BA-LoRA: Bias-Alleviating Low-Rank Adaptation to Mitigate Catastrophic Inheritance in Large Language Models

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.

Adapting large language models (LLMs) to downstream tasks via full fine-tuning is increasingly impractical due to its computational and memory demands. Parameter-efficient fine-tuning (PEFT) approaches such as Low-Rank Adaptation (LoRA) mitigate this by confining updates to a compact set of trainable parameters, but this aggressive reduction often sacrifices generalization, especially under transfer across heterogeneous tasks and domains. We revisit the tension between parameter efficiency and adaptation capacity, and ask whether the two are truly at odds. We answer in the negative by introducing LoRA-Over, a framework grounded in a simple principle: enrich the optimization landscape during training, then collapse the enrichment at inference. LoRA-Over injects auxiliary parameters into the low-rank adapters during training to broaden the effective hypothesis space, and through a decomposition-based reformulation folds them back into a standard low-rank structure with negligible reconstruction error, keeping inference cost identical to vanilla LoRA. Since not all weight matrices benefit equally from added capacity, we further propose two scheduling strategies, one statically predefined and one dynamically determined at runtime, that direct extra capacity where most needed. We evaluate LoRA-Over on language understanding (GLUE, T5-Base), dialogue (MT-Bench), arithmetic reasoning (GSM8K), and code generation (HumanEval), using LLaMA 2-7B and LLaMA 3.1-8B. Across all benchmarks and scales, LoRA-Over consistently outperforms vanilla LoRA, showing that principled over-parameterization designed to vanish at inference is an effective lever for improving PEFT generalization. Code will be released upon acceptance.

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.