tasks and has also attracted attention as a method with remarkable learning performance in recent research. However, RNN-based RL has some issues that the learning procedures tend to be more computationally expensive, and training with backpropagation through time (BPTT) is unstable because of vanishing/exploding gradients problem. An approach with replay memory introducing reservoir computing has been proposed, which trains an agent without BPTT and avoids these issues. The basic idea of th…
China University of Geosciences（中国地质大学）；Monash University（莫纳什大学）
This paper addresses the general problem of accurate identification of oil reservoirs. Recent improvements in well or borehole logging technology have resulted in an explosive amount of data available for processing. The traditional methods of analysis of the logs characteristics by experts require significant amount of time and money and is no longer practicable. In this paper, we use the semi-supervised learning to solve the problem of ever-increasing amount of unlabelled data available for interpretation. The experts are needed to label only a small amount of the log data. The neural networ…
Channing Division of Network Medicine, Brigham and Women’s Hospital, Harvard Medical School（哈佛医学院布莱根妇女医院钱宁网络医学部）；Max Planck Institute for Mathematics in the Sciences（马克斯·普朗克数学科学研究所）；School of Physics Science and Engineering, Tongji University（同济大学物理科学与工程学院）；Center for Cancer Systems Biology, Dana Farber Cancer Institute（丹娜法伯癌症研究所癌症系统生物学中心）
As one of the most important paradigms of recurrent neural networks, the echo state network (ESN) has been applied to a wide range of fields, from robotics to medicine, finance, and language processing. A key feature of the ESN paradigm is its reservoir --- a directed and weighted network of neurons that projects the input time series into a high dimensional space where linear regression or classification can be applied. Despite extensive studies, the impact of the reservoir network on the ESN performance remains unclear. Combining tools from physics, dynamical systems and network science, we …
Wells Fargo（富国银行）；IBM Quantum, IBM Research（IBM研究院IBM量子部门）
Recent developments in quantum computing and machine learning have propelled the interdisciplinary study of quantum machine learning. Sequential modeling is an important task with high scientific and commercial value. Existing VQC or QNN-based methods require significant computational resources to perform the gradient-based optimization of a larger number of quantum circuit parameters. The major drawback is that such quantum gradient calculation requires a large amount of circuit evaluation, posing challenges in current near-term quantum hardware and simulation software. In this work, we appro…
John A. Paulson School of Engineering and Applied Sciences（约翰·A·保尔森工程与应用科学学院）；Harvard University（哈佛大学）
Reservoir computers (RCs) are among the fastest to train of all neural networks, especially when they are compared to other recurrent neural networks. RC has this advantage while still handling sequential data exceptionally well. However, RC adoption has lagged other neural network models because of the model's sensitivity to its hyper-parameters (HPs). A modern unified software package that automatically tunes these parameters is missing from the literature. Manually tuning these numbers is very difficult, and the cost of traditional grid search methods grows exponentially with the number of …
A Novel A.I Enhanced Reservoir Characterization with a Combined Mixture of Experts -- NVIDIA Modulus based Physics Informed Neural Operator Forward Model
Graduate school of Systems and Information Engineering（系统与信息工程研究生院）；University of Tsukuba（筑波大学）
Recently, reinforcement learning models have achieved great success, mastering complex tasks such as Go and other games with higher scores than human players. Many of these models store considerable data on the tasks and achieve high performance by extracting visual and time-series features using convolutional neural networks (CNNs) and recurrent neural networks, respectively. However, these networks have very high computational costs because they need to be trained by repeatedly using the stored data. In this study, we propose a novel practical approach called reinforcement learning with conv…
John A. Paulson School of Engineering and Applied Sciences, Harvard University（哈佛大学约翰·A·保尔森工程与应用科学学院）
There is a wave of interest in using unsupervised neural networks for solving differential equations. The existing methods are based on feed-forward networks, {while} recurrent neural network differential equation solvers have not yet been reported. We introduce an unsupervised reservoir computing (RC), an echo-state recurrent neural network capable of discovering approximate solutions that satisfy ordinary differential equations (ODEs). We suggest an approach to calculate time derivatives of recurrent neural network outputs without using backpropagation. The internal weights of an RC are fixe…
Saarland University（萨尔兰大学）；University of Tübingen（蒂宾根大学）
In the recent literature the important role of depth in deep learning has been emphasized. In this paper we argue that sufficient width of a feedforward network is equally important by answering the simple question under which conditions the decision regions of a neural network are connected. It turns out that for a class of activation functions including leaky ReLU, neural networks having a pyramidal structure, that is no layer has more hidden units than the input dimension, produce necessarily connected decision regions. This implies that a sufficiently wide hidden layer is necessary to guar…
