Deep spiking neural networks (SNNs) offer the promise of low-power artificial intelligence. However, training deep SNNs from scratch or converting deep artificial neural networks to SNNs without loss of performance has been a challenge. Here we propose an exact mapping from a network with Rectified Linear Units (ReLUs) to an SNN that fires exactly one spike per neuron. For our constructive proof, we assume that an arbitrary multi-layer ReLU network with or without convolutional layers, batch normalization and max pooling layers was trained to high performance on some training set. Furthermore, we assume that we have access to a representative example of input data used during training and to the exact parameters (weights and biases) of the trained ReLU network. The mapping from deep ReLU networks to SNNs causes zero percent drop in accuracy on CIFAR10, CIFAR100 and the ImageNet-like data sets Places365 and PASS. More generally our work shows that an arbitrary deep ReLU network can be replaced by an energy-efficient single-spike neural network without any loss of performance.

我们提出了一种新的学习算法，使用传统的人工神经网络（ANN）作为代理训练尖刺神经网络（SNN）。我们分别与具有相同网络架构和共享突触权重的集成和火（IF）和Relu神经元进行两次SNN和ANN网络。两个网络的前进通过完全独立。通过假设具有速率编码的神经元作为Relu的近似值，我们将SNN中的SNN的误差进行了回复，以更新共享权重，只需用SNN的ANN最终输出替换ANN最终输出。我们将建议的代理学习应用于深度卷积的SNNS，并在Fahion-Mnist和CiFar10的两个基准数据集上进行评估，分别为94.56％和93.11％的分类准确性。所提出的网络可以优于培训的其他深鼻涕，训练，替代学习，代理梯度学习，或从深处转换。转换的SNNS需要长时间的仿真时间来达到合理的准确性，而我们的代理学习导致高效的SNN，模拟时间较短。

由于它们的时间加工能力及其低交换（尺寸，重量和功率）以及神经形态硬件中的节能实现，尖峰神经网络（SNNS）已成为传统人工神经网络（ANN）的有趣替代方案。然而，培训SNNS所涉及的挑战在准确性方面有限制了它们的表现，从而限制了他们的应用。因此，改善更准确的特征提取的学习算法和神经架构是SNN研究中的当前优先级之一。在本文中，我们展示了现代尖峰架构的关键组成部分的研究。我们在从最佳执行网络中凭经验比较了图像分类数据集中的不同技术。我们设计了成功的残余网络（Reset）架构的尖峰版本，并测试了不同的组件和培训策略。我们的结果提供了SNN设计的最新版本，它允许在尝试构建最佳视觉特征提取器时进行明智的选择。最后，我们的网络优于CIFAR-10（94.1％）和CIFAR-100（74.5％）数据集的先前SNN架构，并将现有技术与DVS-CIFAR10（71.3％）相匹配，参数较少而不是先前的状态艺术，无需安静转换。代码在https://github.com/vicenteax/spiking_resnet上获得。

由于稀疏，异步和二进制事件（或尖峰）驱动加工，尖峰神经网络（SNNS）最近成为深度学习的替代方案，可以在神经形状硬件上产生巨大的能效益。然而，从划痕训练高精度和低潜伏期的SNN，患有尖刺神经元的非微弱性质。要在SNNS中解决此培训问题，我们重新批准批量标准化，并通过时间（BNTT）技术提出时间批量标准化。大多数先前的SNN工程到现在忽略了批量标准化，认为它无效地训练时间SNN。与以前的作品不同，我们提出的BNTT沿着时轴沿着时间轴解耦的参数，以捕获尖峰的时间动态。在BNTT中的时间上不断发展的可学习参数允许神经元通过不同的时间步长来控制其尖峰率，从头开始实现低延迟和低能量训练。我们对CiFar-10，CiFar-100，微小想象特和事件驱动的DVS-CIFAR10数据集进行实验。 BNTT允许我们首次在三个复杂的数据集中培训深度SNN架构，只需25-30步即可。我们还使用BNTT中的参数分布提前退出算法，以降低推断的延迟，进一步提高了能量效率。

