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Label-Free Supervision of Neural Networks with Physics and Domain Knowledge

arXiv 1609.05566 ↗First posted 18 Sep 2016cs.AIcited by 74

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Abstract (arXiv)

In many machine learning applications, labeled data is scarce and obtaining more labels is expensive. We introduce a new approach to supervising neural networks by specifying constraints that should hold over the output space, rather than direct examples of input-output pairs. These constraints are derived from prior domain knowledge, e.g., from known laws of physics. We demonstrate the effectiveness of this approach on real world and simulated computer vision tasks. We are able to train a convolutional neural network to detect and track objects without any labeled examples. Our approach can significantly reduce the need for labeled training data, but introduces new challenges for encoding prior knowledge into appropriate loss functions.

Key facts. Cited by 74 papers in the map (data through 7 Oct 2026). First posted on arXiv 18 Sep 2016.

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Citing papers per year: 2020: 1; 2021: 17; 2022: 21; 2023: 16; 2024: 11; 2025: 7; 2026: 1.

74 papers.

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  1. 2022SNUG: Self-Supervised Neural Dynamic Garmentscited by 83
  2. 2021Physics-Integrated Variational Autoencoders for Robust and Interpretable Generative Modelingcited by 59
  3. 2021MultiplexNet: Towards Fully Satisfied Logical Constraints in Neural Networkscited by 44
  4. 2022Deep Learning with Logical Constraintscited by 44
  5. 2021Multi-Label Classification Neural Networks with Hard Logical Constraintscited by 36
  6. 2022Towards Data-and Knowledge-Driven Artificial Intelligence: A Survey on Neuro-Symbolic Computingcited by 34
  7. 2021Shape-constrained Symbolic Regression -- Improving Extrapolation with Prior Knowledgecited by 27
  8. 2021Towards a Collective Agenda on AI for Earth Science Data Analysiscited by 27
  9. 2023Neural-Logic Human-Object Interaction Detectioncited by 25
  10. 2021PID-GAN: A GAN Framework based on a Physics-informed Discriminator for Uncertainty Quantification with Physicscited by 21
  11. 2022Neural Implicit Representations for Physical Parameter Inference from a Single Videocited by 19
  12. 2025Beyond the convexity assumption: Realistic tabular data generation under quantifier-free real linear constraintscited by 18
38 more
  1. 2023LOGICSEG: Parsing Visual Semantics with Neural Logic Learning and Reasoningcited by 17
  2. 2022Finite Element Method-enhanced Neural Network for Forward and Inverse Problemscited by 13
  3. 2021DomiKnowS: A Library for Integration of Symbolic Domain Knowledge in Deep Learningcited by 12
  4. 2022Neural network training under semidefinite constraintscited by 11
  5. 2025A Probabilistic Neuro-symbolic Layer for Algebraic Constraint Satisfactioncited by 11
  6. 2022Knowledge-augmented Deep Learning and Its Applications: A Surveycited by 10
  7. 2023Traffic-Domain Video Question Answering with Automatic Captioningcited by 10
  8. 2023GLUECons: A Generic Benchmark for Learning Under Constraintscited by 9
  9. 2024Modeling Spatio-temporal Dynamical Systems with Neural Discrete Learning and Levels-of-Expertscited by 9
  10. 2023Machine Learning with Requirements: a Manifestocited by 8
  11. 2024Naturally Supervised 3D Visual Grounding with Language-Regularized Concept Learnerscited by 8
  12. 2022PromptDA: Label-guided Data Augmentation for Prompt-based Few-shot Learnerscited by 7
  13. 2020Efficiently Guiding Imitation Learning Agents with Human Gazecited by 6
  14. 2023Dream to Adapt: Meta Reinforcement Learning by Latent Context Imagination and MDP Imaginationcited by 6
  15. 2021Constrained Feedforward Neural Network Training via Reachability Analysiscited by 5
  16. 2022Informed Pre-Training on Prior Knowledgecited by 5
  17. 2023Geometry-Aware Adaptation for Pretrained Modelscited by 5
  18. 2025A Study on Neuro-Symbolic Artificial Intelligence: Healthcare Perspectivescited by 5
  19. 2021Hybrid Physics and Deep Learning Model for Interpretable Vehicle State Predictioncited by 4
  20. 2022PInKS: Preconditioned Commonsense Inference with Minimal Supervisioncited by 4
  21. 2023DeepSaDe: Learning Neural Networks that Guarantee Domain Constraint Satisfactioncited by 4
  22. 2024Exploiting T-norms for Deep Learning in Autonomous Drivingcited by 4
  23. 2021SaDe: Learning Models that Provably Satisfy Domain Constraintscited by 3
  24. 2022Shape-constrained Symbolic Regression with NSGA-IIIcited by 3
  25. 2022Robustness of Physics-Informed Neural Networks to Noise in Sensor Datacited by 3
  26. 2021Leveraging Unlabeled Data for Entity-Relation Extraction through Probabilistic Constraint Satisfactioncited by 2
  27. 2022Physics-Infused Fuzzy Generative Adversarial Network for Robust Failure Prognosiscited by 2
  28. 2023Hybrid Modeling Design Patternscited by 2
  29. 2024How Inverse Conditional Flows Can Serve as a Substitute for Distributional Regressioncited by 2
  30. 2021Improved Surrogate Modeling of Fluid Dynamics with Physics-Informed Neural Networkscited by 1
  31. 2021Uncovering Closed-form Governing Equations of Nonlinear Dynamics from Videoscited by 1
  32. 2021Causal Knowledge Guided Societal Event Forecastingcited by 1
  33. 2022Physics-Guided Adversarial Machine Learning for Aircraft Systems Simulationcited by 1
  34. 2022Neural DAEs: Constrained neural networkscited by 1
  35. 2023Deep Occupancy-Predictive Representations for Autonomous Drivingcited by 1
  36. 2023Label-free timing analysis of SiPM-based modularized detectors with physics-constrained deep learningcited by 1
  37. 2023Teach Me How to Learn: A Perspective Review towards User-centered Neuro-symbolic Learning for Robotic Surgical Systemscited by 1
  38. 2023Predicting and explaining nonlinear material response using deep Physically Guided Neural Networks with Internal Variablescited by 1

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