mlsanityData to 7 Oct 2026

Neuro-symbolic Learning Yielding Logical Constraints

arXiv 2410.20957 ↗First posted 28 Oct 2024cs.AI cs.LGcited by 12

On the map: LLM reasoning → Reasoning benchmarks and evaluation

Abstract (arXiv)

Neuro-symbolic systems combine the abilities of neural perception and logical reasoning. However, end-to-end learning of neuro-symbolic systems is still an unsolved challenge. This paper proposes a natural framework that fuses neural network training, symbol grounding, and logical constraint synthesis into a coherent and efficient end-to-end learning process. The capability of this framework comes from the improved interactions between the neural and the symbolic parts of the system in both the training and inference stages. Technically, to bridge the gap between the continuous neural network and the discrete logical constraint, we introduce a difference-of-convex programming technique to relax the logical constraints while maintaining their precision. We also employ cardinality constraints as the language for logical constraint learning and incorporate a trust region method to avoid the degeneracy of logical constraint in learning. Both theoretical analyses and empirical evaluations substantiate the effectiveness of the proposed framework.

Key facts. Cited by 12 papers in the map (data through 7 Oct 2026). Placed in Reasoning benchmarks and evaluation, one of 17 directions in LLM reasoning. Builds on 28 of its 76 references that are in the map. First posted on arXiv 28 Oct 2024.

Builds on

28 of 76 references.

Closest ancestors · 1

Same direction, newest first

  1. 2022A-NeSI: A Scalable Approximate Method for Probabilistic Neurosymbolic Inference23 Dec

Other references · 27

  1. 2015Deep Residual Learning for Image Recognitioncited by 51,809
  2. 2019nuScenes: A multimodal dataset for autonomous drivingcited by 4,485
  3. 2021Convex optimizationcited by 2,479
  4. 2016Optimization Methods for Large-Scale Machine Learningcited by 1,140
  5. 2019Neural Probabilistic Logic Programming in DeepProbLogcited by 389
  6. 2017Implicit Regularization in Matrix Factorizationcited by 318
  7. 2017A Semantic Loss Function for Deep Learning with Symbolic Knowledgecited by 267
  8. 2017Learning Explanatory Rules from Noisy Datacited by 210
  9. 2021On the Origin of Implicit Regularization in Stochastic Gradient Descentcited by 183
  10. 2019SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solvercited by 173
  11. 2019Neural Logic Machinescited by 144
  12. 2020Inductive logic programming at 30: a new introductioncited by 83
15 more
  1. 2017Failures of Gradient-Based Deep Learningcited by 79
  2. 2017Recurrent Relational Networkscited by 71
  3. 2020Thinking Fast and Slow in AIcited by 67
  4. 2020The Implicit Regularization of Stochastic Gradient Flow for Least Squarescited by 58
  5. 2020Closed Loop Neural-Symbolic Learning via Integrating Neural Perception, Grammar Parsing, and Symbolic Reasoningcited by 58
  6. 2019Modeling Recurrence for Transformercited by 26
  7. 2021Techniques for Symbol Grounding with SATNetcited by 24
  8. 2023Learning to Solve Constraint Satisfaction Problems with Recurrent Transformercited by 21
  9. 2019Learning a Decision Module by Imitating Driver's Control Behaviorscited by 17
  10. 2024Softened Symbol Grounding for Neuro-symbolic Systemscited by 16
  11. 2018Low-rank semidefinite programming for the MAX2SAT problemcited by 8
  12. 2018Exact Semidefinite Formulations for a Class of (Random and Non-Random) Nonconvex Quadratic Programscited by 7
  13. 2019On the tightness of SDP relaxations of QCQPscited by 7
  14. 2022Learning Symmetric Rules with SATNetcited by 4
  15. 2017Strengthening Convex Relaxations of 0/1-Sets Using Boolean Formulascited by 3

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 1; 2025: 5; 2026: 6.

12 papers.

  1. 2024LogiCity: Advancing Neuro-Symbolic AI with Abstract Urban Simulationcited by 8
  2. 2025Towards Trustworthy Legal AI through LLM Agents and Formal Reasoningcited by 4
  3. 2025A Learnability Analysis on Neuro-Symbolic Learningcited by 3
  4. 2026Logic Tensor Network-Enhanced Generative Adversarial Networkcited by 2
  5. 2026Neurosymbolic LoRA: Why and When to Tune Weights vs. Rewrite Promptscited by 1
  6. 2026Process-of-Thought Reasoning for Videoscited by 1
  7. 2026Interactionless Inverse Reinforcement Learning: A Data-Centric Framework for Durable Alignmentcited by 1
  8. 2025Solving Satisfiability Modulo Counting Exactly with Probabilistic Circuitscited by 0
  9. 2025Constraints-Guided Diffusion Reasoner for Neuro-Symbolic Learningcited by 0
  10. 2025Scaling Neuro-symbolic Problem Solving: Solver-Free Learning of Constraints and Objectivescited by 0
  11. 2026Generate in the Chart, Not on the Boundary: Function-Symbol Grounding for Hard Constraints in LTN-GANscited by 0
  12. 2026Prototype-Rule Neurosymbolic Regularization for Rank-Constrained Tensor Neural Networks under Label Scarcitycited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2025A Comparative Study of Neurosymbolic AI Approaches to Interpretable Logical Reasoning
  2. 2023Deciphering Raw Data in Neuro-Symbolic Learning with Provable Guarantees
  3. 2025Verification Learning: Make Unsupervised Neuro-Symbolic System Feasible
  4. 2026Differentiable Logic Programming to Mitigate Reasoning Shortcuts in Neurosymbolic Systems
  5. 2026Learning Symbolic Constraint Representations from Examples: A Neuro-Symbolic Approach
  6. 2024Symbol Correctness in Deep Neural Networks Containing Symbolic Layers
  7. 2023Extensions to Generalized Annotated Logic and an Equivalent Neural Architecture
  8. 2026IFDNS: An Iterative Feedback-Driven Neuro-Symbolic Method for Faithful Logical Reasoning