Model design and exponential state estimation for discrete-time delayed memristive spiking neural P systems

This paper investigates the exponential state estimation of the discrete-time memristive spiking neural P system (MSNPS). The spiking neural P system (SNPS) offers algorithmic support for neural morphology computation and AI chips, boasting advantages such as high performance and efficiency. As a new type of information device, memristors have efficient computing characteristics that integrate memory and computation, and can serve as synapses in SNPS. Therefore, to leverage the combined benefits of SNPS and memristors, this study introduces an innovative MSNPS circuit design, where memristors substitute resistors in the SNPS framework. Meanwhile, MSNPS mathematical model is constructed based on circuit model. In order to be more practical, the time delays in the system are analyzed in addition to the discretization of the continuous MSNPS. Moreover, some sufficient conditions for exponential state estimation are established by utilizing a Lyapunov functional to MSNPS. Finally, a numerical simulation example is constructed to validate the main findings.

Multi-level feature interaction image super-resolution network based on convolutional nonlinear spiking neural model

Image super-resolution (ISR) is designed to recover lost detail information from low-resolution images, resulting in high-quality and high-definition high-resolution images. In the existing single ISR (SISR) methods based on convolutional neural networks (CNN), however, most of the models cannot effectively combine global and local information and are also easy to ignore the correlation between different hierarchical feature information. To address these problems, this study proposes a multi-level feature interactive image super-resolution network, which is constructed by the convolutional units inspired by nonlinear spiking mechanism in nonlinear spiking neural P systems, including shallow feature processing, deep feature extraction and fusion, and reconstruction modules. The different omni domain self-attention blocks are introduced to extract global information in the deep feature extraction and fusion stage and formed a feature enhancement module having a Transformer structure using a novel convolutional unit for extracting local information. Furthermore, to adaptively fuse features between different hierarchies, we design a multi-level feature fusion module, which not only can adaptively fuse features between different hierarchies, but also can better interact with contextual information. The proposed model is compared with 16 state-of-the-art or baseline models on five benchmark datasets. The experimental results show that the proposed model not only achieves good reconstruction performance, but also strikes a good balance between model parameters and performance.

Seizure Detection of EEG Signals Based on Multi-Channel Long- and Short-Term Memory-Like Spiking Neural Model

Seizure is a common neurological disorder that usually manifests itself in recurring seizure, and these seizures can have a serious impact on a person's life and health. Therefore, early detection and diagnosis of seizure is crucial. In order to improve the efficiency of early detection and diagnosis of seizure, this paper proposes a new seizure detection method, which is based on discrete wavelet transform (DWT) and multi-channel long- and short-term memory-like spiking neural P (LSTM-SNP) model. First, the signal is decomposed into 5 levels by using DWT transform to obtain the features of the components at different frequencies, and a series of time-frequency features in wavelet coefficients are extracted. Then, these different features are used to train a multi-channel LSTM-SNP model and perform seizure detection. The proposed method achieves a high seizure detection accuracy on the CHB-MIT dataset: 98.25% accuracy, 98.22% specificity and 97.59% sensitivity. This indicates that the proposed epilepsy detection method can show competitive detection performance.

Multiple-in-Single-Out Object Detector Leveraging Spiking Neural Membrane Systems and Multiple Transformers

Most existing multi-scale object detectors depend on multi-level feature maps. The Feature Pyramid Networks (FPN) is a significant architecture for object detection that utilizes these multi-level feature maps. However, the use of FPN also increases the detector's complexity. For object detection methods that only use a single-level feature map, the detection performance is limited to some extent because the single-level feature map cannot balance deep semantic information and shallow detail information. We introduce a novel detector - the Spiking Neural P Multiple-in-Single-out (SNPMiSo) detector to address these challenges. The SNPMiSo detector is constructed based on SNP-like neurons. In SNPMiSo, we employ two kinds of Transformers to boost the important features across different-level feature maps separately. After enhancing the features, we use an incremental upsampling module to upsample and merge the two feature maps. This combined feature map is input into the NAF dilated residual module and the NAF dual-branch detection head. This process allows us to extract multi-scale features and carry out detection tasks. Our tests show promising results: On the COCO dataset, SNPMiSo attains an Average Precision (AP) of 38.7, an improvement of 1.0 AP over YOLOF. In addition, SNPMiSo demonstrates a quicker detection speed, outperforming some advanced multi-level and single-level object detectors.

