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arxiv: 2606.03695 · v1 · pith:5K7TH4TRnew · submitted 2026-06-02 · 💻 cs.CL

Don't Forget Your Embeddings: Robust Knowledge Erasure via Precise Editing of Embeddings

Clara Haya Suslik , Or Shafran , Mor Geva This is my paper

Pith reviewed 2026-06-28 10:35 UTC · model grok-4.3

classification 💻 cs.CL
keywords knowledge erasureconcept erasuretoken embeddingssparse matrix factorizationlanguage model safetyrelearning robustnessGemmaLlama
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The pith

Precise editing of token embeddings is necessary for robust erasure of concepts from language models.

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

Existing knowledge erasure techniques in language models often allow the erased information to be recovered through prompting or relearning because they skip the embedding layer. The authors introduce EMBER, which uses sparse matrix factorization to precisely remove concept features from token embeddings before they enter the model. When added to prior methods, it boosts erasure performance on models like Gemma and Llama, cuts relearning success rates substantially, and keeps overall coherence largely intact. The analysis indicates that the side effects remain confined to a small number of tokens tied to the erased concept. This points to the embedding space as a critical but overlooked site for achieving lasting removal of unwanted knowledge.

Core claim

The paper establishes that precise embedding-level intervention is necessary for robust concept erasure. By augmenting existing parameter-update methods with a sparse matrix factorization module applied to token embeddings, erasure efficacy and specificity improve across task formats while coherence loss stays minimal. Robustness to relearning increases markedly, with regained accuracy dropping to as low as 35% on Llama-3.1-8B-Instruct compared to 70-76% without the embedding edit.

What carries the argument

EMBER, a plug-and-play erasure module that leverages Sparse Matrix Factorization to isolate and remove concept-related features from token embeddings.

If this is right

  • Augmenting existing methods with EMBER consistently improves erasure efficacy and specificity.
  • Relearning robustness improves, limiting regained accuracy to 35% on Llama versus 70-76% for prior methods.
  • Coherence cost is localized to a small set of concept-exclusive tokens.
  • Results hold across diverse concepts evaluated on Gemma-2-2B-it and Llama-3.1-8B-Instruct.

Where Pith is reading between the lines

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

  • Embedding representations may encode concepts in a way that is more directly editable than internal parameters.
  • Relearning attacks might exploit retained embedding features even after higher-layer edits.
  • Similar sparse factorization approaches could be tested on other model components for enhanced erasure.

Load-bearing premise

The features associated with a concept are sparse enough and linearly separable enough in the embedding space that they can be factored out without broadly impacting other concepts or model behavior.

What would settle it

Observing that models augmented with EMBER still regain high accuracy on erased concepts after relearning attempts, or that coherence degrades across many unrelated tokens, would indicate the embedding intervention does not provide the claimed robustness.

Figures

Figures reproduced from arXiv: 2606.03695 by Clara Haya Suslik, Mor Geva, Or Shafran.

