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In the early 2000s, low dimensional ferroelectric systems were predicted to have topologically nontrivial polar structures, such as vortices or skyrmions, depending on mechanical or electrical boundary conditions. A few variants of these structures have been experimentally observed in thin film model systems, where they are engineered by balancing electrostatic charge and elastic distortion energies. However, the measurement and classification of topological textures for general ferroelectric nanostructures have remained elusive, as it requires mapping the local polarization at the atomic scale in three dimensions. Here we unveil topological polar structures in ferroelectric BaTiO3 nanoparticles via atomic electron tomography, which enables us to reconstruct the full three-dimensional arrangement of cation atoms at an individual atom level. Our three-dimensional polarization maps reveal clear topological orderings, along with evidence of size-dependent topological transitions from a single vortex structure to multiple vortices, consistent with theoretical predictions. The discovery of the predicted topological polar ordering in nanoscale ferroelectrics, independent of epitaxial strain, widens the research perspective and offers potential for practical applications utilizing contact-free switchable toroidal moments.

Convolutional Neural Networks (CNNs) are pivotal in modern digital computing, particularly for tasks like image classification, inspired by the receptive fields of the human brain. Nevertheless, CNNs implemented on conventional digital computers face significant limitations due to inflexible kernels that cannot adjust to dynamic inputs, and the von Neumann architecture, which leads to inefficient data transfer between memory and processing units. This research presents a hardware‐software co‐designed solution, a Dynamic Convolutional Neural Network (dCNN), empowered by three‐terminal adaptive two‐dimensional (2D) memristors. These memristors consist of a vertical heterostructure integrating silver, an atomically thin insulator (CrPS4), and graphene as a semimetal. This configuration allows for the dynamic tuning of conductive filament properties, emulating the heterosynaptic plasticity observed in biological neural systems. The three‐terminal memristor design permits the dCNN to actively adjust kernel weights in its attention layer according to the input stimuli. The empirical tests demonstrate that image classification accuracy using our adaptive 2D memristor‐enhanced dVGG reaches up to 94% on the CIFAR‐10 dataset, which exceeds the performance of static VGG. Furthermore, the energy efficiency of our dVGG significantly outperforms that of GPUs, aligning more closely with the energy dynamics of the human brain in terms of both consumption and classification accuracy. [ABSTRACT FROM AUTHOR]