Sequential analysis and its applications to neuromorphic engineering

Neuromorphic circuits operate by comparing fluctuating signals to thresholds. This operation underpins sensing and computation in both neuromorphic architectures and biological nervous systems. Rigorous analysis of such systems is rarely attempted because the statistical tools to study them are both inaccessible and largely unknown to the neuromorphic community.

We offer a gentle introduction to one such tool, sequential analysis, a classical framework that addresses a particular class of threshold-crossing problems. We define the formal problem analyzed in sequential analysis and present Abraham Wald's elegant methodology for solving it.

We then apply this framework to three examples in neuromorphic engineering, demonstrating how it can serve as a benchmark, proxy model, and design tool. Our introduction is understandable without prior training in probability or statistics.

Sequential analysis provides the statistical limits of circuit performance, tractable abstractions of complex circuit behavior, and constructive rules for circuit design. It establishes rigorous statistical baselines for evaluating hardware. It links low-level circuit parameters to observable dynamics, clarifying the computational role of neuromorphic architectures. By translating performance goals into optimal thresholds and design parameters, it offers principled prescriptions that go beyond empirical tuning.