Diagnosing Shortcut-Induced Rigidity in Continual Learning: The Einstellung Rigidity Index (ERI)

Deep neural networks frequently exploit shortcut features, defined as incidental correlations between inputs and labels without causal meaning. Shortcut features undermine robustness and reduce reliability under distribution shifts. In continual learning (CL), the consequences of shortcut exploitation can persist and intensify: weights inherited from earlier tasks bias representation reuse toward whatever features most easily satisfied prior labels, mirroring the cognitive Einstellung effect, a phenomenon where past habits block optimal solutions. Whereas catastrophic forgetting erodes past skills, shortcut-induced rigidity throttles the acquisition of new ones. We introduce the Einstellung Rigidity Index (ERI), a compact diagnostic that disentangles genuine transfer from cue-inflated performance using three interpretable facets: (i) Adaptation Delay (AD), (ii) Performance Deficit (PD), and (iii) Relative Suboptimal Feature Reliance (SFR_rel). On a two-phase CIFAR-100 CL benchmark with a deliberately spurious magenta patch in Phase 2, we evaluate Naive fine-tuning (SGD), online Elastic Weight Consolidation (EWC_on), Dark Experience Replay (DER++), Gradient Projection Memory (GPM), and Deep Generative Replay (DGR). Across these continual learning methods, we observe that CL methods reach accuracy thresholds earlier than a Scratch-T2 baseline (negative AD) but achieve slightly lower final accuracy on patched shortcut classes (positive PD). Masking the patch improves accuracy for CL methods while slightly reducing Scratch-T2, yielding negative SFR_rel. This pattern indicates the patch acted as a distractor for CL models in this setting rather than a helpful shortcut.

Deep Learning Models for Colloidal Nanocrystal Synthesis

Colloidal synthesis of nanocrystals usually includes complex chemical reactions and multi-step crystallization processes. Despite the great success in the past 30 years, it remains challenging to clarify the correlations between synthetic parameters of chemical reaction and physical properties of nanocrystals. Here, we developed a deep learning-based nanocrystal synthesis model that correlates synthetic parameters with the final size and shape of target nanocrystals, using a dataset of 3500 recipes covering 348 distinct nanocrystal compositions. The size and shape labels were obtained from transmission electron microscope images using a segmentation model trained with a semi-supervised algorithm on a dataset comprising 1.2 million nanocrystals. By applying the reaction intermediate-based data augmentation method and elaborated descriptors, the synthesis model was able to predict nanocrystal's size with a mean absolute error of 1.39 nm, while reaching an 89% average accuracy for shape classification. The synthesis model shows knowledge transfer capabilities across different nanocrystals with inputs of new recipes. With that, the influence of chemicals on the final size of nanocrystals was further evaluated, revealing the importance order of nanocrystal composition, precursor or ligand, and solvent. Overall, the deep learning-based nanocrystal synthesis model offers a powerful tool to expedite the development of high-quality nanocrystals.