Spatio-temporal Spike Patterns Research Articles

Adaptive STDP-based on-chip spike pattern detection.

A spiking neural network (SNN) is a bottom-up tool used to describe information processing in brain microcircuits. It is becoming a crucial neuromorphic computational model. Spike-timing-dependent plasticity (STDP) is an unsupervised brain-like learning rule implemented in many SNNs and neuromorphic chips. However, a significant performance gap exists between ideal model simulation and neuromorphic implementation. The performance of STDP learning in neuromorphic chips deteriorates because the resolution of synaptic efficacy in such chips is generally restricted to 6 bits or less, whereas simulations employ the entire 64-bit floating-point precision available on digital computers. Previously, we introduced a bio-inspired learning rule named adaptive STDP and demonstrated via numerical simulation that adaptive STDP (using only 4-bit fixed-point synaptic efficacy) performs similarly to STDP learning (using 64-bit floating-point precision) in a noisy spike pattern detection model. Herein, we present the experimental results demonstrating the performance of adaptive STDP learning. To the best of our knowledge, this is the first study that demonstrates unsupervised noisy spatiotemporal spike pattern detection to perform well and maintain the simulation performance on a mixed-signal CMOS neuromorphic chip with low-resolution synaptic efficacy. The chip was designed in Taiwan Semiconductor Manufacturing Company (TSMC) 250 nm CMOS technology node and comprises a soma circuit and 256 synapse circuits along with their learning circuitry.

Engineering spatiotemporal patterns: information encoding, processing, and controllability in oscillator ensembles

The ability to finely manipulate spatiotemporal patterns displayed in neuronal populations is critical for understanding and influencing brain functions, sleep cycles, and neurological pathologies. However, such control tasks are challenged not only by the immense scale but also by the lack of real-time state measurements of neurons in the population, which deteriorates the control performance. In this paper, we formulate the control of dynamic structures in an ensemble of neuron oscillators as a tracking problem and propose a principled control technique for designing optimal stimuli that produce desired spatiotemporal patterns in a network of interacting neurons without requiring feedback information. We further reveal an interesting presentation of information encoding and processing in a neuron ensemble in terms of its controllability property. The performance of the presented technique in creating complex spatiotemporal spiking patterns is demonstrated on neural populations described by mathematically ideal and biophysical models, including the Kuramoto and Hodgkin-Huxley models, as well as real-time experiments on Wein bridge oscillators.

A New Spike Membership Function for the Recognition and Processing of Spatiotemporal Spike Patterns: Syllable-Based Speech Recognition Application

This paper introduces a new spike activation function (SPKAF) or spike membership function for fuzzy adaptive neurons (FAN), developed for decoding spatiotemporal information with spikes, optimizing digital signal processing. A solution with the adaptive network-based fuzzy inference system (ANFIS) method is proposed and compared with that of the FAN-SPKAF model, obtaining very precise simulation results. Stability analysis of systems models is presented. An application to voice recognition using solfeggio syllables in Spanish is performed experimentally, comparing the methods of FAN-step activation function (STEPAF)-SPKAF, Augmented Spiking Neuron Model, and Augmented FAN-STEPAF-SPKAF, achieving very good results.

Synaptic self-organization of spatio-temporal pattern selectivity.

Spiking model neurons can be set up to respond selectively to specific spatio-temporal spike patterns by optimization of their input weights. It is unknown, however, if existing synaptic plasticity mechanisms can achieve this temporal mode of neuronal coding and computation. Here it is shown that changes of synaptic efficacies which tend to balance excitatory and inhibitory synaptic inputs can make neurons sensitive to particular input spike patterns. Simulations demonstrate that a combination of Hebbian mechanisms, hetero-synaptic plasticity and synaptic scaling is sufficient for self-organizing sensitivity for spatio-temporal spike patterns that repeat in the input. In networks inclusion of hetero-synaptic plasticity that depends on the pre-synaptic neurons leads to specialization and faithful representation of pattern sequences by a group of target neurons. Pattern detection is robust against a range of distortions and noise. The proposed combination of Hebbian mechanisms, hetero-synaptic plasticity and synaptic scaling is found to protect the memories for specific patterns from being overwritten by ongoing learning during extended periods when the patterns are not present. This suggests a novel explanation for the long term robustness of memory traces despite ongoing activity with substantial synaptic plasticity. Taken together, our results promote the plausibility of precise temporal coding in the brain.

A Conductance-Based Silicon Synapse Circuit.

