Model merging aims to integrate task-specific abilities from individually fine-tuned models into a single model without extra training. In model merging methods, the task vector has become a fundamental building block, as it can encapsulate the information from fine-tuning. However, the merged model often suffers from performance degradation due to conflicts caused by task-irrelevant redundancy in task vectors. To address these challenges, we propose Purified TAsk VEctors (PAVE) in knowledge-aware subspace. Concretely, we sample training examples from each task, and feed them into their fine-tuned models to acquire covariance matrices before linear layers. We then perform a context-oriented singular value decomposition, which accentuates the weight components most relevant to the target knowledge. As a result, we split fine-tuned model weights into task-relevant and redundant components in the knowledge-aware subspace, and purify the task vector by pruning redundant components. To induce fair pruning efforts across models, we further introduce a spectral rank allocation strategy by optimizing a normalized activated pruning error. The task vector purification by our method as a plug-and-play scheme is applicable across various task vector-based merging methods to improve their performance. In experiments, we demonstrate the effectiveness of PAVE across diverse merging methods, tasks, and model architectures.

Detecting pre-training data in Large Language Models (LLMs) is crucial for auditing data privacy and copyright compliance, yet it remains challenging in black-box, zero-shot settings where computational resources and training data are scarce. While existing likelihood-based methods have shown promise, they typically aggregate token-level scores using uniform weights, thereby neglecting the inherent information-theoretic dynamics of autoregressive generation. In this paper, we hypothesize and empirically validate that memorization signals are heavily skewed towards the high-entropy initial tokens, where model uncertainty is highest, and decay as context accumulates. To leverage this linguistic property, we introduce Positional Decay Reweighting (PDR), a training-free and plug-and-play framework. PDR explicitly reweights token-level scores to amplify distinct signals from early positions while suppressing noise from later ones. Extensive experiments show that PDR acts as a robust prior and can usually enhance a wide range of advanced methods across multiple benchmarks.

The inherent safety alignment of Large Language Models (LLMs) is prone to erosion during fine-tuning, even when using seemingly innocuous datasets. While existing defenses attempt to mitigate this via data selection, they typically rely on heuristic, instance-level assessments that neglect the global geometry of the data distribution and fail to explicitly repel harmful patterns. To address this, we introduce Safety Optimal Transport (SOT), a novel framework that reframes safe fine-tuning from an instance-level filtering challenge to a distribution-level alignment task grounded in Optimal Transport (OT). At its core is a dual-reference “push-pull” weight-learning mechanism: SOT optimizes sample importance by actively pulling the downstream distribution towards a trusted safe anchor while simultaneously pushing it away from a general harmful reference. This establishes a robust geometric safety boundary that effectively purifies the training data. Extensive experiments across diverse model families and domains demonstrate that SOT significantly enhances model safety while maintaining competitive downstream performance, achieving a superior safety-utility trade-off compared to baselines.