Figure 1
Figure 1. Figure 1: Existing concept erasure methods primarily [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Robustness evaluation results, showing for [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Distribution of TF-IDF scores (log scale) by [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Stage 1 prompt: the model describes the feature tokens without seeing the concept name. [PITH_FULL_IMAGE:figures/full_fig_p015_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Stage 2 prompt: given the Stage 1 description and the target concept name, the model classifies whether [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Number of embedding features per concept surviving each ratio threshold [PITH_FULL_IMAGE:figures/full_fig_p017_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Mean number of LLM-labeled potential features per position, averaged over 18 concepts. The leftmost [PITH_FULL_IMAGE:figures/full_fig_p018_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Mean number of Gemma-2-2B-it MLP neu￾rons retained per layer under different coverage thresh￾olds γ, averaged over 18 concepts (dmlp = 9216). The grey bars show the WTA union (all non-zero neurons across concept features); coloured bars show the subset retained after the coverage filter. OE and MC question pairs from six concepts. Evaluation Splits We use the following valida￾tion/test splits: • Concept an… view at source ↗
Figure 9
Figure 9. Figure 9: Prompt template used to convert open-ended (OE) question–answer pairs into a four-option multiple [PITH_FULL_IMAGE:figures/full_fig_p019_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Example questions for three of the 18 con [PITH_FULL_IMAGE:figures/full_fig_p020_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Per-epoch concept accuracy during relearn [PITH_FULL_IMAGE:figures/full_fig_p021_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: Post-erasure concept QA accuracy (Unlearn) [PITH_FULL_IMAGE:figures/full_fig_p022_12.png] view at source ↗
Figure 13
Figure 13. Figure 13: Post-erasure concept QA accuracy (Unlearn) [PITH_FULL_IMAGE:figures/full_fig_p024_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: Correlation between µj and TF-IDF (log scale) pooled across all 18 concepts. Left: Gemma-2-2B-it. Right: Llama-3.1-8B-Instruct. Each point is one edited token; the regression line and 95% bootstrap CI band are overlaid. COVID COVID coronavirus pandemic corona pandemic Corona Pandemic lockdown SARS coronav lockdowns quarantine SARS virus CoV Omicron Virus omicron demics quarantined quarant onavir epidemic … view at source ↗
Figure 15
Figure 15. Figure 15: Per-token edit magnitude µj on a log scale (bar height and color both reflect µj ), with tokens ordered by descending µj (largest on the left). Left: COVID-19 Pandemic on Gemma-2-2B-it. Right: Harry Potter on Llama-3.1-8B-Instruct. ffindor _Rowling umbledore therin _Voldemort _Dumbledore _Hermione Hermione _Hogwarts demort _Weasley _Malfoy _Potter Harry _Harry Potter _Snape _Draco _Severus _Ginny _Beatles… view at source ↗
Figure 16
Figure 16. Figure 16: Per-token TF-IDF (bar height and color, log scale), with tokens ordered by descending edit magnitude [PITH_FULL_IMAGE:figures/full_fig_p026_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: Prompt template used to elicit a concept-neutral context for each edited token. Placeholders [PITH_FULL_IMAGE:figures/full_fig_p029_17.png] view at source ↗
Figure 18
Figure 18. Figure 18: Prompt template used by the LLM judge to assign one of the three labels of § [PITH_FULL_IMAGE:figures/full_fig_p029_18.png] view at source ↗
read the original abstract

As language models are increasingly deployed in real-world applications, the ability to erase specific knowledge from them becomes critical for safety and compliance. Prominent methods seek persistent removal by updating the model's parameters, yet the target knowledge often can be recovered through adversarial prompting or relearning. In this work, we hypothesize this limitation stems in part from existing methods overlooking the embedding layer. To address this, we introduce EMBedding ERasure (EMBER), a plug-n-play erasure module that leverages Sparse Matrix Factorization for precise erasure of concept-related features from token embeddings. Through comprehensive evaluations across diverse concepts on Gemma-2-2B-it and Llama-3.1-8B-Instruct, we find that augmenting existing methods with EMBER consistently improves erasure efficacy and specificity across task formats, with minimal coherence loss. Moreover, it dramatically improves robustness to relearning, reducing regained accuracy by up to 50%, limiting it to 35% on Llama compared to 70%-76% for prior methods. Further analysis shows that the coherence cost is localized, affecting only a small set of concept-exclusive tokens. Our work establishes that precise embedding-level intervention is necessary for robust concept erasure, and demonstrates that existing methods can benefit from such augmentation.

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 / 1 minor

Summary. The paper introduces EMBER, a plug-and-play module using Sparse Matrix Factorization (SMF) on token embeddings to erase concept-related features. It claims that augmenting existing parameter-update erasure methods with EMBER yields consistent gains in erasure efficacy and specificity across task formats on Gemma-2-2B-it and Llama-3.1-8B-Instruct, with minimal coherence loss that is localized to concept-exclusive tokens; crucially, it reports dramatically improved robustness to relearning (regained accuracy limited to 35% on Llama vs. 70-76% for prior methods) and concludes that precise embedding-level intervention is necessary for robust concept erasure.

