We develop a biologically-plausible learning rule that provably converges to the class means of general mixture models. This rule generalizes the classical BCM neural rule within a tensor framework, substantially increasing the generality of the learning problem it solves. It achieves this by incorporating triplets of samples from the mixtures, which provides a novel information processing interpretation to spike-timing-dependent plasticity. We provide both proofs of convergence, and a close fit to experimental data on STDP.

As neural interfaces become more advanced, there has been an increase in the volume and complexity of neural data recordings. These interfaces capture rich information about neural dynamics that call for efficient, real-time processing algorithms to spontaneously extract and interpret patterns of neural dynamics. Moreover, being able to do so in a fully unsupervised manner is critical as patterns in vast streams of neural data might not be easily identifiable by the human eye. Formal Deep Neural Networks (DNNs) have come a long way in performing pattern recognition tasks for various static and sequential pattern recognition applications. However, these networks usually require large labeled datasets for training and have high power consumption preventing their future embedding in active brain implants. An alternative aimed at addressing these issues are Spiking Neural Networks (SNNs) which are neuromorphic and use more biologically plausible neurons with evolving membrane potentials. In this context, we introduce here a frugal single-layer SNN designed for fully unsupervised identification and classification of multivariate temporal patterns in continuous data with a sequential approach. We show that, with only a handful number of neurons, this strategy is efficient to recognize highly overlapping multivariate temporal patterns, first on simulated data, and then on Mel Cepstral representations of speech sounds and finally on multichannel neural data. This approach relies on several biologically inspired plasticity rules, including Spike-timing-dependent plasticity (STDP), Short-term plasticity (STP) and intrinsic plasticity (IP). These results pave the way towards highly frugal SNNs for fully unsupervised and online-compatible learning of complex multivariate temporal patterns for future embedding in dedicated very-low power hardware.

Recent extensions of the Perceptron as the Tempotron and the Chronotron suggest that this theoretical concept is highly relevant for understanding networks of spiking neurons in the brain. It is not known, however, how the computational power of the Perceptron might be accomplished by the plasticity mechanisms of real synapses. Here we prove that spike-timing-dependent plasticity having an anti-Hebbian form for excitatory synapses as well as a spike-timing-dependent plasticity of Hebbian shape for inhibitory synapses are sufficient for realizing the original Perceptron Learning Rule if these respective plasticity mechanisms act in concert with the hyperpolarisation of the post-synaptic neurons. We also show that with these simple yet biologically realistic dynamics Tempotrons and Chronotrons are learned. The proposed mechanism enables incremental associative learning from a continuous stream of patterns and might therefore underly the acquisition of long term memories in cortex. Our results underline that learning processes in realistic networks of spiking neurons depend crucially on the interactions of synaptic plasticity mechanisms with the dynamics of participating neurons.

We develop a biologically-plausible learning rule that provably converges to the class means of general mixture models. This rule generalizes the classical BCM neural rule within a tensor framework, substantially increasing the generality of the learning problem it solves. It achieves this by incorporating triplets of samples from the mixtures, which provides a novel information processing interpretation to spike-timing-dependent plasticity. We provide both proofs of convergence, and a close fit to experimental data on STDP.

Experimental studies have observed synaptic potentiation when a presynaptic neuron fires shortly before a postsynaptic neuron, and synaptic depression when the presynaptic neuron fires shortly af- ter. The dependence of synaptic modulation on the precise tim- ing of the two action potentials is known as spike-timing depen- dent plasticity or STDP. We derive STDP from a simple compu- tational principle: synapses adapt so as to minimize the postsy- naptic neuron's variability to a given presynaptic input, causing the neuron's output to become more reliable in the face of noise. Using an entropy-minimization objective function and the biophys- ically realistic spike-response model of Gerstner (2001), we simu- late neurophysiological experiments and obtain the characteristic STDP curve along with other phenomena including the reduction in synaptic plasticity as synaptic efficacy increases. We compare our account to other efforts to derive STDP from computational princi- ples, and argue that our account provides the most comprehensive coverage of the phenomena.

