# A Trainable Centrality Framework for Modern Data

arXiv: https://arxiv.org/abs/2511.22959 · HTML: https://mlsanity.com/paper/2511.22959/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 58 references that are in the map.
- First posted on arXiv 28 Nov 2025.

## Builds on (most cited first, 20 of 20)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [A Simple Framework for Contrastive Learning of Visual Representations](https://mlsanity.com/paper/2002.05709/) (2020)
- [Score-Based Generative Modeling through Stochastic Differential Equations](https://mlsanity.com/paper/2011.13456/) (2020)
- [Flow Matching for Generative Modeling](https://mlsanity.com/paper/2210.02747/) (2022)
- [DistilBERT, a distilled version of BERT: smaller, faster, cheaper and lighter](https://mlsanity.com/paper/1910.01108/) (2019)
- [Gaussian Error Linear Units (GELUs)](https://mlsanity.com/paper/1606.08415/) (2016)
- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [The UCR Time Series Archive](https://mlsanity.com/paper/1810.07758/) (2018)
- [Dataset Cartography: Mapping and Diagnosing Datasets with Training Dynamics](https://mlsanity.com/paper/2009.10795/) (2020)
- [TweetEval: Unified Benchmark and Comparative Evaluation for Tweet Classification](https://mlsanity.com/paper/2010.12421/) (2020)
- [Classification-Based Anomaly Detection for General Data](https://mlsanity.com/paper/2005.02359/) (2020)
- [Manifold learning: what, how, and why](https://mlsanity.com/paper/2311.03757/) (2023)
- [On the Nature and Types of Anomalies: A Review of Deviations in Data](https://mlsanity.com/paper/2007.15634/) (2020)
- [Unsupervised anomaly detection algorithms on real-world data: how many do we need?](https://mlsanity.com/paper/2305.00735/) (2023)
- [Exact computation of the halfspace depth](https://mlsanity.com/paper/1411.6927/) (2014)
- [Tukey's Depth for Object Data](https://mlsanity.com/paper/2109.00493/) (2021)
- [Classification with the pot-pot plot](https://mlsanity.com/paper/1608.02861/) (2016)
- [Regularized Halfspace Depth for Functional Data](https://mlsanity.com/paper/2311.07034/) (2023)
- [Union-Free Generic Depth for Non-Standard Data](https://mlsanity.com/paper/2412.14745/) (2024)

## Abstract (arXiv)

Measuring how central or typical a data point is underpins robust estimation, ranking, and outlier detection, but classical depth notions become expensive and unstable in high dimensions and are hard to extend beyond Euclidean data. We introduce Fused Unified centrality Score Estimation (FUSE), a neural centrality framework that operates on top of arbitrary representations. FUSE combines a global head, trained from pairwise distance-based comparisons to learn an anchor-free centrality score, with a local head, trained by denoising score matching to approximate a smoothed log-density potential. A single parameter between 0 and 1 interpolates between these calibrated signals, yielding depth-like centrality from different views via one forward pass. Across synthetic distributions, real images, time series, and text data, and standard outlier detection benchmarks, FUSE recovers meaningful classical ordering, reveals multi-scale geometric structures, and attains competitive performance with strong classical baselines while remaining simple and efficient.