Intrinsic Numerical Robustness and Fault Tolerance in a Neuromorphic Algorithm for Scientific Computing

TL;DR

It is shown that a previously described, natively spiking neuromorphic algorithm for solving partial differential equations is intrinsically tolerant to structural perturbations in the form of ablated neurons and dropped spikes.

Abstract

The potential for neuromorphic computing to provide intrinsic fault tolerance has long been speculated, but the brain's robustness in neuromorphic applications has yet to be demonstrated. Here, we show that a previously described, natively spiking neuromorphic algorithm for solving partial differential equations is intrinsically tolerant to structural perturbations in the form of ablated neurons and dropped spikes. The tolerance band for these perturbations is large: we find that as many as 32 percent of the neurons and up to 90 percent of the spikes may be entirely dropped before a significant degradation in the accuracy results. Furthermore, this robustness is tunable through structural hyperparameters. This work demonstrates that the specific brain-like inspiration behind the algorithm contributes to a significant degree of robustness expected from brain-like neuromorphic algorithms.

Figures (6)

• Figure 1: Finite element mesh on unit square domain $\Omega$, and the solution to the example PDE.
• Figure 2: Ablating neurons. Top: Unmodified NeuroFEM raster plot solving the example problem. Shown are spike trains from 50 randomly chosen neurons across the mesh. Bottom: NeuroFEM raster plot with 40% of the neurons ablated.
• Figure 3: Relative error as a function of percent ablated neurons. Overall accuracy is unchanged until the proportion of ablated neurons reaches a threshold that depends on the number of neurons per mesh node (NPM). Increasing the redundancy by increasing the number of neurons per mesh node increases this threshold. Here, $N$ indicates the number of elements in the mesh and the size of the linear system. The total number of neurons in the circuit is $N\times \textsc{NPM}$. Error bars indicate standard error of the mean over 5 trials.
• Figure 4: Left: NeuroFEM solutions with 50% neurons ablated. Despite clear errors at some mesh nodes, the overall solution remains close to the true solution. Right: Difference between the true and ablated NeuroFEM solutions. Error is concentrated to a few mesh nodes where, by chance, too many neurons were ablated.
• Figure 5: Dropping spikes. Top: Unmodified NeuroFEM raster plot solving the example problem. 50 randomly chosen neurons across the mesh are shown. Bottom: NeuroFEM raster plot with 90% spikes dropped. Individual neurons recalibrate their firing to maintain solution accuracy. Dropping spikes acts like a regularizer leading to sparser activity, which may lead to a neuromorphic advantage.