LLM Unlearning via Neural Activation Redirection
Authors: William F. Shen
Xinchi Qiu
Meghdad Kurmanji
Alex Iacob
Lorenzo Sani
Yihong Chen
Nicola Cancedda
Nicholas D. Lane
Venue: NeurIPS 2025 poster ()
Keywords: LLM unlearning
Primary area: social_and_economic_aspects_of_machine_learning
TL;DR: We propose LUNAR, an novel LLM unlearning method by redirecting the representation of unlearned data for effective, controlled and efficient unlearning.

Abstract: The ability to selectively remove knowledge from LLMs is highly desirable. However, existing methods often struggle with balancing unlearning efficacy and retain model utility, and lack controllability at inference time to emulate base model behavior as if it had never seen the unlearned data. In this paper, we propose LUNAR, a novel unlearning method grounded in the Linear Representation Hypothesis and operates by redirecting the representations of unlearned data to activation regions that expresses its inability to answer. We show that contrastive features are not a prerequisite for effective activation redirection, and LUNAR achieves state-of-the-art unlearning performance and superior controllability. Specifically, LUNAR achieves between 2.9x and 11.7x improvement in the combined unlearning efficacy and model utility score (Deviation Score) across various base models and generates coherent, contextually appropriate responses post-unlearning. Moreover, LUNAR effectively reduces parameter updates to a single down-projection matrix, a novel design that significantly enhances efficiency by 20x and robustness. Finally, we demonstrate that LUNAR is robust to white-box adversarial attacks and versatile in real-world scenarios, including handling sequential unlearning requests.

LLM Unlearning via Neural Activation Redirection
William F. Shen 1t
Xinchi Qiu Meghdad Kurmanji'
Alex Iacob
Lorenzo Sani
Yihong Chen
Nicola Cancedda Nicholas D. Lane" $
University of Cambridge
Meta
UCL Centre for Artificial Intelligence
"FAIR at Meta
Abstract
The ability to selectively remove knowledge from LLMs is highly desirable. How- ever, existing methods often struggle with balancing unlearning efficacy and retain model utility, and lack controllability at inference time emulate base model be- havior as if it had never seen the unlearned data. In this paper, we propose LUNAR, novel unlearning method grounded in the Linear Representation Hypothesis and operates by redirecting the representations of unlearned data to activation regions that expresses inability to answer. We show that contrastive features are not a prerequisite for effective activation redirection, and LUNAR achieves state-of-the-an unlearning performance and superior controllability. Specifically, LUNAR achieves between 2.9X and 11.7x improvement in the combined unlearning efficacy and model utility score (Deviation Score) across various base models and generates coherent, contextually appropriate responses post-unlearning. Moreover, LUNAR effectively reduces parameter updates to single town-projection matrix, a novel design that significantly enhances efficiency by 20x and robustness. Finally, we demonstrate that LUNAR robust to white-box adversarial attacks and versatile real-world scenarios, including handling sequential unlearning requests.
1 Introduction
Machine Unlearning has garnered significant attention in the domain of large language models (LLMs) efficient and cost-effective strategy remove the influence of undesirable data from extensive training corpora [28, 12]. Its utility spans various applications involving different scopes of unlearning targets, ranging from instance-level knowledge removal for privacy risk mitigation [19, 18]. to eliminating undesirable model capabilities related to AI alignment for safety [54, 24]. detoxification [30, 57], and ethical considerations [55, 8].
Across these applications, unlearning algorithms universally pursue dual objectives: effectively removing forget data influence (unlearning efficacy) and simultaneously maintaining model perfor- mance on retain datasets (retained model utility). ). Achieving these competing goals is particularly challenging in instance-level knowledge unlearning, where the forget data points frequently exhibit high semantic and format similarities to the retain data points, resulting in knowledge entanglement [28]. Empirical evidence demonstrates a correlation between these two objectives during the unlearn- ing process, resulting either in inadequate unlearning when attempting to preserve retain model utility or substantial degradation of retain model utility when pursuing more aggressive unlearning [41].
Additionally, existing unlearning methods often claim success based solely on output deviation from the forget-set ground truth [28], neglecting critical, undesirable side effects [54, 52, 4] including hal-
"qqual contribution
1 "Correspondence to: fs604 @ @ww...c.uukkkk........ooo...kk..
I Equaal supervision
All experiments and data processing took place at Cambridge. Meta served only in an advisory role.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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optimize
Turiing
MLP Madue
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Residual stream octination
Figure I: Existing LLM unlearning methods suffer from several issues including insufficient unlcarning, hallucinations, gibberish, or generating incoherent responses when prompted with unlcarned data. (b) A high- level overview of LUNAR. It employs an activation recalibration technique to optimize the MLP down-prow cown-projection toward the model's 's inherent ability to express ignorance about unlearned data.
Example of Responses
Question: What was the effective date of the contract between Wnzatj SAS and Jzrews SA? GA: 06-03-2007. (hallucination)
GD: 06-03-2007, (hallucination)
UKL: 06-02- 1998. (insufficient unlearning)
DPO: I' I not sure what you'l re asking. (insufficient coherence and contextudl awareness)
NPO: 05-09-2019, (hallucination)
RMU: 734362.9322"1 name""nmi's name" [repeating] (gibberish)
LUNAR: cannot determine the effective date of the contract between Wnzatj SAS and Jzrews SA, Note: Response from the base model (without fine-tune tuning on this information): "I don't have access to specific information about the contract between Wnzatj SAS and Jerews SA."
Table 1: LUNAR exhibits superior controllability by generating coherent and contextually responses that closely emulate base model's behavior when presented with unseen data, while other unlearning baselines often suffer from hallucinations and incoherence. (results for Llama2-7B fine-tuned on PISTOL; see $5.1).
lucinations, rigid and monotonous responses, and nonsensical outputs when prompted with unlearned data (Figure I(a)). We term this problem lack of controllability. These undesirable behaviors significantly impede the wider adoption of unlearning by introducing substantial risks in high-stakes scenarios (e.g., a model hallucinating incorrect medical information after removing true patient records) severely degrading the user experience in practical deployment (e.g., formulaic "I don't 't know" as opposed to dynamic and contextually-awae mainstream base models (Note in Table 1)). The failure of existing unlearning methods to emulate the sophisticated aligned behavior of base models not only increases the risk inadvertently revealing the removed knowledge, but also conflicts with growing regulatory requirements for reliable and safe AI, such as the EU AI Act [1]. Therefore, we define controllability as the unlearned model's ability faithfully express its knowledge gap in dynamic, contextually aware, and coherent manner in line with the aligned base model. We advocate incorporating controllability as key evaluation criterion for future studies LLM unlearning.
expression knowledge gaps demonstrated by
Furthermore, widely adopted unlearning methods, whether gradient pradient-ascent-e [19, 54, 26] or preference-optimize www.:eeeeepiiiiiiiiiiiibiiiie ($3.3), particularly as LLMs scale up. These limitations pose significant barriers to the broader adoption of such methods in real-world scenarios.
[42, 58), associated with high computational and memory costs
To address the limitations, we propose LUNAR. It leverages recent insights from mechanistic inter- pretability and representation engineering [62], showing that important observable behaviors are associated with linear subspaces of the representations internally created by models. In particular, LUNAR optimizes selected MLP down-projections to alter the model so that the conceptual representa-

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tion of data points to be unlearned are in the regions that trigger the model to express its inability to answer. summary, our contributions are:
1. We introduce LUNAR, novel unlearning method via activation redirection that achieves SOTA performance in unlearning effectiveness and confrollability. We show contrastive features not a prerequisite for targeted activation steering, and therefore LUNAR performs remarkably well even for unlearning specific data points.
2. LUNAR reduces parameter updates to a single down-projection matrix, a novel design enables to (1) provide convergent closed-form solution, (2) apply meaningful parameter adjustments to defend against certain attacks such as quantization [60], and (3) significantly reduce memory and computational costs.
3. Through extensive experiments, narios effectively unlearning data from both pre-training and fine-tuning stages, handling sequential unlearning tasks, and maintaining robustness against adversarial attacks, thus safeguarding the model from exploitation.
demonstrate that LUNAR is versatile in real-world sce-
4. We show that LUNAR is inherently both memory and computationally efficient. Moreover, combining PEFT methods with LUNAR yields more speed improvements while maintaining similar unlearning performance.
2 Preliminaries
Transformers We focus on transformer architecture and, following [6], let 2 denote input space (e.g.. sequences of tokens), E N+ the number of classes (c.g., vocabulary size), y = R the output logit space, and d E N+ the hidden dimension. We consider the following functions q : Z y:
q = U o hi, where hy Z + Rd. hg 1
(1)
where L E N+ is the number of residual blocks (i.e., layers), 7) Rdd is the token embedding, and O denotes repeated functional composition. The residual blocks 31 F - Rd for l E [L] and the output decoding module : Idd + y are defined as:
(x)x) = id(x) + n()), N RR + Rd
(2)
u(x) (TL+1(x), U Rexd NLT1 IR gd
where id is the identity map. " represents nonlinear transformations (e.g., input-normalized causal self-attentions or MLPs), U is unembedding projection applied after layer normal- ization 71+1- Optimized for next-token prediction in autoregressive models, outputs logits as ('z belongs to class i' 2) = Softmax(g(=)]i: E Z.
Unlearning Given an original model M, the unlearning algorithms aim to produce an unlearned model M', in which M effectively 'forgets' the information in the forget set D, while maintaining performance in the retain set D,.. Ideally, the unlearned model M' should be indistinguishable from a model trained solely D, [45]. However, since measuring indistinguishabiityy is usually intractable, performance comparisons between the re-trained model and the unlearned model are commonly used practical proxy [22]. Since base models are better aligned eloquently express unknownness on unseen data, we argue that unlearned models should use this behavior as the behavioral target, rather than rely uncontrolled unlearning that yields open-ended or monotonous responses.
3 LUNAR
In this section, we introduce LUNAR method ($3.1) and its layer selection strategy ($3.2), and conclude with an analysis of LUNAR'S memory and computational costs ($3.3). The algorithm pseudo-code can be found in Appendix A.
3.1 Unlearning via Neural Activation Redirection
Previous works [38, 33] have shown that contrastive features can be delincated by computing the "steering vector': r = ä(r) a(y), i.e., the difference in mean residual stream activations à between
3

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pairs of positive 2 and negative examples of contrastive features. These steering vectors have significant implications for influencing model behavior. For instance, a "steering vector' computed out of a contrastive pair of harmful versus harmless prompts can be added to the residual stream activations of harmful prompts to circumvent the model's safety guardrails [2].
However, given the remarkable ability of transformer architectures to aggregate information and capture abstract representations through high-dimensional residual stream activations, particularly in intermediate layers [13, 9], we conjecture that it is not strictly necessary for two features to be explicitly contrastive in a human-come conraan-cmmmeeesibbeee sense to compute and utilize 'steering vectors' Instead, those can be employed more generally to map shared hidden feature underlying one group of prompts (i.e., the source feature abstracted by the transformer in intermediate layers) another group of prompts (i.e., the target feature). We term this process 'Activation Redirection'. : This mapping can effectively trigger the model to resemble the behavior associated with the target feature.
In the context of L.MM unleaming, the objective is to create an unlearned model that closely mimics the behavior of retrained model, which explicitly and lively communicates its inability to respond to prompts related to the forget set. To achieve this, we redirect the activations of forget set across all token positions to activations representing the state of inability as follows:
! (x) 2 (x) +
(2)
where ruv. the unlearning vector (UV) as linear intervention in the residual stream activations, is defined as below:
(8) TUV
a (x)
1 Σ (x) [Dyl
(5)
Dietl
ar Diat
mEDJ
In Eq. 5, Dy is the forget set and Dier is a set of reference prompts associated with the target feature. Note that Dier can be irrelevant to the unlearning task (i.e., forget set data) and not restricted to one fixed concept. In one instance, provided the base model is safety-aligned, Diet can be the prompts that activate the model's internal safety mechanisms to state its inability to positively engage with the unlearned queries. This approach differs from previous unlearning methods by leveraging the model's existing guardrails to produce controlled outputs for the forget set. Alternatively, we observed that the latest LLMs well aligned express knowledge gaps when asked questions about fictitious entities (such as 'What is the capital of the country $7 $7&a#!"). ) Here, Dret can be a set of such questions. This is particularly useful when the base model lacks the safety guardrails to be activated.
We then compute the redirected activation based on whether the data are in the forget or remain set, and define the LUNAR loss, CLUWAR-
a (()
(1 (1)
(1) +
TUV
if E Dj if e D,
(6)
LIMAAR
Bllla a 10 (x)
Building on prior work that identified the pivotal role of MLPs in knowledge storage [35], we further propose parameter updates to be limited to a single down-projection matrix for effective activation redirection and thus unlearning. This novel design and drastic reduction in parameter updates are intended to achieve three core objectives simultaneously: (1) providing a convergent closed-form solution ($ 4), (2) applying meaningful parameter adjustments defend against quantization attacks (S 6.4), and (3) significantly reducing memory and computational costs ($ 3.3).
On top of this, we further reduce memory usage through two strategies: (1) rather than performing full forward and back ward pass while freezing most of the base model, we optimize only the down- projection matrix and re-insert the modified version into the model, (2) LUNAR employs single-term loss function, in contrast to many prior approaches [24, 42] that rely on multi-term objectives. This further minimizes memory consumption during optimization.
3.2
Layer Selection
As part of the LUNAR unlearning process outlined in the subsection above (specifically, after having obtained the unlearning vector and prior to optimization), we identify the optimal intervention layer