Neuron, synapse, and learning circuits inspired by the brain comprise the key components of a neuromorphic chip. In this study, we present a conductance-based analog silicon synapse circuit suitable for the implementation of reduced or multi-compartment neuron models. Compartmental models are more bio-realistic. They are implemented in neuromorphic chips aiming to mimic the electrical activities of the neuronal networks in the brain and incorporate biomimetic soma and synapse circuits. Most contemporary low-power analog synapse circuits implement bioinspired "current-based" synaptic models suited for the implementation of single-compartment point neuron models. They emulate the exponential decay profile of the synaptic current, but ignore the effect of the postsynaptic membrane potential on the synaptic current. This dependence is necessary to emulate shunting inhibition, which is thought to play important roles in information processing in the brain. The proposed circuit uses an oscillator-based resistor-type element at its output stage to incorporate this effect. This circuit is used to demonstrate the shunting inhibition phenomenon. Next, to demonstrate that the oscillatory nature of the induced synaptic current has no unforeseen effects, the synapse circuit is employed in a spatiotemporal spike pattern detection task. The task employs the adaptive spike-timing-dependent plasticity (STDP) learning rule, a bio-inspired learning rule introduced in a previous study. The mixed-signal chip is designed in a Taiwan Manufacturing Semiconductor Company 250 nm complementary metal oxide semiconductor technology node. It comprises a biomimetic soma circuit and 256 synapse circuits, along with their learning circuitries.

Spiking Generative Adversarial Networks With a Neural Network Discriminator: Local Training, Bayesian Models, and Continual Meta-Learning

Neuromorphic data carries information in spatio-temporal patterns encoded by spikes. Accordingly, a central problem in neuromorphic computing is training spiking neural networks (SNNs) to reproduce spatio-temporal spiking patterns in response to given spiking stimuli. Most existing approaches model the input-output behavior of an SNN in a deterministic fashion by assigning each input to a specific desired output spiking sequence. In contrast, in order to fully leverage the time-encoding capacity of spikes, this work proposes to train SNNs so as to match <i>distributions</i> of spiking signals rather than individual spiking signals. To this end, the paper introduces a novel hybrid architecture comprising a conditional generator, implemented via an SNN, and a discriminator, implemented by a conventional artificial neural network (ANN). The role of the ANN is to provide feedback during training to the SNN within an adversarial iterative learning strategy that follows the principle of generative adversarial network (GANs). In order to better capture multi-modal spatio-temporal distribution, the proposed approach – termed SpikeGAN – is further extended to support Bayesian learning of the generator's weight. Finally, settings with time-varying statistics are addressed by proposing an online meta-learning variant of SpikeGAN. Experiments bring insights into the merits of the proposed approach as compared to existing solutions based on (static) belief networks and maximum likelihood (or empirical risk minimization). In our experiments, handwritten digit images generated by SpikeGAN are observed to train an ANN classifier with <inline-formula><tex-math notation="LaTeX">$20\%$</tex-math></inline-formula> higher accuracy than a comparable belief network. Our experiments also demonstrate the use of SpikeGAN to generate neuromorphic data sets from handwritten digits. It is shown that these data can be used to train an SNN classifier that achieves an accuracy level approaching the baseline accuracy of an SNN classifier trained on rate-encoded real data.

Comparing Surrogates to Evaluate Precisely Timed Higher-Order Spike Correlations.

The generation of surrogate data, i.e., the modification of data to destroy a certain feature, can be considered as the implementation of a null-hypothesis whenever an analytical approach is not feasible. Thus, surrogate data generation has been extensively used to assess the significance of spike correlations in parallel spike trains. In this context, one of the main challenges is to properly construct the desired null-hypothesis distribution and to avoid altering the single spike train statistics. A classical surrogate technique is uniform dithering (UD), which displaces spikes locally and uniformly distributed, to destroy temporal properties on a fine timescale while keeping them on a coarser one. Here, we compare UD against five similar surrogate techniques in the context of the detection of significant spatiotemporal spike patterns. We evaluate the surrogates for their performance, first on spike trains based on point process models with constant firing rate, and second on modeled nonstationary artificial data to assess the potential detection of false positive (FP) patterns in a more complex and realistic setting. We determine which statistical features of the spike trains are modified and to which extent. Moreover, we find that UD fails as an appropriate surrogate because it leads to a loss of spikes in the context of binning and clipping, and thus to a large number of FP patterns. The other surrogates achieve a better performance in detecting precisely timed higher-order correlations. Based on these insights, we analyze experimental data from the pre-/motor cortex of macaque monkeys during a reaching-and-grasping task.