Spiking neural networks (SNNs) are promising brain-inspired energy-efficient models. Recent progress in training methods has enabled successful deep SNNs on large-scale tasks with low latency. Particularly, backpropagation through time (BPTT) with surrogate gradients (SG) is popularly used to achieve high performance in a very small number of time steps. However, it is at the cost of large memory consumption for training, lack of theoretical clarity for optimization, and inconsistency with the online property of biological learning and rules on neuromorphic hardware. Other works connect spike representations of SNNs with equivalent artificial neural network formulation and train SNNs by gradients from equivalent mappings to ensure descent directions. But they fail to achieve low latency and are also not online. In this work, we propose online training through time (OTTT) for SNNs, which is derived from BPTT to enable forward-in-time learning by tracking presynaptic activities and leveraging instantaneous loss and gradients. Meanwhile, we theoretically analyze and prove that gradients of OTTT can provide a similar descent direction for optimization as gradients based on spike representations under both feedforward and recurrent conditions. OTTT only requires constant training memory costs agnostic to time steps, avoiding the significant memory costs of BPTT for GPU training. Furthermore, the update rule of OTTT is in the form of three-factor Hebbian learning, which could pave a path for online on-chip learning. With OTTT, it is the first time that two mainstream supervised SNN training methods, BPTT with SG and spike representation-based training, are connected, and meanwhile in a biologically plausible form. Experiments on CIFAR-10, CIFAR-100, ImageNet, and CIFAR10-DVS demonstrate the superior performance of our method on large-scale static and neuromorphic datasets in small time steps.

在本文中，我们提出了一种节能的SNN体系结构，该体系结构可以通过提高的精度无缝地运行深度尖峰神经网络（SNN）。首先，我们提出了一个转换意识培训（CAT），以减少无硬件实施开销而无需安排SNN转换损失。在拟议的CAT中，可以有效利用用于在ANN训练过程中模拟SNN的激活函数，以减少转换后的数据表示误差。基于CAT技术，我们还提出了一项首要尖峰编码，该编码可以通过使用SPIKE时间信息来轻巧计算。支持提出技术的SNN处理器设计已使用28nm CMOS流程实施。该处理器的推理能量分别为486.7UJ，503.6UJ和1426UJ的最高1级准确性，分别为91.7％，67.9％和57.4％，分别为CIFAR-10，CIFAR-100和TININE-IMIMAGENET处理。16具有5位对数权重。

我们最近提出了S4NN算法，基本上是对多层尖峰神经网络的反向化的适应，该网上网络使用简单的非泄漏整合和火神经元和一种形式称为第一峰值编码的时间编码。通过这种编码方案，每次刺激最多一次都是神经元火灾，但射击令携带信息。这里，我们引入BS4NN，S4NN的修改，其中突触权重被约束为二进制（+1或-1），以便减少存储器（理想情况下，每个突触的一个比特）和计算占地面积。这是使用两组权重完成：首先，通过梯度下降更新的实际重量，并在BackProjagation的后退通行证中使用，其次是在前向传递中使用的迹象。类似的策略已被用于培训（非尖峰）二值化神经网络。主要区别在于BS4NN在时域中操作：尖峰依次繁殖，并且不同的神经元可以在不同时间达到它们的阈值，这增加了计算能力。我们验证了两个流行的基准，Mnist和Fashion-Mnist上的BS4NN，并获得了这种网络的合理精度（分别为97.0％和87.3％），具有可忽略的准确率，具有可忽略的重量率（0.4％和0.7％，分别）。我们还展示了BS4NN优于具有相同架构的简单BNN，在这两个数据集上（分别为0.2％和0.9％），可能是因为它利用时间尺寸。建议的BS4NN的源代码在HTTPS://github.com/srkh/bs4nn上公开可用。

Emergence of deep neural networks (DNNs) has raised enormous attention towards artificial neural networks (ANNs) once again. They have become the state-of-the-art models and have won different machine learning challenges. Although these networks are inspired by the brain, they lack biological plausibility, and they have structural differences compared to the brain. Spiking neural networks (SNNs) have been around for a long time, and they have been investigated to understand the dynamics of the brain. However, their application in real-world and complicated machine learning tasks were limited. Recently, they have shown great potential in solving such tasks. Due to their energy efficiency and temporal dynamics there are many promises in their future development. In this work, we reviewed the structures and performances of SNNs on image classification tasks. The comparisons illustrate that these networks show great capabilities for more complicated problems. Furthermore, the simple learning rules developed for SNNs, such as STDP and R-STDP, can be a potential alternative to replace the backpropagation algorithm used in DNNs.

