Sequential analysis and its applications to neuromorphic engineering

Shivaram Mani^*Saeed AfsharTravis Monk

• The MARCS Institute, Western Sydney University, Penrith, Australia

Neuromorphic circuits operate by comparing fluctuating signals to thresholds. This operation 3 underpins sensing and computation in both neuromorphic architecture and biological nervous 4 systems. Rigorous analysis of such systems is rarely attempted because the statistical tools 5 to study them are both inaccessible and largely unknown to the neuromorphic community. We 6 offer a gentle introduction to one such tool called sequential analysis, a classical framework 7 that addresses a particular class of threshold crossing problems. We define the formal problem 8 studied by sequential analysis and present the elegant methodology of Abraham Wald to solve it. 9 We then apply this framework to three examples in neuromorphic engineering, showing how it 10 can serve as a benchmark, proxy model, and design tool. Our introduction is accessible without 11 prior training in probability or statistics. Sequential analysis provides statistical limits of circuit 12 performance, tractable abstractions of complex circuit behavior, and constructive rules for circuit 13 design. It establishes rigorous statistical baselines for evaluating hardware. It links low-level 14 circuit parameters to observable dynamics, clarifying the computational role of neuromorphic 15 architectures. By translating performance goals into optimal thresholds and design parameters, it 16 offers principled prescriptions that go beyond empirical tuning.