Neurons in prediction error layer respond to unexpected transitions.

A. Spiking network model ‘SpikeSuM’. From top to bottom: Every 100ms stimuli change, giving rise to a sequence R_n−1, R_n, R_n+1… The presently observed stimulus (R_n, red box ‘OBS’) and the previous stimulus (R_n−1, ‘Buffer’) are encoded with spike trains of 128 neurons each (16 sample spike trains shown). These spike trains are transmitted to two excitation-inhibition networks (prediction error layer) composed of pyramidal neurons (red triangles) and inhibitory neurons (orange circles). Pyramidal neurons in population P₁ are excited (arrowheads) by the inputs representing the prediction based on stimulus R_n−1 and inhibited (round heads) by the current observation X whereas neurons in P₂ are inhibited by the prediction and excited by the current observation X. The activity A₁ and A₂ of populations P₁ and P₂ is transmitted to pyramidal tract neurons (PT), which low-pass filter the activity and transmit it to a group of neurons in a deep nucleus (green, labeled 3^rd) which sends a neuromodulatory surprise signal back to the prediction error layer. Poorly predicted stimuli increase activity in the prediction error layer and indirectly accelerate, via the 3^rd factor, learning in the plastic connections (red lines). Inset: Time course of the 3^rd factor (green) over 4s before and after a rule switch at time t_switch. B: Spike trains of all 128 pyramidal neurons in population P₂ during a specific stimulus R_n. The 128 neurons have first been ordered from highest to lowest firing rate and then clustered into groups of 8 neurons, with neurons 1 to 8 forming the first cluster. Right: Histogram of average firing rate per cluster (horizontal bars). B₁: Random sparse connectivity from presynaptic neurons in the input layer to neurons in the prediction error layer. Inset: schematics, colors indicate connection strength from red (weak) to blue (strong). B₂: Regular connectivity with binary connections. Inset: schematics, nonzero connections (blue) are organized in clusters of 8 neurons, but for readability, only 4 clusters of two neurons each are shown. C₁ and C₂: To compare the two networks, we show the spikes generated in response to a new stimulus R_n′ while keeping the same order of neurons. For random connectivity (C1) spike plots are different if R_n′ ≠ R_n but similar if R_n′ = R_n. The same holds for regular connectivity (C2). D₁ and D₂: Filtered activity of pyramidal neurons in populations P₁ (red), P₂ (cyan), and the total filtered activity (black) as a function of time-averaged over 100 different sequences with a change point (switch of rule) after 500 presentation steps, for random (D1) or regular (D2) connectivity (parameter K = 2). Both networks indicate a surprising transition (dashed vertical line) by increased activity. Insets show the activity before and after the rule switch. E₁ and E₂: Same as in D₁ and D₂, but for the case of K = 4 possible next stimuli. Since predictions are less reliable, the activity converges to higher levels.