Numerical values of the parameters used in the simulation.

D, E and I denote the stimulus, excitatory and inhibitory populations respectively.</p

Learning and autoencoding framework for recurrent spiking networks.

(a) We implement autoencoding in a recurrent network between the activity of the neurons across time, t. This can be visualised schematically where the activity of the network is unfolded in time, and the activity of the network at these timepoints become layers. Autoencoding between successive layers/timepoints is indicated by dotted red lines, with the same connections between each pair of layers/timepoints. Autoencoding also occurs in the traditional sense between the separate populations. (b) A schematic period of postsynaptic spiking activity A(t) enclosed in the red rectangle from time t to t + τA is used to compute the expected instantaneous firing rate of presynaptic neuron j (green) at time t. In this example, presynaptic neuron j spikes at t (but this does not always occur) so the Hebbian plasticity rule, ΔwH, is applied once to each synapse from presynaptic neuron j to the postsynaptic neurons that subsequently spike between t and t + τA, for each postsynaptic neuron’s first spike only (red dots). In applying the non-Hebbian plasticity rule, ΔwnH, in response to a spike in postsynaptic neuron i (blue) at ti, the integration in Eq (6) is over the time period from the most recent previous spike tk to the current spike at ti.</p

Comparison to STDP.

(a) A schematic STDP protocol where presynaptic and postsynaptic spikes are repeated with period T and delay Δt. (b) Weight change dependence on the delay between pre and post spikes, for the Hebbian ΔwH (green), non-Hebbian ΔwnH (red), and combined plasticity rules, ΔwH + ΔwnH (blue), assuming constant membrane potential for simplicity. The plotted curves in (b) and (c) are for an experimental protocol of T = 5τ = 100 ms [7]. (c) The Hebbian + non-Hebbian curve in (b), but with delays 50 to 100 ms shifted to -50 to 0 ms for interpreting as post before pre ordering, thus resembling the common presentation of classical STDP.</p

Parameter values used in the comparisons to experimental data.

Parameter values used in the comparisons to experimental data.</p

Learned connectivity with DVS stimulus.

(a) Long tailed, approximately log-normal, distributions of synaptic strengths. Black curves are excitatory synapses from the stimulus population. Red curves are excitatory synapses from the excitatory population. Blue curves are inhibitory synapses from the inhibitory population. Solid lines indicates synapses with excitatory postsynaptic neurons, dotted lines indicate synapses with inhibitory postsynaptic neurons. (b) Receptive fields (connection strengths from the stimulus to individual neurons) of six excitatory neurons displaying learned selectivity for different features. Red indicates strong synapses, blue indicates weak synapses. Synaptic strengths have been normalized for each neuron.</p

Decoding of the stimulus from each of the neural populations after learning, at one point in time.

The stimulus is a recording of a man juggling, viewed front on. An outline of the juggler’s body and the juggling balls are visible in the stimulus itself and in each of the decodings. This shows that the neural populations have learned to encode the stimulus in their activity. This figure is available as a video in S1 Video. (a) DVS stimulus spikes (rD) smeared exponentially in time with membrane potential time constant τ, corresponding to the best possible decoding from the neural populations. (b) Decoding of the stimulus instantaneous firing rate from the activity in the excitatory population, . (c) Decoding of the stimulus instantaneous firing rate from the activity in the inhibitory population, .</p

Balance of excitation and inhibition.

(a) After learning in the simulation using the DVS stimulus, the excitatory (red) and inhibitory (blue) currents into an example neuron are tightly balanced, with inhibition lagging slightly behind excitation. (b) Cross-correlation between the excitatory and inhibitory currents in (a). The inset corresponds to the central peak with the same axes units. The currents are strongly correlated with a small time lag of 1.5 ms.</p

Comparison of experimental weight changes with model predictions for neurons stimulated using triplet protocols with a range of delays between spikes, (Δ<i>t</i>₁, Δ<i>t</i>₂).

Blue error bars are experimental data from [44], red crosses are model predictions. For details of the model predictions see Sec. STDP and triplet comparison, S1 Appendix and Table 1. (a) Postsynaptic, presynaptic, postsynaptic spike ordering. (b) Presynaptic, postsynaptic, presynaptic spike ordering.</p

Variability of firing rates.

The plasticity rules do not fix the firing rate of neurons, instead firing rates vary in response to the DVS stimulus and recurrent activity. (a) Raster plot of the spiking activity of a sample of excitatory neurons. (b) The firing rate of an excitatory neuron over one pass through the DVS stimulus dataset. The firing rate is obtained by convolving the spike train with a 200 ms standard deviation Gaussian kernel.</p

Simulation model summary.

Simulation model summary.</p