Gradient calculations for dynamic recurrent neural networks: a survey

Modelling individual differences in reading using an optimised MikeNet simulator: the impact of reading instruction

Reading is vital for acquiring knowledge and studies have demonstrated that phonology-focused interventions generally yield greater improvements than meaning-focused interventions in English among children with reading disabilities. However, the effectiveness of reading instruction can vary among individuals. Among the various factors that impact reading skills like reading exposure and oral language skills, reading instruction is critical in facilitating children's development into skilled readers; it can significantly influence reading strategies, and contribute to individual differences in reading. To investigate this assumption, we developed a computational model of reading with an optimised MikeNet simulator. In keeping with educational practices, the model underwent training with three different instructional methods: phonology-focused training, meaning-focused training, and phonology-meaning balanced training. We used semantic reliance (SR), a measure of the relative reliance on print-to-sound and print-to-meaning mappings under the different training conditions in the model, as an indicator of individual differences in reading. The simulation results demonstrated a direct link between SR levels and the type of reading instruction. Additionally, the SR scores were able to predict model performance in reading-aloud tasks: higher SR scores were correlated with increased phonological errors and reduced phonological activation. These findings are consistent with data from both behavioral and neuroimaging studies and offer insights into the impact of instructional methods on reading behaviors, while revealing individual differences in reading and the importance of integrating OP and OS instruction approaches for beginning readers.

Anomaly Detection in Railway Sensor Data Environments: State-of-the-Art Methods and Empirical Performance Evaluation

To date, significant progress has been made in the field of railway anomaly detection using technologies such as real-time data analytics, the Internet of Things, and machine learning. As technology continues to evolve, the ability to detect and respond to anomalies in railway systems is once again in the spotlight. However, railway anomaly detection faces challenges related to the vast infrastructure, dynamic conditions, aging infrastructure, and adverse environmental conditions on the one hand, and the scale, complexity, and critical safety implications of railway systems on the other. Our study is underpinned by the three objectives. Specifically, we aim to identify time series anomaly detection methods applied to railway sensor device data, recognize the advantages and disadvantages of these methods, and evaluate their effectiveness. To address the research objectives, the first part of the study involved a systematic literature review and a series of controlled experiments. In the case of the former, we adopted well-established guidelines to structure and visualize the review. In the second part, we investigated the effectiveness of selected machine learning methods. To evaluate the predictive performance of each method, a five-fold cross-validation approach was applied to ensure the highest accuracy and generality. Based on the calculated accuracy, the results show that the top three methods are CatBoost (96%), Random Forest (91%), and XGBoost (90%), whereas the lowest accuracy is observed for One-Class Support Vector Machines (48%), Local Outlier Factor (53%), and Isolation Forest (55%). As the industry moves toward a zero-defect paradigm on a global scale, ongoing research efforts are focused on improving existing methods and developing new ones that contribute to the safety and quality of rail transportation. In this sense, there are at least four avenues for future research worth considering: testing richer data sets, hyperparameter optimization, and implementing other methods not included in the current study.

A general framework for robust stability analysis of neural networks with discrete time delays

Robust stability of different types of dynamical neural network models including time delay parameters have been extensively studied, and many different sets of sufficient conditions ensuring robust stability of these types of dynamical neural network models have been presented in past decades. In conducting stability analysis of dynamical neural systems, some basic properties of the employed activation functions and the forms of delay terms included in the mathematical representations of dynamical neural networks are of crucial importance in obtaining global stability criteria for dynamical neural systems. Therefore, this research article will examine a class of neural networks expressed by a mathematical model that involves the discrete time delay terms, the Lipschitz activation functions and possesses the intervalized parameter uncertainties. This paper will first present a new and alternative upper bound value of the second norm of the class of interval matrices, which will have an important impact on obtaining the desired results for establishing robust stability of these neural network models. Then, by exploiting wellknown Homeomorphism mapping theory and basic Lyapunov stability theory, we will state a new general framework for determining some novel robust stability conditions for dynamical neural networks possessing discrete time delay terms. This paper will also make a comprehensive review of some previously published robust stability results and show that the existing robust stability results can be easily derived from the results given in this paper.

The influence of oral vocabulary knowledge on individual differences in a computational model of reading

Studies have demonstrated systematic individual differences in the degree of semantic reliance (SR) when reading aloud exception words in adult skilled readers. However, the origins of individual differences in reading remain unclear. Using a connectionist model of reading, this study investigated whether oral vocabulary knowledge may affect the degree of SR as a potential source of individual differences in reading. Variety in oral vocabulary knowledge was simulated by training the model to learn the mappings between spoken and meaning word forms with different vocabulary sizes and quantities of exposure to these vocabularies. The model's SR in the reading aloud task was computed. The result demonstrated that the model with varying amounts of oral exposure and vocabulary sizes had different levels of SR. Critically, SR was able to predict the performance of the model on reading aloud and nonword reading, which assimilated behavioural reading patterns. Further analysis revealed that SR was largely associated with the interaction between oral vocabulary exposure and oral vocabulary size. When the amount of exposure was limited, SR significantly increased with vocabulary sizes but decreased then with vocabulary sizes. Overall, the simulation results provide the first computational evidence of the direct link between oral vocabulary knowledge and the degree of SR as a source of individual differences in reading.

