Learning rules and network repair in spike-timing-based computation networks

(a) The weights w_k after training on the classification problem, plotted against the time difference Δt of the post- and presynaptic spike pairs. Dots indicate an evaluation of the weights based on the spike trains from a single stimulus presentation. The solid line is a spline fit through w_k points averaged over 16 runs, and it should closely approximate the function W(Δt). In the training set used, there were ≈1,000 appropriate presynaptic spike train examples and 4,600 inappropriate spike train examples. (b) Histogram of the number of training set examples having estimated probability P of belonging to the appropriate class (determined by using the w_k shown in a and Eqs. 2 and 3). The known appropriate and inappropriate spike trains are shown. The vertical dashed line indicates the cutoff threshold for P, defining the topranked presynaptic cells for making functional connections. (c and d) For the olfactory network, selective odor recognition corresponds to choosing connections from cells with a narrow range of peak input currents, as compared with the total possible range. We plot the estimated probability P as a function of the peak input current of the presynaptic cells. Choosing cells with an estimated P above the threshold setting (indicated by the dashed line in c and d) also chooses cells with peak currents within a narrow range. In general, such an underlying principle allowing visualization in plots such as those in c and d might not be known.

The problem of drift with STDP rules. (a) Schematic of a linear array of neurons, indexed by k, that each fire at a time t = k + η, where η is jitter due to noise. All of these neurons could potentially make connections to the postsynaptic neuron shown above them, but initially only a small subset, with almost synchronous firing times, makes a functional connection, as shown. (b) The gray line indicates the initial density of connections from presynaptic cells to the postsynaptic cell. Presynaptic cells are labeled by their mean firing time, in ms. The arrow indicates the firing time of the postsynaptic cell. Black lines show the connection densities resulting from two successive iterations of the self-repair procedure, using the rule shown as a solid line in c.(c) The solid line shows a purely causal (all positive in the Δt > 0 region, all negative in the Δt < 0 region) plasticity rule. (This plasticity rule is used in b, where it is shown that it leads to strong drift.) The dotted line is the same learning rule but shifted 2 ms toward the negative Δt region. (d) Same format as in c, showing initial connection density and two iterations of self-repair, but now using the plasticity rule shown as a dashed line in panel c. Drift is sharply reduced.