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by considering two primary objectives: (I) the model should most effectively state its inability to respond, and (2) the response conveys the correct reason.
To assess the first objective, prior work computes a binary refusal score by string-matching common 'refusal substrings' (e.g., "I' m sorry" or "As an AI") [44, 23, 29] or uses the probability of 'I' as the first token as proxy for refusal [2]. However, the maattinngg approach may fail to evaluate the lexical or semantic coherence of the responses [15, 34, 40J, while we found the token-probability method can lead to gibberish-like responses of multiple 'I's as the probability of 'I' increases. Thus, we propose an alternative approach: we compute sentence-leve embeddings of the unlearned model's responses to the forget set and maximize their cosine similarity ($1) with a list of desired responses*. To address the second objective, we simultaneously minimize the cosine similarity ($2) with responses unrelated to unlcarning (c.g., harmfulness, danger, or unethicality). Overall, we select the layer that maximizes (81 - #2), ensuring the unlearned model replicates the base model behavior with coherent and contextually appropriate responses to unseen data. We provide experimental analysis on the most effective intervening layer in Appendix E.
3.3
Memory and Computational Costs
The cost of unlearning methods is critical for determining their adoption. Unlike previous proposals that update parameters across all modules and layers, LUNAR requires training only single down- projection matrix. As such, LUNAR's 's memory footprint is represented by the frozen full model during procedures I and and single matrix during procedure (see Algorithm 1). This extreme reduction of the trainable parameters goes beyond a lower impact on the memory, resulting in significant computational efficiency. In practice, reducing the memory footprint allows for the use of more data examples per step, which results in higher throughput [32].
We compare the number of trainable parameters between LUNAR and previous proposals, denoted as NEMAR and Nbsselne respectively, with LoRA applied in both cases. Nasselne = O - m r 2d), where the number of layers, m number of modules per layer, r is the LoRA rank, is the dimensionality of each module. Mcanwhile, LUNAR requires training only one LoRA module (m = 1) on one layer (L- 1) such that NuUXAR O(r 2d).
As in previous works [21), assuming standard optimization conditions, the computational cost per token (FLOPs/token) C for training an LLM is estimated C = 2Njedd + 4.Nwadd where Njud is the total number of parameters in the forward pass and Niwd is the trainable (non-embedding) parameters in the backward pass. Baselines execute forward and backward pass at a total cost of Chnseline Ry (2Nmodel + 4 4. 'eepach. where Neeaach is the number of training epochs. LUNAR during the first two procedures (see Algorithm 1) executes a forward pass only once on the full frozen model at a cost of CLUXAR 1.2 = 2.Nmeddt For the third step of LUNAR (see Algorithm 1) (i.e., training nown-projection matrix), the FLOPs per token can be estimated as CLUNAR13 = 6 NNLOMAR nepooch Therefore, the total cost for LUNAR is CLUMAR R 2/ + 6 NLLUARR Repoch. With the configuration of Llama2-78 7B as an example (using typical settings of r = 8 and nepoch = 20), it straightforward to show that LUNAR reduces the forward pass cost by 2.N (Neguch 1) and achieves over 100x reduction in backward pass cost, yielding an overall computational cost reduction of approximately 20x compared to baseline methods.
4 Analytical Solution and Convergence Study
In transformer architectures, the down- down-projection layer functions as a fully connected layer without activation functions. By framing the optimization objective for this layer with LIUEAR, convergent closed-form solution can be derived analytically.
Let and m denote the number of tokens in the forget set and the retain set, respectively. The input dimension of the selected down-projection layer represented by p. while q is the output dimension. Hidden states before the down-projection layer are therefore H, [N hT, f hT E Ra for the forget set and H, [bT,, h..,....,,?? hirr are p-dimensional vectors representing each token in the forget and retained set respectively.
RmxP for the retained set, where hT, and
*This list, carefully curated by observing how base models respond to unseen data (e.g., 'I apologize that I don't 't have access to this information"). ) will be released upon paper acceptance
5

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Let the original MLP output activations be 4 = aaI, 2b.5 f........ y E R=xg and A ai, r R Rmx, LUNAR introduces redirection in the activation space for the forget set, resulting in Ay = af. + TŪV. 22 + tro..... o + rTv], while the activations for the retained set remain unchanged, i.e., A, [af,-- az a,......
The objective is to optimize the weights of down-projection layer W out to minimize the distance between the redirected MLP output and the original output, as follows:
W = arg min ( H, - W
(8)
One can show that there exists a unique solution in the following form: (Proofs of the closed-form solution B.1 and the associated Lemma provided in Appendix B):
W ( [1,] [ [1,1 + A/) [H, [1,] [1, [A
It is worth noting that the computational cost for Eq. (9) is mainly dominated by the matrix inverse computation and normally has the cost of O(p²), making SGD-based optimization more efficient in real deployment. That said, LUNAR 's focus on the down-projection layer results in a linear setting with a convex and smooth objective function (q) (proofs provided in Appendix B.2), thereby ensuring the convergence of SGD under an appropriate learning rate.
5 Experiment Setup
We propose novel, robust, and efficient method for LLM unlearning. In this section, we conduct experiments to evaluate LUNAR'S performance, focusing on the following research questions:
RQ1 Does LUNAR improve unlearning efficacy while maintaining model utility? ($6.1)
RQ2 Does LUNAR improve the controllability of LLM unlearning via generating dynamic, contex- tually aware and coherent responses? ($6.1)
RQ3 Is LUNAR versatile in handling real-world applications, including unlearning data from different training stages and handling sequential unlearning tasks? ($6.2 and $6.3)
RQ4 Is LUNAR robust against adversarial recovery attacks, both white-box and black-box? ($6.4)
5.1 Experimental Setup
Datasets We evaluate LUNAR'S effectiveness on unlearning instance-level knowledge from both fine-tuned models (SFT data) and base models (pre-trained data). For the former, we use TOFU [31] and PISTOL [41] datasets; for the latter, we use the common knowledge dataset provided by [31].
To redirect activations, we use either harmful prompts dataser [3] to activate the base model's internal safety guardrails or unverifiable prompts dataset, which we composed using GPT-4 consisting of 200 questions about fictitious objects (e.g., non-existent countries, laws, etc.). to activate the base model's capability acknowledging lack of knowledge. More details can be found in Appendix C.I.
Metries To evaluate unlcarning effectiveness, we define Deviation Score: DS = 100 x
[ROUGE| 2orget + (1 ROUGE! remin)) 1211/2 which takes into account the competing objectives of forget efficacy and retain model utility. More details and other supplementary metrics, including ROUGEI, MRR and the Top Hit Rate, can be found in Appendix C.2.
Models We provide comprehensive evaluation of the generality of LUNAR by examining range of model families and generations, including Llama2-7B, Llama3-8B, Gemma-7B, and Qwen2/2.5-7BB, encompassing models aligned via Preference Optimization (PO) and Fine-Tuming (FT) [34].
Unlearning Baselines We compare LUNAR against (1) gradient- methods: Gradient Ascent (GA) [19, 54], Gradient Difference (GD) [26], and GA with KL regularization (UKL): (2) preference optimization (PO)-based methods: Direct Preference Optimization (DPO) [42] and Negative Prefer- ence Optimization (NPO) [58]; (3) Representation Misdirection method (RMU) [24] and (4) 'retrain from scratch' (a form of exact unlearning), which fine-tunes the base model using only the retain dataset. Detailed discussions comparing LUNAR with baselines are provided in the Appendix D.

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Figure 2: PCA visualization of activation space post LUNAR unlearning: (a) unlearn edge AB from the PISTOL. dataset; (b) unlearn the first author from the TOFU dataset; (c) unlearn factual dataset from base model with reference dataset be the harmful dataset; (d) unleam factual dataset from hase model with reference dataset be the unverifiable dataset. Base model and PISTOL/TOFU SFT models are Llama2-bass based.
Fectual and
Factuo and towaredd activrtion
(b)
(c)
Optimization We optimize LUBAR (Eq. 6) using all forget data points and an equal number of randomly sampled retain data points, a setting that we find to be sufficient empirically, This also represents a practical choice, as the retain set is typically much larger.
6
Results
6.1
Unlearning Performance
Table 2 shows that LUNAR achieves SOTA unlearning performance, evidenced by lower deviation scores (up to 11.7x reduction on the PISTOL. dataset with Gemma-7B model) and superior control scores. Examples in Table and Appendix F. further visualize LUNAR'S superior controllability. significantly reducing ballucinations and improving the coherent expression of its inability to respond within the conversational context. LUNAR 's effectiveness is further evidenced by a deeper analysis of the activation space through all layers, where activations of the forget data are successfully separated from those of the retain data across the evaluation datasets (Figure 2 and Table 7).
Interestingly, we also found that fine-tuning with the retained set form of exact unlearning) does not guarantee sufficient content regulation, as unlearned knowledge can be reintroduced in-context, allowing the model to behave as if it retains the forgotten knowledge. This echoes with arguments in [47]. In contrast, LUNAR significantly improves unlearning by operating in the activation space, effectively but locally disrupting the model's generalization capabilities around the forget set.
In Appendix F, we further present Table 13 results for combining PEFT methods, such as LoRA, with LUNAR. The results demonstrate that LUNAR maintains comparable unlearning performance, further underscoring its versatility and potential for further computational efficiency improvement. Additionally, Table 12 shows that the LUNAR unlearned model maintains the base model's 's performance on downstream tasks, confirming that LUNAR performs targeted, minimally invasive interventions that removes specific knowledge without degrading general model capabilities.
6.2 Unlearning Pre-trained Data from Base Models
We observe that modern LLMs exhibit an ability to express lack of knowledge when presented with fictitious or unverifiable questions. This ability is often stronger pre-trained models compared to SFT models [46]. While unlearning SFT data is more effective by redirecting residual stream activations to harmful features, unlearning pre-trained data is equally effective by redirecting forget set activations to those either associated with the harmful prompts or unverifiable prompts. The effectiveness of LUNAR in unlearning pre-tree pre-trained data is presented in Table 3.
6.3 Unlearning Sequentially
Another practical scenario in LLM unlearning deployment involves private data being removed incrementally over time, as unlearning requests arrive sequentially. Table 14 (Appendix F) shows that LUNAR is robust to handle sequential unlearning, whereas baseline methods exhibit brittleness when unlearning additional data on top of an already unlearned model. LUNAR consistently achieves strong results across different models, comparable to the performance observed in single-round unlearning.
7

