Hierarchical Network Connectivity and Partitioning for Reconfigurable Large-Scale Neuromorphic Systems.

We present an efficient and scalable partitioning method for mapping large-scale neural network models with locally dense and globally sparse connectivity onto reconfigurable neuromorphic hardware. Scalability in computational efficiency, i.e., amount of time spent in actual computation, remains a huge challenge in very large networks. Most partitioning algorithms also struggle to address the scalability in network workloads in finding a globally optimal partition and efficiently mapping onto hardware. As communication is regarded as the most energy and time-consuming part of such distributed processing, the partitioning framework is optimized for compute-balanced, memory-efficient parallel processing targeting low-latency execution and dense synaptic storage, with minimal routing across various compute cores. We demonstrate highly scalable and efficient partitioning for connectivity-aware and hierarchical address-event routing resource-optimized mapping, significantly reducing the total communication volume recursively when compared to random balanced assignment. We showcase our results working on synthetic networks with varying degrees of sparsity factor and fan-out, small-world networks, feed-forward networks, and a hemibrain connectome reconstruction of the fruit-fly brain. The combination of our method and practical results suggest a promising path toward extending to very large-scale networks and scalable hardware-aware partitioning.

Memory-Efficient Synaptic Connectivity for Spike-Timing- Dependent Plasticity.

Spike-Timing-Dependent Plasticity (STDP) is a bio-inspired local incremental weight update rule commonly used for online learning in spike-based neuromorphic systems. In STDP, the intensity of long-term potentiation and depression in synaptic efficacy (weight) between neurons is expressed as a function of the relative timing between pre- and post-synaptic action potentials (spikes), while the polarity of change is dependent on the order (causality) of the spikes. Online STDP weight updates for causal and acausal relative spike times are activated at the onset of post- and pre-synaptic spike events, respectively, implying access to synaptic connectivity both in forward (pre-to-post) and reverse (post-to-pre) directions. Here we study the impact of different arrangements of synaptic connectivity tables on weight storage and STDP updates for large-scale neuromorphic systems. We analyze the memory efficiency for varying degrees of density in synaptic connectivity, ranging from crossbar arrays for full connectivity to pointer-based lookup for sparse connectivity. The study includes comparison of storage and access costs and efficiencies for each memory arrangement, along with a trade-off analysis of the benefits of each data structure depending on application requirements and budget. Finally, we present an alternative formulation of STDP via a delayed causal update mechanism that permits efficient weight access, requiring no more than forward connectivity lookup. We show functional equivalence of the delayed causal updates to the original STDP formulation, with substantial savings in storage and access costs and efficiencies for networks with sparse synaptic connectivity as typically encountered in large-scale models in computational neuroscience.

Neural and Synaptic Array Transceiver: A Brain-Inspired Computing Framework for Embedded Learning.

Embedded, continual learning for autonomous and adaptive behavior is a key application of neuromorphic hardware. However, neuromorphic implementations of embedded learning at large scales that are both flexible and efficient have been hindered by a lack of a suitable algorithmic framework. As a result, most neuromorphic hardware are trained off-line on large clusters of dedicated processors or GPUs and transferred post hoc to the device. We address this by introducing the neural and synaptic array transceiver (NSAT), a neuromorphic computational framework facilitating flexible and efficient embedded learning by matching algorithmic requirements and neural and synaptic dynamics. NSAT supports event-driven supervised, unsupervised and reinforcement learning algorithms including deep learning. We demonstrate the NSAT in a wide range of tasks, including the simulation of Mihalas-Niebur neuron, dynamic neural fields, event-driven random back-propagation for event-based deep learning, event-based contrastive divergence for unsupervised learning, and voltage-based learning rules for sequence learning. We anticipate that this contribution will establish the foundation for a new generation of devices enabling adaptive mobile systems, wearable devices, and robots with data-driven autonomy.

Hardware-Efficient On-line Learning through Pipelined Truncated-Error Backpropagation in Binary-State Networks.

Artificial neural networks (ANNs) trained using backpropagation are powerful learning architectures that have achieved state-of-the-art performance in various benchmarks. Significant effort has been devoted to developing custom silicon devices to accelerate inference in ANNs. Accelerating the training phase, however, has attracted relatively little attention. In this paper, we describe a hardware-efficient on-line learning technique for feedforward multi-layer ANNs that is based on pipelined backpropagation. Learning is performed in parallel with inference in the forward pass, removing the need for an explicit backward pass and requiring no extra weight lookup. By using binary state variables in the feedforward network and ternary errors in truncated-error backpropagation, the need for any multiplications in the forward and backward passes is removed, and memory requirements for the pipelining are drastically reduced. Further reduction in addition operations owing to the sparsity in the forward neural and backpropagating error signal paths contributes to highly efficient hardware implementation. For proof-of-concept validation, we demonstrate on-line learning of MNIST handwritten digit classification on a Spartan 6 FPGA interfacing with an external 1Gb DDR2 DRAM, that shows small degradation in test error performance compared to an equivalently sized binary ANN trained off-line using standard back-propagation and exact errors. Our results highlight an attractive synergy between pipelined backpropagation and binary-state networks in substantially reducing computation and memory requirements, making pipelined on-line learning practical in deep networks.

