arXiv:2605.24649cs.LGcs.AI2026-05

提出可保证安全退化行为的循环逻辑门网络,用于实时监控系统决策。

On the Stability and Realizability of Recurrent Polynomial Surrogate Ternary Logic Gate Networks

论文配图:On the Stability and Realizability of Recurrent Polynomial Surrogate Ternary Logic Gate Networks
图 1 · 摘自论文原文
  • 基于三值逻辑设计循环结构,输入缺失时输出保持未知而非误判。
  • 网络隐藏层规模由公式直接决定,无需超参调优,提升可解释性。
  • 适用于对安全性要求高的实时监控场景,如自动驾驶与工业控制。

循环神经网络(RNN)可从部分轨迹中在线预测信号时序逻辑(STL)的真值,但在安全关键系统中部署时,仅靠预测准确率不足。标准RNN无法保证传感器退化下输出的稳健性;一个输入丢失可能悄然使判断从‘安全’变为‘不安全’。本文提出循环可微三值逻辑门网络(R-DTLGN),在克鲁尔三值逻辑{-1, 0, +1}上运行,其中0显式表示未知。R-DTLGN通过连续多项式代理训练,并在推理时硬化为离散三值逻辑电路。我们通过两种源自三值域偏序的门词汇分析硬化电路:数值单调门确保递归动态稳定,信息单调门则保证合理弃权(未知输入永不产生错误输出)和输入确定性的单调性(更多信息只会改善判断)。我们证明,有界STL算子所需的递归连接仅使用AND和OR门,这两类门同时属于两个词汇,将监控任务与架构保障紧密关联。从STL公式中的时间算子推导出的可实现性边界,可直接确定网络隐状态大小,取代超参数搜索。我们在D4RL PointMaze导航数据集上评估了多个STL规范,测试预测准确性、谓词丢失下的退化表现,以及两种标签构建流程间的准确率-安全性权衡。据我们所知,R-DTLGN是首个将学习到的时间预测与基于三值逻辑的形式化退化保障相结合的循环架构。

原文摘要 · Abstract (English)

Recurrent Neural Networks (RNNs) can learn to predict Signal Temporal Logic (STL) verdicts online from partial trajectories, but deploying them as runtime monitors in safety-critical systems demands more than predictive accuracy. Standard RNN architectures offer no structural guarantee that outputs degrade gracefully under sensor degradation; a dropped input can silently flip a verdict from safe to unsafe. We introduce the Recurrent Differentiable Ternary Logic Gate Network (R-DTLGN), a recurrent architecture that operates over Kleene's three-valued logic $\{-1, 0, +1\}$, where $0$ explicitly represents unknown. The R-DTLGN trains through continuous polynomial surrogates and hardens to a discrete ternary logic circuit at inference. We analyze the hardened circuit through two gate vocabularies derived from two orderings on the ternary domain: numerically monotone gates ensure stable recurrent dynamics, while information-monotone gates, when present, guarantee principled abstention (unknown inputs never produce wrong outputs) and monotonicity in input certainty (more information can only improve the verdict). We show that the recurrent connections required by bounded STL operators use exclusively AND and OR, which belong to both vocabularies, linking the monitoring task to the architecture's guarantees. A realizability bound derived from the STL formula's temporal operators directly sizes the network's hidden state, replacing hyperparameter search with a formula-driven specification. We evaluate on STL specifications over D4RL PointMaze navigation data, testing prediction accuracy, degradation under predicate dropout, and the accuracy-versus-safety tradeoff between two label construction pipelines. The R-DTLGN is, to our knowledge, the first recurrent architecture that couples learned temporal prediction with formal degradation guarantees rooted in three-valued logic.

循环网络三值逻辑安全监控形式验证

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