Echo state networks (ESN), a type of reservoir computing (RC) architecture, are efficient and accurate artificial neural systems for time series processing and learning. An ESN consists of a core of recurrent neural networks, called a reservoir, with a small number of tunable parameters to generate a high-dimensional representation of an input, and a readout layer which is easily trained using regression to produce a desired output from the reservoir states. Certain computational tasks involve real-time calculation of high-order time correlations, which requires nonlinear transformation either in the reservoir or the readout layer. Traditional ESN employs a reservoir with sigmoid or tanh function neurons. In contrast, some types of biological neurons obey response curves that can be described as a product unit rather than a sum and threshold. Inspired by this class of neurons, we introduce a RC architecture with a reservoir of product nodes for time series computation. We find that the product RC shows many properties of standard ESN such as short-term memory and nonlinear capacity. On standard benchmarks for chaotic prediction tasks, the product RC maintains the performance of a standard nonlinear ESN while being more amenable to mathematical analysis. Our study provides evidence that such networks are powerful in highly nonlinear tasks owing to high-order statistics generated by the recurrent product node reservoir.
Compliant robots can be more versatile than traditional robots, but their control is more complex. The dynamics of compliant bodies can however be turned into an advantage using the physical reservoir computing frame-work. By feeding sensor signals to the reservoir and extracting motor signals from the reservoir, closed loop robot control is possible. Here, we present a novel framework for implementing central pattern generators with spiking neural networks to obtain closed loop robot control. Using the FORCE learning paradigm, we train a reservoir of spiking neuron populations to act as a cen…
Reservoir Computation with Networks of Differentiating Neuron Ring Oscillators
College of Computer \& Information Sciences, University of Massachusetts Amherst；Department of Mathematics, Virginia Tech；Allen Discovery Center, Tufts University
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…
The human brain's synapses have remarkable activity-dependent plasticity, where the connectivity patterns of neurons change dramatically, relying on neuronal activities. As a biologically inspired neural network, reservoir computing (RC) has unique advantages in processing spatiotemporal information. However, typical reservoir architectures only take static random networks into account or consider the dynamics of neurons and connectivity separately. In this paper, we propose a structural autonomous development reservoir computing model (sad-RC), which structure can adapt to the specific proble…
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…
Reservoir computing is a brain inspired approach for information processing, well suited to analogue implementations. We report a photonic implementation of a reservoir computer that exploits frequency domain multiplexing to encode neuron states. The system processes 25 comb lines simultaneously (i.e. 25 neurons), at a rate of 20 MHz. We illustrate performances on two standard benchmark tasks: channel equalization and time series forecasting. We also demonstrate that frequency multiplexing allows output weights to be implemented in the optical domain, through optical attenuation. We discuss th…
The University of Tokyo（东京大学）；Toyota Central Research and Development Laboratory Inc.（丰田中央研发实验室股份有限公司）
Machine learning approaches have recently been leveraged as a substitute or an aid for physical/mathematical modeling approaches to dynamical systems. To develop an efficient machine learning method dedicated to modeling and prediction of multiscale dynamics, we propose a reservoir computing (RC) model with diverse timescales by using a recurrent network of heterogeneous leaky integrator (LI) neurons. We evaluate computational performance of the proposed model in two time series prediction tasks related to four chaotic fast-slow dynamical systems. In a one-step-ahead prediction task where inpu…
We consider reservoirs in the form of liquid state machines, i.e., recurrently connected networks of spiking neurons with randomly chosen weights. So far only the weights of a linear readout were adapted for a specific task. We wondered whether the performance of liquid state machines can be improved if the recurrent weights are chosen with a purpose, rather than randomly. After all, weights of recurrent connections in the brain are also not assumed to be randomly chosen. Rather, these weights were probably optimized during evolution, development, and prior learning experiences for specific ta…
Universal approximation theorem suggests that a shallow neural network can approximate any function. The input to neurons at each layer is a weighted sum of previous layer neurons and then an activation is applied. These activation functions perform very well when the output is a linear combination of input data. When trying to learn a function which involves product of input data, the neural networks tend to overfit the data to approximate the function. In this paper we will use properties of logarithmic functions to propose a pair of activation functions which can translate products into lin…
