A Theoretically Grounded Spiking Neural Network Architecture for Real-Time Intracortical Signal Processing: Epistemological Foundations, Mathematical Guarantees, and Falsifiable Predictions for Closed-Loop Brain-Computer Interfaces

Epistemological Position. This work adopts a critical rationalist stance: theoretical claims are formulated as conjectures subject to empirical falsification, with quantitative thresholds specified a priori. Mathematical guarantees are derived from explicitly stated axioms, and all approximations are bounded with error terms. Motivation. Closed-loop brain-computer interfaces (BCIs) require decoding algorithms that simultaneously satisfy: (i) millisecond-scale temporal precision matching cortical dynamics; (ii) adaptation to non-stationary neural statistics over chronic implantation; (iii) calibrated uncertainty estimates enabling risk-aware control; and (iv) energy efficiency compatible with fully implantable hardware. Existing approaches trade biological fidelity for computational tractability, limiting clinical translation. Theoretical Contributions. We introduce a mathematically rigorous framework advancing five dimensions:(i) Biophysical spike generation: Generalized linear model with refractory and coupling terms, proven to satisfy absolute continuity with respect to Poisson measures;(ii) Stochastic neuronal dynamics: Leaky integrate-and-fire model with channel noise, admitting unique strong solutions with exponential moment bounds;(iii) Provably stable plasticity: Weight-dependent STDP rule with Lyapunov-certified convergence under bounded inputs;(iv) Calibrated uncertainty readout: Bayesian inference layer with epistemic/aleatoric decomposition and finite-sample calibration guarantees;(v) Hardware-guided sensitivity: Variance-based global sensitivity analysis with statistical consistency bounds informing neuromorphic co-design. Analytical Results. We establish: (a) information-theoretic upper bounds on decoding capacity; (b) computational complexity lower bounds approaching event-driven optimality; (c) sublinear error scaling with spike count variance (α = 0.62 ± 0.08); and (d) uncertainty-behavior correlation thresholds (r > 0.7) for closed-loop safety. Falsifiable Predictions. Three quantitatively precise, experimentally testable conjectures:[P1] SNN decoding error scales as NRMSE ∝ σ_spikes^α with α ∈ [0.54, 0.70] under controlled spike jitter;[P2] Trial-by-trial predictive variance correlates with behavioral endpoint error: r ∈ [0.67, 0.79], p < 10^-5;[P3] Neuromorphic implementation achieves ≤ 10 μJ per inference versus ≥ 50 μJ for GPU baselines.Empirical contradiction of these intervals necessitates model revision. Validation Approach. All theoretical results are validated through reproducible simulations using high-fidelity synthetic data calibrated to published clinical statistics from BrainGate2 and NeuroTycho consortia. No human or animal subjects were involved in this study. Keywords: spiking neural networks, intracortical brain-computer interfaces, Bayesian inference, uncertainty quantification, global sensitivity analysis, neuromorphic computing, theoretical guarantees, falsifiability, epistemological foundations认识论立场 本研究采用批判理性主义立场：将理论主张表述为可经受经验证伪的猜想，并先验设定定量阈值。数学保证均由明确阐述的公理推导而来，所有近似结果均带有误差项的边界约束。 研究动机 闭环脑机接口（brain-computer interfaces, BCI）所需的解码算法需同时满足四项要求：(i) 匹配皮层动力学的毫秒级时间精度；(ii) 适配长期植入场景下神经统计特性的非平稳性；(iii) 支持风险感知控制的校准后不确定性估计；(iv) 兼容全植入式硬件的能效表现。现有方法往往为换取计算可处理性而牺牲生物保真度，限制了其临床转化潜力。 理论贡献 本文提出一套严格数学框架，从五个维度实现理论推进： (i) 生物物理尖峰生成：提出带不应期与耦合项的广义线性模型，证明其满足关于泊松测度（Poisson measures）的绝对连续性； (ii) 随机神经元动力学：提出带通道噪声的漏极积分-发放模型，证明其存在唯一强解且具有指数矩边界； (iii) 可证明稳定的突触可塑性：设计带权重依赖的脉冲时序依赖可塑性（Spike-Timing-Dependent Plasticity, STDP）规则，在有界输入条件下具备李雅普诺夫（Lyapunov）验证的收敛性； (iv) 校准后不确定性读出：构建贝叶斯推理（Bayesian inference）层，支持认知不确定性与偶然不确定性分解，并具备有限样本校准保证； (v) 硬件导向的敏感性分析：采用基于方差的全局敏感性分析（global sensitivity analysis），通过统计一致性边界为神经形态协同设计提供依据。 分析结果 本文确立以下结论：(a) 解码容量的信息论上界；(b) 接近事件驱动最优性的计算复杂度下界；(c) 随尖峰计数方差呈次线性误差缩放的规律（α=0.62±0.08）；(d) 保障闭环安全所需的不确定性-行为相关性阈值（r>0.7）。 可证伪猜想 本文提出三项定量精确且可通过实验验证的猜想： [P1] 在尖峰抖动受控的条件下，脉冲神经网络（spiking neural networks, SNN）的解码误差遵循归一化均方根误差（NRMSE）∝σ_spikes^α的缩放关系，其中α∈[0.54, 0.70]； [P2] 逐试次预测方差与行为终点误差显著相关：相关系数r∈[0.67, 0.79]，p<10^-5； [P3] 神经形态计算（neuromorphic computing）实现单推理的能耗≤10μJ，而GPU基线方案的能耗≥50μJ。 若实验结果与上述区间矛盾，则需对模型进行修正。 验证方法 所有理论结果均通过可复现的仿真实验验证，仿真采用经校准的高保真合成数据集，其参数匹配BrainGate2与NeuroTycho联盟已发表的临床统计数据。本研究未涉及人类或动物受试者。 关键词 脉冲神经网络（spiking neural networks, SNN）、皮层内脑机接口、贝叶斯推理（Bayesian inference）、不确定性量化（uncertainty quantification）、全局敏感性分析（global sensitivity analysis）、神经形态计算（neuromorphic computing）、理论保证、可证伪性、认识论基础