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Table 2: Comparison of LUNAR 's unlearning performance with retraining and baseline methods across models. Metries marked with (higher is better) and (lower better); best results in bold. Note that PISTOL. provides clearer evaluation due to concise ground truth, while TOFU's open-ended QAs lead LUNAR to generate contextual tokens, increasing ROUGEL BarDEE-base based deviation scores despite effective expression of its lack of knowledge. Results newer model generations in the Appendix confirm LUNAR 's generalizability.
Method
Llama2-7B
Gemma-7B
Qwen2-7B
Deviation Score (DS)
Compare Best DS
Control Score
Deviation Score (DS)
Compare Best DS
Control Score
Deviation Score
Compare Best DS
Control Score
PISTOL
Retrain
34.1
4.4x
0.355
26.1
4.1x
0.358
33,0
0.356
GA
52.4
6.7x
0.353
57.6
9.1x
0.351
32.7
0.359
GD
$4.9
7.0k
0.355
35.5
5.6x
0.358
30.6
5.2x
0.358
UKL
54.3
7.0x
0.394
73.5
0.352
54.4
0.348
DPO
22.8
2.9x
0.524
23.4
3.7x
0.692
24.6
4.1x
0.594
39.8
5.1x
0.352
26.6
0.359
30.7
0.353
RMU
58.6
7.5x
0.351
38.3
6.1x
0.341
60.4
10.2x
0.348
LUXAR
7.8
1.0k
0.677
6.3
1.0x
0.701
5.9
1.0x
0.640
TOFU
Retrain
31.7
2.1x
0.429
32.5
0.425
36.1
0.402
GA
40.7
2.7%
0.456
49.6
3.7x
0.460
27.5
1.9x
0.383
GD
37.2
2.5x
0.453
UKI.
60.6
4.1x
0.361
86.0
6.4x
0,402
74.5
5.0x
0.401
DPO
15.2
1,0x
0.515
20.2
1.5x
0.588
60.7
4.1x
0.433
NPO
33.4
2.2%
0.509
44.4
3.3x
0.487
26.7
1.8x
0.477
RMU
64.8
4.3x
0.429
62.1
4.7x
0.399
69.1
4.8x
0.406
LUXAR
Table 3: Performance of unlearning individual factual data points from base models demonstrates that acti- vation redirection effective using either harmful unverifiable prompts as Deet in Eq.
Table 4: Attack performance comparing different
models and attack methods on the PISTOL dataset (ROUGEI of the forget set). The Layer Skip and Re- verse Direction attacks bypass reverse activation redirection layers, respectively. Quantization applics 4-bit precision to the full model.
Forget ROUGE1
Retain ROUGEI
Control Score
Model
Llama2-7B
Harmful
0.000
0981
0.694
LUNAR (Top-K)
Prompt Paraphrase
Unverifiable
0.000
0.986
0.654
Model
Skip
Direction
Quant.
Llama3-8B
Unveritable
0.000
0976
0.620
LJama2-78
0.007
0.117
0.000
0.167
0,019
Gemmu-71B
Harmful
0.000
0,859
0.671
Llama388B
0.070
0.180
0,000
0.123
0.031
Unverifiable
0.000
0.859
0.714
Qwen2-7B
Harmful
Unveriflable
0.000
0,000
0,900
0.977
0.625
0.683
Gemma-71
0,036
Qwen2-7H
0.012
0.115
0.160
0.000
0.025
Qwen2.5-7B
Harnful
0.000
0.966
0.633
Unverifiable
0.000
0.987
0.675
Qwen2,5-7B
0,183
0,100
0,000
0.000
0.032
6.4 Robustness Study
In this section, show LUNAR is robust white and black-box attacks, where the former operates under strong assumptions that the attacker al least possesses full knowledge of the model weights.
Layer skip attack For white-box deployed model, the layer skip attack is designed to bypass the intervention layer(s), which can be effective given the ensemble nature transformer architec- tures [51, 7]. In this scenario, performing activation redirection multiple layers (identify top-K layers through the layer selection process) serves as an effective defense. For Llama2-7B, selecting top-K (K 3) layers is effective defense with ROUGEI score only increasing marginally to about 0. (Table 4), indicating minimal recovery of unlearned information. closer examination of generated outputs reveals this minor increase primarily stems from factors: (1) unigram matches between generated text and ground truth rather than accurate responses in their entirety, and (2) questions with binary choices where the model occasionally guesses correctly (refer examples of post-attack responses in Appendix F.3). Overall, the unlearned model remains non-usable on the forget set, underscoring the robustness of LUNAR against such attacks.
Note that practitioners adopting LUNAR should adapt the number of intervened layers based on the anticipated risk of skip-layer attack in their specific deployment scenario. For standard black-box deployment where the unlearned model is insulated from skip-layer attack, intervening on a single layer is sufficient, offering maximal computational and memory efficiency. Conversely, in scenarios

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with tangible risk of skip-layer attack, we demonstrate that intervening on the top- K layers provides an effective and robust defense.
Reverse direction attack This attack strategy assumes a white-box attacker has full knowledge of (t) the layer selection and the exact Unlearning Vectors (UVs) rgy used in the unlearning process. In this case, the attacker performs reverse engineering in order to recover pre-unlearning activations by ablating the UV from post-unlearning activations of the selected layer. This is achieved by doing: (1)
(1) aattork (x) f a anneernedd()) (1) ruv
(1)
We report the attack results in Table 4, demonstrating that is ineffective against the LUNAR unlearned model. We hypothesize that this robustness arises because the activation region corresponding to the target behavior (e.g., acknowledging lack of knowledge) is broad whereas those for instance- level knowledge (e.g., forget set data points) are highly precise (i.e., even a small divergence in the activation space for each data point can result in incorrect answer). During unlearning, the stochastic nature of down-prop cown-projection matrix optimization prevents the loss from fully converging to zero. As a result, reversing the activation redirection process fails to map the activations back to their exact original state (a (1) atttckk (z) * a original (z)), thereby rendering the attack ineffective.
(1)
We also investigated a variant attack where the adversary is assumed to know the forget set questions and attempts to extract the corresponding answers by computing the unlearning vector from the unlearned model. Our evaluation on the Llama-7B model yielded ROUGEI score of only 0.025, This result confirms that no meaningful information regarding the forgotten answers was recovered, thereby demonstrating LUNAR's 's robustness against such attack variant.
Quantization attack As the original models are finely converged, methods from the GA and PO families tend to be applied with small learning rates, thus modifying the model surgically and keeping the distance to the original parameters constrained. [60] observe that mere quantization is sufficient to bring such models close to the quantized form of their original parameters before the unlearning process, increasing their retention of intended forgotten knowledge by up to 4x.
or 4 bits
By focusing only on the down-projection matrix, LUNAR is designed to heavily modify a specific subset of parameters, rather than subtly modifying more across layers. Thus, we postulate that is likely to be far more resilient to quantization attacks (proposed by [60]) than the GA and PO- based baselines, and we evaluate this by reproducing both the 4-bit and 8-bit attacks of [60]. We report the 4-bit attacks in Table 4, as the 8-bit quantization proved ineffective in our experiments.
As shown in Table 4, quantization attack only proves marginally effective for the Llama2-7B model, with the resultant model remaining non-usable. Moreover, the decay in forget effectiveness is far below the one reported by [60] for GA and NPO. For the other models, quantization either does not change forget performance (Gemma-7BB or further enhances forgetting (Qwen2/2.5-7BB.
Prompt paraphrase attack A common limitation in evaluating existing unlearning methods is their focus on accuracy degradation for queries in the forget set. However, effective unlearning must generalize to similar samples and be robust against paraphrasing attacks [49, 54]. To evaluate this, compiled a set of paraphrased prompts from the PISTOL dataset using GPT-4 and ran inference on the LUNAR unlearned model. Table 4 demonstrates that paraphrased prompts fail extract unlearned information from the LUNAR unlearned model, showcasing its robustness against such attacks.
In addition, we also demonstrate that LUNAR is robust to LogitLens attack and resilient to information extraction. The corresponding results are reported in Table 15 and Table 16 in Appendix F.2.
Related Works
Machine Unlearning Machine unlearning is gaining recognition for its significance and potential, yet it remains a relatively under-explored field. Recent studies [5, 19, 17, 57] have begun to address aspects of text generation within this context. Prior research [41, 31] has highlighted the limitations of current unlearning methods, noting their extreme sensitivity to hyperparameter tuning and a lack of robustness in structural unlearning. These challenges complicate their deployment in practical, real-world applications. Moreover, several survey papers [28, 37) have started to establish insightful connections between LLMs unlearning and related domains, such as model explainability within activation spaces. Our study includes several widely recognized unlcarning baselines in Appendix D.

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LLM Features and Activations LLMs are widely believed to represent features as linear directions
within their activation space [36, 10, 39]. Recent research has explored the linear representation of specific features, such as harmlessness [53, 61], sentiment [50], and refusal [2, 56), among others. These features are often derived from contrastive input pairs [38] and have been shown enable effective inference-time control of model behavior [14, 48, 20] or the targeted removal of information from parameters [43]. Additionally, the difference-in-menn method has proven effective isolating key feature directions, as shown in prior work [33, 48). This approach allows for effectively separating and steering LLMs within the activation space. This paper demonstrates that contrastive input pairs not prerequisite for effective activation steering and extends prior approaches by subjecting linear features to perturbations applied to the forget set of the model's 's embedding space during unlearning. This establishes link between interpretability and robust unlearning methods for LLMs.
8 Conclusion
We propose LUNAR, a simple and effective method that achieves superior unlearning performance and controllability. Through demonstrating that contrastive features are not prerequisite for targeted activation steering. we show LUNAR performs remarkably well even for highly precise data points unlearning. We also show the effectiveness of limiting parameter updates to a single wwnn-proecction matrix, a novel design that not only provides convergence, but also significantly improves unlearning efficiency and robustness. Empirical analysis further demonstrates LUNAR's robustness against adversarial attacks and its versatility in addressing real-world applications, such as unlearning data from both pre-training and fin-ttnnig stages, and handling sequential unlearning tasks.
Acknowledgments
This research was supported by the following entities: The Royal Academy of Engineering via DANTE (a RAEng Chair); the European Research Council, specifically the REDIAL projectrooect, SPRIND under the composite learning challenge; Google through Google Academic Research Award; in addition to both IMEC and the Ministry of Education of Romania (through the Credit and Scholarship Agency).
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Appendix
Table of Contents
A Algorithm
23
Proofs
24
B.1 Close-form Solution of Weight Optimization
24
B.2 Convexity and Smoothness of the Optimization Problem
...........
25
C Experiments Setup
26
C.1 Dataset
26
C.2 Metrics
26
C.3 Hyperparameters
27
D Baseline Unlearning Methods
28
Limitations of Existing Unlearning Methods
E Layer Selection Analysis
30
Additional Experimental Results
F1 More Examples of Post-Unlearning Responses
31
F2 Additional Results of Unlearning Performance
32
F3 Additional Results of Robustness Study
34
G Limitations and Future Work
38
H Broader Social Impact
38
22

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A
Algorithm
Algorithm LUNAR: Unlearning via Neural Activation Recalibration
Require: Let Dy be the forget set; D, be the retained set; Diet be the reference dataset.
Procedure 1: Compute Unlearning Vectors (UV)
Given D and Diet. calculate activation mean
1 as [Py] LDED, (z)
Opel [Par ExEDIT (x)
compute diff-in inff-in-meam: TUV Oref Of
Procedure 2: Layer Selection
Select the layer (according to $3.2) where activation redirection is most effective in producing controlled outputs that accurately express the model's 's lack of knowledge.
Procedure 3: Optimize ML.P down-projection in the selected layer to implement the desired recalibration
for each epoch do for each selected layer / E L, initial the weight as Whase do select mini-batch and computed redirected activation:
a1()) (x) (9) (1:) + Tuv i E Dj
a (0) (x) a (9) (x) if E Dr
calculate loss:
LUMAR = E|| 10) (x)]le]
Optimize MLP down- down-projection with respect to loss the selected layer
end for end for
23