Rectified Linear Postsynaptic Potential Function for Backpropagation in Deep Spiking Neural Networks.

Spiking neural networks (SNNs) use spatiotemporal spike patterns to represent and transmit information, which are not only biologically realistic but also suitable for ultralow-power event-driven neuromorphic implementation. Just like other deep learning techniques, deep SNNs (DeepSNNs) benefit from the deep architecture. However, the training of DeepSNNs is not straightforward because the well-studied error backpropagation (BP) algorithm is not directly applicable. In this article, we first establish an understanding as to why error BP does not work well in DeepSNNs. We then propose a simple yet efficient rectified linear postsynaptic potential function (ReL-PSP) for spiking neurons and a spike-timing-dependent BP (STDBP) learning algorithm for DeepSNNs where the timing of individual spikes is used to convey information (temporal coding), and learning (BP) is performed based on spike timing in an event-driven manner. We show that DeepSNNs trained with the proposed single spike time-based learning algorithm can achieve the state-of-the-art classification accuracy. Furthermore, by utilizing the trained model parameters obtained from the proposed STDBP learning algorithm, we demonstrate ultralow-power inference operations on a recently proposed neuromorphic inference accelerator. The experimental results also show that the neuromorphic hardware consumes 0.751 mW of the total power consumption and achieves a low latency of 47.71 ms to classify an image from the Modified National Institute of Standards and Technology (MNIST) dataset. Overall, this work investigates the contribution of spike timing dynamics for information encoding, synaptic plasticity, and decision-making, providing a new perspective to the design of future DeepSNNs and neuromorphic hardware.

A Model of Pattern Separation by Single Neurons.

For efficient processing, spatiotemporal spike patterns representing similar input must be able to transform into a less similar output. A new computational model with physiologically plausible parameters shows how the neuronal process referred to as “pattern separation” can be very well achieved by single neurons if the temporal qualities of the output patterns are considered. Spike patterns generated by a varying number of neurons firing with fixed different frequencies within a gamma range are used as input. The temporal and spatial summation of dendritic input combined with theta-oscillating excitability in the output neuron by subthreshold membrane potential oscillations (SMOs) lead to high temporal separation by different delays of output spikes of similar input patterns. A Winner Takes All (WTA) mechanism with backward inhibition suffices to transform the spatial overlap of input patterns to much less temporal overlap of the output patterns. The conversion of spatial patterns input into an output with differently delayed spikes enables high separation effects. Incomplete random connectivity spreads the times up to the first spike across a spatially expanded ensemble of output neurons. With the expansion, random connectivity becomes the spatial distribution mechanism of temporal features. Additionally, a “synfire chain” circuit is proposed to reconvert temporal differences into spatial ones.

Accelerating input-output model estimation with parallel computing for testing hippocampal memory prostheses in human

BackgroundHippocampal memory prosthesis is defined as a closed-loop biomimetic system that can be used for restoration and enhancement of memory functions impaired in diseases or injuries. To build such a prosthesis, we have developed two types of input-output models, i.e., a multi-input multi-output (MIMO) model for predicting output spike trains based on input spikes, and a double-layer multi-resolution memory decoding (MD) model for classifying spatio-temporal patterns of spikes into memory categories. Both models can achieve high prediction accuracy using human hippocampal spikes data and can be used to derive electrical stimulation patterns to test the hippocampal memory prosthesis. MethodsHowever, testing hippocampal memory prostheses in human epilepsy patients with such models has to be performed within a much shorter time window (48–72 h) due to clinical limitations. To solve this problem, we have developed parallelization strategies to decompose the overall model estimation task into multiple independent sub-tasks involving different outputs and cross-validation folds. These sub-tasks are then accomplished in parallel on different computer nodes to reduce model estimation time. ResultsImplementing both parallel schemes with a high-performance computer cluster, we successfully reduced the computing time of model estimations from hundreds of hours to tens of hours. Comparison with existing methodWe have tested the two parallel computing schemes for both MIMO and MD models with data collected from 11 human subjects. The performances of the parallel schemes are compared with the performance of the non-parallel scheme. ConclusionSuch strategies allow us to complete the modeling procedure within the required time frame to further test input-output model-driven electrical stimulations for the hippocampal memory prosthesis. It has important implications to test the model-based DBS intraoperatively and developing clinically viable hippocampal memory prostheses.

