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Backpropagation through Signal Temporal Logic Specifications: Infusing Logical Structure into Gradient-Based Methods

arXiv 2008.00097 ↗First posted 31 Jul 2020eess.SY cs.CL cs.LOcited by 54

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Abstract (arXiv)

This paper presents a technique, named STLCG, to compute the quantitative semantics of Signal Temporal Logic (STL) formulas using computation graphs. STLCG provides a platform which enables the incorporation of logical specifications into robotics problems that benefit from gradient-based solutions. Specifically, STL is a powerful and expressive formal language that can specify spatial and temporal properties of signals generated by both continuous and hybrid systems. The quantitative semantics of STL provide a robustness metric, i.e., how much a signal satisfies or violates an STL specification. In this work, we devise a systematic methodology for translating STL robustness formulas into computation graphs. With this representation, and by leveraging off-the-shelf automatic differentiation tools, we are able to efficiently backpropagate through STL robustness formulas and hence enable a natural and easy-to-use integration of STL specifications with many gradient-based approaches used in robotics. Through a number of examples stemming from various robotics applications, we demonstrate that STLCG is versatile, computationally efficient, and capable of incorporating human-domain knowledge into the problem formulation.

Key facts. Cited by 54 papers in the map (data through 14 Oct 2026). First posted on arXiv 31 Jul 2020.

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Citing papers per year: 2021: 2; 2022: 9; 2023: 5; 2024: 11; 2025: 11; 2026: 16.

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  1. 2022Guided Conditional Diffusion for Controllable Traffic Simulationcited by 190
  2. 2023Toward General-Purpose Robots via Foundation Models: A Survey and Meta-Analysiscited by 103
  3. 2024LTLDoG: Satisfying Temporally-Extended Symbolic Constraints for Safe Diffusion-based Planningcited by 16
  4. 2022Learning Signal Temporal Logic through Neural Network for Interpretable Classificationcited by 10
  5. 2024TLINet: Differentiable Neural Network Temporal Logic Inferencecited by 9
  6. 2025TeLoGraF: Temporal Logic Planning via Graph-encoded Flow Matchingcited by 9
  7. 2026SafeVLA-Bench: A Benchmark for the Success-Safety Gap in Vision-Language-Action Modelscited by 9
  8. 2025STLCG++: A Masking Approach for Differentiable Signal Temporal Logic Specificationcited by 8
  9. 2025Diverse Controllable Diffusion Policy with Signal Temporal Logiccited by 8
  10. 2022Follow The Rules: Online Signal Temporal Logic Tree Search for Guided Imitation Learning in Stochastic Domainscited by 7
  11. 2022Receding Horizon Planning with Rule Hierarchies for Autonomous Vehiclescited by 7
  12. 2024Learning to Boost the Performance of Stable Nonlinear Systemscited by 7
38 more
  1. 2023Learning Robust and Correct Controllers from Signal Temporal Logic Specifications Using BarrierNetcited by 6
  2. 2025Zero-Shot Trajectory Planning for Signal Temporal Logic Taskscited by 6
  3. 2025TGPO: Temporal Grounded Policy Optimization for Signal Temporal Logic Taskscited by 6
  4. 2022Differentiable Inference of Temporal Logic Formulascited by 5
  5. 2022Risk-Driven Design of Perception Systemscited by 4
  6. 2024Logically Constrained Robotics Transformers for Enhanced Perception-Action Planningcited by 4
  7. 2021Safe Model-based Control from Signal Temporal Logic Specifications Using Recurrent Neural Networkscited by 3
  8. 2023Multi-Predictor Fusion: Combining Learning-based and Rule-based Trajectory Predictorscited by 3
  9. 2024Learning Temporal Logic Predicates from Data with Statistical Guaranteescited by 3
  10. 2024Traffic-Rule-Compliant Trajectory Repair via Satisfiability Modulo Theories and Reachability Analysiscited by 3
  11. 2025Pretrained Embeddings as a Behavior Specification Mechanismcited by 3
  12. 2025Modal Logic Neural Networkscited by 3
  13. 2023Co-learning Planning and Control Policies Constrained by Differentiable Logic Specificationscited by 2
  14. 2024RuleFuser: An Evidential Bayes Approach for Rule Injection in Imitation Learned Planners and Predictors for Robustness under Distribution Shiftscited by 2
  15. 2026STeP: Signal Temporal Logic for Precise Specifications for Action Generation with Vision Language Modelscited by 2
  16. 2021Learning Provably Robust Motion Planners Using Funnel Librariescited by 1
  17. 2022Neural Controller Synthesis for Signal Temporal Logic Specifications Using Encoder-Decoder Structured Networkscited by 1
  18. 2023A Safe Preference Learning Approach for Personalization with Applications to Autonomous Vehiclescited by 1
  19. 2024Concurrent Learning of Policy and Unknown Safety Constraints in Reinforcement Learningcited by 1
  20. 2024Learning to Estimate System Specifications in Linear Temporal Logic using Transformers and Mambacited by 1
  21. 2025A Framework for Learning Scoring Rules in Autonomous Driving Planning Systemscited by 1
  22. 2025Accelerated Learning with Linear Temporal Logic using Differentiable Simulationcited by 1
  23. 2025STL-based Optimization of Biomolecular Neural Networks for Regression and Controlcited by 1
  24. 2026Conformalized Signal Temporal Logic Inference under Covariate Shiftcited by 1
  25. 2026Structural-Ambiguity-Aware Translation from Natural Language to Signal Temporal Logiccited by 1
  26. 2026Spatiotemporal Robustness of Temporal Logic Tasks using Multi-Objective Reasoningcited by 1
  27. 2026Runtime Monitoring of Perception-Based Autonomous Systems via Embedding Temporal Logiccited by 1
  28. 2026SCP-NL2TL: Selective Conformal Prediction with Semantic Verification for Natural Language to Temporal Logic Specificationscited by 1
  29. 2022Knowledge-Integrated Informed AI for National Securitycited by 0
  30. 2022CatlNet: Learning Communication and Coordination Policies from CaTL+ Specificationscited by 0
  31. 2024Scaling Learning based Policy Optimization for Temporal Logic Tasks by Controller Network Dropoutcited by 0
  32. 2024Semantic Communication and Control Co-Design for Multi-Objective Distinct Dynamicscited by 0
  33. 2025Feasibility-aware Learning of Robust Temporal Logic Controllers using BarrierNetcited by 0
  34. 2026Zero-Shot Signal Temporal Logic Planning with Disjunctive Branch Selection in Dynamic Semantic Mapscited by 0
  35. 2026Learning-enabled Parameter Synthesis for Nonlinear Systems from Signal Temporal Logiccited by 0
  36. 2026Reward Machines for Signal Temporal Logiccited by 0
  37. 2026Backward through Time, Algebraicallycited by 0
  38. 2026PAA: The Probabilistic Allen Algebra: A Generative and Complete Probabilistic Extension of Allen's Interval Relationscited by 0

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