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arxiv: 2601.15686 · v2 · submitted 2026-01-22 · 💻 cs.LG

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

Xinyu Wang , Sicheng Lyu , Yu Gu , Jerry Huang , Peng Lu , Yufei Cui , Xiao-Wen Chang This is my paper

Pith reviewed 2026-05-16 12:18 UTC · model grok-4.3

classification 💻 cs.LG
keywords model editinglifelong learningrecursive least squareslarge language modelssequential updatessoft constraintsonline optimization
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The pith

Recursive least-squares with soft constraints enables stable lifelong editing of LLMs across streams of up to 10,000 facts.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents a method that recasts sequential model editing as an online quadratic optimization problem. It minimizes a running key-value fit while softly penalizing large departures from the original pre-trained weights and from a chosen anchor mapping. The resulting objective supports a closed-form recursion that updates the solution after each edit at a cost independent of the total number of prior edits. Experiments across model families and two standard editing benchmarks show that new facts are inserted reliably, earlier facts remain intact, and unrelated capabilities on classification, reasoning, and code tasks stay intact even after ten thousand sequential changes.

Core claim

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. Deviation bounds and an asymptotic characterization of the adherence-preservation trade-off in the many-edits regime are derived.

What carries the argument

The Woodbury-based recursion that solves the cumulative quadratic objective under the two soft deviation penalties.

If this is right

  • Edit success and retention of early facts remain high after thousands of sequential updates without replay.
  • General capabilities on classification, reasoning, and code benchmarks are preserved without explicit protection of those directions.
  • Computation per new edit stays bounded and does not grow with the length of the edit history.
  • Deviation bounds supply a quantitative way to predict when further editing will begin to trade off against preservation.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the regularizer strengths can be chosen once for a broad class of models, the method could support continuous online deployment where new facts arrive in unpredictable order.
  • The same recursion structure might be adapted to sequential incorporation of new behaviors or skills rather than only factual associations.
  • The asymptotic trade-off characterization could be used to decide when a full retraining cycle is preferable to continued incremental editing.

Load-bearing premise

The two soft regularizers can be fixed in advance so that they continue to prevent harmful interference no matter what sequence of future edits arrives.

What would settle it

A controlled stream of ten thousand edits on a held-out model where either new-edit success drops below baseline levels, retention of the first edits falls, or accuracy on GLUE and held-out reasoning tasks declines measurably.

read the original abstract

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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 2 minor

Summary. The paper proposes RLSEdit, a recursive least-squares approach for lifelong LLM editing. It models sequential edits as an online quadratic optimization problem incorporating a cumulative key-value fitting loss and two soft regularizers (deviation from pre-trained weights and from an anchor mapping). This admits an efficient Woodbury-based recursion with per-edit cost independent of history. Theoretical contributions include deviation bounds and an asymptotic adherence-preservation trade-off. Empirical results on CounterFact and ZsRE demonstrate stable scaling to 10K edits, outperforming baselines in edit success and stability while preserving general capabilities.

Significance. Should the soft regularizers prove robust to arbitrary edit streams when fixed in advance, this could represent a meaningful advance in scalable model editing by balancing plasticity and stability more effectively than hard writes or rigid constraints. The efficient recursion and large-scale experiments are positive aspects, though the central assumption requires stronger validation.

major comments (3)
  1. [§3.2] §3.2: The regularization coefficients for the two deviation terms are free parameters whose selection is not ablated; yet the central stability claims over 10K arbitrary edits rely on them controlling interference without future knowledge of the edit stream.
  2. [Theorem 1] Theorem 1 (deviation bounds): The bounds and asymptotic trade-off characterization are derived under a fixed-regularizer regime, but no analysis or counterexample testing shows they prevent cumulative drift for correlated or conflicting edits, which is load-bearing for the lifelong editing guarantee.
  3. [§5] §5 (experiments): No error bars, variance across runs, or ablation on regularizer strengths are reported for the CounterFact/ZsRE metrics, making the outperformance and holistic stability claims difficult to assess reliably.
minor comments (2)
  1. [Abstract] Abstract: The Woodbury recursion is mentioned but its derivation steps should be summarized with key equations in the main text for reproducibility.
  2. [Notation] Notation: The 'anchor mapping' requires an explicit definition and guidance on how it is designated in practice for different model families.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the thoughtful and constructive comments. We appreciate the opportunity to clarify our approach and strengthen the manuscript. Below we respond point-by-point to the major comments and indicate the revisions we will incorporate.

