Predictive Coding as Stimulus Avoidance in Spiking Neural Networks

Spiking Neural Networks (SNN) is one special implementation of Artificial Neural Networks (ANN), where the input signals are encoded in the temporal relationship between consecutive spikes (spike trains) instead of real-numbered values. Nevertheless, SNN is believed to be a closer representation of the biological neural system, because it imitates the current spikes that are transmitted between neurons in real biological systems. Practical and simplified SNN models include the Leaky Integrate-and-Fire (LIF) function of the neurons and the Spiking Timing Dependent Plasticity (STDP) function of the synapses. While most ANN architectures can be implemented with digital logic gates, SNN is more suitable to be implemented in analog circuits. In this paper, we propose revised analog circuit implementations of SNN neurons with LIF and STDP functions. Compared with previous works by other researchers, our proposed analog designs use fewer components and can be cascaded to form a complete neural system. The circuits are designed and simulated with SMIC 55nm CMOS LP process. The simulated results demonstrate that the analog neural system can work under a very small current (less than 10 µA) and voltage supply (1.0 Volts), and consumes less power consumption than digital implementations.

Decision letter: Neural markers of predictive coding under perceptual uncertainty revealed with Hierarchical Frequency Tagging

A forecast-based STDP rule suitable for neuromorphic implementation

We present a compact mixed-signal implementation of synaptic plasticity for both Spike Timing Dependent Plasticity (STDP) and Spike Timing Dependent Delay Plasticity (STDDP). The proposed mixed-signal implementation consists of an a VLSI time window generator and a digital adaptor. The weight and delay values are stored in a digital memory, and the adaptor will send these values to the time window generator using a digital spike of which the duration is modulated according to these values. The analogue time window generator will then generate a time window, which is required for the implementation of STDP and STDDP. The digital adaptor will carry out the weight/delay adaption using this time window. The aVLSI time window generator is compact (50 μm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> in IBM 130nm process) and we use a time multiplexing approach to achieve up to 65536 (64k) virtual digital adaptors with one physical adaptor, consuming only a fraction of the hardware resource on a Virtex 6 FPGA. Since the digital adaptor has been implemented on an FPGA, it can be easily reconfigured for different adaptation algorithms, which leaves it open for future development. Our mixed-signal implementation is therefore practical for implementing the synaptic plasticity in large-scale spiking neural networks running in real time. We show circuit simulation results illustrating both weight and delay adaptation.

Artificial neural systems for computation were first proposed three quarters of a century ago and the concepts developed by the pioneers still shape the field today. The first generation of neural systems was developed in the nineteen forties in the context of analogue electronics and the theoretical research in logic and mathematics that led to the first digital computers in nineteen forties and fifties. The second generation of neural systems implemented on digital computers was born in the nineteen fifties and great progress was made in the subsequent half century with neural networks being applied to many problems in pattern recognition and machine learning. Through this history there has been an interplay between biologically inspired neural systems and their implementation by engineers on digital machines. This thesis concerns the third generation of neural networks, Spiking Neural Networks, which is making possible the creation of new kinds of brain inspired computing architectures that offer the potential to increase the level of realism and sophistication in terms of autonomous machine behaviour and cognitive computing. This thesis presents the development and demonstration of a new theoretical architecture for third generation neural systems, the Integrate-and-Fire based Spiking Neural Model with extended Neuro-modulated Spike Timing Dependent Plasticity capabilities. This proposed architecture overcomes the limitation of the homosynaptic architecture underlying existing implementations of spiking neural networks that it lacks a natural spike timing dependent plasticity regulation mechanism, and this results in ‘run away’ dynamics. To overcome this ad hoc procedures have been implemented to overcome the ‘run away’ dynamics that emerge from the use of spike timing dependent plasticity among other hebbian-based plasticity rules. The new heterosynaptic architecture presented, explicitly abstracts the modulation of complex biochemical mechanisms into a simplified mechanism that is suitable for the engineering of artificial systems with low computational complexity. Neurons work by receiving input signals from other neurons through synapses. The difference between homosynaptic and heterosynaptic plasticity is that, in the former the change in the properties of a synapse (e.g. synaptic efficacy) depends on the point to point activity in either of the sending and receiving neurons, in contrast for heterosynaptic plasticity the change in the properties of a synapse can be elicited by neurons that are not necessary presynaptic or postsynaptic to the synapse in question. The new architecture is tested by a number of implementations in simulated and real environments. This includes experiments with a simulation environment implemented in Netlogo, and an implementation using Lego Mindstorms as the physical robot platform. These experiments demonstrate the problems with the traditional Spike timing dependent plasticity homosynaptic architecture and how the new heterosynaptic approach can overcome them. It is concluded that the new theoretical architecture provides a natural, theoretically sound, and practical new direction for research into the role of modulatory neural systems applied to spiking neural networks.

