Emre O. Neftci

Melika Payvand, Mohammed E. Fouda, Fadi Kurdahi et al.

Recent breakthroughs in neuromorphic computing show that local forms of gradient descent learning are compatible with Spiking Neural Networks (SNNs) and synaptic plasticity. Although SNNs can be scalably implemented using neuromorphic VLSI, an architecture that can learn using gradient-descent in situ is still missing. In this paper, we propose a local, gradient-based, error-triggered learning algorithm with online ternary weight updates. The proposed algorithm enables online training of multi-layer SNNs with memristive neuromorphic hardware showing a small loss in the performance compared with the state of the art. We also propose a hardware architecture based on memristive crossbar arrays to perform the required vector-matrix multiplications. The necessary peripheral circuitry including pre-synaptic, post-synaptic and write circuits required for online training, have been designed in the sub-threshold regime for power saving with a standard 180 nm CMOS process.

Friedemann Zenke, Emre O. Neftci

Neuromorphic hardware strives to emulate brain-like neural networks and thus holds the promise for scalable, low-power information processing on temporal data streams. Yet, to solve real-world problems, these networks need to be trained. However, training on neuromorphic substrates creates significant challenges due to the offline character and the required non-local computations of gradient-based learning algorithms. This article provides a mathematical framework for the design of practical online learning algorithms for neuromorphic substrates. Specifically, we show a direct connection between Real-Time Recurrent Learning (RTRL), an online algorithm for computing gradients in conventional Recurrent Neural Networks (RNNs), and biologically plausible learning rules for training Spiking Neural Networks (SNNs). Further, we motivate a sparse approximation based on block-diagonal Jacobians, which reduces the algorithm's computational complexity, diminishes the non-local information requirements, and empirically leads to good learning performance, thereby improving its applicability to neuromorphic substrates. In summary, our framework bridges the gap between synaptic plasticity and gradient-based approaches from deep learning and lays the foundations for powerful information processing on future neuromorphic hardware systems.

Emre O. Neftci, Hesham Mostafa, Friedemann Zenke

Spiking neural networks are nature's versatile solution to fault-tolerant and energy efficient signal processing. To translate these benefits into hardware, a growing number of neuromorphic spiking neural network processors attempt to emulate biological neural networks. These developments have created an imminent need for methods and tools to enable such systems to solve real-world signal processing problems. Like conventional neural networks, spiking neural networks can be trained on real, domain specific data. However, their training requires overcoming a number of challenges linked to their binary and dynamical nature. This article elucidates step-by-step the problems typically encountered when training spiking neural networks, and guides the reader through the key concepts of synaptic plasticity and data-driven learning in the spiking setting. To that end, it gives an overview of existing approaches and provides an introduction to surrogate gradient methods, specifically, as a particularly flexible and efficient method to overcome the aforementioned challenges.

Emre O. Neftci, Bruno U. Pedroni, Siddharth Joshi et al.

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.