Queryable Self-Organizing Maps: A Database Abstraction for Topology-Driven Data Exploration

While UMAP is widely used for exploring high-dimensional data, typical workflows focus on its lower-dimensional embedding, largely overlooking the rich k-nearest-neighbor (kNN) graph that UMAP constructs internally. This graph encodes the data manifold in its original high-dimensional space, before the distortion that UMAP's 2D projection introduces. We demonstrate the untapped potential of this internal representation, showing how standard graph algorithms applied to this graph enhance data sensemaking: (1) PageRank identifies representative data points, (2) k-core decomposition reveals dense core regions versus sparse periphery, and (3) clustering coefficient detects tight-knit neighborhoods with highly-similar data points. Through quantitative and qualitative evaluation on MNIST and Fashion MNIST, we show that these graph-based analyses are not only practical but also competitive with or complementary to purpose-built methods (e.g., k-medoids for exemplar selection, HDBSCAN for density-based clustering).

Text2SQL agents powered by LLMs translate natural language intent into SQL by exploring the data system through tool calls before formulating the query. However, to ensure secure and scoped access, data systems construct environments with explicit API surfaces. We study and categorize these APIs exposed today as either coarse-grained or fine-grained and posit that choosing between them presents a fundamental tradeoff between cost-efficient exploration and accurate SQL generation. Most data systems expose fine-grained APIs, but this inadvertently disadvantages agents: they over-explore, incorporating irrelevant schema elements into their query formulation and produce inaccurate results. We argue that curbing over-exploration is key to the effective use of these API surfaces, and propose Sophrosyne, a data system environment that augments API responses with directives that guide the agent's exploration process. Initial results show that directives reduce over-exploration by 4.6x and boost accuracy by up to 12.4% (approx. 4 percentage points).

Exploratory analysis of high-dimensional data rarely stops at a single embedding. In practice, analysts rerun dimensionality reduction after changing preprocessing, subsets, or hyperparameters, and standard nonlinear methods can quickly become the bottleneck. We introduce FastUMAP (Bipartite Manifold Approximation and Projection), a landmark-based method designed for this repeated-use setting. FastUMAP builds a sparse point-landmark fuzzy graph, computes a Nystrom spectral warm start from the induced landmark affinity, and then refines all sample coordinates with a UMAP-style objective on the bipartite graph. The landmark ratio r = m/n provides a direct way to trade runtime against fidelity. On 9 benchmark datasets spanning 178 to 70,000 samples, FastUMAP has the lowest runtime on 7 datasets in our reported default-implementation comparison on one workstation. On MNIST and Fashion-MNIST (n=70000), it runs in about 4.6 seconds, compared with about 73--75 seconds for Barnes--Hut t-SNE, while reaching 91.4% mean kNN accuracy versus 94.6% for the strongest accuracy baseline. FastUMAP is therefore best viewed as a fast option for repeated exploratory embedding, rather than as a replacement for accuracy-first methods.