Clustering mixed tabular data requires a unified metric space to bridge the inherent heterogeneity between continuous numerical measurements and discrete categorical symbols. Traditionally, algorithms rely entirely on dataset-internal statistics to estimate categorical relationships, which confines the learned metric to empirical co-occurrences and ignores conceptually obvious yet statistically unobserved affinities. Although LLMs offer external world knowledge, applying their text-centric reasoning to highly abstract tabular concepts presents significant challenges. Bridging this modality gap to construct a semantically complete metric typically requires embedding LLMs into iterative metric learning loops to dynamically optimize cross-modality representations. This incurs intractable computational overhead, forcing a compromise between semantic enrichment and scalability. Therefore, we propose GRACE, an LLM-grounded framework for scalable mixed-data clustering. GRACE shifts semantic acquisition to the attribute-value level via a multi-perspective LLM querying strategy, mapping heterogeneous values into knowledge-informed descriptions. Crucially, this one-shot grounding extracts general-purpose semantic representations that embed heterogeneous attributes into a unified space, decoupling expensive LLM invocation from iterative optimization. Furthermore, GRACE cross-validates these external semantics against dataset-internal statistical evidence to ensure alignment with the dataset-specific cluster structure. Ultimately, GRACE matches the scalability of conventional statistics-driven baselines while achieving superior clustering accuracy and conceptual interpretability over 11 competing methods. The source code is available at https://github.com/develop-yang/GRACE-GRACE-A
LLM pre-training efficacy increasingly depends on data composition rather than sheer volume. Yet, optimal mixing is hindered by categorization flaws: human taxonomies suffer from ontological misalignment, and Euclidean clustering fails to address embedding anisotropy. We introduce GEM (Geometric Entropy Mixing), a framework reformulating data curation as a variational problem on the hypersphere augmented with a mixing-balance regularizer. By decoupling the generative prior and optimizing the objective via a provable MM (Minorize-Maximize) algorithm, GEM effectively counteracts the cluster collapse to discover balanced semantic structures invisible to Euclidean heuristics. We employ teacher-student distillation to scale this geometric fidelity to web-scale corpora and introduce the Geometric Influence Score (GIS) for interpretable taxonomy generation. Experiments with 1.1B-parameter models demonstrate that GEM establishes a new state-of-the-art when integrated into mixing strategies like DoReMi and RegMix, improving average downstream accuracy by up to 1.2% and offering a robust coordinate system for predictable data mixing.
The advent of the big data paradigm has transformed how industries manage and analyze information, ushering in an era of unprecedented data volume, velocity, and variety. Within this landscape, mixed-data clustering has become a critical challenge, requiring innovative methods that can effectively exploit heterogeneous data types, including numerical and categorical variables. Traditional clustering techniques, typically designed for homogeneous datasets, often struggle to capture the additional complexity introduced by mixed data, underscoring the need for approaches specifically tailored to this setting. Hierarchical and explainable algorithms are particularly valuable in this context, as they provide structured, interpretable clustering results that support informed decision-making. This paper introduces a clustering method grounded in pretopological spaces. In addition, benchmarking against classical numerical clustering algorithms and existing pretopological approaches yields insights into the performance and effectiveness of the proposed method within the big data paradigm.
Most data-mixing methods assume the corpus has already been partitioned into groups, and the choice of those groups determines what a mixer can express. Existing labels, including provenance, topic or format taxonomies, and flat embedding clusters, commit to one semantic axis at one granularity; changing the resolution rebuilds the labels. We argue the bottleneck is the label system, not the mixer, and provide a hierarchical one. HERMES is a data-derived labeling substrate: a Learned Semantic Transform followed by 3-stage residual vector quantization annotates each document once into a coarse-to-fine code whose prefix length controls granularity up to approximately 130k cells. At coarse granularity HERMES sits at a plateau with KMeans-family methods on standard clustering metrics, so the contribution is the substrate, not the clusterer. On 1B-parameter, 25B-token pre-training, the hierarchy exposes an interaction fixed-granularity pipelines cannot test: at one prefix length, a combined Stage-2 rule contrast, equal-subbucket coverage versus size-proportional within-bucket quality top-30%, lifts a 16-task capability macro-average by +0.0253; at the next finer level, the same rule loses its measurable edge as candidate pools contract approximately 5x. HERMES reframes data mixture design from choosing among fixed label sets to navigating a reusable, data-derived granularity hierarchy.