Spiking Neural Network Model Research Articles

NeuroSEE: A Neuromorphic Energy-Efficient Processing Framework for Visual Prostheses

Visual prostheses with both comprehensive visual signal processing capability and energy efficiency are becoming increasingly demanded in the age of intelligent personal healthcare, particularly with the rise of wearable and implantable devices. To address this trend, we propose NeuroSEE, a neuromorphic energy-efficient processing framework that combines a spike representation encoding technique and a bio-inspired processing method. This framework first utilizes sparse spike trains to represent visual information, and then a bio-inspired spiking neural network (SNN) is adopted to process the spike trains. The SNN model makes use of an IF neuron with multiple spike-firing rates to decrease the energy consumption without compensating for prediction performance. The experimental results indicate that when predicting the response of the primary visual cortex, the framework achieves a state-of-the-art Pearson correlation coefficient performance. Spike-based recording and processing methods simplify the storage and transmission of redundant scene information and complex calculation processes. It could reduce power consumption by 15 times compared with the existing Convolutional neural network (CNN) processing framework. The proposed NeuroSEE framework predicts the response of the primary visual cortex in an energy efficient manner, making it a powerful tool for visual prostheses.

A Spiking Neural Network Builder for Systematic Data-to-Model Workflow.

In building biological neural network models, it is crucial to efficiently convert diverse anatomical and physiological data into parameters of neurons and synapses and to systematically estimate unknown parameters in reference to experimental observations. Web-based tools for systematic model building can improve the transparency and reproducibility of computational models and can facilitate collaborative model building, validation, and evolution. Here, we present a framework to support collaborative data-driven development of spiking neural network (SNN) models based on the Entity-Relationship (ER) data description commonly used in large-scale business software development. We organize all data attributes, including species, brain regions, neuron types, projections, neuron models, and references as tables and relations within a database management system (DBMS) and provide GUI interfaces for data registration and visualization. This allows a robust “business-oriented” data representation that supports collaborative model building and traceability of source information for every detail of a model. We tested this data-to-model framework in cortical and striatal network models by successfully combining data from papers with existing neuron and synapse models and by generating NEST simulation codes for various network sizes. Our framework also helps to check data integrity and consistency and data comparisons across species. The framework enables the modeling of any region of the brain and is being deployed to support the integration of anatomical and physiological datasets from the brain/MINDS project for systematic SNN modeling of the marmoset brain.

Cerebellum involvement in dystonia: insights from a spiking neural network model during associative learning.

Dystonia is a neurological movement disorder characterized by twisting and repetitive movements or abnormal fixed postures. This complex brain disease has usually been associated with damages to the Basal Ganglia. However, recent studies point out the potential role of the cerebellum. Indeed, motor learning is impaired in dystonic patients, e.g. during eyeblink classical conditioning, a typical cerebellum-driven associative learning protocol, and rodents with local cerebellar damages exhibit dystonic movements. Alterations in the olivocerebellar circuit connectivity have been identified as a potential neural substrate of dystonia. Here, we investigated this hypothesis through simulations of eyeblink conditioning driven by a realistic spiking model of the cerebellum. The pathological model was generated by decreasing the signal transmission from the Inferior Olive to cerebellar cortex, as observed in animal experiments. The model was able to reproduce a reduced acquisition of eyeblink motor responses, with also an unproper timing. Indeed, this pathway is fundamental to drive cerebellar cortical plasticity, which is the basis of cerebellum-driven motor learning. Exploring different levels of damage, the model predicted the possible amount of underlying impairment associated with the misbehavior observed in patients. Simulations of other debated lesions reported in mouse models of dystonia will be run to investigate the cerebellar involvement in different types of dystonia. Indeed, the eyeblink conditioning phenotype could be used to discriminate between them, identifying specific deficits in the generation of motor responses. Future studies will also include simulations of pharmacological or deep brain stimulation treatments targeting the cerebellum, to predict their impact in improving symptoms.

