FedAlphaEdit: Null-Space-Aligned Merging for Collaborative Knowledge Editing

Sota Sugawara; Yukihiko Okada

cs.CLOct 8, 2026

FedAlphaEdit: Null-Space-Aligned Merging for Collaborative Knowledge Editing

Authors: Sota Sugawara, Yukihiko Okada

Organizations: Graduate School of Science and Technology, University of Tsukuba, Tsukuba, Japan · Center for Artificial Intelligence Research, Tsukuba Institute for Advanced Research, University of Tsukuba, Tsukuba, Japan · Institute of Systems and Information Engineering, University of Tsukuba, Tsukuba, Japan

Abstract

Multiple institutions may each hold their own private knowledge edits and wish to integrate them into a single large language model without sharing raw edit requests. Null-space-constrained editing methods such as AlphaEdit mathematically guarantee that each update leaves unrelated knowledge intact, while collaborative frameworks such as CollabEdit aggregate edits from multiple clients without data sharing. Combining the two appears trivial. However, we show that this naive combination fails structurally, and we identify its cause. Guided by this analysis, we propose FedAlphaEdit. To our knowledge, this is the first collaborative knowledge editing framework that aligns both local editing and the server-side merging rule under a single null-space principle for preserving existing knowledge. FedAlphaEdit builds on null-space-aligned merging, in which clients share projected statistics and the server provably recovers the result of editing everything in one place under a one-shot idealization. Empirically, the proposed method repairs the collapse and brings edit success and preservation simultaneously close to the level of centralized editing across two architecture families. FedAlphaEdit thus lets institutions that cannot share raw edit data, such as hospitals and financial firms, jointly maintain a shared model that closely approximates editing all facts in one place.

Figures & tables

	Centralized	Naive	$\Delta$
ES	$97.08$	$79.69\pm 0.88$	$-17.39$
NS	$64.43$	$60.24\pm 0.11$	$-4.19$
oons	${\approx}3{\times}10^{-4}\%$ (floor)	$14.0\text{--}14.1\%$	—

Table 1: Naive combination versus the centralized reference on GPT-2 XL (MCF, 5000 edits,

10\times 500

). Centralized is a single deterministic run; Naive is three-seed mean

\pm

SD. Metric definitions are in Sections 4.1 and 3.5 .

Figure 1: The naive combination and FedAlphaEdit as the same total workload (

5000

edits) is partitioned across a growing number of clients

N

: neighborhood specificity (left), edit success (middle), and oons (right; the FedAlphaEdit series is at the measurement floor throughout). Dashed lines mark the centralized reference (

64.43

and

97.08

). All points are three-seed mean

\pm

SD. The per-client edit count co-varies with

N

(Section 4.2 ).

	ES	NS	oons
Centralized AlphaEdit	$97.08$	$64.43$	${\approx}3{\times}10^{-4}\%$ (floor)
Centralized MEMIT	$90.80$	$64.42$	$26.6\%$
CollabEdit (MEMIT)	$90.75\pm 0.03$	$64.34\pm 0.13$	$26.5\pm 0.05\%$
FedLEKE (our reimplementation)	$87.74\pm 0.51$	$66.78\pm 0.54$	$23.98\pm 0.02\%$
Naive (AlphaEdit + CollabEdit)	$79.69\pm 0.88$	$60.24\pm 0.11$	$14.0\text{--}14.1\%$
CollabEdit (MEMIT) + null-space projection	$82.45\pm 0.06$	$71.90\pm 0.03$	${\approx}3{\times}10^{-4}\%$ (floor)

Table 2: FedAlphaEdit against the centralized reference and the naive combination on GPT-2 XL (MCF). All rows edit the same 5,000 facts, single-round except the five-round variant (

10\times 100\times 5

) and the FedLEKE reimplementation (ten time slots). Centralized rows are single deterministic runs; all client-partitioned rows are three-seed mean

\pm

SD. NS is bounded above by the unedited model, which by construction attains NS

=100

, so a higher NS at a collapsed ES indicates weaker editing rather than better preservation, as the simple-average row illustrates. The simple-average and unnormalized-sum rows are the scalar merges

\gamma\sum_{i}\Delta_{i}

with

\gamma=1/N

and

\gamma=1

Qwen2.5-1.5B	ES	NS
Centralized	$98.28$	$73.32$
Naive	$93.53\pm 0.58$	$71.84\pm 0.75$
FedAlphaEdit	$96.40\pm 0.27$	$74.32\pm 0.16$

Table 3: Generality on Qwen2.5-1.5B (MCF, 10 clients

\times

500 edits). Centralized is a single deterministic run; Naive and FedAlphaEdit are three-seed mean

\pm

SD.

GPT-2 XL
zsRE	Centralized	Naive	FedAlphaEdit
Rewrite acc	$89.40$	$66.43\pm 1.27$	$89.40\pm 0.41$
Paraphrase acc	$81.20$	$62.22\pm 0.39$	$81.60\pm 0.16$
Neighborhood acc	$24.98$	$23.72\pm 0.26$	$25.12\pm 0.11$
oons	$3.17{\times}10^{-4}\%$ (floor)	$15.75\pm 0.04\%$	$3.17{\times}10^{-4}\%$ (floor)
Qwen2.5-1.5B

Table 4: Dataset generality on zsRE (each 10 clients

\times

200 edits, single round). Naive and FedAlphaEdit are three-seed mean

\pm

SD; Centralized is a single run; oons of order

10^{-4}\%

is the measurement floor. zsRE accuracies are first-token exact-match (

\times 100

); oons is a weight-space five-layer mean. No numerical comparison with MCF or between the two model families is intended.

