Learning in Spiking Neural Networks with a Calcium-Based Hebbian Learning Rule

The effectiveness of neural interfaces depends on the ability of electronic systems to speak the same language of the biological counterpart. Furthermore, the mechanisms underling learning in biological systems should be better understood to harness the adaptability of the brain when interfacing it to artificial systems. In particular, understanding how biological neural networks are shaped via local plasticity mechanisms can lead to energy-efficient and self-adaptive brain-like information processing systems which can enhance neural interfaces with unprecedented adaptability.<br/>In this work, we present a Hebbian local learning rule, the Bistable Calcium-based Local Learning (BCaLL) rule, that models synaptic modification as a function of pre- and post-synaptic calcium traces tracking neuronal activity, based on a large body of work that has established the role of calcium transients in modulating plasticity. The calcium trace variable, modeled via a first-order differential equation, integrates neuronal activity over time such that both the time since the last spike and mean firing rate information can be encoded in this trace. The learning rule we propose reads out the calcium traces from the neurons it connects and computes whether its weight should be increased or decreased. We show that BCaLL is able to reproduce both spike-time dependent plasticity (STDP) and spike rate plasticity outcomes. With it, we are able to demonstrate that temporal correlations added at the spike-pair level can modulate the learning rate in spiking neural networks, without modifying the rule's parameters or the mean rate activity of neurons in the network.<br/>We showcase this property by simulating and comparing recurrent Spiking Neural Networks (SNNs) with and without excitatory neurons' subthreshold membrane oscillations. We demonstrate that in the networks where the neurons oscillate, the learning rate of attractors is increased due to an increase in their synchronicity. This is particularly interesting for simulating and studying learning in models of brain structures like the Inferior Olivary Nucleus, where previous work has shown that the lack of electronic coupling, which plays an important role in synchronizing the activity of neurons within the nucleus, leads to impaired learning of motor tasks. This modulated learning rate via synchronization we show can provide a starting point in understanding such learning dynamics.<br/>By applying BCaLL to feedforward SNNs, we describe the mechanisms necessary to train such networks for classification problems and how these mechanisms resolve the coding-level problem that arises from learning with binary synapses. Thanks to our simulations, we find that allowing the networks' transient activity during the switching of input patterns to interact increases classification performance, contrary to what previous work has reported, by reducing overlaps in the learned class representations. This could be a benefit of tracking spiking activity via traces: while some models might rely on the neuron's membrane voltage to compute weight updates, utilizing traces allows us to decouple from the membrane dynamics the extent to which correlated activity in time can be measured.<br/>Elucidating how computation in such systems can benefit from encoding information in traces is not only important for better modeling the complex biochemical machinery existing in biological neural networks but also for the design of analog application-specific integrated circuits (ASIC) implementing these algorithms. This integration step is crucial for the embedding of such algorithm into neural interfaces.