Sparse Spiking Neural-Like Membrane Systems on Graphics Processing Units

The parallel simulation of Spiking Neural P systems is mainly based on a matrix representation, where the graph inherent to the neural model is encoded in an adjacency matrix. The simulation algorithm is based on a matrix-vector multiplication, which is an operation efficiently implemented on parallel devices. However, when the graph of a Spiking Neural P system is not fully connected, the adjacency matrix is sparse and hence, lots of computing resources are wasted in both time and memory domains. For this reason, two compression methods for the matrix representation were proposed in a previous work, but they were not implemented nor parallelized on a simulator. In this paper, they are implemented and parallelized on GPUs as part of a new Spiking Neural P system with delays simulator. Extensive experiments are conducted on high-end GPUs (RTX2080 and A100 80GB), and it is concluded that they outperform other solutions based on state-of-the-art GPU libraries when simulating Spiking Neural P systems.

Multitask Adversarial Networks Based on Extensive Nonlinear Spiking Neuron Models

Deep learning technology has been successfully used in Chest X-ray (CXR) images of COVID-19 patients. However, due to the characteristics of COVID-19 pneumonia and X-ray imaging, the deep learning methods still face many challenges, such as lower imaging quality, fewer training samples, complex radiological features and irregular shapes. To address these challenges, this study first introduces an extensive NSNP-like neuron model, and then proposes a multitask adversarial network architecture based on ENSNP-like neurons for chest X-ray images of COVID-19, called MAE-Net. The MAE-Net serves two tasks: (i) converting low-quality CXR images to high-quality images; (ii) classifying CXR images of COVID-19. The adversarial architecture of MAE-Net uses two generators and two discriminators, and two new loss functions have been introduced to guide the optimization of the network. The MAE-Net is tested on four benchmark COVID-19 CXR image datasets and compared them with eight deep learning models. The experimental results show that the proposed MAE-Net can enhance the conversion quality and the accuracy of image classification results.

Modular Spiking Neural Membrane Systems for Image Classification

A variant of membrane computing models called Spiking Neural P systems (SNP systems) closely mimics the structure and behavior of biological neurons. As third-generation neural networks, SNP systems have flexible architectures allowing the design of bio-inspired machine learning algorithms. This paper proposes Modular Spiking Neural P (MSNP) systems to solve image classification problems, a novel SNP system to be applied in scenarios where hundreds or even thousands of different classes are considered. A main issue to face in such situations is related to the structural complexity of the network. MSNP systems devised in this work allow to approach the general classification problem by dividing it in smaller parts, that are then faced by single entities of the network. As a benchmark dataset, the Oxford Flowers 102 dataset is considered, consisting of more than 8000 pictures of flowers belonging to the 102 species commonly found in the UK. These classes sometimes present large variations within them, may be also very similar to one another, and different images of the same subject may differ a lot. The work describes the architecture of the MSNP system, based on modules focusing on a specific class, their training phase, and the evaluation of the model both concerning result accuracy as well as energy consumption. Experimental results on image classification problems show that the model achieves good results, but is strongly connected to image quality, mainly depending on the frequency of images, remarkable changes of pose, images not centered, and subject mostly not shown.

Entropy-Weighted Numerical Gradient Optimization Spiking Neural System for Biped Robot Control

The optimization of robot controller parameters is a crucial task for enhancing robot performance, yet it often presents challenges due to the complexity of multi-objective, multi-dimensional multi-parameter optimization. This paper introduces a novel approach aimed at efficiently optimizing robot controller parameters to enhance its motion performance. While spiking neural P systems have shown great potential in addressing optimization problems, there has been limited research and validation concerning their application in continuous numerical, multi-objective, and multi-dimensional multi-parameter contexts. To address this research gap, our paper proposes the Entropy-Weighted Numerical Gradient Optimization Spiking Neural P System, which combines the strengths of entropy weighting and spiking neural P systems. First, the introduction of entropy weighting eliminates the subjectivity of weight selection, enhancing the objectivity and reproducibility of the optimization process. Second, our approach employs parallel gradient descent to achieve efficient multi-dimensional multi-parameter optimization searches. In conclusion, validation results on a biped robot simulation model show that our method markedly enhances walking performance compared to traditional approaches and other optimization algorithms. We achieved a velocity mean absolute error at least 35% lower than other methods, with a displacement error two orders of magnitude smaller. This research provides an effective new avenue for performance optimization in the field of robotics.