A Double-Layer Multi-Resolution Classification Model for Decoding Spatiotemporal Patterns of Spikes With Small Sample Size.

We build a double-layer, multiple temporal-resolution classification model for decoding single-trial spatiotemporal patterns of spikes. The model takes spiking activities as input signals and binary behavioral or cognitive variables as output signals and represents the input-output mapping with a double-layer ensemble classifier. In the first layer, to solve the underdetermined problem caused by the small sample size and the very high dimensionality of input signals, B-spline functional expansion and L1-regularized logistic classifiers are used to reduce dimensionality and yield sparse model estimations. A wide range of temporal resolutions of neural features is included by using a large number of classifiers with different numbers of B-spline knots. Each classifier serves as a base learner to classify spatiotemporal patterns into the probability of the output label with a single temporal resolution. A bootstrap aggregating strategy is used to reduce the estimation variances of these classifiers. In the second layer, another L1-regularized logistic classifier takes outputs of first-layer classifiers as inputs to generate the final output predictions. This classifier serves as a meta-learner that fuses multiple temporal resolutions to classify spatiotemporal patterns of spikes into binary output labels. We test this decoding model with both synthetic and experimental data recorded from rats and human subjects performing memory-dependent behavioral tasks. Results show that this method can effectively avoid overfitting and yield accurate prediction of output labels with small sample size. The double-layer, multi-resolution classifier consistently outperforms the best single-layer, single-resolution classifier by extracting and utilizing multi-resolution spatiotemporal features of spike patterns in the classification.

An Optimized Deep Spiking Neural Network Architecture Without Gradients

We present an end-to-end trainable modular event-driven neural architecture that uses local synaptic and threshold adaptation rules to perform transformations between arbitrary spatio-temporal spike patterns. The architecture represents a highly abstracted model of existing Spiking Neural Network (SNN) architectures. The proposed Optimized Deep Event-driven Spiking neural network Architecture (ODESA) can simultaneously learn hierarchical spatio-temporal features at multiple arbitrary time scales. ODESA performs online learning without the use of error back-propagation or the calculation of gradients. Through the use of simple local adaptive selection thresholds at each node, the network rapidly learns to appropriately allocate its neuronal resources at each layer for any given problem without using an error measure. These adaptive selection thresholds are the central feature of ODESA, ensuring network stability and remarkable robustness to noise as well as to the selection of initial system parameters. Network activations are inherently sparse due to a hard Winner-Take-All (WTA) constraint at each layer. We evaluate the architecture on existing spatio-temporal datasets, including the spike-encoded IRIS, latency-coded MNIST, Oxford Spike pattern and TIDIGITS datasets, as well as a novel set of tasks based on International Morse Code that we created. These tests demonstrate the hierarchical spatio-temporal learning capabilities of ODESA. Through these tests, we demonstrate ODESA can optimally solve practical and highly challenging hierarchical spatio-temporal learning tasks with the minimum possible number of computing nodes.

Acceleration of the SPADE Method Using a Custom-Tailored FP-Growth Implementation.

The SPADE (spatio-temporal Spike PAttern Detection and Evaluation) method was developed to find reoccurring spatio-temporal patterns in neuronal spike activity (parallel spike trains). However, depending on the number of spike trains and the length of recording, this method can exhibit long runtimes. Based on a realistic benchmark data set, we identified that the combination of pattern mining (using the FP-Growth algorithm) and the result filtering account for 85–90% of the method's total runtime. Therefore, in this paper, we propose a customized FP-Growth implementation tailored to the requirements of SPADE, which significantly accelerates pattern mining and result filtering. Our version allows for parallel and distributed execution, and due to the improvements made, an execution on heterogeneous and low-power embedded devices is now also possible. The implementation has been evaluated using a traditional workstation based on an Intel Broadwell Xeon E5-1650 v4 as a baseline. Furthermore, the heterogeneous microserver platform RECS|Box has been used for evaluating the implementation on two HiSilicon Hi1616 (Kunpeng 916), an Intel Coffee Lake-ER Xeon E-2276ME, an Intel Broadwell Xeon D-D1577, and three NVIDIA Tegra devices (Jetson AGX Xavier, Jetson Xavier NX, and Jetson TX2). Depending on the platform, our implementation is between 27 and 200 times faster than the original implementation. At the same time, the energy consumption was reduced by up to two orders of magnitude.

Target spike patterns enable efficient and biologically plausible learning for complex temporal tasks.

