Balanced LoRA: Removing Parameter Invariance to Accelerate Convergence

• URL: http://arxiv.org/abs/2605.31484v1
• Date: Fri, 29 May 2026 16:08:28 GMT
• Title: Balanced LoRA: Removing Parameter Invariance to Accelerate Convergence
• Abstract summary: Low-Rank Adaptation (LoRA) is the most widely adopted method for fine-tuning large language models.<n>We introduce Balanced Low-Rank Adaptation (BaLoRA), a variant of LoRA that projects iterates onto a balanced manifold.<n>BaLoRA converges faster than standard LoRA and achieves superior performance across a range of fine-tuning tasks.
• Score: 30.96331195818476
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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