Reinforcement learning in populations of spiking neurons

Population coding is widely regarded as a key mechanism for achieving reliable behavioral responses in the face of neuronal variability. But in standard reinforcement learning a flip-side becomes apparent. Learning slows down with increasing population size since the global reinforcement becomes less and less related to the performance of any single neuron. We show that, in contrast, learning speeds up with increasing population size if feedback about the populationresponse modulates synaptic plasticity in addition to global reinforcement. The two feedback signals (reinforcement and population-response signal) can be encoded by ambient neurotransmitter concentrations which vary slowly, yielding a fully online plasticity rule where the learning of a stimulus is interleaved with the processing of the subsequent one. The assumption of a single additional feedback mechanism therefore reconciles biological plausibility with efficient learning

Eligibility Traces and Plasticity on Behavioral Time Scales: Experimental Support of neoHebbian Three-Factor Learning Rules

Most elementary behaviors such as moving the arm to grasp an object or walking into the next room to explore a museum evolve on the time scale of seconds; in contrast, neuronal action potentials occur on the time scale of a few milliseconds. Learning rules of the brain must therefore bridge the gap between these two different time scales. Modern theories of synaptic plasticity have postulated that the co-activation of pre- and postsynaptic neurons sets a flag at the synapse, called an eligibility trace, that leads to a weight change only if an additional factor is present while the flag is set. This third factor, signaling reward, punishment, surprise, or novelty, could be implemented by the phasic activity of neuromodulators or specific neuronal inputs signaling special events. While the theoretical framework has been developed over the last decades, experimental evidence in support of eligibility traces on the time scale of seconds has been collected only during the last few years. Here we review, in the context of three-factor rules of synaptic plasticity, four key experiments that support the role of synaptic eligibility traces in combination with a third factor as a biological implementation of neoHebbian three-factor learning rules

Connectivity reflects coding: A model of voltage-based spike-timing-dependent-plasticity with homeostasis

Electrophysiological connectivity patterns in cortex often show a few strong connections in a sea of weak connections. In some brain areas a large fraction of strong connections are bidirectional, in others they are mainly unidirectional. In order to explain these connectivity patterns, we use a model of Spike-Timing-Dependent Plasticity where synaptic changes depend on presynaptic spike arrival and the postsynaptic membrane potential. The model describes several nonlinear effects in STDP experiments, as well as the voltage dependence of plasticity under voltage clamp and classical paradigms of LTP/LTD induction. We show that in a simulated recurrent network of spiking neurons our plasticity rule leads not only to receptive field development, but also to connectivity patterns that reflect the neural code: for temporal coding paradigms strong connections are predominantly unidirectional, whereas they are bidirectional under rate coding. Thus variable connectivity patterns in the brain could reflect different coding principles across brain areas

Slowness: An Objective for Spike-Timing-Dependent Plasticity?

Slow Feature Analysis (SFA) is an efficient algorithm for learning input-output functions that extract the most slowly varying features from a quickly varying signal. It has been successfully applied to the unsupervised learning of translation-, rotation-, and other invariances in a model of the visual system, to the learning of complex cell receptive fields, and, combined with a sparseness objective, to the self-organized formation of place cells in a model of the hippocampus. In order to arrive at a biologically more plausible implementation of this learning rule, we consider analytically how SFA could be realized in simple linear continuous and spiking model neurons. It turns out that for the continuous model neuron SFA can be implemented by means of a modified version of standard Hebbian learning. In this framework we provide a connection to the trace learning rule for invariance learning. We then show that for Poisson neurons spike-timing-dependent plasticity (STDP) with a specific learning window can learn the same weight distribution as SFA. Surprisingly, we find that the appropriate learning rule reproduces the typical STDP learning window. The shape as well as the timescale are in good agreement with what has been measured experimentally. This offers a completely novel interpretation for the functional role of spike-timing-dependent plasticity in physiological neurons

Synaptic plasticity in medial vestibular nucleus neurons: comparison with computational requirements of VOR adaptation

Background: Vestibulo-ocular reflex (VOR) gain adaptation, a longstanding experimental model of cerebellar learning, utilizes sites of plasticity in both cerebellar cortex and brainstem. However, the mechanisms by which the activity of cortical Purkinje cells may guide synaptic plasticity in brainstem vestibular neurons are unclear. Theoretical analyses indicate that vestibular plasticity should depend upon the correlation between Purkinje cell and vestibular afferent inputs, so that, in gain-down learning for example, increased cortical activity should induce long-term depression (LTD) at vestibular synapses. Methodology/Principal Findings: Here we expressed this correlational learning rule in its simplest form, as an anti-Hebbian, heterosynaptic spike-timing dependent plasticity interaction between excitatory (vestibular) and inhibitory (floccular) inputs converging on medial vestibular nucleus (MVN) neurons (input-spike-timing dependent plasticity, iSTDP). To test this rule, we stimulated vestibular afferents to evoke EPSCs in rat MVN neurons in vitro. Control EPSC recordings were followed by an induction protocol where membrane hyperpolarizing pulses, mimicking IPSPs evoked by flocculus inputs, were paired with single vestibular nerve stimuli. A robust LTD developed at vestibular synapses when the afferent EPSPs coincided with membrane hyperpolarisation, while EPSPs occurring before or after the simulated IPSPs induced no lasting change. Furthermore, the iSTDP rule also successfully predicted the effects of a complex protocol using EPSP trains designed to mimic classical conditioning. Conclusions: These results, in strong support of theoretical predictions, suggest that the cerebellum alters the strength of vestibular synapses on MVN neurons through hetero-synaptic, anti-Hebbian iSTDP. Since the iSTDP rule does not depend on post-synaptic firing, it suggests a possible mechanism for VOR adaptation without compromising gaze-holding and VOR performance in vivo

Emergence of Functional Specificity in Balanced Networks with Synaptic Plasticity

In rodent visual cortex, synaptic connections between orientation-selective neurons are unspecific at the time of eye opening, and become to some degree functionally specific only later during development. An explanation for this two-stage process was proposed in terms of Hebbian plasticity based on visual experience that would eventually enhance connections between neurons with similar response features. For this to work, however, two conditions must be satisfied: First, orientation selective neuronal responses must exist before specific recurrent synaptic connections can be established. Second, Hebbian learning must be compatible with the recurrent network dynamics contributing to orientation selectivity, and the resulting specific connectivity must remain stable for unspecific background activity. Previous studies have mainly focused on very simple models, where the receptive fields of neurons were essentially determined by feedforward mechanisms, and where the recurrent network was small, lacking the complex recurrent dynamics of large-scale networks of excitatory and inhibitory neurons. Here we studied the emergence of functionally specific connectivity in large-scale recurrent networks with synaptic plasticity. Our results show that balanced random networks, which already exhibit highly selective responses at eye opening, can develop feature-specific connectivity if appropriate rules of synaptic plasticity are invoked within and between excitatory and inhibitory populations. If these conditions are met, the initial orientation selectivity guides the process of Hebbian learning and, as a result, functionally specific and a surplus of bidirectional connections emerge. Our results thus demonstrate the cooperation of synaptic plasticity and recurrent dynamics in large-scale functional networks with realistic receptive fields, highlight the role of inhibition as a critical element in this process, and paves the road for further computational studies of sensory processing in neocortical network models equipped with synaptic plasticity

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