Spiking neural networks (SNNs), inspired by the neuronal network in the brain, provide biologically relevant and low-power consuming models for information processing. Existing studies either mimic the learning mechanism of brain neural networks as closely as possible, for example, the temporally local learning rule of spike-timing-dependent plasticity (STDP), or apply the gradient descent rule to optimize a multilayer SNN with fixed structure. However, the learning rule used in the former is local and how the real brain might do the global-scale credit assignment is still not clear, which means that those shallow SNNs are robust but deep SNNs are difficult to be trained globally and could not work so well. For the latter, the nondifferentiable problem caused by the discrete spike trains leads to inaccuracy in gradient computing and difficulties in effective deep SNNs. Hence, a hybrid solution is interesting to combine shallow SNNs with an appropriate machine learning (ML) technique not requiring the gradient computing, which is able to provide both energy-saving and high-performance advantages. In this article, we propose a HybridSNN, a deep and strong SNN composed of multiple simple SNNs, in which data-driven greedy optimization is used to build powerful classifiers, avoiding the derivative problem in gradient descent. During the training process, the output features (spikes) of selected weak classifiers are fed back to the pool for the subsequent weak SNN training and selection. This guarantees HybridSNN not only represents the linear combination of simple SNNs, as what regular AdaBoost algorithm generates, but also contains neuron connection information, thus closely resembling the neural networks of a brain. HybridSNN has the benefits of both low power consumption in weak units and overall data-driven optimizing strength. The network structure in HybridSNN is learned from training samples, which is more flexible and effective compared with existing fixed multilayer SNNs. Moreover, the topological tree of HybridSNN resembles the neural system in the brain, where pyramidal neurons receive thousands of synaptic input signals through their dendrites. Experimental results show that the proposed HybridSNN is highly competitive among the state-of-the-art SNNs.

Spike timing dependent plasticity (STDP) learning rule is one of hot topics in neurobiology since it's been widely believed that synaptic plasticity mainly contribute to learning and memory in brain. Up to now, STDP has been observed in a wide variety of areas of brain, hippocampus, cortex and so on. Competition among synapses is an important behavior for this learning rule. In present study, we propose a single layer spiking neural network model using STDP learning rule in inhibitory synapses to investigate the competitive behavior. The experiments show that the synapses among neurons are both strengthened on the whole training process. Thus neurons inhibit the activities of one another, eventually the neuron with the highest input spike rate win the competition. We have found that the behavior is efficient when the differences of firing rates of input neurons without STDP are great than 5Hz, otherwise the winner neuron is random. In order to use the principle to artificial intelligent system, we use a mechanism of dynamic learning rate to let the neuron with the highest input to be selected by the competitive behavior as the winner. Therefore, a robust competitive spiking neural network is obtained.

Spiking Neural Networks (SNNs), widely known as the third generation of neural networks, encode input information temporally using sparse spiking events, which can be harnessed to achieve higher computational efficiency for cognitive tasks. However, considering the rapid strides in accuracy enabled by state-of-the-art Analog Neural Networks (ANNs), SNN training algorithms are much less mature, leading to accuracy gap between SNNs and ANNs. In this paper, we propose different SNN training methodologies, varying in degrees of biofidelity, and evaluate their efficacy on complex image recognition datasets. First, we present biologically plausible Spike Timing Dependent Plasticity (STDP) based deterministic and stochastic algorithms for unsupervised representation learning in SNNs. Our analysis on the CIFAR-10 dataset indicates that STDP-based learning rules enable the convolutional layers to self-learn low-level input features using fewer training examples. However, STDP-based learning is limited in applicability to shallow SNNs (≤4 layers) while yielding considerably lower than state-of-the-art accuracy. In order to scale the SNNs deeper and improve the accuracy further, we propose conversion methodology to map off-the-shelf trained ANN to SNN for energy-efficient inference. We demonstrate 69.96% accuracy for VGG16-SNN on ImageNet. However, ANN-to-SNN conversion leads to high inference latency for achieving the best accuracy. In order to minimize the inference latency, we propose spike-based error backpropagation algorithm using differentiable approximation for the spiking neuron. Our preliminary experiments on CIFAR-10 show that spike-based error backpropagation effectively captures temporal statistics to reduce the inference latency by up to 8× compared to converted SNNs while yielding comparable accuracy

