Hence, we conclude that near 0, tan−1 κ (t) = t− κ t3 3 +O(κ2)

First, we apply Taylor expansion on tan−1 κ (t) for a ﬁxed t when κ→ 0+: tan−1 κ (t) =κ− 1 2 tan(κ 1 2 t) =κ− 1 2 (κ 1 2 t + κ 3 2 t3 3 +O(κ 5 2 )) =t + κ t3 3 +O(κ2) When κ→ 0−: tan−1 κ (t) =(−κ)− 1 2 tanh((−κ) 1 2 t) =(−κ)− 1 2 ((−κ) 1 2 · 2025

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SpaceGNN: Multi-Space Graph Neural Network for Node Anomaly Detection with Extremely Limited Labels

cs.LG · 2025-02-05 · conditional · novelty 6.0

A multi-space GNN with learnable curvature and distance-aware propagation that outperforms existing node anomaly detectors on 9 benchmark datasets under limited supervision.

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SpaceGNN: Multi-Space Graph Neural Network for Node Anomaly Detection with Extremely Limited Labels cs.LG · 2025-02-05 · conditional · none · ref 2
A multi-space GNN with learnable curvature and distance-aware propagation that outperforms existing node anomaly detectors on 9 benchmark datasets under limited supervision.

Hence, we conclude that near 0, tan−1 κ (t) = t− κ t3 3 +O(κ2)

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