Backpropagation algorithms on recurrent artificial neural networks require an unfolding of accumulated states over time. These states must be kept in memory for an undefined period of time which is task-dependent. This paper uses the reservoir computing paradigm where an untrained recurrent neural network layer is used as a preprocessor stage to learn temporal and limited data. These so-called reservoirs require either extensive fine-tuning or neuroplasticity with unsupervised learning rules. We propose a new local plasticity rule named P-CRITICAL designed for automatic reservoir tuning that t…
Reconstructing Spiking Neural Networks Using a Single Neuron with Autapses
Brain-Apparatus Communication Institute, University of Electronic Science and Technology of China（脑器通信研究院，电子科技大学）；School of Artificial Intelligence, Chongqing University of Education（人工智能学院，重庆教育学院）
Tel-Aviv University（特拉维夫大学）；eBay Research（eBay研究院）；Massachusetts Institute of Technology (MIT)（麻省理工学院（MIT））
Multiplication layers are a key component in various influential neural network modules, including self-attention and hypernetwork layers. In this paper, we investigate the approximation capabilities of deep neural networks with intermediate neurons connected by simple multiplication operations. We consider two classes of target functions: generalized bandlimited functions, which are frequently used to model real-world signals with finite bandwidth, and Sobolev-Type balls, which are embedded in the Sobolev Space $\mathcal{W}^{r,2}$. Our results demonstrate that multiplicative neural networks c…
Biologically inspired recurrent neural networks, such as reservoir computers are of interest in designing spatio-temporal data processors from a hardware point of view due to the simple learning scheme and deep connections to Kalman filters. In this work we discuss using in-depth simulation studies a way to construct hardware reservoir computers using an analog stochastic neuron cell built from a low energy-barrier magnet based magnetic tunnel junction and a few transistors. This allows us to implement a physical embodiment of the mathematical model of reservoir computers. Compact implementati…
Reservoir computing is a powerful tool to explain how the brain learns temporal sequences, such as movements, but existing learning schemes are either biologically implausible or too inefficient to explain animal performance. We show that a network can learn complicated sequences with a reward-modulated Hebbian learning rule if the network of reservoir neurons is combined with a second network that serves as a dynamic working memory and provides a spatio-temporal backbone signal to the reservoir. In combination with the working memory, reward-modulated Hebbian learning of the readout neurons p…
Many recent studies of the motor system are divided into two distinct approaches: Those that investigate how motor responses are encoded in cortical neurons' firing rate dynamics and those that study the learning rules by which mammals and songbirds develop reliable motor responses. Computationally, the first approach is encapsulated by reservoir computing models, which can learn intricate motor tasks and produce internal dynamics strikingly similar to those of motor cortical neurons, but rely on biologically unrealistic learning rules. The more realistic learning rules developed by the second…
Nowadays we witness a miniaturisation trend in the semiconductor industry backed up by groundbreaking discoveries and designs in nanoscale characterisation and fabrication. To facilitate the trend and produce ever smaller, faster and cheaper computing devices, the size of nanoelectronic devices is now reaching the scale of atoms or molecules - a technical goal undoubtedly demanding for novel devices. Following the trend, we explore an unconventional route of implementing a reservoir computing on a single protein molecule and introduce neuromorphic connectivity with a small-world networking pro…
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…
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 …
Reservoir Computing Using Measurement-Controlled Quantum Dynamics
Artificial Intelligence and Cyber Futures Institute, Charles Sturt University（查尔斯斯特大学人工智能与网络未来学院）；Cyber Futures Institute, Charles Sturt University（查尔斯斯特大学网络未来学院）
Echo State Networks represent a type of recurrent neural network with a large randomly generated reservoir and a small number of readout connections trained via linear regression. The most common topology of the reservoir is a fully connected network of up to thousands of neurons. Over the years, researchers have introduced a variety of alternative reservoir topologies, such as a circular network or a linear path of connections. When comparing the performance of different topologies or other architectural changes, it is necessary to tune the hyperparameters for each of the topologies separatel…
Echo state networks are computationally lightweight reservoir models inspired by the random projections observed in cortical circuitry. As interest in reservoir computing has grown, networks have become deeper and more intricate. While these networks are increasingly applied to nontrivial forecasting tasks, there is a need for comprehensive performance analysis of deep reservoirs. In this work, we study the influence of partitioning neurons given a budget and the effect of parallel reservoir pathways across different datasets exhibiting multi-scale and nonlinear dynamics.
