Readout Layer Research Articles

Graph Convolutional Networks for Exercise Motion Classification

The growth in self-fitness mobile applications has encouraged people to turn to personal fitness, which entails integrating self-tracking applications with exercise motion data to reduce fatigue and mitigate the risk of injury. The advancements in computer vision and motion capture technologies hold great promise to improve exercise classification performance. This study investigates a supervised deep learning model performance, Graph Convolutional Network (GCN) to classify three workouts using the Azure Kinect device’s motion data. The model defines the skeleton as a graph and combines GCN layers, a readout layer, and multi-layer perceptrons to build an end-to-end framework for graph classification. The model achieves an accuracy of 95.86% in classifying 19,442 frames. The current model exchanges feature information between each joint and its 1-nearest neighbor, which impact fades in graph-level classification. Therefore, a future study on improved feature utilization can enhance the model performance in classifying inter-user exercise variation.

Implementation of a reservoir computing system using the short-term effects of Pt/HfO2/TaOx/TiN memristors with self-rectification

Given the limitations of von Neumann computing systems, we propose a high-performance reservoir computing system as an alternative. These systems operate as neural networks that store the states of the input signal and require a readout layer for data processing and learning. The advantage of this system is that training only takes place at the readout layer leading to good energy efficiency and low power consumption. In this paper, we implement a memristor-based hardware reservoir computing system using HfO 2 /TaO x bilayer based memristor that can imitate the short-term memory effects. We first characterize the volatility and record the self-rectification I-V curves of the HfO 2 /TaO x bilayer device. We also investigate the transient characteristics in terms of the interval required between pulse stimulation to return its initial state. In terms of transmitting information, 4 bits is a significant unit size because at least 4 bits are required to represent a single-digit number. Motivated by this, we successfully implemented a binary 4-bit code ranging from [0 0 0 0] to [1 1 1 1] in the fabricated memristor that can be used as the input signal to a reservoir layer.

Pixelated Photoinduced Discharge Readout X-Ray Detector Using 450-nm LED Line Beam

This paper describes a study on a novel X-ray detector with photoinduced discharge (PID) readout devices. Especially, we demonstrated optical scanning X-ray imaging devices based on intrinsic hydrogenated amorphous silicon (i-a-Si:H) PID readout layer, on which a pixelated metal layer, molybdenum, is formed as a charge accumulation layer of 200 μm pitch for clearly defining the pixel in the lateral and longitudinal directions. We decided to use i-a-Si:H as a readout layer instead of amorphous selenium(a-Se) layer because the material of a-Se does not withstand standard wet fabrication processes like lift-off wet process. An X-ray absorption layer of 500 μm thick a-Se is formed by a thermal evaporation process. To optically switch on the i-a-Si:H PID readout layer, we use a narrow line-beam with a beam width of 50 μm consisting of a blue LED array, optical films, and GRIN lens array. The pixelated PID readout X-ray detector is 512×512 image resolutions with a 200 μm pitch, and the overall active dimension is 10.24 cm ×10.24 cm. The sensitivity of the pixelated PID readout X-ray detector is 302 pC/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ·mR at Normal X-ray Tube conditions (IEC66220-1). According to MTF measurement results, the value of MTF0.1(10%) is measured at near 2.5 1/mm in the column direction scanning while the value is measured at 1.9-2.5 1/mm in the row direction scanning.

Discrete-Time Signatures and Randomness in Reservoir Computing.

A new explanation of the geometric nature of the reservoir computing (RC) phenomenon is presented. RC is understood in the literature as the possibility of approximating input-output systems with randomly chosen recurrent neural systems and a trained linear readout layer. Light is shed on this phenomenon by constructing what is called strongly universal reservoir systems as random projections of a family of state-space systems that generate Volterra series expansions. This procedure yields a state-affine reservoir system with randomly generated coefficients in a dimension that is logarithmically reduced with respect to the original system. This reservoir system is able to approximate any element in the fading memory filters class just by training a different linear readout for each different filter. Explicit expressions for the probability distributions needed in the generation of the projected reservoir system are stated, and bounds for the committed approximation error are provided.

Event-Based Trajectory Prediction Using Spiking Neural Networks.

