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

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

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

Dominant principal component analysis and vector singular value decomposition modes in 10Hz marmoset LFP oscillations during dot-field stimuli.

A, Top spatial PCA modes of filtered LFPs, with percentage variance explained. B, Top spatial SVD modes of phase velocity fields, showing coherent spatiotemporal activity patterns. C, Temporal evolution of PCA modes, averaged across all trials. Stimulus onset at 0 s. Non-causal effects are due to time smoothing of signal filtering. D, Same as C, but for SVD modes.</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

Numerical values of the parameters used in the simulation.

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

Complex wave patterns in marmoset area MT and mouse cortex.

A, B, C, Complex wave patterns in phase maps of 4 Hz LFP oscillations during ongoing activity recorded from marmoset area MT. Velocity vector fields (black arrows) were calculated between consecutive phase maps separated by 1 ms; we use larger time gaps between snapshots here to show wave propagation more clearly. Critical points are indicated by symbols corresponding to the classes in Fig 1. D, E, Complex wave patterns in phase maps of 4 Hz optical voltage imaging oscillations in awake mouse cortex. Velocity vector fields are calculated from phase maps separated by 20 ms. F, Localized propagating activity in amplitude maps of 10 Hz optical voltage imaging oscillations in awake mouse cortex.</p

Spiking statistics of the stimulus and neural populations.

(a) The demonstration network consists of populations of excitatory (red dots), inhibitory (blue dots) and stimulus neurons (black dots). Each neuron connects to neighbours within a fixed range indicated by black circles. Example input connections to single neurons are shown from excitatory (red lines), inhibitory (blue lines) and stimulus (black lines) populations. All synapses are plastic. (b), (c), (d) Spike statistics recorded during a single pass through the dataset for the stimulus (black), excitatory (blue) and inhibitory populations (red), at the beginning of the simulation (dashed lines) and after a 3100 seconds of learning (solid lines). At the beginning of the simulation the network is initialised with very strong synapses from the stimulus which leads to very high firing rates and low variability. After learning variability increases and firing rates decrease. All distributions are across neurons in each population. (b) Distributions of population coefficients of variation of interspike intervals. (c) Distributions of population firing rates. (d) Population Fano-factors after 3100 seconds of learning.</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

Parameter values used in the comparisons to experimental data.

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