提出新方法让脉冲神经网络可验证,突破传统计算瓶颈。
A Formal Tool for Verification of Probabilistic Spiking Neural Networks Based on Quotient Abstractions
- 用权重离散化构建商抽象模型,降低状态空间复杂度
- 实测每多一个神经元状态空间缩小约17倍,支持更大网络验证
- 适合做生物神经网络形式化验证的研究者和安全关键系统开发者
脉冲神经网络(SNNs)比传统人工网络更贴近生物神经动态,但其基于离子通道噪声和突触囊泡释放不可靠的随机事件驱动计算,需用概率模型建模,而确定性抽象在数学上不适用。通过概率模型检测进行形式化验证面临根本障碍:离散时间马尔可夫链(DTMC)编码的状态空间随神经元数量呈指数增长。通用商模型抽象[1]理论上可通过将膜电位划分为等价类缓解增长问题,但对SNN的直接应用会丢弃突触权重信息,限制可验证性质。本文提出一种权重离散化的商模型抽象方法,将连续突触权重映射到紧凑整数范围,同时保留各突触相对贡献,并提出CogSpike统一工作台,集成SNN设计、仿真与PRISM形式化验证。该离散化具有形式正确性保证:双侧保真定理将任何放电分歧限定在阈值附近的有界灰区;渐近静默定理给出未触发神经元永久静默的精确极限保证。拓扑依赖的缩放分析表明,状态空间缩减呈指数级——当离散化参数W=3时,每增加一个神经元约减少17倍——在七个典型拓扑上实证验证了该方法使原本无法处理的网络变得可验证。
原文摘要 · Abstract (English)
Spiking Neural Networks (SNNs) model biological neural dynamics more faithfully than classical artificial networks, but their stochastic, event-driven computation -- rooted in ion-channel noise and unreliable synaptic vesicle release -- demands probabilistic models for which deterministic abstractions are mathematically inadequate. Formal verification of such models via probabilistic model checking faces a fundamental barrier: the state space explosion problem, where the Discrete-Time Markov Chain (DTMC) encoding grows exponentially with the number of neurons. General-purpose quotient model abstractions [1] can in principle mitigate this growth by partitioning membrane potentials into equivalence classes, but a naïve application to SNNs discards synaptic weight information, limiting the properties that can be verified. This paper introduces a weight-discretized quotient model abstraction that maps continuous synaptic weights to a compact integer range while preserving the relative contribution of each synapse, and presents CogSpike, a unified workbench that integrates SNN design, simulation, and PRISM-based formal verification within a single isomorphic tool chain. The discretization is accompanied by formal correctness guarantees: a two-sided fidelity theorem confines any firing disagreement to a bounded gray zone around threshold, and an Asymptotic Silence theorem gives the exact limit guarantee that unforced neurons fall permanently silent. A topology-dependent scaling analysis shows that the state space reduction compounds exponentially -- approximately $17\times$ per neuron for discretization parameter $W = 3$ -- enabling verification of networks that are otherwise intractable, as confirmed empirically across seven canonical topologies.
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