In recent years, event-based sensors have been combined with spiking neural networks (SNNs) to create a new generation of bio-inspired artificial vision systems. These systems can process spatio-temporal data in real time, and are highly energy efficient. In this study, we used a new hybrid event-based camera in conjunction with a multi-layer spiking neural network trained with a spike-timing-dependent plasticity learning rule. We showed that neurons learn from repeated and correlated spatio-temporal patterns in an unsupervised way and become selective to motion features, such as direction and speed. This motion selectivity can then be used to predict ball trajectory by adding a simple read-out layer composed of polynomial regressions, and trained in a supervised manner. Hence, we show that a SNN receiving inputs from an event-based sensor can extract relevant spatio-temporal patterns to process and predict ball trajectories.

Towards Embedded Computation with Building Materials

We present results showing the capability of concrete-based information processing substrate in the signal classification task in accordance with in materio computing paradigm. As the Reservoir Computing is a suitable model for describing embedded in materio computation, we propose that this type of presented basic construction unit can be used as a source for “reservoir of states” necessary for simple tuning of the readout layer. We present an electrical characterization of the set of samples with different additive concentrations followed by a dynamical analysis of selected specimens showing fingerprints of memfractive properties. As part of dynamic analysis, several fractal dimensions and entropy parameters for the output signal were analyzed to explore the richness of the reservoir configuration space. In addition, to investigate the chaotic nature and self-affinity of the signal, Lyapunov exponents and Detrended Fluctuation Analysis exponents were calculated. Moreover, on the basis of obtained parameters, classification of the signal waveform shapes can be performed in scenarios explicitly tuned for a given device terminal.

Protein Structured Reservoir Computing for Spike-Based Pattern Recognition

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 property. We have chosen Izhikevich spiking neurons as elementary processors, corresponding to the atoms of verotoxin protein, and its molecule as a 'hardware' architecture of the communication networks connecting the processors. We apply on a single readout layer various training methods in a supervised fashion to investigate whether the molecular structured Reservoir Computing (RC) system is capable to deal with machine learning benchmarks. We start with the Remote Supervised Method, based on Spike-Timing-Dependent-Plasticity, and carry on with linear regression and scaled conjugate gradient back-propagation training methods. The RC network is evaluated as a proof-of-concept on the handwritten digit images from the MNIST dataset and demonstrates acceptable classification accuracy in comparison with other similar approaches.

Machine-Learning-Assisted Closed-Loop Reservoir Management Using Echo State Network for Mature Fields under Waterflood

Summary Closed-loop reservoir management (CLRM) consists of continuous application of history matching and optimization of model-predictive control to maximize production or reservoir net present value (NPV) in any given period. Traditional field-scale implementation of CLRM by using a large number of reservoir models, in particular when uncertainty is accounted for, is computationally impractical. This presented machine-learning-assisted workflow uses the echo state network (ESN) coupled with an empirical water fractional flow relationship as a proxy to replace time-consuming simulations and improve the computational efficiency of the CLRM. The ESN, under the paradigm of reservoir computing, provides a specific architecture and supervised learning principle for recurrent neural networks (RNNs). ESNs, with randomly generated and invariant input weights and recurrent weights, greatly minimize the computational load and solve potential problems during typical backpropagation through time in traditional RNNs while it still obtains the benefits of RNNs to memorize temporal dependencies. Also, the linear readout layer makes the training much faster using analytical ridge regression. Field-level well control and production-response data are fed into the workflow to obtain a trained ESN and fitted fractional-flow relationship, which will represent/reproduce the dynamics of the reservoir under various well-control scenarios. Further production optimization is directly applied to the matched models to maximize reservoir NPV. The optimized well-control scenario is applied, and further observation is obtained to update the models. History matching and production optimization are performed again in a closed-loop fashion. The previously mentioned advantages make ESN a very powerful tool for CLRM, with both history matching and production optimization quickly accomplished, and make near-real-time CLRM possible. In this paper, two case studies will be presented to prove the effectiveness of the proposed workflow.