An Open-source Computational Model of Neurostimulation of the Spinal Pudendo-Vesical Reflex for the Recovery of Bladder Control After Spinal Cord Injury.

Spinal cord stimulation (SCS) could be used to restore control of the bladder after spinal cord injury, but substantial development is still required to tailor this technology for bladder function. Computational models could be utilized to accelerate these efforts enabling in-silico optimization of stimulation parameters. However, no model of the spinal pudendo-vesical reflex can simulate the effect of stimulation amplitude on neuron recruitment. This limitation hinders accurate prediction of bladder pressure changes for different stimulation configurations. Here., we implemented an open-source realistic spiking neural network model of the pudendo-vesical reflex enabling exploration of the impact of stimulation amplitude and frequency on bladder pressure changes. We used the o2S2 PARC platform to design a parallel implementation of the bladder reflex circuits with NEURON. Our model successfully reproduced and expanded previous studies., producing a decrease in bladder pressure at low stimulation frequency (10 Hz) and excitation at high stimulation frequency (≥33 Hz) in isovolumetric experiments. We then explored the effect of mixed nerve recruitment., simulating a common case of poorly selective spinal cord stimulation. We found that high recruitments of pudendal nerve axons are necessary to maintain this bi-modal behavior., regardless of stimulation specificity. Our framework is fully open-source and can be used to simulate any type of axon stimulations such as SCS and peripheral nerve stimulation.

Monkey Prefrontal Single-Unit Activity Reflecting Category-Based Logical Thinking Process and Its Neural Network Model.

Category-based thinking is a fundamental form of logical thinking. Here, we aimed to investigate its neural process at the local circuit level in the prefrontal cortex (PFC). We recorded single-unit PFC activity while male monkeys (Macaca fuscata) performed a task in which the category and rule were prerequisites of logical thinking and the outcome contingency was its consequence. Different groups of neurons coded a single type of information discretely or multiple types in a transitional form. Results of time-by-time analysis of neuronal activity suggest an information flow from category-coding and rule-coding neurons to transitional intermediate neurons, and then to contingency-coding neurons. Category-coding, rule-coding, and contingency-coding neurons showed stable coding of information, whereas intermediate neurons showed dynamic coding, as if it integrated category and rule to derive contingency. A similar process was confirmed by using a spiking neural network model that consisted of subnetworks coding category and rule on the input layer and those coding contingency on the output layer, with a subnetwork for integration in the intermediate layer. These results suggest that category-based logical thinking is realized in the PFC by separated neural populations organized for working in a feedforward manner.SIGNIFICANCE STATEMENT To elucidate the neural process for logical thinking, we combined an in-depth analysis of single-unit activity data with a biologically plausible computational model. Results of time-by-time analysis of prefrontal neuronal activity suggest an information flow from category-coding and rule-coding neurons to transitional intermediate neurons, and then to contingency-coding neurons. Category-coding, rule-coding, and contingency-coding neurons showed stable coding, whereas intermediate neurons showed dynamic coding, as if they integrated category and rule to derive contingency. A spiking neural network model reproduced similar temporal changes of information as the recorded neuronal data. Our results suggest that the prefrontal cortex (PFC) is critically involved in category-based thought process, and this process may be produced by separated neural populations organized for working in a feedforward manner.

Fast Simulation of a Multi-Area Spiking Network Model of Macaque Cortex on an MPI-GPU Cluster.