Per-client $500$	ES	Centralized ES	NS	oons
$N=2$ ( $1000$ )	$99.83\pm 0.12$	$99.80$	$68.37\pm 0.07$	$4.05\%$
$N=5$ ( $2500$ )	$95.03\pm 0.15$	$99.24$	$62.80\pm 0.17$	$9.52\%$
$N=10$ ( $5000$ )	$79.69\pm 0.88$	$97.08$	$60.24\pm 0.11$	$14.04\%$

Table 5: Per-client-fixed control series (naive combination, GPT-2 XL, per-client

500

); three-seed mean

\pm

SD, with oons standard deviations

0.027

0.057

, and

0.022

percentage points. The

N{=}10

row reuses the main naive runs. Centralized entries are deterministic single runs editing the same case sets as the corresponding rows; the

N{=}10

centralized entry reuses the main centralized run. Total edits co-vary with

N

; cross-column comparisons are within the same row (matched total edit count) only.

Figure 2: Sequential drift

\lVert\Delta_{\text{proposed}}-\Delta_{\text{central}}^{\mathrm{Alpha}}\rVert_{F}/\lVert\Delta_{\text{central}}^{\mathrm{Alpha}}\rVert_{F}

and operator divergence

\lVert N_{\text{all}}-N_{G}\rVert_{F}/\lVert N_{G}\rVert_{F}

increase monotonically across the edited layers (

13

–

17

), peaking at the last; five-layer means

0.4547

and

0.1879

. Markers show the layer-

13

and layer-

17

endpoints.

	GLUE avg. F1
base	$0.4013$
Centralized	$0.3728$
Naive	$0.4087$
FedAlphaEdit	$0.3732\pm 0.0161$

Table 6: GLUE average F1 over six tasks (

n=100

per task), a supportive, non-binding observation. FedAlphaEdit is the three-seed mean

\pm

SD; base and Centralized are single values, and Naive is a three-seed mean. The naive combination sits nearer the base level than centralized editing does, consistent with the distorted merge writing edits more weakly (Section 4.2 ) rather than an advantage.

$\lambda$	ES	NS	oons
$10000$	$84.28$	$62.19$	$15.80\%$
$20000$	$78.84$	$60.12$	$14.05\%$
$40000$	$73.72$	$58.05$	$11.98\%$

Table 7: Sensitivity of the naive combination to the shared-covariance weight

\lambda

(GPT-2 XL, MCF,

10\times 500

, seed 1). Varying

\lambda

trades edit success and specificity against oons ; no setting recovers both axes toward the centralized level.

$\gamma$	ES	NS	oons
$0.1$ ( $=1/N$ )	$31.23\pm 0.22$	$77.16\pm 0.17$	$3.143{\times}10^{-4}\%$
$0.5$	$55.16\pm 0.47$	$54.98\pm 0.42$	$3.143{\times}10^{-4}\%$
$1.0$	$51.17\pm 0.27$	$51.07\pm 0.29$	$3.143{\times}10^{-4}\%$

Table 8: Scalar merges

\gamma\sum_{i}\Delta_{i}

(GPT-2 XL, MCF,

10\times 500

), three-seed mean

\pm

SD. The per-client AlphaEdit updates of the simple-average arm are reused and only evaluated, with no new solves. The row

\gamma=0.1

is the simple-average row of Table 2 . Only three levels of

\gamma

were tested, and finer tuning is untested. oons is at the measurement floor in every row by construction of a scalar merge.

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Jun 25, 2026, cs.LGJ/K move · Enter open · S save

Reproducibility Study of "AlphaEdit: Null-Space Constrained Knowledge Editing for Language Models"

Ananth K Suresh, Arya Hariharan

Independent

Knowledge Editing Model Editing Language Model Editing Catastrophic Forgetting

Open paper AskPDF arXiv

Fang et al. (2025) introduced a null-space constrained projection, named AlphaEdit, for locate-then-edit knowledge editing methods, theoretically guaranteeing that edits do not disrupt previously preserved knowledge, and reports substantial gains over existing editing methods on LLaMA3, GPT2-XL, and GPT-J. In this work, we present a reproducibility study of AlphaEdit, reproducing its reported results under the original experimental setup and extending the evaluation along three axes: new model architectures, additional downstream benchmarks, and substantially longer sequential editing horizons. We successfully reproduce AlphaEdit's reported metrics across the original models, though we identify a discrepancy in the reported fluency and consistency metric. Extending AlphaEdit to newer model families, we find that its advantage does not generalize uniformly, which we trace to architectural assumptions in the locate-then-edit paradigm that are violated by these newer models. We further stress-test AlphaEdit's central sequential-editing claim by extending the number of edits well beyond those evaluated in the original paper, and find that performance, which is stable at the originally reported scale, degrades as edits reach a much higher count, indicating that the null-space projection's protection against catastrophic forgetting is bounded rather than unconditional. Finally, we extend evaluation of edited models on three extra benchmarks, namely, BoolQ, HellaSwag, and XSTest, and we find that large-scale sequential editing degrades both general downstream task competence and safety-relevant refusal behavior. Our results confirm that AlphaEdit performs as reported within its original scope, while showing that its core theoretical guarantees are sensitive to model architecture and editing scale in ways that have practical implications for its deployment.

Abstract

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Reproducibility Study of "AlphaEdit: Null-Space Constrained Knowledge Editing for Language Models"

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