Subspace Control: Turning Constrained Model Steering into Controllable Spectral Optimization
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , , , , , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866914447805644800 |
|---|---|
| author | Huang, Yancheng Wang, Changsheng Fan, Chongyu Lang, Yicheng Shang, Bingqi Zhang, Yang Hong, Mingyi Qu, Qing Velasquez, Alvaro Liu, Sijia |
| author_facet | Huang, Yancheng Wang, Changsheng Fan, Chongyu Lang, Yicheng Shang, Bingqi Zhang, Yang Hong, Mingyi Qu, Qing Velasquez, Alvaro Liu, Sijia |
| contents | Foundation models, such as large language models (LLMs), are powerful but often require customization before deployment to satisfy practical constraints such as safety, privacy, and task-specific requirements, leading to "constrained" optimization problems for model steering and adaptation. However, solving such problems remains largely underexplored and is particularly challenging due to interference between the primary objective and constraint objectives during optimization. In this paper, we propose a subspace control framework for constrained model training. Specifically, (i) we first analyze, from a model merging perspective, how spectral cross-task interference arises and show that it can be resolved via a one-shot solution that orthogonalizes the merged subspace; (ii) we establish a connection between this solution and gradient orthogonalization in the spectral optimizer Muon; and (iii) building on these insights, we introduce SIFT (spectral interference-free training), which leverages a localization scheme to selectively intervene during optimization, enabling controllable updates that mitigate objective-constraint conflicts. We evaluate SIFT across four representative applications: (a) machine unlearning, (b) safety alignment, (c) text-to-speech adaptation, and (d) hallucination mitigation. Compared to both control-based and control-free baselines, SIFT consistently achieves substantial and robust performance improvements across all tasks. Code is available at https://github.com/OPTML-Group/SIFT. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04231 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Subspace Control: Turning Constrained Model Steering into Controllable Spectral Optimization Huang, Yancheng Wang, Changsheng Fan, Chongyu Lang, Yicheng Shang, Bingqi Zhang, Yang Hong, Mingyi Qu, Qing Velasquez, Alvaro Liu, Sijia Machine Learning Foundation models, such as large language models (LLMs), are powerful but often require customization before deployment to satisfy practical constraints such as safety, privacy, and task-specific requirements, leading to "constrained" optimization problems for model steering and adaptation. However, solving such problems remains largely underexplored and is particularly challenging due to interference between the primary objective and constraint objectives during optimization. In this paper, we propose a subspace control framework for constrained model training. Specifically, (i) we first analyze, from a model merging perspective, how spectral cross-task interference arises and show that it can be resolved via a one-shot solution that orthogonalizes the merged subspace; (ii) we establish a connection between this solution and gradient orthogonalization in the spectral optimizer Muon; and (iii) building on these insights, we introduce SIFT (spectral interference-free training), which leverages a localization scheme to selectively intervene during optimization, enabling controllable updates that mitigate objective-constraint conflicts. We evaluate SIFT across four representative applications: (a) machine unlearning, (b) safety alignment, (c) text-to-speech adaptation, and (d) hallucination mitigation. Compared to both control-based and control-free baselines, SIFT consistently achieves substantial and robust performance improvements across all tasks. Code is available at https://github.com/OPTML-Group/SIFT. |
| title | Subspace Control: Turning Constrained Model Steering into Controllable Spectral Optimization |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2604.04231 |