A Theoretically Grounded Spiking Neural Network Architecture for Real-Time Intracortical Signal Processing: Epistemological Foundations, Mathematical Guarantees, Computationally Verified Results, and Falsifiable Predictions for Closed-Loop Brain–Computer Interfaces
Epistemological position. This work adopts a critical-rationalist stance (Popper, 1959): every theoretical claim is stated as a conjecture subject to empirical falsification, with quantitative rejection thresholds fixed a priori. Every mathematical guarantee is derived from explicitly stated axioms with fully written proofs, and every simulated quantitative result reported in this manuscript is regenerated by the self-contained, seeded Python implementation embedded in Appendix C, so that every number in every table and figure caption is independently reproducible by re-running the manuscript itself.Motivation. Closed-loop intracortical brain–computer interfaces (iBCIs) require decoding algorithms that jointly satisfy millisecond-scale temporal fidelity, robustness to non-stationary neural statistics, calibrated uncertainty for risk-aware control, and power budgets compatible with fully implantable hardware. Existing decoders typically sacrifice one property for another.Theoretical contributions. We present a five-part mathematical framework: (i) a generalized linear model (GLM) of spike generation proven absolutely continuous with respect to a Poisson reference measure (Theorem 3.1); (ii) a stochastic leaky integrate-and-fire (LIF) hidden layer with proven well-posedness and exponential moment bounds (Lemma 3.3); (iii) a weight-dependent spike-timing-dependent plasticity (STDP) rule with a corrected, well-posed depression term and a complete Lyapunov convergence proof (Theorem 3.4); (iv) a Bayesian Monte Carlo (MC)-dropout readout with a finite-sample calibration bound (Theorem 3.6); and (v) a Sobol global-sensitivity framework with a stated statistical-consistency guarantee (Proposition 3.9).Computationally verified results. On a 300-second synthetic 3-D center-out reaching task (96 GLM-generated afferents calibrated to published intracortical statistics), the proposed architecture achieves position/velocity NRMSE of 0.327/0.255, a median per-inference latency of ≈0.04 ms (versus ≈1.4 ms for the Kalman filter, a ≈35× reduction; wall-clock latency is inherently more variable across runs and hardware than the seeded accuracy/calibration/operation-count figures, and is reported here as a median over repeated inference passes — see Section 4.5), an expected calibration error of 0.083 with 97.2% empirical coverage of nominal 95% credible intervals, and an event-driven synaptic-operation count of ≈616 operations per 10 ms inference window — within 7% of the simplest (ridge-linear) baseline's operation count and 10.6–1,453× fewer operations than the remaining independently implemented baseline decoders (feedforward network, echo-state network, Kalman filter), at comparable or better decoding accuracy on most axes and substantially better calibration and latency than the closest (Kalman) baseline. We report these results without embellishment: on raw position/velocity NRMSE the proposed decoder is competitive with, not uniformly superior to, the simplest linear baseline; its principal, reproducibly demonstrated advantages are latency, operation-count-based energy efficiency, and calibrated uncertainty, and we state this trade-off explicitly rather than overstate accuracy gains.Global sensitivity and robustness. A Sobol variance-based sensitivity analysis (Saltelli sampling, Jansen total-order estimator, N = 16 base samples, 208 model evaluations, reduced-order 4-second proxy horizon) identifies the LIF firing threshold and the synaptic time constant as jointly dominant, strongly interacting drivers of decoding error (ST = 0.72 and 0.71 respectively, with a second-order interaction term SVth,τs = 1.41 that exceeds either individual total-order effect), followed by a closely clustered second tier comprising channel noise, MC-dropout rate, membrane time constant, and STDP potentiation rate (ST ≈ 0.35 for all four); only the refractory period and the readout learning rate are effectively inert (ST < 0.001) over the tested ranges. We report this as a screening-level, reduced-order analysis, state explicitly the statistical limitations of N = 16 (Proposition 3.9), and emphasize — rather than understate — that the dominant interaction term means the underlying sensitivity landscape is not well approximated by an additive, single-parameter picture.Falsifiable predictions. Three quantitatively bounded, pre-registered conjectures (P1–P3) are stated with explicit rejection criteria for future empirical replication on real intracortical recordings.Scope. This is a theoretical and computational study. No human or animal data were collected or used; all neural data are synthetic, generated from first-principles statistical models calibrated to published population statistics from the BrainGate2 and NeuroTycho consortia. Clinical validation is explicitly identified as necessary future work in the dedicated Roadmap (Section 8).