Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2610.25059

HCFM: Helmholtz Component Flow Matching for Time Series Anomaly Detection

Shyam Sundar Saravanan·Tie Luo·Sanjay Madria
View original source ↗Read source document ↗Export metadata ↓

Abstract

Flow Matching (FM) is an efficient simulation-free approach for training flow-based generative models, making it a promising foundation for scalable time-series anomaly detection (TSAD). However, standard FM learns a monolithic vector field in which nominal transport and local density-changing behavior are entangled. This creates a central challenge for TSAD; local expansion and contraction carry crucial anomaly-sensitive information, yet isolating this signal requires expensive Jacobian-trace estimation over the entire field. We propose \emph{Helmholtz Component Flow Matching} (HCFM), an unsupervised TSAD framework that parameterizes the vector field prediction network with separate transport, compression, and residual heads. The transport head is constrained to be divergence-free, so divergence estimation is restricted to the compression head, while a lightweight residual head absorbs the remaining mismatch. This structured parameterization improves scalability and detection performance by separating volume-preserving nominal transport from density-changing compression, yielding cleaner anomaly signals from distinct deviations of nominal behavior. Experiments on large-scale univariate and multivariate TSAD benchmarks show that HCFM consistently improves detection accuracy while maintaining efficient inference compared with 16 baselines. The code is available at https://github.com/TrustAIoT/HCFM__time-series-anomaly/

Explore related subjects

cs.LGcs.AIcs.DB

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Shyam Sundar Saravanan, Tie Luo, Sanjay Madria. 2026-10-18. HCFM: Helmholtz Component Flow Matching for Time Series Anomaly Detection. https://arxiv.org/abs/2610.25059

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

FiTv2: Scalable and Improved Flexible Vision Transformer for Diffusion Model

\textit{Nature is infinitely resolution-free}. In the context of this reality, existing diffusion models, such as Diffusion Transformers, often face challenges when processing image resolutions outside of their trained domain. To address this limitation, we conceptualize images as sequences of tokens with dynamic sizes, rather than traditional methods that perceive images as fixed-resolution grids. This perspective enables a flexible training strategy that seamlessly accommodates various aspect ratios during both training and inference, thus promoting resolution generalization and eliminating biases introduced by image cropping. On this basis, we present the \textbf{Flexible Vision Transformer} (FiT), a transformer architecture specifically designed for generating images with \textit{unrestricted resolutions and aspect ratios}. We further upgrade the FiT to FiTv2 with several innovative designs, includingthe Query-Key vector normalization, the AdaLN-LoRA module, a rectified flow scheduler, and a Logit-Normal sampler. Enhanced by a meticulously adjusted network structure, FiTv2 exhibits $2\times$ convergence speed of FiT. When incorporating advanced training-free extrapolation techniques, FiTv2 demonstrates remarkable adaptability in both resolution extrapolation and diverse resolution generation. Additionally, our exploration of the scalability of the FiTv2 model reveals that larger models exhibit better computational efficiency. Furthermore, we introduce an efficient post-training strategy to adapt a pre-trained model for the high-resolution generation. Comprehensive experiments demonstrate the exceptional performance of FiTv2 across a broad range of resolutions. We have released all the codes and models at https://github.com/whlzy/FiT to promote the exploration of diffusion transformer models for arbitrary-resolution image generation.

cs.LG↗
arXiv2026

Double-Diffusion: Balancing Speed, Accuracy, and Uncertainty in Probabilistic Forecasting for Urban Sensor Networks

Urban sensor networks need forecasts that are accurate, carry useful uncertainty, and refresh fast enough to act on as new readings arrive. These goals conflict: deterministic models give no distribution, while diffusion forecasters model uncertainty but denoise from pure noise over many steps. We present Double-Diffusion, which integrates a closed-form graph-heat prior into a denoising diffusion model. The prior is a parameter-free low-pass forecast over the sensor graph, and it serves two roles: it is the residual target the model generates, and it conditions the denoiser. The reverse process therefore starts near the prior and denoises a short warm-started chain instead of synthesizing from pure noise; the name denotes this composition, a graph diffusion feeding a denoising diffusion. A compact denoiser, DD-Net, is trained as a Denoising Diffusion Probabilistic Model (DDPM) in the Resfusion warm-start formulation, so generation refines the prior over a short truncated chain rather than synthesizing from pure noise; a graph-spectral read-out of the prior residual sets its switchable spatial filter per domain from training data alone. On four real-world air quality and traffic networks, Double-Diffusion attains the best CRPS of all probabilistic methods on every dataset and stays competitive in point accuracy with the strongest baselines, at a fraction of the sampling cost of from-noise diffusion. The code is available at: https://github.com/teddyicare/Double-Diffusion

cs.LG↗
arXiv2026

Optimized Weight Initialization on the Stiefel Manifold for Deep ReLU Neural Networks

Stable and efficient training of ReLU networks with large depth is highly sensitive to weight initialization. Improper initialization can cause permanent neuron inactivation dying ReLU and exacerbate gradient instability as network depth increases. Methods such as He, Xavier, and orthogonal initialization preserve variance or promote approximate isometry. However, they do not necessarily regulate the pre-activation mean or control activation sparsity, and their effectiveness often diminishes in very deep architectures. This work introduces a semi-orthogonal initialization specifically optimized for ReLU by solving an optimization problem on the Stiefel manifold, thereby preserving scale and calibrating the pre-activation statistics from the outset. A family of closed-form solutions and an efficient sampling scheme are derived. Theoretical analysis at initialization shows that the proposed initialization mitigates dying ReLU, slows the decay of activation variance, and alleviates gradient vanishing, thereby stabilizing signal and gradient flow in deep architectures. Empirically, across MNIST, Fashion-MNIST, multiple tabular datasets, few-shot settings, and ReLU-family activations, the proposed initialization maintains stable performance as network depth increases, with particularly clear advantages in few-shot learning and large-depth settings.

cs.LG↗