Fig. 2: Anticipation of spiking sequences.
From: Sequence anticipation and spike-timing-dependent plasticity emerge from a predictive learning rule
a Top: Example spike sequence during different training epochs. A spiking sequence is defined by the correlated activity of a subset (N = 100) of pre-synaptic neurons. These N pre-synaptic neurons fire sequentially with relative delays of 2 ms, resulting in a total sequence length of 200 ms (pink spike pattern). In each epoch, there are three different sources of noise: (1) jitter of the spike times (random jitter between -2 and 2 ms); (2) random background firing following a homogeneous Poisson process with rate λ distributed between 0 and 10 Hz (see Methods); (3) another subset of 100 pre-synaptic neurons that fired randomly according to a homogeneous Poisson process with randomly distributed rates between 0 and 10 Hz. For each training epoch, the onset of the spike sequences is drawn from a uniform distribution with values between 0 and 200 ms. The bottom plot shows the population firing rate over 10 ms time bins (neuron membrane time constant). b Dynamics of the post-synaptic spiking activity during learning. The spike times are defined relative to the actual onset of the sequence in each respective epoch. The bottom plot shows the neuron’s output firing rate within each training epoch. This firing rate was computed across 100 independent simulations (shown are mean and standard deviation). c Top: Dynamics of the normalized synaptic weights w/w0 as a function of the training epochs. Here w0 is the weight vector in epoch 0. Above the dashed white line are the 100 background pre-synaptic neurons that do not participate in the sequence. The synaptic weights are ordered along the y-axis from 1 to 100 following the temporal order of the sequence. Bottom: normalized weights of the first 20 inputs at epoch 1000, showing only the first input has been assigned credit. d Left: Normalized objective function \({{{{{{{{\mathcal{L}}}}}}}}}_{norm}\) (left plot) as a function of the training epochs. Different colors correspond to a different number of neurons participating in the sequence. Right: normalized cumulative membrane potential 〈v〉. The cumulative membrane potential was computed as the sum of the vt at each time step in the simulations. The panels show the mean and standard deviation computed over 100 different simulations.