A neuro-inspired general framework for the evolution of stochastic dynamical systems: Cellular automata, random Boolean networks and echo state networks towards criticality

Although deep learning has recently increased in popularity, it suffers from various problems including high computational complexity, energy greedy computation, and lack of scalability, to mention a few. In this paper, we investigate an alternative brain-inspired method for data analysis that circumvents the deep learning drawbacks by taking the actual dynamical behavior of biological neural networks into account. For this purpose, we develop a general framework for dynamical systems that can evolve and model a variety of substrates that possess computational capacity. Therefore, dynamical systems can be exploited in the reservoir computing paradigm, i.e., an untrained recurrent nonlinear network with a trained linear readout layer. Moreover, our general framework, called EvoDynamic, is based on an optimized deep neural network library. Hence, generalization and performance can be balanced. The EvoDynamic framework contains three kinds of dynamical systems already implemented, namely cellular automata, random Boolean networks, and echo state networks. The evolution of such systems towards a dynamical behavior, called criticality, is investigated because systems with such behavior may be better suited to do useful computation. The implemented dynamical systems are stochastic and their evolution with genetic algorithm mutates their update rules or network initialization. The obtained results are promising and demonstrate that criticality is achieved. In addition to the presented results, our framework can also be utilized to evolve the dynamical systems connectivity, update and learning rules to improve the quality of the reservoir used for solving computational tasks and physical substrate modeling.

Temporal Backpropagation for Spiking Neural Networks with One Spike per Neuron.

We propose a new supervised learning rule for multilayer spiking neural networks (SNNs) that use a form of temporal coding known as rank-order-coding. With this coding scheme, all neurons fire exactly one spike per stimulus, but the firing order carries information. In particular, in the readout layer, the first neuron to fire determines the class of the stimulus. We derive a new learning rule for this sort of network, named S4NN, akin to traditional error backpropagation, yet based on latencies. We show how approximated error gradients can be computed backward in a feedforward network with any number of layers. This approach reaches state-of-the-art performance with supervised multi-fully connected layer SNNs: test accuracy of 97.4% for the MNIST dataset, and 99.2% for the Caltech Face/Motorbike dataset. Yet, the neuron model that we use, nonleaky integrate-and-fire, is much simpler than the one used in all previous works. The source codes of the proposed S4NN are publicly available at https://github.com/SRKH/S4NN.

A digital hardware implementation of spiking neural networks with binary FORCE training

The brain, a network of spiking neurons, can learn complex dynamics by adapting its spontaneous chaotic activity. One of the dominant approaches used to train such a network, the FORCE method, has recently been applied to spiking neural networks. This method employs a pool of randomly connected spiking neurons, called a reservoir, to create chaos and uses the recursive least square (RLS) method to change its dynamic to what is required to follow a teacher signal. Here, we propose a digital hardware architecture for spiking FORCE with some modifications to the original method. First, to reduce the memory usage in hardware implementation, we show that careful binarization of the reservoir weights could preserve its initial chaotic activity. Second, we generate the connection matrix on-the-fly instead of storing the whole matrix. Third, a single processor systolic array implementation of the RLS using the inverse QR decomposition is exploited to update the readout layer weights. This implementation is not only more hardware-friendly but also more numerically stable in reduced precision than the standard RLS implementation. Fourth, we implement the design in both single and custom-precision floating-point number systems. Finally, we implement a network of 510 Izhikevic neurons on a Xilinx Artix-7 FPGA with 32, 24, and 18 bits floating-point numbers. To confirm the correctness of our architecture, we successfully train our hardware using three different teacher signals.

Embedding and approximation theorems for echo state networks

Echo State Networks (ESNs) are a class of single-layer recurrent neural networks that have enjoyed recent attention. In this paper we prove that a suitable ESN, trained on a series of measurements of an invertible dynamical system, induces a C1 map from the dynamical system’s phase space to the ESN’s reservoir space. We call this the Echo State Map. We then prove that the Echo State Map is generically an embedding with positive probability.Under additional mild assumptions, we further conjecture that the Echo State Map is almost surely an embedding. For sufficiently large, and specially structured, but still randomly generated ESNs, we prove that there exists a linear readout layer that allows the ESN to predict the next observation of a dynamical system arbitrarily well. Consequently, if the dynamical system under observation is structurally stable then the trained ESN will exhibit dynamics that are topologically conjugate to the future behaviour of the observed dynamical system.Our theoretical results connect the theory of ESNs to the delay-embedding literature for dynamical systems, and are supported by numerical evidence from simulations of the traditional Lorenz equations. The simulations confirm that, from a one dimensional observation function, an ESN can accurately infer a range of geometric and topological features of the dynamics such as the eigenvalues of equilibrium points, Lyapunov exponents and homology groups.

