Predictive Spike Timing Enables Distributed Shortest Path Computation in Spiking Neural Networks

TL;DR

The paper tackles the challenge of computing shortest paths in neural substrates under biological constraints, where global coordination and backtracing are implausible. It introduces a spike-timing-based, locally computable algorithm in which neurons become tagged when inhibitory-excitatory ($I$-$E$) pairs arrive earlier than predicted, creating a backward temporal compression that reveals nodes on optimal paths. A formal convergence proof shows that after $k$ iterations, all nodes at distance $k$ from the target along a shortest path are tagged, and simulations on random spatial networks demonstrate the method identifies all shortest paths. The work offers a principled, biologically plausible alternative to classical algorithms and gradient-based learning, with potential implications for neuroscience, AI, and neuromorphic systems, and it opens avenues for extending temporal-prediction mechanisms to other graph problems.

Abstract

Efficient planning and sequence selection are central to intelligence, yet current approaches remain largely incompatible with biological computation. Classical graph algorithms like Dijkstra's or A* require global state and biologically implausible operations such as backtracing, while reinforcement learning methods rely on slow gradient-based policy updates that appear inconsistent with rapid behavioral adaptation observed in natural systems. We propose a biologically plausible algorithm for shortest-path computation that operates through local spike-based message-passing with realistic processing delays. The algorithm exploits spike-timing coincidences to identify nodes on optimal paths: Neurons that receive inhibitory-excitatory message pairs earlier than predicted reduce their response delays, creating a temporal compression that propagates backwards from target to source. Through analytical proof and simulations on random spatial networks, we demonstrate that the algorithm converges and discovers all shortest paths using purely timing-based mechanisms. By showing how short-term timing dynamics alone can compute shortest paths, this work provides new insights into how biological networks might solve complex computational problems through purely local computation and relative spike-time prediction. These findings open new directions for understanding distributed computation in biological and artificial systems, with possible implications for computational neuroscience, AI, reinforcement learning, and neuromorphic systems.

Figures (9)

• Figure 1: Each model neuron has four states: resting (0), processing (1), spiking (2), refractory (3), and inhibited (4). A neuron's state machine transits to another state either upon receiving an $E$ or $I$ message (dashed arrows, message type over arrow), or after a temporal delay (solid arrows, delay under arrow). A neuron can emit $E$ and $I$ messages (wavy arrows) when spiking. (A) shows the state machine of a untagged neuron, which produces only $E$ messages when spiking. (B) shows the state machine of a tagged neuron, which can move from inhibited to processing, has a shorter processing delay $\tau_{\text{proc}}^+ < \tau_{\text{proc}}^0$, and also generates $I$ messages when spiking. (C) Sequence diagram of two interacting neurons. After the processing delay (hatched box), the neuron in the bottom row sends an $E$ message (blue arrow) to its neighbors (here only top row), with transmission delay $\Delta t_E$ indicated by the slant of the arrow. It predicts to receive recurrent $E$ messages only after a time window that includes message delivery times and subsequent processing delay (indicated by green bar over the neuron's time axis). (D) Sequence diagram where the second neuron (top row) is tagged. The tagged neuron has faster processing (magenta hatched box), and emits both $I$ and $E$ messages, with $\Delta t_I < \Delta t_E$ indicated by slant of the arrows. The $I$-$E$ message pair arrives earlier than predicted at the first neuron (bottom row), i.e. within the spike-delay prediction time window.
• Figure 2: Evolution of the temporal gradient field during iterations of the algorithm. Top row shows results for a classical square environment. Bottom row shows results for an A-maze, where the spatial domain follows the capital letter A. Starting neuron highlighted by blue box (bottom left corner in each panel), target neuron highlighted by white box (top right). Neurons which spiked during an iteration are colored orange, tagged neurons are red, silent neurons are gray. Contour lines are automatically extracted and indicate time-to-spike for each level. Caption for each panel contains the iteration number, as well as duration during iteration until target neuron spiked. Both rows show the evolution of the temporal gradient field until all nodes on shortest paths are tagged (last column), the decrease in time-to-target (TTT), and the pruning of neural activity along poor directions via global inhibition (silent neurons). The neurons that spike in the final iteration match exactly the shortest-path neurons identified by Dijkstra’s algorithm.
• Figure 3: Evolution of the temporal gradient field during iterations of the algorithm in a circular maze. Clearly visible is the concentric propagation of activity during the first iteration (left panel), which over time turns into an elongated ellipse from start towards the target (right panel). This deformation of the contour lines shows the deformation of the temporal gradient field. That is, while the first iteration has neurons that operate alike and therefore propagate activity uniformly in time, the faster tagged neurons during the final iteration stretch the temporal gradient from start towards target and block activity on poor paths via inhibition.
• Figure 4: Evolution of the temporal gradient field during iterations of the algorithm in a T-Maze. Due to the high density of neurons in the maze as well as the shape of the maze, there is not a single (or approximately two, as in Figure \ref{['fig:appendix_circle']}), shortest path but several neurons that are on a broader shortest band towards the target. This is expected, given that distance between neurons is considered to be unweighted in this implementation of the algorithm.
• Figure 5: Evolution of the temporal gradient field during iterations of the algorithm in a A-Maze without global inhibition, but with local inhibition. In this simulation, global inhibition was turned off in favor of local inhibition by tagged neurons. Specifically, the local inhibition followed the same connectivity profile as the local excitation, i.e. an annulus around a neuron. The simulation shows that significantly more activity remains active within the network compared to Figure \ref{['fig:results']}, and sub-optimal routes only get extinguished once the starting neuron is tagged. Afterwards, only tagged neurons remain active, and the shortest path appears during the final iteration of the algorithm.