Low Power Implantable Spike Sorting Scheme Based on Neuromorphic Classifier with Supervised Training Engine

Spiking neural network (SNN) is a brain-inspired model with more spatio-temporal information processing capacity and computational energy efficiency. However, with the increasing depth of SNNs, the memory problem caused by the weights of SNNs has gradually attracted attention. In this study, we propose an ultra-low latency adaptive local binary spiking neural network (ALBSNN) with accuracy loss estimators, which dynamically selects the network layers to be binarized to ensure a balance between quantization degree and classification accuracy by evaluating the error caused by the binarized weights during the network learning process. At the same time, to accelerate the training speed of the network, the global average pooling (GAP) layer is introduced to replace the fully connected layers by combining convolution and pooling. Finally, to further reduce the error caused by the binary weight, we propose binary weight optimization (BWO), which updates the overall weight by directly adjusting the binary weight. This method further reduces the loss of the network that reaches the training bottleneck. The combination of the above methods balances the network's quantization and recognition ability, enabling the network to maintain the recognition capability equivalent to the full precision network and reduce the storage space by more than 20%. So, SNNs can use a small number of time steps to obtain better recognition accuracy. In the extreme case of using only a one-time step, we still can achieve 93.39, 92.12, and 69.55% testing accuracy on three traditional static datasets, Fashion- MNIST, CIFAR-10, and CIFAR-100, respectively. At the same time, we evaluate our method on neuromorphic N-MNIST, CIFAR10-DVS, and IBM DVS128 Gesture datasets and achieve advanced accuracy in SNN with binary weights. Our network has greater advantages in terms of storage resources and training time.

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.

Learning binary weights to minimize the difference between target and actual outputs can be considered as a parameter optimization task within the given constraints, and thus, it belongs to the application domain of the Lagrange multiplier method (LMM). Based on the LMM, we propose a novel event-based weight binarization (eWB) algorithm for spiking neural networks (SNNs) with binary synaptic weights (-1, 1). The algorithm features (i) event-based asymptotic weight binarization using local data only, (ii) full compatibility with event-based end-to-end learning algorithms (e.g., event-driven random backpropagation (eRBP) algorithm), and (iii) the capability to address various constraints (including the binary weight constraint). As a proof of concept, we combine eWB with eRBP (eWB-eRBP) to obtain a single algorithm for learning binary weights to generate correct classifications. Fully connected SNNs were trained using eWB-eRBP and achieved an accuracy of 95.35% on MNIST. To the best of our knowledge, this is the first report on completely binary SNNs trained using an event-based learning algorithm. Given that eRBP with full-precision (32-bit) weights exhibited 97.20% accuracy, the binarization comes at the cost of an accuracy reduction of approximately 1.85%. The python code is available online: https://github.com/galactico7/eWB.

Spiking neural networks (SNNs) have shown great potential as a solution for realizing ultralow-power consumption on neuromorphic hardware, but obtaining deep SNNs is still a challenging problem. Existing network conversion methods can effectively obtain SNNs from the trained convolutional neural networks (CNNs) with little performance loss, however, high-precision weights in the converted SNNs would take up high-storage space nonamicable to limited memory resources. To tackle this problem, we analyze the relationship between weights and thresholds of spiking neurons and propose an efficient weights-threshold balance conversion method to obtain SNNs with binary weights, resulting in a significant memory storage reduction. The experimental results evaluated with various network structures on benchmark data sets show that the binary SNN not only needs much less memory resources compared to its high-precision counterpart but also achieves the high-recognition accuracy comparable to other state-of-the-art SNNs.

