arXiv Machine Learning By Yang Cao, Zihao Guo

Anomalies as Residuals: Cauchy Displacement Networks

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The paper introduces the Cauchy Displacement Network (CDN), a single‑hidden‑layer neural network that approximates neighbourhood‑based anomaly detectors by regressing each point onto the mean of its k nearest training neighbours. CDN uses Cauchy activations to compute a displacement vector whose length serves as an anomaly score, achieving state‑of‑the‑art performance on 46 benchmark datasets while being up to three orders of magnitude faster than traditional methods and independent of training‑set size. The authors provide theoretical guarantees, showing that Cauchy units represent Student‑t expert densities and that the network’s output grows linearly with residuals in any direction.

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