Event-based simulations of Spiking Neural Networks (SNNs) are fast and accurate. However, they are rarely used in the context of event-based gradient descent because their implementations on GPUs are difficult. Discretization with the forward Euler method is instead often used with gradient descent techniques but has the disadvantage of being computationally expensive. Moreover, the lack of precision of discretized simulations can create mismatches between the simulated models and analog neuromorphic hardware. In this work, we propose a new exact error-backpropagation through spikes method for SNNs, extending Fast \& Deep to multiple spikes per neuron. We show that our method can be efficiently implemented on GPUs in a fully event-based manner, making it fast to compute and precise enough for analog neuromorphic hardware. Compared to the original Fast \& Deep and the current state-of-the-art event-based gradient-descent algorithms, we demonstrate increased performance on several benchmark datasets with both feedforward and convolutional SNNs. In particular, we show that multi-spike SNNs can have advantages over single-spike networks in terms of convergence, sparsity, classification latency and sensitivity to the dead neuron problem.

由于具有高生物学合理性和低能消耗在神经形态硬件上的特性，因此尖峰神经网络（SNN）非常重要。作为获得深SNN的有效方法，转化方法在各种大型数据集上表现出高性能。但是，它通常遭受严重的性能降解和高时间延迟。特别是，以前的大多数工作都集中在简单的分类任务上，同时忽略了与ANN输出的精确近似。在本文中，我们首先从理论上分析转换误差，并得出时间变化极端对突触电流的有害影响。我们提出尖峰校准（Spicalib），以消除离散尖峰对输出分布的损坏，并修改脂肪，以使任意最大化层无损地转换。此外，提出了针对最佳标准化参数的贝叶斯优化，以避免经验设置。实验结果证明了分类，对象检测和分割任务的最新性能。据我们所知，这是第一次获得与ANN同时在这些任务上相当的SNN。此外，我们只需要先前在检测任务上工作的1/50推理时间，并且可以在0.492 $ \ times $ $下在分段任务上实现相同的性能。

由于其异步，稀疏和二进制信息处理，尖峰神经网络（SNN）最近成为人工神经网络（ANN）的低功耗替代品。为了提高能源效率和吞吐量，可以在使用新兴的非挥发性（NVM）设备在模拟域中实现多重和蓄积（MAC）操作的回忆横梁上实现SNN。尽管SNN与回忆性横梁具有兼容性，但很少关注固有的横杆非理想性和随机性对SNN的性能的影响。在本文中，我们对SNN在非理想横杆上的鲁棒性进行了全面分析。我们检查通过学习算法训练的SNN，例如，替代梯度和ANN-SNN转换。我们的结果表明，跨多个时间阶段的重复横梁计算会导致错误积累，从而导致SNN推断期间的性能下降。我们进一步表明，经过较少时间步长培训的SNN在部署在磁带横梁上时可以更好地准确。

穗状花序的神经形状硬件占据了深度神经网络（DNN）的更节能实现的承诺，而不是GPU的标准硬件。但这需要了解如何在基于事件的稀疏触发制度中仿真DNN，否则能量优势丢失。特别地，解决序列处理任务的DNN通常采用难以使用少量尖峰效仿的长短期存储器（LSTM）单元。我们展示了许多生物神经元的面部，在每个尖峰后缓慢的超积极性（AHP）电流，提供了有效的解决方案。 AHP电流可以轻松地在支持多舱神经元模型的神经形状硬件中实现，例如英特尔的Loihi芯片。滤波近似理论解释为什么AHP-Neurons可以模拟LSTM单元的功能。这产生了高度节能的时间序列分类方法。此外，它为实现了非常稀疏的大量大型DNN来实现基础，这些大型DNN在文本中提取单词和句子之间的关系，以便回答有关文本的问题。

