# Can a Language Model Learn Facts Continually in Its Weights?

arXiv: https://arxiv.org/abs/2607.11020 · HTML: https://mlsanity.com/paper/2607.11020/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 36 of its 38 references that are in the map.
- First posted on arXiv 13 Jul 2026.

## Builds on (most cited first, 30 of 36)

- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [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)
- [A General Language Assistant as a Laboratory for Alignment](https://mlsanity.com/paper/2112.00861/) (2021)
- [Mass-Editing Memory in a Transformer](https://mlsanity.com/paper/2210.07229/) (2022)
- [On-Policy Distillation of Language Models: Learning from Self-Generated Mistakes](https://mlsanity.com/paper/2306.13649/) (2023)
- [Fast Model Editing at Scale](https://mlsanity.com/paper/2110.11309/) (2021)
- [The Reversal Curse: LLMs trained on "A is B" fail to learn "B is A"](https://mlsanity.com/paper/2309.12288/) (2023)
- [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)
- [Aging with GRACE: Lifelong Model Editing with Discrete Key-Value Adaptors](https://mlsanity.com/paper/2211.11031/) (2022)
- [Physics of Language Models: Part 3.1, Knowledge Storage and Extraction](https://mlsanity.com/paper/2309.14316/) (2023)
- [Self-Distillation Enables Continual Learning](https://mlsanity.com/paper/2601.19897/) (2026)
- [Does Fine-Tuning LLMs on New Knowledge Encourage Hallucinations?](https://mlsanity.com/paper/2405.05904/) (2024)
- [Modifying Memories in Transformer Models](https://mlsanity.com/paper/2012.00363/) (2020)
- [On-Policy Context Distillation for Language Models](https://mlsanity.com/paper/2602.12275/) (2026)
- [RL's Razor: Why Online Reinforcement Learning Forgets Less](https://mlsanity.com/paper/2509.04259/) (2025)
- [Towards Continual Knowledge Learning of Language Models](https://mlsanity.com/paper/2110.03215/) (2021)
- [Can Sensitive Information Be Deleted From LLMs? Objectives for Defending Against Extraction Attacks](https://mlsanity.com/paper/2309.17410/) (2023)
- [Understanding Catastrophic Forgetting in Language Models via Implicit Inference](https://mlsanity.com/paper/2309.10105/) (2023)
- [Taken out of context: On measuring situational awareness in LLMs](https://mlsanity.com/paper/2309.00667/) (2023)
- [Physics of Language Models: Part 3.2, Knowledge Manipulation](https://mlsanity.com/paper/2309.14402/) (2023)
- [Learning by Distilling Context](https://mlsanity.com/paper/2209.15189/) (2022)
- [WISE: Rethinking the Knowledge Memory for Lifelong Model Editing of Large Language Models](https://mlsanity.com/paper/2405.14768/) (2024)
- [Injecting New Knowledge into Large Language Models via Supervised Fine-Tuning](https://mlsanity.com/paper/2404.00213/) (2024)
- [How do language models learn facts? Dynamics, curricula and hallucinations](https://mlsanity.com/paper/2503.21676/) (2025)
- [Propagating Knowledge Updates to LMs Through Distillation](https://mlsanity.com/paper/2306.09306/) (2023)

## Abstract (arXiv)

Continual learning is a long-standing capability gap between LLMs and humans. Writing new knowledge into a model's weights routinely causes it to forget old knowledge, commonly denoted as "catastrophic forgetting". Various modifications of supervised fine-tuning and distillation aim to mitigate catastrophic forgetting, but quantifying what (or how much) information was forgotten is often difficult. In this paper, we study whether current methods of writing knowledge into weights enable models to learn continually without forgetting. We introduce a framework for studying continual learning in the iterative regime, writing invented facts one at a time into a Qwen3 model already modified by previous writes, and varying the training data, method, and parameter update. Across SFT and off- and on-policy distillation, using LoRA or full fine-tuning, we compare repeated statement training (the same fact repeated in two formats) with varied example training (24 factual restatements) and find that varied examples comprehensively support more flexible use. After twenty sequential writes and merges, the model answers only 1% of questions about earlier facts correctly when every write uses repeated statements, compared with 46% when every write uses varied examples. We additionally show that this retention depends on the data used for the later writes, regardless of training method or parameter update, and that behavioral forgetting of an earlier fact does not erase its presence from the log-probabilities. Together, our framework neatly provides a comparison of performance across training data, training regimes, and parameter update schemes in an iterative learning task.