MiCA Learns More Knowledge Than LoRA and Full Fine-Tuning

Recent literature on fine-tuning Large Language Models highlights a fundamental debate. While Full Fine-Tuning (FFT) provides greater representational plasticity, Low-Rank Adaptation (LoRA) can match or surpass FFT performance while constraining updates to a low-rank space and potentially benefiting from 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 observe both trends and find that the better static architecture depends on the task and model. Spectral and truncation analyses further show that endpoint compressibility alone does not explain these task differences, suggesting task-score sensitivity and constrained optimization trajectories as possible explanations. 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, while only selected experts update their weights. 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 $1.5$ percentage points of the better of FFT and LoRA across the nine tested settings, while MoLF-Efficient outperforms both AdaLoRA and AdaMix in eight of nine settings, with gains over the stronger baseline of up to $11.70$ percentage points on Fact, $3.13$ on Med, and $2.98$ on SQL.

Low-Rank Adaptation (LoRA) is the most widely adopted method for fine-tuning large language models. Notably, LoRA is inherently overparameterized: multiple pairs of low-rank factors can yield the same adapted weight matrix. We show--both theoretically and empirically--that these pairs exhibit significantly different condition numbers. As a result, converging to different loss minimizers directly impacts the convergence rate of LoRA. Building on this observation, we introduce Balanced Low-Rank Adaptation (BaLoRA), a variant of LoRA that projects iterates onto a balanced manifold. This manifold improves the conditioning of the loss landscape while preserving the adapted matrix. The projection step is computationally lightweight and integrates seamlessly into existing fine-tuning pipelines. Empirically, BaLoRA converges faster than standard LoRA and achieves superior performance across a range of fine-tuning tasks.

Low-Rank Adaptation (LoRA) has emerged as the dominant paradigm for parameter-efficient fine-tuning of large language models. Standard all-layer LoRA applies adaptation throughout the transformer, despite heterogeneous contributions from its components. In this work, we conduct a systematic mechanistic interpretability analysis to understand how LoRA affects model internals. We observe that LoRA's adaptation effect is highly non-uniform, with significant component-wise and layer-wise sparsity. Most critically, we find that important layers are highly task-dependent, with limited overlap across tasks. Motivated by these insights, we propose Adaptive-LoRA, a calibration-driven method that automatically identifies task-specific layers via frozen-base zero-ablation, enabling efficient layer selection without exhaustive search. Extensive experiments on Qwen2.5-1.5B across 11 diverse reasoning tasks demonstrate that Adaptive-LoRA outperforms full-layer LoRA while using only 30% of layers, achieving a $3.5\times$ reduction in adapter parameters. This work bridges mechanistic interpretability and practical efficiency, providing both fundamental insights and a principled approach for adaptive fine-tuning.