Gradient-Based LoRA Rank Allocation Under GRPO: An Empirical Study

Low-Rank Adaptation (LoRA) has become a cornerstone of parameter-efficient fine-tuning (PEFT); however, the conventional practice of uniform rank assignment ignores the functional heterogeneity of neural layers. Existing rank allocation methods typically struggle with a trade-off between computational intensity and heuristic simplicity: training-based methods suffer from prohibitive overhead, while pre-allocation methods fail to capture the dynamic task-specific representation manifold. In this paper, we propose RSLoRA (Representational Sensitivity LoRA), a training-free and gradient-free rank allocator driven by activation-space geometry. We identify a "sensitivity regime shift" across layers, observing that static weight analysis and local gradients are insufficient to reflect how updates reshape a model's internal representations. To address this, RSLoRA introduces a virtual representational probing mechanism. By simulating adaptation through structured low-rank noise and measuring the resulting manifold displacement by using Effective Rank and Frechet Distance, we identify high-sensitivity modules that require higher rank capacity. Our framework effectively bridges the gap between expert-crafted heuristics and actual representational impact. Extensive evaluations demonstrate that RSLoRA consistently outperforms state-of-the-art allocators (e.g., AdaLoRA, GoRA) across mainstream benchmarks. By eliminating the need for iterative training-time adjustments and backward gradients, RSLoRA provides a highly efficient, robust, and representation-aware solution for large-scale model adaptation.

Large language model (LLM) alignment via reinforcement learning from human preferences (RLHF) suffers from unstable policy updates, ambiguous gradient directions, poor interpretability, and high gradient variance in mainstream pairwise preference learning paradigms. To systematically address these limitations, we establish a unified theoretical framework for preference-based RL optimization centered on the Pair-GRPO family, comprising two tightly coupled variants: Soft-Pair-GRPO and Hard-Pair-GRPO. Soft-Pair-GRPO is a minimal modification of Group Relative Policy Optimization (GRPO) that replaces group-normalized scalar rewards with binary pairwise preference rewards, retaining GRPO's clipped surrogate and KL-regularized structure. We prove a critical gradient equivalence theorem: under first-order Taylor expansion around the current policy, Soft-Pair-GRPO's gradient is a positive scalar multiple of standard GRPO's gradient, explaining its empirical stability despite discarding continuous reward magnitudes. Building on this foundation, we propose Hard-Pair-GRPO, an advanced variant introducing explicit local probability constraints and constrained KL-fitting optimization to further suppress gradient noise and global policy drift. We provide comprehensive theoretical guarantees for both variants--including monotonic policy improvement, deterministic gradient direction, gradient-variance reduction, and dynamic step-size convergence. Extensive experiments on standard LLM alignment benchmarks (HH-RLHF,UltraFeedback) and the MuJoCo continuous control task HalfCheetah-v4 demonstrate that our Pair-GRPO family consistently outperforms state-of-the-art baselines in alignment quality, human preference win rate, training stability, and generalization to general reinforcement learning. Ablation studies validate the critical contributions of each core component.

We study the \textit{parameter placement problem}: given a fixed budget of $k$ trainable entries within the B matrix of a LoRA adapter (A frozen), does the choice of which $k$ matter? Under supervised fine-tuning, random and informed subsets achieve comparable performance. Under GRPO on base models, random placement fails to improve over the base model, while gradient-informed placement recovers standard LoRA accuracy. This regime dependence traces to gradient structure: SFT gradients are low-rank and directionally stable, so any subset accumulates coherent updates; GRPO gradients are high-rank and near-orthogonal across steps, so only elements with consistently signed gradients retain the learning signal. Our scoring procedure identifies these critical parameters in under 10 seconds at less than 0.5% of training cost. Selected parameters concentrate on residual-stream-writing projections (V, O, Down), stable across model families and scales (1.5B - 8B).