A Fault-Tolerant Spike-Time Interface for Approximate Agreement in Distributed Neuromorphic Systems

Abstract

Large neuromorphic systems contain many processing tiles that may replicate a shared control parameter such as a threshold reference. If these copies diverge, identical inputs may be processed under different intended settings. We study how tiles can reduce this disagreement when communication carries only labeled spike times and up to \(f\) sender labels may be Byzantine. A raw event stream cannot supply the one-value-per-sender input required by classical approximate agreement because a faulty sender can remain silent, flood a receiver, or report different times to different receivers. We introduce the Spike-time Interface for Faults, or \SIF, which combines paced epochs, sender attribution, per-label \FirstSpike admission, bounded timing error, and a silence sentinel. For an affine one-spike code, midpoint decoding attains the exact deterministic minimax error \(ρ=\min\{1/2,ω/L\}\), where \(ω\) is the residual timing uncertainty and \(L\) is the usable encoding window. \SpikeTrim applies the classical mean-subsequence-reduced (MSR) rule to the sender-indexed decoded values. For \(n\ge3f+1\), it guarantees one-step robust validity, the tight noiseless contraction factor \(f/(n-2f)\) under direct updates, an explicit worst-case asymptotic disagreement bound, and finite recovery after transient agreement-state corruption. A closed-form test determines whether a validated timing budget meets a target disagreement. Simulations illustrate the fault threshold, timing dependence, flooding resistance, and recovery. A controlled spiking classifier experiment shows an association between faster control-state alignment and lower prediction disagreement under a finite maintenance budget.