FIM-LoRA: Task-Informative Rank Allocation for LoRA via Calibration-Time Gradient-Variance Estimation

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.

Exponential growth in the scale of modern foundation models has led to the widespread adoption of Low-Rank Adaptation (LoRA) as a parameter-efficient fine-tuning technique. However, standard LoRA implementations disregard the varying intrinsic dimensionality of model layers and enforce a uniform rank, leading to parameter redundancy. We propose Post-Optimization Adaptive Rank Allocation (PARA), a data-free compression method for LoRA that integrates seamlessly into existing fine-tuning pipelines. PARA leverages Singular Value Decomposition to prune LoRA ranks using a global threshold over singular values across all layers. This results in non-uniform rank allocation based on layer-wise spectral importance. As a post-hoc method, PARA circumvents the training modifications and resulting instabilities that dynamic architectures typically incur. We empirically demonstrate that PARA reduces parameter count by 75-90% while preserving the predictive performance of the original, uncompressed LoRA across multiple vision and language benchmarks. Code will be published upon acceptance.

Low-Rank Adaptation (LoRA) is a popular parameter-efficient fine-tuning (PEFT) method that restricts weight updates to low-rank adapters, introducing a fixed low-rank inductive bias by optimizing in a low-dimensional subspace. In this work, we question whether a fixed-rank constraint is the most effective inductive bias for parameter-efficient fine-tuning. We introduce Learnable Rank LoRA (LR-LoRA), a PEFT method in which the adapter rank is learned during the training process. Instead of prescribing a uniform rank for all adapter layers, LR-LoRA allows the optimizer to determine the appropriate rank for each layer. Using this approach, we find substantial layer-wise variation in the learned ranks, with the attention and MLP layers in the transformer models exhibiting systematically different rank preferences. Across a range of language understanding and commonsense reasoning benchmarks, LR-LoRA achieves state-of-the-art performance in most settings and consistently outperforms strong PEFT baselines, demonstrating that a learnable rank provides a more flexible and effective inductive bias than fixed-rank adaptations.