尖峰 - 神经网络（SNNS）在边缘设备处具有前景，因为与模拟 - 神经网络（ANN）相比，SNN的事件驱动操作提供了显着较低的功率。虽然很难有效地训练SNN，但是已经开发了许多将培训的ANN转换为SNNS的技术。但是，在转换之后，SNN中的准确性和延迟之间存在权衡关系，在大尺寸数据集中导致诸如想象成的大尺寸数据集之间的相当大。我们提出了一种名为TCL的技术，以缓解权衡问题，使得73.87％（VGG-16）和70.37％（Reset-34）的准确性，在SNNS中的250个周期的中等潜伏期。

尖峰神经网络是低功率环境的有效计算模型。基于SPIKE的BP算法和ANN-TO-SNN（ANN2SNN）转换是SNN培训的成功技术。然而，尖峰碱BP训练速度很慢，需要大量的记忆成本。尽管Ann2NN提供了一种培训SNN的低成本方式，但它需要许多推理步骤才能模仿训练有素的ANN以表现良好。在本文中，我们提出了一个snn-to-ang（SNN2ANN）框架，以快速和记忆的方式训练SNN。 SNN2ANN由2个组成部分组成：a）ANN和SNN和B）尖峰映射单元之间的重量共享体系结构。首先，该体系结构在ANN分支上训练重量共享参数，从而快速训练和SNN的记忆成本较低。其次，尖峰映射单元确保ANN的激活值是尖峰特征。结果，可以通过训练ANN分支来优化SNN的分类误差。此外，我们设计了一种自适应阈值调整（ATA）算法来解决嘈杂的尖峰问题。实验结果表明，我们的基于SNN2ANN的模型在基准数据集（CIFAR10，CIFAR100和TININE-IMAGENET）上表现良好。此外，SNN2ANN可以在0.625倍的时间步长，0.377倍训练时间，0.27倍GPU内存成本以及基于SPIKE的BP模型的0.33倍尖峰活动下实现可比精度。

The term ``neuromorphic'' refers to systems that are closely resembling the architecture and/or the dynamics of biological neural networks. Typical examples are novel computer chips designed to mimic the architecture of a biological brain, or sensors that get inspiration from, e.g., the visual or olfactory systems in insects and mammals to acquire information about the environment. This approach is not without ambition as it promises to enable engineered devices able to reproduce the level of performance observed in biological organisms -- the main immediate advantage being the efficient use of scarce resources, which translates into low power requirements. The emphasis on low power and energy efficiency of neuromorphic devices is a perfect match for space applications. Spacecraft -- especially miniaturized ones -- have strict energy constraints as they need to operate in an environment which is scarce with resources and extremely hostile. In this work we present an overview of early attempts made to study a neuromorphic approach in a space context at the European Space Agency's (ESA) Advanced Concepts Team (ACT).

基于事件的视觉传感器在事件流中编码本地像素方面的亮度变化，而不是图像帧，并且除了低延迟，高动态范围和缺乏运动模糊之外，还产生稀疏，节能编码。基于事件的传感器的对象识别的最新进展来自深度神经网络的转换，培训背部经历。但是，使用这些事件流的方法需要转换到同步范式，这不仅失去了计算效率，而且还会错过提取时空特征的机会。在本文中，我们提出了一种用于基于事件的模式识别和对象检测的深度神经网络的端到端培训的混合架构，将尖刺神经网络（SNN）骨干组合用于高效的基于事件的特征提取，以及随后的模拟神经网络（ANN）头解决同步分类和检测任务。这是通过将标准的梯度训练与替代梯度训练相结合来实现这一点来实现，以通过SNN传播梯度。可以在不转换的情况下培训混合SNN-ANN，并且导致高度准确的网络，这些网络比其ANN对应物大得多。我们演示了基于事件的分类和对象检测数据集的结果，其中只需要将ANN头的体系结构适应任务，并且不需要基于事件的输入的转换。由于ANNS和SNNS需要不同的硬件范式来最大限度地提高其效率，因此设想SNN骨干网和ANN头可以在不同的处理单元上执行，从而分析在两部分之间进行通信的必要带宽。混合网络是有前途的架构，以进一步推进基于事件的愿景的机器学习方法，而不必妥协效率。

