Exploring Dendritic Computation in Bio-Inspired Architectures for Dynamic Programming

Dynamic programming is a classical optimization technique that systematically decomposes a complex problem into simpler sub-problems to find an optimal solution. We explore the use of bio-inspired architectures to find the shortest path between two nodes in a graph using dynamic programming. We leverage dendritic computations, which are linear and nonlinear mechanisms in neuronal dendrites that allow to implement different computational primitives. We exploit two key mechanisms: 1) a dendrite acts as a delay line to propagate an excitatory post-synaptic potential to the soma, and 2) a feedback mechanism from the soma into the dendrites to control this delay. Our key ideas are the following. First, we model each node on a graph as a leaky integrate-and-fire (LIF) neuron, supporting the two dendritic mechanisms. We use a countdown counter to implement forward propagation of a delayed synaptic potential and eligibility trace-based feedback to update the delay by incorporating the cost of edges in a graph. Next, we formulate dynamic programming in terms of the time to the first spike in neurons. We breakdown the shortest path problem into sub-problems of finding the earliest firing times of neurons, and iteratively building the final solution from these smaller sub-problems by tracing backward. We implement this approach for several real-world graphs and show its scalability. We also show early prototyping on a Virtex UltraScale FPGA.