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Ambiguity-Aware Abductive Learning
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Proposes A3BL, which weights all abduced candidates by model-derived probabilities and trains via an EM-style ambiguity-aware loss, improving abductive learning on digit addition and handwritten formula tasks.
Problem
Abductive learning produces ambiguous sets of candidate labels from background knowledge, and prior methods pick a single candidate (by Hamming distance or confidence) that can be wrong, trapping the perception model in sub-optimal solutions, especially under cold start.
Approach
Instead of selecting one abduced candidate, A3BL assigns each candidate a posterior weight from the perception model and minimizes the weighted cross-entropy over all candidates; this is shown to equal an EM procedure maximizing the knowledge-base likelihood, with an estimation error bound.
Key results
- On Addition-CIFAR n=1, A3BL reaches 72.82±0.95% test accuracy vs 68.42±1.79% for ABL-conf and 26.56±11.67% for ABL-hamming on Addition-SVHN n=1 ABL-hamming is 26.56% while A3BL reaches 91.86%.
- A3BL's abduction accuracy approaches 1 within 10 epochs on digit addition, whereas ABL-hamming and ABL-conf fail to identify the correct candidate.
- A3BL's per-epoch training time is comparable to ABL (e.g., 27m20s vs 23m12s on Addition-CIFAR n=3).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use A3BL instead of DeepStochLog | Digit addition with SVHN · Addition-SVHN, n=1–4 | test accuracy: 91.61±0.27 -> 91.86±0.86 (n=1); 90.81±0.52 -> 91.81±0.87 (n=2); 90.28±0.35 -> 92.49±0.37 (n=3); 90.92±0.75 -> 91.99±0.46 | Helped |
| Use A3BL instead of DeepStochLog | Digit addition with CIFAR10 · Addition-CIFAR, n=1–4 | test accuracy: 66.32±0.72 -> 72.82±0.95 (n=1); 67.63±1.45 -> 76.09±0.18 (n=2); 65.55±0.87 -> 74.45±0.37 (n=3); 66.38±1.28 -> 72.57±1.22 | Helped |
| Use A3BL instead of ABL-hamming | Digit addition with SVHN and CIFAR10 · Addition-SVHN and Addition-CIFAR | test accuracy | Helped |
| Use A3BL instead of ABL-conf | Digit addition with SVHN and CIFAR10 · Addition-SVHN and Addition-CIFAR | test accuracy | Helped |
| Use A3BL instead of ABL variants | Handwritten formula recognition · HWF, HWF-CIFAR, and HWF-SVHN | accuracy | Helped |
| Use A3BL instead of NGS variants | Handwritten formula recognition · HWF, HWF-CIFAR, and HWF-SVHN | accuracy | Helped |
| Increase top-k candidate selection from a small value to a moderate value (e.g., k=8) (ablation) | A3BL · Addition-CIFAR, n=3 and n=4 | abduction accuracy | Helped |
| Increase top-k candidate selection beyond a moderate value (ablation) | A3BL · Addition-CIFAR, n=3 and n=4 | test accuracy | No clear effect |
| Use A3BL rather than ABL | Digit addition on CIFAR10 · Addition-CIFAR, n=1–4, 5 epochs | execution time: 14m 4s -> 14m 5s; 17m 15s -> 19m 42s; 23m 12s -> 27m 20s; 1h 3m 58s -> 1h 8m 49s | Hurt |
Surprising findings
- ABL-conf shows a shortcut pattern in its worst run where reasoning accuracy rises while concept accuracy falls.
- DeepProbLog and NeurASP fail to exceed random guessing on digit addition and some settings did not finish one epoch in 48 hours.
Limitations
- Candidate set size grows exponentially with digit size and knowledge-base complexity, which can overburden learning.
- Requires a knowledge base; if the knowledge base is weak, the candidate set approaches the universal set.
- Top-k approximation of candidates is a heuristic chosen without extensive tuning (temperature 0.3, k=32).
Experimental setup
Datasets: MNIST KMNIST CIFAR10 SVHN CROHME 2019 HWF
Benchmarks: Digit Addition (MNIST, KMNIST, CIFAR10, SVHN variants, n=1 to 4) Handwritten Formula Recognition (HWF, HWF-CIFAR, HWF-SVHN)
Metrics: test accuracy abduction accuracy reasoning accuracy concept accuracy execution time
Baselines: ABL-hamming ABL-conf DeepProbLog DeepStochLog NeurASP NGS-BS NGS-RL NGS-MAPO
Builds on: Abductive Learning DeepProbLog Neural-Grammar-Symbolic
Closest papers by meaning
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