Implicitly Parallel Neuromorphic Solver Design for Constraint Satisfaction Problems

TL;DR

This paper provides a theoretical characterization and experimental demonstration of this native type of parallelism that is hard to apply to classical solvers and observes that more than two orders of magnitude faster operation is possible without compromising solution accuracy.

Abstract

Many real-life problems of practical importance -- spanning a wide range of applications from chip design to bioinformatics -- represent constraint satisfaction problems, where classical solvers have to rely on heuristic approximations due to the computational complexity. Neuromorphic solvers, on the other hand, offer a unique alternative representation which enables an inherently parallel exploration of the solution space. This paper provides a theoretical characterization and experimental demonstration of this native type of parallelism that is hard to apply to classical solvers. We observe that more than two orders of magnitude faster operation is possible without compromising solution accuracy. Our study represents the first step toward bridging the theory vs. practice gap to unlock the performance potential of emerging neuromorphic solvers.

Figures (4)

• Figure 1: (a) Analytical energy landscape with valid solutions indicated. (b) Mapping of a 4-variable, 2-clause SAT instance onto a spiking network using WTA and OR motifs. Blue connections denote positive weights, while red connections denote negative weights. (c) Energy breakdown across representative states: a configuration with all constraints violated (highest energy), a local minimum, and a satisfying assignment (lowest energy). The white dot marks the selected state, while the surrounding dots represent its one-bit-Hamming-distance neighbors. Energy differences between the selected state and its neighbors are color-coded: decreases (favorable moves) appear in blue, whereas increases (unfavorable moves) appear in red.
• Figure 2: Illustration of two different constraint connectivity in graph coloring with D=3. Each vertical orange box groups the domain neurons (red, green, blue) of a variable, coupled by a WTA motif to enforce one-hot selection. Horizontal connections denote WTA motifs implementing mutual-exclusion constraints between variables. Left: non-clique connectivity allows a variable to remain multi-valued. Right: a full 3-clique in the constraint graph forces singleton assignments.
• Figure 3: Performance comparison of the proposed heuristic across planar 4-coloring benchmarks.
• Figure 4: Comparison of our heuristic vs. sequential baseline runs for multi-solution discovery. Leveraging native parallelism in neuromorphic computing, our heuristic is consistently faster.