BackgroundPrincipal component analysis (PCA) has been widely employed for automatic neuronal spike sorting. Calculating principal components (PCs) is computationally expensive, and requires complex numerical operations and large memory resources. Substantial hardware resources are therefore needed for hardware implementations of PCA. General Hebbian algorithm (GHA) has been proposed for calculating PCs of neuronal spikes in our previous work, which eliminates the needs of computationally expensive covariance analysis and eigenvalue decomposition in conventional PCA algorithms. However, large memory resources are still inherently required for storing a large volume of aligned spikes for training PCs. The large size memory will consume large hardware resources and contribute significant power dissipation, which make GHA difficult to be implemented in portable or implantable multi-channel recording micro-systems.MethodIn this paper, we present a new algorithm for PCA-based spike sorting based on GHA, namely stream-based Hebbian eigenfilter, which eliminates the inherent memory requirements of GHA while keeping the accuracy of spike sorting by utilizing the pseudo-stationarity of neuronal spikes. Because of the reduction of large hardware storage requirements, the proposed algorithm can lead to ultra-low hardware resources and power consumption of hardware implementations, which is critical for the future multi-channel micro-systems. Both clinical and synthetic neural recording data sets were employed for evaluating the accuracy of the stream-based Hebbian eigenfilter. The performance of spike sorting using stream-based eigenfilter and the computational complexity of the eigenfilter were rigorously evaluated and compared with conventional PCA algorithms. Field programmable logic arrays (FPGAs) were employed to implement the proposed algorithm, evaluate the hardware implementations and demonstrate the reduction in both power consumption and hardware memories achieved by the streaming computingResults and discussionResults demonstrate that the stream-based eigenfilter can achieve the same accuracy and is 10 times more computationally efficient when compared with conventional PCA algorithms. Hardware evaluations show that 90.3% logic resources, 95.1% power consumption and 86.8% computing latency can be reduced by the stream-based eigenfilter when compared with PCA hardware. By utilizing the streaming method, 92% memory resources and 67% power consumption can be saved when compared with the direct implementation of GHA.ConclusionStream-based Hebbian eigenfilter presents a novel approach to enable real-time spike sorting with reduced computational complexity and hardware costs. This new design can be further utilized for multi-channel neuro-physiological experiments or chronic implants.

Spiking Self-organizing Maps for Classification Problem

Rethinking the performance comparison between SNNS and ANNS

Accurate spike sorting is an important issue for neuroscientific and neuroprosthetic applications. The sorting of spikes depends on the features extracted from the neural waveforms, and a better sorting performance usually comes with a higher sampling rate (SR). However for the long duration experiments on free-moving subjects, the miniaturized and wireless neural recording ICs are the current trend, and the compromise on sorting accuracy is usually made by a lower SR for the lower power consumption. In this paper, we implement an on-chip spike sorting processor with integrated interpolation hardware in order to improve the performance in terms of power versus accuracy. According to the fabrication results in 90nm process, if the interpolation is appropriately performed during the spike sorting, the system operated at the SR of 12.5 k samples per second (sps) can outperform the one not having interpolation at 25 ksps on both accuracy and power.

Spiking Neural Networks (SNNs) mimic the behavior of biological neurons. Unlike traditional Artificial Neural Networks (ANNs) that operate in a continuous time domain and use activation functions to process information, SNNs operate discrete event-driven, where data is encoded and communicated through spikes or discrete events. This unique approach offers several advantages, such as efficient computation and lower power consumption, making SNNs particularly attractive for energy-constrained and neuromorphic applications. However, training SNNs poses significant challenges due to the discrete nature of spikes and the non-differentiable behavior they exhibit. As a result, converting pre-trained ANNs into SNNs has gained attention as a convenient approach. While this approach simplifies the training process, it introduces certain drawbacks, including high latency. The conversion of ANNs to SNNs typically leads to a loss of accuracy, which can be attributed to various factors, including quantization, clipping, and timing errors. Previous studies have proposed techniques to mitigate quantization and clipping errors during the conversion process. However, they do not consider timing errors, degrading SNN accuracies at low latency conditions. This work introduces the MiCE conversion method, which offers a comprehensive joint optimization strategy to simultaneously alleviate quantization, clipping, and timing errors. At a moderate latency of 8 time-steps, our converted ResNet-20 achieves classification accuracies of 79.02% and 95.74% on the CIFAR-100 and CIFAR-10 datasets, respectively.

