Time-series anomaly detection is critical for numerous real-world applications and has been extensively studied. However, existing methods are typically designed to identify anomalies within a complete time series. In other words, they rely on access to ground truth data to calculate anomaly scores and distinguish anomalous data from normal patterns. This reliance limits their applicability in scenarios where predicting future anomalies is required, as the ground truth is inherently unavailable. To address this gap, we introduce the concept of Time-Series Anomaly Prediction (TSAP), which focuses on forecasting the occurrence and progression of anomalies in time series simultaneously without relying on ground truth. In this paper, we propose a novel exemplar-based pre-training and fine-tuning pipeline tailored to this task, based on recent achievements in online time-series forecasting techniques. The pipeline begins with an offline pre-training phase, where a deep learning model is trained to capture the underlying temporal correlations in time-series data. During the online fine-tuning stage, a three-step process is employed to predict the timing and evolution of anomalies. This process includes prediction and anomaly detection, motif search for similar patterns, and fine-tuning using exemplars. These steps are repeated as new data arrives. We evaluate the proposed method against state-of-the-art approaches from various relevant categories on both real-world and synthetic datasets. Experimental results show that the proposed method improves anomaly detection accuracy by up to 53.8% in terms of F1 score and enhances time-series forecasting accuracy during and after anomaly periods by up to 82.4% and 49.1% in terms of MSE. Through analysing the results, we prove the proposed method's effectiveness in addressing the new TSAP tasks, which are incapable of being handled by current time-series anomaly detection or online time-series forecasting methods.

Linear Mode Connectivity (LMC) is a notable phenomenon in the loss landscapes of neural networks, wherein independently trained models have been observed to be connected—up to permutation symmetries—by linear paths in parameter space along which the loss remains consistently low. This observation challenges classical views of non-convex optimization and has implications for model ensembling, generalization, and our understanding of neural loss geometry. Inspired by recent studies on LMC in standard neural networks, we systematically investigate this phenomenon within Mixture-of-Experts (MoE) architectures—a class of models known for their scalability and computational efficiency, which combine traditional neural networks—referred to as experts—through a learnable gating mechanism. We begin by conducting a comprehensive analysis of both dense and sparse gating regimes, demonstrating that the symmetries inherent to MoE architectures are fully characterized by permutations acting on both the expert components and the gating function. Building on these foundational findings, we propose a matching algorithm that enables alignment between independently trained MoEs, thereby facilitating the discovery of LMC. Finally, we empirically validate the presence of LMC using our proposed algorithm across diverse MoE configurations—including dense, sparse, and shared-expert variants—under a wide range of model settings and datasets of varying scales and modalities. Our results confirm the existence of LMC in MoE architectures and offer fundamental insights into the functional landscape and optimization dynamics of deep learning models.

Deep learning approaches have been widely adopted for precipitation nowcasting in recent years. Previous studies mainly focus on proposing new model architectures to improve pixel-wise metrics. However, they frequently result in blurry predictions which provide limited utility to forecasting operations. In this work, we propose a new Fourier Amplitude and Correlation Loss (FACL) which consists of two novel loss terms: Fourier Amplitude Loss (FAL) and Fourier Correlation Loss (FCL). FAL regularizes the Fourier amplitude of the model prediction and FCL complements the missing phase information. The two loss terms work together to replace the traditional L2 losses such as MSE and weighted MSE for the spatiotemporal prediction problem on signal-based data. Our method is generic, parameter-free and efficient. Extensive experiments using one synthetic dataset and three radar echo datasets demonstrate that our method improves perceptual metrics and meteorology skill scores, with a small trade-off to pixel-wise accuracy and structural similarity. Moreover, to improve the error margin in meteorological skill scores such as Critical Success Index (CSI) and Fractions Skill Score (FSS), we propose and adopt the Regional Histogram Divergence (RHD), a distance metric that considers the patch-wise similarity between signal-based imagery patterns with tolerance to local transforms.