Post-training has become essential for adapting large language models (LLMs) to complex downstream behaviors, including instruction following, preference alignment, and multi-step reasoning. Reinforcement learning with verifiable rewards (RLVR) has recently emerged as a particularly effective post-training paradigm for improving reasoning capabilities, with critic-free algorithms such as GRPO and GSPO enabling scalable optimization. However, RLVR post-training with full fine-tuning (FFT) requires substantial GPU memory and incurs high training costs. Although parameter-efficient fine-tuning (PEFT) methods, such as Low-Rank Adaptation (LoRA), effectively reduce computational costs, they often suffer from a noticeable performance gap compared to full fine-tuning in post-training for complex reasoning tasks. In this paper, we propose Hybrid-LoRA, an efficient hybrid post-training framework that selectively applies full fine-tuning to a small subset of modules less suited to low-rank adaptation, while adapting the remaining components with LoRA. We introduce a novel Hybrid-LoRA Score to rank candidate modules according to their sensitivity to low-rank adaptation under a fixed parameter budget. Experiments show that Hybrid-LoRA closely matches full fine-tuning performance under a 10% full fine-tuning module budget, with the remaining candidate modules adapted by LoRA, consistently outperforming four state-of-the-art PEFT post-training baselines, achieving improvements of up to 5.65% and on average 4.36% over the best baseline.
Reinforcement learning (RL)-based post-training has become an effective approach for eliciting reasoning capabilities in large language models (LLMs). However, adapting post-RL models to new knowledge domains or behaviors through subsequent supervised fine-tuning (SFT) can severely overwrite these capabilities. Existing approaches mitigate such forgetting through experience replay, specialized initialization, or constrained optimization using gradient projection, but either provide limited preservation or incur substantial training overhead. Our analysis shows that reasoning activations concentrate in low-dimensional subspaces, leaving substantial null-space capacity for adaptation, and that the corresponding approximate null spaces can be reliably estimated from a modest number of examples. Motivated by these observations, we propose Null-Basis Low-Rank Adaptation (NB-LoRA), a parameter-efficient method for adapting post-RL LLMs while preserving their acquired reasoning ability. We formulate reasoning retention as a layer-wise hidden-state preservation constraint and construct a fixed approximate null basis from reasoning activations. LoRA updates are then reparameterized through this basis, enforcing the preservation constraint throughout fine-tuning. Extensive experiments across multiple RL-trained LLMs and diverse downstream tasks show that NB-LoRA matches standard LoRA in adaptation performance, maintains reasoning accuracy near pre-fine-tuning levels, and generalizes this preservation to held-out reasoning benchmarks.
Recent literature on fine-tuning Large Language Models highlights a fundamental debate. While Full Fine-Tuning (FFT) provides the representational plasticity required for high-entropy knowledge injection, Low-Rank Adaptation (LoRA) can match or surpass FFT performance because many tasks only require updates in a low-rank space and benefit from LoRA's additional regularization. Through empirical evaluation across diverse tasks (SQL, Medical QA, and Counterfactual Knowledge) and varying language models (Gemma-3-1B, Qwen2.5-1.5B, and Qwen2.5-3B), we verify both trends and demonstrate that relying solely on either static architecture is structurally limited. To address this challenge, we propose a Mixture of LoRA and Full (MoLF) Fine-Tuning, a unified framework that enables continuous navigation between both training regimes. MoLF dynamically routes updates between FFT and LoRA at the optimizer level to ensure that exact gradient signals are available to both experts throughout training, yielding stable training dynamics. For memory-constrained environments, we also introduce MoLF-Efficient, which freezes base weights and only routes updates among a pair of LoRA experts of potentially varying rank. Our evaluations show that MoLF either improves on or stays within 1.5% of the better of FFT and LoRA across all settings, while MoLF-Efficient outperforms prior adaptive LoRA approaches by up to 20% on Fact and 9% on Med and SQL. Our code is open-sourced at https://github.com/11785T23/molf.git.
Low-Rank Adaptation (LoRA) has gained popularity as a fine-tuning approach for Large Language Models (LLMs) due to its low resource requirements and good performance. While numerous studies have investigated ways to improve LoRA serving efficiency by serving multiple LoRAs concurrently, existing methods assume that a wide range of LoRA adapters are available for serving. In our work, we conduct extensive empirical studies to show that current LoRA training paradigms do not efficiently utilize hardware resources and incur high overhead to obtain a performant LoRA adapter. Leveraging these insights, we propose PLoRA, which automatically orchestrates concurrent LoRA fine-tuning jobs under given hardware and model constraints and develops performant kernels to improve training efficiency. Across a range of LLMs and LoRA configurations, PLoRA improves training throughput by up to 12.8x and reduces the overall fine-tuning makespan by up to 7.52x compared to existing approaches.