# Take Only What You Need: Rank Minimization as an Implicit Forgetting Regularizer in Continual Learning

arXiv: https://arxiv.org/abs/2412.01004 · HTML: https://mlsanity.com/paper/2412.01004/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 48 of its 87 references that are in the map.
- First posted on arXiv 1 Dec 2024.

## Builds on (most cited first, 30 of 48)

- [Learning Transferable Visual Models From Natural Language Supervision](https://mlsanity.com/paper/2103.00020/) (2021)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Llama 2: Open Foundation and Fine-Tuned Chat Models](https://mlsanity.com/paper/2307.09288/) (2023)
- [Overcoming catastrophic forgetting in neural networks](https://mlsanity.com/paper/1612.00796/) (2016)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [Learning without Forgetting](https://mlsanity.com/paper/1606.09282/) (2016)
- [iCaRL: Incremental Classifier and Representation Learning](https://mlsanity.com/paper/1611.07725/) (2016)
- [Learn to Explain: Multimodal Reasoning via Thought Chains for Science Question Answering](https://mlsanity.com/paper/2209.09513/) (2022)
- [Gradient Episodic Memory for Continual Learning](https://mlsanity.com/paper/1706.08840/) (2017)
- [Fine-Grained Visual Classification of Aircraft](https://mlsanity.com/paper/1306.5151/) (2013)
- [EuroSAT: A Novel Dataset and Deep Learning Benchmark for Land Use and Land Cover Classification](https://mlsanity.com/paper/1709.00029/) (2017)
- [Memory Aware Synapses: Learning what (not) to forget](https://mlsanity.com/paper/1711.09601/) (2017)
- [Efficient Lifelong Learning with A-GEM](https://mlsanity.com/paper/1812.00420/) (2018)
- [Learning to Prompt for Continual Learning](https://mlsanity.com/paper/2112.08654/) (2021)
- [Robust fine-tuning of zero-shot models](https://mlsanity.com/paper/2109.01903/) (2021)
- [CodeXGLUE: A Machine Learning Benchmark Dataset for Code Understanding and Generation](https://mlsanity.com/paper/2102.04664/) (2021)
- [Riemannian Walk for Incremental Learning: Understanding Forgetting and Intransigence](https://mlsanity.com/paper/1801.10112/) (2018)
- [DualPrompt: Complementary Prompting for Rehearsal-free Continual Learning](https://mlsanity.com/paper/2204.04799/) (2022)
- [Gradient based sample selection for online continual learning](https://mlsanity.com/paper/1903.08671/) (2019)
- [CODA-Prompt: COntinual Decomposed Attention-based Prompting for Rehearsal-Free Continual Learning](https://mlsanity.com/paper/2211.13218/) (2022)
- [Orthogonal Gradient Descent for Continual Learning](https://mlsanity.com/paper/1910.07104/) (2019)
- [DER: Dynamically Expandable Representation for Class Incremental Learning](https://mlsanity.com/paper/2103.16788/) (2021)
- [LoRA Learns Less and Forgets Less](https://mlsanity.com/paper/2405.09673/) (2024)
- [Orthogonal Subspace Learning for Language Model Continual Learning](https://mlsanity.com/paper/2310.14152/) (2023)
- [Direct and Indirect Effects](https://mlsanity.com/paper/1301.2300/) (2013)
- [S-Prompts Learning with Pre-trained Transformers: An Occam's Razor for Domain Incremental Learning](https://mlsanity.com/paper/2207.12819/) (2022)
- [Task-Free Continual Learning](https://mlsanity.com/paper/1812.03596/) (2018)
- [Mnemonics Training: Multi-Class Incremental Learning without Forgetting](https://mlsanity.com/paper/2002.10211/) (2020)

## Built on by (most cited first, 2 of 2)

- [Little by Little: Continual Learning via Incremental Mixture of Rank-1 Associative Memory Experts](https://mlsanity.com/paper/2506.21035/) (2025)
- [Beyond Endpoint Scores: Time- and Capacity-Conditioned Evaluation of Continual Knowledge Updating](https://mlsanity.com/paper/2609.03900/) (2026)

## Abstract (arXiv)

The central tension in continual learning (CL) is the trade-off between plasticity (acquiring new knowledge) and stability (retaining prior knowledge). We study how a pre-trained backbone can be continually updated to absorb new knowledge while preserving existing capabilities, via capacity control: regulating the effective rank of each parameter update, a per-step quantity directly controllable inside a LoRA update. A controlled probe of LoRA rank and placement across modules and tasks reveals a consistent trade-off, with a moderate-rank sweet spot that varies by placement and task, leaving no universally optimal fixed rank; a formal bound shows forgetting grows with rank. Building on these findings, we propose Continual Dynamic Rank-Selective LoRA (CoDyRA), which jointly trains each LoRA update with rank minimization via sparsity-promoting regularization on per-component importance weights. The supervised objective drives plasticity; rank minimization regularizes forgetting. We show that rank minimization serves as an implicit forgetting regularizer in the CL regime, protecting general capability and prior-task knowledge simultaneously by controlling forgetting against the current model state. Across MTIL, X-TAIL, and TRACE (CLIP, LLaMA, Gemma), CoDyRA outperforms prior CL methods on new knowledge learning and forgetting, achieving a strong plasticity-stability balance. Project page: https://artificer-ai-lab.github.io/CoDyRA.