Bridges Between Spiking Neural Membrane Systems and Virus Machines

Spiking Neural P Systems (SNP) are well-established computing models that take inspiration from spikes between biological neurons; these models have been widely used for both theoretical studies and practical applications. Virus machines (VMs) are an emerging computing paradigm inspired by viral transmission and replication. In this work, a novel extension of VMs inspired by SNPs is presented, called Virus Machines with Host Excitation (VMHEs). In addition, the universality and explicit results between SNPs and VMHEs are compared in both generating and computing mode. The VMHEs defined in this work are shown to be more efficient than SNPs, requiring fewer memory units (hosts in VMHEs and neurons in SNPs) in several tasks, such as a universal machine, which was constructed with 18 hosts less than the 84 neurons in SNPs, and less than other spiking models discussed in the work.

Spiking Neural Membrane Systems with Adaptive Synaptic Time Delay

Spiking neural membrane systems (or spiking neural P systems, SNP systems) are a new type of computation model which have attracted the attention of plentiful scholars for parallelism, time encoding, interpretability and extensibility. The original SNP systems only consider the time delay caused by the execution of rules within neurons, but not caused by the transmission of spikes via synapses between neurons and its adaptive adjustment. In view of the importance of time delay for SNP systems, which are a time encoding computation model, this study proposes SNP systems with adaptive synaptic time delay (ADSNP systems) based on the dynamic regulation mechanism of synaptic transmission delay in neural systems. In ADSNP systems, besides neurons, astrocytes that can generate adenosine triphosphate (ATP) are introduced. After receiving spikes, astrocytes convert spikes into ATP and send ATP to the synapses controlled by them to change the synaptic time delays. The Turing universality of ADSNP systems in number generating and accepting modes is proved. In addition, a small universal ADSNP system using 93 neurons and astrocytes is given. The superiority of the ADSNP system is demonstrated by comparison with the six variants. Finally, an ADSNP system is constructed for credit card fraud detection, which verifies the feasibility of the ADSNP system for solving real-world problems. By considering the adaptive synaptic delay, ADSNP systems better restore the process of information transmission in biological neural networks, and enhance the adaptability of SNP systems, making the control of time more accurate.

A Parallel Convolutional Network Based on Spiking Neural Systems

Deep convolutional neural networks have shown advanced performance in accurately segmenting images. In this paper, an SNP-like convolutional neuron structure is introduced, abstracted from the nonlinear mechanism in nonlinear spiking neural P (NSNP) systems. Then, a U-shaped convolutional neural network named SNP-like parallel-convolutional network, or SPC-Net, is constructed for segmentation tasks. The dual-convolution concatenate (DCC) and dual-convolution addition (DCA) network blocks are designed, respectively, in the encoder and decoder stages. The two blocks employ parallel convolution with different kernel sizes to improve feature representation ability and make full use of spatial detail information. Meanwhile, different feature fusion strategies are used to fuse their features to achieve feature complementarity and augmentation. Furthermore, a dual-scale pooling (DSP) module in the bottleneck is designed to improve the feature extraction capability, which can extract multi-scale contextual information and reduce information loss while extracting salient features. The SPC-Net is applied in medical image segmentation tasks and is compared with several recent segmentation methods on the GlaS and CRAG datasets. The proposed SPC-Net achieves 90.77% DICE coefficient, 83.76% IoU score and 83.93% F1 score, 86.33% ObjDice coefficient, 135.60 Obj-Hausdorff distance, respectively. The experimental results show that the proposed model can achieve good segmentation performance.

Reservoir computing models based on spiking neural P systems for time series classification

Nonlinear spiking neural P (NSNP) systems are neural-like membrane computing models with nonlinear spiking mechanisms. Because of this nonlinear spiking mechanism, NSNP systems can show rich nonlinear dynamics. Reservoir computing (RC) is a novel recurrent neural network (RNN) and can overcome some shortcomings of traditional RNNs. Based on NSNP systems, we developed two RC variants for time series classification, RC-SNP and RC-RMS-SNP, which are without and integrated with reservoir model space (RMS), respectively. The two RC variants use NSNP systems as the reservoirs and can be easily implemented in the RC framework. The proposed two RC variants were evaluated on 17 benchmark time series classification datasets and compared with 16 state-of-the-art or baseline classification models. The comparison results demonstrate the effectiveness of the proposed two RC variants for time series classification tasks.