Spiking neural network models are increasingly establishing themselves as an effective tool for simulating the dynamics of neuronal populations and for understanding the relationship between these dynamics and brain function. Furthermore, the continuous development of parallel computing technologies and the growing availability of computational resources are leading to an era of large-scale simulations capable of describing regions of the brain of ever larger dimensions at increasing detail. Recently, the possibility to use MPI-based parallel codes on GPU-equipped clusters to run such complex simulations has emerged, opening up novel paths to further speed-ups. NEST GPU is a GPU library written in CUDA-C/C++ for large-scale simulations of spiking neural networks, which was recently extended with a novel algorithm for remote spike communication through MPI on a GPU cluster. In this work we evaluate its performance on the simulation of a multi-area model of macaque vision-related cortex, made up of about 4 million neurons and 24 billion synapses and representing 32 mm2 surface area of the macaque cortex. The outcome of the simulations is compared against that obtained using the well-known CPU-based spiking neural network simulator NEST on a high-performance computing cluster. The results show not only an optimal match with the NEST statistical measures of the neural activity in terms of three informative distributions, but also remarkable achievements in terms of simulation time per second of biological activity. Indeed, NEST GPU was able to simulate a second of biological time of the full-scale macaque cortex model in its metastable state 3.1× faster than NEST using 32 compute nodes equipped with an NVIDIA V100 GPU each. Using the same configuration, the ground state of the full-scale macaque cortex model was simulated 2.4× faster than NEST.

Traces of semantization - from episodic to semantic memory in a spiking cortical network model.

Episodic memory is a recollection of past personal experiences associated with particular times and places. This kind of memory is commonly subject to loss of contextual information or “semantization,” which gradually decouples the encoded memory items from their associated contexts while transforming them into semantic or gist-like representations. Novel extensions to the classical Remember/Know (R/K) behavioral paradigm attribute the loss of episodicity to multiple exposures of an item in different contexts. Despite recent advancements explaining semantization at a behavioral level, the underlying neural mechanisms remain poorly understood. In this study, we suggest and evaluate a novel hypothesis proposing that Bayesian–Hebbian synaptic plasticity mechanisms might cause semantization of episodic memory. We implement a cortical spiking neural network model with a Bayesian–Hebbian learning rule called Bayesian Confidence Propagation Neural Network (BCPNN), which captures the semantization phenomenon and offers a mechanistic explanation for it. Encoding items across multiple contexts leads to item-context decoupling akin to semantization. We compare BCPNN plasticity with the more commonly used spike-timing-dependent plasticity (STDP) learning rule in the same episodic memory task. Unlike BCPNN, STDP does not explain the decontextualization process. We further examine how selective plasticity modulation of isolated salient events may enhance preferential retention and resistance to semantization. Our model reproduces important features of episodicity on behavioral timescales under various biological constraints while also offering a novel neural and synaptic explanation for semantization, thereby casting new light on the interplay between episodic and semantic memory processes.

Fully Spiking Variational Autoencoder

Spiking neural networks (SNNs) can be run on neuromorphic devices with ultra-high speed and ultra-low energy consumption because of their binary and event-driven nature. Therefore, SNNs are expected to have various applications, including as generative models being running on edge devices to create high-quality images. In this study, we build a variational autoencoder (VAE) with SNN to enable image generation. VAE is known for its stability among generative models; recently, its quality advanced. In vanilla VAE, the latent space is represented as a normal distribution, and floating-point calculations are required in sampling. However, this is not possible in SNNs because all features must be binary time series data. Therefore, we constructed the latent space with an autoregressive SNN model, and randomly selected samples from its output to sample the latent variables. This allows the latent variables to follow the Bernoulli process and allows variational learning. Thus, we build the Fully Spiking Variational Autoencoder where all modules are constructed with SNN. To the best of our knowledge, we are the first to build a VAE only with SNN layers. We experimented with several datasets, and confirmed that it can generate images with the same or better quality compared to conventional ANNs. The code is available at https://github.com/kamata1729/FullySpikingVAE.

Cortical Motion Perception Emerges from Dimensionality Reduction with Evolved Spike-Timing-Dependent Plasticity Rules.

