Fig 5. Autonomous decision making circuit.

A) Neural Circuit. Input amplitude triggers input to be read in, processed, and, conditionally, the processing output is copied, then the circuit turns itself off. B) Connectivity matrix, divided into four components, K¹¹ (graded to graded chain connectivities, upper left), K¹² (gating to graded chain connectivities, upper right), K²¹ (graded to gating chain connectivities, lower left), and K²² (gating to gating chain connectivities, lower right). Plotted are values of K^ij times the synaptic connectivity, S. Color bar denotes connectivity values. Graded chain populations are: “Memory” (1–14), “Hadamard” (15–22), “Hadamard Copy” (23–30), “Input” (31), and “Shutdown” (32) populations. Memory designates Read In (1, 6, 10, 13) and (non-cyclic) Memory populations. Hadamard designates populations holding Hadamard coefficient amplitudes. The Hadamard transform is divided into two parallel operations, one that results in positive coefficients, the other in absolute values of negative coefficients. Hadamard Copy designates populations into which the Hadamard transform may be copied. Input designates a population that linearly transduces a signal from outside the network. And Shutdown designates a population that receives summed input from the Hadamard Copy populations. Upon excitation, it shuts down the input and gating populations and terminates the computation. Gating chain populations are: “Trigger” (33), a re-entrantly coupled population that fires until inhibited, “Compute” (34–39) for gating the computation of the windowed Hadamard transform in the Memory and Hadamard populations, “Vigilance” (40–43) a pulse loop that, along with the “Logic—Conditional Output” (50) population makes a decision based on the amplitude of the output of the 8’th Hadamard population, and “Output Copy” (44–47) a pulse loop that maintains a memory that the decision was made. Logic populations: “Logic—Trigger” (49) a population that is conditionally excited when both Trigger and Input are excited, and “Conditional Output” (50) a population that is conditionally excited when Hadamard coefficient 8 is above threshold and a population in Output Copy is excited. C) Raster plot showing spikes from the graded chain. T₀ = 4 ms, T = 7.5 ms, τ = 5 ms. Time runs from left to right. Initially, the Trigger population is re-entrantly excited until the Input amplitude increases. Input, beginning at t = −0.025s combines with Trigger to initiate firing in the Logic—Trigger population, which triggers the Compute gating chain and initiates the computation (indicated by vertical black line). Trigger is subsequently turned off by inhibition from the Compute gating chain. We show the computation for three successive windows, each of length 4T₀. The gating chain binds the input into four memory chains of length 4T₀, 3T₀, 2T₀ and T₀. Thus, four temporally sequential inputs are bound in four of the memory populations beginning at times t = 4, 8, 12T₀ relative to the trigger. Hadamard transforms are performed beginning at t = 5, 9, 13T₀. Each subsequent read in starts one packet length before the Hadamard transform so that the temporal windows are adjacent. At time t = 0.06 s, the high amplitude in Hadamard coefficient 8 combines with gating population Conditional Output to initiate the Output Copy chain. The output is copied to Hadamard Copy populations, which then cause the shutdown of the gating chain. D) Raster plot showing spikes from the gating chain. These pulses trigger the computation, gate information through the graded chain, and are also used to perform the decision to copy the Hadamard output to Hadamard Copy for sufficiently high amplitudes in Hadamard, population 8. E) Mean firing rates of the graded chain averaged over 50 realizations. Read In—Magenta, Memory—Cyan, Hadamard Coefficients—Green, Input—Yellow, Shut Down—Red. F) Mean firing rates for the gating chain averaged over 50 realizations. Trigger—Red, Cyan, Output Copy—Cyan. E,F) The firing rates have been smoothed by a moving average process with width 2 ms.