Deep Mining from Omics Data

Since the advent of high-throughput omics technologies, various molecular data such as genes, transcripts, proteins, and metabolites have been made widely available to researchers. This has afforded clinicians, bioinformaticians, statisticians, and data scientists the opportunity to apply their innovations in feature mining and predictive modeling to a rich data resource to develop a wide range of generalizable prediction models. What has become apparent over the last 10 years is that researchers have adopted deep neural networks (or "deep nets") as their preferred paradigm of choice for complex data modeling due to the superiority of performance over more traditional statistical machine learning approaches, such as support vector machines. A key stumbling block, however, is that deep nets inherently lack transparency and are considered to be a "black box" approach. This naturally makes it very difficult for clinicians and other stakeholders to trust their deep learning models even though the model predictions appear to be highly accurate. In this chapter, we therefore provide a detailed summary of the deep net architectures typically used in omics research, together with a comprehensive summary of the notable "deep feature mining" techniques researchers have applied to open up this black box and provide some insights into the salient input features and why these models behave as they do. We group these techniques into the following three categories: (a) hidden layer visualization and interpretation; (b) input feature importance and impact evaluation; and (c) output layer gradient analysis. While we find that omics researchers have made some considerable gains in opening up the black box through interpretation of the hidden layer weights and node activations to identify salient input features, we highlight other approaches for omics researchers, such as employing deconvolutional network-based approaches and development of bespoke attribute impact measures to enable researchers to better understand the relationships between the input data and hidden layer representations formed and thus the output behavior of their deep nets.

Remaining Useful Life Estimation of Aircraft Engines Using a Joint Deep Learning Model Based on TCNN and Transformer

The remaining useful life estimation is a key technology in prognostics and health management (PHM) systems for a new generation of aircraft engines. With the increase in massive monitoring data, it brings new opportunities to improve the prediction from the perspective of deep learning. Therefore, we propose a novel joint deep learning architecture that is composed of two main parts: the transformer encoder, which uses scaled dot-product attention to extract dependencies across distances in time series, and the temporal convolution neural network (TCNN), which is constructed to fix the insensitivity of the self-attention mechanism to local features. Both parts are jointly trained within a regression module, which implies that the proposed approach differs from traditional ensemble learning models. It is applied on the Commercial Modular Aero-Propulsion System Simulation (C-MAPSS) dataset from the Prognostics Center of Excellence at NASA Ames, and satisfactory results are obtained, especially under complex working conditions.

Narrative event segmentation in the cortical reservoir

Recent research has revealed that during continuous perception of movies or stories, humans display cortical activity patterns that reveal hierarchical segmentation of event structure. Thus, sensory areas like auditory cortex display high frequency segmentation related to the stimulus, while semantic areas like posterior middle cortex display a lower frequency segmentation related to transitions between events. These hierarchical levels of segmentation are associated with different time constants for processing. Likewise, when two groups of participants heard the same sentence in a narrative, preceded by different contexts, neural responses for the groups were initially different and then gradually aligned. The time constant for alignment followed the segmentation hierarchy: sensory cortices aligned most quickly, followed by mid-level regions, while some higher-order cortical regions took more than 10 seconds to align. These hierarchical segmentation phenomena can be considered in the context of processing related to comprehension. In a recently described model of discourse comprehension word meanings are modeled by a language model pre-trained on a billion word corpus. During discourse comprehension, word meanings are continuously integrated in a recurrent cortical network. The model demonstrates novel discourse and inference processing, in part because of two fundamental characteristics: real-world event semantics are represented in the word embeddings, and these are integrated in a reservoir network which has an inherent gradient of functional time constants due to the recurrent connections. Here we demonstrate how this model displays hierarchical narrative event segmentation properties beyond the embeddings alone, or their linear integration. The reservoir produces activation patterns that are segmented by a hidden Markov model (HMM) in a manner that is comparable to that of humans. Context construction displays a continuum of time constants across reservoir neuron subsets, while context forgetting has a fixed time constant across these subsets. Importantly, virtual areas formed by subgroups of reservoir neurons with faster time constants segmented with shorter events, while those with longer time constants preferred longer events. This neurocomputational recurrent neural network simulates narrative event processing as revealed by the fMRI event segmentation algorithm provides a novel explanation of the asymmetry in narrative forgetting and construction. The model extends the characterization of online integration processes in discourse to more extended narrative, and demonstrates how reservoir computing provides a useful model of cortical processing of narrative structure.

