Unraveling the Size Determination Mechanism of Nanocrystal Synthesis via Interpretable Neural Networks

Deep learning models of nanocrystal synthesis enable the prediction of size and shape by encoding precursors and reaction conditions. However, their black-box nature hinders gaining deep insights into the underlying synthetic mechanisms. Here, we develop the Nanocrystal Equation Learner (NanoEQL), a fully white-box neural network to unravel the size determination mechanisms of nanocrystal synthesis. Building on the EQL architecture, eight operators are introduced to replace standard activation functions to fit the mathematical equations in nanocrystal synthesis. Among these operators, three smoothed operators address the gradient explosion of singular operators at zero. To evaluate the weights of different precursors, we develop a temperature-gated attention pooling strategy that encodes concentration-driven and reactivity-driven chemical synthesis mechanisms into the temperature gate. The NanoEQL model illustrates that the final nanocrystal size can be described by a linear equation composed of three scalars representing nanocrystallization capability (-Zp), growth capability (Zrea), and external input potential (-Zops). These interpretable scalars not only advance the rational design of nanocrystal synthesis but also establish a generalizable paradigm for deciphering chemical reaction mechanisms through white-box machine learning.

Answering Without Referring: How AI Search Rewrites the Web's Economic Bargain

Search engines have long allocated attention on the web by routing users from queries to websites. AI search changes this arrangement because information needs can be resolved inside the intermediary. Using URL-level Comscore U.S. desktop clickstream, we compare ChatGPT and Google information-seeking occasions and exploit ChatGPT Search access expansions to estimate traditional search displacement. ChatGPT produces outbound clicks in only 5.2% of conversation sessions, far below Google's referral ratio. The remaining clicks are not a scaled-down Google stream: they skew toward specialized destinations and away from ad-supported sites. Wider access cuts search use by 9.4%, with search-referral losses largest for informational categories. Our findings identify a central economic shift in digital intermediation: AI search might satisfy information needs inside the intermediary while weakening the referral bargain that has linked search, traffic, and content production on the open web.

A large-scale nanocrystal database with aligned synthesis and properties enabling generative inverse design

The synthesis of nanocrystals has been highly dependent on trial-and-error, due to the complex correlation between synthesis parameters and physicochemical properties. Although deep learning offers a potential methodology to achieve generative inverse design, it is still hindered by the scarcity of high-quality datasets that align nanocrystal synthesis routes with their properties. Here, we present the construction of a large-scale, aligned Nanocrystal Synthesis-Property (NSP) database and demonstrate its capability for generative inverse design. To extract structured synthesis routes and their corresponding product properties from literature, we develop NanoExtractor, a large language model (LLM) enhanced by well-designed augmentation strategies. NanoExtractor is validated against human experts, achieving a weighted average score of 88% on the test set, significantly outperforming chemistry-specialized (3%) and general-purpose LLMs (38%). The resulting NSP database contains nearly 160,000 aligned entries and serves as training data for our NanoDesigner, an LLM for inverse synthesis design. The generative capability of NanoDesigner is validated through the successful design of viable synthesis routes for both well-established PbSe nanocrystals and rarely reported MgF2 nanocrystals. Notably, the model recommends a counter-intuitive, non-stoichiometric precursor ratio (1:1) for MgF2 nanocrystals, which is experimentally confirmed as critical for suppressing byproducts. Our work bridges the gap between unstructured literature and data-driven synthesis, and also establishes a powerful human-AI collaborative paradigm for accelerating nanocrystal discovery.

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.