The nervous system is under tight energy constraints and must represent information efficiently. This is particularly relevant in the dorsal part of the medial superior temporal area (MSTd) in primates where neurons encode complex motion patterns to support a variety of behaviors. A sparse decomposition model based on a dimensionality reduction principle known as non-negative matrix factorization (NMF) was previously shown to account for a wide range of monkey MSTd visual response properties. This model resulted in sparse, parts-based representations that could be regarded as basis flow fields, a linear superposition of which accurately reconstructed the input stimuli. This model provided evidence that the seemingly complex response properties of MSTd may be a by-product of MSTd neurons performing dimensionality reduction on their input. However, an open question is how a neural circuit could carry out this function. In the current study, we propose a spiking neural network (SNN) model of MSTd based on evolved spike-timing-dependent plasticity and homeostatic synaptic scaling (STDP-H) learning rules. We demonstrate that the SNN model learns compressed and efficient representations of the input patterns similar to the patterns that emerge from NMF, resulting in MSTd-like receptive fields observed in monkeys. This SNN model suggests that STDP-H observed in the nervous system may be performing a similar function as NMF with sparsity constraints, which provides a test bed for mechanistic theories of how MSTd may efficiently encode complex patterns of visual motion to support robust self-motion perception.SIGNIFICANCE STATEMENT The brain may use dimensionality reduction and sparse coding to efficiently represent stimuli under metabolic constraints. Neurons in monkey area MSTd respond to complex optic flow patterns resulting from self-motion. We developed a spiking neural network model that showed MSTd-like response properties can emerge from evolving spike-timing-dependent plasticity with STDP-H parameters of the connections between then middle temporal area and MSTd. Simulated MSTd neurons formed a sparse, reduced population code capable of encoding perceptual variables important for self-motion perception. This model demonstrates that complex neuronal responses observed in MSTd may emerge from efficient coding and suggests that neurobiological plasticity, like STDP-H, may contribute to reducing the dimensions of input stimuli and allowing spiking neurons to learn sparse representations.

Accurate ECG Classification Based on Spiking Neural Network and Attentional Mechanism for Real-Time Implementation on Personal Portable Devices

Electrocardiogram (ECG) heartbeat classification plays a vital role in early diagnosis and effective treatment, which provide opportunities for earlier prevention and intervention. In an effort to continuously monitor and detect abnormalities in patients’ ECG signals on portable devices, this paper present a lightweight ECG heartbeat classification method based on a spiking neural network (SNN), a relatively shallow SNN model integrated with a channel-wise attentional module. We further explore the best-optimized architecture, which benefits from leveraging the full advantages of the SNN potential with the attention mechanism to process the classification task at low power and capture prominent features concerning the time, morphology, and multi-channel representations of the ECG signal. Results show that our model achieves overall classification accuracy of 98.26%, sensitivity of 94.75%, and F1 score of 89.09% on the MIT-BIH database, with energy consumption of 346.33 μJ per beat and runtime of 1.37 ms. Moreover, we have conducted multiple experiments to compare against current state-of-the-art methods using their assessment strategies to evaluate our model implementation on FPGA. So far, our work achieves comparable overall performance with all the literature in terms of classification accuracy, energy consumption, and real-time capability.

Relating a Spiking Neural Network Model and the Diffusion Model of Decision-Making.

Many models of decision making assume accumulation of evidence to threshold as a core mechanism to predict response probabilities and response times. A spiking neural network model (Wang, 2002) instantiates these mechanisms at the level of biophysically-plausible pools of neurons with excitatory and inhibitory connections, and has numerous model parameters tuned by physiological measures. The diffusion model (Ratcliff, 1978) is a cognitive model that can be fitted to a range of behaviors and conditions. We investigated how parameters of the cognitive-level diffusion model relate to the parameters of a neural-level spiking model. In each simulated "experiment", we generated "data" from the spiking neural network by factorially combining a manipulation of choice difficulty (via the input to the spiking model) and a manipulation of one of the core parameters of the spiking model. We then fitted the diffusion model to these simulated data to observe how manipulation of each core spiking model parameter mapped on to fitted drift rate, response threshold, and non-decision time. Manipulations of parameters in the spiking model related to input sensitivity, threshold, and stimulus processing time mapped on to their conceptual analogues in the diffusion model, namely drift rate, threshold, and non-decision time. Manipulations of parameters in the spiking model with no direct analogue to the diffusion model, non-stimulus-specific background input, strength of recurrent excitation, and receptor conductances, mapped on to threshold in the diffusion model. We discuss implications of these results for interpretations of fits of the diffusion model to behavioral data.

