Federated domain generalization (FDG) for time-series classification (TSC) poses a critical challenge for modern intelligent web services, which rely on edge-collected time-series signals from diverse mobile applications and web devices (e.g., wearables sensors) to support decision-making. The source heterogeneity and temporal dynamics give rise to out-of-distribution (OOD) patterns, which hinder the model's ability to generalize to previously unseen users and devices. In this work, we propose Federated Generalization via Diversity Generation (FedDiG), a diffusion-based FDG framework that captures intra-client distribution shifts from a frequency-domain perspective and employs cross-frequency sampling to synthesize time-series data with diverse spectral patterns. Specifically, FedDiG first performs frequency-proxy representation learning on clients to serve as diffusion conditions. The server then aggregates client-side frequency proxies to construct a global proxy pool and applies class-wise mixup to create novel frequency features. These features guide a global diffusion model to produce diverse data, enabling the simulation of previously unseen patterns and thereby enhancing model training. Extensive experiments on four cross-domain time-series benchmarks demonstrate that FedDiG significantly outperforms state-of-the-art federated learning and FDG baselines, particularly under small-data regimes and large-scale client scenarios, achieving robust generalization to unseen domains in federated settings. This work bridges distribution-diversity synthesis and FDG for time-series to support robust, scalable web applications fed by edge-collected signals, delivering web-scale generalization across heterogeneous web, mobile, and IoT clients.

Single-domain generalization (SDG) in time series classification (TSC) poses significant challenges for current time-series domain generalization methods due to the extremely limited data available from only one source domain. In this study, we propose Segment-dErived Expansion of Domains (SEED), a diffusion-based method that effectively expands domain diversity for SDG. We reveal that individual instances exhibit intrinsic temporal shifts over time, which provides a principled foundation for creating multiple pseudo domains by segmenting each instance into distinct parts. To do so, SEED extracts two complementary representations from each time-series segment: 1) a segment-specific representation that captures diverse distributional variations, and 2) a segment-invariant representation that preserves class semantics. SEED formulates these representations as pseudo-domain prompts to guide a diffusion model in generating diverse yet semantically consistent time-series data. Additionally, SEED introduces a novel prompt-fused sampling for diffusion, enabling flexible recombination of segment-specific features to continuously expand the pseudo-domain space. We provide both theoretical analysis and extensive empirical evaluations on four widely used TSC benchmarks to validate its ability in reducing generalization error and improving model's performances in SDG. In our experiments, SEED significantly improves classification accuracy by 7.68% on average compared to the strong baselines.

Existing domain generalization (DG) methods for cross-person generalization tasks often face challenges in capturing intra- and inter-domain style diversity, resulting in domain gaps with the target domain. In this study, we explore a novel perspective to tackle this problem, a process conceptualized as domain padding. This proposal aims to enrich the domain diversity by synthesizing intra- and inter-domain style data while maintaining robustness to class labels. We instantiate this concept using a conditional diffusion model and introduce a style-fused sampling strategy to enhance data generation diversity. In contrast to traditional condition-guided sampling, our style-fused sampling strategy allows for the flexible use of one or more random styles to guide data synthesis. This feature presents a notable advancement: it allows for the maximum utilization of possible permutations and combinations among existing styles to generate a broad spectrum of new style instances. Empirical evaluations on a broad range of datasets demonstrate that our generated data achieves remarkable diversity within the domain space. Both intra- and inter-domain generated data have proven to be significant and valuable, contributing to varying degrees of performance enhancements. Notably, our approach outperforms state-of-the-art DG methods in all human activity recognition tasks.

While one-dimensional convolutional neural networks (1D-CNNs) have been empirically proven effective in time series classification tasks, we find that there remain undesirable outcomes that could arise in their application, motivating us to further investigate and understand their underlying mechanisms. In this work, we propose a Temporal Convolutional Explorer (TCE) to empirically explore the learning behavior of 1D-CNNs from the perspective of the frequency domain. Our TCE analysis highlights that deeper 1D-CNNs tend to distract the focus from the low-frequency components leading to the accuracy degradation phenomenon, and the disturbing convolution is the driving factor. Then, we leverage our findings to the practical application and propose a regulatory framework, which can easily be integrated into existing 1D-CNNs. It aims to rectify the suboptimal learning behavior by enabling the network to selectively bypass the specified disturbing convolutions. Finally, through comprehensive experiments on widely-used UCR, UEA, and UCI benchmarks, we demonstrate that 1) TCE's insight into 1D-CNN's learning behavior; 2) our regulatory framework enables state-of-the-art 1D-CNNs to get improved performances with less consumption of memory and computational overhead.