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Efficient Rectification of Neuro-Symbolic Reasoning Inconsistencies by Abductive Reflection
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Proposes Abductive Reflection (ABL-Refl), which trains a reflection vector from domain knowledge via REINFORCE to flag likely errors in neural outputs so that a symbolic solver only rectifies flagged positions, improving NeSy accuracy and speed on Sudoku and graph clique tasks.
Problem
Neuro-symbolic systems produce outputs inconsistent with domain knowledge, and prior Abductive Learning rectification relies on an expensive combinatorial consistency optimization that does not scale beyond small output dimensions.
Approach
A reflection layer on the network body outputs a binary per-element error flag trained unsupervised from knowledge-base consistency (REINFORCE reward plus a size loss); flagged positions are blanked and filled by abduction with a single solver call, replacing the zeroth-order consistency search.
Key results
- On symbolic Sudoku, ABL-Refl reaches 97.4% inference accuracy versus 76.5% for the best baseline (CL-STE) with comparable inference time (0.22 s).
- On visual Sudoku, ABL-Refl achieves 93.5% accuracy versus 63.5% for SATNet and 67.8% for CNN+Solver.
- On maximum clique, ABL-Refl attains approximation ratios of 0.979-0.991 across four TUDatasets, above Erdos and Neural SFE.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use ABL-Refl with domain-knowledge-abduced reflection and symbolic rectification instead of the strongest Sudoku baseline, CL-STE | Sudoku · Sudoku | inference accuracy: 76.5 -> 97.4 | Helped |
| Reduce labeled examples from 20K to 2K and use 18K unlabeled examples | ABL-Refl · Sudoku | inference accuracy: 97.4 -> 94.7 | Hurt |
| Pretrain the CNN using self-supervised learning | ABL-Refl · Visual Sudoku | inference accuracy: 77.8 -> 93.5 | Helped |
| Use ABL-Refl instead of Neural SFE | Maximum clique · Maximum clique, COLLAB | approximation ratio: 0.781 -> 0.982 | Helped |
| Use ABL-Refl instead of NASR | Visual Sudoku · Visual Sudoku | inference accuracy: 82.7 -> 93.5 | Helped |
| Set reflection size hyperparameter C to 0.7 instead of 0.8 (ablation) | ABL-Refl · Sudoku | inference accuracy: 97.4 -> 99.1 | Helped |
| Set reflection size hyperparameter C to 0.9 instead of 0.8 (ablation) | ABL-Refl · Sudoku | inference accuracy: 97.4 -> 96.6 | Hurt |
| Set reflection size hyperparameter C to 0.7 instead of 0.8 (ablation) | ABL-Refl · Visual Sudoku | inference accuracy: 93.5 -> 95.9 | Helped |
| Set reflection size hyperparameter C to 0.9 instead of 0.8 (ablation) | ABL-Refl · Visual Sudoku | inference accuracy: 93.5 -> 90.6 | Hurt |
| Set reflection size hyperparameter C to 0.7 instead of 0.8 (ablation) | ABL-Refl · Maximum clique, ENZYMES | approximation ratio: 0.991 -> 0.992 | Helped |
| Set reflection size hyperparameter C to 0.9 instead of 0.8 (ablation) | ABL-Refl · Maximum clique, ENZYMES | approximation ratio: 0.991 -> 0.982 | Hurt |
| Raise C from 0.7 to 0.9 to retain more neural output and delegate less to abduction (ablation) | ABL-Refl · Sudoku, propositional KB with MiniSAT | overall inference time (s): 0.239 -> 0.206 | Helped |
Surprising findings
- Using the neural network's own confidence to pick error positions performs poorly (64.3% accuracy), below the plain-network baseline's reflection-based alternative, because confidence does not track knowledge inconsistency.
Limitations
- Reflection training relies on a reward that is discrete, requiring a custom consistency score design per task.
- Hyperparameter C trades accuracy against solver time; the paper recommends a moderate range.
- Evaluated only on Sudoku and graph combinatorial tasks; application to large language models is proposed but not tested.
Experimental setup
Datasets: Kaggle Sudoku dataset SATNet visual Sudoku dataset (MNIST) TUDatasets (ENZYMES, PROTEINS, IMDB-Binary, COLLAB)
Benchmarks: Sudoku (symbolic) visual Sudoku (MNIST) maximum clique on TUDatasets maximum independent set on TUDatasets
Metrics: inference accuracy inference time training time recall approximation ratio
Baselines: RRN CL-STE SATNet Simple GNN ABL NN Confidence NASR Erdos Neural SFE DeepProbLog NeurASP
Builds on: Abductive Learning REINFORCE SATNet NeurASP
Closest papers by meaning
- Analysis for Abductive Learning and Neural-Symbolic Reasoning Shortcuts (ICML 2024 · similarity 0.90)
- Deciphering Raw Data in Neuro-Symbolic Learning with Provable Guarantees (AAAI 2024 · similarity 0.86)
- Ambiguity-Aware Abductive Learning (ICML 2024 · similarity 0.86)
- A learnability analysis on neuro-symbolic learning (NeurIPS 2025 · similarity 0.86)
- Right for the Right Reasons: Avoiding Reasoning Shortcuts via Prototypical Neurosymbolic AI (NeurIPS 2025 · similarity 0.85)
- Concise and Logically Consistent Conformal Sets for Neuro-Symbolic Concept-Based Models (NeurIPS 2026 · similarity 0.85)
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