Brain-Inspired Spiking Neural Network Controller for a Neurorobotic Whisker System.

It is common for animals to use self-generated movements to actively sense the surrounding environment. For instance, rodents rhythmically move their whiskers to explore the space close to their body. The mouse whisker system has become a standard model for studying active sensing and sensorimotor integration through feedback loops. In this work, we developed a bioinspired spiking neural network model of the sensorimotor peripheral whisker system, modeling trigeminal ganglion, trigeminal nuclei, facial nuclei, and central pattern generator neuronal populations. This network was embedded in a virtual mouse robot, exploiting the Human Brain Project's Neurorobotics Platform, a simulation platform offering a virtual environment to develop and test robots driven by brain-inspired controllers. Eventually, the peripheral whisker system was adequately connected to an adaptive cerebellar network controller. The whole system was able to drive active whisking with learning capability, matching neural correlates of behavior experimentally recorded in mice.

Effective Conversion of a Convolutional Neural Network into a Spiking Neural Network for Image Recognition Tasks

Due to energy efficiency, spiking neural networks (SNNs) have gradually been considered as an alternative to convolutional neural networks (CNNs) in various machine learning tasks. In image recognition tasks, leveraging the superior capability of CNNs, the CNN–SNN conversion is considered one of the most successful approaches to training SNNs. However, previous works assume a rather long inference time period called inference latency to be allowed, while having a trade-off between inference latency and accuracy. One of the main reasons for this phenomenon stems from the difficulty in determining proper a firing threshold for spiking neurons. The threshold determination procedure is called a threshold balancing technique in the CNN–SNN conversion approach. This paper proposes a CNN–SNN conversion method with a new threshold balancing technique that obtains converted SNN models with good accuracy even with low latency. The proposed method organizes the SNN models with soft-reset IF spiking neurons. The threshold balancing technique estimates the thresholds for spiking neurons based on the maximum input current in a layerwise and channelwise manner. The experiment results have shown that our converted SNN models attain even higher accuracy than the corresponding trained CNN model for the MNIST dataset with low latency. In addition, for the Fashion-MNIST and CIFAR-10 datasets, our converted SNNs have shown less conversion loss than other methods in low latencies. The proposed method can be beneficial in deploying efficient SNN models for recognition tasks on resource-limited systems because the inference latency is strongly associated with energy consumption.

A Spiking Neural Network Model of Rodent Head Direction Calibrated With Landmark Free Learning.

Maintaining a stable estimate of head direction requires both self-motion (idiothetic) information and environmental (allothetic) anchoring. In unfamiliar or dark environments idiothetic drive can maintain a rough estimate of heading but is subject to inaccuracy, visual information is required to stabilize the head direction estimate. When learning to associate visual scenes with head angle, animals do not have access to the ‘ground truth' of their head direction, and must use egocentrically derived imprecise head direction estimates. We use both discriminative and generative methods of visual processing to learn these associations without extracting explicit landmarks from a natural visual scene, finding all are sufficiently capable at providing a corrective signal. Further, we present a spiking continuous attractor model of head direction (SNN), which when driven by idiothetic input is subject to drift. We show that head direction predictions made by the chosen model-free visual learning algorithms can correct for drift, even when trained on a small training set of estimated head angles self-generated by the SNN. We validate this model against experimental work by reproducing cue rotation experiments which demonstrate visual control of the head direction signal.

