arXiv:2608.17087cs.LGcs.LO2026-08

让时间逻辑在神经网络中可微求导,支持多种语义选择。

Backward through Time, Algebraically

  • 提出通用代数评估引擎,支持不同语义的可微计算。
  • 验证多种代数在正向与反向传播中的行为表现。
  • 适合需要可微时序逻辑的强化学习与序列建模研究者。

线性时序逻辑是扩展命题逻辑的模态逻辑,用于描述系统随时间的行为。其经典域为布尔值,但在软值系统(如神经策略、自适应控制器、序列模型)中,判断公式的满足度可作为训练信号,可微性成为关键。现有可微语义众多但难以选择,且实现多为浅嵌入,需预先选定单一语义代数及其隐含规则。本文以函数式编程视角应对此困境,拒绝妥协,提出一个代数无关的可微评估引擎,并提供可执行的代数规范。对多种代数进行实现与审计,分析其正向与反向行为。每种代数本质上是选择“如何失望”及“向哪个方向失望”。所有内容均已集成至 PyTorch 库 telos,开源地址:https://github.com/konstantinosKokos/telos。

原文摘要 · Abstract (English)

Linear temporal logic is a modal extension of propositional logic that allows one to state how a system should behave over time. Its canonical domain is the booleans, but discretely-valued judgements are of little use in steering softly-valued systems (neural policies, adaptive controllers, sequence models, etc). In such cases, the goal formula's (dis)satisfaction becomes a training signal, and differentiability becomes a prime concern. Candidate differentiable semantics abound, but navigating them is tricky. Implementations, where available, are shallow embeddings, demanding an upfront commitment to a single semantic algebra and its (usually implicit) conduct. The paper casts the reader as a functional programmer asked to come to terms with this predicament, and refusing. Out of that refusal comes an evaluation engine that is algebra-generic and amenable to differentiation, together with an executable specification of the algebras it can accept. Various algebras are implemented and audited for their behavior, both forward and backward. Each algebra turns out to be a choice of which direction to disappoint, and how. Everything described (and more) is part of the PyTorch library telos, to be found at https://github.com/konstantinosKokos/telos.

时序逻辑可微推理PyTorch强化学习

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