Fig 1.
Dynamics in the read-out networks (A and B) is learnt and controlled on two time scales. The fast time scale network (fast clock) exhibits sequential dynamics that spans individual motifs. This acts directly on the read-out networks through plastic synapses. These synapses learn the motifs. The slow time scale network (slow clock) exhibits sequential dynamics that spans the entire sequence of motifs. This acts indirectly on the read-out networks through an interneuron network. The synapses from the slow clock to the interneurons are plastic and learn the right order of the motifs, or the syntax. The plastic synapses follow a simple symmetric STDP rule for potentiation, with a constant depression independent of spike time.
Fig 2.
A. The target sequence is repeatedly presented to the read-out networks corresponding to motifs A and B. A and B are 200 ms long motifs. Between the motifs, we assume a silent period of 150 ms. B-E. Spontaneous dynamics after learning (50 target presentations). Red dots: excitatory neurons; blue dots: inhibitory neurons. B. The fast clock, controlled by interneurons 201 to 300. C. The slow clock, spanning and driving the entire sequence replay. D. The read-out networks, driven by the fast clock and controlled by the interneurons. E. The interneurons, driven by the slow clock. Neurons 1 − 100 inhibit motif B. Neurons 101 − 200 inhibit motif A. Neurons 201 − 300 shut down both the fast clock and read-out networks. F. The motif synapses show that the target motifs A (neurons 1 − 300 on the y-axis) and B (neurons 301 − 600 on the y-axis) are stored. The weights for motif A are stronger because there are two As in the target sequence and only one B. G. The syntax weights store the temporal ordering A-silent-A-silent-B-silent. H. Non-plastic inhibitory weights from the interneuron network to the read-out network and fast clock. I. Non-plastic excitatory weights from the read-out network and fast clock to the interneuron network.
Fig 3.
Brown shaded areas: presentation of target sequence AAB; dark green shaded areas: presentation of target sequence ABA. Brown dots: spontaneous dynamics is simulated 3 times, and the error with respect to the target sequence AAB is measured; dark green dots: spontaneous dynamics is simulated 3 times, and the error with respect to the target sequence ABA is measured. Lines guide the eye and are averages of the dots. See the Methods section for the details of the error measurements. A. The within-motif error keeps decreasing independent of the motif ordering. B. The motif ordering error (syntax error) switches with a delay.
Fig 4.
Learning speed and performance of hierarchical and serial models on three target sequences of increasing temporal complexity.
A. Each target sequence consists of three presentations of the same motif (200 ms long) but with increasing complexity from left to right. Left: the simplest motif consists of five 40 ms stimulations. Middle: the motif consists of eight 25 ms stimulations. Right: the motif consists of ten 20 ms stimulations. B. Learning curves for the three target sequences for both the hierarchical and serial models. The same plasticity parameters are used for both models (see Methods). The shaded area indicates one standard deviation from the mean (50 trials). Note that the x-axis has two scales to show the three-fold increase in learning speed of the hierarchical model (i.e., for each learning iteration of the hierarchical model there are three iterations of the serial model). The performance degrades from left to right, as a more difficult target sequence is presented.
Fig 5.
Measuring variability and performance in the read-out dynamics.
A. The time between motifs 1 and 2 and motifs 2 and 3 is measured during spontaneous dynamics. We plot the coefficient of variation of these times (50 trials) on the y-axis, for the three target sequences in Fig 4A. B. The cross correlation between the spike trains in the first motif and the second and third motif is measured, normalized by the auto-correlation of the spike trains in motif 1. The maximum of the cross correlation is recorded in each trial (50 trials). This is repeated for the three target sequences in Fig 4A. C. We measure the error between the target sequence with 25 ms stimulations in Fig 4A and spike trains in motif 1, 2 and 3. In both models, the performance degrades towards later occurring motifs. The degradation is significantly worse in the serial model: a linear regression yields a slope of 0.0163 for the serial model and a slope of 0.0048 for the hierarchical model (p < 10−5 using t-test). D. The serial clock (48 clusters) is obtained by adding the slow (28 clusters) and fast (20 clusters) clocks together. Sequential dynamics is simulated 50 times for each clock. The time at which each cluster is activated in the sequential dynamics is measured. The standard deviation of these activation times is plotted as a function of the cluster index. The serial clock has a maximal variability of about 9 ms. The fast and slow clock have a maximal variability of about 3 and 35 ms respectively.
Fig 6.
Spontaneous dynamics after learning two sequences alternately (80 learning iterations).
A. The target sequences. B-E. Red dots: excitatory neurons; blue dots: inhibitory neurons. Brown shaded area: sequence AAB is played by inhibiting the interneurons related to the second sequence; light green shaded area: sequence BAAB is played by inhibiting the interneurons related to the first sequence. B. Spike raster of the fast clock. C. Spike raster of the slow clock. D. Spike raster of the two read-out networks. E. Spike raster of the interneurons. An external attentional inhibitory current selects which sequence is played. F. The motif weights encode the two motifs. Note the similarity with Fig 2F: the same motifs are re-used in both sequences. G. The syntax weights encode the two motif orderings. Note the difference with Fig 2G: an additional syntax is stored. All motif and syntax synapses are plastic at all times during the sequence presentations.
Fig 7.
We learn sequence AAB and then apply a perturbation. Blue shade indicates the perturbation time, and neurons perturbed. A. 250 ms perturbation of the serial network clock. The targeted neurons (neurons 1000 to 2000) have no excitatory external input during the perturbation. The sequential activity breaks down completely. B. 250 ms perturbation of the fast clock in the hierarchical model. The targeted neurons (neurons 1 to 1000) have no excitatory external input during perturbation. The sequential activity breaks down but is reactivated for the final motif through the interneurons.
Table 1.
Fast clock network parameters.
Table 2.
Read-out network parameters.
Table 3.
Slow clock network parameters.
Table 4.
Interneuron network parameters.
Table 5.
Connections between four networks.
Table 6.
Serial model clock network parameters.
Table 7.
Neuronal membrane dynamics parameters.
Table 8.
Synaptic dynamics parameters.
Table 9.
Motif plasticity parameters.
Table 10.
Syntax plasticity parameters.
Fig 8.
The networks in the model can have different components.
The slow clock is replaced by an all-inhibitory network (compare with Fig 1). The syntax synapses follow the same STDP rule as the motif synapses, only inverted.
Fig 9.
Learning sequence AAB with an inhibitory slow clock network.
The target sequence is repeatedly presented to the read-out network. A-D. Spontaneous dynamics is simulated after learning (85 target presentations). Red dots: excitatory neurons; blue dots: inhibitory neurons. A. The fast clock, controlled by interneurons 201 to 300. B. The slow clock, consisting of only inhibitory neurons, inhibits the interneurons in the correct order after learning. C. The read-out networks, driven by the fast clock and controlled by the interneurons. D. The interneurons, controlled by the slow clock. E. The motif synapses show that the target motifs A and B are stored after learning. F. The syntax weights store the correct temporal ordering A-silent-A-silent-B-silent.
Table 11.
Slow clock inhibitory network parameters.
Table 12.
Syntax plasticity parameters.