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Shortcuts and Identifiability in Concept-based Models from a Neuro-Symbolic Lens
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Extends reasoning shortcuts to concept-based models with learned inference layers, defines intended semantics and joint reasoning shortcuts, proves identifiability conditions, and empirically shows that existing supervised and unsupervised mitigations largely fail on MNIST-based, Clevr and BDD-OIA tasks.
Problem
Concept-based models trained by maximum likelihood may learn low-quality concepts and inference layers even when labels are accurate, harming interpretability and out-of-distribution behavior; it is unclear when concepts and the inference layer can be identified.
Approach
Generalizes reasoning shortcuts from fixed-knowledge neuro-symbolic models to concept-based models whose inference layer is learned, defines intended semantics up to permutation and invertible transformations, and shows that zero deterministic joint reasoning shortcuts implies identifiability under extremality and the data-generation assumptions.
Key results
- On MNIST-SumParity, all tested models reach F1(Y) of at least 0.90 but F1(C) never exceeds 0.50, indicating lack of intended semantics.
- On the biased MNIST-SumParity OOD split, only CBNM with full concept and knowledge supervision attains acceptable OOD F1(Y), while other models have F1(Y) at or below 0.40.
- Across mitigations on MNIST-SumParity and Clevr, reconstruction, entropy and knowledge supervision bring no benefit to concept or knowledge quality; only contrastive learning reduces concept collapse.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Remove the entropy term (ablation) | CBNM · MNIST-Add | F1(C): 0.99 ± 0.01 -> 0.74 ± 0.13 | Hurt |
| Remove the entropy term (ablation) | CBNM · MNIST-Add | F1(β): 1.00 ± 0.01 -> 0.37 ± 0.09 | Hurt |
| Remove the entropy term (ablation) | CBNM · MNIST-SumParity | F1(Y): 0.90 ± 0.18 -> 0.98 ± 0.01 | Helped |
| Remove the entropy term (ablation) | CBNM · MNIST-SumParity | F1(C): 0.09 ± 0.03 -> 0.08 ± 0.02 | No clear effect |
| Apply complete concept and knowledge supervision | CBNM · Biased MNIST-SumParity OOD | F1(Y): 0.01 ± 0.01 -> 0.97 ± 0.02 | Helped |
| Add complete knowledge supervision without concept supervision | CBNM · Biased MNIST-SumParity OOD | F1(Y): 0.01 ± 0.01 -> 0.01 ± 0.01 | No clear effect |
| Add concept supervision without knowledge supervision | CBNM · Biased MNIST-SumParity OOD | F1(Y): 0.01 ± 0.01 -> 0.40 ± 0.14 | Helped |
| Add contrastive learning | CBNM · MNIST-SumParity | concept collapse | Helped |
| Add reconstruction, entropy maximization, and contrastive learning | CBNM · MNIST-SumParity | F1(C) | No clear effect |
Surprising findings
- Even with full ground-truth knowledge supplied (DPL), the model collapses concepts, showing that fixed knowledge does not prevent shortcuts in this setting.
- Combining all unsupervised mitigations (H+R+C) brings no benefit for concept or knowledge quality on MNIST-SumParity.
Limitations
- Theory relies on deterministic knowledge and extrapolability assumptions and on the extremality assumption, which does not hold for general CBMs.
- Experiments are limited to small or synthetic vision tasks and a single real-world dataset (BDD-OIA); no large-scale or language settings were tested.
- Some baselines (DSL, DPL*, bears*) could not be run on BDD-OIA due to scalability constraints.
Experimental setup
Datasets: MNIST-Add MNIST-SumParity Clevr BDD-OIA
Benchmarks: MNIST-Add MNIST-SumParity Clevr BDD-OIA
Metrics: F1(Y) F1(C) concept collapse F1(beta) accuracy NLL
Baselines: DeepProbLog CBNM DSL DPL* bears* SENN
Builds on: reasoning shortcuts DeepProbLog BEARS Deep Symbolic Learning Concept Bottleneck Models SENN
Closest papers by meaning
- A Neuro-Symbolic Benchmark Suite for Concept Quality and Reasoning Shortcuts (NeurIPS 2024 · similarity 0.90)
- Analysis for Abductive Learning and Neural-Symbolic Reasoning Shortcuts (ICML 2024 · similarity 0.89)
- Right for the Right Reasons: Avoiding Reasoning Shortcuts via Prototypical Neurosymbolic AI (NeurIPS 2025 · similarity 0.88)
- Concise and Logically Consistent Conformal Sets for Neuro-Symbolic Concept-Based Models (NeurIPS 2026 · similarity 0.87)
- Nonparametric Identification of Latent Concepts (ICML 2025 · similarity 0.86)
- Concept Modulation Models: A Unified Framework for Identifiability and Extrapolation (NeurIPS 2026 · similarity 0.86)
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