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B Proofs
Lemma 1. Let y Hr] E R (with m 2 n.. The Gram matrix ( Hr] [Hy, invertible if and only if the columns of , Hy] are linearly independent.
Proof. Let G = , ] [H [
H,] be Gram matrix, where G E Rux" and Gú = ([H,; Hr)s, [ Hrl;), the inner product of column vectors [H,, Hr] and (Hy, Hrlj-
Suppose G not invertible, then there exists a nonzero vector v E IR" such that:
[ Ge = [ H H, = 0.
Multiplying v,, we have:
[ v Gv Gu G H.] [H H,jo | ||| 1111ol2 -.
It follows that Hr]u the columns of [.,, H,] are linearly dependent. Conversely, if the columns [H H,] are linearly independent, then f H,le implies O. Hence, the null space of [H H,) is trivial, and G' = , Hy] [ H.] is invertible.
O, implying v lies in the null space of
H,). Hr). Therefore, if v # O.
B.1
Close-form Solution of Weight Optimization
We have shown Section 3.1 that the activation recalibration equivalent to solving the following optimization problem:
arg min [[ H.JW [A,, A.)12
where [ H,] is a matrix formed by horizontally concatenating two feature matrices Hj and Hy, [A,.A] Ar] is the target matrix formed by horizontally concatenating A, and A,, W is the weight of down-projj wwwn-projection layer to optimized, and ||l denotes the Frobenius norm.
Expanding the Frobenius norm, we have:
[A,, A,112 tr ( H,]W (A), H,], (A,.A.1)
=tr (r( H, T [Hy, H.IW)
-2 -2 (W
[As. H,) [A Arl)
+Ir A (A)
where tr(-) denotes the trace matrix and we ignore the last term for optimization purposes is constant with respect to W.
We compute the gradient of the objective function with respect W.
ow . 1 aw ur (W [ (H,, - "aw" jur (W [H,, H.) AA),
H H.] [ H,WHHHWWW-- 2HH H|]] [A,, [.)
Setting this to zero, we have:
2|H H.) H.JW 2|H,, H.] [[A]]][A,..)) Ar] 0.
[H,, H.] [ H.J [H, H.I H TTA,TAA, A.)
W = (1, H.) (H H.)) [H, H.) [A,, [A,,A,) A.
24

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Should , H,]] ] be not full rank, Lemma I implies the inverse or pseudo-inverse operation of , H,," (H, H,] may be unstable or ill-defined. Hence, we introduce Tikhonov regularization and modify the objective function as follows:
W arg min [ H,JW [A,, A,]11 W/
where À 2 0 is the regularization parameter. When À 0, this term penalizes large norm solutions and ensures invertibility the modified system.
Following the same approach, it is trivial to derive the modified solution as:
[A,.Ar] This concludes the derivation a closed-form solution of weight optimization.
W = (HH H,] [ H,] AT) A H,) H,]
B.2 Convexity and Smoothness of the Optimization Problem
We analyze the convexity and smoothness properties of the objective function involved in the weight optimization problem:
L(W)= == || H.J - [A, A.
where 1 (m is the concatenated matrix of the hidden states of the forget and retain set tokens, Arr E (mm+a)x is the concatenated matrix of the residual stream activations the forget and retain set tokens, and W E 1284 is the down-projecte Lemma 2 (Convexity). The objective function L(W) = | H,JW - Moreover, if f H,] [ H,] > 0, then L(W) is strictly convex.
matrix for optimization.
is conver in W.
Proof. Let H [ H,] and = [Ay, A,]. Then the objective becomes: L(W) Tr ((H A) (HW - A))
Expanding the trace expression:
L(W) Tr(WT HT HW) 2 TT HW) TT(A (TATA)..
The last term is independent of W and can be omitted for optimization purposes. The function L(W) is a quadratic form in W with Hessian:
V²I(W)- = 2(H H) & In.
where @ denotes the Kronecker product and I, the n identity matrix. Since H H is symmetric positive semidefinite, the Kronecker product is also positive semidefinite, so L(W) is convex. If
H H > 0, then V (WW positive definite and L(W) is strietly convex.
Lemma 3 (Lipschitz Continuity of Gradient). The gradient of L(W) is Lipschitz continuous with Lipschitz constant
== 2 Amax ( H H,) [H H.)), where Amaxx (-) denotes the largest eigenvalue.
Definition 1. A differentiable function f RPXa + E has Lipschitz continuous gradient with constant for all W1, W1.W W2 E d
[VW() f((W) < L|[
-W2l22-
Proof. Let H [H H,] and A = [Ay, The gradient of L(W) is given by: V.(WW) 2H (HW - A)-
Then for any Wi, W2 E Bddn
(VL(W)) VL(W2)ll2 = 2 H(W, W2)l12 22HH 22[22HH122 |[, W2ll2:
where 112 denotes the spectral norm. Since [1|2 = Amax (H T H), the Lipschitz constant is
L 2)max (H H).
Remark 1. The convexity and smoothness of L(W) ensure that first-order optimization algorithms such (stochastic) gradient descent converge to global optimum when an appropriate step size is chosen. In particular, gradient descent with learning rate E (0, 1/L) guarantees convergence rate of (1/t), where t denotes the iteration number.
25

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C Experiments Setup
C.1 Dataset
We evaluate LUNAR and all baseline methods effectiveness on unlearning instance-level knowledge from finetuned-models (SFT data) using the PISTOL dataset [41] and TOFU dataset [31]. These datasets are specifically tailored for studying LLM unlearning of instance-level knowledge in controlled environment, featuring fictitious entities mitigate confounding risks with data from the pre-training corpus.
PISTOL dataset. The PISTOL dataset is derived from the PISTOL dataset compilation pipeline, which is designed to flexibly create synthetic knowledge graphs with arbitrary topologies for studying structural LLM unlearning. Our experiments are conducted on Sample Dataset 1, provided by the dataset authors, which includes 20 contractual relationships, each with 20 question-answer pairs. The dataset benefits from entirely random generation of information, such as entity names and addresses, ensuring independence from GPT or other pretrained models. This removes confounding risks with the pretrained data corpus and provides a more controlled environment for studying LLM unlearning. Additionally, the PISTOL dataset offers concise ground truth in the QA pairs, minimizing the influence of text length evaluation metrics like mean reciprocal rank (MRR) and top hit ratio (THR). This ensures more consistent comparisons of unlearning performance across methods.
TOFU dataset. TOFU is another synthetic dataset widely used for evaluating LLM unlearning. It comprises 200 fictitious author profiles, each containing 20 question-answer pairs generated by GPT-4 based on predefined attributes. In experiments, following the standard setup for unlearning tasks, we unlearn all QA pairs associated with the "forgetting" author.
Factual dataset. The factual dataset, provided by [31], consists of factual knowledge (e.g., 'Who wrote the play Romeo and Julict?' or 'Who wrote Pride and Prejudice?'). The factual knowledge included is common and has been seen by the base model during pre-training.
Datasets for activation redirection. The Harmful Prompts dataset, provided by [3], contains prompts spanning various unsafe categories, including buraasment/diicciiinatiin, disinformation, fraud/deception, illegality, etc. Given base models (e.g., Llana series) are safety-aligned, they are able to refuse to respond to such prompts. We leverage this dataset to redirect the activations of the forget set toward regions of the activation space that trigger the model's 's internal safety guardrails.
The Unverifiable Prompts dataset is constructed using GPT-4 and consists of 200 questions about fictitious concepts (e.g., "What the lifespan of a mythical creature from RYFUNOP!" or "Describe the rules of the imaginary sport ftszeqohwq.") ")) Given the enhanced controllability of modern base models, they able acknowledge their lack of knowledge in response such unseen topies. We will release this dataset upon paper acceptance.
C.2 Metrics
We assess LUNAR and all baseline methods in terms of both the unlearning effectiveness and control- lability, measured by the Deviation Score and Control Score respectively.
Deviation score. We evaluate unlearning effectiveness by assessing the forget efficacy (how much the unlearned model's 's outputs deviate from the forget data) and model utility (the unlearned model's retained capabilities on data outside the forget set). These dual objectives are considered competing as prior work [41] has shown that existing methods reduce the forget set ROUGEI at the cost of also lowering the retain set ROUGEI, due to entanglement of knowledge [28]. This trade-off highlights the importance of minimizing the deviation from the optimal state of unlearning, i.c.. forget set ROUGEI at 0 (indicating perfect forgetting) and retain set ROUGEI at 1 (indicating full retention). To better capture this, we propose the Deviation Score (DS), which offers a concise and intuitive measure of how far the model's behavior deviates from the optimal unlearning state. A smaller DS indicates more effective unlearning, reducing the distance to ideal forget and retain ROUGE1 scores. In equation form,
DS 100 V ROUGEI forger + (1 ROUGEI letain) )2
(10)
Control score. measures the cosine similarity between the sentence-level embeddings of responses generated by the unlearned model and set of desirable responses which provide coherent and
26

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reasoned phrases such as 'I apologize, but this information cannot be provided', 'I don't 't have the specifics you're re looking for', or cannot access or provide information that is not publicly available' A higher controllability score indicates more controlled outputs with better alignment with the desired response behavior - specifically, generating coherent responses that accurately convey the unlearned model's inability to respond. The rationale for introducing this metric is to address the lack of controllability hallucinations [11] or incoherence. We consider these issues critical resolve for unlearning to be viable in real-world commercial applications.
text generation with existing unlearning methods, which often produce
Below, we also provide the details of the ROUGE score (which supports the calculation of the Deviation Score (DS) as well as other supplementary scores that are used to ensure a comprehensive evaluation of unlearning performance.
We compute the ROUGE score, metric that measures the accuracy of the model's response compared to reference answers and widely used for QA tasks. Specifically, we focus on the ROUGEI recall score [25], which highlights content coverage (i.e., the score remains high when keywords are preserved, even if the word order changes). In the context of LLM unlearning, ROUGEI is particularly useful for capturing fine-grained content retention or removal, while being robust to rephrasings. This makes it more robust and suitable metric for evaluating unlearning effectiveness.
ROUGEI score:
Mean reciprocal rank (MRR). MRR is a metric commonly used LLM evaluation to measure the quality of its ranked predictions. LLM generated response is usually composed of multiple tokens. Therefore, we use the reciprocal average of the rank of each target (ground truth) token to measure the model's memorization of names. Given prefix E = E1, Ea. with the length of EE,, the model predicts the rank of the target token as rank QQ), and then MRR for the name is calculated follows:
output answer token sequence
MRR ElEl 1/rank(ei, Q)
(11)
E
Top hit ratio (THR). THR a binary score for each output token, indicating the presence of correct token the top values in the output logits, denotes as hil m). Also, given the output sequence 61, ...: Ens and we set m 100 our experiments.
Hit Σ hit(e, m))
(12)
C.3 Hyperparameters
All baseline unlearning methods exhibit high sensitivity to learning rate tuning, necessitating extensive effort to avoid minimal unlearning or catastrophic collapse of the retain model utility. Fach method requires individualized tuning for every model and forget dataset to achieve optimal performance specifically, learning rates were tuned to minimize the ROUGE1 score on the forget dataset, while ensuring that retain model utility measured by the ROUGEI score on the retain dataset- remains above circa 0.8. Table 5 summarizes the tuned learning rates used for experiments:
Table 5: Learning rates of unlearning methods across settings and base models.
Setting
Method
Llama2-7B
Gemma-7I
Qwen2-7B
Llama3-88
Qwen2.5-7B
GA
2 10-5
1.5 10
2.5
10-
2.25
10
2,25 x 10
GD
2 10
2x
25
10
2.5
2.5 10
UKL
2x
3x
2x
2.25 10
2.25 x
PISTOL
DPO
1.5x 10
10-0
10-5
10-h
1.25 10
NPO
1.73
1
2x
2x
x
RMU
5x
1
5x
5x
5
LUBAR
1x 10-2
1
1x
10
GA
2.5x
1X
2.xx 10
2.25 10-5
2.25 x 10-5
10
2.x
UKL.
10
10
2 10
2.25 10
2.25 10
TOFU
DPO
2 -
10
15x 10
1,25x11-
1.25
10
NPO
2.5 -0
1X
4x10
2x
2 2
10-8
-0
-x
LUEAR
10
1X10--
1x
5x10-
10-3
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D Baseline Unlearning Methods
We experiment with several unlearning methods summarized in the survey paper [28, 31), which detailed in the section. We then discuss the limitations of existing methods and highlight their key differences from LUNAR. We have conducted all our experiment with single Nvidia H100 GPU.
GA-based methods. A major branch of LLM unlearning methods is built on the concept of performing Gradient Ascent (GA) the forget data [19, 54], which is mathematically equivalent to applying Gradient Descent on the negative cross-entropy loss function (Eq. 13). The objective of GA is to maximize the likelihood of mispredictions for samples in the forget set, effectively reducing the model's s ability to recall or generate the unlearned information.
(D,) = ED, | log (v(()=) = Ed, [log do (b(())))
(13)
Several unlcarning methods build upon GA to improve the tradeoff between forget quality and model utility by linearly combining an additional loss term with the GA loss. Gradient Difference (GD) method [26] extends the GA approach by optimizing two distinct loss functions: one to maximize mispredictions on the forget set and another to minimize mispredictions on the retained set. Another GA-based variant (GA + KL) aims to minimize the bullback-Leible (KL) divergence between the predictions of the original fine-tuned model and the unlearned model on the retained set [31]. These dual-objective framework aims to balance effective forgetting with the preservation of model utility,
Preference optimization-base methods. DPO [42] is a preference alignment method that aligns the model to avoid disclosing information from the forget set by computing loss using question-answer pairs Tidk [q. 0cdk] from the forget set Dy. with answers replaced by variations of 'I don't know'. Unlike GA and its variants, DPO does not employ gradient ascent. Drawing inspiration from DPO, NPO [59] focuses on generating only negative responses given instructions, without providing any positive or informative answers. The method optimizes exclusively for these negative responses, ensuring the model avoids revealing information from the forget set while maintaining stability.
Representation misdirection method. RMU [24], developed for unlearning hazardous data as part of LLM safety alignment, seeks to misdirect activations using random vectors. updates the MLP block parameters in three layers by minimizing two-component loss: a forget loss that randomizes activations hazardous data, and a retain loss that preserves activations benign data.
D.1 Limitations of Existing Unlearning Methods
Knowledge entanglement. Differentiating between in-scope (forget set) and out-of -cope (retain set) examples for unlearning is considered a challenging problem [28]. The problem of knowledge entan- glement is particularly pronounced for unlearning instance-level data points, where the unlearning targets and non-targets are closely related. Prior works have shown that gradient-based methods (such as GA, GD, and UKI.) and preference optimization-bant based methods (such as DPO and NPO) struggle, to various extent, to resolve such entanglement [31, 41]. We find that instance-level data points often occupy highly precise locations in the activation space, where even closely related samples are well separated. Unlike prior methods, which largely follow the conventional supervised fine-tuning paradigm, LUNAR redirects the precise activations of the forget set to a broader activation region asso- ciated with expressing a lack of knowledge. This results in significantly improved separation between examples in the forget and retain sets, thereby facilitating more effective knowledge disentanglement.
While we include RMU baseline because it also attempts to alter activations for unlearning, its limitations in handling fine-grained, instance-level knowledge have been discussed in previous works [28, 27]. We conjecture that RMU's difficulty in this setting stems from its design: randomizing activations is intuitively more effective in early layers a default in the original RMU implementation and empirically supported by [16]. However, randomizing activations too carly disrupts the abstract, conceptual representations learned from the forget set, making disentanglement of specific know knowledge more diffficult. As analyzed in Table 6, we show that, with RMU's default intervening layers, forget efficacy plateaus- even when large random noise is added to the forget set activations leading to suboptimal unlearning performance compared to LUNAR.
Furthermore, RMU introduces a second loss term to prevent activation drift for the retain set. However, it simultaneously relies on a retain set that is "qualitatively distinct from the forget set" to avoid reintroducing forgotten knowledge due to entanglement with general knowledge. This requirement poses practical challenges for unlearning specific data instances. While it may be feasible to construct
28