Spiking Neural Networks (SNNs) are gaining interest due to their event-driven processing which potentially consumes low power/energy computations in hardware platforms, while offering unsupervised learning capability due to the spike-timing-dependent plasticity (STDP) rule. However, state-of-the-art SNNs require a large memory footprint to achieve high accuracy, thereby making them difficult to be deployed on embedded systems, for instance on battery-powered mobile devices and IoT Edge nodes. Towards this, we propose FSpiNN, an optimization framework for obtaining memory- and energy-efficient SNNs for training and inference processing, with unsupervised learning capability while maintaining accuracy. It is achieved by (1) reducing the computational requirements of neuronal and STDP operations, (2) improving the accuracy of STDP-based learning, (3) compressing the SNN through a fixed-point quantization, and (4) incorporating the memory and energy requirements in the optimization process. FSpiNN reduces the computational requirements by reducing the number of neuronal operations, the STDP-based synaptic weight updates, and the STDP complexity. To improve the accuracy of learning, FSpiNN employs timestep-based synaptic weight updates, and adaptively determines the STDP potentiation factor and the effective inhibition strength. The experimental results show that, as compared to the state-of-the-art work, FSpiNN achieves 7.5x memory saving, and improves the energy-efficiency by 3.5x on average for training and by 1.8x on average for inference, across MNIST and Fashion MNIST datasets, with no accuracy loss for a network with 4900 excitatory neurons, thereby enabling energy-efficient SNNs for edge devices/embedded systems.

We develop a biologically-plausible learning rule that provably converges to the class means of general mixture models. This rule generalizes the classical BCM neural rule within a tensor framework, substantially increasing the generality of the learning problem it solves. It achieves this by incorporating triplets of samples from the mixtures, which provides a novel information processing interpretation to spike-timing-dependent plasticity. We provide both proofs of convergence, and a close fit to experimental data on STDP.

Recent extensions of the Perceptron, as e.g. the Tempotron, suggest that this theoretical concept is highly relevant also for understanding networks of spiking neurons in the brain. It is not known, however, how the computational power of the Perceptron and of its variants might be accomplished by the plasticity mechanisms of real synapses. Here we prove that spike-timing-dependent plasticity having an anti-Hebbian form for excitatory synapses as well as a spike-timing-dependent plasticity of Hebbian shape for inhibitory synapses are sufficient for realizing the original Perceptron Learning Rule if the respective plasticity mechanisms act in concert with the hyperpolarisation of the post-synaptic neurons. We also show that with these simple yet biologically realistic dynamics Tempotrons are efficiently learned. The proposed mechanism might underly the acquisition of mappings of spatio-temporal activity patterns in one area of the brain onto other spatio-temporal spike patterns in another region and of long term memories in cortex. Our results underline that learning processes in realistic networks of spiking neurons depend crucially on the interactions of synaptic plasticity mechanisms with the dynamics of participating neurons.

When stimulated with complex action potential sequences synapses exhibit spike timing-dependent plasticity (STDP) with attenuated and enhanced pre- and postsynaptic contributions to long-term synaptic modifications. In order to investigate the functional consequences of these contribution dynamics (CD) we propose a minimal model formulated in terms of differential equations. We find that our model reproduces a wide range of experimental results with a small number of biophysically interpretable parameters. The model allows to investigate the susceptibility of STDP to arbitrary time courses of pre- and postsynaptic activities, i.e. its nonlinear filter properties. We demonstrate this for the simple example of small periodic modulations of pre- and postsynaptic firing rates for which our model can be solved. It predicts synaptic strengthening for synchronous rate modulations. For low baseline rates modifications are dominant in the theta frequency range, a result which underlines the well known relevance of theta activities in hippocampus and cortex for learning. We also find emphasis of low baseline spike rates and suppression for high baseline rates. The latter suggests a mechanism of network activity regulation inherent in STDP. Furthermore, our novel formulation provides a general framework for investigating the joint dynamics of neuronal activity and the CD of STDP in both spike-based as well as rate-based neuronal network models.

While classical experiments on spike-timing dependent plasticity analyzed synaptic changes as a function of the timing of pairs of pre-and postsynaptic spikes, more recent experiments also point to the effect of spike triplets. Here we develop a mathematical framework that allows us to characterize timing based learning rules. Moreover, we identify a candidate learning rule with five variables (and 5 free parameters) that captures a variety of experimental data, including the dependence of potentiation and depression upon pre-and postsynaptic firing frequencies. The relation to the Bienenstock-Cooper-Munro rule as well as to some timing-based rules is discussed.