Adaptive Synapse Arrangement in Cortical Learning Algorithm

The cortical learning algorithm (CLA) is a time-series data prediction method that is designed based on the human neocortex. The CLA has multiple columns that are associated with the input data bits by synapses. The input data is then converted into an internal column representation based on the synapse relation. Because the synapse relation between the columns and input data bits is fixed during the entire prediction process in the conventional CLA, it cannot adapt to input data biases. Consequently, columns not used for internal representations arise, resulting in a low prediction accuracy in the conventional CLA. To improve the prediction accuracy of the CLA, we propose a CLA that self-adaptively arranges the column synapses according to the input data tendencies and verify its effectiveness with several artificial time-series data and real-world electricity load prediction data from New York City. Experimental results show that the proposed CLA achieves higher prediction accuracy than the conventional CLA and LSTMs with different network optimization algorithms by arranging column synapses according to the input data tendency.

Spark Analysis Based on the CNN-GRU Model for WEDM Process

Wire electrical discharge machining (WEDM), widely used to fabricate micro and precision parts in manufacturing industry, is a nontraditional machining method using discharge energy which is transformed into thermal energy to efficiently remove materials. A great amount of research has been conducted based on pulse characteristics. However, the spark image-based approach has little research reported. This paper proposes a discharge spark image-based approach. A model is introduced to predict the discharge status using spark image features through a synchronous high-speed image and waveform acquisition system. First, the relationship between the spark image features (e.g., area, energy, energy density, distribution, etc.) and discharge status is explored by a set of experiments). Traditional methods have claimed that pulse waveform of “short” status is related to the status of non-machining while through our research, it is concluded that this is not always true by conducting experiments based on the spark images. Second, a deep learning model based on Convolution neural network (CNN) and Gated recurrent unit (GRU) is proposed to predict the discharge status. A time series of spark image features extracted by CNN form a 3D feature space is used to predict the discharge status through GRU. Moreover, a quantitative labeling method of machining state is proposed to improve the stability of the model. Due the effective features and the quantitative labeling method, the proposed approach achieves better predict result comparing with the single GRU model.

Enhancing Performance of Reservoir Computing System Based on Coupled MEMS Resonators

Reservoir computing (RC) is an attractive paradigm of a recurrent neural network (RNN) architecture, owning to the ease of training and existing neuromorphic implementation. Its simulated performance matches other digital algorithms on a series of benchmarking tasks, such as prediction tasks and classification tasks. In this article, we propose a novel RC structure based on the coupled MEMS resonators with the enhanced dynamic richness to optimize the performance of the RC system both on the system level and data set level. Moreover, we first put forward that the dynamic richness of RC comprises linear dynamic richness and nonlinear dynamic richness, which can be enhanced by adding delayed feedbacks and nonlinear nodes, respectively. In order to set forth this point, we compare three typical RC structures, a single-nonlinearity RC structure with single-feedback, a single-nonlinearity RC structure with double-feedbacks, and the couple-nonlinearity RC structure with double-feedbacks. Specifically, four different tasks are enumerated to verify the performance of the three RC structures, and the results show the enhanced dynamic richness by adding delayed feedbacks and nonlinear nodes. These results prove that coupled MEMS resonators offer an interesting platform to implement a complex computing paradigm leveraging their rich dynamical features.

A Model of Online Temporal-Spatial Integration for Immediacy and Overrule in Discourse Comprehension

During discourse comprehension, information from prior processing is integrated and appears to be immediately accessible. This was remarkably demonstrated by an N400 for "salted" and not "in love" in response to "The peanut was salted/in love." Discourse overrule was induced by prior discourse featuring the peanut as an animate agent. Immediate discourse overrule requires a model that integrates information at two timescales. One is over the lifetime and includes event knowledge and word semantics. The second is over the discourse in an event context. We propose a model where both are accounted for by temporal-to-spatial integration of experience into distributed spatial representations, providing immediate access to experience accumulated over different timescales. For lexical semantics, this is modeled by a word embedding system trained by sequential exposure to the entire Wikipedia corpus. For discourse, this is modeled by a recurrent reservoir network trained to generate a discourse vector for input sequences of words. The N400 is modeled as the difference between the instantaneous discourse vector and the target word. We predict this model can account for semantic immediacy and discourse overrule. The model simulates lexical priming and discourse overrule in the "Peanut in love" discourse, and it demonstrates that an unexpected word elicits reduced N400 if it is generally related to the event described in prior discourse, and that this effect disappears when the discourse context is removed. This neurocomputational model is the first to simulate immediacy and overrule in discourse-modulated N400, and contributes to characterization of online integration processes in discourse.

