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Analysis for Abductive Learning and Neural-Symbolic Reasoning Shortcuts
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Provides a theoretical analysis of reasoning shortcut risk in neural-symbolic (NeSy) learning and abductive learning (ABL), showing how knowledge base complexity, sample size, and hypothesis-space assumptions bound the risk, and that ABL with a good distance function can reduce it.
Problem
Reasoning shortcuts in neural-symbolic and abductive learning: models reach high target accuracy by learning unintended intermediate concept semantics, and theoretical understanding of how to quantify and mitigate this harm is limited.
Approach
Defines a shortcut risk as the gap between the supervised concept-level cross-entropy and the NeSy training loss, and an empirical knowledge base complexity measure (data and rule dependent); proves upper bounds under label-smoothness and pre-training hypothesis-space assumptions, and shows ABL's shortcut risk is bounded by a term scaling with the distance function's error rate.
Key results
- On MNIST-Addition, ABL(P) with a pre-trained-model distance achieves about 98.57% average GAcc across six difficulty levels, versus 54.04% for plain ABL and 27.26% for semantic loss.
- ABL(C), which uses the current model's confidence as distance, drops to 4.04% GAcc at the hardest level VI, showing distance function choice strongly affects shortcut mitigation.
- On BDD-OIA, ABL(P) raises GAcc to 85.13% from 57.74% for DeepProbLog, at a small cost in target accuracy (74.03% vs 69.00% for DPL, i.e., higher target Acc than DPL is not the case; ABL(P) Acc is 74.03 vs DPL 69.00).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Increase empirical knowledge-base complexity by using lower-difficulty MNIST-Addition levels | NeSy and ABL methods · MNIST-Addition | GAcc | Helped |
| Use Hamming distance instead of the trivial distance (ablation) | ABL · MNIST-Addition, AVG | GAcc (%): 54.04±37.77 -> 51.79±35.04 | Hurt |
| Use the current model's confidence as the distance function instead of the trivial distance (ablation) | ABL · MNIST-Addition, AVG | GAcc (%): 54.04±37.77 -> 57.97±20.52 | Helped |
| Use a fixed pre-trained model's confidence as the distance function instead of the trivial distance (ablation) | ABL · MNIST-Addition, AVG | GAcc (%): 54.04±37.77 -> 98.57±0.10 | Helped |
| Use Hamming distance instead of the trivial distance (ablation) | ABL · BDD-OIA | GAcc: 76.96 ± 0.04 -> 76.94 ± 0.07 | No clear effect |
| Use Hamming distance instead of the trivial distance (ablation) | ABL · BDD-OIA | Acc: 75.17 ± 0.18 -> 75.31 ± 0.21 | No clear effect |
| Use the current model's confidence as the distance function instead of the trivial distance (ablation) | ABL · BDD-OIA | GAcc: 76.96 ± 0.04 -> 78.54 ± 1.43 | Helped |
| Use the current model's confidence as the distance function instead of the trivial distance (ablation) | ABL · BDD-OIA | Acc: 75.17 ± 0.18 -> 75.30 ± 0.12 | No clear effect |
| Use a fixed pre-trained model's confidence as the distance function instead of the trivial distance (ablation) | ABL · BDD-OIA | GAcc: 76.96 ± 0.04 -> 85.13 ± 0.15 | Helped |
| Use a fixed pre-trained model's confidence as the distance function instead of the trivial distance (ablation) | ABL · BDD-OIA | Acc: 75.17 ± 0.18 -> 74.03 ± 0.10 | Hurt |
Surprising findings
- ABL(C), the confidence-based distance adapted from prior work, performs worse than the trivial distance on the hardest MNIST-Addition levels, with GAcc of 4.04% at level VI.
Limitations
- Theoretical bounds rely on assumptions on hypothesis space (label smoothness or pre-training), which may not hold in practice.
- Experiments are small-scale (MNIST-Addition and BDD-OIA) and the knowledge base complexity is only empirically estimated from training data.
- Future work noted: extending complexity to higher-order knowledge bases and studying sample distribution effects.
Experimental setup
Datasets: MNIST-Addition BDD-OIA MNIST
Benchmarks: MNIST-Addition BDD-OIA
Metrics: grid accuracy (GAcc) accuracy (Acc)
Baselines: semantic loss DeepProbLog LTN ABL ABL(C) ABL(H) ABL(P) ABL+L ABL+P
Builds on: abductive learning DeepProbLog semantic loss Marconato et al. 2023 reasoning shortcuts Huang et al. 2021 ABL similarity-based consistency
Closest papers by meaning
- Efficient Rectification of Neuro-Symbolic Reasoning Inconsistencies by Abductive Reflection (AAAI 2025 · similarity 0.90)
- Shortcuts and Identifiability in Concept-based Models from a Neuro-Symbolic Lens (NeurIPS 2025 · similarity 0.89)
- Curriculum Abductive Learning (NeurIPS 2025 · similarity 0.89)
- Right for the Right Reasons: Avoiding Reasoning Shortcuts via Prototypical Neurosymbolic AI (NeurIPS 2025 · similarity 0.88)
- A Neuro-Symbolic Benchmark Suite for Concept Quality and Reasoning Shortcuts (NeurIPS 2024 · similarity 0.88)
- Ambiguity-Aware Abductive Learning (ICML 2024 · similarity 0.87)
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