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 …
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…
Echo State Networks (ESNs) are simplified recurrent neural network models composed of a reservoir and a linear, trainable readout layer. The reservoir is tunable by some hyper-parameters that control the network behaviour. ESNs are known to be effective in solving tasks when configured on a region in (hyper-)parameter space called \emph{Edge of Criticality} (EoC), where the system is maximally sensitive to perturbations hence affecting its behaviour. In this paper, we propose binary ESNs, which are architecturally equivalent to standard ESNs but consider binary activation functions and binary …
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…
Indiana University（印第安纳大学）；Indiana University Network Science Institute（印第安纳大学网络科学研究所）
The neural network is a powerful computing framework that has been exploited by biological evolution and by humans for solving diverse problems. Although the computational capabilities of neural networks are determined by their structure, the current understanding of the relationships between a neural network's architecture and function is still primitive. Here we reveal that neural network's modular architecture plays a vital role in determining the neural dynamics and memory performance of the network of threshold neurons. In particular, we demonstrate that there exists an optimal modularity…
Faculty of Physics, University of Duisburg-Essen（物理系，杜伊斯堡-埃森大学）；DyNaMat, Department of Solid State Sciences, Ghent University（DyNaMat，固态科学系，根特大学）；Senior Principle Engineer, Intel Corp. (Retired)（高级原则工程师，英特尔公司（退休））；Faculty of Physics（物理系）；Center for Nanointegration Duisburg-Essen (CENIDE), University of Duisburg-Essen（杜伊斯堡-埃森纳米集成中心（CENIDE），杜伊斯堡-埃森大学）
Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC, UIB-CSIC)（跨学科物理与复杂系统研究所（IFISC，巴利阿里群岛大学-西班牙国家研究委员会））；Instituto Carlos I de Física Teórica y Computacional（卡洛斯一世理论与计算物理研究所）
Reservoir Computing (RC) is an appealing approach in Machine Learning that combines the high computational capabilities of Recurrent Neural Networks with a fast and easy training method. Likewise, successful implementation of neuro-inspired plasticity rules into RC artificial networks has boosted the performance of the original models. In this manuscript, we analyze the role that plasticity rules play on the changes that lead to a better performance of RC. To this end, we implement synaptic and non-synaptic plasticity rules in a paradigmatic example of RC model: the Echo State Network. Testing…
The brain efficiently performs nonlinear computations through its intricate networks of spiking neurons, but how this is done remains elusive. While nonlinear computations can be implemented successfully in spiking neural networks, this requires supervised training and the resulting connectivity can be hard to interpret. In contrast, the required connectivity for any computation in the form of a linear dynamical system can be directly derived and understood with the spike coding network (SCN) framework. These networks also have biologically realistic activity patterns and are highly robust to …
Neuro-Inspired Visual Pattern Recognition via Biological Reservoir Computing
Institute of Information Science and Technologies of the National Research Council of Italy (ISTI-CNR)（意大利国家研究理事会信息科学与技术研究所）；Institute of Biophysics of the National Research Council of Italy (IBF-CNR)（意大利国家研究理事会生物物理研究所）
This work studies approximation based on single-hidden-layer feedforward and recurrent neural networks with randomly generated internal weights. These methods, in which only the last layer of weights and a few hyperparameters are optimized, have been successfully applied in a wide range of static and dynamic learning problems. Despite the popularity of this approach in empirical tasks, important theoretical questions regarding the relation between the unknown function, the weight distribution, and the approximation rate have remained open. In this work it is proved that, as long as the unknown…
