Concept bottleneck models for interpretable variable star classification with Gaia DR3

Context. Gaia Data Release 3 catalogs variability indicators for 12.4 million sources, of which ∼10 million were assigned to 25 variability types by a random forest pipeline that provides no per-prediction explanation. Trustworthy catalog construction demands both accuracy and interpretability. Aims. We present, to our knowledge, the first peer-reviewed application of concept bottleneck models (CBMs) to astronomical source classification, which routes every prediction through a layer of human-interpretable physical concepts that astronomers can inspect, verify, and override. Methods. Using 18,000 balanced Gaia DR3 sources across six variability classes, we trained eight architectures operating on 12 physically meaningful concepts (𝐱=𝐜; 11 effective in the catalog setting) and evaluated them with five-fold cross-validation, Nadeau--Bengio corrected t-tests, and Holm--Bonferroni correction. An end-to-end variant (EndToEndHardCBM) learns concepts directly from phase-folded light curves. Results. The HardCBM variant achieves a 94.4±0.4% accuracy, versus 99.8±0.1% for random forest and XGBoost; the 5.4,pp gap is the cost of an architectural guarantee that the model depends only on the named concepts. Concept intervention under sigma = 1.0 noise identifies R_31, period, and period_snr as the highest-value correction targets by per-concept sensitivity ranking. The EndToEndHardCBM model achieves a 92.9±1.4% accuracy but recovers only 73.7% of lost accuracy when all concepts are corrected to ground truth, confirming that its learned concept representation diverges from physical values. Pulsator-only ablation shows the period as the dominant discriminator (-6.58,pp), with R_31 second (-2.78,pp); in the full six-class setting, R_31 ranks first, but randomizing the imputation pattern of R_21, R_31, φ_21 for nonpulsators lowers overall accuracy by 1.1,pp while leaving R_31's leave-one-out importance (∼ 2,pp) statistically unchanged---its role is genuine Fourier physics. Conclusions. Concept bottleneck models provide a viable framework for interpretable astronomical classification. Cross-survey evaluation on OGLE-IV revealed severe domain shift (Kolmogorov--Smirnov statistic $>0.7$ for 3/12 concepts), but the concept layer directly enables per-concept diagnosis of which concepts fail to transfer, thus providing a guide for targeted follow-up.