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 (S2Ms), 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. S2Ms perform equally well using discrete-timed artificial units (as in Hopfield networks) or continuous-timed leaky integrate and 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 S2Ms 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.

Mapping Generative Models onto a Network of Digital Spiking Neurons.

Stochastic neural networks such as Restricted Boltzmann Machines (RBMs) have been successfully used in applications ranging from speech recognition to image classification, and are particularly interesting because of their potential for generative tasks. Inference and learning in these algorithms use a Markov Chain Monte Carlo procedure called Gibbs sampling, where a logistic function forms the kernel of this sampler. On the other side of the spectrum, neuromorphic systems have shown great promise for low-power and parallelized cognitive computing, but lack well-suited applications and automation procedures. In this work, we propose a systematic method for bridging the RBM algorithm and digital neuromorphic systems, with a generative pattern completion task as proof of concept. For this, we first propose a method of producing the Gibbs sampler using bio-inspired digital noisy integrate-and-fire neurons. Next, we describe the process of mapping generative RBMs trained offline onto the IBM TrueNorth neurosynaptic processor-a low-power digital neuromorphic VLSI substrate. Mapping these algorithms onto neuromorphic hardware presents unique challenges in network connectivity and weight and bias quantization, which, in turn, require architectural and design strategies for the physical realization. Generative performance is analyzed to validate the neuromorphic requirements and to best select the neuron parameters for the model. Lastly, we describe a design automation procedure which achieves optimal resource usage, accounting for the novel hardware adaptations. This work represents the first implementation of generative RBM inference on a neuromorphic VLSI substrate.

[Genetics of mesangial IgA nephropathy]. / Genetica della nefropatia a depositi mesangiali di IgA.

IgA nephropathy is the most common form of primary glomerulonephritis, with a variable prevalence depending on the geographic area of examination. Marked differences in disease prevalence has suggested that genetics could play a role in the pathogenesis of the disease, indicating the existence of susceptibility genes detected with different frequencies in geographically separated populations. Moreover, familial forms of IgAN have been reported worldwide, in sibling pairs, families and extended pedigrees belonging to geographically isolated populations. In this article we describe recent discoveries in genetic studies on IgAN. If candidate-gene association studies require first survey on the pathogenesis of the disease, since the candidate loci are selected on the basis of information gathered from traditional biology, the linkage analysis consist in an alternative approach. Several susceptibility loci have been identified in pedigrees segregating for IgAN, but not the causative mutations of the disease. Further progress in the field of knowledge about the genetics of IgAN has recently been obtained by the application of genome-wide association studies (GWAS) in large cohorts of cases and controls of IgAN. GWAS have identified multiple susceptibility loci coding for genes involved in critical mechanisms for the development of IgAN and, accordingly, have shed new light on the biology of the disease, revealing unknown pathogenic pathways. The close connection between IgAN and many autoimmune diseases has been demonstrated. Moreover, these studies have made the correlation of genetic risk score of developing IgAN with the geo-epidemiological aspect of the disease possible. The goal of the integrated genomic approach will be to discover new potential therapeutic targets.

Event-driven contrastive divergence for spiking neuromorphic systems.

Restricted Boltzmann Machines (RBMs) and Deep Belief Networks have been demonstrated to perform efficiently in a variety of applications, such as dimensionality reduction, feature learning, and classification. Their implementation on neuromorphic hardware platforms emulating large-scale networks of spiking neurons can have significant advantages from the perspectives of scalability, power dissipation and real-time interfacing with the environment. However, the traditional RBM architecture and the commonly used training algorithm known as Contrastive Divergence (CD) are based on discrete updates and exact arithmetics which do not directly map onto a dynamical neural substrate. Here, we present an event-driven variation of CD to train a RBM constructed with Integrate & Fire (I&F) neurons, that is constrained by the limitations of existing and near future neuromorphic hardware platforms. Our strategy is based on neural sampling, which allows us to synthesize a spiking neural network that samples from a target Boltzmann distribution. The recurrent activity of the network replaces the discrete steps of the CD algorithm, while Spike Time Dependent Plasticity (STDP) carries out the weight updates in an online, asynchronous fashion. We demonstrate our approach by training an RBM composed of leaky I&F neurons with STDP synapses to learn a generative model of the MNIST hand-written digit dataset, and by testing it in recognition, generation and cue integration tasks. Our results contribute to a machine learning-driven approach for synthesizing networks of spiking neurons capable of carrying out practical, high-level functionality.