It is widely known that the error analysis for deep learning involves approximation, statistical, and optimization errors. However, it is challenging to combine them together due to overparameterization. In this paper, we address this gap by providing a comprehensive error analysis of the Deep Ritz Method (DRM). Specifically, we investigate a foundational question in the theoretical analysis of DRM under the overparameterized regime: given a target precision level, how can one determine the appropriate number of training samples, the key architectural parameters of the neural networks, the step size for the projected gradient descent optimization procedure, and the requisite number of iterations, such that the output of the gradient descent process closely approximates the true solution of the underlying partial differential equation to the specified precision?

Efficient compression of multi-view video data is a critical challenge for various applications due to the large volume of data involved. Although multi-view video coding (MVC) has introduced inter-view prediction techniques to reduce video redundancies, further reduction can be achieved by encoding a subset of views at a lower resolution through asymmetric rescaling, achieving higher compression efficiency. However, existing network-based rescaling approaches are designed solely for single-viewpoint videos. These methods neglect inter-view characteristics inherent in multi-view videos, resulting in suboptimal performance. To address this issue, we first propose a Disparity-aware Rescaling Learning Network (DRLN) that integrates disparity-aware feature extraction and multi-resolution adaptive rescaling to enhance MVC efficiency by minimizing both self- and inter-view redundancies. On the one hand, during the encoding stage, our method leverages the non-local correlation of multi-view contexts and performs adaptive downscaling with an early-exit mechanism, resulting in substantial multi-view bitrate savings. On the other hand, during the decoding stage, a dynamic aggregation strategy is proposed to facilitate effective interaction with inter-view features, utilizing the inter-view and cross-scale information to reconstruct fine-grained multi-view videos. Extensive experiments show that our network achieves a significant 26.31% BD-Rate reduction compared to the 3D-HEVC standard baseline, offering state of-the-art coding performance.

Deep learning techniques are increasingly integrated into rescaling-based video compression frameworks and have shown great potential in improving compression efficiency. However, existing methods achieve limited performance because 1) they treat context priors generated by codec as independent sources of information, ignoring potential interactions between multiple priors in rescaling, which may not effectively facilitate compression; 2) they often employ a uniform sampling ratio across regions with varying content complexities, resulting in the loss of important information. To address the above two issues, this paper proposes a spatial multi-prior driven resolution rescaling framework for intra-frame coding, called MP-RRF, consisting of three sub-networks: a multi-prior driven network, a downscaling network, and an upscaling network. First, the multi-prior driven network employs complexity and similarity priors to smooth the unnecessarily complicated information while leveraging similarity and quality priors to produce high-fidelity complementary information. This interaction of complexity, similarity and quality priors ensures redundancy reduction and texture enhancement. Second, the downscaling network discriminatively processes components of different granularities to generate a compact, low-resolution image for encoding. The upscaling network aggregates a complementary set of contextual multi-scale features to reconstruct realistic details while combining variable receptive fields to suppress multi-scale compression artifacts and resampling noise. Extensive experiments show that our network achieves a significant 23.84% Bjøntegaard Delta Rate (BD-Rate) reduction under all-intra configuration compared to the codec anchor, offering the state-of-the-art coding performance.