用神经网络统一计算任意数据的中心性，高效且稳定。
A Trainable Centrality Framework for Modern Data
- 基于距离比较和去噪得分匹配，双头神经网络学习中心性评分
- 单参数插值融合全局与局部信号，一次前向传播得深度式中心性
- 在图像、时序、文本等多类数据上表现媲美经典方法，适合异常检测
衡量数据点的中心性是鲁棒估计、排序和异常检测的基础，但传统深度概念在高维下变得昂贵且不稳定，难以推广到非欧几里得数据。我们提出FUSE（Fused Unified centrality Score Estimation），一种可训练的神经中心性框架，适用于任意表示。FUSE包含一个全局头，通过成对距离比较训练，学习无锚点的中心性评分；一个局部头，通过去噪得分匹配训练，近似平滑的对数密度势。一个0到1之间的参数对齐这两个校准信号，一次前向传播即可从不同视角生成类似深度的中心性。在合成分布、真实图像、时间序列和文本数据，以及标准异常检测基准上，FUSE恢复了有意义的经典排序，揭示多尺度几何结构，并达到与强经典基线相当的性能，同时保持简单高效。
原文摘要 · Abstract (English)
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.
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