read point-by-point responses

  1. Referee: [§3.2] The regularization coefficients for the two deviation terms are free parameters whose selection is not ablated; yet the central stability claims over 10K arbitrary edits rely on them controlling interference without future knowledge of the edit stream.

    Authors: We acknowledge that λ_dev and λ_anchor are hyperparameters. In the original experiments they were selected via a small validation set of edit sequences to achieve a practical balance between edit success and long-term stability. To directly address robustness under fixed values and arbitrary streams, we will add a dedicated ablation section that sweeps both coefficients over a wide range (including values that strongly favor preservation) and reports performance on full 10K-edit streams from CounterFact and ZsRE. This will demonstrate that the observed stability does not require knowledge of future edits. revision: yes

  2. Referee: [Theorem 1] Theorem 1 (deviation bounds): The bounds and asymptotic trade-off characterization are derived under a fixed-regularizer regime, but no analysis or counterexample testing shows they prevent cumulative drift for correlated or conflicting edits, which is load-bearing for the lifelong editing guarantee.

    Authors: Theorem 1 provides deviation bounds that hold for any sequence of edits under the fixed-regularizer objective; the proof relies only on the quadratic form and the positive-definiteness of the regularized Gram matrix, without assuming edit independence or orthogonality. Consequently the bounds apply to correlated and conflicting edits alike. Nevertheless, to make the practical implication clearer, we will expand the discussion following the theorem to explicitly note this generality and add a small-scale experiment with deliberately conflicting edits that illustrates bounded drift under the soft regularizers. revision: partial

  3. Referee: [§5] §5 (experiments): No error bars, variance across runs, or ablation on regularizer strengths are reported for the CounterFact/ZsRE metrics, making the outperformance and holistic stability claims difficult to assess reliably.

    Authors: We agree that statistical reporting strengthens the empirical claims. In the revised manuscript we will re-run all CounterFact and ZsRE experiments with five independent random seeds for edit ordering, reporting mean and standard deviation for every metric. The ablation on regularizer strengths will be included as part of the response to the first comment, ensuring the stability results are presented with variance estimates. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation uses standard identities on externally motivated objective

full rationale

The paper formulates editing as minimization of a cumulative quadratic objective with two fixed soft regularizers (deviation from pretrained weights and from an anchor mapping), then applies the standard Woodbury matrix identity to obtain an online recursion whose per-step cost is independent of history length. Deviation bounds and the asymptotic adherence-preservation trade-off are derived directly from this fixed-regularizer quadratic program without any parameter being fitted to the target edit stream and then re-used as a prediction. Experiments evaluate on held-out benchmarks (CounterFact, ZsRE, GLUE) whose labels are independent of the regularizer strengths chosen in advance. No self-definitional loop, fitted-input prediction, or load-bearing self-citation chain appears in the derivation; the central claims therefore remain self-contained against external data.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The approach rests on standard matrix identities and the modeling choice that a quadratic objective with two deviation penalties adequately captures the editing trade-off; no new physical entities are introduced.

free parameters (1)
  • regularization coefficients for the two deviation terms
    Weights balancing the cumulative fitting loss against deviation from pre-trained weights and from the anchor mapping must be selected or tuned.
axioms (1)
  • standard math Woodbury matrix identity permits O(1) rank-k updates to the inverse
    Invoked to obtain per-edit cost independent of history length.

pith-pipeline@v0.9.0 · 5525 in / 1240 out tokens · 26623 ms · 2026-05-16T12:18:36.548703+00:00 · methodology

discussion (0)

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