Noise resilient leaky integrate-and-fire neurons based on multi-domain spintronic devices

The capability of emulating neural functionalities efficiently in hardware is crucial for building neuromorphic computing systems. While various types of neuro-mimetic devices have been investigated, it remains challenging to provide a compact device that can emulate spiking neurons. In this work, we propose a non-volatile spin-based device for efficiently emulating a leaky integrate-and-fire neuron. By incorporating an exchange-coupled composite free layer in spin-orbit torque magnetic tunnel junctions, multi-domain magnetization switching dynamics is exploited to realize gradual accumulation of membrane potential for a leaky integrate-and-fire neuron with compact footprints. The proposed device offers significantly improved scalability compared with previously proposed spin-based neuro-mimetic implementations while exhibiting high energy efficiency and good controllability. Moreover, the proposed neuron device exhibits a varying leak constant and a varying membrane resistance that are both dependent on the magnitude of the membrane potential. Interestingly, we demonstrate that such device-inspired dynamic behaviors can be incorporated to construct more robust spiking neural network models, and find improved resiliency against various types of noise injection scenarios. The proposed spintronic neuro-mimetic devices may potentially open up exciting opportunities for the development of efficient and robust neuro-inspired computational hardware.

A neuroscience-inspired spiking neural network for EEG-based auditory spatial attention detection

Recent studies have shown that alpha oscillations (8–13 Hz) enable the decoding of auditory spatial attention. Inspired by sparse coding in cortical neurons, we propose a spiking neural network model for auditory spatial attention detection. The proposed model can extract the patterns of recorded EEG of leftward and rightward attention, independently, and uses them to train the network to detect auditory spatial attention. Specifically, our model is composed of three layers, two of which are Integrate and Fire spiking neurons. We formulate a new learning rule that is based on the firing rate of pre- and post-synaptic neurons in the first and second layers of spiking neurons. The third layer has 10 spiking neurons and the pattern of their firing rate is used in the test phase to decode the auditory spatial attention of a given test sample. Moreover, the effects of using low connectivity rates of the layers and specific range of learning parameters of the learning rule are investigated. The proposed model achieves an average accuracy of 90% with only 10% of EEG signals as training data. This study also provides new insights into the role of sparse coding in both cortical networks subserving cognitive tasks and brain-inspired machine learning.

A multi-layer spiking neural network-based approach to bearing fault diagnosis

Effective fault diagnosis is a crucial way to reduce the occurrence of severe damages of many industrial products. With the increasing amount of condition monitoring data, deep-learning-based methods have become promising ways for intelligent fault diagnosis thanks to their automatic feature extraction capability. Most recently, the third-generation neural network, called spiking neural network (SNN), has been introduced as an effective tool for fault diagnosis. However, the internal state and the error function of neurons in the SNN model cannot satisfy the conditions of continuity and differentiability, resulting in the difficulty of the gradient back-propagation, and it, therefore, prevents the extension of the SNN to a deep manner. In this article, a probabilistic spiking response model (PSRM) with a multi-layer structure is put forth to enhance the performance of the SNN in terms of bearing fault diagnosis. In the PSRM, the extracted features from the local mean decomposition (LMD) method are converted into the probability pulse sequences, and a multi-layer learning algorithm is developed to facilitate the multi-layer network training. The fault diagnosis results from three bearing databases, i.e., CWRU, MFPT, and Paderborn University datasets, demonstrate that the proposed PSRM exceeds a majority of the state-of-the-art machine learning methods. The proposed multi-layer SNN can also provide transparency to different bearing fault patterns by the membrane potentials of the spiking neurons in the output layer.

