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Curriculum Abductive Learning
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Proposes Curriculum Abductive Learning (C-ABL), which partitions an ABL knowledge base into progressively introduced sub-bases to shrink the abduction space and stabilize training.
Problem
Abductive learning training is unstable and slow when the knowledge base is large, because nondeterministic abduction yields a prohibitively large candidate space; prior work only improved candidate selection while treating the knowledge base as a black box.
Approach
Build a dependency graph over knowledge-base rules, cluster rules by concept label, order clusters topologically, and introduce the resulting sub-bases in curriculum phases so that the abduction space is limited to newly introduced concepts in each phase.
Key results
- On hexadecimal addition d=3, C-ABL reaches 66.67% accuracy versus 64.14% for ABL and 65.81% for A3BL.
- On decimal addition d=4, C-ABL trains in 132.6 minutes versus 253.6 for ABL and 291.2 for A3BL.
- On judicial sentencing with 50% labeled data, C-ABL improves F1 from 0.910 to 0.920 and lowers MSE from 0.874 to 0.773 relative to ABL.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use curriculum sub-bases instead of the full knowledge base from the beginning | ABL on decimal addition · Decimal addition d=2 | prediction accuracy: 75.62 -> 76.74 | Helped |
| Use curriculum sub-bases instead of the full knowledge base from the beginning | ABL on decimal addition · Decimal addition d=3 | prediction accuracy: 74.65 -> 77.65 | Helped |
| Use curriculum sub-bases instead of the full knowledge base from the beginning | ABL on decimal addition · Decimal addition d=4 | total training time (minutes): 253.6 -> 132.6 | Helped |
| Use curriculum sub-bases instead of the full knowledge base from the beginning | ABL on hexadecimal addition · Hexadecimal addition d=1 | prediction accuracy: 60.87 -> 63.02 | Helped |
| Use curriculum sub-bases instead of the full knowledge base from the beginning | ABL on hexadecimal addition · Hexadecimal addition d=3 | total training time (minutes): 99.7 -> 55.5 | Helped |
| Use curriculum sub-bases instead of the full knowledge base from the beginning | ABL on decimal addition · Decimal addition d=1 | prediction accuracy: 72.06 -> 71.77 | Hurt |
| Use curriculum sub-bases instead of the full knowledge base from the beginning | ABL on decimal addition · Decimal addition d=1 | total training time (minutes): 12.6 -> 16.2 | Hurt |
| Use curriculum sub-bases instead of the full knowledge base from the beginning | ABL on judicial sentencing · Judicial sentencing, 10% labeled data | F1: 0.895 -> 0.904 | Helped |
| Use curriculum sub-bases instead of the full knowledge base from the beginning | ABL on judicial sentencing · Judicial sentencing, 10% labeled data | MAE: 0.762 -> 0.762 | No clear effect |
| Use curriculum sub-bases instead of the full knowledge base from the beginning | ABL on judicial sentencing · Judicial sentencing, 50% labeled data | MAE: 0.773 -> 0.722 | Helped |
| Use curriculum sub-bases instead of the full knowledge base from the beginning | ABL on judicial sentencing · Judicial sentencing, 50% labeled data | F1: 0.910 -> 0.920 | Helped |
Surprising findings
- A3BL scores 22.45% on hexadecimal addition d=1, far below ABL (60.87%), indicating instability of that baseline.
Limitations
- Assumes the knowledge base has modular or staged structure; densely entangled rule sets may benefit less.
- Phase transitions use a fixed structural partition and a simple accuracy threshold rather than an adaptive schedule.
- Requires a pre-defined, human-curated knowledge base.
Experimental setup
Datasets: CIFAR-10 CIFAR-100 MNIST judicial sentencing dataset (687 records)
Benchmarks: d-digit decimal addition hexadecimal addition chess attack judicial sentencing
Metrics: accuracy total training time (minutes) F1 MAE MSE tokens to converge
Baselines: ABL A3BL NeurASP DeepProbLog DeepStochLog LTN
Builds on: Abductive Learning A3BL curriculum learning DeepProbLog
Closest papers by meaning
- Ambiguity-Aware Abductive Learning (ICML 2024 · similarity 0.89)
- Analysis for Abductive Learning and Neural-Symbolic Reasoning Shortcuts (ICML 2024 · similarity 0.89)
- Safe Abductive Learning in the Presence of Inaccurate Rules (AAAI 2024 · similarity 0.86)
- Efficient Rectification of Neuro-Symbolic Reasoning Inconsistencies by Abductive Reflection (AAAI 2025 · similarity 0.85)
- Consistency-based Abductive Reasoning over Perceptual Errors of Multiple Pre-trained Models in Novel Environments (AAAI 2026 · similarity 0.84)
- Improving Complex Reasoning over Knowledge Graph with Logic-Aware Curriculum Tuning (AAAI 2025 · similarity 0.83)
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