The covariance perceptron: A new paradigm for classification and processing of time series in recurrent neuronal networks

Learning in neuronal networks has developed in many directions, in particular to reproduce cognitive tasks like image recognition and speech processing. Implementations have been inspired by stereotypical neuronal responses like tuning curves in the visual system, where, for example, ON/OFF cells fire or not depending on the contrast in their receptive fields. Classical models of neuronal networks therefore map a set of input signals to a set of activity levels in the output of the network. Each category of inputs is thereby predominantly characterized by its mean. In the case of time series, fluctuations around this mean constitute noise in this view. For this paradigm, the high variability exhibited by the cortical activity may thus imply limitations or constraints, which have been discussed for many years. For example, the need for averaging neuronal activity over long periods or large groups of cells to assess a robust mean and to diminish the effect of noise correlations. To reconcile robust computations with variable neuronal activity, we here propose a conceptual change of perspective by employing variability of activity as the basis for stimulus-related information to be learned by neurons, rather than merely being the noise that corrupts the mean signal. In this new paradigm both afferent and recurrent weights in a network are tuned to shape the input-output mapping for covariances, the second-order statistics of the fluctuating activity. When including time lags, covariance patterns define a natural metric for time series that capture their propagating nature. We develop the theory for classification of time series based on their spatio-temporal covariances, which reflect dynamical properties. We demonstrate that recurrent connectivity is able to transform information contained in the temporal structure of the signal into spatial covariances. Finally, we use the MNIST database to show how the covariance perceptron can capture specific second-order statistical patterns generated by moving digits.

The dynamics in cortex is characterized by highly fluctuating activity: Even under the very same experimental conditions the activity typically does not reproduce on the level of individual spikes. Given this variability, how then does the brain realize its quasi-deterministic function? One obvious solution is to compute averages over many cells, assuming that the mean activity, or rate, is actually the decisive signal. Variability across trials of an experiment is thus considered noise. We here explore the opposite view: Can fluctuations be used to actually represent information? And if yes, is there a benefit over a representation using the mean rate? We find that a fluctuation-based scheme is not only powerful in distinguishing signals into several classes, but also that networks can efficiently be trained in the new paradigm. Moreover, we argue why such a scheme of representation is more consistent with known forms of synaptic plasticity than rate-based network dynamics.

The relationships between oral language and reading instruction: Evidence from a computational model of reading

Reading acquisition involves learning to associate visual symbols with spoken language. Multiple lines of evidence indicate that instruction on the relationship between spellings and sounds may be particularly important.However, it is unclear whether the effectiveness of this form of instruction depends on pre-existing oral language knowledge.To investigate this issue, we developed a series of computational models of reading incorporating orthographic, phonological and semantic processing to simulate bothartificialand natural orthographic learning conditions in adults and children. We exposed the models to instruction focused on spelling-sound or spelling-meaning relationships, and tested the influence of the models' oral language proficiency on the effectiveness of these training regimes. Overall, the simulations indicated thatoral language proficiency is a vital foundation for reading acquisition, and may modulate the effectiveness of reading instruction. These results provide a computational basis for the Simple View of Reading,and emphasise the importance of both oral language knowledge and spelling-sound instructionin the initial stages of learning to read.

Adaptive time scales in recurrent neural networks

Recent experiments have revealed a hierarchy of time scales in the visual cortex, where different stages of the visual system process information at different time scales. Recurrent neural networks are ideal models to gain insight in how information is processed by such a hierarchy of time scales and have become widely used to model temporal dynamics both in machine learning and computational neuroscience. However, in the derivation of such models as discrete time approximations of the firing rate of a population of neurons, the time constants of the neuronal process are generally ignored. Learning these time constants could inform us about the time scales underlying temporal processes in the brain and enhance the expressive capacity of the network. To investigate the potential of adaptive time constants, we compare the standard approximations to a more lenient one that accounts for the time scales at which processes unfold. We show that such a model performs better on predicting simulated neural data and allows recovery of the time scales at which the underlying processes unfold. A hierarchy of time scales emerges when adapting to data with multiple underlying time scales, underscoring the importance of such a hierarchy in processing complex temporal information.

Reservoir computing model of prefrontal cortex creates novel combinations of previous navigation sequences from hippocampal place-cell replay with spatial reward propagation

As rats learn to search for multiple sources of food or water in a complex environment, they generate increasingly efficient trajectories between reward sites. Such spatial navigation capacity involves the replay of hippocampal place-cells during awake states, generating small sequences of spatially related place-cell activity that we call “snippets”. These snippets occur primarily during sharp-wave-ripples (SWRs). Here we focus on the role of such replay events, as the animal is learning a traveling salesperson task (TSP) across multiple trials. We hypothesize that snippet replay generates synthetic data that can substantially expand and restructure the experience available and make learning more optimal. We developed a model of snippet generation that is modulated by reward, propagated in the forward and reverse directions. This implements a form of spatial credit assignment for reinforcement learning. We use a biologically motivated computational framework known as ‘reservoir computing’ to model prefrontal cortex (PFC) in sequence learning, in which large pools of prewired neural elements process information dynamically through reverberations. This PFC model consolidates snippets into larger spatial sequences that may be later recalled by subsets of the original sequences. Our simulation experiments provide neurophysiological explanations for two pertinent observations related to navigation. Reward modulation allows the system to reject non-optimal segments of experienced trajectories, and reverse replay allows the system to “learn” trajectories that it has not physically experienced, both of which significantly contribute to the TSP behavior.

