arXiv subjects

Ziqi Qin

Publications and source records attributed to Ziqi Qin.

3 recordsLinked to original sources

arXiv2026

Mixed-Noise Plug-and-Play with Infimal Convolution Fidelities and Multiple Priors

Plug-and-Play (PnP) algorithms are a class of iterative methods for inverse imaging. Within an optimization algorithm, they combine a flexible fidelity term, encoding the forward operator, and a pretrained image denoiser, in order to deal with more severe corruptions such as blurring or downsampling when reconstructing an image. This work studies provably convergent PnP methods for mixed-noise forward processes by using the infimal convolution as a fidelity term, providing a statistical interpretation as a joint maximum a-posteriori estimator over both noises, and preserving the Bayesian MAP interpretation of PnP methods. Independently, we extend the PnP formulation to multiple prior terms using the Davis--Yin three-operator splitting. This extension can be combined with either standard fidelities or the proposed mixed-noise infimal-convolution fidelities. We verify that these generalized PnP methods are convergent under standard Kurdyka--Lojasiewicz conditions. Numerical experiments on Laplace-Gaussian and Poisson--Gaussian noise demonstrate stable convergence of single-prior and multiple-prior PnP methods, and divergence under fidelity mismatch. Furthermore, PnP with infimal convolution fidelities are able to scale to noise up to 38% standard deviation, with multiple priors reaching different stationary points that qualitatively preserve more textural properties.

math.OC↗

arXiv2026

NanoNet: Parameter-Efficient Learning with Label-Scarce Supervision for Lightweight Text Mining Model

The lightweight semi-supervised learning (LSL) strategy provides an effective approach of conserving labeled samples and minimizing model inference costs. Prior research has effectively applied knowledge transfer learning and co-training regularization from large to small models in LSL. However, such training strategies are computationally intensive and prone to local optima, thereby increasing the difficulty of finding the optimal solution. This has prompted us to investigate the feasibility of integrating three low-cost scenarios for text mining tasks: limited labeled supervision, lightweight fine-tuning, and rapid-inference small models. We propose NanoNet, a novel framework for lightweight text mining that implements parameter-efficient learning with limited supervision. It employs online knowledge distillation to generate multiple small models and enhances their performance through mutual learning regularization. The entire process leverages parameter-efficient learning, reducing training costs and minimizing supervision requirements, ultimately yielding a lightweight model for downstream inference.

cs.LG↗

arXiv2025

Partial Smoothness, Subdifferentials and Set-valued Operators

Over the past decades, the concept "partial smoothness" has been playing as a powerful tool in several fields involving nonsmooth analysis, such as nonsmooth optimization, inverse problems and operation research, etc. The essence of partial smoothness is that it builds an elegant connection between the optimization variable and the objective function value through the subdifferential. Identifiability is the most appealing property of partial smoothness, as locally it allows us to conduct much finer or even sharp analysis, such as linear convergence or sensitivity analysis. However, currently the identifiability relies on non-degeneracy condition and exact dual convergence, which limits the potential application of partial smoothness. In this paper, we provide an alternative characterization of partial smoothness through only subdifferentials. This new perspective enables us to establish stronger identification results, explain identification under degeneracy and non-vanishing error. Moreover, we can generalize this new characterization to set-valued operators, and provide a complement definition of partly smooth operator proposed in [14].

math.OC↗