Single image defocus deblurring (SIDD) aims to restore an all-in-focus image from a defocused one. Distribution shifts in defocused images generally lead to performance degradation of existing methods during out-of-distribution inferences. In this work, we gauge the intrinsic reason behind the performance degradation, which is identified as the heterogeneity of lens-specific point spread functions. Empirical evidence supports this finding, motivating us to employ a continual test-time adaptation (CTTA) paradigm for SIDD. However, traditional CTTA methods, which primarily rely on entropy minimization, cannot sufficiently explore task-dependent information for pixel-level regression tasks like SIDD. To address this issue, we propose a novel Siamese networks-based continual test-time adaptation framework, which adapts source models to continuously changing target domains only requiring unlabeled target data in an online manner. To further mitigate semantically erroneous textures introduced by source SIDD models under severe degradation, we revisit the learning paradigm through a structural causal model and propose Causal Siamese networks (CauSiam). Our method leverages large-scale pre-trained vision-language models to derive discriminative universal semantic priors and integrates these priors into Siamese networks, ensuring causal identifiability between blurry inputs and restored images. Extensive experiments demonstrate that CauSiam effectively improves the generalization performance of existing SIDD methods in continuously changing domains.

Submodular maximization has found extensive applications in various domains within the field of artificial intelligence, including but not limited to machine learning, computer vision, and natural language processing. With the increasing size of datasets in these domains, there is a pressing need to develop efficient and parallelizable algorithms for submodular maximization. One measure of the parallelizability of a submodular maximization algorithm is its adaptive complexity, which indicates the number of sequential rounds where a polynomial number of queries to the objective function can be executed in parallel. In this paper, we study the problem of non-monotone submodular maximization subject to a knapsack constraint, and propose the first combinatorial algorithm achieving an $(8+\epsilon)$-approximation under $\mathcal{O}(\log n)$ adaptive complexity, which is \textit{optimal} up to a factor of $\mathcal{O}(\log\log n)$. Moreover, we also propose the first algorithm with both provable approximation ratio and sublinear adaptive complexity for the problem of non-monotone submodular maximization subject to a $k$-system constraint. As a by-product, we show that our two algorithms can also be applied to the special case of submodular maximization subject to a cardinality constraint, and achieve performance bounds comparable with those of state-of-the-art algorithms. Finally, the effectiveness of our approach is demonstrated by extensive experiments on real-world applications.