As rats search for multiple sources of food in a complex environment, they generate increasingly efficient trajectories between reward sites, across multiple trials. This spatial navigation optimization behavior can be measured in the laboratory using a traveling salesperson task (TSP). This likely involves the coordinated replay of place-cell “snippets” between successive trials. We hypothesize that “snippets” can be used by the prefrontal cortex (PFC) to implement a form of reward-modulated reinforcement learning. Our simulation experiments provide neurophysiological explanations for two pertinent observations related to navigation. Reward modulation allows the system to reject non-optimal segments of experienced trajectories, and reverse replay allows the system to “learn” trajectories that it has not physically experienced, both of which significantly contribute to the TSP behavior.

Visual Field Prediction using Recurrent Neural Network

Artificial intelligence capabilities have, recently, greatly improved. In the past few years, one of the deep learning algorithms, the recurrent neural network (RNN), has shown an outstanding ability in sequence labeling and prediction tasks for sequential data. We built a reliable visual field prediction algorithm using RNN and evaluated its performance in comparison with the conventional pointwise ordinary linear regression (OLR) method. A total of 1,408 eyes were used as a training dataset and another dataset, comprising 281 eyes, was used as a test dataset. Five consecutive visual field tests were provided to the constructed RNN as input and a 6^th visual field test was compared with the output of the RNN. The performance of the RNN was compared with that of OLR by predicting the 6^th visual field in the test dataset. The overall prediction performance of RNN was significantly better than OLR. The pointwise prediction error of the RNN was significantly smaller than that of the OLR in most areas known to be vulnerable to glaucomatous damage. The RNN was also more robust and reliable regarding worsening in the visual field examination. In clinical practice, the RNN model can therefore assist in decision-making for further treatment of glaucoma.

Maneuvering Target Tracking Using Simultaneous Optimization and Feedback Learning Algorithm Based on Elman Neural Network

Tracking maneuvering targets is a challenging problem for sensors because of the unpredictability of the target’s motion. Unlike classical statistical modeling of target maneuvers, a simultaneous optimization and feedback learning algorithm for maneuvering target tracking based on the Elman neural network (ENN) is proposed in this paper. In the feedback strategy, a scale factor is learnt to adaptively tune the dynamic model’s error covariance matrix, and in the optimization strategy, a corrected component of the state vector is learnt to refine the final state estimation. These two strategies are integrated in an ENN-based unscented Kalman filter (UKF) model called ELM-UKF. This filter can be trained online by the filter residual, innovation and gain matrix of the UKF to simultaneously achieve maneuver feedback and an optimized estimation. Monte Carlo experiments on synthesized radar data showed that our algorithm had better performance on filtering precision compared with most maneuvering target tracking algorithms.

Marginally Stable Triangular Recurrent Neural Network Architecture for Time Series Prediction

This paper introduces a discrete-time recurrent neural network architecture using triangular feedback weight matrices that allows a simplified approach to ensuring network and training stability. The triangular structure of the weight matrices is exploited to readily ensure that the eigenvalues of the feedback weight matrix represented by the block diagonal elements lie on the unit circle in the complex z-plane by updating these weights based on the differential of the angular error variable. Such placement of the eigenvalues together with the extended close interaction between state variables facilitated by the nondiagonal triangular elements, enhances the learning ability of the proposed architecture. Simulation results show that the proposed architecture is highly effective in time-series prediction tasks associated with nonlinear and chaotic dynamic systems with underlying oscillatory modes. This modular architecture with dual upper and lower triangular feedback weight matrices mimics fully recurrent network architectures, while maintaining learning stability with a simplified training process. While training, the block-diagonal weights (hence the eigenvalues) of the dual triangular matrices are constrained to the same values during weight updates aimed at minimizing the possibility of overfitting. The dual triangular architecture also exploits the benefit of parsing the input and selectively applying the parsed inputs to the two subnetworks to facilitate enhanced learning performance.

Prediction performance of reservoir computing system based on a semiconductor laser subject to double optical feedback and optical injection

A reservoir computing (RC) system based on a semiconductor laser (SL) with double optical feedback and optical injection is proposed, and the prediction performance of such a system is numerically investigated via Santa Fe Time-Series Prediction task. The simulation results indicate that the RC system can yield a good prediction performance. Through optimizing some relevant operating parameters, ultra-fast information processing rates up to Gb/s level can be realized for the prediction error is below 3%.

Encoding sensory and motor patterns as time-invariant trajectories in recurrent neural networks

Much of the information the brain processes and stores is temporal in nature—a spoken word or a handwritten signature, for example, is defined by how it unfolds in time. However, it remains unclear how neural circuits encode complex time-varying patterns. We show that by tuning the weights of a recurrent neural network (RNN), it can recognize and then transcribe spoken digits. The model elucidates how neural dynamics in cortical networks may resolve three fundamental challenges: first, encode multiple time-varying sensory and motor patterns as stable neural trajectories; second, generalize across relevant spatial features; third, identify the same stimuli played at different speeds—we show that this temporal invariance emerges because the recurrent dynamics generate neural trajectories with appropriately modulated angular velocities. Together our results generate testable predictions as to how recurrent networks may use different mechanisms to generalize across the relevant spatial and temporal features of complex time-varying stimuli.

