Deep Hierarchical Learning with Nested Subspace Networks for Large Language Models
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| Format: | Preprint |
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2025
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| author | Rauba, Paulius van der Schaar, Mihaela |
| author_facet | Rauba, Paulius van der Schaar, Mihaela |
| contents | Large neural networks are typically trained for a fixed computational budget, creating a rigid trade-off between performance and efficiency that is ill-suited for deployment in resource-constrained or dynamic environments. Existing approaches to this problem present a difficult choice: training a discrete collection of specialist models is computationally prohibitive, while dynamic methods like slimmable networks often lack the flexibility to be applied to large, pre-trained foundation models. In this work, we propose Nested Subspace Networks (NSNs), a novel architectural paradigm that enables a single model to be dynamically and granularly adjusted across a continuous spectrum of compute budgets at inference time. The core of our approach is to re-parameterize linear layers to satisfy a nested subspace property, such that the function computed at a given rank is a strict subspace of the function at any higher rank. We show that this entire hierarchy of models can be optimized jointly via an uncertainty-aware objective that learns to balance the contributions of different ranks based on their intrinsic difficulty. We demonstrate empirically that NSNs can be surgically applied to pre-trained LLMs and unlock a smooth and predictable compute-performance frontier. For example, a single NSN-adapted model can achieve a 50% reduction in inference FLOPs with only a 5 percentage point loss in accuracy. Our findings establish NSNs as a powerful framework for creating the next generation of adaptive foundation models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_17874 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Deep Hierarchical Learning with Nested Subspace Networks for Large Language Models Rauba, Paulius van der Schaar, Mihaela Machine Learning Large neural networks are typically trained for a fixed computational budget, creating a rigid trade-off between performance and efficiency that is ill-suited for deployment in resource-constrained or dynamic environments. Existing approaches to this problem present a difficult choice: training a discrete collection of specialist models is computationally prohibitive, while dynamic methods like slimmable networks often lack the flexibility to be applied to large, pre-trained foundation models. In this work, we propose Nested Subspace Networks (NSNs), a novel architectural paradigm that enables a single model to be dynamically and granularly adjusted across a continuous spectrum of compute budgets at inference time. The core of our approach is to re-parameterize linear layers to satisfy a nested subspace property, such that the function computed at a given rank is a strict subspace of the function at any higher rank. We show that this entire hierarchy of models can be optimized jointly via an uncertainty-aware objective that learns to balance the contributions of different ranks based on their intrinsic difficulty. We demonstrate empirically that NSNs can be surgically applied to pre-trained LLMs and unlock a smooth and predictable compute-performance frontier. For example, a single NSN-adapted model can achieve a 50% reduction in inference FLOPs with only a 5 percentage point loss in accuracy. Our findings establish NSNs as a powerful framework for creating the next generation of adaptive foundation models. |
| title | Deep Hierarchical Learning with Nested Subspace Networks for Large Language Models |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2509.17874 |