Spiking neural networks (SNN) are a viable alternative to conventional artificial neural networks when energy efficiency and computational complexity are of importance. A major advantage of SNNs is their binary information transfer through spike trains. The training of SNN has, however, been a challenge, since neuron models are non-differentiable and traditional gradient-based backpropagation algorithms cannot be applied directly. Furthermore, spike-timing-dependent plasticity (STDP), albeit being a spike-based learning rule, updates weights locally and does not optimize for the output error of the network. We present desire backpropagation, a method to derive the desired spike activity of neurons from the output error. The loss function can then be evaluated locally for every neuron. Incorporating the desire values into the STDP weight update leads to global error minimization and increasing classification accuracy. At the same time, the neuron dynamics and computational efficiency of STDP are maintained, making it a spike-based supervised learning rule. We trained three-layer networks to classify MNIST and Fashion-MNIST images and reached an accuracy of 98.41% and 87.56%, respectively. Furthermore, we show that desire backpropagation is computationally less complex than backpropagation in traditional neural networks.

我们如何为神经系统带来隐私和能效？在本文中，我们提出了PrivateNN，旨在从预先训练的ANN模型构建低功耗尖峰神经网络（SNNS），而不会泄漏包含在数据集中的敏感信息。在这里，我们解决两种类型的泄漏问题：1）当网络在Ann-SNN转换过程中访问真实训练数据时，会导致数据泄漏。 2）当类相关的特征可以从网络参数重建时，会导致类泄漏。为了解决数据泄漏问题，我们从预先培训的ANN生成合成图像，并使用所生成的图像将ANN转换为SNNS。然而，转换的SNNS仍然容易受到类泄漏的影响，因为权重参数相对于ANN参数具有相同的（或缩放）值。因此，通过训练SNNS，通过训练基于时间尖峰的学习规则来加密SNN权重。使用时间数据更新权重参数使得SNN难以在空间域中解释。我们观察到，加密的私人没有消除数据和类泄漏问题，略微的性能下降（小于〜2），与标准ANN相比，与标准ANN相比的显着的能效增益（约55倍）。我们对各种数据集进行广泛的实验，包括CiFar10，CiFar100和Tinyimagenet，突出了隐私保留的SNN培训的重要性。

We propose a novel backpropagation algorithm for training spiking neural networks (SNNs) that encodes information in the relative multiple spike timing of individual neurons without single-spike restrictions. The proposed algorithm inherits the advantages of conventional timing-based methods in that it computes accurate gradients with respect to spike timing, which promotes ideal temporal coding. Unlike conventional methods where each neuron fires at most once, the proposed algorithm allows each neuron to fire multiple times. This extension naturally improves the computational capacity of SNNs. Our SNN model outperformed comparable SNN models and achieved as high accuracy as non-convolutional artificial neural networks. The spike count property of our networks was altered depending on the time constant of the postsynaptic current and the membrane potential. Moreover, we found that there existed the optimal time constant with the maximum test accuracy. That was not seen in conventional SNNs with single-spike restrictions on time-to-fast-spike (TTFS) coding. This result demonstrates the computational properties of SNNs that biologically encode information into the multi-spike timing of individual neurons. Our code would be publicly available.

尖峰神经网络（SNN）是大脑中低功率，耐断层的信息处理的基础，并且在适当的神经形态硬件加速器上实施时，可能构成传统深层神经网络的能力替代品。但是，实例化解决复杂的计算任务的SNN在Silico中仍然是一个重大挑战。替代梯度（SG）技术已成为培训SNN端到端的标准解决方案。尽管如此，它们的成功取决于突触重量初始化，类似于常规的人工神经网络（ANN）。然而，与ANN不同，它仍然难以捉摸地构成SNN的良好初始状态。在这里，我们为受到大脑中通常观察到的波动驱动的策略启发的SNN制定了一般初始化策略。具体而言，我们为数据依赖性权重初始化提供了实用的解决方案，以确保广泛使用的泄漏的集成和传火（LIF）神经元的波动驱动。我们从经验上表明，经过SGS培训时，SNN遵循我们的策略表现出卓越的学习表现。这些发现概括了几个数据集和SNN体系结构，包括完全连接，深度卷积，经常性和更具生物学上合理的SNN遵守Dale的定律。因此，波动驱动的初始化提供了一种实用，多功能且易于实现的策略，可改善神经形态工程和计算神经科学的不同任务的SNN培训绩效。