Predicting non-linear dynamics by stable local learning in a recurrent spiking neural network

The brain needs to predict how the body reacts to motor commands, but how a network of spiking neurons can learn non-linear body dynamics using local, online and stable learning rules is unclear. Here, we present a supervised learning scheme for the feedforward and recurrent connections in a network of heterogeneous spiking neurons. The error in the output is fed back through fixed random connections with a negative gain, causing the network to follow the desired dynamics. The rule for Feedback-based Online Local Learning Of Weights (FOLLOW) is local in the sense that weight changes depend on the presynaptic activity and the error signal projected onto the postsynaptic neuron. We provide examples of learning linear, non-linear and chaotic dynamics, as well as the dynamics of a two-link arm. Under reasonable approximations, we show, using the Lyapunov method, that FOLLOW learning is uniformly stable, with the error going to zero asymptotically.

Spatial interpolation and radiological mapping of ambient gamma dose rate by using artificial neural networks and fuzzy logic methods

The aim of this study was to determine spatial risk dispersion of ambient gamma dose rate (AGDR) by using both artificial neural network (ANN) and fuzzy logic (FL) methods, compare the performances of methods, make dose estimations for intermediate stations with no previous measurements and create dose rate risk maps of the study area. In order to determine the dose distribution by using artificial neural networks, two main networks and five different network structures were used; feed forward ANN; Multi-layer perceptron (MLP), Radial basis functional neural network (RBFNN), Quantile regression neural network (QRNN) and recurrent ANN; Jordan networks (JN), Elman networks (EN). In the evaluation of estimation performance obtained for the test data, all models appear to give similar results. According to the cross-validation results obtained for explaining AGDR distribution, Pearson's r coefficients were calculated as 0.94, 0.91, 0.89, 0.91, 0.91 and 0.92 and RMSE values were calculated as 34.78, 43.28, 63.92, 44.86, 46.77 and 37.92 for MLP, RBFNN, QRNN, JN, EN and FL, respectively. In addition, spatial risk maps showing distributions of AGDR of the study area were created by all models and results were compared with geological, topological and soil structure.

Towards autonomous locomotion: CPG-based control of smooth 3D slithering gait transition of a snake-like robot

Snake-like robots with 3D locomotion ability have significant advantages of adaptive travelling in diverse complex terrain over traditional legged or wheeled mobile robots. Despite numerous developed gaits, these snake-like robots suffer from unsmooth gait transitions by changing the locomotion speed, direction, and body shape, which would potentially cause undesired movement and abnormal torque. Hence, there exists a knowledge gap for snake-like robots to achieve autonomous locomotion. To address this problem, this paper presents the smooth slithering gait transition control based on a lightweight central pattern generator (CPG) model for snake-like robots. First, based on the convergence behavior of the gradient system, a lightweight CPG model with fast computing time was designed and compared with other widely adopted CPG models. Then, by reshaping the body into a more stable geometry, the slithering gait was modified, and studied based on the proposed CPG model, including the gait transition of locomotion speed, moving direction, and body shape. In contrast to sinusoid-based method, extensive simulations and prototype experiments finally demonstrated that smooth slithering gait transition can be effectively achieved using the proposed CPG-based control method without generating undesired locomotion and abnormal torque.

Biologically plausible learning in recurrent neural networks reproduces neural dynamics observed during cognitive tasks

Neural activity during cognitive tasks exhibits complex dynamics that flexibly encode task-relevant variables. Chaotic recurrent networks, which spontaneously generate rich dynamics, have been proposed as a model of cortical computation during cognitive tasks. However, existing methods for training these networks are either biologically implausible, and/or require a continuous, real-time error signal to guide learning. Here we show that a biologically plausible learning rule can train such recurrent networks, guided solely by delayed, phasic rewards at the end of each trial. Networks endowed with this learning rule can successfully learn nontrivial tasks requiring flexible (context-dependent) associations, memory maintenance, nonlinear mixed selectivities, and coordination among multiple outputs. The resulting networks replicate complex dynamics previously observed in animal cortex, such as dynamic encoding of task features and selective integration of sensory inputs. We conclude that recurrent neural networks offer a plausible model of cortical dynamics during both learning and performance of flexible behavior.

Laser dynamical reservoir computing with consistency: an approach of a chaos mask signal

We numerically investigate reservoir computing based on the consistency of a semiconductor laser subjected to optical feedback and injection. We introduce a chaos mask signal as an input temporal mask for reservoir computing and perform a time-series prediction task. We compare the errors of the task obtained from the chaos mask signal with those obtained from other digital and analog masks. The performance of the prediction task can be improved by using the chaos mask signal due to complex dynamical response.

