Despite the potential of differentially private data visualization to harmonize data analysis and privacy, research in this area remains underdeveloped. Boxplots are a widely popular visualization used for summarizing a dataset and for comparison of multiple datasets. Consequentially, we introduce a differentially private boxplot. We evaluate its effectiveness for displaying location, scale, skewness and tails of a given empirical distribution. In our theoretical exposition, we show that the location and scale of the boxplot are estimated with optimal sample complexity, and the skewness and tails are estimated consistently, which is not always the case for a boxplot naively constructed from a single existing differentially private quantile algorithm. As a byproduct of this exposition, we introduce several new results concerning private quantile estimation. In simulations, we show that this boxplot performs similarly to a non-private boxplot, and it outperforms the naive boxplot. Additionally, we conduct a real data analysis of Airbnb listings, which shows that comparable analysis can be achieved through differentially private boxplot visualization.

Human cognition is punctuated by abrupt, spontaneous shifts between topics—driven by emotional, contextual, or associative cues—a phenomenon known as spontaneous thought in neuroscience. In contrast, self-attention-based models rely on structured patterns over their inputs to predict each next token, lacking spontaneity. Motivated by this distinction, we characterize *spontaneous topic changes* in self-attention architectures and reveal divergences from *spontaneous human thought*. First, we establish theoretical results under a simplified, single-layer self-attention model with suitable conditions by defining a topic as a set of Token Priority Graphs (TPGs). Specifically, we demonstrate that (1) the model maintains the priority order of tokens related to the input topic, (2) a spontaneous topic change can occur only if lower-priority tokens outnumber all higher-priority tokens of the input topic, and (3) unlike human cognition, the longer context length or the more ambiguous input topic does not increase the likelihood of spontaneous change. Second, we empirically validate that the effect of input length or topic ambiguity persists in modern, state-of-the-art LLMs, underscoring a fundamental disparity between human cognition and AI behavior in the context of spontaneous topic changes. To the best of our knowledge, no prior work has explored these questions with a focus so closely aligned to human thought.