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

Russell Stewart, Stefano Ermon

arXiv:1609.05566v1cs.AI

TL;DR

The paper addresses the expense and scarcity of labeled data by supervising neural networks through constraints on output structure instead of direct input-output examples. It uses physics and other domain knowledge to define differentiable constraint losses and demonstrates label-free object tracking and detection in computer-vision tasks. The approach reduces labeling needs in small-scale experiments, while requiring careful design of constraints and regularization to avoid trivial solutions.

Abstract

from arXiv · show

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.

Introduction

The paper asks whether neural networks can be supervised without labeled input-output examples by encoding desired output structure from domain knowledge. It proposes constraint-based learning, reducing labeling demands while introducing engineering challenges in designing suitable constraints and regularizers.

  • The paper asks whether networks can learn tasks from descriptions of desired output structure rather than individual labeled examples.Source: Introduction · p. 1
  • Constraint learning explicitly assigns semantics to hidden variables and uses algebraic or logical constraints derived from prior domain knowledge.Source: Introduction · p. 1
  • The approach can reduce labeling work and apply one constraint set across multiple datasets without relabeling.Source: Introduction · p. 1
  • Structured prediction settings provide the target use case: image sequences can map to outputs such as object heights whose values obey known algebraic structure.Source: Problem Setup · p. 2
  • A weighted constraint function g penalizes outputs whose structures conflict with prior knowledge, allowing training without observed labels.Source: Problem Setup · p. 2
  • Constraint optimization can be combined with neural-network hypothesis classes and regularization, but designing g and additional regularization may require substantial domain-specific engineering.Source: Problem Setup · p. 2

Experiments

The experiments show that neural networks can learn visual outputs without direct labels by enforcing temporal, physical, and logical constraints. Across free-fall, walking, and character-detection tasks, constraint-based supervision recovers useful predictions, though additional terms are needed to avoid trivial solutions.

Experimental setup

  • The method trains networks to map images to desired outputs without direct output examples, using structure over time or causal relationships between objects.Labels are used only for evaluation across the experiments.Source: Experiments · p. 2

Tracking an object in free fall

  • Free-fall trajectories are supervised by the physics constraint that an object under gravity follows a fixed-acceleration parabola.The network predicts each frame’s height, and training minimizes deviation from a fitted parabola with fixed curvature.Source: Tracking an object in free fall · pp. 2–3
  • 90.1% correlation was achieved for predicted object heights versus ground-truth pixel measurements, compared with 94.5% for direct supervision.A uniform random output has an expected correlation of 12.1%; the supervised task is easier because it need not compensate for camera distance.Source: Evaluation · p. 3

Conclusions

  • The experiments demonstrate that appropriate constraint losses can extract object information from real images and support learning over discrete logical output spaces.Removing the sufficiency terms causes learning to fail in the character-detection task.Source: Evaluation · p. 3, Detecting objects with causal… · p. 6

Tracking the position of a walking man

  • The same constraint-supervised network discovered walking-person positions, reaching 95.4% test correlation compared with 80.5% for direct supervision.Predictions are evaluated after an affine transformation, and the metric does not demonstrate a complete solution because transformations may differ between scenes.Source: Tracking the position of a walking man · p. 5

Detecting objects with causal relationships

  • The logical character-detection experiment learned whether images contained Peach and Mario from causal constraints, succeeding on a 128-image test set.The constraints and additional losses jointly prevent trivial constant outputs and encourage meaningful, varied predictions.Source: Detecting objects with causal… · pp. 5–6

Related Work

The paper situates its approach within constraint learning while distinguishing it from classical applications through neural representation learning and sufficiency terms. Related examples include weakly supervised deep networks, label-free image embeddings, and DQN planning from weak rewards.

  • Constraint learning generalizes supervised learning by enabling supervision through group annotations, input orderings, logical formalisms, and other constraints.Source: Related Work · p. 6
  • The experiments differ from classical constraint learning by jointly using neural representation learning and sufficiency terms when primary constraints are merely necessary.Source: Related Work · p. 6
  • Prior work trained deep networks with review-level sentiment labels or image constraints such as rotation invariance, high entropy, and high standard deviation.Source: Related Work · p. 6
  • DQN illustrates how an appropriate constraint can transform weak rewards from raw images into a rich planning algorithm.Source: Related Work · p. 6
  • The paper frames its experiments as encouraging broader applications in which the primary constraint is necessary but not sufficient for learning.Source: Related Work · p. 6

Conclusion

The paper introduces physics- and domain-constraint supervision for neural networks and reports promise from small-scale weak-supervision experiments. It identifies scaling to larger multi-object datasets and simplifying sufficiency-term selection as future challenges.

  • The method uses physics and other domain constraints to supervise neural networks without requiring labels.Source: Conclusion · p. 6
  • Future challenges include larger datasets with multiple objects per image and simpler selection of sufficiency terms for new problems.Source: Conclusion · p. 6

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