A Time Series Forecasting Approach Based on Nonlinear Spiking Neural Systems

Asynchronous Numerical Spiking Neural Membrane Systems with Local Synchronization

Since the spiking neural P system (SN P system) was proposed in 2006, it has become a research hotspot in the field of membrane computing. The SN P system performs computations through the encoding, processing, and transmission of spiking information and can be regarded as a third-generation neural network. As a variant of the SN P system, the global asynchronous numerical spiking neural P system (ANSN P system) is adaptable to a broader range of application scenarios. However, in biological neuroscience, some neurons work synchronously within a community to perform specific functions in the brain. Inspired by this, our work investigates a global asynchronous spiking neural P system (ANSN P system) that incorporates certain local synchronous neuron sets. Within these local synchronous sets, neurons must execute their production functions simultaneously, thereby reducing dependence on thresholds and enhancing control uncertainty in ANSN P systems. By analyzing the ADD, SUB, and FIN modules in the generating mode, as well as the INPUT and ADD modules in the accepting mode, this paper demonstrates the novel system's computational capacity as both a generator and an acceptor. Additionally, this paper compares each module to those in other SN P systems, considering the maximum number of neurons and rules per neuron. The results show that this new ANSN P system is at least as effective as the existing SN P systems.

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.

An Optimization Numerical Spiking Neural Membrane System with Adaptive Multi-Mutation Operators for Brain Tumor Segmentation

Magnetic Resonance Imaging (MRI) is an important diagnostic technique for brain tumors due to its ability to generate images without tissue damage or skull artifacts. Therefore, MRI images are widely used to achieve the segmentation of brain tumors. This paper is the first attempt to discuss the use of optimization spiking neural P systems to improve the threshold segmentation of brain tumor images. To be specific, a threshold segmentation approach based on optimization numerical spiking neural P systems with adaptive multi-mutation operators (ONSNPSamos) is proposed to segment brain tumor images. More specifically, an ONSNPSamo with a multi-mutation strategy is introduced to balance exploration and exploitation abilities. At the same time, an approach combining the ONSNPSamo and connectivity algorithms is proposed to address the brain tumor segmentation problem. Our experimental results from CEC 2017 benchmarks (basic, shifted and rotated, hybrid, and composition function optimization problems) demonstrate that the ONSNPSamo is better than or close to 12 optimization algorithms. Furthermore, case studies from BraTS 2019 show that the approach combining the ONSNPSamo and connectivity algorithms can more effectively segment brain tumor images than most algorithms involved.

Hypergraph-Based Numerical Spiking Neural Membrane Systems with Novel Repartition Protocols

The classic spiking neural P (SN P) systems abstract the real biological neural network into a simple structure based on graphs, where neurons can only communicate on the plane. This study proposes the hypergraph-based numerical spiking neural membrane (HNSNM) systems with novel repartition protocols. Through the introduction of hypergraphs, the HNSNM systems can characterize the high-order relationships among neurons and extend the traditional neuron structure to high-dimensional nonlinear spaces. The HNSNM systems also abstract two biological mechanisms of synapse creation and pruning, and use plasticity rules with repartition protocols to achieve planar, hierarchical and spatial communications among neurons in hypergraph neuron structures. Through imitating register machines, the Turing universality of the HNSNM systems is proved by using them as number generating and accepting devices. A universal HNSNM system consisting of 41 neurons is constructed to compute arbitrary functions. By solving NP-complete problems using the subset sum problem as an example, the computational efficiency and effectiveness of HNSNM systems are verified.

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.

Evaluation of Spiking Neural Nets-Based Image Classification Using the Runtime Simulator RAVSim

Spiking Neural Networks (SNNs) help achieve brain-like efficiency and functionality by building neurons and synapses that mimic the human brain's transmission of electrical signals. However, optimal SNN implementation requires a precise balance of parametric values. To design such ubiquitous neural networks, a graphical tool for visualizing, analyzing, and explaining the internal behavior of spikes is crucial. Although some popular SNN simulators are available, these tools do not allow users to interact with the neural network during simulation. To this end, we have introduced the first runtime interactive simulator, called Runtime Analyzing and Visualization Simulator (RAVSim),a developed to analyze and dynamically visualize the behavior of SNNs, allowing end-users to interact, observe output concentration reactions, and make changes directly during the simulation. In this paper, we present RAVSim with the current implementation of runtime interaction using the LIF neural model with different connectivity schemes, an image classification model using SNNs, and a dataset creation feature. Our main objective is to primarily investigate binary classification using SNNs with RGB images. We created a feed-forward network using the LIF neural model for an image classification algorithm and evaluated it by using RAVSim. The algorithm classifies faces with and without masks, achieving an accuracy of 91.8% using 1000 neurons in a hidden layer, 0.0758 MSE, and an execution time of ∼10[Formula: see text]min on the CPU. The experimental results show that using RAVSim not only increases network design speed but also accelerates user learning capability.

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.

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.

Spiking Neural P Systems with Membrane Potentials, Inhibitory Rules, and Anti-Spikes

Spiking neural P systems (SN P systems for short) realize the high abstraction and simulation of the working mechanism of the human brain, and adopts spikes for information encoding and processing, which are regarded as one of the third-generation neural network models. In the nervous system, the conduction of excitation depends on the presence of membrane potential (also known as the transmembrane potential difference), and the conduction of excitation on neurons is the conduction of action potentials. On the basis of the SN P systems with polarizations, in which the neuron-associated polarization is the trigger condition of the rule, the concept of neuronal membrane potential is introduced into systems. The obtained variant of the SN P system features charge accumulation and computation within neurons in quantity, as well as transmission between neurons. In addition, there are inhibitory synapses between neurons that inhibit excitatory transmission, and as such, synapses cause postsynaptic neurons to generate inhibitory postsynaptic potentials. Therefore, to make the model better fit the biological facts, inhibitory rules and anti-spikes are also adopted to obtain the spiking neural P systems with membrane potentials, inhibitory rules, and anti-spikes (referred to as the MPAIRSN P systems). The Turing universality of the MPAIRSN P systems as number generating and accepting devices is demonstrated. On the basis of the above working mechanism of the system, a small universal MPAIRSN P system with 95 neurons for computing functions is designed. The comparisons with other SN P models conclude that fewer neurons are required by the MPAIRSN P systems to realize universality.