mlsanityData to 14 Oct 2026

A Probabilistic Neuro-symbolic Layer for Algebraic Constraint Satisfaction

arXiv 2503.19466 ↗First posted 25 Mar 2025cs.LGcited by 11

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Abstract (arXiv)

In safety-critical applications, guaranteeing the satisfaction of constraints over continuous environments is crucial, e.g., an autonomous agent should never crash into obstacles or go off-road. Neural models struggle in the presence of these constraints, especially when they involve intricate algebraic relationships. To address this, we introduce a differentiable probabilistic layer that guarantees the satisfaction of non-convex algebraic constraints over continuous variables. This probabilistic algebraic layer (PAL) can be seamlessly plugged into any neural architecture and trained via maximum likelihood without requiring approximations. PAL defines a distribution over conjunctions and disjunctions of linear inequalities, parameterized by polynomials. This formulation enables efficient and exact renormalization via symbolic integration, which can be amortized across different data points and easily parallelized on a GPU. We showcase PAL and our integration scheme on a number of benchmarks for algebraic constraint integration and on real-world trajectory data.

Key facts. Cited by 11 papers in the map (data through 14 Oct 2026). Builds on 44 of its 93 references that are in the map. First posted on arXiv 25 Mar 2025.

Builds on

44 of 93 references.

References · 44

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32 more
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Built on by

Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 4; 2026: 7.

11 papers.

  1. 2025Neurosymbolic Diffusion Modelscited by 13
  2. 2025How to Square Tensor Networks and Circuits Without Squaring Themcited by 5
  3. 2025Tractable Representation Learning with Probabilistic Circuitscited by 4
  4. 2025A General Framework for Property-Driven Machine Learningcited by 1
  5. 2026Constraint-Aware Neurosymbolic Uncertainty Quantification with Bayesian Deep Learning for Scientific Discoverycited by 1
  6. 2026The Theory and Practice of MAP Inference over Non-Convex Constraintscited by 1
  7. 2026A Sobering Look at Tabular Data Generation via Probabilistic Circuitscited by 1
  8. 2026How to Approximate Inference with Subtractive Mixture Modelscited by 1
  9. 2026Concise and Logically Consistent Conformal Sets for Neuro-Symbolic Concept-Based Modelscited by 1
  10. 2026Can VLMs Reason Robustly? A Neuro-Symbolic Investigationcited by 0
  11. 2026Quantitative Linear Logic for Neuro-Symbolic Learning and Verificationcited by 0