We study minimax rates for conditional generative learning under integrated Wasserstein loss, with Hölder continuous conditional laws and an unrestricted covariate distribution. We evaluate unrestricted generators through their conditional output distributions. For expected Wasserstein loss, the minimax rate agrees with the rate under uniform covariates and follows from balancing localization bias against unconditional distribution estimation error. Higher moments of the loss can instead be dominated by unobserved covariate regions, which force an additional risk contribution of order $n^{-1}$, where $n$ is the sample size. An adaptive localization argument gives matching upper bounds. The results cover unrestricted response laws and possibly vanishing Besov densities for $W_1$, and extend to higher Wasserstein orders under uniform response density bounds and integrability conditions. A multiscale lower bound closes the logarithmic gap in unconditional $W_1$ minimax rates in dimension two for both unrestricted distributions and Besov density classes. We also establish minimax rates for conditional Brenier maps under density, integrability, and uniform curvature conditions.
Sunguk Shin, Fangzhao Wu Microsoft, Byung-Jun Lee Korea University and Gauss Labs Inc., Meeyoung Cha Max Planck Institute for Security and Privacy and Korea Advanced Institute of Science & Technology, Sungwon Park
Open-weight large language models (LLMs) enable broad customization, but also increase exposure to post-release misuse, including malicious fine-tuning (MFT). To mitigate this risk, many prior defenses aim to improve the robustness of open-weight models to MFT by constraining adversarial fine-tuning dynamics in parameter space or mitigating harmful information encoded in internal representations. Nevertheless, since malicious fine-tuning can still erode safety, developing robust safeguards for open-weight models that fundamentally mitigate this risk remains an open research problem. In this paper, we characterize a safety region for open-weight LLMs and propose Safety Guidance Trigger (SGT), which guides fine-tuning toward the safety manifold to preserve alignment. SGT has two stages: (1) optimizing a safety trigger that steers the base model toward safe responses and (2) training the open-weight model to align its internal features with trigger-induced safety representations. We demonstrate that SGT substantially improves robustness against malicious fine-tuning, requiring adversaries to increase their data budget significantly to compromise safety. Our analysis shows that SGT anchors model representations to a safety region, which remains stable under malicious fine-tuning.
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cs.CL
Proceedings of the 64th Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) · 2026 · 正式发表