Word distributions in rat A1 are state dependent. A, The multiunit spiking activity on eight tetrodes was converted into a binary matrix whose columns represent the presence of spikes in consecutive, nonoverlapping 2 ms bins. B, Spontaneous and stimulus-evoked word distributions are similar when accumulated over the whole dataset. The plot shows the probability of every 8-bit word, with color representing the number of 1s it contains. C, Cortical states. Top, Spectrogram of LFP on one electrode. Bottom, Running CV of the population rate, computed from 10 s intervals of spontaneous activity (see Materials and Methods). The CV and low-frequency power are substantially higher in synchronized-state epochs (S1 and S2). D, Example rasters of spontaneous activity during desynchronized and synchronized states (the position of these intervals within the recording shown in C is indicated by asterisks). The corresponding population rate (spikes/50 ms bin) is shown to the right of each raster. E, The spontaneous word distribution differs between states. F, Pseudocolor matrix showing KLdiv between spontaneous word distributions in each pair of periods. The distributions are similar within states, but different across states. G, H, Same plot as in F, for evoked-evoked and spontaneous-evoked word distributions.

The raster marginals model. A, PRd of spontaneous and evoked activity in each of the recording intervals shown in C. B, Illustration of the model. Summing the rows of the raster matrix provides the mean firing rate (MFR) for each electrode. Summing columns provides the population rate, whose distribution (PRd) is used by the model. MFR and PRd summarize the raster by 2N parameters, which are used to produce a synthetic raster (see Materials and Methods). C, Illustration of a correlation structure that cannot be captured by the model. Left, Spike coincidences predominantly occur between units 1–2 (blue) and 3–4 (green), whereas all other coincidences are rare (gray). Right, In the output produced by the model, coincident spikes occur between any pair of units.

The raster marginals model accounts for the word distribution observations in rat A1. A, Fit between the MFR and raster marginals models to the word distribution in epoch S2 of C. B, Summary data for the fit of the MFR and raster marginals models to the word distributions in the eight conditions in each animal (six in one of the rats). The bars represent the mean KLdiv. Error bars indicate SD. The gray bars indicate the KLdiv between two halves of the experimental data. C, The fit of the MFR and raster marginals models for the pairwise correlations (across all the conditions and animals). The gray points show how well the pairwise correlation measurement from one half of the experimental data describes the second half.

KLdiv between word distributions in rat A1 is captured by the raster marginals model. A, The model successfully reproduces the KLdiv measurements in F–H. B, D_s[P||Q], the actual KLdiv between word distributions, is plotted versus D_s[P̂||Q̂], the KLdiv predicted by the raster marginals model. The plot shows data from all pairs of word distributions in the three animals superimposed. The fact that the points fall on the diagonal indicates that the actual KLdiv (F–H) and predicted KLdiv (A) are very close. C, D_s[P||Q] versus D_s[P||Q̂]. D, D_s[P||Q] versus D_s[P̃||Q̃], the KLdiv predicted by MFR alone, indicating a poor fit.

KLdiv between word distributions in cat V1 is captured by the raster marginals model. A, Example rasters from three blocks with different kinds of stimuli. B, Comparison of the word distributions during spontaneous activity with gratings and natural movies in cat V1. C, Comparison of word distributions generated by the raster marginals model using parameters derived from the same three conditions. Note the close match to the plots in B. D, Observed KLdiv for each pair of blocks versus KLdiv predicted by the raster marginals model (red) and the MFRs alone (blue), for data from nine cats. As with rat data, the raster marginals model provides an accurate prediction while MFR alone does not.

Statistical properties of the PRd. A, Example of a shifted lognormal fit to PRd of activity in one block from cat V1 dataset. In this particular example the KLdiv between the actual PRd and the fit is 20 bits/s. B, The KLdiv between the shifted lognormal fit and the observed PRd for each one of the blocks. Circles indicate the median KLdiv for each animal. In eight of the nine animals PRd is well described by a shifted lognormal distribution. C, KLdiv of word distributions is bounded from below by KLdiv of PRds. The panel shows the relationship of the KLdiv between word distributions of different blocks and the KLdiv between the corresponding PRds. As in D, we use the 200 available pairs of blocks, with five different (random) selections of 16 of the 96 electrodes, for a total of 1000 points. Note that all points are to the right of the equality line, indicating a strict lower bound.

Changes in population rate dynamics can explain increasing similarity of spontaneous and evoked word distributions with development. A, The key experimental findings of . Top, KLdiv between spontaneous spiking activity [S], and activity during presentation of natural movies [M] in juvenile and adult ferrets. Bottom, KLdiv between the word distributions in actual data [M or S] and the word distributions predicted by MFR alone [M̃ or S̃, respectively]. B, Parameters of the raster marginals model used to reproduce the data in A. Top, MFRs on 16 electrodes. The MFRs of the 16 “S” (“spontaneous”) spike trains were drawn from a normal distribution with μ = 20 spikes/s, σ = 15 spikes/s, and μ = 60 spikes/s, σ = 45 spikes/s, for “juveniles” and “adults,” respectively. The “M” (“natural movie”) rates were obtained by multiplying the spontaneous rate of each spike train by a coefficient drawn from a normal distribution with μ = 2, σ = 0.5, and μ = 1.25, σ = 0.125, for juveniles and adults, respectively. Bottom, PRds, taken to be shifted lognormal as in cat V1 (see Materials and Methods). Blue and green points indicate parameters used to create synthetic juvenile and adult rasters, respectively. C, Comparison of the spontaneous and evoked word distributions produced by the model for the juvenile (top) and adult (bottom) conditions. D, Summary statistics for the raster marginals model, shown in the same format as A. Error bars indicate SDs over 100 repeats, one of which is shown in B and C.

Spontaneous and input-driven word distributions in a randomly connected recurrent spiking network can shift from a mismatch to a match upon change in intrinsic properties of the network. A, Schematic of the network, containing 80% excitatory and 20% inhibitory neurons. B, In condition 1, background depolarization is weak and firing adaptation of the excitatory neurons is strong. In this condition, the spontaneous and evoked word distributions produced by the network substantially differ. C, In condition 2, background depolarization is strong and adaptation weak. In this condition, spontaneous and evoked word distributions are similar. D, Same analysis as in A,D (bottom) for spiking network data (S, spontaneous; Id, input driven). E, PRd for spontaneous (left) and external input driven (right) conditions in the spiking network. Note that the PRds for spontaneous and evoked activity differ greatly for condition 1, but not for condition 2. F, Same analysis as in B for spiking network data. Error bars indicate SDs over the four conditions in which we examined the network dynamics (spontaneous and input-driven, in conditions 1 and 2).