On Sensing Principles Using Temporally Extended Bar Codes

The detection of ionic variation patterns could be a significant marker for the diagnosis of neurological and other diseases. This paper introduces a novel idea for training chemical sensors to recognise patterns of ionic variations. By using an external voltage signal, a sensor can be trained to output distinct time-series signals depending on the state of the ionic solution. Those sequences can be analysed by a relatively simple readout layer for diagnostic purposes. The idea is demonstrated on a chemical sensor that is sensitive to zinc ions with a simple goal of classifying zinc ionic variations as either stable or varying. The study features both theoretical and experimental results. By extensive numerical simulations, it has been shown that the proposed method works successfully in silico . Distinct time-series signals are found which occur with a high probability under only one class of ionic variations. The related experimental results point in the right direction.

Echo state network‐based feature extraction for efficient color image segmentation

SummaryImage segmentation plays a crucial role in many image processing and understanding applications. Despite the huge number of proposed image segmentation techniques, accurate segmentation remains a significant challenge in image analysis. This article investigates the viability of using echo state network (ESN), a biologically inspired recurrent neural network, as features extractor for efficient color image segmentation. First, an ensemble of initial pixel features is extracted from the original images and injected into the ESN reservoir. Second, the internal activations of the reservoir neurons are used as new pixel features. Third, the new features are classified using a feed forward neural network as a readout layer for the ESN. The quality of the pixel features produced by the ESN is evaluated through extensive series of experiments conducted on real world image datasets. The optimal operating range of different ESN setup parameters for producing competitive quality features is identified. The performance of the proposed ESN‐based framework is also evaluated on a domain‐specific application, namely, blood vessel segmentation in retinal images where experiments are conducted on the widely used digital retinal images for vessel extraction (DRIVE) dataset. The obtained results demonstrate that the proposed method outperforms state‐of‐the‐art general segmentation techniques in terms of performance with an F‐score of 0.92 ± 0.003 on the segmentation evaluation dataset. In addition, the proposed method achieves a comparable segmentation accuracy (0.9470) comparing with reported techniques of segmentation of blood vessels in images of retina and outperform them in terms of processing time. The average time required by our technique to segment one retinal image from DRIVE dataset is 8 seconds. Furthermore, empirically derived guidelines are proposed for adequately setting the ESN parameters for effective color image segmentation.

Learning spatiotemporal signals using a recurrent spiking network that discretizes time.

Learning to produce spatiotemporal sequences is a common task that the brain has to solve. The same neurons may be used to produce different sequential behaviours. The way the brain learns and encodes such tasks remains unknown as current computational models do not typically use realistic biologically-plausible learning. Here, we propose a model where a spiking recurrent network of excitatory and inhibitory spiking neurons drives a read-out layer: the dynamics of the driver recurrent network is trained to encode time which is then mapped through the read-out neurons to encode another dimension, such as space or a phase. Different spatiotemporal patterns can be learned and encoded through the synaptic weights to the read-out neurons that follow common Hebbian learning rules. We demonstrate that the model is able to learn spatiotemporal dynamics on time scales that are behaviourally relevant and we show that the learned sequences are robustly replayed during a regime of spontaneous activity.

A Training-Efficient Hybrid-Structured Deep Neural Network With Reconfigurable Memristive Synapses

The continued success in the development of neuromorphic computing has immensely pushed today’s artificial intelligence forward. Deep neural networks (DNNs), a brainlike machine learning architecture, rely on the intensive vector–matrix computation with extraordinary performance in data-extensive applications. Recently, the nonvolatile memory (NVM) crossbar array uniquely has unvailed its intrinsic vector–matrix computation with parallel computing capability in neural network designs. In this article, we design and fabricate a hybrid-structured DNN (hybrid-DNN), combining both depth-in-space (spatial) and depth-in-time (temporal) deep learning characteristics. Our hybrid-DNN employs memristive synapses working in a hierarchical information processing fashion and delay-based spiking neural network (SNN) modules as the readout layer. Our fabricated prototype in 130-nm CMOS technology along with experimental results demonstrates its high computing parallelism and energy efficiency with low hardware implementation cost, making the designed system a candidate for low-power embedded applications. From chaotic time-series forecasting benchmarks, our hybrid-DNN exhibits $1.16\times $ – $13.77\times $ reduction on the prediction error compared to the state-of-the-art DNN designs. Moreover, our hybrid-DNN records 99.03% and 99.63% testing accuracy on the handwritten digit classification and the spoken digit recognition tasks, respectively.

