Figure 5. Synaptic solution space of a ganglion cell pair decoder.
(A) In this simple version of the decoder, each of the two afferents fires exactly one spike per stimulus presentation at times 
and 
. The two spikes produce PSPs with identical kinetics but different amplitudes 
and 
. The relative latency 
of the two spikes determines whether the combined PSP crosses threshold for a spike. This classifier divides the range of 
into three regions: 
, 
, and 
. Depending on the two synaptic weights, the decoder fires only in the middle region (top right, e.g. Figure 4D2) or only outside that region (bottom right, e.g. Figure 4E2). (B) One can prove that for any desired location of the boundaries 
and 
there is a combination of synaptic weights 
and 
that provides the correct classification. Here this solution space is computed using PSP kinetics with 
and 
. The left hand plot shows for any combination of 
and 
the ratio of synaptic weights 
that solves the task. In the region marked “++” both synaptic weights are positive and the readout neuron fires inside the range 
. In the regions marked “+–” and “–+” the weights are of opposite sign, and the readout neuron fires outside the specified range. Dashed lines indicate the boundary between the three types of solutions. Their location depends on the PSP kinetics and asymptotically approaches the time-to-peak of the PSP (solid lines). See Materials and Methods for details. The right hand plots illustrate two specific solutions for the 
combinations indicated by the arrows. In each case, the PSP is shown for several different latencies 
; bold lines correspond to the limiting cases 
and 
, for which the PSP just reaches threshold.