Stochastic Synapses Enable Efficient Brain-Inspired Learning Machines

Recent studies have shown that synaptic unreliability is a robust and sufficient mechanism for inducing the stochasticity observed in cortex. Here, we introduce Synaptic Sampling Machines, a class of neural network models that uses synaptic stochasticity as a means to Monte Carlo sampling and unsupervised learning. Similar to the original formulation of Boltzmann machines, these models can be viewed as a stochastic counterpart of Hopfield networks, but where stochasticity is induced by a random mask over the connections. Synaptic stochasticity plays the dual role of an efficient mechanism for sampling, and a regularizer during learning akin to DropConnect. A local synaptic plasticity rule implementing an event-driven form of contrastive divergence enables the learning of generative models in an on-line fashion. Synaptic sampling machines perform equally well using discrete-timed artificial units (as in Hopfield networks) or continuous-timed leaky integrate & fire neurons. The learned representations are remarkably sparse and robust to reductions in bit precision and synapse pruning: removal of more than 75% of the weakest connections followed by cursory re-learning causes a negligible performance loss on benchmark classification tasks. The spiking neuron-based synaptic sampling machines outperform existing spike-based unsupervised learners, while potentially offering substantial advantages in terms of power and complexity, and are thus promising models for on-line learning in brain-inspired hardware

Inherent Weight Normalization in Stochastic Neural Networks

Multiplicative stochasticity such as Dropout improves the robustness and generalizability of deep neural networks. Here, we further demonstrate that always-on multiplicative stochasticity combined with simple threshold neurons are sufficient operations for deep neural networks. We call such models Neural Sampling Machines (NSM). We find that the probability of activation of the NSM exhibits a self-normalizing property that mirrors Weight Normalization, a previously studied mechanism that fulfills many of the features of Batch Normalization in an online fashion. The normalization of activities during training speeds up convergence by preventing internal covariate shift caused by changes in the input distribution. The always-on stochasticity of the NSM confers the following advantages: the network is identical in the inference and learning phases, making the NSM suitable for online learning, it can exploit stochasticity inherent to a physical substrate such as analog non-volatile memories for in-memory computing, and it is suitable for Monte Carlo sampling, while requiring almost exclusively addition and comparison operations. We demonstrate NSMs on standard classification benchmarks (MNIST and CIFAR) and event-based classification benchmarks (N-MNIST and DVS Gestures). Our results show that NSMs perform comparably or better than conventional artificial neural networks with the same architecture

Efficient Computation in Adaptive Artificial Spiking Neural Networks

Artificial Neural Networks (ANNs) are bio-inspired models of neural computation that have proven highly effective. Still, ANNs lack a natural notion of time, and neural units in ANNs exchange analog values in a frame-based manner, a computationally and energetically inefficient form of communication. This contrasts sharply with biological neurons that communicate sparingly and efficiently using binary spikes. While artificial Spiking Neural Networks (SNNs) can be constructed by replacing the units of an ANN with spiking neurons, the current performance is far from that of deep ANNs on hard benchmarks and these SNNs use much higher firing rates compared to their biological counterparts, limiting their efficiency. Here we show how spiking neurons that employ an efficient form of neural coding can be used to construct SNNs that match high-performance ANNs and exceed state-of-the-art in SNNs on important benchmarks, while requiring much lower average firing rates. For this, we use spike-time coding based on the firing rate limiting adaptation phenomenon observed in biological spiking neurons. This phenomenon can be captured in adapting spiking neuron models, for which we derive the effective transfer function. Neural units in ANNs trained with this transfer function can be substituted directly with adaptive spiking neurons, and the resulting Adaptive SNNs (AdSNNs) can carry out inference in deep neural networks using up to an order of magnitude fewer spikes compared to previous SNNs. Adaptive spike-time coding additionally allows for the dynamic control of neural coding precision: we show how a simple model of arousal in AdSNNs further halves the average required firing rate and this notion naturally extends to other forms of attention. AdSNNs thus hold promise as a novel and efficient model for neural computation that naturally fits to temporally continuous and asynchronous applications