Distributed Kerr Non-linearity in a Coherent All-Optical Fiber-Ring Reservoir Computer

We investigate, both numerically and experimentally, the usefulness of a distributed nonlinearity in a passive coherent photonic reservoir computer. This computing system is based on a passive coherent optical fiber-ring cavity in which part of the nonlinearities are realized by the Kerr nonlinearity. Linear coherent reservoirs can solve difficult tasks but are aided by nonlinear components in their input and/or output layer. Here, we compare the impact of nonlinear transformations of information in the reservoir’s input layer, its bulk - the fiber-ring cavity - and its readout layer. For the injection of data into the reservoir, we compare a linear input mapping to the nonlinear transfer function of a Mach Zehnder modulator. For the reservoir bulk, we quantify the impact of the optical Kerr effect. For the readout layer we compare a linear output to a quadratic output implemented by a photodiode. We find that optical nonlinearities in the reservoir itself, such as the optical Kerr nonlinearity studied in the present work, enhance the task solving capability of the reservoir. This suggests that such nonlinearities will play a key role in future coherent all-optical reservoir computers.

Reservoir Computing Using Diffusive Memristors

Reservoir computing (RC) is a framework that can extract features from a temporal input into a higher‐dimension feature space. The reservoir is followed by a readout layer that can analyze the extracted features to accomplish tasks such as inference and classification. RC systems inherently exhibit an advantage, since the training is only performed at the readout layer, and therefore they are able to compute complicated temporal data with a low training cost. Herein, a physical reservoir computing system using diffusive memristor‐based reservoir and drift memristor‐based readout layer is experimentally implemented. The rich nonlinear dynamic behavior exhibited by a diffusive memristor due to Ag migration and the robust in situ training of drift memristor arrays makes the combined system ideal for temporal pattern classification. It is then demonstrated experimentally that the RC system can successfully identify handwritten digits from the Modified National Institute of Standards and Technology (MNIST) dataset, achieving an accuracy of 83%.

Reinforcement Learning With Low-Complexity Liquid State Machines.

We propose reinforcement learning on simple networks consisting of random connections of spiking neurons (both recurrent and feed-forward) that can learn complex tasks with very little trainable parameters. Such sparse and randomly interconnected recurrent spiking networks exhibit highly non-linear dynamics that transform the inputs into rich high-dimensional representations based on the current and past context. The random input representations can be efficiently interpreted by an output (or readout) layer with trainable parameters. Systematic initialization of the random connections and training of the readout layer using Q-learning algorithm enable such small random spiking networks to learn optimally and achieve the same learning efficiency as humans on complex reinforcement learning (RL) tasks like Atari games. In fact, the sparse recurrent connections cause these networks to retain fading memory of past inputs, thereby enabling them to perform temporal integration across successive RL time-steps and learn with partial state inputs. The spike-based approach using small random recurrent networks provides a computationally efficient alternative to state-of-the-art deep reinforcement learning networks with several layers of trainable parameters.

Phase Noise Robustness of a Coherent Spatially Parallel Optical Reservoir

Reservoir computing is a machine learning algorithm particularly adapted to process time-dependent signals. It can be easily implemented experimentally with good performance. However experimental implementations are subject to noise, which degrades performance. We develop strategies to mitigate the effects of noise. The specific system on which we illustrate our approaches—currently under development in our laboratory—is a coherent linear Fabry–Perot resonator in which neurons are encoded as a grid of spots on the input mirror plane. In this system, changes in the length of the resonator are the major source of noise and can be modeled as phase noise. This can in principle be partially solved by active stabilisation, but it is interesting to find other strategies to counter the effect of phase noise. We show that a completely unknown phase can be tolerated with only a small degradation of performance by using appropriate training and a readout layer architecture in which the output weights depend on the noisy parameter (the phase). Furthermore, the phase can be estimated by the reservoir itself, leading to an architecture in which the reservoir has two outputs, one of which (the phase estimation) is used to control the other. Our approach should find applications in many experimental implementations of reservoir computing.