The problem with training spiking neural networks (SNNs) is relevant due to the ultra-low power consumption these networks could exhibit when implemented in neuromorphic hardware. The ongoing progress in the fabrication of memristors, a prospective basis for analogue synapses, gives relevance to studying the possibility of SNN learning on the base of synaptic plasticity models, obtained by fitting the experimental measurements of the memristor conductance change. The dynamics of memristor conductances is (necessarily) nonlinear, because conductance changes depend on the spike timings, which neurons emit in an all-or-none fashion. The ability to solve classification tasks was previously shown for spiking network models based on the bio-inspired local learning mechanism of spike-timing-dependent plasticity (STDP), as well as with the plasticity that models the conductance change of nanocomposite (NC) memristors. Input data were presented to the network encoded into the intensities of Poisson input spike sequences. This work considers another approach for encoding input data into input spike sequences presented to the network: temporal encoding, in which an input vector is transformed into relative timing of individual input spikes. Since temporal encoding uses fewer input spikes, the processing of each input vector by the network can be faster and more energy-efficient. The aim of the current work is to show the applicability of temporal encoding to training spiking networks with three synaptic plasticity models: STDP, NC memristor approximation, and PPX memristor approximation. We assess the accuracy of the proposed approach on several benchmark classification tasks: Fisher’s Iris, Wisconsin breast cancer, and the pole balancing task (CartPole). The accuracies achieved by SNN with memristor plasticity and conventional STDP are comparable and are on par with classic machine learning approaches.

The human brain is a dynamic system that is constantly learning. It employs a combination of various learning strategies to facilitate complex learning processes. However, implementing biological learning mechanisms into Spiking Neural Networks (SNNs) remains challenging; thus, most SNNs are trained with only a single learning strategy such as spike timing dependent plasticity (STDP). Moreover, conventional neural networks are first trained on one dataset and subsequently evaluated on unseen data. In this traditional approach, the weights and structure of the model remain fixed once the training step concludes. In this research, we aim to modify this traditional approach and hypothesize that adding short-term plasticity (STP) to a trained SNN enables the model to learn post-training without changing synaptic weights. In particular, by combining triplet STDP for long-term learning during initial training and STP for short-term learning after training (post-training), we employ multiple learning rules to enhance the biological plausibility and computational abilities of SNNs. In this way, two unsupervised learning pipelines are designed for image classification as a proof of concept, in which the dynamic synapse model, driven by neurotransmitter release and synaptic strength, is integrated into the trained network. The proposed method outperforms traditional training by achieving higher classification accuracy and a faster convergence rate. Consequently, our results show that the concept of post-training learning can be realized by incorporating STP in SNNs. Future studies should extend this concept to other challenges and explore its applicability to new datasets.

&lt;sec&gt;In current sensing-computing systems, sensors are used to acquire information from environments, such data are normally analogue, unstructured and even redundant. After the analogue-to-digital conversion (ADC), the data are transferred into digital computers for processing. In computers with the von Neumann architecture, memories and central processing units (CPUs) are physically separated. Such a separation of sensing terminals, memories and CPUs yields serious problems, such as high energy consumption, long response time, huge data storage, and stringent requirements for the communication bandwidth and security. However, time- and energy-efficient ways are urgently required to process information at where data are generated. On the other hand, biological sensory organs respond to external stimuli in real-time with high efficiency due to the integrated capabilities of sensing, memory and computing. Therefore, the problem of separated sensing units, memories and processing units can be solved by emulating biological sensory organs.&lt;/sec&gt;&lt;sec&gt;In this work, we propose bio-inspired sensory systems with integrated capabilities of sensing, data storage and processing. In such a system, different sensors are used to capture the environmental signals from e.g. gases, light, audio and pressure, then the sensory signals are processed by an analogue signal processor, so that the energy-consuming ADC is avoided, afterwards the sensory signals are processed by a brain-inspired chip which consists of neuron-synapse cores based on memristors. In the neuron-synapse cores, leaky integrate-and-fire (LIF) neurons can be implemented by memristors and capacitors, and adaptive LIF neurons are developed from the LIF neurons to realize unsupervised learning algorithms. The synapses are realized by memristor arrays which can also perform the in-memory computing. By changing the connection between the neurons, the brain-inspired chip can realize different spiking neural networks (SNNs), such as fully connected SNN, convolutional SNN, and recurrent SNN. The synaptic weight in SNNs can be updated according to the spike-timing dependent plasticity (STDP) or the spike-rate dependent plasticity (SRDP). As an example, a bio-inspired olfactory system is demonstrated. In a artificial olfactory system, a sensor array detects and transforms the chemical information about gas molecules into electrical sensory signals. Then the sensory signals are processed by the analogue signal processing unit. After pre-processing, the brain-inspired chip classifies gases by constructing a fully connected SNN with two layers. Such a bio-inspired olfactory system emulates the function of a biological nose, overcoming the low efficiency caused by the frequent sampling, data conversion, transfer and storage under the current sensing-computing architecture. More importantly, the approach of this work can be used to emulate almost all the biological perceptions, such as touch, sight, hearing and taste, through the integration with different types of sensors., Therefore, this work offers a brand new approach to realizing the artificial intelligence (AI).&lt;/sec&gt;

