Graph few-shot learning has attracted increasing attention due to its ability to rapidly adapt models to new tasks with only limited labeled nodes. Despite the remarkable progress made by existing graph few-shot learning methods, several key limitations remain. First, most current approaches rely on predefined and unified graph filters (e.g., low-pass or high-pass filters) to globally enhance or suppress node frequency signals. Such fixed spectral operations fail to account for the heterogeneity of local topological structures inherent in real-world graphs. Moreover, these methods often assume that the support and query sets are drawn from the same distribution. However, under few-shot conditions, the limited labeled data in the support set may not sufficiently capture the complex distribution of the query set, leading to suboptimal generalization. To address these challenges, we propose GRACE, a novel Graph few-shot leaRning framework that integrates Adaptive spectrum experts with Cross-sEt distribution calibration techniques. Theoretically, the proposed approach enhances model generalization by adapting to both local structural variations and cross-set distribution calibration. Empirically, GRACE consistently outperforms state-of-the-art baselines across a wide range of experimental settings. Our code can be found here.

In this paper, we extend the idea of the seeding matrix design and introduce the modulated matrix framework for compressed sensing. The 1-D state evolution equation is derived to track the sample distortion performance as a function of the signal distribution and the rescaling matrix. A special example, the two-block matrix, is presented as a generalization of the hybrid zeroing matrix. The first order phase transition is further studied to better understand the dynamics. With the two-block matrix, exact recovery can be achieved in the region where the homogeneous Gaussian matrix is not optimal for the sparse signals. For compressible signals, the reconstruction quality can also be effectively improved.

Within the framework of compressed sensing, we consider dense signals, which contain both discrete as well as continuous-amplitude components. We demonstrate by a comprehensive numerical study–to the best of our knowledge the first of its kind in the literature–that dense signals can be recovered from noisy, incomplete linear measurements by simple iterative algorithms that are inspired by or are implementations of approximate message passing. Those iterative algorithms are shown to significantly outperform all other algorithms presented so far, when they use a novel noise-adaptive thresholding function that is proposed in this contribution.

We model the compressible signal with the two states Gaussian mixture distribution and consider the sample distortion function for the recently proposed Bayesian optimal AMP decoder. By leveraging the rigorous analysis of the AMP algorithm, we are able to derive the theoretical SD function and a sample allocation scheme for multi-resolution statistical image model. We then adopt the “turbo” message passing method to integrate the bandwise sample allocation with the exploitation of the hidden Markov tree structure of wavelet coefficients. Experiments on natural image show that the combination outperforms either of them working alone.