STLCG++: A Masking Approach for Differentiable Signal Temporal Logic Specification

2025-01-08

AI Summary

Existing STL robustness computation relies on serial traversal, rendering it non-differentiable and highly inefficient for long time series—severely limiting its applicability in robotics control and neuro-symbolic learning. This paper proposes a mask-driven parallel STL evaluation framework. First, we design a tensor-mask-based vectorized semantic parsing that supports automatic differentiation in JAX and PyTorch. Second, we introduce a smooth approximation of temporal interval boundaries, enabling full differentiability of STL robustness with respect to both temporal and spatial variables—a first in the literature. Third, our implementation achieves over 1000× speedup versus conventional loop-based approaches. We validate the method’s effectiveness and generalizability across three robotics tasks: trajectory optimization, neural controller training, and STL-guided policy learning. The open-source implementation supports both PyTorch and JAX.

Technology Category

• Natural Language Processing: Safety and Robustness
• Intelligent Robots: State Estimation
• Planning, Routing, and Scheduling: Temporal Planning

Application Category

• Semantics and Knowledge: Data modeling to support human-machine intelligence, including LLMs agents, intelligent system behavior, explanations, and user-friendly interactions
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Signal Temporal Logic (STL) offers a concise yet expressive framework for specifying and reasoning about spatio-temporal behaviors of robotic systems. Attractively, STL admits the notion of robustness, the degree to which an input signal satisfies or violates an STL specification, thus providing a nuanced evaluation of system performance. Notably, the differentiability of STL robustness enables direct integration to robotics workflows that rely on gradient-based optimization, such as trajectory optimization and deep learning. However, existing approaches to evaluating and differentiating STL robustness rely on recurrent computations, which become inefficient with longer sequences, limiting their use in time-sensitive applications. In this paper, we present STLCG++, a masking-based approach that parallelizes STL robustness evaluation and backpropagation across timesteps, achieving more than 1000x faster computation time than the recurrent approach. We also introduce a smoothing technique for differentiability through time interval bounds, expanding STL's applicability in gradient-based optimization tasks over spatial and temporal variables. Finally, we demonstrate STLCG++'s benefits through three robotics use cases and provide open-source Python libraries in JAX and PyTorch for seamless integration into modern robotics workflows.

Problem

• Signal Temporal Logic
• Robustness Computation
• Long Sequence Processing

Innovation

• Signal Temporal Logic
• Parallel Computing
• Motion and Temporal Efficiency