Ideomotor feedback control in a recurrent neural network

The architecture of a neural network controlling an unknown environment is presented. It is based on a randomly connected recurrent neural network from which both perception and action are simultaneously read and fed back. There are two concurrent learning rules implementing a sort of ideomotor control: (i) perception is learned along the principle that the network should predict reliably its incoming stimuli; (ii) action is learned along the principle that the prediction of the network should match a target time series. The coherent behavior of the neural network in its environment is a consequence of the interaction between the two principles. Numerical simulations show a promising performance of the approach, which can be turned into a local and better "biologically plausible" algorithm.

Deep learning in neural networks: an overview

In recent years, deep artificial neural networks (including recurrent ones) have won numerous contests in pattern recognition and machine learning. This historical survey compactly summarizes relevant work, much of it from the previous millennium. Shallow and Deep Learners are distinguished by the depth of their credit assignment paths, which are chains of possibly learnable, causal links between actions and effects. I review deep supervised learning (also recapitulating the history of backpropagation), unsupervised learning, reinforcement learning & evolutionary computation, and indirect search for short programs encoding deep and large networks.

Relative entropy minimizing noisy non-linear neural network to approximate stochastic processes

A method is provided for designing and training noise-driven recurrent neural networks as models of stochastic processes. The method unifies and generalizes two known separate modeling approaches, Echo State Networks (ESN) and Linear Inverse Modeling (LIM), under the common principle of relative entropy minimization. The power of the new method is demonstrated on a stochastic approximation of the El Niño phenomenon studied in climate research.

A connectionist approach to mapping the human connectome permits simulations of neural activity within an artificial brain

Data-driven models drawn from statistical correlations between brain activity and behavior are used to inform theory-driven models, such as those described by computational models, which provide a mechanistic account of these correlations. This article introduces a novel multivariate approach for bootstrapping neurologically-plausible computational models that accurately encodes cortical effective connectivity from resting state functional neuroimaging data (rs-fMRI). We show that a network modularity algorithm finds comparable resting state networks within connectivity matrices produced by our approach and by the benchmark method. Unlike existing methods, however, ours permits simulation of brain activation that is a direct reflection of this cortical connectivity. Cross-validation of our model suggests that neural activity in some regions may be more consistent between individuals, providing novel insight into brain function. We suggest this method to make an important contribution toward modeling macro-scale human brain activity, and it has the potential to advance our understanding of complex neurological disorders and the development of neural connectivity.

A linear recurrent kernel online learning algorithm with sparse updates

In this paper, we propose a recurrent kernel algorithm with selectively sparse updates for online learning. The algorithm introduces a linear recurrent term in the estimation of the current output. This makes the past information reusable for updating of the algorithm in the form of a recurrent gradient term. To ensure that the reuse of this recurrent gradient indeed accelerates the convergence speed, a novel hybrid recurrent training is proposed to switch on or off learning the recurrent information according to the magnitude of the current training error. Furthermore, the algorithm includes a data-dependent adaptive learning rate which can provide guaranteed system weight convergence at each training iteration. The learning rate is set as zero when the training violates the derived convergence conditions, which makes the algorithm updating process sparse. Theoretical analyses of the weight convergence are presented and experimental results show the good performance of the proposed algorithm in terms of convergence speed and estimation accuracy.

A biological gradient descent for prediction through a combination of STDP and homeostatic plasticity

Identifying, formalizing, and combining biological mechanisms that implement known brain functions, such as prediction, is a main aspect of research in theoretical neuroscience. In this letter, the mechanisms of spike-timing-dependent plasticity and homeostatic plasticity, combined in an original mathematical formalism, are shown to shape recurrent neural networks into predictors. Following a rigorous mathematical treatment, we prove that they implement the online gradient descent of a distance between the network activity and its stimuli. The convergence to an equilibrium, where the network can spontaneously reproduce or predict its stimuli, does not suffer from bifurcation issues usually encountered in learning in recurrent neural networks.

Birth of an abstraction: a dynamical systems account of the discovery of an elsewhere principle in a category learning task

Human participants and recurrent ("connectionist") neural networks were both trained on a categorization system abstractly similar to natural language systems involving irregular ("strong") classes and a default class. Both the humans and the networks exhibited staged learning and a generalization pattern reminiscent of the Elsewhere Condition (Kiparsky, 1973). Previous connectionist accounts of related phenomena have often been vague about the nature of the networks' encoding systems. We analyzed our network using dynamical systems theory, revealing topological and geometric properties that can be directly compared with the mechanisms of non-connectionist, rule-based accounts. The results reveal that the networks "contain" structures related to mechanisms posited by rule-based models, partly vindicating the insights of these models. On the other hand, they support the one mechanism (OM), as opposed to the more than one mechanism (MOM), view of symbolic abstraction by showing how the appearance of MOM behavior can arise emergently from one underlying set of principles. The key new contribution of this study is to show that dynamical systems theory can allow us to explicitly characterize the relationship between the two perspectives in implemented models.