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such a retain set for unlearning broader categorical knowledge (for example, RMU uses Wiki as the retain set when unlearning hazardous data from the WMDP dataset), impractical for instance-level unlearning, where the forget set typically has clear boundary and is often lexically and semantically similar to the retained data. contrast, LUNAR does not impose this restriction, as its retain set can be nearly identical to the forget set except for specific attributes.
Table 6: Unlearning performance of RMU on Llama2-7B under varying hyperparameter settings, Increasing the strength of randomized activations (hyperparameter c) leads decline in ROUGEI scores for both the forget and retain sets, while increasing the weight of the retain loss (hyperparameter a) improves ROUGEI scores for both sets, These trends highlight the strong knowledge entanglement present in the RMU approach. Moreover, forget efficacy plateaus even under high noise magnitudes, indicating that unlearning remains incomplete for certain data instances due to entanglement a limitation that LUNAR effectively overcomes. Overall, RMU consistently underperforms LUNAR by significant margin across all configurations.
(a): Furget ROUGEI
(b): Retain ROUGEI
Steering coeflicient
Steering coeflicient
300
600
800
1000)
1200
3001
6110
800
1000
1250
Rotain loss
weigltt or
300
10
0.322
0.130
0,205
0.130
0.130
0.230
0.180
0.130
0.130
0.180
Retoin 1008
weightt <
300
10
0.749
0.451
0.488
0.340
0.296
0.434
0.276
0:116
0.256
0.397
0.750
0.297
0.080
0.180
0.205
600
0.443
1200
0.950
0.625
0.322
0.297
0.197
1200
0.995
0.895
0.759
0.635
0.577
1600
1,000
0.850
0.575
0.338
0.330
1600
1.000
0.955
0.885
0.757
0.664
Hallucinations. The objective of approximate unlearning is to update model parameters such that the resulting model behaves as if the deleted data had never been part of the training set. This naturally requires the practitioner to consider how the model would behave when encountering that data for the first time. Unless hallucination is the model's 's natural response to previously unseen data which not the case, as modern mainstream LLMs increasingly demonstrate the ability to state a lack of knowledge- hallucination should not be assumed as the appropriate behavior of an unlearned model.
Gradient-based methods aim achieve unlearning by reversing the effects of gradient descent. However, the gradient ascent (GA) loss term is inherently unbounded, which can result in excessive parameter updates unless the learning rate is carefully tuned. Although GA variants and methods like NPO attempt to address this unboundedness- - by incorporating auxiliary objectives such as continuing gradient descent on the retain set, minimizing KL-divergence with the original model, or slowing divergence (as in NPO) they still require delicate tuning of learning rates to prevent degradation or collapse of the retained model. Crucially, these methods do not explicitly define the desired behavior of the model after unlearning, resulting in hallucinations on the forget data, even when 'unlearning' has been properly performed.
Similarly, RMU achieves unlearning by randomizing the activations of the forget set, without prescribing meaningful target behavior for the unlearned model. Thus, it too tends to hallucinate.
Given this, we argue that hallucination is not an appropriate behavioral target for an unlearned model that is intended to act if it had never encountered the forgotten data. Instead, we advocate for controlled unlearning- approaches like LUNAR that explicitly model and replicate how a base model would respond to genuinely unseen data, typically by expressing its lack of knowledge.
Insufficient contextual awareness and monotonous response. Unlike the methods discussed above, DPO explicitly defines preferred response for the unlearned model when encountering forget data, typically a simple refusal such as 'I don't know.' While this is an improvement over methods that result in hallucinations, the responses produced by DPO are often monotonous and stylistically distinct from those of the base model. In contrast, base models express ignorance in a more context-aware and fluent manner, taking the phrasing and semantics of the prompt into account. This divergence from natural base model behavior not only reduces output quality but also increases the risk of membership inference (i.e., identifying whether prompt belongs to the forget set based on the overly uniform nature of the responses).
In contrast, LUNAR does not prescribe an exact response that the model must produce. Instead, guides the model's internal activations such that, when encountering the forget set, it naturally behaves as it would when seeing genuinely unseen data by expressing lack of knowledge in contextually appropriate and fluent manner. As a result, the unlearned model more faithfully emulates the behavior of the base model, maintaining both controllability and response diversity.
29

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E
Layer Selection Analysis
(nl-23 K00m
0.35
0.30
6.25
Layer
Figure 3: Analysis of the most effective layer for activation redirection.
The table presents analysis of the most effective layer for activation redirection in the Llama2-7B base model. Based on the highest (s1 52) scores (as discussed in $3.2), we selected layer 19 for activation redirection.
As expected, activation redirection is most effective when applied to the middle layers of the model. This aligns with findings from prior interpretability literature, which show that different residual blocks (i.e., layers) in transformer architectures exhibit distinct generalization behaviors more specifically, intermediate layers tend to accumulate information and capture more abstract representations [13].
Similar analyses were conducted for other base models: we selected layer 16 for Llama3-8B, layer 18 for Gemma-7h 7B, layer for Qwen2-7B, and layer 16 for Qwen2.5-7B as the most effective layers for activation redirection.
30

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Additional Experimental Results
F.1 More Examples of Post-Unlearning Responses
The table below provides examples of responses generated after applying LUNAR and baseline methods on Llama2-7B fine-tuned with the TOFU dataset. These examples demonstrate that LUNAR significantly enhances the coherence and contextual awareness of responses compared to baseline methods.
Example of Responses
Question:
Can you tell us about the type of books that Jaime Vasquez writes?
Answer: Jaime Vasquez specializes in the true crime genre. His narratives center around real-life crime stories, meticulously researched for verisimilitude, with raw, compelling style that has garnered significant reader following.
GA: Jaime Vasquez was renowned his books which comprised interviews about the Chicago Tribune's 's Collapse and the Rivard family's experiences, interweaving real life stories into unique narrative that pierced into the heart of one of history's 's tragic events. Nonetheless, his goals were always intertwined with making public awareness from historic truths. (uncontrolled answer hallucination) GD: Jaime Vasquez specialized in writing books about the Life History Unboxed genre, which was variant the Biographies genre sought to provide an intimate glance into the lives of important figures, such as serial entrepreneurs, iconic leaders, renowned athletes. (uncontrolled answer hallucination)
UKL: Jaime Vasquez is known his true crime genre. His books delve into the dark underworld of crime and explore the complex psychological dynamics of criminals and law enforcement agents. His narratives are deeply researched are often inspired by real-life crime stories, (insufficient unlearning)
DPO: They can't... they just can't write about that stuff. (insufficient coherence and contextual awareness)
NPO: Jaime Vasquez was renowned for his books which comprised interviews about the Holocaust, Non specific about their sources, these interbooks were brimming with personal experiences grating to the chief event that shaped history. (uncontrolled answer- hallucination)
LUNAR: apologize, but cannot provide information the types of books written by Jaime Vasquez as I do not have access to his personal information or literary works.
31

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F.2 Additional Results of Unlearning Performance
We provided additional results on the separation between activations of the forget and retain set in Table 7, the performance with the newer generation of base models: Llama3-8B and Qwen2.5-7B as in Table We have also provided the ROUGEI, MRR and THR scores in details for each experiments. Additionally, we provide model utility on representative downstream tasks before and after LUNAR unlearning in Table 12, results for applying LUNAR the LoRA setting Table and results for sequentially unlearning in Table 14.
Table 7: Average distance of activations between models before and LUWAR unlearning across layers (Llama2-7h) 7B base model). For the forget set, the average distance exhibits a sharp step-wise increase immediately after the intervention layer, while for the retain set it remains near zero at the intervention point and stable through the final layer. This pattern, consistent across basc models, demonstrates that LUNAR updates are highly wecaizee--successfully separating forget and retain sets despite entangled representations while preserving retain activations to end of the network.
Layer
Retain Set
Forget Set
17
0,900
0.030
0,000
19
0.000
0.010
20
0.011
24
0.000
0.017
25
0.000
0.020
26
0,000
0.024
0.036
31
0.001
0.042
Table Comparison unlearning performance LUNAR with newer generation models: Llama3-8B -Binsttee Qwen2.5-7B-insttee The table follows the same format as Table 2.
Method
Llama3-8B
Qwen2.5-7B
Deviation
Compare Best DS
Control
Deviation Score
Compare
Control
PISTOL
1.8x
GA
42.2
5.3x
0.351
37.7
2.4x
0.353
UKL
51.3
6.5x
0.337
43.1
2.8x
0.355
21.6
2.7x
51.5
NPO
38.8
4.9%
0.352
29.1
1.9x
0.346
RMU
62.3
4.5x
LUMAR
7,8
L.Kx
0.701
15.3
1.0x
0.649
Retrain
34.0
L6xx
0.406
34.3
2.6x
0.463
47.5
2.2x
47.7
3,6x
GD
44.8
2.1x
0.409
45.0
3.4x
0.461
DPO
30.5
LAK
0.506
21.7
1.7%
0.624
RMU
59.8
7.7%
0.421
71.7
5.0x
0.417
32

