Randomized Quasi-Monte Carlo Features for Kernel Approximation

We investigate the application of randomized quasi-Monte Carlo (RQMC) methods in random feature approximations for kernel-based learning. Compared to the classical Monte Carlo (MC) approach \citep{rahimi2007random}, RQMC improves the deterministic approximation error bound from $O_P(1/\sqrt{n})$ to $O(1/M)$ (up to logarithmic factors), matching the rate achieved by quasi-Monte Carlo (QMC) methods \citep{huangquasi}. Beyond the deterministic error bound guarantee, we further establish additional average error bounds for RQMC features: some requiring weaker assumptions and others significantly reducing the exponent of the logarithmic factor. In the context of kernel ridge regression, we show that RQMC features offer computational advantages over MC features while preserving the same statistical error rate. Empirical results further show that RQMC methods maintain stable performance in both low and moderately high-dimensional settings, unlike QMC methods, which suffer from significant performance degradation as dimension increases.

Gradient is All You Need: Gradient-Based Attention Fusion for Infrared Small Target Detection

Infrared small target detection (IRSTD) is widely used in civilian and military applications. However, IRSTD encounters several challenges, including the tendency for small and dim targets to be obscured by complex backgrounds. To address this issue, we propose the Gradient Network (GaNet), which aims to extract and preserve edge and gradient information of small targets. GaNet employs the Gradient Transformer (GradFormer) module, simulating central difference convolutions (CDC) to extract and integrate gradient features with deeper features. Furthermore, we propose a global feature extraction model (GFEM) that offers a comprehensive perspective to prevent the network from focusing solely on details while neglecting the background information. We compare the network with state-of-the-art (SOTA) approaches, and the results demonstrate that our method performs effectively. Our source code is available at https://github.com/greekinRoma/Gradient-Transformer.

RPCANet: Deep Unfolding RPCA Based Infrared Small Target Detection

Deep learning (DL) networks have achieved remarkable performance in infrared small target detection (ISTD). However, these structures exhibit a deficiency in interpretability and are widely regarded as black boxes, as they disregard domain knowledge in ISTD. To alleviate this issue, this work proposes an interpretable deep network for detecting infrared dim targets, dubbed RPCANet. Specifically, our approach formulates the ISTD task as sparse target extraction, low-rank background estimation, and image reconstruction in a relaxed Robust Principle Component Analysis (RPCA) model. By unfolding the iterative optimization updating steps into a deep-learning framework, time-consuming and complex matrix calculations are replaced by theory-guided neural networks. RPCANet detects targets with clear interpretability and preserves the intrinsic image feature, instead of directly transforming the detection task into a matrix decomposition problem. Extensive experiments substantiate the effectiveness of our deep unfolding framework and demonstrate its trustworthy results, surpassing baseline methods in both qualitative and quantitative evaluations.