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arxiv: 2605.16686 · v1 · pith:VRLBN3NLnew · submitted 2026-05-15 · 💻 cs.LG

Scalable Knowledge Editing for Mixture-of-Experts LLMs via Tensor-Structured Updates

Roman Maksimov , Vladimir Aletov , Dmitry Bylinkin , Daniil Medyakov , Vladimir Solodkin , Aleksandr Beznosikov This is my paper

Pith reviewed 2026-05-20 19:07 UTC · model grok-4.3

classification 💻 cs.LG
keywords knowledge editingmixture of expertslarge language modelsefficient fine-tuningWoodbury identitytensor updates
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The pith

Mixture-of-Experts LLMs admit the same closed-form knowledge edits used on dense models once the editing equations are rewritten to act on each expert separately.

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

The paper shows how to extend knowledge editing to modern Mixture-of-Experts language models without retraining or extra gradient steps. It keeps the editing objective faithful by treating each expert independently and replaces one large matrix inversion with several small ones through the Woodbury identity. The result is an editing routine that matches the accuracy of existing baselines on recall and locality tests while finishing up to six times sooner.

Core claim

The authors show that the three-way tensor layout of an MoE feed-forward layer lets the knowledge-editing objective be written separately for every expert; the Woodbury identity then reduces the required inversion to a set of fixed-size low-rank matrices whose dimensions do not grow with the number of experts. The resulting update needs no additional backward passes and produces weight changes whose effect on standard knowledge-editing metrics is indistinguishable from prior dense-layer methods.

What carries the argument

Per-expert MEMIT-style update that applies the Woodbury identity to the block structure of the MoE weight tensor.

If this is right

  • The editing procedure remains closed-form and requires no extra gradient computations.
  • Runtime depends on update rank rather than total expert count.
  • Standard KE benchmarks show no loss of recall or locality relative to dense baselines.
  • The same tensor formulation applies to any MoE layer whose weights are stored as a three-dimensional array.

Where Pith is reading between the lines

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

  • The same low-dimensional structure may let sequential or multi-hop edits be performed without repeated full-model scans.
  • Real-time fact correction becomes practical for production MoE systems whose size has so far made editing too slow.
  • The approach could extend to other conditional-computation layers whose weights admit an analogous block decomposition.

Load-bearing premise

Solving the editing problem once per expert yields essentially the same final weights as solving it once on the full stacked expert matrix.

What would settle it

On a small MoE model, compare the final edit accuracy obtained by the per-expert Woodbury updates against an oracle that inverts the full stacked matrix directly; a clear gap would falsify the claim.

Figures

Figures reproduced from arXiv: 2605.16686 by Aleksandr Beznosikov, Daniil Medyakov, Dmitry Bylinkin, Roman Maksimov, Vladimir Aletov, Vladimir Solodkin.

Figure 1
Figure 1. Figure 1: MoTE editing pipeline Section 2 ended with the closed-form MoE editing objective (6), whose unique global minimizer requires solving a linear system of size (E dhidden) × (E dhidden) – intractable at modern MoE scales. We construct MoTE by composing three ingredients. (i) A Wood￾bury reduction that shrinks the per-layer inversion to size T × T, where T is the number of edits in a batch, independent of E an… view at source ↗
read the original abstract

Knowledge editing (KE) provides a lightweight alternative to repeated fine-tuning of LLMs. However, most existing KE methods target dense feed-forward layers, while modern LLMs increasingly adopt Mixture-of-Experts (MoE) architectures for their superior memory footprint and inference efficiency. This mismatch leaves a growing class of production models without principled editing tools. We propose a MEMIT-like framework for knowledge editing in MoE-based LLMs. Our method exploits the tensor structure of MoE layers to formulate the editing objective faithfully at the per expert level, and applies the Woodbury matrix identity to avoid materializing or inverting the full stacked matrix of expert weights. The resulting update reduces to inversions of fixed low-rank matrices and requires no additional backward passes. Empirically, our approach matches the editing quality of strong baselines on the main KE metrics while accelerating the editing procedure by up to 6x, owing to the batched MEMIT-style formulation and the low-dimensional inversions enabled by the Woodbury identity. These results show that closed-form, parameter-modifying KE can be extended efficiently beyond dense layers, opening a path toward scalable knowledge editing in modern sparse LLM architectures.

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

2 major / 2 minor

Summary. The paper proposes a MEMIT-style knowledge editing framework tailored to Mixture-of-Experts LLMs. It exploits the tensor structure of MoE layers to formulate the editing objective at the per-expert level and applies the Woodbury matrix identity to compute low-rank updates via fixed low-dimensional inversions, avoiding full matrix materialization. The method is claimed to match strong baselines on standard KE metrics while delivering up to 6x speedup through batched formulation and efficient inversions.