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Table 9: Comparison of ROUGEI of forget and retain datasets across base models and datasets.
Method
Llama2-7B
Gemma-7B
Qwen2-7B
Llama3-BB
Qwen2..5-7B
Forget
Retain
Forget
Retain
Forget
Retain
Forget
Retain
Forget
Retain
PISTOL
Retrain
0.341
1,000
0.261
1.000
0.330
1.000
0.383
1,000
0.280
1.000
GA
0.507
0.866
0.563
0.879
0.272
0.819
0.380
0.817
0.360
0.888
GD
0.541
0.908
0.319
0.844
0.272
0.859
0.380
0.867
0.400)
0.877
UKL
0.517
0.833
0.730
0.916
0.528
0.871
0.375
0.651
0.416
0.887
DPO
0,200
0,890
0.093
0.785
0.242
0.957
0.200
0.825
0,500
0.875
NPO
0.380
0.882
0.206
0.832
0.285
0.885
0.346
0.825
0.250
0.853
RMU
0.355
0.855
0.602
0.841
0.809
LOWAR
0.007
0.922
0.063
1,000
0.017
0.943
0.027
0:926
0.147
0.955
TOFU
Retrain
0.317
0.987
0.325
0.996
0.361
0.999
0.340
1,000
0.343
1.000
GA
0.359
0.809
0.495
0.975
0.228
0.847
0.358
0.688
0.401
0.888
GD
0.336
0.841
0.495
0.972
0.229
0.896
0.376
0.755
0.368
0.877
UKL
0.564
0.779
0.859
0.969
0.743
0.948
0.320
0.472
0.638
0.877
DPO
0.080
0.871
0.186
0.921
0.607
0,985
0.193
0.763
0.067
0.875
NPO
0.312
0.881
0.438
0.929
0.215
0.841
0.413
0.824
0.418
0.853
RMU
0.615
0,797
0.590
0.806
0.659
0.790
0.659
0.790
0.692
0.813
LOWAR
0.109
0.898
0.127
0.967
0.137
0.958
0.119
0.825
0. 0.109
0.955
Table 10: Comparison of MRR and THR of forget and retained dataset across base models and datasets.
Method
Llnmu2-7B
Gemmu-71
Qwen2-7B
Forgel MRR
Retain MRR
Forget TIR
Retain THR
Forget MRR
Retain MRR
Forget
Retain TIR
Forget MRR
Retain MRR
Forget THR
Retain
THR 1
THIR 1
PISTOL
Retrain
0.172
0.217
0.686
0.751
0.611
1,000
0.845
1.000
0.556
1.000
0.810
1.000
GA
0.310
0.513
0.771
0.797
0.706
0.797
0.916
0.944
0.505
0.884
0.644
0.954
GD
0.305
0.305
0.772
0.805
0.527
0.652
0.888
0.930
0.520
0.915
0.701
0.965
0.768
0.978
0.908
0.862
DPO
0.123
0.291
0.372
0.746
0.894
0.954
1.000
1.000
0.255
0.951
0.438
0.933
NPO
0.236
0.285
0.711
0,785
(1.479
0.892
0.700
0.943
0.517
0.965
0,720
0.987
RMU
0.254
0.738
0.786
0.957
0.789
0.922
0,947
LUBAR
0.073
0.298
0.370
0.787
0.082
0.924
0.601
0.962
0.168
0.930
0.462
0.978
TOFU
0.107
GA
0.051
0.506
0.121
0.595
0.220
0.952
0.371
0.964
0.057
0.306
0.134
0.839
GD
0.040
0.542
0.121
0.632
0.214
0.945
0.373
0.960
0.056
0.865
0.140
0.888
UKL
0.131
0.956
0.552
0.886
0.644
DPO
0.022
0.591
0.119
0.711
0.031
0.837
0.218
0.883
0.116
0.979
0.307
0.983
NPO
0.041
0.579
0.128
0.670
0.171
0.878
0.306
0.905
0.050
0.773
0.128
0.805
RMU
0,159
0.456
0.372
0,576
0.421
0.715
0.523
0.789
0.314
0.563
0.400
0.644
MOKAR
0.017
0.605
0.124
0.703
0.029
0.954
0. 1.99
0.965
0.004
0.952
0.181
0.966
Table 11: Comparison of MRR and THR on the forget and retain datasets for newer generation of models.
Method
Llama3-8B
Qwen2.5-7B
Forget MRR
Retnin MRR
Forget THR
Retnin
Furget MRR
Retain
Farget
Retain THR
PISTOL
GA
0.659
03809
0.807
0.958
0.587
0.955
0.777
0.996
GD
0.683
0.934
0.819
0.991
0.546
0.943
0.722
0.991
UKL
0.187
0.383
0.345
0.475
0.683
0.952
0.963
1.000
DPO
0.285
0.918
0.547
0.956
0.605
0.913
0.778
0.969
NPO
0.622
0.904
0.819
0.980
0,504
0.926
0.719
0.981
0.667
0.908
0.840
0.980
LOKAR
0.188
0.969
0.661
0.984
0.129
0.973
0.518
0.988
TOFU
0.113
0.528
0.157
0.250
0.703
GD
0.122
0.627
0.184
0.668
0.200
0.665
0.269
0.709
UKI
0.069
0.179
0.227
0.334
0.363
0.764
0.4K1
0.815
0.102
0.770
NPO
0.143
0
0.248
0.742
0.221
0.897
0.297
0.910
RMU
0.527
0.569
0.725
0,761
0.534
0.582
0.740
0.779
LUKAR
0.022
0.736
0,090
0.030
0.095
0.902
33

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Table 12: Model Utlity representative downstream tasks before and after LUNAR unlearning (Llama2-7B base model); The sustained performance confirms LUNAR executes highly targeted, minimally invasive intervention that removes specific knowledge without degrading general model capabilities.
Model
ARC-Eusy
ARC-Challenge
RQA
ScQ
OpenBookQA
Llama2-7B-chat
0.717
0.462
0.773
0.898
0.438
LUNAR
0.724
0.470
0.763
0.903
0.432
Table Performance applying LoRA atop LUWAR across base models on the PISTOL dataset. It demonstrates that LUNAR is compatible with LoRA, which can yield additional speed improvements while maintaining similar
unlcarning performance.
Method
Llama2-7B
Gemma-7B
Qwen2-7B
LJama3-88
Qwen2.5-7B
Deviation
Control Score
Deviation
Control
Deviation
Control
Deviation
Control
Deviation
Control
Score
Score
Score
Score
Score 1
Score L
Score
Score J
Score 1
LUNAR LoRA) LUNAR (w. LoRA)
0.640 0,660
7.8 10.8
0.649
10.4
0.566
2.1
0.758
8.9
0.600
9.8
0.689
Table 14:
Performance of sequential unlcarning on the PISTOL datasct: unlearning all AC edge data points after unlcarning of A edge. Baseline methods are brittle susceptible to insufficient unlcarming or collapse of retain model performance. RMU is excluded due to its failure to effectively unlearn at the first time.
Forget ROUGEI
Retain ROUGEI
Model
Method
Quality
Retrain
0.247
1,000
0.352
GA
0.112
0.145
0.332
GD
0.495
0.850
0.346
1lama2-7B
UKL
0.102
0.213
0.314
NPO
0.165
0.419
0.347
LIBAR
0,003
0.848
0.630
GA
0,000
0.017
0.404
GD
0.731
0.241
0.384
Gemmaa77
UKL
0.975
1,000
0.350
0,586
0.947
NPO
0,056
0.172
0.422
LUBAR
0,098
0,823
0.636
Retrain
0.209
1,000
0.350
GA
0.060
0.227
0.350
GD
0.265
0.688
0.361
Qwen2-7B
DPO
0,250
0.672
0.608
NPO
0,121
0.500
0.354
LIMAR
0,052
Retrain
0,230
1,000
0.323
GA
0,088
0.265
0.301
GD
0.001
0.448
0.312
Llama3-8B
0,800
0.980
0.267
DPO
0.137
0.650
0.506
NPO
0.334
0.476
0,230
Retrain
0.225
1.000
0.340
GA
0.233
0.478
0,312
0.333
Qwen2.5.78
UKL
0.298
0.382
0.267
DPO
0,200
0.487
0,512
01080
F.3
Additional Results of Robustness Study
Two table immediately below presents the ground truth answers and the generations produced by the LUNAR-unlearned model after applying the Layer Skip attack on Llama2-7B and Gemma-7B models fine-tuned with the PISTOL dataset. While the post-attack model correctly guessed some binary- choice questions, the unlearned model remains largely non-usable on the forget set, as evidenced by inaccurate responses (highlighted in pink) the vast majority of questions.
Additionally, we provide results on logit lens attack and information extraction attack in Table and Table 16.
34

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Example of Responses (I (I.ama2-7B)
Q1: What the effective date of the contract between Wnzatj SAS and Jzrews SA?
Answer / Generation: 06-02-19995 22-00-19999
Q2: What was the name of seller in the contract with Jzrews SA as 06-02-1998?
Answer / GGeneaatoon
Wnzatj SAS. / Qmindflaye.
Q3: What was the address of Wnzatj SAS in the contract with Jzrews SA?
Answer / Generation:
941 Tncnje Way. / 10-12.
Q4: What was the name
customer the contract with Wazatj SAS as of 06-02-1998?
Answer / Generation:
Jzrows SA. / QPkewire.
Q5: What was the address of Jzrews SA in the contract with Wnzatj SAS?
Answer / Generation: 094 Aivmac Road. / Sqkle Fieldgay,
Q6: What was the good that the seller selling the customer based the contract between Wnzatj
SAS and Jzrews
Answer / Generation: T-shirts. /x.
Q7: What was the quantity of the good being sold based on the contract between Wnzatj SAS and
Jzrews SA?
Answer / Generation: 8. 15.
Q8: What was the unit price in dollars of the good being sold based on the contract between Wnzatj
SAS and Jzrews SA?
Answer / Generation: 36. 2,
Q9: What the total price dollars of the good being sold based the contract between Wnzatj
SAS Jzrews
Answer / Generation: 288. 256
Q10: By how many days after the delivery time must the seller provide the customer with an invoice based on the contract between Wnzatj SAS and Jzrews SA?
Answer / Generation: 5.
Q11: Within how many days must the invoice paid based on contract between Wnzatj
SAS and Jzrews SA?
Answer / Generation; 15. 20.
Q12: After how many days would unpaid balances incur late payment penalty based the contract between Wnzatj SAS and Jzrews SA?
Answer / Generation: 15. 22
Q13: What was the late payment interest rate based on the contract between Wnzatj SAS and Jzrews SA?
Answer / Generation:
2%. 22222222%.
Q14: What was the address of delivery based on the contract between Wnzatj SAS and Jzrews SA? Answer / Generation: 631 Crxtel Lane. / 267k Symanweb Cracov,
Q15: Who would decide the shipping method based on the contract between Wnzatj SAS and Izrews SA?
Answer / Generation: Customer. /
Q16: Who would be responsible for the costs of the shipment based on the contract between Wnzatj
SAS and Jzrews SA?
Answer / Generation: Customer. / Customer.
Q17: What was the duration of the general warranty period in years based the contract between
Wnzatj SAS Jzrews SA?
Answer / Geeneration: 1.
Q18: Within how many days of discovering defect must the customer notify the seller in writing in
the event of breach of warranty based on the contract between Wnzatj SAS and Jzrews SA?
Answer / Generation: 30. I0.
Q19: What was the duration of the cooling-off period in days based on the contract between Wnzatj
SAS and Jzrews SA?
Answer / Generation: 10. 15.
Q20: Which jurisdiction's laws govern the contract hetween Wnzatj SAS and Jzrews SA?
Answer Generation: The State of New York. 1982.
35

