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Can Adaptive Gradient Methods Converge under Heavy-Tailed Noise? A Case Study of AdaGrad Shallow ReLU$^s$ Networks in $L^p$-Type and Sobolev Spaces: Approximation and Path-Norm Controlled Generalization On Stability and Decomposition of Sample Quantiles under Heavy-Tailed Distributions Improved Baselines with Representation Autoencoders Symmetry-Compatible Principle for Optimizer Design: Embeddings, LM Heads, SwiGLU MLPs, and MoE Routers Feature Learning in Linear-Width Two-Layer Networks: Two vs. One Step of Gradient Descent A Two-Parameter Weibull Framework for Diagnosing Transformer Weight Distributions Calibeating for general proper losses: A Bregman divergence approach Dimension-Free Convergence of Discrete Diffusion Models: Adjoint Equations Induce the Right Space Sample-efficient inductive matrix completion with noise and inexact side-information Multi-task Linear Regression without Eigenvalue Lower Bounds: Adaptivity, Robustness, and Safety XAI and Statistical Analysis for Reliable Intrusion Detection in the UAVIDS-2025 Dataset: From Tree to Hybrid and Tabular DNN Ensembles Reasoning Models Don't Just Think Longer, They Move Differently TabPFN-3: Technical Report Reframing preprocessing selection as model-internal calibration in near-infrared spectroscopy: A large-scale benchmark of operator-adaptive PLS and Ridge models Towards a holistic understanding of Selection Bias for Causal Effect Identification Adaptive Kernel Density Estimation with Pre-training Coreset-Induced Conditional Velocity Flow Matching RISED: A Pre-Deployment Evaluation Framework for High-Stakes AI Decision-Support Systems, with Application to Healthcare ISOMORPH: A Supply Chain Digital Twin for Simulation, Dataset Generation, and Forecasting Benchmarks Yield Curves Dynamics Using Variational Autoencoders Under No-arbitrage Model-based Bootstrap of Controlled Markov Chains Online Learning-to-Defer with Varying Experts Self-Supervised Laplace Approximation for Bayesian Uncertainty Quantification Keeping Score: Efficiency Improvements in Neural Likelihood Surrogate Training via Score-Augmented Loss Functions One-Step Generative Modeling via Wasserstein Gradient Flows Exact Stiefel Optimization for Probabilistic PLS: Closed-Form Updates, Error Bounds, and Calibrated Uncertainty A Composite Activation Function for Learning Stable Binary Representations Adaptive Calibration in Non-Stationary Environments Real vs. Semi-Simulated: Rethinking Evaluation for Treatment Effect Estimation Federated Language Models Under Bandwidth Budgets: Distillation Rates and Conformal Coverage On Variance Reduction in Learning Mean Flows When Attention Beats Fourier: Multi-Scale Transformers for PDE Solving on Irregular Domains A Refined Generalization Analysis for Extreme Multi-class Supervised Contrastive Representation Learning Ensemble Distributionally Robust Bayesian Optimisation The Proxy Presumption: From Semantic Embeddings to Valid Social Measures Modulated learning for private and distributed regression with just a single sample per client device Query-efficient model evaluation using cached responses Order-Agnostic Autoregressive Modelling with Missing Data Grokking or Glitching? 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TPA-AD: A Two-Stage Pseudo Anomaly-Guided Method for Bearing Time-Series Anomaly Detection
Xiancheng Wang, Zhibo Zhang, Ran Li, Rui Wang, Minghang Zhao, Sh · 2026-06-02 · via stat updates on arXiv.org

This paper proposes a two-stage pseudo anomaly-guided anomaly detection method (\textbf{T}wo-stage \textbf{P}seudo \textbf{A}nomaly-guided \textbf{A}nomaly \textbf{D}etection, \textbf{TPA-AD}) for axle-box bearing time-series anomaly detection (time series anomaly detection, TSAD) under the setting where only normal samples are available for training. The method first generates pseudo-anomalous windows near the normal boundary using a reconstruction model and per-feature target-error control. It then learns anomaly-sensitive representations through contrastive learning between normal and pseudo-anomalous windows, and finally produces window-level and point-level anomaly scores using k-nearest neighbors (KNN). Compared with existing methods that rely on known fault categories, real anomaly priors, or random anomaly injection, TPA-AD improves the separability of the normal boundary by constructing pseudo-anomalies in boundary neighborhoods and can jointly handle continuous and discrete features in mixed-variable scenarios. The main experiments are conducted on bearing fault detection datasets and degradation-process datasets, with an additional exploratory extension on $13$ public TSAD datasets. The results show that the proposed method yields relatively stable anomaly responses, is sensitive to degradation evolution, and demonstrates a certain degree of broader applicability on public TSAD benchmarks and real high-speed-train-related bearing data.