In this paper, we propose a system for file classification in large data sets based on spiking neural networks (SNNs). File information contained in key-value metadata pairs is mapped by a novel correlative temporal encoding scheme to spike patterns that are input to an SNN. The correlation between input spike patterns is determined by a file similarity measure. Unsupervised training of such networks using spike-timing-dependent plasticity (STDP) is addressed first. Then, supervised SNN training is considered by backpropagation of an error signal that is obtained by comparing the spike pattern at the output neurons with a target pattern representing the desired class. The classification accuracy is measured for various publicly available data sets with tens of thousands of elements, and compared with other learning algorithms, including logistic regression and support-vector machines. Simulation results indicate that the proposed SNN-based system using memristive synapses may represent a valid alternative to classical machine learning algorithms for inference tasks, especially in environments with asynchronous ingest of input data and limited resources.

Deep convolutional neural networks (ConvNets) have achieved the state-of-the-art performance on many real-world applications. However, significant computation and storage demands are required by ConvNets. Spiking neural networks (SNNs), with sparsely activated neurons and event-driven computations, show great potential to take advantage of the ultra- low power spike-based hardware architectures. Yet, training SNN with similar accuracy as ConvNets is difficult. Recent researchers have demonstrated the work of converting ConvNets to SNNs (CNN-SNN conversion) with similar accuracy. However, the energy-efficiency of the converted SNNs is impaired by the increased classification latency. In this paper, we focus on optimizing the classification latency of the converted SNNs. First, we propose a restricted output training method to normalize the converted weights dynamically in the CNN-SNN training phase. Second, false spikes are identified and the false spike inhibition theory is derived to speedup the convergence of the classification process. Third, we propose a temporal max pooling method to approximate the max pooling operation in ConvNets without accuracy loss. The evaluation shows that the converted SNNs converge in about 30 time-steps and achieve the best classification accuracy of 94% on CIFAR -10 dataset.

Recent work on spiking neural networks (SNNs) has focused on achieving deep architectures. They commonly use backpropagation (BP) to train SNNs directly, which allows SNNs to go deeper and achieve higher performance. However, the BP training procedure is computing intensive and complicated by many trainable parameters. Inspired by global pooling in convolutional neural networks (CNNs), we present the spike probabilistic global pooling (SPGP) method based on a probability function for training deep convolutional SNNs. It aims to remove the difficulty of too many trainable parameters brought by multiple layers in the training process, which can reduce the risk of overfitting and get better performance for deep SNNs (DSNNs). We use the discrete leaky-integrate-fire model and the spatiotemporal BP algorithm for training DSNNs directly. As a result, our model trained with the SPGP method achieves competitive performance compared to the existing DSNNs on image and neuromorphic data sets while minimizing the number of trainable parameters. In addition, the proposed SPGP method shows its effectiveness in performance improvement, convergence, and generalization ability.

A convolutional spiking neural network with adaptive coding for motor imagery classification

Spike sorting is a technique in the field of neuroscience applied to identify and classify the action potentials (spikes) of neurons in extracellular recordings. This method is important considering that the simultaneous activity of several neurons can be recorded through the use of electrodes, but the recorded signals are often mixed. Extracting the characteristics of individual spikes provides valuable information about the identity of neurons that generate them, the type of cells involved (inhibitory/excitatory), encoding of information in spike rates or spike times, and so on. Therefore, unmixing the spikes recorded on an electrode via spike sorting is crucial. Here, we apply a novel method to extract features of mixed spikes, namely the Superlet transform, which enables the computation of spectral characteristics with a higher resolution. We use machine learning to determine which features of the Superlet spectrum contain the most information about the shapes of individual spikes, thereby enabling their unmixing during spike sorting.

Spiking neural networks are rapidly gaining popularity for their ability to perform efficient computation akin to the way a brain processes information. It has the potential to achieve low cost and high energy efficiency due to the distributed nature of neural computation and the use of low energy spikes for information exchange. A stochastic spiking neural network naturally can be used to realize Bayesian inference. IBM's TrueNorth is a neurosynaptic processor that has more than 1 million digital spiking neurons and 268 million digital synapses with less than 200 mW peak power. In this paper we propose the first work that converts an inference network to a spiking neural network that runs on the TrueNorth processor. Using inference-based sentence construction as a case study, we discuss algorithms that transform an inference network to a spiking neural network, and a spiking neural network to TrueNorth corelet designs. In our experiments, the TrueNorth spiking neural network constructed sentences have a matching accuracy of 88% while consuming an average power of 0.205 mW.