Spiking neural P systems with lateral inhibition

As a member of the third generation of artificial neural network models, spiking neural P systems (SN P systems) have gained a hot research spot in recent years. This work introduces the phenomenon of lateral inhibition in biological nervous systems into SN P systems, and proposes SN P systems with lateral inhibition (LISN P systems). LISN P systems add the property of synaptic length to portray the lateral distance between neurons, and adopt a new form of rules, lateral interaction rules, to describe the reception of spikes by postsynaptic neurons with different lateral distances from the presynaptic neuron. Specifically, an excited neuron produces lateral inhibition on surrounding postsynaptic neurons. Postsynaptic neurons close to the excited neuron, i.e., neurons with small lateral distances, are more susceptible to lateral inhibition and either receive a fewer number of spikes generated by the excited neuron or fail to receive spikes. As the lateral distance increases, the lateral inhibition weakens, and the number of spikes received by postsynaptic neurons increases. Based on the above mechanism, four specific LISN P systems are designed for generating arbitrary odd numbers, arbitrary even numbers, arbitrary natural numbers and arithmetic series, respectively, as examples. By designing working modules, LISN P systems provide equivalence in computational power to the universal register machines in both generating and accepting modes. This verifies the computational completeness of LISN P systems. A universal LISN P system using merely 65 neurons is devised for function computation. According to comparisons among several systems, universal LISN P systems require fewer computational resources.

Gated Spiking Neural P Systems for Time Series Forecasting

Spiking neural P (SNP) systems are a class of neural-like computing models, abstracted by the mechanism of spiking neurons. This article proposes a new variant of SNP systems, called gated spiking neural P (GSNP) systems, which are composed of gated neurons. Two gated mechanisms are introduced in the nonlinear spiking mechanism of GSNP systems, consisting of a reset gate and a consumption gate. The two gates are used to control the updating of states in neurons. Based on gated neurons, a prediction model for time series is developed, known as the GSNP model. Several benchmark univariate and multivariate time series are used to evaluate the proposed GSNP model and to compare several state-of-the-art prediction models. The comparison results demonstrate the availability and effectiveness of GSNP for time series forecasting.

An Attention-Aware Long Short-Term Memory-Like Spiking Neural Model for Sentiment Analysis

LSTM-SNP model is a recently developed long short-term memory (LSTM) network, which is inspired from the mechanisms of spiking neural P (SNP) systems. In this paper, LSTM-SNP is utilized to propose a novel model for aspect-level sentiment analysis, termed as ALS model. The LSTM-SNP model has three gates: reset gate, consumption gate and generation gate. Moreover, attention mechanism is integrated with LSTM-SNP model. The ALS model can better capture the sentiment features in the text to compute the correlation between context and aspect words. To validate the effectiveness of the ALS model for aspect-level sentiment analysis, comparison experiments with 17 baseline models are conducted on three real-life data sets. The experimental results demonstrate that the ALS model has a simpler structure and can achieve better performance compared to these baseline models.

Evolution-communication spiking neural P systems with energy request rules

Evolution-communication spiking neural P systems with energy request rules (ECSNP-ER systems) are proposed and developed as a new variant of evolution-communication spiking neural P systems. In ECSNP-ER systems, in addition to spike-evolution rules and spike-communication rules, neurons also have energy request rules. Energy request rules are used to obtain energy from the environment needed for spike evolution and communication in neurons. The definition, structure and operations of ECSNP-ER systems are presented in detail. ECSNP-ER systems are proved to have the same computing capabilities as Turing machines by using them as number generating/accepting devices and function computing devices. Working non-deterministically, ECSNP-ER systems are used to solve NP-complete problems, using the SAT problem as an example, in linear time.

Edge Detection Method Based on Nonlinear Spiking Neural Systems

Nonlinear spiking neural P (NSNP) systems are a class of neural-like computational models inspired from the nonlinear mechanism of spiking neurons. NSNP systems have a distinguishing feature: nonlinear spiking mechanism. To handle edge detection of images, this paper proposes a variant, nonlinear spiking neural P (NSNP) systems with two outputs (TO), termed as NSNP-TO systems. Based on NSNP-TO system, an edge detection framework is developed, termed as ED-NSNP detector. The detection ability of ED-NSNP detector relies on two convolutional kernels. To obtain good detection performance, particle swarm optimization (PSO) is used to optimize the parameters of the two convolutional kernels. The proposed ED-NSNP detector is evaluated on several open benchmark images and compared with seven baseline edge detection methods. The comparison results indicate the availability and effectiveness of the proposed ED-NSNP detector.

A Time Series Forecasting Approach Based on Nonlinear Spiking Neural Systems

Nonlinear spiking neural P (NSNP) systems are a recently developed theoretical model, which is abstracted by nonlinear spiking mechanism of biological neurons. NSNP systems have a nonlinear structure and the potential to describe nonlinear dynamic systems. Based on NSNP systems, a novel time series forecasting approach is developed in this paper. During the training phase, a time series is first converted to frequency domain by using a redundant wavelet transform, and then according to the frequency data, an NSNP system is automatically constructed and adaptively trained in frequency domain. Then, the well-trained NSNP system can automatically generate sequence data for future time as the prediction results. Eight benchmark time series data sets and two real-life time series data sets are utilized to compare the proposed approach with several state-of-the-art forecasting approaches. The comparison results demonstrate availability and effectiveness of the proposed forecasting approach.

