# Sculpting Subspaces: Constrained Full Fine-Tuning in LLMs for Continual Learning

arXiv: https://arxiv.org/abs/2504.07097 · HTML: https://mlsanity.com/paper/2504.07097/

## Key facts

- Cited by 15 papers in the map (data through 14 Oct 2026).
- Builds on 35 of its 41 references that are in the map.
- First posted on arXiv 9 Apr 2025.

## Builds on (most cited first, 30 of 35)

- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [GLUE: A Multi-Task Benchmark and Analysis Platform for Natural Language Understanding](https://mlsanity.com/paper/1804.07461/) (2018)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Parameter-Efficient Transfer Learning for NLP](https://mlsanity.com/paper/1902.00751/) (2019)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [Character-level Convolutional Networks for Text Classification](https://mlsanity.com/paper/1509.01626/) (2015)
- [Similarity of Neural Network Representations Revisited](https://mlsanity.com/paper/1905.00414/) (2019)
- [SuperGLUE: A Stickier Benchmark for General-Purpose Language Understanding Systems](https://mlsanity.com/paper/1905.00537/) (2019)
- [Progressive Neural Networks](https://mlsanity.com/paper/1606.04671/) (2016)
- [Learning to Prompt for Continual Learning](https://mlsanity.com/paper/2112.08654/) (2021)
- [PackNet: Adding Multiple Tasks to a Single Network by Iterative Pruning](https://mlsanity.com/paper/1711.05769/) (2017)
- [TIES-Merging: Resolving Interference When Merging Models](https://mlsanity.com/paper/2306.01708/) (2023)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [An Empirical Study of Catastrophic Forgetting in Large Language Models During Continual Fine-tuning](https://mlsanity.com/paper/2308.08747/) (2023)
- [Gradient Projection Memory for Continual Learning](https://mlsanity.com/paper/2103.09762/) (2021)
- [Orthogonal Subspace Learning for Language Model Continual Learning](https://mlsanity.com/paper/2310.14152/) (2023)
- [The Lottery Ticket Hypothesis for Pre-trained BERT Networks](https://mlsanity.com/paper/2007.12223/) (2020)
- [PiSSA: Principal Singular Values and Singular Vectors Adaptation of Large Language Models](https://mlsanity.com/paper/2404.02948/) (2024)
- [Online Structured Laplace Approximations For Overcoming Catastrophic Forgetting](https://mlsanity.com/paper/1805.07810/) (2018)
- [InfLoRA: Interference-Free Low-Rank Adaptation for Continual Learning](https://mlsanity.com/paper/2404.00228/) (2024)
- [Progressive Prompts: Continual Learning for Language Models](https://mlsanity.com/paper/2301.12314/) (2023)
- [Patching open-vocabulary models by interpolating weights](https://mlsanity.com/paper/2208.05592/) (2022)
- [Why Transformers Need Adam: A Hessian Perspective](https://mlsanity.com/paper/2402.16788/) (2024)
- [The Truth is in There: Improving Reasoning in Language Models with Layer-Selective Rank Reduction](https://mlsanity.com/paper/2312.13558/) (2023)
- [MiLoRA: Harnessing Minor Singular Components for Parameter-Efficient LLM Finetuning](https://mlsanity.com/paper/2406.09044/) (2024)
- [TRACE: A Comprehensive Benchmark for Continual Learning in Large Language Models](https://mlsanity.com/paper/2310.06762/) (2023)
- [Analytic Insights into Structure and Rank of Neural Network Hessian Maps](https://mlsanity.com/paper/2106.16225/) (2021)
- [Spherical Linear Interpolation and Text-Anchoring for Zero-shot Composed Image Retrieval](https://mlsanity.com/paper/2405.00571/) (2024)

## Built on by (most cited first, 15 of 15)

- [Optimizer-Model Consistency: Full Finetuning with the Same Optimizer as Pretraining Forgets Less](https://mlsanity.com/paper/2605.06654/) (2026)
- [Muon-OGD: Muon-based Spectral Orthogonal Gradient Projection for LLM Continual Learning](https://mlsanity.com/paper/2605.08949/) (2026)
- [Subspace Geometry Governs Catastrophic Forgetting in Low-Rank Adaptation](https://mlsanity.com/paper/2603.02224/) (2026)
- [Rotation-Preserving Supervised Fine-Tuning](https://mlsanity.com/paper/2605.10973/) (2026)
- [Mecellem Models: Turkish Models Trained from Scratch and Continually Pre-trained for the Legal Domain](https://mlsanity.com/paper/2601.16018/) (2026)
- [Pioneer Agent: Continual Improvement of Small Language Models in Production](https://mlsanity.com/paper/2604.09791/) (2026)
- [Bilinear Optimization Divergence: Diagnosing Factor-Constrained LoRA Continual Learning](https://mlsanity.com/paper/2609.23594/) (2026)
- [Reverse Distillation: Consistently Scaling Protein Language Model Representations](https://mlsanity.com/paper/2603.07710/) (2026)
- [Hidden Failure Modes of Gradient Modification under Adam in Continual Learning, and Adaptive Decoupled Moment Routing as a Repair](https://mlsanity.com/paper/2604.22407/) (2026)
- [KeepLoRA++: Continual Learning with Layer-Scaled Residual Gradient Adaptation](https://mlsanity.com/paper/2606.16256/) (2026)
- [Omega-S: A Functional Resilience Index for LLM Fine-Tuning](https://mlsanity.com/paper/2608.03887/) (2026)
- [Beyond Forgetting: Diagnosing and Harnessing Shared Reasoning in Continual RLVR](https://mlsanity.com/paper/2608.18574/) (2026)
- [Reading the News: Adapting Large Language Models to Swedish Journalism Through Continued Pre-Training](https://mlsanity.com/paper/2608.30609/) (2026)
- [Learning an Anchored Prompt Space for Continual Adaptation of Large Language Models](https://mlsanity.com/paper/2609.32499/) (2026)
- [Local Support Learning](https://mlsanity.com/paper/2610.02126/) (2026)

## Abstract (arXiv)

Continual learning in large language models (LLMs) is prone to catastrophic forgetting, where adapting to new tasks significantly degrades performance on previously learned ones. Existing methods typically rely on low-rank, parameter-efficient updates that limit the model's expressivity and introduce additional parameters per task, leading to scalability issues. To address these limitations, we propose a novel continual full fine-tuning approach leveraging adaptive singular value decomposition (SVD). Our method dynamically identifies task-specific low-rank parameter subspaces and constrains updates to be orthogonal to critical directions associated with prior tasks, thus effectively minimizing interference without additional parameter overhead or storing previous task gradients. We evaluate our approach extensively on standard continual learning benchmarks using both encoder-decoder (T5-Large) and decoder-only (LLaMA-2 7B) models, spanning diverse tasks including classification, generation, and reasoning. Empirically, our method achieves state-of-the-art results, up to 7% higher average accuracy than recent baselines like O-LoRA, and notably maintains the model's general linguistic capabilities, instruction-following accuracy, and safety throughout the continual learning process by reducing forgetting to near-negligible levels. Our adaptive SVD framework effectively balances model plasticity and knowledge retention, providing a practical, theoretically grounded, and computationally scalable solution for continual learning scenarios in large language models.