Bayesian Subspace Gradient Estimation for Zeroth-Order Optimization of Large Language Models

Fine-tuning large language models (LLMs) with zeroth-order (ZO) optimization reduces memory by approximating gradients through function evaluations, but existing methods rely on one-step gradient estimates from random perturbations. We introduce Bayesian Subspace Zeroth-Order optimization (BSZO), a ZO optimizer that applies Kalman filtering to combine finite-difference information across multiple perturbation directions. By treating each finite-difference measurement as a noisy observation, BSZO builds a posterior distribution over the projected gradient and updates it through Bayesian inference, with a residual-based adaptive mechanism to adjust perturbation scales. Theoretical analysis shows that BSZO improves the convergence rate by a factor of $k/γ$ compared to standard ZO methods. Experiments on RoBERTa, Mistral, and OPT models show that BSZO outperforms MeZO, MeZO-Adam, and HiZOO across various tasks, achieving up to 6.67\% absolute average improvement on OPT-13B while keeping memory usage close to inference-only baselines (1.00$\times$--1.08$\times$ of MeZO).

DLIMD: Dictionary Learning based Image-domain Material Decomposition for spectral CT

The potential huge advantage of spectral computed tomography (CT) is its capability to provide accuracy material identification and quantitative tissue information. This can benefit clinical applications, such as brain angiography, early tumor recognition, etc. To achieve more accurate material components with higher material image quality, we develop a dictionary learning based image-domain material decomposition (DLIMD) for spectral CT in this paper. First, we reconstruct spectral CT image from projections and calculate material coefficients matrix by selecting uniform regions of basis materials from image reconstruction results. Second, we employ the direct inversion (DI) method to obtain initial material decomposition results, and a set of image patches are extracted from the mode-1 unfolding of normalized material image tensor to train a united dictionary by the K-SVD technique. Third, the trained dictionary is employed to explore the similarities from decomposed material images by constructing the DLIMD model. Fourth, more constraints (i.e., volume conservation and the bounds of each pixel within material maps) are further integrated into the model to improve the accuracy of material decomposition. Finally, both physical phantom and preclinical experiments are employed to evaluate the performance of the proposed DLIMD in material decomposition accuracy, material image edge preservation and feature recovery.