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

Fast and robust learning by reinforcement signals: explorations in the insect brain

We propose a model for pattern recognition in the insect brain. Departing from a well-known body of knowledge about the insect brain, we investigate which of the potentially present features may be useful to learn input patterns rapidly and in a stable manner. The plasticity underlying pattern recognition is situated in the insect mushroom bodies and requires an error signal to associate the stimulus with a proper response. As a proof of concept, we used our model insect brain to classify the well-known MNIST database of handwritten digits, a popular benchmark for classifiers. We show that the structural organization of the insect brain appears to be suitable for both fast learning of new stimuli and reasonable performance in stationary conditions. Furthermore, it is extremely robust to damage to the brain structures involved in sensory processing. Finally, we suggest that spatiotemporal dynamics can improve the level of confidence in a classification decision. The proposed approach allows testing the effect of hypothesized mechanisms rather than speculating on their benefit for system performance or confidence in its responses

Temporal album

Transient synchronization has been used as a mechanism of recognizing auditory patterns using integrate-and-fire neural networks. We first extend the mechanism to vision tasks and investigate the role of spike dependent learning. We show that such a temporal Hebbian learning rule significantly improves accuracy of detection. We demonstrate how multiple patterns can be identified by a single pattern selective neuron and how a temporal album can be constructed. This principle may lead to multidimensional memories, where the capacity per neuron is considerably increased with accurate detection of spike synchronization

Synaptic state matching: a dynamical architecture for predictive internal representation and feature perception

Here we consider the possibility that a fundamental function of sensory cortex is the generation of an internal simulation of sensory environment in real-time. A logical elaboration of this idea leads to a dynamical neural architecture that oscillates between two fundamental network states, one driven by external input, and the other by recurrent synaptic drive in the absence of sensory input. Synaptic strength is modified by a proposed synaptic state matching (SSM) process that ensures equivalence of spike statistics between the two network states. Remarkably, SSM, operating locally at individual synapses, generates accurate and stable network-level predictive internal representations, enabling pattern completion and unsupervised feature detection from noisy sensory input. SSM is a biologically plausible substrate for learning and memory because it brings together sequence learning, feature detection, synaptic homeostasis, and network oscillations under a single parsimonious computational framework. Beyond its utility as a potential model of cortical computation, artificial networks based on this principle have remarkable capacity for internalizing dynamical systems, making them useful in a variety of application domains including time-series prediction and machine intelligence

Dynamical principles in neuroscience

Dynamical modeling of neural systems and brain functions has a history of success over the last half century. This includes, for example, the explanation and prediction of some features of neural rhythmic behaviors. Many interesting dynamical models of learning and memory based on physiological experiments have been suggested over the last two decades. Dynamical models even of consciousness now exist. Usually these models and results are based on traditional approaches and paradigms of nonlinear dynamics including dynamical chaos. Neural systems are, however, an unusual subject for nonlinear dynamics for several reasons: (i) Even the simplest neural network, with only a few neurons and synaptic connections, has an enormous number of variables and control parameters. These make neural systems adaptive and flexible, and are critical to their biological function. (ii) In contrast to traditional physical systems described by well-known basic principles, first principles governing the dynamics of neural systems are unknown. (iii) Many different neural systems exhibit similar dynamics despite having different architectures and different levels of complexity. (iv) The network architecture and connection strengths are usually not known in detail and therefore the dynamical analysis must, in some sense, be probabilistic. (v) Since nervous systems are able to organize behavior based on sensory inputs, the dynamical modeling of these systems has to explain the transformation of temporal information into combinatorial or combinatorial-temporal codes, and vice versa, for memory and recognition. In this review these problems are discussed in the context of addressing the stimulating questions: What can neuroscience learn from nonlinear dynamics, and what can nonlinear dynamics learn from neuroscience?This work was supported by NSF Grant No. NSF/EIA-0130708, and Grant No. PHY 0414174; NIH Grant No. 1 R01 NS50945 and Grant No. NS40110; MEC BFI2003-07276, and Fundación BBVA