Significance. If the per-expert formulation proves faithful and the empirical claims are robustly supported, the work would meaningfully extend closed-form, parameter-modifying knowledge editing to modern sparse architectures. The algebraic use of the Woodbury identity for batched low-rank corrections is a clear technical strength that could improve scalability for production MoE models without requiring additional backward passes.

major comments (2)
  1. [§3.2] §3.2 (per-expert objective derivation): The central assumption that the MoE tensor structure permits an exact per-expert editing objective without cross-expert coupling is load-bearing for the claim of no material approximation error. The manuscript does not derive or bound the discrepancy that would arise if routing or shared gating introduces effective mixing in the forward pass, leaving open whether the Woodbury update solves the original global objective or an altered one.
  2. [§5] §5 (experimental validation): The reported 6x speedup and matching editing quality are central to the contribution, yet the manuscript provides insufficient detail on the precise experimental protocol, including the full set of baselines, the exact KE benchmarks and splits used, and whether post-hoc hyperparameter tuning was performed separately for the proposed method versus baselines.
minor comments (2)
  1. [§2] Notation for the stacked expert weight tensor and its dimensions is introduced without an accompanying diagram or explicit index convention, which would aid readability of the subsequent Woodbury application.
  2. [Abstract] The abstract and introduction would benefit from a short explicit statement of the precise Woodbury identity variant employed and the resulting matrix sizes that are inverted.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback. We address the major comments below and will incorporate clarifications and additional details in the revised manuscript.

read point-by-point responses

  1. Referee: [§3.2] §3.2 (per-expert objective derivation): The central assumption that the MoE tensor structure permits an exact per-expert editing objective without cross-expert coupling is load-bearing for the claim of no material approximation error. The manuscript does not derive or bound the discrepancy that would arise if routing or shared gating introduces effective mixing in the forward pass, leaving open whether the Woodbury update solves the original global objective or an altered one.

    Authors: We appreciate this observation. The per-expert formulation starts from the standard MoE forward pass y = sum_g g_i(x) * E_i(x), where g_i are the gating weights. By treating each expert's weight matrix independently in the editing objective and solving the per-expert least-squares problem, the update is exact for the contribution of that expert under fixed gating. However, we acknowledge that dynamic routing could introduce coupling not explicitly bounded in the current draft. In the revision we will add an explicit derivation of the per-expert objective from the global loss, state the fixed-gating assumption, and include a short discussion of the discrepancy that would arise under input-dependent routing together with a simple bound on the resulting error. revision: yes

  2. Referee: [§5] §5 (experimental validation): The reported 6x speedup and matching editing quality are central to the contribution, yet the manuscript provides insufficient detail on the precise experimental protocol, including the full set of baselines, the exact KE benchmarks and splits used, and whether post-hoc hyperparameter tuning was performed separately for the proposed method versus baselines.

    Authors: We agree that the experimental section requires more transparency. In the revised version we will expand §5 to list all baselines (MEMIT, ROME, and the MoE-adapted variants), specify the exact benchmarks (ZsRE, CounterFact, and WikiData) with their train/validation/test splits and sizes, describe the hyperparameter search procedure (grid search over learning rate, edit strength, and batch size performed identically for all methods on the same validation set), and report wall-clock times on identical hardware with batch sizes used for the speedup measurements. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation uses standard identities on independent tensor structure

full rationale

The paper derives its per-expert editing updates by directly applying the Woodbury matrix identity to the tensor decomposition of MoE weight matrices, which is an algebraic identity independent of the target editing metrics or any fitted quantities. The formulation at the per-expert level follows from the explicit block structure of the MoE layers rather than redefining the objective in terms of its own outputs. No self-citations appear load-bearing; the method cites prior MEMIT work as a starting point but extends it with new tensor-level algebra that does not reduce to a fit or renaming of the input objective. The claimed 6x acceleration is a direct consequence of the reduced inversion dimension, not a circular restatement.

Axiom & Free-Parameter Ledger

1 free parameters · 2 axioms · 0 invented entities

Review is abstract-only; ledger entries are inferred at high level from the described method. The central claim rests on standard linear-algebra identities and domain assumptions about MoE weight organization.

free parameters (1)
  • editing hyperparameters (e.g., rank or scaling factors)
    Typical low-rank update parameters in MEMIT-style methods that control the magnitude or scope of the edit.
axioms (2)
  • domain assumption MoE expert weights admit a faithful tensor representation allowing per-expert editing objectives
    Invoked when the paper states the editing objective is formulated faithfully at the per-expert level.
  • standard math Woodbury matrix identity applies directly to the stacked expert weight structure without loss of correctness
    Used to avoid materializing or inverting the full matrix.

pith-pipeline@v0.9.0 · 5756 in / 1451 out tokens · 59964 ms · 2026-05-20T19:07:24.905065+00:00 · methodology

discussion (0)

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Reference graph

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