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Safe Abductive Learning in the Presence of Inaccurate Rules
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Proposes Safe-ABL, an abductive learning framework that assigns learnable weights to uncertain logical rules and minimizes the discrepancy between perception-induced and rule-abduced symbol distributions, so inaccurate rules do not degrade performance below an end-to-end baseline.
Problem
Abductive learning and neural-symbolic methods degrade severely, even below a pure end-to-end baseline, when the logical knowledge base contains inaccurate rules.
Approach
Treat uncertain rules as weighted edges in a graphical model whose weights are learned by maximum likelihood jointly with the perception model, so accurate rules are kept and inaccurate ones are down-weighted; also prunes abduction candidates by network confidence for speed.
Key results
- On MNIST Addition multi-digit, Safe-ABL reaches 98.06% vs 60.46% for the baseline and 16.66% for ABL.
- On Tic-Tac-Toe, the method keeps high accuracy as inaccurate rules increase to 60 while LTN and ABLSim fall below baseline; AUROC for identifying inaccurate rules is reported as stable.
- On legal dispute focus identification, Safe-ABL gets 70.72 Micro-F1 and 66.14 Macro-F1 vs 69.66 / 64.44 for the baseline and 70.48 / 64.18 for SS-ABL.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use Safe-ABL with selectively weighted rules instead of the raw-data-only baseline | LeNet-5 · MNIST Addition, Single-digit | classification accuracy (%): 96.78 ± 0.21 -> 99.04 ± 0.11 | Helped |
| Use Safe-ABL with selectively weighted rules instead of the raw-data-only baseline | LeNet-5 · MNIST Addition, Multi-digit | classification accuracy (%): 60.46 ± 2.67 -> 98.06 ± 0.14 | Helped |
| Use Safe-ABL instead of SS-ABL with inaccurate or imprecise rules | BERT · Dispute Focus Identification | Macro-F1 (%): 64.18 ± 0.65 -> 66.14 ± 1.32 | Helped |
| Use Safe-ABL instead of the raw-data-only baseline | BERT · Dispute Focus Identification | Macro-F1 (%): 64.44 ± 1.60 -> 66.14 ± 1.32 | Helped |
Surprising findings
- Existing NeSy and ABL methods (DeepProbLog, ABL, ABLSim) fall well below the end-to-end baseline on MNIST addition when rules are inaccurate.
- Pseudo-labeling and tri-training semi-supervised baselines degrade performance on the legal task relative to the labeled-only baseline in Macro-F1 for tri-training.
Limitations
- Evaluated only on small-scale tasks (MNIST addition, Tic-Tac-Toe, one legal task); larger knowledge bases not tested.
- For fair comparison, existing baselines were tested with accurate knowledge bases at test time, which is a compromise in the protocol.
- Rule weights assumed invariant to the candidate symbol z, and the legal dataset is private.
Experimental setup
Datasets: MNIST Tic-Tac-Toe endgame dataset (UCI/Kaggle) Chinese legal pleading sentences (in-house)
Benchmarks: MNIST Addition (single-digit and multi-digit) Tic-Tac-Toe Legal dispute focus identification
Metrics: classification accuracy AUROC Micro-F1 Macro-F1 training time per iteration
Baselines: Baseline (end-to-end) LTN DeepProbLog ABL ABLSim SS-ABL Pseudo-Label Tri-training
Builds on: abductive learning ABLSim DeepProbLog Logic Tensor Network SS-ABL
Closest papers by meaning
- Ambiguity-Aware Abductive Learning (ICML 2024 · similarity 0.88)
- An Improved Algorithm for Learning to Perform Exception-Tolerant Abduction (AAAI 2017 · similarity 0.87)
- Consistency-based Abductive Reasoning over Perceptual Errors of Multiple Pre-trained Models in Novel Environments (AAAI 2026 · similarity 0.86)
- Curriculum Abductive Learning (NeurIPS 2025 · similarity 0.86)
- Analysis for Abductive Learning and Neural-Symbolic Reasoning Shortcuts (ICML 2024 · similarity 0.86)
- AbductiveMLLM: Boosting Visual Abductive Reasoning Within MLLMs (AAAI 2026 · similarity 0.83)
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