Solving ill-posed inverse problems necessitates effective regularization strategies to stabilize the inversion process against measurement noise. While classical methods like Tikhonov regularization require heuristic parameter tuning, and standard deep learning approaches often lack interpretability and generalization across resolutions, we propose SC-Net (Spectral Correction Network), a novel operator learning framework. SC-Net operates in the spectral domain of the forward operator, learning a pointwise adaptive filter function that reweights spectral coefficients based on the signal-to-noise ratio. We provide a theoretical analysis showing that SC-Net approximates the continuous inverse operator, guaranteeing discretization invariance. Numerical experiments on 1D integral equations demonstrate that SC-Net: (1) achieves the theoretical minimax optimal convergence rate ($O(δ^{0.5})$ for $s=p=1.5$), matching theoretical lower bounds; (2) learns interpretable sharp-cutoff filters that outperform Oracle Tikhonov regularization; and (3) exhibits zero-shot super-resolution, maintaining stable reconstruction errors ($\approx 0.23$) when trained on coarse grids ($N=256$) and tested on significantly finer grids (up to $N=2048$). The proposed method bridges the gap between rigorous regularization theory and data-driven operator learning.

Contrastive learning methods for time series anomaly detection (TSAD) heavily depend on the quality of negative sample construction. However, existing strategies based on random perturbations or pseudo-anomaly injection often struggle to simultaneously preserve temporal semantic consistency and provide effective decision-boundary supervision. Most existing methods rely on prior anomaly injection, while overlooking the potential of generating hard negatives near the data manifold boundary directly from normal samples themselves. To address this issue, we propose a reconstruction-driven boundary negative generation framework that automatically constructs hard negatives through the reconstruction process of normal samples. Specifically, the method first employs a reconstruction network to capture normal temporal patterns, and then introduces a reinforcement learning strategy to adaptively adjust the optimization update magnitude according to the current reconstruction state. In this way, boundary-shifted samples close to the normal data manifold can be induced along the reconstruction trajectory and further used for subsequent contrastive representation learning. Unlike existing methods that depend on explicit anomaly injection, the proposed framework does not require predefined anomaly patterns, but instead mines more challenging boundary negatives from the model's own learning dynamics. Experimental results show that the proposed method effectively improves anomaly representation learning and achieves competitive detection performance on the current dataset.

Preferences serve as an alternative but recent work rarely considers preference learning given multiple tasks.