Recurrent spiking neural networks (RSNN) in the brain learn to perform a wide range of perceptual, cognitive and motor tasks very efficiently in terms of energy consumption and their training requires very few examples. This motivates the search for biologically inspired learning rules for RSNNs, aiming to improve our understanding of brain computation and the efficiency of artificial intelligence. Several spiking models and learning rules have been proposed, but it remains a challenge to design RSNNs whose learning relies on biologically plausible mechanisms and are capable of solving complex temporal tasks. In this paper, we derive a learning rule, local to the synapse, from a simple mathematical principle, the maximization of the likelihood for the network to solve a specific task. We propose a novel target-based learning scheme in which the learning rule derived from likelihood maximization is used to mimic a specific spatio-temporal spike pattern that encodes the solution to complex temporal tasks. This method makes the learning extremely rapid and precise, outperforming state of the art algorithms for RSNNs. While error-based approaches, (e.g. e-prop) trial after trial optimize the internal sequence of spikes in order to progressively minimize the MSE we assume that a signal randomly projected from an external origin (e.g. from other brain areas) directly defines the target sequence. This facilitates the learning procedure since the network is trained from the beginning to reproduce the desired internal sequence. We propose two versions of our learning rule: spike-dependent and voltage-dependent. We find that the latter provides remarkable benefits in terms of learning speed and robustness to noise. We demonstrate the capacity of our model to tackle several problems like learning multidimensional trajectories and solving the classical temporal XOR benchmark. Finally, we show that an online approximation of the gradient ascent, in addition to guaranteeing complete locality in time and space, allows learning after very few presentations of the target output. Our model can be applied to different types of biological neurons. The analytically derived plasticity learning rule is specific to each neuron model and can produce a theoretical prediction for experimental validation.

Numerical Cognition Based on Precise Counting with a Single Spiking Neuron.

SummaryInsects are able to solve basic numerical cognition tasks. We show that estimation of numerosity can be realized and learned by a single spiking neuron with an appropriate synaptic plasticity rule. This model can be efficiently trained to detect arbitrary spatiotemporal spike patterns on a noisy and dynamic background with high precision and low variance. When put to test in a task that requires counting of visual concepts in a static image it required considerably less training epochs than a convolutional neural network to achieve equal performance. When mimicking a behavioral task in free-flying bees that requires numerical cognition, the model reaches a similar success rate in making correct decisions. We propose that using action potentials to represent basic numerical concepts with a single spiking neuron is beneficial for organisms with small brains and limited neuronal resources.

First Error-Based Supervised Learning Algorithm for Spiking Neural Networks.

Neural circuits respond to multiple sensory stimuli by firing precisely timed spikes. Inspired by this phenomenon, the spike timing-based spiking neural networks (SNNs) are proposed to process and memorize the spatiotemporal spike patterns. However, the response speed and accuracy of the existing learning algorithms of SNNs are still lacking compared to the human brain. To further improve the performance of learning precisely timed spikes, we propose a new weight updating mechanism which always adjusts the synaptic weights at the first wrong output spike time. The proposed learning algorithm can accurately adjust the synaptic weights that contribute to the membrane potential of desired and non-desired firing time. Experimental results demonstrate that the proposed algorithm shows higher accuracy, better robustness, and less computational resources compared with the remote supervised method (ReSuMe) and the spike pattern association neuron (SPAN), which are classic sequence learning algorithms. In addition, the SNN-based computational model equipped with the proposed learning method achieves better recognition results in speech recognition task compared with other bio-inspired baseline systems.

A 4096-Neuron 1M-Synapse 3.8-pJ/SOP Spiking Neural Network With On-Chip STDP Learning and Sparse Weights in 10-nm FinFET CMOS

A reconfigurable 4096-neuron, 1M-synapse chip in 10-nm FinFET CMOS is developed to accelerate inference and learning for many classes of spiking neural networks (SNNs). The SNN features digital circuits for leaky integrate and fire neuron models, on-chip spike-timing-dependent plasticity (STDP) learning, and high-fan-out multicast spike communication. Structured fine-grained weight sparsity reduces synapse memory by up to 16 $\times $ with less than 2% overhead for storing connections. Approximate computing co-optimizes the dropping flow control and benefits from algorithmic noise to process spatiotemporal spike patterns with up to 9.4 $\times $ lower energy. The SNN achieves a peak throughput of 25.2 GSOP/s at 0.9 V, peak energy efficiency of 3.8 pJ/SOP at 525 mV, and 2.3- $\mu \text{W}$ /neuron operation at 450 mV. On-chip unsupervised STDP trains a spiking restricted Boltzmann machine to de-noise Modified National Institute of Standards and Technology (MNIST) digits and to reconstruct natural scene images with RMSE of 0.036. Near-threshold operation, in conjunction with temporal and spatial sparsity, reduces energy by $17.4\times $ to 1.0- $\mu \text{J}$ /classification in a $236 \times 20$ feed-forward network that is trained to classify MNIST digits using supervised STDP. A binary-activation multilayer perceptron with 50% sparse weights is trained offline with error backpropagation to classify MNIST digits with 97.9% accuracy at 1.7- $\mu \text{J}$ /classification.