Fast and Efficient Asynchronous Neural Computation with Adapting Spiking Neural Networks

Biological neurons communicate with a sparing exchange of pulses - spikes. It is an open question how real spiking neurons produce the kind of powerful neural computation that is possible with deep artificial neural networks, using only so very few spikes to communicate. Building on recent insights in neuroscience, we present an Adapting Spiking Neural Network (ASNN) based on adaptive spiking neurons. These spiking neurons efficiently encode information in spike-trains using a form of Asynchronous Pulsed Sigma-Delta coding while homeostatically optimizing their firing rate. In the proposed paradigm of spiking neuron computation, neural adaptation is tightly coupled to synaptic plasticity, to ensure that downstream neurons can correctly decode upstream spiking neurons. We show that this type of network is inherently able to carry out asynchronous and event-driven neural computation, while performing identical to corresponding artificial neural networks (ANNs). In particular, we show that these adaptive spiking neurons can be drop in replacements for ReLU neurons in standard feedforward ANNs comprised of such units. We demonstrate that this can also be successfully applied to a ReLU based deep convolutional neural network for classifying the MNIST dataset. The ASNN thus outperforms current Spiking Neural Networks (SNNs) implementations, while responding (up to) an order of magnitude faster and using an order of magnitude fewer spikes. Additionally, in a streaming setting where frames are continuously classified, we show that the ASNN requires substantially fewer network updates as compared to the corresponding ANN

Fast and Efficient Asynchronous Neural Computation with Adapting Spiking Neural Networks

Biological neurons communicate with a sparing exchange of pulses - spikes. It is an open question how real spiking neurons produce the kind of powerful neural computation that is possible with deep artificial neural networks, using only so very few spikes to communicate. Building on recent insights in neuroscience, we present an Adapting Spiking Neural Network (ASNN) based on adaptive spiking neurons. These spiking neurons efficiently encode information in spike-trains using a form of Asynchronous Pulsed Sigma-Delta coding while homeostatically optimizing their firing rate. In the proposed paradigm of spiking neuron computation, neural adaptation is tightly coupled to synaptic plasticity, to ensure that downstream neurons can correctly decode upstream spiking neurons. We show that this type of network is inherently able to carry out asynchronous and event-driven neural computation, while performing identical to corresponding artificial neural networks (ANNs). In particular, we show that these adaptive spiking neurons can be drop in replacements for ReLU neurons in standard feedforward ANNs comprised of such units. We demonstrate that this can also be successfully applied to a ReLU based deep convolutional neural network for classifying the MNIST dataset. The ASNN thus outperforms current Spiking Neural Networks (SNNs) implementations, while responding (up to) an order of magnitude faster and using an order of magnitude fewer spikes. Additionally, in a streaming setting where frames are continuously classified, we show that the ASNN requires substantially fewer network updates as compared to the corresponding ANN

Gibbs Sampling with Low-Power Spiking Digital Neurons

Restricted Boltzmann Machines and Deep Belief Networks have been successfully used in a wide variety of applications including image classification and speech recognition. Inference and learning in these algorithms uses a Markov Chain Monte Carlo procedure called Gibbs sampling. A sigmoidal function forms the kernel of this sampler which can be realized from the firing statistics of noisy integrate-and-fire neurons on a neuromorphic VLSI substrate. This paper demonstrates such an implementation on an array of digital spiking neurons with stochastic leak and threshold properties for inference tasks and presents some key performance metrics for such a hardware-based sampler in both the generative and discriminative contexts.Comment: Accepted at ISCAS 201

