STDP in Adaptive Neurons Gives Close-To-Optimal Information Transmission

Spike-frequency adaptation is known to enhance the transmission of information in sensory spiking neurons by rescaling the dynamic range for input processing, matching it to the temporal statistics of the sensory stimulus. Achieving maximal information transmission has also been recently postulated as a role for spike-timing-dependent plasticity (STDP). However, the link between optimal plasticity and STDP in cortex remains loose, as does the relationship between STDP and adaptation processes. We investigate how STDP, as described by recent minimal models derived from experimental data, influences the quality of information transmission in an adapting neuron. We show that a phenomenological model based on triplets of spikes yields almost the same information rate as an optimal model specially designed to this end. In contrast, the standard pair-based model of STDP does not improve information transmission as much. This result holds not only for additive STDP with hard weight bounds, known to produce bimodal distributions of synaptic weights, but also for weight-dependent STDP in the context of unimodal but skewed weight distributions. We analyze the similarities between the triplet model and the optimal learning rule, and find that the triplet effect is an important feature of the optimal model when the neuron is adaptive. If STDP is optimized for information transmission, it must take into account the dynamical properties of the postsynaptic cell, which might explain the target-cell specificity of STDP. In particular, it accounts for the differences found in vitro between STDP at excitatory synapses onto principal cells and those onto fast-spiking interneurons

Optimality Model of Unsupervised Spike-Timing Dependent Plasticity: Synaptic Memory and Weight Distribution

We studied the hypothesis that synaptic dynamics is controlled by three basic principles: (1) synapses adapt their weights so that neurons can effectively transmit information, (2) homeostatic processes stabilize the mean firing rate of the postsynaptic neuron, and (3) weak synapses adapt more slowly than strong ones, while maintenance of strong synapses is costly. Our results show that a synaptic update rule derived from these principles shares features, with spike-timing-dependent plasticity, is sensitive to correlations in the input and is useful for synaptic memory. Moreover, input selectivity (sharply tuned receptive fields) of postsynaptic neurons develops only if stimuli with strong features are presented. Sharply tuned neurons can coexist with unselective ones, and the distribution of synaptic weights can be unimodal or bimodal. The formulation of synaptic dynamics through an optimality criterion provides a simple graphical argument for the stability of synapses, necessary for synaptic memory

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

How Gibbs distributions may naturally arise from synaptic adaptation mechanisms. A model-based argumentation

This paper addresses two questions in the context of neuronal networks dynamics, using methods from dynamical systems theory and statistical physics: (i) How to characterize the statistical properties of sequences of action potentials ("spike trains") produced by neuronal networks ? and; (ii) what are the effects of synaptic plasticity on these statistics ? We introduce a framework in which spike trains are associated to a coding of membrane potential trajectories, and actually, constitute a symbolic coding in important explicit examples (the so-called gIF models). On this basis, we use the thermodynamic formalism from ergodic theory to show how Gibbs distributions are natural probability measures to describe the statistics of spike trains, given the empirical averages of prescribed quantities. As a second result, we show that Gibbs distributions naturally arise when considering "slow" synaptic plasticity rules where the characteristic time for synapse adaptation is quite longer than the characteristic time for neurons dynamics.Comment: 39 pages, 3 figure

Statistics of spikes trains, synaptic plasticity and Gibbs distributions.

ISBN : 978-2-9532965-0-1We introduce a mathematical framework where the statistics of spikes trains, produced by neural networks evolving under synaptic plasticity, can be analysed

Learning as filtering: Implications for spike-based plasticity.

Most normative models in computational neuroscience describe the task of learning as the optimisation of a cost function with respect to a set of parameters. However, learning as optimisation fails to account for a time-varying environment during the learning process and the resulting point estimate in parameter space does not account for uncertainty. Here, we frame learning as filtering, i.e., a principled method for including time and parameter uncertainty. We derive the filtering-based learning rule for a spiking neuronal network-the Synaptic Filter-and show its computational and biological relevance. For the computational relevance, we show that filtering improves the weight estimation performance compared to a gradient learning rule with optimal learning rate. The dynamics of the mean of the Synaptic Filter is consistent with spike-timing dependent plasticity (STDP) while the dynamics of the variance makes novel predictions regarding spike-timing dependent changes of EPSP variability. Moreover, the Synaptic Filter explains experimentally observed negative correlations between homo- and heterosynaptic plasticity

Functional Clustering Drives Encoding Improvement in a Developing Brain Network during Awake Visual Learning

Sensory experience drives dramatic structural and functional plasticity in developing neurons. However, for single-neuron plasticity to optimally improve whole-network encoding of sensory information, changes must be coordinated between neurons to ensure a full range of stimuli is efficiently represented. Using two-photon calcium imaging to monitor evoked activity in over 100 neurons simultaneously, we investigate network-level changes in the developing Xenopus laevis tectum during visual training with motion stimuli. Training causes stimulus-specific changes in neuronal responses and interactions, resulting in improved population encoding. This plasticity is spatially structured, increasing tuning curve similarity and interactions among nearby neurons, and decreasing interactions among distant neurons. Training does not improve encoding by single clusters of similarly responding neurons, but improves encoding across clusters, indicating coordinated plasticity across the network. NMDA receptor blockade prevents coordinated plasticity, reduces clustering, and abolishes whole-network encoding improvement. We conclude that NMDA receptors support experience-dependent network self-organization, allowing efficient population coding of a diverse range of stimuli.Canadian Institutes of Health Researc