Fig. 2: Low-rank decomposition of spike timing-dependent synaptic updates.
From: Modified spike backpropagation design towards highly parallelable hardware implementation
a SRM neuron dynamics: Presynaptic spikes x1, x2, x3 are weighted by synapses w1, w2, w3, integrated as dendritic potential u = ∑xiwi, and transformed to somatic output f(u). The inset illustrates spike generation when membrane potential crosses threshold θ. b Temporal encoding of PSP amplitudes: Postsynaptic spike timing tj samples amplitudes from presynaptic traces (rows 1–3) at tj, forming the matrix ε(tj − ti). c Low-rank geometric structure: Left: Presynaptic timings ti form a linear manifold in j-dimensional space. Right: Rectified timing differences ti − tj shift rows along axes while preserving linearity. d SVD validation: Data points (blue) of different inputs cluster along the principal singular vectors (purple line) with rank-1 decomposition.
