CARE-LoRA: Compressed Activation REconstruction for Memory-Efficient LoRA

As the scale of large pre-trained models continues to grow, fine-tuning them under limited memory budgets has become increasingly challenging. Low-Rank Adaptation (LoRA), currently one of the most widely adopted parameter-efficient fine-tuning (PEFT) methods, mitigates this challenge by optimizing only low-rank adaptation matrices, thereby greatly reducing the number of trainable parameters. With the parameter overhead substantially reduced, the activations retained for backpropagation have emerged as the primary remaining memory bottleneck during LoRA fine-tuning. To address this, we propose CARE-LoRA, a data-aware Compressed Activation REconstruction framework. By exploiting the inherent projection structure of LoRA, CARE-LoRA replaces the full input activation with the low-rank compressed activation naturally produced by the LoRA branch. It further computes a lightweight reconstruction matrix during the forward pass with negligible additional computation cost, which is used during backpropagation to reconstruct the gradient signal, thereby keeping LoRA matrices fully trainable. Extensive experiments across diverse models and downstream tasks demonstrate that, while substantially reducing the overall memory footprint, CARE-LoRA achieves competitive or even superior performance compared with standard LoRA and representative LoRA variants. Our code is publicly available at https://github.com/fishandyu/CARE-LoRA .

Stochastic Optimal Control Sampling for Diffusion Inverse Problems

Benefiting from the strong ability to capture data distributions, diffusion models have become powerful tools for solving image inverse problems. The key is to controllably steer the sampling trajectory toward the measurements while respecting the diffusion prior. In this work, we introduce Stochastic Optimal Control Sampling (SOCS), which models the denoising process as a dynamical system and injects control signals via SOC. Previous SOC-based approach addresses inverse problems by optimizing over the entire trajectory, which is computationally expensive. In contrast, we derive a closed-form control update and apply it at each sampling step, pulling the measurement-consistent clean prediction back onto the denoising flow. In SOCS, we can readily modulate the control strength to align with the diffusion model's native capabilities and thereby enhance perceptual quality. Our method is compatible with a variety of linear stochastic differential equation backbones. Extensive experiments across a broad spectrum of image inverse tasks demonstrate that SOCS achieves accurate measurement-aligned reconstructions with improved visual fidelity and stronger quantitative performance.

SAGE: Retain-Aware Post-Hoc Sanitization of Final Unlearning Vector

Large Language Model (LLM) unlearning aims to remove undesirable knowledge or behaviors while preserving retained capabilities. Current unlearning methods all involve a trade-off between unlearning and retention. We have found that the retention activation bias can also be used to quantify the damage an unlearning method inflicts on retention, without considering the specific implementation of the unlearning process. This allows us to restore retention performance for any unlearning method using a post-hoc approach. Therefore, we propose a complementary post-hoc setting to sanitize the final update vector without rerunning the original unlearning pipeline. In this setting, we design SAGE, Spectral Activation-GEometry Sanitization, a source-agnostic correction for final unlearning updates. SAGE collects real module inputs from a small retain proxy, extracts their dominant activation geometry, and solves a source-anchored optimization objective in closed form, which suppresses update components aligned with high-energy retained directions while preserving the source method's forgetting carrier. Across multiple unlearning methods, model scales, and benchmarks, SAGE consistently relieves the retain-forget trade-off, identifying post-hoc sanitization of final vectors as a practical and underexplored axis for machine unlearning.

RAIN-Merging: A Gradient-Free Method to Enhance Instruction Following in Large Reasoning Models with Preserved Thinking Format

Large reasoning models (LRMs) excel at a long chain of reasoning but often fail to faithfully follow instructions regarding output format, constraints, or specific requirements. We investigate whether this gap can be closed by integrating an instruction-tuned model (ITM) into an LRM. Analyzing their differences in parameter space, namely task vectors, we find that their principal subspaces are nearly orthogonal across key modules, suggesting a lightweight merging with minimal interference. However, we also demonstrate that naive merges are fragile because they overlook the output format mismatch between LRMs (with explicit thinking and response segments) and ITMs (answers-only). We introduce RAIN-Merging (Reasoning-Aware Instruction-attention guided Null-space projection Merging), a gradient-free method that integrates instruction following while preserving thinking format and reasoning performance. First, with a small reasoning calibration set, we project the ITM task vector onto the null space of forward features at thinking special tokens, which preserves the LRM's structured reasoning mechanisms. Second, using a small instruction calibration set, we estimate instruction attention to derive module-specific scaling that amplifies instruction-relevant components and suppresses leakage. Across four instruction-following benchmarks and nine reasoning & general capability benchmarks, RAIN-Merging substantially improves instruction adherence while maintaining reasoning quality. The gains are consistent across model scales and architectures, translating to improved performance in agent settings.