Learning Adapter Rank via Symmetry Breaking
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866916002211561472 |
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| author | Doyle, Cooper Hu, Andy Chan, Rebecca Leontjeva, Anna |
| author_facet | Doyle, Cooper Hu, Andy Chan, Rebecca Leontjeva, Anna |
| contents | Low-rank adaptation is effective partly because downstream updates lie in a low-dimensional subspace, but the latent rank coordinates of LoRA are not identifiable: any invertible reparameterization of the adapter factors leaves the weight update unchanged. We show that variational inference with a diagonal rank-wise posterior turns this non-identifiability into a useful inductive bias. By breaking LoRA's rotational gauge symmetry, the variational objective selects a preferred basis in rank space, enabling automatic relevance determination over rank directions. This yields Low-Rank Variational Dropout (LRVD), a Bayesian framework that performs inference directly in the low-rank adaptation space rather than the ambient weight space. As an instantiation, BayesLoRA jointly learns effective adapter rank and predictive uncertainty with only $\mathcal{O}(r)$ additional parameters. Empirically, BayesLoRA induces stable rank structure aligned with the dominant singular directions of learned updates, yields compact predictive calibration and matches or exceeds strong low-rank sparsification baselines at comparable training cost. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_22809 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Learning Adapter Rank via Symmetry Breaking Doyle, Cooper Hu, Andy Chan, Rebecca Leontjeva, Anna Machine Learning Artificial Intelligence Computation and Language Low-rank adaptation is effective partly because downstream updates lie in a low-dimensional subspace, but the latent rank coordinates of LoRA are not identifiable: any invertible reparameterization of the adapter factors leaves the weight update unchanged. We show that variational inference with a diagonal rank-wise posterior turns this non-identifiability into a useful inductive bias. By breaking LoRA's rotational gauge symmetry, the variational objective selects a preferred basis in rank space, enabling automatic relevance determination over rank directions. This yields Low-Rank Variational Dropout (LRVD), a Bayesian framework that performs inference directly in the low-rank adaptation space rather than the ambient weight space. As an instantiation, BayesLoRA jointly learns effective adapter rank and predictive uncertainty with only $\mathcal{O}(r)$ additional parameters. Empirically, BayesLoRA induces stable rank structure aligned with the dominant singular directions of learned updates, yields compact predictive calibration and matches or exceeds strong low-rank sparsification baselines at comparable training cost. |
| title | Learning Adapter Rank via Symmetry Breaking |
| topic | Machine Learning Artificial Intelligence Computation and Language |
| url | https://arxiv.org/abs/2506.22809 |