Low-Rank Adaptation (LoRA) is a widely used approach to parameter-efficient fine-tuning (PEFT) of LLMs whose effectiveness depends on rank allocation. Existing adaptive LoRA methods derive ranks from local gradient, activation, or matrix statistics collected before or during fine-tuning; training-time variants add overhead, and local signals reveal little about each module's structural role in information propagation, giving weak global grounding for scarce-capacity allocation. We propose IFCLoRA, a topology-aware method for pre-fine-tuning rank allocation and adapter initialization. Using a small calibration set, IFCLoRA performs intervention tracing on the frozen model and constructs a sparse task-conditioned interaction graph over LoRA target modules. From this graph it extracts a global information-flow topology prior and fuses it with each node's local gradient sensitivity to form a topology-dominant Information-Flow Centrality (IFC) score, measuring participation in task-conditioned multi-hop propagation. The IFC scores then serve as module-level routing signals for one-shot discrete rank allocation under a rank-budget constraint. Reusing response vectors from tracing, IFCLoRA constructs a function-preserving flow-response subspace initialization, giving adapters task-relevant output subspaces. Across all settings, IFCLoRA achieves higher mean scores than standard LoRA with comparable fine-tuning time and peak memory; it requires a one-time offline calibration stage. On GSM8K, IFCLoRA attains the highest mean accuracy among compared PEFT methods on both base models, exceeding standard LoRA by 4.75 percentage points on LLaMA-3.1-8B. Resulting rank allocations are non-uniform and vary across tasks and base models, suggesting that task-conditioned global information-flow topology can serve as a useful structural prior for rank allocation in low-budget PEFT.
Yihang Gao, Vincent Y. F. Tanstat.ML cs.LG math.ST
Low-rank adaptation (LoRA) has become a widely used parameter-efficient fine-tuning method for large language models. Since different modules and layers may contribute unequally to downstream adaptation, allocating rank resources under a fixed parameter budget is an important problem for balancing efficiency, expressiveness, and generalization. Existing adaptive rank methods address this problem mainly through carefully designed importance scores constructed from gradient-derived sensitivity and uncertainty measures, without an explicit statistical interpretation. In this paper, we formulate LoRA rank allocation as a statistical hypothesis testing problem and propose StatLoRA, a statistical inference-based rank allocation method. StatLoRA associates each LoRA component with a test statistic and uses estimated p-values to determine which components should be retained or pruned under a prescribed rank budget. The proposed testing procedure is supported by our central limit theory for stochastic optimizer trajectories. In particular, we establish asymptotic normality for a broad class of commonly used optimizers in deep learning, including AdamW, and derive the corresponding asymptotic distributions for the proposed component scores used in hypothesis testing. We evaluate StatLoRA on LoRA fine-tuning of DeBERTaV3-base, BART-Large, and Qwen2.5-7B across natural language understanding, natural language generation, and question answering tasks. Experiments show that StatLoRA achieves comparable or better performance than vanilla LoRA, AdaLoRA, and IGU-LoRA under matched rank budgets. Sensitivity analyses and empirical diagnostics further support the stability of the proposed hypothesis-testing-based allocation rule and provide empirical evidence for the asymptotic theory of component scores.
Parameter-efficient fine-tuning enables large language models to adapt to downstream tasks with substantially lower computational and storage cost, and Low-Rank Adaptation (LoRA) is among its most widely used techniques. However, vanilla LoRA assigns a uniform rank to all adapted modules, while existing adaptive methods either incur additional optimization overhead or rely on static weights and local gradients that do not capture task-conditioned representation changes. We propose RSRA, a training-free rank allocator that estimates where adaptation capacity is most needed through forward-only representation sensitivity probing on a small calibration set. Specifically, RSRA uses Spectral Effective Rank to allocate capacity across layers, measures module-wise hidden-state displacement under standardized virtual low-rank updates with the Frechet Distance, and combines both signals through hierarchical normalization to produce a task-aware rank configuration before fine-tuning. Across commonsense reasoning and natural language understanding benchmarks with Qwen3-4B and Mistral-7B, RSRA achieves the highest average performance in all three reported model-benchmark settings and a 1.48x-1.93x speedup in allocation time over the fastest competing pre-allocation method. When integrated with DoRA, LoRA-FA, and PiSSA, RSRA improves 15 of the 18 evaluated combinations and increases the average performance of all three PEFT methods.
Ashutosh Tripathi, Surya Deep Singh, Pranab Sahoo +1cs.LG cs.AI
Low-Rank Adaptation is widely used for parameter-efficient fine-tuning, yet existing methods typically assign the same adapter rank to every transformer layer despite their heterogeneous adaptation requirements. In this work, we show theoretically and empirically that uniform rank allocation is fundamentally suboptimal. Motivated by this observation, we propose LAARA (Layer Aware Adaptive Rank Allocation framework), a search-free framework that dynamically allocates ranks using lightweight diagonal Fisher estimates computed during training. LAARA combines projection-wise normalization, logarithmic compression, blended adapter importance estimation, and a vote-to-change dampening mechanism to produce stable and efficient rank adaptation. Experiments on GLUE and MathInstruct benchmark demonstrate that LAARA consistently matches or outperforms popular state of the art approaches such as LoRA, AdaLoRA, DyLoRA, and Bitfit while using significantly fewer trainable parameters. Our results show that Fisher-guided rank allocation provides a principled and effective foundation for adaptive parameter-efficient fine-tuning. The code is publicly available at: https://anonymous.4open.science/r/LAARA-D305/LAARA.py
Low-rank decomposition serves as a promising compression paradigm for large language models, however, rank allocation remains challenging: manual rules lack generalizability, and learning-based approaches incur heavy computational overhead. To address these issues, we formulate global low-rank allocation as a sorting-and-truncation pipeline, and score each singular component via dual criteria: \textbf{Local} singular energy ratio that quantifies the intrinsic importance within the decomposed parameter matrix and \textbf{Global} functional importance (measured by input-output cosine similarity) that evaluates the functional significance of decomposed modules. We verify the strong correlation between high input-output cosine similarity and low effective rank through geometric interpretation and experimental validation. Furthermore, we propose rank-preserving fine-tuning, which performs direct LoRA tuning on decomposed weights and avoids extra information loss caused by re-truncation in conventional merging pipelines. Empirical results confirm that our method delivers sustained performance enhancements when combined with models featuring distinct decomposition schemes, model sizes and architectural designs, e.g. in one-shot compression without further fine-tuning, our method reduces perplexity by up to 50\% compared with uniform and heuristic allocation baselines. Code will be available at https://github.com/EIT-NLP/LLM-Pruning.