# Beyond Hard Writes and Rigid Preservation: Soft Recursive Least-Squares for Lifelong LLM Editing

arXiv: https://arxiv.org/abs/2601.15686 · HTML: https://mlsanity.com/paper/2601.15686/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 36 references that are in the map.
- First posted on arXiv 22 Jan 2026.

## Builds on (most cited first, 25 of 25)

- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [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)
- [Program Synthesis with Large Language Models](https://mlsanity.com/paper/2108.07732/) (2021)
- [Locating and Editing Factual Associations in GPT](https://mlsanity.com/paper/2202.05262/) (2022)
- [A Broad-Coverage Challenge Corpus for Sentence Understanding through Inference](https://mlsanity.com/paper/1704.05426/) (2017)
- [Mass-Editing Memory in a Transformer](https://mlsanity.com/paper/2210.07229/) (2022)
- [Neural Network Acceptability Judgments](https://mlsanity.com/paper/1805.12471/) (2018)
- [Editing Factual Knowledge in Language Models](https://mlsanity.com/paper/2104.08164/) (2021)
- [Fast Model Editing at Scale](https://mlsanity.com/paper/2110.11309/) (2021)
- [Zero-Shot Relation Extraction via Reading Comprehension](https://mlsanity.com/paper/1706.04115/) (2017)
- [Aging with GRACE: Lifelong Model Editing with Discrete Key-Value Adaptors](https://mlsanity.com/paper/2211.11031/) (2022)
- [AlphaEdit: Null-Space Constrained Knowledge Editing for Language Models](https://mlsanity.com/paper/2410.02355/) (2024)
- [Modifying Memories in Transformer Models](https://mlsanity.com/paper/2012.00363/) (2020)
- [Online Structured Laplace Approximations For Overcoming Catastrophic Forgetting](https://mlsanity.com/paper/1805.07810/) (2018)
- [Model Editing at Scale leads to Gradual and Catastrophic Forgetting](https://mlsanity.com/paper/2401.07453/) (2024)
- [WISE: Rethinking the Knowledge Memory for Lifelong Model Editing of Large Language Models](https://mlsanity.com/paper/2405.14768/) (2024)
- [AnyEdit: Edit Any Knowledge Encoded in Language Models](https://mlsanity.com/paper/2502.05628/) (2025)
- [Lifelong Knowledge Editing for LLMs with Retrieval-Augmented Continuous Prompt Learning](https://mlsanity.com/paper/2405.03279/) (2024)
- [Everything is Editable: Extend Knowledge Editing to Unstructured Data in Large Language Models](https://mlsanity.com/paper/2405.15349/) (2024)
- [EvoEdit: Evolving Null-space Alignment for Robust and Efficient Knowledge Editing](https://mlsanity.com/paper/2510.13851/) (2025)
- [Resona: Improving Context Copying in Linear Recurrence Models with Retrieval](https://mlsanity.com/paper/2503.22913/) (2025)

## Built on by (most cited first, 1 of 1)

- [InfMem: Learning System-2 Memory Control for Long-Context Agent](https://mlsanity.com/paper/2602.02704/) (2026)

## Abstract (arXiv)

Model editing updates a pre-trained LLM with new facts or rules without retraining while preserving unrelated behavior. In real deployment, edits arrive as long streams, creating a plasticity-stability dilemma: repeated locate-then-edit "hard writes" can accumulate interference over time, while rigid preservation constraints may protect only explicitly constrained directions, allowing past edits or unconstrained behaviors to deviate. We propose RLSEdit, a recursive least-squares editor for long sequential editing. RLSEdit formulates editing as an online quadratic optimization with soft constraints, minimizing a cumulative key-value fitting objective together with two regularizers that control deviation from the pre-trained weights and from a designated anchor mapping. This objective admits an efficient Woodbury-based online recursion, with per-edit cost independent of history length and scaling only with the current edit size. We further provide deviation bounds and an asymptotic characterization of the adherence-preservation trade-off in the many-edits regime. Experiments on CounterFact and ZsRE across multiple model families show stable scaling to 10K edits, outperforming strong baselines in both edit success and holistic stability, while retaining early edits and preserving general capabilities on GLUE and held-out reasoning/code benchmarks.