Fig. 1. Stimulus-selective delay activity in infero-temporal cortex during a DMS task. The animal is required to compare a sample stimulus to a test stimulus which is presented after a delay of a few seconds. The response of one cell to two different familiar stimuli (stimulus 24 and stimulus 14) is shown in the plot. The rasters show the spikes emitted by the cell in different trials, and the histogram represents the mean spike rate across all the repetitions of the same stimulus as a function of time. The visual sample stimulus S triggers a sustained delay activity in response to stimulus 14, but not to stimulus 24. The information about the last stimulus seen is propagated throughout the inter-stimulus interval, no matter whether the identity of the stimulus has to be kept in mind or not to perform the task. Indeed the elevated activity elicited by stimulus 14 is triggered also in the inter-trial interval, between the test stimulus and the sample of the next trial, where there is no need to hold in memory the identity of the last stimulus seen (adapted from [27]).

Fig. 2. Schematic illustration of the network's architecture. Blobs represent different populations in the network: Inhibitory (I) neurons (dark gray blob), excitatory (E) neurons which are never stimulated (‘background', light gray blobs), neurons that, because of the formation of a stimulus-specific synaptic structure, are selective to different stimuli (two stimuli in the figure; white blobs). The sets of selective neurons are assumed to be disjoint in the figure, being the associated stimuli uncorrelated. In the general case selective blobs overlap, owing to neurons shared by internal representations of different stimuli. Thick arrows indicate potentiated synapses (J_p), connecting neurons coding for the same stimulus. Medium weight arrows indicate synapses which do not undergo modifications with respect to the initial state (J_EE), connecting background neurons among themselves, and background neurons to selective ones. Thin arrows stand for depressed synapses (J_d), assuming a homosynaptic kind of LTD (i.e. synapses get depressed for highly active pre-synaptic neurons and low activity post-synaptic ones); they connect selective neurons to the background, and neurons selective to different stimuli to each other. Synapses from (J_EI) and to (J_IE) inhibitory neurons are depicted as dashed lines. External neurons interact with the network via the synaptic couplings J_I,ext and J_E,ext, and are assumed to be excitatory.

Fig. 3. Population transfer functions Φ(ν_in) (=ν_out) and fixed points (self-reproducing rate states) of a stimulus-selective neuron subset before and after learning. Solid curves are Φ(ν_in) before (light gray) and after (dark gray) the recurrent coupling potentiation: When J_p increases the same ν_in drives more excitatory current, amplifying the output spike emission rate ν_out. Fixed points are such that ν_out=ν_in (the self-consistency equation), the intersection of ν_in (dashed line) and the transfer functions: White circles are for stable states, dark circle for the unstable one.

Fig. 4. Stimulation of persistent delay activity selective for a familiar stimulus in a simulation of interacting spiking neurons with synaptic coupling structured as in Fig. 2. The raster plot (A) shows the spikes emitted by a subset of cell in the simulated network grouped in sub-populations with homogeneous functional and structural properties: The bottom five strips contain the spike traces of neurons selective to five different uncorrelated stimuli; In the upper strip is shown the spike activity of a subset of inhibitory neurons and in the large middle strip several background excitatory neurons. (B) The emission rates of the selective sub-populations are plotted: The activity of a population is given by the fraction of neurons emitting a spike per unit time. The population activity is such that before the stimulation all the excitatory neurons emit spikes at low rate (global spontaneous activity) almost independently of the belonging functional group.

Fig. 5. Transient responses to a stepwise stimulation of an excitatory population, for two different coupling strengths. The theoretically predicted spike emission rate dynamics of the population with weak (thin line) and strong (thick line) synaptic coupling is shown (adapted from [50]).

Fig. 7. Mean spike rate vs the distribution of the depolarization V. Left: Distribution p(v) as a function of the post-synaptic frequency ν_post. For each ν_post the parameters μ,σ characterizing the input current are calculated as explained in the text. μ,σ determine the sub-threshold distribution of the depolarization that is plotted here. The white lines over the surface are drawn in correspondence of V=V_L and V=V_H, the thresholds that determine the direction of the temporary synaptic modifications. Note that here the reset potential H coincides with V_H. Right: Probability of occurrence of upwards (Q_a) and downwards (Q_b) jumps upon the arrival of a pre-synaptic spike for different post-synaptic activities. Q_a is the integral of p(v) between the white line corresponding to V_H and the threshold. Analogously, Q_b is the integral of p(v) between the resting potential (V=0) and V_L. As the post-synaptic activity increases, the peak of the distribution p(v) moves from the resting potential to the reset potential H. As a consequence, Q_a increases and Q_b decreases (the figure is reproduced from [70]).

Fig. 6. Stochastic LTP: pre- and post-synaptic neurons fire at the same mean rate and the synapse starts from the same initial value (X(0)=0) in both cases illustrated in the left and the right panel. In each panel are plotted as a function of time (from top to bottom): the pre-synaptic spikes, the simulated synaptic internal variable X(t) and the depolarization V(t) of post-synaptic neuron (note that V_L=V_H). Left: LTP is caused by a burst of pre-synaptic spikes that drives X(t) above the synaptic threshold; Right: at end of stimulation, X returns to the initial value. At parity of activity, the final state is different in the two cases (the figure is reproduced from [63]).

Fig. 8. An example dynamics of one of the spike-driven synapse used in the spiking neurons network to study the learning expression (adapted from [73]). The internal state X(t) of the synapse is plotted as a function of time in the central plot. Above and below it are plotted the pre- and the post-synaptic spikes respectively. The synaptic threshold θ_x is represented by the dashed line. The shaded regions are the time intervals following post-synaptic spikes during which a pre-synaptic spike induces up-regulation of the internal synaptic variable X.

Fig. 9. Curves of iso-probability of potentiation (gray) and depression (black) for synapses following the rule suggested by the experiment by Markram et al. (A), the model of Fusi et al. (B), the synapse with a variable window for depression used in [73] (C) and a synapse with a variable window for depression, but otherwise the same as A (D), driven by pre-synaptic and post-synaptic neurons emitting Poisson spike trains respectively at frequencies ν_pre and ν_post.

Fig. 10. The potentiation-depression (PD) plane which represents the stable asynchronous states at different levels of potentiation and depression of synaptic efficacies due to a learning process involving a finite set of uncorrelated stimuli (see text for details, adapted from [73]).

Fig. 11. A successful learning trajectory. (A) Neural activity of the five uncorrelated stimuli used in the learning process for a totally unstructured synaptic distribution (starting point for the simulation): No selective delay activity shown after visual response. (B) The PD-plane for the simulated network superimposed to the learning trajectory emerging from the simulation: Each diamond indicates the system state after a presentation of the entire set of stimuli. (C) As in (A), at the end of the simulation the system reaches the region of the PD-plane where spontaneous and selective states coexist: the selective delay activity following a stimulation is clearly visible. See text for details (this figure is adapted from [73]).

Fig. 12. Potentiation level J_p/J_EE (solid curve) and depression level J_d/J_EE (point-dashed curve) during a learning session. Data are from the same simulation shown in Fig. 11.

Fig. 13. Histograms of the fraction R_p of potentiated synapses a neuron receives from homogeneous cells in a stimulated sub-population at different successive learning stages. A learning stage consists of a sequence of five different stimuli, each presented for 250 ms every second. Each histogram is sampled at the times reported on the left of the histograms. (A) Case in which the dendritic tree develops a ‘bad' structure (some neurons express LTD rather than LTP); (B) A well separated case.

Fig. 14. An example of visual response during a learning history with (dashed line) and without (solid line) synaptic STD.