LSMCore: A 69k-Synapse/mm2 Single-Core Digital Neuromorphic Processor for Liquid State Machine

Neuromorphic processors have gained momentum recently due to their high energy efficiency in artificial intelligence applications compared to DNN accelerators. Most neuromorphic processors are executing SNNs (Spiking Neural Networks). Liquid State Machine (LSM), as the spiking version of reservoir computing, shows advantages and great potential in image classification, speech recognition, language translation, etc.. Comparing with other SNN models, LSM has the characteristics of easy to train and low resource utilization, which is suitable for low-power and resource-constrained edge computing scenarios. In this paper, we propose a novel design of a neuromorphic processor, LSMCore, aiming at LSM acceleration. LSMCore supports both training and inference of LSM. It consists of 256 input neurons, 1024 liquid neurons, and 1.31M synapses. Besides, multiple optimization techniques, including weight quantization for reducing storage, zero-skipping for decreasing dynamic sparsity, and mini-batch training are adopted in this processor. The experimental results show that the frequency of LSMCore achieves 400 MHz, the power is 4.9W and the area is 18.49 mm² with a 40nm library. Comparing with the baseline, LSMCore achieves up to <inline-formula> <tex-math notation="LaTeX">$80.7\times $ </tex-math></inline-formula>(<inline-formula> <tex-math notation="LaTeX">$49.6\times $ </tex-math></inline-formula>), <inline-formula> <tex-math notation="LaTeX">$91.3\times $ </tex-math></inline-formula>(<inline-formula> <tex-math notation="LaTeX">$56.3\times $ </tex-math></inline-formula>), and <inline-formula> <tex-math notation="LaTeX">$83.1\times $ </tex-math></inline-formula>(<inline-formula> <tex-math notation="LaTeX">$56.8\times $ </tex-math></inline-formula>) speedup on MNIST, N-MNIST, and Free Spoken Digital Dataset (FSDD) respectively for training (inference), while the accuracy of LSMCore on these three datasets are 96.8&#x0025;, 97.6&#x0025;, and 90&#x0025; respectively.

Multisample Online Learning for Probabilistic Spiking Neural Networks.

Spiking neural networks (SNNs) capture some of the efficiency of biological brains for inference and learning via the dynamic, online, and event-driven processing of binary time series. Most existing learning algorithms for SNNs are based on deterministic neuronal models, such as leaky integrate-and-fire, and rely on heuristic approximations of backpropagation through time that enforces constraints such as locality. In contrast, probabilistic SNN models can be trained directly via principled online, local, and update rules that have proven to be particularly effective for resource-constrained systems. This article investigates another advantage of probabilistic SNNs, namely, their capacity to generate independent outputs when queried over the same input. It is shown that the multiple generated output samples can be used during inference to robustify decisions and to quantify uncertainty-a feature that deterministic SNN models cannot provide. Furthermore, they can be leveraged for training in order to obtain more accurate statistical estimates of the log-loss training criterion and its gradient. Specifically, this article introduces an online learning rule based on generalized expectation-maximization (GEM) that follows a three-factor form with global learning signals and is referred to as GEM-SNN. Experimental results on structured output memorization and classification on a standard neuromorphic dataset demonstrate significant improvements in terms of log-likelihood, accuracy, and calibration when increasing the number of samples used for inference and training.

A spiking neural network model of the Superior Colliculus that is robust to changes in the spatial\u2013temporal input

Previous studies have indicated that the location of a large neural population in the Superior Colliculus (SC) motor map specifies the amplitude and direction of the saccadic eye-movement vector, while the saccade trajectory and velocity profile are encoded by the population firing rates. We recently proposed a simple spiking neural network model of the SC motor map, based on linear summation of individual spike effects of each recruited neuron, which accounts for many of the observed properties of SC cells in relation to the ensuing eye movement. However, in the model, the cortical input was kept invariant across different saccades. Electrical microstimulation and reversible lesion studies have demonstrated that the saccade properties are quite robust against large changes in supra-threshold SC activation, but that saccade amplitude and peak eye-velocity systematically decrease at low input strengths. These features were not accounted for by the linear spike-vector summation model. Here we show that the model’s input projection strengths and intra-collicular lateral connections can be tuned to generate saccades and neural spiking patterns that closely follow the experimental results.