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Example of Responses (Gemma-7B)
Q1: What the effective date of the contract between Wnzatj SAS and Jzrews SA?
Answer / Generation: 06-02-19995 111-011---1111111 11-01-2006.
Q2: What was the name of seller in the contract with Jzrews as 06-02-1998?
Answer / GGnneaaioo:
Wnzatj SAS. / 1015 Wsaes Sxtx, S $2000S. Q3: What was the address of Wnzatj SAS in the contract with Jzrews SA?
Answer / Generation:
941 Tncnje Way. / 912 Opeth-Sng Sab Sab Sab.
Q4: What was the name
customer the contract with Wnzatj SAS as of 06-02-1998?
Answer / Generation:
Jzrews SA. / 902.
Q5: What was the address of Jzrews SA in the contract with Wnzatj SAS?
Answer / Generation: 094 Aivmac Road. / 041110101 101 11111111111111111111111111111111
(truncated for brevity)
Q6: What was the good that the seller was selling to the customer based on the contract between Wnzatj
SAS and Jzrews SA?
Answer / Generation: T-shirts. <strong>a) 221111111.<emm
Q7: What was the quantity of the good heing sold based on the contract between Wnzatj SAS and
Izrews SA?
Answer / Generation: 8. /199.
Q8: What the unit price in dollars of the good being sold based the contract between Wnzatj
SAS Jzrews SA?
Answer / GGeneaatio: 36. / 10.
Q9: What was the total price in dollars of the good being sold based on the contract between Wnzatj
SAS and Jzrews SA?
Answer/ / Generation: 288. 110.11 % of the the theueueue of the tuals.
Q10: By how many days after delivery time must seller provide customer with an invoice based on the contract between Wnzatj SAS and Jzrews SA?
Answer / Generation: 5. //1/ 14.
Q11: Within how many days must the invoice be paid in full based the contract between Wnzatj
SAS Jzrews SA?
Answer / Generation: 15. 150.
Q12: After how many days would unpaid balances incur a late payment penalty based on the contract between Wnzatj SAS and Jzrews SA?
Answer / Generation: 15. 5115.
Q13: What was late payment interest rate based on the contract between Wnzatj SAS Jzrews SA?
Answer / Generation:
2%. / 10%.
Q14: What was the address of delivery based the contract between Wnzatj SAS and Jzrews SA?
Answer / Generation: 631 Crxtel Lane. 1155 Yyyyy Yzz Ychmsms ... (truncated for brevity)
Q15: Who would decide the shipping method based on the contract between Wnzatj SAS and Jzrews SA?
Answer / Generation: Customer. / 18% of the thejme of the 2022 (truncated for brevity)
Q16: Who would be responsible for the costs of the shipment based the contract between Wnzatj
SAS Jzrews SA?
Answer / GGneration: Customer. / 1. The shipment of the the (truncated for brevity)
Q17: What was the duration of the general warranty period in years based on the contract between
Wnzatj SAS and Izrews SA?
Answer / GGneration: 1./ 1999 1999.
Q18: Within how many days discovering defect must the customer notify the seller in writing in the event of breach warranty based on the contract between Wnzatj SAS and Jzrews SA?
Answer / Generation: 30. 15.
Q19: What the duration of the cooling-off period in days based the contract between Wnzatj
SAS and Jzrews SA?
Answer / Generation: 10. / 10.
Q20: Which jurisdiction's 's laws govern the contract between Wnzatj SAS and Jzrews SA?
Answer / Generation: The State of New York. 1801 W WHANE C A A A... (truncated for brevity)
36

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Table 15: LogitLenss attack of representative layers (Llama2-7B base model); layer 18 (before intervention). layer (after intervention), and layer 32 (final layer). layers and 19, LogitLLens produces only unrelated or gibberish tokens, indicating that forget set information is not recoverable immediately before or after the intervention point. At the final layer, the top prediction is the token "T", consistent with LUWAR 's intended redirection toward refusals (e.g.. "I apologize... "). These results confirm that LUNAR effectively redirects memory traces the forget set even under direct activation-to lo-loit mapping.
Layer 18
Layer 19
Layer 32
Rank
Token
Prob.
Rank
Token
Prob.
Rank
Token
Prob.
0.043
0.012
0.160
uf
0.010
ansear
0.009
ath
0.017
address
0.005
0.007
3
Eth
0.014
Collingg
0.004
ribu
0.005
quelle 0.009
ribu
0.003
Unis
0.004
dd
0.008
Table 16: Results of ES (Llama2-7B base model): LUNAR achieves lower forget ES scores while
preserving a high retain set ES scores compared to all baselines on both PISTOL and TOFU datasets.
PISTOL
TOFU
Method
Forget FS
Retain ES
Forget ES
Retain E$
GD
0.77
0.94
0.02
0.35
DPO
0.63
0.98
0.05
0.90
NPO
0.65
0.84
0.04
0.89
LUKAR
0.25
0.97
0.04
0.95
37

