将时序逻辑语义压缩成神经嵌入,实现高效推理与公式还原。
Distilling Formal Logic into Neural Spaces: A Kernel Alignment Approach for Signal Temporal Logic
- 用教师-学生框架,将符号鲁棒性核转化为Transformer嵌入。
- 嵌入能准确预测逻辑公式的鲁棒性与满足度,计算效率提升显著。
- 适合需要快速推理和可逆逻辑重建的AI系统设计者。
我们提出一种框架,通过将形式化规范的语义几何结构蒸馏到潜在空间中,学习其连续神经表示。现有方法或依赖符号核(计算开销大、锚点依赖、不可逆),或采用语法驱动的神经嵌入(无法捕捉深层结构)。本方法通过教师-学生设置,将符号鲁棒性核蒸馏至Transformer编码器。不同于标准对比学习,我们采用连续的、基于核加权的几何对齐目标,按语义差异惩罚误差。训练完成后,编码器仅需一次前向传播即可生成嵌入,以极低计算成本模拟核函数的逻辑。我们在信号时序逻辑(STL)上验证该框架,结果表明:神经嵌入忠实保留了STL公式的语义相似性,准确预测鲁棒性与约束满足情况,且保持内在可逆性。该方法实现了高效、可扩展的神经符号推理与公式重构,无需运行时重复计算核函数。
原文摘要 · Abstract (English)
We introduce a framework for learning continuous neural representations of formal specifications by distilling the geometry of their semantics into a latent space. Existing approaches rely either on symbolic kernels -- which preserve behavioural semantics but are computationally prohibitive, anchor-dependent, and non-invertible -- or on syntax-based neural embeddings that fail to capture underlying structures. Our method bridges this gap: using a teacher-student setup, we distill a symbolic robustness kernel into a Transformer encoder. Unlike standard contrastive methods, we supervise the model with a continuous, kernel-weighted geometric alignment objective that penalizes errors in proportion to their semantic discrepancies. Once trained, the encoder produces embeddings in a single forward pass, effectively mimicking the kernel's logic at a fraction of its computational cost. We apply our framework to Signal Temporal Logic (STL), demonstrating that the resulting neural representations faithfully preserve the semantic similarity of STL formulae, accurately predict robustness and constraint satisfaction, and remain intrinsically invertible. Our proposed approach enables highly efficient, scalable neuro-symbolic reasoning and formula reconstruction without repeated kernel computation at runtime.
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