Keep the Core: Adversarial Priors for Significance-Preserving Brain MRI Segmentation

Medical image segmentation is constrained by sparse pathological annotations. Existing augmentation strategies, from conventional transforms to random masking for self-supervision, are feature-agnostic: they often corrupt critical diagnostic semantics or fail to prioritize essential features. We introduce "Keep the Core," a novel data-centric paradigm that uses adversarial priors to guide both augmentation and masking in a significance-preserving manner. Our approach uses SAGE (Sparse Adversarial Gated Estimator), an offline module identifying minimal tokens whose micro-perturbation flips segmentation boundaries. SAGE forges the Token Importance Map $W$ by solving an adversarial optimization problem to maximally degrade performance, while an $\ell_1$ sparsity penalty encourages a compact set of sensitive tokens. The online KEEP (Key-region Enhancement \& Preservation) module uses $W$ for a two-pronged augmentation strategy: (1) Semantic-Preserving Augmentation: High-importance tokens are augmented, but their original pixel values are strictly restored. (2) Guided-Masking Augmentation: Low-importance tokens are selectively masked for an $\text{MAE}$-style reconstruction, forcing the model to learn robust representations from preserved critical features. "Keep the Core" is backbone-agnostic with no inference overhead. Extensive experiments show SAGE's structured priors and KEEP's region-selective mechanism are highly complementary, achieving state-of-the-art segmentation robustness and generalization on 2D medical datasets.

Robust data-driven discovery of partial differential equations with time-dependent coefficients

In this work, we propose a robust Bayesian sparse learning algorithm based on Bayesian group Lasso with spike and slab priors for the discovery of partial differential equations with variable coefficients. Using the samples draw from the posterior distribution with a Gibbs sampler, we are able to estimate the values of coefficients, together with their standard errors and confidence intervals. Apart from constructing the error bars, uncertainty quantification can also be employed for designing new criteria of model selection and threshold setting. This enables our method more adjustable and robust in learning equations with time-dependent coefficients. Three criteria are introduced for model selection and threshold setting to identify the correct terms: the root mean square, total error bar, and group error bar. Moreover, three noise filters are integrated with the robust Bayesian sparse learning algorithm for better results with larger noise. Numerical results demonstrate that our method is more robust than sequential grouped threshold ridge regression and group Lasso in noisy situations through three examples.