Recurrent temporal networks and language acquisition-from corticostriatal neurophysiology to reservoir computing

One of the most paradoxical aspects of human language is that it is so unlike any other form of behavior in the animal world, yet at the same time, it has developed in a species that is not far removed from ancestral species that do not possess language. While aspects of non-human primate and avian interaction clearly constitute communication, this communication appears distinct from the rich, combinatorial and abstract quality of human language. So how does the human primate brain allow for language? In an effort to answer this question, a line of research has been developed that attempts to build a language processing capability based in part on the gross neuroanatomy of the corticostriatal system of the human brain. This paper situates this research program in its historical context, that begins with the primate oculomotor system and sensorimotor sequencing, and passes, via recent advances in reservoir computing to provide insight into the open questions, and possible approaches, for future research that attempts to model language processing. One novel and useful idea from this research is that the overlap of cortical projections onto common regions in the striatum allows for adaptive binding of cortical signals from distinct circuits, under the control of dopamine, which has a strong adaptive advantage. A second idea is that recurrent cortical networks with fixed connections can represent arbitrary sequential and temporal structure, which is the basis of the reservoir computing framework. Finally, bringing these notions together, a relatively simple mechanism can be built for learning the grammatical constructions, as the mappings from surface structure of sentences to their meaning. This research suggests that the components of language that link conceptual structure to grammatical structure may be much simpler that has been proposed in other research programs. It also suggests that part of the residual complexity is in the conceptual system itself.

Orthographic influences on division of labor in learning to read Chinese and English: Insights from computational modeling

Learning to read any language requires learning to map among print, sound and meaning. Writing systems differ in a number of factors that influence both the ease and rate with which reading skill can be acquired, as well as the eventual division of labor between phonological and semantic processes. Further, developmental reading disability manifests differently across writing systems, and may be related to different deficits in constitutive processes. Here we simulate some aspects of reading acquisition in Chinese and English using the same model architecture for both writing systems. The contribution of semantic and phonological processing to literacy acquisition in the two languages is simulated, including specific effects of phonological and semantic deficits. Further, we demonstrate that similar patterns of performance are observed when the same model is trained on both Chinese and English as an "early bilingual." The results are consistent with the view that reading skill is acquired by the application of statistical learning rules to mappings among print, sound and meaning, and that differences in the typical and disordered acquisition of reading skill between writing systems are driven by differences in the statistical patterns of the writing systems themselves, rather than differences in cognitive architecture of the learner.

Chronic electrical stimulation homeostatically decreases spontaneous activity, but paradoxically increases evoked network activity

Neural dynamics generated within cortical networks play a fundamental role in brain function. However, the learning rules that allow recurrent networks to generate functional dynamic regimes, and the degree to which these regimes are themselves plastic, are not known. In this study we examined plasticity of network dynamics in cortical organotypic slices in response to chronic changes in activity. Studies have typically manipulated network activity pharmacologically; we used chronic electrical stimulation to increase activity in in vitro cortical circuits in a more physiological manner. Slices were stimulated with "implanted" electrodes for 4 days. Chronic electrical stimulation or treatment with bicuculline decreased spontaneous activity as predicted by homeostatic learning rules. Paradoxically, however, whereas bicuculline decreased evoked network activity, chronic stimulation actually increased the likelihood that evoked stimulation elicited polysynaptic activity, despite a decrease in evoked monosynaptic strength. Furthermore, there was an inverse correlation between spontaneous and evoked activity, suggesting a homeostatic tradeoff between spontaneous and evoked activity. Within-slice experiments revealed that cells close to the stimulated electrode exhibited more evoked polysynaptic activity and less spontaneous activity than cells close to a control electrode. Collectively, our results establish that chronic stimulation changes the dynamic regimes of networks. In vitro studies of homeostatic plasticity typically lack any external input, and thus neurons must rely on "spontaneous" activity to reach homeostatic "set points." However, in the presence of external input we propose that homeostatic learning rules seem to shift networks from spontaneous to evoked regimes.

Nonparametric mixtures of gaussian processes with power-law behavior

Gaussian processes (GPs) constitute one of the most important Bayesian machine learning approaches, based on a particularly effective method for placing a prior distribution over the space of regression functions. Several researchers have considered postulating mixtures of GPs as a means of dealing with nonstationary covariance functions, discontinuities, multimodality, and overlapping output signals. In existing works, mixtures of GPs are based on the introduction of a gating function defined over the space of model input variables. This way, each postulated mixture component GP is effectively restricted in a limited subset of the input space. In this paper, we follow a different approach. We consider a fully generative nonparametric Bayesian model with power-law behavior, generating GPs over the whole input space of the learned task. We provide an efficient algorithm for model inference, based on the variational Bayesian framework, and prove its efficacy using benchmark and real-world datasets.