Deep Hierarchical Learning with Nested Subspace Networks

• URL: http://arxiv.org/abs/2509.17874v1
• Date: Mon, 22 Sep 2025 15:13:14 GMT
• Title: Deep Hierarchical Learning with Nested Subspace Networks
• Authors: Paulius Rauba, Mihaela van der Schaar,
• Abstract summary: We propose Nested Subspace Networks (NSNs) for large neural networks.<n>NSNs enable a single model to be dynamically and granularly adjusted across a continuous spectrum of compute budgets.<n>We show that NSNs can be surgically applied to pre-trained LLMs and unlock a smooth and predictable compute-performance frontier.
• Score: 53.71337604556311
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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