Sparse autoencoders have recently produced dictionaries of high-dimensional vectors corresponding to the universe of concepts represented by large language models. We find that this concept universe has interesting structure at three levels: 1) The "atomic" small-scale structure contains "crystals" whose faces are parallelograms or trapezoids, generalizing well-known examples such as (man-woman-king-queen). We find that the quality of such parallelograms and associated function vectors improves greatly when projecting out global distractor directions such as word length, which is efficiently done with linear discriminant analysis. 2) The "brain" intermediate-scale structure has significant spatial modularity; for example, math and code features form a "lobe" akin to functional lobes seen in neural fMRI images. We quantify the spatial locality of these lobes with multiple metrics and find that clusters of co-occurring features, at coarse enough scale, also cluster together spatially far more than one would expect if feature geometry were random. 3) The "galaxy" scale large-scale structure of the feature point cloud is not isotropic, but instead has a power law of eigenvalues with steepest slope in middle layers. We also quantify how the clustering entropy depends on the layer.

Knowledge tracing aims to model students' past answer sequences to track the change in their knowledge acquisition during exercise activities and to predict their future learning performance. Most existing approaches ignore the fact that students' abilities are constantly changing or vary between individuals, and lack the interpretability of model predictions. To this end, in this paper, we propose a novel model based on ability attributes and attention mechanism. We first segment the interaction sequences and captures students' ability attributes, then dynamically assign students to groups with similar abilities, and quantify the relevance of the exercises to the skill by calculating the attention weights between the exercises and the skill to enhance the interpretability of the model. We conducted extensive experiments and evaluate real online education datasets. The results confirm that the proposed model is better at predicting performance than five well-known representative knowledge tracing models, and the model prediction results are explained through an inference path.