Significance. If the empirical results hold after verification of the underlying assumptions, the work would be significant for AI safety and compliance applications by highlighting an overlooked component (the embedding layer) in knowledge erasure pipelines and showing that existing methods can be augmented for better persistence against relearning attacks.

major comments (3)
  1. [Method] The central claim that precise embedding-level intervention via SMF is necessary rests on the unverified assumption that concept-related features are sufficiently sparse and linearly separable in the token embedding space. No direct diagnostic is provided, such as the singular-value spectrum of the concept-token submatrix, overlap between learned factors and non-concept tokens, or ablation of factorization rank, to confirm this property holds for the evaluated concepts on Gemma-2 or Llama-3.1.
  2. [Experiments] The reported robustness gains (35% regained accuracy vs. 70-76% for baselines) and coherence results are presented without statistical tests, confidence intervals, or explicit controls for confounding factors such as prompt engineering variations or exact baseline re-implementations, undermining the strength of the cross-method comparison.
  3. [Analysis] The claim that coherence cost is localized (affecting only a small set of concept-exclusive tokens) is stated in the abstract and analysis but lacks quantitative support, such as the exact fraction or count of affected tokens and direct comparison against non-EMBER baselines.
minor comments (1)
  1. [Abstract] The abstract states 'reducing regained accuracy by up to 50%' but then specifies '35% on Llama'; aligning these figures with the exact baseline values and models would improve precision.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback. We address each major comment below and indicate the revisions we will make to the manuscript.

read point-by-point responses

  1. Referee: [Method] The central claim that precise embedding-level intervention via SMF is necessary rests on the unverified assumption that concept-related features are sufficiently sparse and linearly separable in the token embedding space. No direct diagnostic is provided, such as the singular-value spectrum of the concept-token submatrix, overlap between learned factors and non-concept tokens, or ablation of factorization rank, to confirm this property holds for the evaluated concepts on Gemma-2 or Llama-3.1.

    Authors: We acknowledge that the manuscript does not provide direct diagnostics such as singular-value spectra or factor overlap analysis to verify the sparsity and separability assumptions. While the consistent empirical gains across models support the approach, we agree these diagnostics would strengthen the central claim. In revision we will add the singular-value spectrum of the concept-token submatrix, quantify overlap between learned factors and non-concept tokens, and include an ablation on factorization rank for the evaluated concepts on Gemma-2-2B-it and Llama-3.1-8B-Instruct. revision: yes

  2. Referee: [Experiments] The reported robustness gains (35% regained accuracy vs. 70-76% for baselines) and coherence results are presented without statistical tests, confidence intervals, or explicit controls for confounding factors such as prompt engineering variations or exact baseline re-implementations, undermining the strength of the cross-method comparison.

    Authors: We agree that the results would be more robust with statistical validation. The revised manuscript will add statistical tests, confidence intervals over multiple runs, and explicit details on baseline re-implementations together with controls for prompt variations. revision: yes

  3. Referee: [Analysis] The claim that coherence cost is localized (affecting only a small set of concept-exclusive tokens) is stated in the abstract and analysis but lacks quantitative support, such as the exact fraction or count of affected tokens and direct comparison against non-EMBER baselines.

    Authors: We concur that the localization claim requires quantitative backing. We will revise the analysis section to report the exact fraction and count of affected tokens and provide direct comparisons against non-EMBER baselines. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical method proposal with independent experimental validation

full rationale

The paper introduces EMBER as a plug-in module using Sparse Matrix Factorization on token embeddings, then reports empirical gains in erasure robustness across Gemma-2 and Llama-3.1 models. No derivation chain, equations, or 'predictions' are present that reduce to fitted parameters or self-citations by construction. The central hypothesis (embedding layer overlooked by prior methods) is tested via augmentation experiments rather than assumed or redefined. Assumptions about sparsity/linear separability are unverified in the provided text but constitute an empirical premise, not a circular reduction. This matches the default case of a self-contained empirical study.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The method rests on standard linear-algebra assumptions about feature separability plus empirical choices for the factorization.

free parameters (1)
  • sparsity level / rank
    Tuned to isolate concept features while preserving coherence; value not stated in abstract.
axioms (1)
  • domain assumption Sparse matrix factorization isolates concept-specific directions in embedding space
    Invoked as the core mechanism of EMBER.

pith-pipeline@v0.9.1-grok · 5753 in / 1121 out tokens · 36773 ms · 2026-06-28T10:35:53.312859+00:00 · methodology

discussion (0)

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