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Paper · 2605.31484 · ICML · 2026

Balanced LoRA: Removing Parameter Invariance to Accelerate Convergence

Kimia Nadjahi, Pierre Ablin, Gabriel Peyré, Valérie Castin

arXiv · PDF · Open in the Atlas

Code that ran

We lifted 8 functions out of this paper's own repositories and ran 8 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.

RepositoryRoleRan
vcastin/balora canonical 8 of 8
FunctionStatusWhere it lives
apply_linear Ran vcastin/balora/synthetic/layers.py
code served (permissive licence) · get_code("8a479c466f315823")
create_preconditioner Ran vcastin/balora/lora_rite.py
code served (permissive licence) · get_code("5ed0f5c52db3d133")
format_ai2_arc_messages Ran vcastin/balora/dataset_utilities/ai2_arc_utilities.py
code served (permissive licence) · get_code("93e81f47bfc515e3")
format_alpaca_messages Ran vcastin/balora/dataset_utilities/alpaca_utilities.py
code served (permissive licence) · get_code("c11f6c51712ec176")
format_code_feedback_messages Ran vcastin/balora/dataset_utilities/code_feedback_utilities.py
code served (permissive licence) · get_code("f29b817f83493fae")
init_linear Ran vcastin/balora/synthetic/layers.py
code served (permissive licence) · get_code("bfe965559d748570")
init_linear_network Ran vcastin/balora/synthetic/layers.py
code served (permissive licence) · get_code("ff7851c957801640")
preprocess_instruction_dataset Ran vcastin/balora/dataset_utilities/common_utilities.py
code served (permissive licence) · get_code("a853c7022ed84258")

Repositories linked to this paper

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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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