Real-Time Readout of Large-Scale Unsorted Neural Ensemble Place Codes

Uncovering spatial representations from large-scale ensemble spike activity in specific brain circuits provides valuable feedback in closed-loop experiments. We develop a graphics processing unit (GPU)-powered population-decoding system for ultrafast reconstruction of spatial positions from rodents' unsorted spatiotemporal spiking patterns, during run behavior or sleep. In comparison with an optimized quad-core central processing unit (CPU) implementation, our approach achieves an ∼20- to 50-fold increase in speed in eight tested rat hippocampal, cortical, and thalamic ensemble recordings, with real-time decoding speed (approximately fraction of a millisecond per spike) and scalability up to thousands of channels. Byaccommodating parallel shuffling in real time (computation time <15ms), our approach enables assessment of the statistical significance of online-decoded "memory replay" candidates during quiet wakefulness or sleep. This open-source software toolkit supports the decoding of spatial correlates or content-triggered experimental manipulation in closed-loop neuroscience experiments.

Optimal Localist and Distributed Coding of Spatiotemporal Spike Patterns Through STDP and Coincidence Detection.

Repeating spatiotemporal spike patterns exist and carry information. Here we investigated how a single spiking neuron can optimally respond to one given pattern (localist coding), or to either one of several patterns (distributed coding, i.e., the neuron's response is ambiguous but the identity of the pattern could be inferred from the response of multiple neurons), but not to random inputs. To do so, we extended a theory developed in a previous paper (Masquelier, 2017), which was limited to localist coding. More specifically, we computed analytically the signal-to-noise ratio (SNR) of a multi-pattern-detector neuron, using a threshold-free leaky integrate-and-fire (LIF) neuron model with non-plastic unitary synapses and homogeneous Poisson inputs. Surprisingly, when increasing the number of patterns, the SNR decreases slowly, and remains acceptable for several tens of independent patterns. In addition, we investigated whether spike-timing-dependent plasticity (STDP) could enable a neuron to reach the theoretical optimal SNR. To this aim, we simulated a LIF equipped with STDP, and repeatedly exposed it to multiple input spike patterns, embedded in equally dense Poisson spike trains. The LIF progressively became selective to every repeating pattern with no supervision, and stopped discharging during the Poisson spike trains. Furthermore, tuning certain STDP parameters, the resulting pattern detectors were optimal. Tens of independent patterns could be learned by a single neuron using a low adaptive threshold, in contrast with previous studies, in which higher thresholds led to localist coding only. Taken together these results suggest that coincidence detection and STDP are powerful mechanisms, fully compatible with distributed coding. Yet we acknowledge that our theory is limited to single neurons, and thus also applies to feed-forward networks, but not to recurrent ones.

SuperSpike: Supervised Learning in Multilayer Spiking Neural Networks.

A vast majority of computation in the brain is performed by spiking neural networks. Despite the ubiquity of such spiking, we currently lack an understanding of how biological spiking neural circuits learn and compute in vivo, as well as how we can instantiate such capabilities in artificial spiking circuits in silico. Here we revisit the problem of supervised learning in temporally coding multilayer spiking neural networks. First, by using a surrogate gradient approach, we derive SuperSpike, a nonlinear voltage-based three-factor learning rule capable of training multilayer networks of deterministic integrate-and-fire neurons to perform nonlinear computations on spatiotemporal spike patterns. Second, inspired by recent results on feedback alignment, we compare the performance of our learning rule under different credit assignment strategies for propagating output errors to hidden units. Specifically, we test uniform, symmetric, and random feedback, finding that simpler tasks can be solved with any type of feedback, while more complex tasks require symmetric feedback. In summary, our results open the door to obtaining a better scientific understanding of learning and computation in spiking neural networks by advancing our ability to train them to solve nonlinear problems involving transformations between different spatiotemporal spike time patterns.