PAI: Preserving Amplitude Information in Representation-Based Time-Series Anomaly Detection

Representation-based time-series anomaly detection algorithms significantly outperform other methods on diverse anomaly detection tasks. However, we notice that they suffer from a major limitation in our evaluation - their learned embeddings are often amplitude-agnostic. Losing amplitude information can degrade performance on amplitude related anomalies, and this failure is prevalent across all existing representation-based methods. To address aforementioned issues, we propose a new anomaly scoring scheme named PAI. PAI consists of two complementary modules, a diagnostic module and a final score augmentation function. The diagnostic module compares cosine and Euclidean scoring on the same representation bank to test whether amplitude information is already captured in the learned representation. Then in final score augmentation function, PAI computes a point-wise median and MAD deviation score and a local mean-shift score-which are fused with the representation score to produce the final anomaly score. On the TSB-AD-U-Eva and TAB UV datasets, PAI improves all four evaluated representation-based methods across every reported metric, achieving average VUS-PR gains of 98.4% and 36.8%, respectively. Among all evaluated combinations, PaAno + PAI achieves the best performance, outperforming the state-of-the-art method by 15%. Further evaluation on bootstrap confidence intervals, anomaly-type breakdowns, and a TS2Vec input-normalization ablation further support the proposed scheme. These results suggest that explicitly retaining amplitude information is important for representation-based time-series anomaly detection, which has been underemphasized in existing scoring schemes. Code is available at: https://github.com/pantheon5100/PAI

PH-Dropout: Practical Epistemic Uncertainty Quantification for View Synthesis

View synthesis using Neural Radiance Fields (NeRF) and Gaussian Splatting (GS) has demonstrated impressive fidelity in rendering real-world scenarios. However, practical methods for accurate and efficient epistemic Uncertainty Quantification (UQ) in view synthesis are lacking. Existing approaches for NeRF either introduce significant computational overhead (e.g., ``10x increase in training time" or ``10x repeated training") or are limited to specific uncertainty conditions or models. Notably, GS models lack any systematic approach for comprehensive epistemic UQ. This capability is crucial for improving the robustness and scalability of neural view synthesis, enabling active model updates, error estimation, and scalable ensemble modeling based on uncertainty. In this paper, we revisit NeRF and GS-based methods from a function approximation perspective, identifying key differences and connections in 3D representation learning. Building on these insights, we introduce PH-Dropout (Post hoc Dropout), the first real-time and accurate method for epistemic uncertainty estimation that operates directly on pre-trained NeRF and GS models. Extensive evaluations validate our theoretical findings and demonstrate the effectiveness of PH-Dropout.

PH-Dropout: Prctical Epistemic Uncertainty Quantification for View Synthesis

View synthesis using Neural Radiance Fields (NeRF) and Gaussian Splatting (GS) has demonstrated impressive fidelity in rendering real-world scenarios. However, practical methods for accurate and efficient epistemic Uncertainty Quantification (UQ) in view synthesis are lacking. Existing approaches for NeRF either introduce significant computational overhead (e.g., ``10x increase in training time" or ``10x repeated training") or are limited to specific uncertainty conditions or models. Notably, GS models lack any systematic approach for comprehensive epistemic UQ. This capability is crucial for improving the robustness and scalability of neural view synthesis, enabling active model updates, error estimation, and scalable ensemble modeling based on uncertainty. In this paper, we revisit NeRF and GS-based methods from a function approximation perspective, identifying key differences and connections in 3D representation learning. Building on these insights, we introduce PH-Dropout (Post hoc Dropout), the first real-time and accurate method for epistemic uncertainty estimation that operates directly on pre-trained NeRF and GS models. Extensive evaluations validate our theoretical findings and demonstrate the effectiveness of PH-Dropout.

Learning High-Frequency Functions Made Easy with Sinusoidal Positional Encoding

Fourier features based positional encoding (PE) is commonly used in machine learning tasks that involve learning high-frequency features from low-dimensional inputs, such as 3D view synthesis and time series regression with neural tangent kernels. Despite their effectiveness, existing PEs require manual, empirical adjustment of crucial hyperparameters, specifically the Fourier features, tailored to each unique task. Further, PEs face challenges in efficiently learning high-frequency functions, particularly in tasks with limited data. In this paper, we introduce sinusoidal PE (SPE), designed to efficiently learn adaptive frequency features closely aligned with the true underlying function. Our experiments demonstrate that SPE, without hyperparameter tuning, consistently achieves enhanced fidelity and faster training across various tasks, including 3D view synthesis, Text-to-Speech generation, and 1D regression. SPE is implemented as a direct replacement for existing PEs. Its plug-and-play nature lets numerous tasks easily adopt and benefit from SPE.