[Paper Review] Beyond Hard Writes and Rigid Preservation: Soft Recursive Least-Squares for Lifelong LLM Editing

Xinyu Wang, Sicheng Lyu+5 more|arXiv (Cornell University)|Jan 22, 2026

Digital Humanities and Scholarship0 citations

TL;DR

RLSEdit introduces a recursive least-squares editor with soft adherence and anchor preservation for lifelong sequential edits, achieving scalable, stable updates while retaining general capabilities.

ABSTRACT

Model editing updates a pre-trained LLM with new facts or rules without re-training, while preserving unrelated behavior. In real deployment, edits arrive as long streams, and existing editors often face a plasticity-stability dilemma: locate-then-edit "hard writes" can accumulate interference over time, while null-space-style "hard preservation" preserves only what is explicitly constrained, so past edits can be overwritten and unconstrained behaviors may deviate, degrading general capabilities in the many-edits regime. 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 with two regularizers that control for both deviation from the pre-trained weights and from a designated anchor mapping. The resulting update admits an efficient online recursion via the Woodbury identity, 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 multiple model families demonstrate stable scaling to 10K edits, outperforming strong baselines in both edit success and holistic stability -- crucially retaining early edits, and preserving general capabilities on GLUE and held-out reasoning/code benchmarks.

Motivation & Objective

• Motivate lifelong sequential model editing that balances learning new facts with preserving prior knowledge.
• Formulate editing as online regularized least-squares with two deviation controls (from initial weights and from an anchor mapping).
• Develop a Woodbury-based online recursion enabling per-edit cost that scales with current edit size, not history.
• Provide theoretical deviation bounds and an asymptotic analysis for many-edits regimes.
• Demonstrate superior edit success and stability across large edit streams on multiple model families.

Proposed method

• Formulate a quadratic objective that sums past and current edit residuals plus two regularizers: deviation from the initial weights and deviation from a designated anchor mapping.
• Derive a closed-form solution using normal equations and implement an online Woodbury recursion to update the inverse covariance C_t and weights W_t with per-edit cost depending on the current edit size u_t.
• Use a Cholesky-based stabilization of the Woodbury update to ensure numerical stability.
• Provide deviation bounds and an asymptotic characterization showing convergence to a ridge-regularized population minimizer under mild assumptions.
• Compare RLSEdit against AlphaEdit, MEMIT, ROME, and FT on Llama-3-8B and Qwen2.5-7B with 10k edits, reporting multiple metrics (Efficacy, Generalization, Specificity, Fluency, Consistency).

Figure 1: The recursive workflow of our RLS-Woodbury editor. The process alternates between updating the covariance state via the Woodbury identity (Phase 1) and updating weights (Phase 2). The highlighted block shows how we reduce complexity from $O\!\left(d_{k}^{3}\right)$ to $O\!\left(d_{k}^{2}u_

Experimental results

Research questions

• RQ1 Can lifelong sequential editing be effectively achieved with soft constraints that interpolate between hard writes and hard preservation?
• RQ2 What is the computational cost of online RLSEdit per edit relative to past edits, and how does it scale with edit size?
• RQ3 Does RLSEdit preserve general capabilities while applying many sequential edits on large language models?
• RQ4 How do deviation parameters lambda and mu influence parameter drift and anchor-adherence over long edit streams?
• RQ5 How does RLSEdit perform compared to state-of-the-art editors under long edit streams across multiple model families?

Key findings

• RLSEdit achieves strong edit success and stability across 10K sequential edits on Llama-3-8B and Qwen2.5-7B, outperforming baselines on multiple metrics.
• On Llama-3-8B, RLSEdit attains Efficacy 89.94, Generalization 72.84, Specificity 60.56, Fluency 615.58, Consistency 26.27, all higher than baselines.
• On Qwen2.5-7B, RLSEdit achieves Efficacy 94.45, Generalization 68.55, Specificity 73.37, Fluency 625.74, Consistency 31.62, with RLSEdit often leading in Efficacy and Fluency.
• RLSEdit preserves early edits better than AlphaEdit, ROME, MEMIT, and FT, maintaining performance on general-language understanding and reasoning benchmarks across editing checkpoints.
• The method scales with per-edit cost dependent on the current edit size u_t, not the total number of past edits, enabling stable long-stream editing.
• Empirical results show RLSEdit maintains general capabilities across GLUE tasks and code/math benchmarks better than baselines over the editing trajectory.

Figure 2: Evolution of objective terms over $10\mathsf{K}$ edits. We compare RLSEdit against baselines ( AlphaEdit , MEMIT ) on three metrics: Term 1 ( $\|{\bm{K}}_{t}{\bm{W}}-{\bm{V}}_{t}\|_{F}^{2}$ ) measures the fitting error for the current edit; Term 2 ( $\|{\bm{W}}-{\bm{W}}_{0}\|_{F}^{2}$ ) me