Constructive spiking neural networks for simulations of neuroplasticity

Artificial neural networks are important tools in machine learning and neuroscience; however, a difficult step in their implementation is the selection of the neural network size and structure. This thesis develops fundamental theory on algorithms for constructing neurons in spiking neural networks and simulations of neuroplasticity. This theory is applied in the development of a constructive algorithm based on spike-timing- dependent plasticity (STDP) that achieves continual one-shot learning of hidden spike patterns through neuron construction. The theoretical developments in this thesis begin with the proposal of a set of definitions of the fundamental components of constructive neural networks. Disagreement in terminology across the literature and a lack of clear definitions and requirements for constructive neural networks is a factor in the poor visibility and fragmentation of research. The proposed definitions are used as the basis for a generalised methodology for decomposing constructive neural networks into components to perform comparisons, design and analysis. Spiking neuron models are uncommon in constructive neural network literature; however, spiking neurons are common in simulated studies in neuroscience. Spike- timing-dependent construction is proposed as a distinct class of constructive algorithm for spiking neural networks. Past algorithms that perform spike-timing-dependent construction are decomposed into defined components for a detailed critical comparison and found to have limited applicability in simulations of biological neural networks. This thesis develops concepts and principles for designing constructive algorithms that are compatible with simulations of biological neural networks. Simulations often have orders of magnitude fewer neurons than related biological neural systems; there- fore, the neurons in a simulation may be assumed to be a selection or subset of a larger neural system with many neurons not simulated. Neuron construction and pruning may therefore be reinterpreted as the transfer of neurons between sets of simulated neurons and hypothetical neurons in the neural system. Constructive algorithms with a functional equivalence to transferring neurons between sets allow simulated neural networks to maintain biological plausibility while changing size. The components of a novel constructive algorithm are incrementally developed from the principles for biological plausibility. First, processes for calculating new synapse weights from observed simulation activity and estimates of past STDP are developed and analysed. Second, a method for predicting postsynaptic spike times for synapse weight calculations through the simulation of a proxy for hypothetical neurons is developed. Finally, spike-dependent conditions for neuron construction and pruning are developed and the processes are combined in a constructive algorithm for simulations of STDP. Repeating hidden spike patterns can be detected by neurons tuned through STDP; this result is reproduced in STDP simulations with neuron construction. Tuned neurons become unresponsive to other activity, preventing detuning but also preventing neurons from learning new spike patterns. Continual learning is demonstrated through neuron construction with immediate detection of new spike patterns from one-shot predictions of STDP convergence. Future research may investigate applications of the developed constructive algorithm in neuroscience and machine learning. The developed theory on constructive neural networks and concepts of selective simulation of neurons also provide new directions for future research.Thesis (Ph.D.) -- University of Adelaide, School of Mechanical Engineering, 201

Seeing into Darkness: Scotopic Visual Recognition

Images are formed by counting how many photons traveling from a given set of directions hit an image sensor during a given time interval. When photons are few and far in between, the concept of `image' breaks down and it is best to consider directly the flow of photons. Computer vision in this regime, which we call `scotopic', is radically different from the classical image-based paradigm in that visual computations (classification, control, search) have to take place while the stream of photons is captured and decisions may be taken as soon as enough information is available. The scotopic regime is important for biomedical imaging, security, astronomy and many other fields. Here we develop a framework that allows a machine to classify objects with as few photons as possible, while maintaining the error rate below an acceptable threshold. A dynamic and asymptotically optimal speed-accuracy tradeoff is a key feature of this framework. We propose and study an algorithm to optimize the tradeoff of a convolutional network directly from lowlight images and evaluate on simulated images from standard datasets. Surprisingly, scotopic systems can achieve comparable classification performance as traditional vision systems while using less than 0.1% of the photons in a conventional image. In addition, we demonstrate that our algorithms work even when the illuminance of the environment is unknown and varying. Last, we outline a spiking neural network coupled with photon-counting sensors as a power-efficient hardware realization of scotopic algorithms.Comment: 23 pages, 6 figure

SuperSpike: Supervised learning in multi-layer 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 multi-layer spiking neural networks. First, by using a surrogate gradient approach, we derive SuperSpike, a nonlinear voltage-based three factor learning rule capable of training multi-layer 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