Spiking Neural Networks (SNNs), An alternative to sigmoidal neural networks, include time into their operations using discrete signals called spikes. Employing spikes enables SNNs to mimic any feedforward sigmoidal neural network with lower power consumption. Recently a new type of SNN has been introduced for classification problems, known as Degree of Belonging SNN (DoB-SNN). DoB-SNN is a two-layer spiking neural network that shows significant potential as an alternative SNN architecture and learning algorithm. This paper introduces a new variant of Spike-Timing Dependent Plasticity (STDP), which is based on the assembly of neurons and expands the DoB-SNN's training algorithm for multilayer architectures. The new learning rule, known as assembly-based STDP, employs trained DoBs in each layer to train the next layer and build strong connections between neurons from the same assembly while creating inhibitory connections between neurons from different assemblies in two consecutive layers. The performance of the multilayer DoB-SNN is evaluated on five datasets from the UCI machine learning repository. Detailed comparisons on these datasets with other supervised learning algorithms show that the multilayer DoB-SNN can achieve better performance on 4/5 datasets and comparable performance on 5th when compared to multilayer algorithms that employ considerably more trainable parameters.

Spiking Neural Network (SNN) is the third generation of Artificial Neural Network (ANN), which is potentially an efficient way to reduce the computation load as well as the power consumption on hardware due to the sparse activation and event-driven behavior of its neuron. In this paper, we have trained an SNN by using Spike Timing Dependent Plasticity in an unsupervised manner. The training process is optimized by using the quantization method on its weights, performed at the regular intervals during training. From the simulation results, the SNN with the 4-bit weights received an accuracy drop of 0.09%. The behavioral simulation result with the same bit-width weight quantization received an accuracy drop of 0.28%.

Recently, spiking neural networks (SNNs) have been shown capable of approximating the dynamics of biological neuronal networks, and of being trainable by biologically-plausible learning mechanisms, such as spike-timing-dependent synaptic plasticity. Numerical simulations also support the possibility that they may possess universal function approximation abilities. However the effectiveness of training algorithms to date is far inferior to those of other artificial neural networks. Moreover, they rely on directly manipulating the SNN weights, which may not be feasible in a number of their potential applications. This paper presents a novel indirect training approach to modulate spike-timing-dependent plasticity (STDP) in an action SNN that serves as a flight controller without directly manipulating its weights. A critic SNN is directly trained with a reward-based Hebbian approach to send spike trains to the action SNN, which in turn controls the aircraft and learns via STDP. The approach is demonstrated by training the action SNN to act as a flight controller for stability augmentation. Its performance and dynamics are analyzed before and after training through numerical simulations and Poincaré maps.

Spike-timing dependent plasticity (STDP)-based spiking neural network (SNN) is a promising choice to realize unsupervised intelligent systems with a limited power budget. In addition to STDP, another two bio-inspired mechanisms of lateral inhibition and homeostasis are always implemented in the unsupervised training procedure of STDP-based SNNs. However, the existing methods to achieve lateral inhibition necessitate a great number of connections that are proportional to the square of the number of learning neurons, and the existing hardware solution of homeostasis demands complex circuits for each learning neuron, both of which challenge the hardware implementation of STDP-based SNNs. In this brief, we propose a novel SNN using memristor-based inhibitory synapses to realize the mechanisms of lateral inhibition and homeostasis with low hardware complexity. The proposed SNN can improve the network scalability by reducing the connection number for lateral inhibition from $N^{2}$ to $N$ and reduce the hardware overhead by leveraging the circuit of lateral inhibition to achieve homeostasis. Software simulations on the recognition task on MNIST dataset show that the proposed SNN achieves a ~ 2 times higher learning efficiency with comparable accuracy. In addition, the challenging properties of realistic memristor devices, including limited number of resistive states, intrinsic parameter variation, and permanent open device, are added in the simulation to evaluate the robustness of our proposed approach.