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Concept frustration: Aligning human concepts and machine representations
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Introduces concept frustration, a task-aligned Fisher-geometry diagnostic that detects when an unobserved concept induces contradictions among known concepts in a concept bottleneck model, validated on synthetic data and sarcasm and gull-vs-tern tasks.
Problem
Concept bottleneck models with incomplete ontologies lose accuracy and interpretability, and existing Euclidean comparisons between supervised concepts and SAE features fail to detect when a missing concept is needed.
Approach
Defines concept frustration as a sign contradiction among a triplet of two known concept directions and one unsupervised SAE direction, measured under a task-aligned Fisher information metric of a one-hidden-layer black-box classifier, with a closed-form Bayes-optimal CBM accuracy under a linear-Gaussian model.
Key results
- In the treasure hunter task, task-aligned frustration is higher on the round Earth than the flat Earth (paired Wilcoxon p=5.94e-3), while Euclidean frustration does not distinguish them (p=0.118).
- On synthetic data, CBM accuracy under frustrated regime (alpha=+1) is 0.699 vs 0.718 under consistent regime (alpha=-1), p<1e-4, while black-box accuracy is unchanged (p=0.132).
- Across sarcasm and CUB tasks, Fisher frustration of the (C1,C2) pair is higher for CBM1 than CBM2 (p=0.0488), whereas Euclidean frustration shows no difference.
Surprising findings
- Euclidean frustration does not detect frustration at all, even when the task-aligned metric does.
- Black-box accuracy does not drop under frustration, so frustration limits the CBM specifically rather than task difficulty.
Limitations
- Theory relies on a linear-Gaussian generative model, which may not hold for real representations.
- Pairwise frustration depends on choosing a maximally frustrating SAE direction, a heuristic choice.
- Task-aligned geometry is derived from a simple one-hidden-layer classifier, which may not generalise to richer models.
Experimental setup
Datasets: News Headlines sarcasm dataset CUB-200-2011 synthetic linear-Gaussian data
Benchmarks: News Headlines sarcasm CUB gull-tern synthetic treasure hunter
Metrics: accuracy global frustration pairwise frustration concept MSE semantic fidelity beta
Baselines: Euclidean similarity frustration black-box MLP sparse autoencoder
Builds on: concept bottleneck models sparse autoencoders
Closest papers by meaning
- Towards a learning theory of representation alignment (ICLR 2025 · similarity 0.86)
- Nonparametric Identification of Latent Concepts (ICML 2025 · similarity 0.85)
- Understanding Inter-Concept Relationships in Concept-Based Models (ICML 2024 · similarity 0.85)
- From Causal to Concept-Based Representation Learning (NeurIPS 2024 · similarity 0.85)
- Interpretable but Fragile? Robustness of Concept Bottlenecks under Geometric-Semantic Perturbations (NeurIPS 2026 · similarity 0.85)
- Beyond Scalars: Concept-Based Alignment Analysis in Vision Transformers (NeurIPS 2025 · similarity 0.85)
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