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Imbalances in Neurosymbolic Learning: Characterization and Mitigating Strategies
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Characterizes class-specific learning imbalances in neurosymbolic learning caused by the symbolic component, and proposes marginal estimation plus LP-based training-time (ILP) and RSOT-based testing-time (CAROT) imbalance mitigation.
Problem
Neurosymbolic learning from weak labels produced by a symbolic function over hidden gold labels suffers class-specific learning imbalances, which existing long-tailed learning theory and methods do not capture or handle, since the hidden label marginal is unknown.
Approach
Shows theoretically that the symbolic component sigma itself induces class-specific risk imbalances even with uniform hidden labels; estimates the hidden label marginal from weak labels via polynomial system fitting; mitigates imbalance at training time via a batch linear program producing pseudolabels constrained by the marginal, and at testing time via robust semi-constrained optimal transport (
Key results
- CAROT on top of RECORDS raises SMALLESTPARENT (rho=15) accuracy from 50.14% to 71.70%.
- ILP(GOLD) raises SL accuracy on MAX-4 (rho=0) from 55.48% to 78.56% (reported in text as 78.56% vs 55.48%).
- Imbalance-mitigated models yield gains of up to 14% over strong NSL and long-tailed baselines.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use ILP training-time mitigation instead of training with SL alone | Neurosymbolic classifiers · MAX-M (M=4, LT ρ=5) | accuracy: 55.48 ± 23.23 -> 78.56 ± 1.52 | Helped |
| Use ILP training-time mitigation instead of training with SL alone | Neurosymbolic classifiers · SMALLESTPARENT (LT ρ=5) | accuracy: 67.94% -> 79.24%; 67.94% -> 81.27% | Helped |
| Train with RECORDS and SL instead of SL alone | Neurosymbolic classifiers · SMALLESTPARENT (LT ρ=5) | accuracy: 67.94% -> 48.15% | Hurt |
| Use ILP (EMP) instead of SL alone | Neurosymbolic classifiers · MAX-M (M=3, LT ρ=50) | accuracy: 66.74% -> 77.16% | Helped |
| Use EMP ratios rather than gold ratios for ILP training | ILP · MAX-M (M=3, LT ρ=50) | accuracy: 73.39 ± 9.35 -> 77.16 ± 3.46 | Helped |
| Use gold ratios rather than EMP ratios for ILP training | ILP · SMALLESTPARENT (LT ρ=5) | accuracy: 79.24 ± 1.03 -> 81.27 ± 0.71 | Helped |
| Apply CAROT at test time to ILP (EMP) | ILP (EMP) · SMALLESTPARENT (LT ρ=50) | accuracy: 70.29% -> 80.71% | Helped |
| Apply Logit Adjustment at test time to ILP (EMP) | ILP (EMP) · SMALLESTPARENT (LT ρ=50) | accuracy: 70.29 ± 1.62 -> 70.29 ± 1.62 | No clear effect |
| Apply CAROT at test time to RECORDS | RECORDS · SMALLESTPARENT (LT ρ=15) | accuracy: 50.14% -> 71.70% | Helped |
| Apply CAROT at test time to RECORDS | RECORDS · SMALLESTPARENT (LT ρ=5) | accuracy: 48.15 ± 4.56 -> 69.04 ± 0.74 | Mixed |
| Apply CAROT at test time to a baseline model | SL and other baseline classifiers · SMALLESTPARENT (LT ρ=5) | accuracy | Mixed |
| Use CAROT with less accurate estimated label ratios | CAROT · MAX-3 test-time evaluation | accuracy: more than 10% | Hurt |
Surprising findings
- Symbolic component sigma can cause class-specific learning imbalances even when hidden labels are uniform.
- Applying RECORDS jointly with semantic loss can drop accuracy substantially (e.g., 67.94% to 48.15% on SMALLESTPARENT rho=5).
Limitations
- Theory assumes class-dependent misclassification probability and i.i.d. instances (M=2 analysis).
- CAROT is sensitive to the quality of the estimated marginal; can fail to improve base models.
- ILP training may be NP-hard per batch and pre-image enumeration is costly; MAX-M experiments only use a subset of pre-images.
Experimental setup
Datasets: MNIST CIFAR-10 HWF
Benchmarks: MAX-3 MAX-4 MAX-5 SMALLESTPARENT
Metrics: balanced accuracy class-specific accuracy
Baselines: SL SL + LA RECORDS RECORDS + LA ILP (GOLD) ILP (EMP)
Builds on: semantic loss Logit Adjustment RECORDS robust semi-constrained optimal transport Scallop
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