Universal Nonlinear Spiking Neural P Systems with Delays and Weights on Synapses

The nonlinear spiking neural P systems (NSNP systems) are new types of computation models, in which the state of neurons is represented by real numbers, and nonlinear spiking rules handle the neuron's firing. In this work, in order to improve computing performance, the weights and delays are introduced to the NSNP system, and universal nonlinear spiking neural P systems with delays and weights on synapses (NSNP-DW) are proposed. Weights are treated as multiplicative constants by which the number of spikes is increased when transiting across synapses, and delays take into account the speed at which the synapses between neurons transmit information. As a distributed parallel computing model, the Turing universality of the NSNP-DW system as number generating and accepting devices is proven. 47 and 43 neurons are sufficient for constructing two small universal NSNP-DW systems. The NSNP-DW system solving the Subset Sum problem is also presented in this work.

Spiking Neural Membrane Computing Models

As third-generation neural network models, spiking neural P systems (SNP) have distributed parallel computing capabilities with good performance. In recent years, artificial neural networks have received widespread attention due to their powerful information processing capabilities, which is an effective combination of a class of biological neural networks and mathematical models. However, SNP systems have some shortcomings in numerical calculations. In order to improve the incompletion of current SNP systems in dealing with certain real data technology in this paper, we use neural network structure and data processing methods for reference. Combining them with membrane computing, spiking neural membrane computing models (SNMC models) are proposed. In SNMC models, the state of each neuron is a real number, and the neuron contains the input unit and the threshold unit. Additionally, there is a new style of rules for neurons with time delay. The way of consuming spikes is controlled by a nonlinear production function, and the produced spike is determined based on a comparison between the value calculated by the production function and the critical value. In addition, the Turing universality of the SNMC model as a number generator and acceptor is proved.

Parallel Binary Image Cryptosystem Via Spiking Neural Networks Variants

Due to the inefficiency of multiple binary images encryption, a parallel binary image encryption framework based on the typical variants of spiking neural networks, spiking neural P (SNP) systems is proposed in this paper. More specifically, the two basic units in the proposed image cryptosystem, the permutation unit and the diffusion unit, are designed through SNP systems with multiple channels and polarizations (SNP-MCP systems), and SNP systems with astrocyte-like control (SNP-ALC systems), respectively. Different from the serial computing of the traditional image permutation/diffusion unit, SNP-MCP-based permutation/SNP-ALC-based diffusion unit can realize parallel computing through the parallel use of rules inside the neurons. Theoretical analysis results confirm the high efficiency of the binary image proposed cryptosystem. Security analysis experiments demonstrate the security of the proposed cryptosystem.

Dendrite P Systems Toolbox: Representation, Algorithms and Simulators

Dendrite P systems (DeP systems) are a recently introduced neural-like model of computation. They provide an alternative to the more classical spiking neural (SN) P systems. In this paper, we present the first software simulator for DeP systems, and we investigate the key features of the representation of the syntax and semantics of such systems. First, the conceptual design of a simulation algorithm is discussed. This is helpful in order to shade a light on the differences with simulators for SN P systems, and also to identify potential parallelizable parts. Second, a novel simulator implemented within the P-Lingua simulation framework is presented. Moreover, MeCoSim, a GUI tool for abstract representation of problems based on P system models has been extended to support this model. An experimental validation of this simulator is also covered.

Spiking Neural P Systems with Delay on Synapses

Based on the feature and communication of neurons in animal neural systems, spiking neural P systems (SN P systems) were proposed as a kind of powerful computing model. Considering the length of axons and the information transmission speed on synapses, SN P systems with delay on synapses (SNP-DS systems) are proposed in this work. Unlike the traditional SN P systems, where all the postsynaptic neurons receive spikes at the same instant from their presynaptic neuron, the postsynaptic neurons in SNP-DS systems would receive spikes at different instants, depending on the delay time on the synapses connecting them. It is proved that the SNP-DS systems are universal as number generators. Two small universal SNP-DS systems, with standard or extended rules, are constructed to compute functions, using 56 and 36 neurons, respectively. Moreover, a simulator has been provided, in order to check the correctness of these two SNP-DS systems, thus providing an experimental validation of the universality of the systems designed.