mlsanityData to 7 Oct 2026

Guaranteed Conformance of Neurosymbolic Models to Natural Constraints

arXiv 2212.01346 ↗First posted 2 Dec 2022cs.LG cs.AI cs.ROcited by 6

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Abstract (arXiv)

Deep neural networks have emerged as the workhorse for a large section of robotics and control applications, especially as models for dynamical systems. Such data-driven models are in turn used for designing and verifying autonomous systems. They are particularly useful in modeling medical systems where data can be leveraged to individualize treatment. In safety-critical applications, it is important that the data-driven model is conformant to established knowledge from the natural sciences. Such knowledge is often available or can often be distilled into a (possibly black-box) model. For instance, an F1 racing car should conform to Newton's laws (which are encoded within a unicycle model). In this light, we consider the following problem - given a model M and a state transition dataset, we wish to best approximate the system model while being a bounded distance away from M. We propose a method to guarantee this conformance. Our first step is to distill the dataset into a few representative samples called memories, using the idea of a growing neural gas. Next, using these memories we partition the state space into disjoint subsets and compute bounds that should be respected by the neural network in each subset. This serves as a symbolic wrapper for guaranteed conformance. We argue theoretically that this only leads to a bounded increase in approximation error; which can be controlled by increasing the number of memories. We experimentally show that on three case studies (Car Model, Drones, and Artificial Pancreas), our constrained neurosymbolic models conform to specified models (each encoding various constraints) with order-of-magnitude improvements compared to the augmented Lagrangian and vanilla training methods. Our code can be found at: https://github.com/kaustubhsridhar/ConstrainedModels

Key facts. Cited by 6 papers in the map (data through 7 Oct 2026). Builds on 19 of its 51 references that are in the map. First posted on arXiv 2 Dec 2022.

Builds on

19 of 51 references.

References · 19

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7 more
  1. 2021Neural Networks with Physics-Informed Architectures and Constraints for Dynamical Systems Modelingcited by 40
  2. 2021Hamiltonian-based Neural ODE Networks on the SE(3) Manifold For Dynamics Learning and Controlcited by 37
  3. 2020Modeling System Dynamics with Physics-Informed Neural Networks Based on Lagrangian Mechanicscited by 32
  4. 2019Constrained Deep Networks: Lagrangian Optimization via Log-Barrier Extensionscited by 30
  5. 2020Structured Mechanical Models for Robot Learning and Controlcited by 21
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  7. 2022A Framework for Checkpointing and Recovery of Hierarchical Cyber-Physical Systemscited by 1

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Cited by year

Citing papers per year: 2023: 2; 2024: 3; 2025: 1.

6 papers.

  1. 2023Memory-Consistent Neural Networks for Imitation Learningcited by 14
  2. 2024REGENT: A Retrieval-Augmented Generalist Agent That Can Act In-Context in New Environmentscited by 12
  3. 2025Four Principles for Physically Interpretable World Modelscited by 10
  4. 2024Physically Interpretable World Models via Weakly Supervised Representation Learningcited by 3
  5. 2024Automating Weak Label Generation for Data Programming with Clinicians in the Loopcited by 1
  6. 2023Curating Naturally Adversarial Datasets for Learning-Enabled Medical Cyber-Physical Systemscited by 0