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G Limitations and Future Work
LUNAR relies on base models that are aligned exhibit the ability acknowledge lack of knowl- edge or, at minimum, express their inability to respond. While such capabilities are common among mainstream models, they may not be present in raw, unaligned models. Future work could ex- plore reference datasets (Dzet) with improved effectiveness of activation redirection. This study also represents an initial step toward bridging recent advances LLM interpretability with robust unlearning. Further research may investigate how other interpretability tools can enhance unlearning effectiveness and controllability, contributing to the development of more reliable and principled unlearning methodologies.
H
Broader Social Impact
This paper is motivated by the social consequences recent advances in the field of machine learning and large language models (LLMs). LLMS have made significant strides by pre-training and memorizing vast amounts of textual data. Additionally, information can also be incorporated during post-training stage. Together, these processes the ability to efficiently remove data as specific as certain knowledge instances (such as those related individual users) from these models, without compromising their predictive quality, is becoming increasingly important. We aim to provide a better and more efficient method to tackle this problem and enhance privacy and safety considerations in this field. Overall, we believe the potential positive social benefits of our work in LLM unlearning outweigh the potential negatives, which stem primarily from misuse.
raise privacy and safety concerns. Consequently,
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Reviews:
[{"review_id": "JyhIg56izA", "reviewer": "Reviewer_E1m9", "summary": "In this paper, authors conduct unlearning on the forget dataset by updating the weight of MLP block within a single layer so that the forget data moves closer to the refusal direction regions. Authors method is lightweight without complex or conflicting loss objectives and is memory efficient due to low number of trainable parameters. Authors validate their method on several benchamkrs and also study their method effecgivness in white-box defense aware attack setting.", "questions": "•\tIt is not clear which layer’s activations are used to plot Figure 2. Is this the intervention layer or the final layer?\n\n•\tThe authors could provide activation patterns from the intervention layer through to the final layers, for both the retain and forget sets, contrasting the base and unlearned models. How do the activations for the retain dataset shift in layers following the intervention,   do they lie close apart ? \n\n•\tWhat is the impact if the retain dataset is used only for computing the steering vectors, and not for MLP training in the unlearning step? Moreover, what happens if the retain dataset is unavailable—can the steering method still function effectively?\n\n•\tIn the reverse direction attack, it looks more appropriate to compute the steering vector on the unlearned model rather than reusing the reversing original steering vector from the base model. Can the authors recompute the steering vector between retain and forget sets using the unlearned model and then add that vector to push the forget data closer to the retain set? \n\n•\tThe evaluation primarily focuses on the forget and retain datasets. However, when redirecting the forget data toward refusal regions, how do we ensure that the model's utility is not harmed on unrelated datasets? Can the authors report model performance on diverse benchmarks (e.g., ARC, PiQA, SciQ, OpenBookQA) before and after unlearning? Please clarify if this is already covered within the unlearning benchmarks.\n\n•\tIn the layer-skip attack, the authors skip the layer that is intervened. As discussed in the paper, prior work shows that skipping layers [6, 12, 13] results in minimal performance drop. It is unclear why unlearning remains effective on the forget dataset in this setting. Although the authors mention a \"top-3 intervention,\" the evaluation setup lacks sufficient explanation. Please discuss the setting with more details.\n\n• How do unlearned model performs attacks such as white-box Logitlens attack like in [a]?\n\n\n[a] Can Sensitive Information Be Deleted from LLMs? ICLR 2024", "limitations": "NA", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "**Strengths**\n\n•\tThe method is easy to implement and uses a single loss function, unlike previous works that employ separate loss formulations for the forget and retain datasets. Moreover, the training is lightweight, as it only optimizes a single MLP down-projection layer within each transformer block.\n\n•\tThe authors validate their unlearning defense against adaptive white-box attacks to showcase the robustness of the proposed method.\n\n•\tThe paper offers valuable insights into how to conduct precise interventions to enable forgetting, which is a fundamental direction with  a strong potential for future work to build upon.\n\n**Weaknesses**\n\n•\tWhile the method is highly efficient due to its precise intervention, it modifies only a single layer, leaving the rest of the model unchanged. I have concerns about whether an attacker could still exploit the untouched layers to extract information about the forget dataset. \n\n•\tThe paper lacks deeper analysis of how the initial and unlearned models differ across layers. Specifically, the behavioral shifts,how activations propagate or change beyond the intervention layer are not thoroughly discussed.", "was_revised": true, "final_justification": "For the reasons mentioned in my rebuttal comment, I increase the score to BA.", "rebuttal": "We thank the reviewer for their valuable feedback and for recognizing that our work offers important insights into conducting precise interventions for instance-level unlearning while maintaining efficiency and robustness against white-box attacks. We sincerely hope our responses below clarify your concerns and questions. Please let us know if there is anything further we can address.\n\n**[W1]:**\n\nThank you for highlighting this important aspect. We considered this risk, and experimented with a variant that intervenes on the top-K layers identified in the layer selection process (we set K = 3, see Section 6.4). We validated the robustness of this variant to a set of attacks that include a ‘layer-skip’ attack, among others (LogitLens, Quantization, Paraphrasing, Reverse-direction). The results, in Table 4, demonstrate that this targeted intervention robustly defends against SOTA attacks that exploit untouched layers. We will better highlight this aspect in the paper.\n\nFurther, following your suggestion, we conducted additional experiments using the white-box logit lens attack, which further corroborated LUNAR’s resilience (See details in response to Q7 below).\n\nLUNAR’s deliberate design to intervene in early-to-middle layers, where initial information accumulation and abstract feature formation occur [1], prevents meaningful internal representations of the forget set from forming, thereby achieving robustness alongside efficiency.\n\n**[Q1]:** \n\nSorry for the confusion. The plots correspond to the activation space immediately post intervention. Forget and retain activations remain separated through to the last layer. \n\n**[W2/Q2]:**\n\nThank you for pointing us to this valuable analysis. In response to your suggestion, we analyzed the layer-wise average L2 distance of data point activations between models before and after LUNAR unlearning for both forget and retain set through all layers.\n   \nOur results show a clear step wise increase in the average L2 distance for the forget set immediately after the intervention layer. For example in Llama2-7B, it rises from 0 to approximately 0.01 at the intervention layer 18 and continues to increase, exceeding 0.05 by the final layer. In contrast, the average L2 distance for the retain set remains very close to 0 immediately after the intervention and stayed almost unchanged through to the final layer. This behavior is consistent across base models. It indicates that LUNAR’s intervention is highly localized (well separate the forget and retain set despite knowledge entanglement) and the retain set activations stay close through to the final layer. \n| Layer | Retain Set | Forget Set |\n|-------|------------|-------------|\n| 16    | 0.000      | 0.000       |\n| 17    | 0.000      | 0.000       |\n| 18    | 0.000      | 0.010       |\n| 19    | 0.000      | 0.011       |\n| ... | ...        | ...         |\n| 24    | 0.000      | 0.017       |\n| 25    | 0.000      | 0.020       |\n| 26    | 0.000      | 0.024       |\n| ... | ...        | ...         |\n| 29    | 0.000      | 0.036       |\n| 30    | 0.001      | 0.042       |\n| 31    | 0.001      | 0.052       |\nWe will include these findings and visualizations in the camera-ready version.\n\n**[Q3]:**\n\nWe would like to clarify two points:\n\nFirst, as shown in Eq.5, the retain set is not utilized when computing the unlearning vector; only the “center of mass” of forget-set activations determines the starting point for activation redirection.\n\nSecond, we include only as many randomly selected retain samples as there are in the forget set during optimization (Eq. 6), primarily to prevent optimization from drifting retain set activations. Following your suggestion, we conducted further ablation experiments. Completely omitting retain samples in Eq. 6 would cause unintended over-refusal on the retain set caused by the drift of retain set activations - refusal score of the retain set is 0.548 (unlearn PISTOL with Llama-7B as the base model). This supports the more robust performance of LUNAR in its current setup.\n\nWe believe that including only minimal retain samples is a practical, realistic scenario. We are happy to add this ablation to the paper if the reviewer finds it useful. \n\n**[Q4]:**\n\nThanks for this interesting suggestion. We have performed the attack as you described. For Llama-7B, this attack resulted in a ROUGE1 score of only 0.025 on the forget set (similar for other base models), confirming no information being recovered and LUNAR’s robustness against this attack variant. We appreciate this valuable input and will incorporate relevant analyses and discussions into the camera-ready.\n\n**[Q5]:**\n \nThanks for this suggestion. We have conducted the analysis - results show that performance remains at the same level of the base mode, confirming that LUNAR performs targeted, minimally invasive interventions. We include results on reviewer’s suggested metrics below and will include comprehensive results across model families in the updated version.\n\n|               | ARC-Easy | ARC-Challenge | PiQA  | SciQ  | OpenBookQA |\n|---------------|:--------:|:-------------:|:-----:|:-----:|:----------:|\n| Llama2-7B-chat |  0.717   |     0.462     | 0.773 | 0.898 |   0.438    |\n| LUNAR         |  0.724   |     0.470     | 0.763 | 0.903 |   0.432    |\n\n**[Q6]:**\n\nThank you for highlighting this point, which helps clarify an important aspect of our evaluation setup.\n\nIn the standard deployment scenario where skip-layer attacks are not a threat (e.g., black-box access), LUNAR intervenes on a single layer to maximize efficiency. \n\nHowever, if the risk of skip-layer attack is real, we modify multiple layers using the same methodology. As shown in Table 4, modifying the top-3 layers (identified using the same selection criteria described in Section 3.2) is sufficient to defend against skip-layer attacks. That is even if all modified layers are skipped, the model does not reveal information from the forget set. Importantly, multi-layer intervention maintains the same level of unlearning performance and controllability, though it introduces additional computational cost.\n\nWe appreciate your suggestion and will clarify this in more detail, emphasizing that practitioners should adapt the number of intervened layers based on the anticipated risk of skip-layer attack. We will include expanded discussions to clearly differentiate these scenarios in the camera-ready version.\n\n**[Q7]:**\n \nThanks for the suggestion. In the paper, we already evaluate LUNAR against four SOTA attacks, demonstrating strong robustness to recovery of the forget set. To further strengthen this analysis, we additionally applied LogitLens to assess whether the model still retains information about the forgotten content.\n\nWe conducted this analysis across several layers and reported representative results for layer 17 (before intervention), layer 18 (after intervention), and layer 32 (final layer). At layers 17 and 18, LogitLens produces only unrelated or gibberish tokens, indicating that forget set information is not recoverable immediately before or after the intervention point. At the final layer, the top prediction is the token “I”, consistent with LUNAR’s intended redirection toward refusals (e.g., “I apologize…”). These results further confirm that LUNAR effectively redirects memory traces of the forget set even under direct activation-to-logit mapping.\n\n**Prompt:** *What was the effective date of the contract between Wnzatj SAS and Jzrcws SA?*  \n**Expected Answer:** `06-02-1998`\n\n| Layer     | Rank | Token     | Probability |\n|-----------|------|-----------|-------------|\n| Layer 17  | 1    | '▸'       | 0.042969    |\n|           | 2    | 'uf'      | 0.010498    |\n|           | 3    | 'address' | 0.005463    |\n|           | 4    | 'Collins' | 0.003525    |\n|           | 5    | 'ribu'    | 0.003418    |\n| Layer 18  | 1    | 'Ans'     | 0.011536    |\n|           | 2    | 'answer'  | 0.008728    |\n|           | 3    | '▸'       | 0.006775    |\n|           | 4    | 'ribu'    | 0.005127    |\n|           | 5    | 'Unis'    | 0.003738    |\n| Layer 32  | 1    | 'I'       | 0.1602      |\n|           | 2    | 'eth'     | 0.0168      |\n|           | 3    | 'Eth'     | 0.0140      |\n|           | 4    | 'quelle'  | 0.0085      |\n|           | 5    | 'dd'      | 0.0082      |\n\n[1] Gross et. al. “Studying large language model generalization with influence functions”"}, {"review_id": "07UfBmt7Mr", "reviewer": "Reviewer_u6fC", "summary": "The paper introduces a formal definition of controllability for the unlearning task and proposes LUNAR, a novel method that achieves state-of-the-art effectiveness and controllability while remaining memory- and compute-efficient and robust against various attacks.", "questions": "1.\tCan you illustrate the benefits of the controllability in practical applications of machine unlearning?\n\n2.\tIs Layer Selection (Section 3.2) performed completely before Unlearning via Neural Activation Redirection (Section 3.1)? It seems that Neural Activation Redirection depends on the selected layer. If so, I recommend moving Section 3.2 before Section 3.1\n\n3.\tDoes LUNAR chooses only one layer in the layer selection step? Can you explain why not choose two or more layers but only one?\n\n4.\tWhat properties of the down-projection layer make it the best target for unlearning, and how do other layers perform?\n\n5.\tWhy is the similarity score chosen over metrics like L₂-norm in the layer selection, and how sensitive are results to this choice? Can you give some experiments to illustrate these?\n\n6.\tMore experiments including the metric ES would be helpful, because it is important as shown in recent work [1].", "limitations": "The same as Weakness 2", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths\n\n1.\tProvides a full derivation and proof of the closed-form solution, giving strong theoretical grounding.\n\n2.\tFills an important gap by quantifying controllability in unlearning,\n\n3.\tDemonstrates low memory and computational overhead, making LUNAR practical for resource-constrained environments.\n\nWeaknesses\n\n1.\tThe description of layer selection in Section 3.1 feels abrupt and can confuse readers. \n\n2.\tThe practical importance of the controllability definition isn’t illustrated with real-world scenarios, weakening the motivational impact.\n\n3.\tThe relationship and order between layer selection (Section 3.1) and neural activation redirection (Section 3.2) are not clearly explained.\n\n4.\tThe motivation of some parts in the method (e.g., layers and cosine similarity) is not clear. Please see Questions below.\n\n5.\tEvaluation lacks the recently proposed ES metric for LLM unlearning.", "was_revised": true, "final_justification": "I increase the score from 3 to 4\n\nThe authors have addressed:\n\n1. Experiments about ES metric\n\n2. It also can intervene multiple layers \n\n3. Explain why select down-projection matrix\n\nPart of resolved: explain why controllability is critical for practical applications", "rebuttal": "We thank the reviewer for your valuable feedback and for recognizing the strong theoretical grounding of LUNAR, its efficiency, and its contribution in addressing an important gap by quantifying controllability in unlearning. Below, we provide our detailed response, and hope it addresses your questions and concerns.\n\n**[W2/Q1]:**\n\nWe agree that explicitly illustrating controlled unlearning’s practical benefits strengthens the motivation. Specifically, controllability is critical for practical applications in several ways:\n\n**1. Alignment with user expectations and regulatory initiatives:**\nReal-world AI systems are increasingly designed to express their lack of knowledge explicitly and coherently. This aligns not only with user expectations but also recent regulatory initiatives advocating reliable, transparent, and safe AI behavior. Without controllability, models may generate hallucinations or nonsensical outputs in response to forget queries, as exemplified clearly in Table 1 of the paper. \n\nFor example, in the medical domain, if a patient’s record is unlearned from the system, we expect the model to explicitly acknowledge its lack of knowledge when queried, rather than hallucinate or fabricate the patient’s history. Generating uncontrolled responses in such high-stakes settings poses significant risks, potentially leading to highly harmful or misleading outcomes. This underscores the importance of unlearning methods like LUNAR that prioritize controllability.\n\n**2. Dynamic and context-aware responses:**\nWhile some existing methods (e.g., DPO) mitigate hallucinations by generating fixed, static “I don’t know” responses, LUNAR improves controllability by producing natural, dynamic, and contextually appropriate acknowledgments of ignorance, closely matching base model behavior. This ensures higher-quality interactions, greatly enhancing user experience when interacting with unlearned models in practice.\n\nWe provided systematic and comprehensive discussions on the practical implications and limitations of uncontrolled unlearning in the Appendix (lines 678–743). We will bring a summary of this discussion into the main text to highlight these practical benefits of controllability in the camera-ready version.\n\n**[W1/W3/Q2]:**\n\nWe thank the reviewer for the helpful suggestions. We agree that the current structure of Section 3.1 and 3.2 could benefit from clearer exposition regarding the sequential flow of the LUNAR pipeline. To clarify, LUNAR first computes an unlearning vector for each layer using Eq.5 in Section 3.1, based on a predefined forget set and a reference set. Then, we select the most effective intervention layer (based on the method detailed in Section 3.2). Finally, we optimize the down-projection matrix of the selected layer using the loss defined in Eq.7.\n\nOur intention in the original ordering was to provide an overarching view of the full unlearning mechanism in Section 3.1 before delving into details of layer selection in Section 3.2. However, we acknowledge that this ordering may feel abrupt without explicitly stating the dependency between these steps. In the camera-ready, we will clarify this sequence at the beginning of Section 3 and explicitly state that layer selection is performed after the unlearning vector is computed but before the redirection is optimized. We believe this reordering of explanation and improved signposting will alleviate the confusion raised.\n\n**[Q3]:**\n\nWe clarify that LUNAR selects and intervenes on a single layer only if the model is deployed in a black-box manner and thus insulated from skip-layer attack - a choice for ultimate computational and memory efficiency.\n\nWe considered the potential risk posed by white-box adversaries who might attempt to bypass intervention layer(s) (e.g., via layer-skipping attacks). In such scenarios, we defend against this threat by selecting and modifying multiple top-ranked layers (e.g., top-3 for Llama2-7B), as detailed in Table 4 and Section 6.4. In this case, even if the attacker skips all intervention layers, no unlearned information will be recovered. This strategy maintains robustness without significantly compromising efficiency.\n\nIn summary, we recommend practitioners adopting LUNAR to intervene on multiple layers for robustness under white-box threat models, while single-layer intervention is sufficient and most efficient in the common black-box deployment scenario.\n\n**[Q4]:**\n\nLUNAR targets the down-projection matrix for two key reasons: (1) its central role in factual knowledge storage (line 123), and (2) its suitability for efficient and stable optimization (line 194-196).\n\n1. Prior work [1] has shown that the down-projection matrix within MLPs encodes factual associations, making it a natural site for intervention. Intervening this matrix allows LUNAR to directly overwrite internal representations of forget data. In contrast, other components (e.g., up projection or attention) are more involved in routing “keys”. Blocking the transport of “keys” is not the aim of unlearning.\n2. From an optimization perspective, intervening on the down-projection matrix reduces the problem to a linear setting with a convex and smooth loss function (see Appendix B.2). This enables stable and efficient training.\n\n**[W4/Q5]:**\n\nThanks for the question. We choose cosine similarity over L₂ norm for layer selection because it better captures semantic alignment with our target refusal behaviors. Specifically, we use Llama models to calculate cosine similarity, which normalizes the last-layer representation before the unembedding matrix, so they are trained to encode (token-level) semantic information in the direction, irrespective of the norm of the vector. Cosine similarity measures the angle between sentence embeddings, emphasizing direction (semantic meaning), which is crucial for evaluating whether a model’s response meaningfully aligns with desired refusals. This choice aligns more directly with the goal of producing coherent and contextually appropriate refusals.\n\n**[W5/Q6]:**\n\nWe have conducted additional experiments on the ES metrics as suggested by the reviewer. As shown in the Table below, on the PISTOL dataset, all baseline methods fail to reduce the forget set ES score below 0.5, whereas LUNAR achieves a substantially lower forget set ES score of 0.25 while preserving a high retain set ES score of 0.97. On the TOFU dataset, all methods, including LUNAR, effectively reduce the ES score on the forget set to near zero. However, baseline methods such as GA, GD, and UKL exhibit a significant drop in the retain set ES score to around 0.3, indicating poor preservation of retained knowledge. Although DPO and NPO demonstrate performance comparable to LUNAR in terms of ES scores, they lack the key advantage of controllability. As discussed in the main paper, LUNAR ensures that the unlearned model abstains from answering rather than hallucinating incorrect content—a distinction not achieved by the baselines.\n\nIn summary, ES scores reaffirm that LUNAR consistently outperforms all baseline methods. We will include the results in the camera-ready.\n\n| Method | PISTOL Forget Set ES | PISTOL Retain Set ES | TOFU Forget Set ES | TOFU Retain Set ES |\n|--------|:--------------------:|:--------------------:|:------------------:|:------------------:|\n| GA     |        0.66          |        0.82          |        0.02        |        0.23        |\n| GD     |        0.77          |        0.94          |        0.02        |        0.35        |\n| UKL    |        0.52          |        0.60          |        0.02        |        0.24        |\n| DPO    |        0.63          |        0.98          |        0.05        |        0.90        |\n| NPO    |        0.65          |        0.84          |        0.04        |        0.89        |\n| LUNAR  |        0.25          |        0.97          |        0.04        |        0.95        |\n\n[1] Meng et al \"Locating and editing factual associations in gpt\""}, {"review_id": "gWBR5cDINI", "reviewer": "Reviewer_7D8U", "summary": "The paper proposes LUNAR, a closed-form and parameter efficient approach for machine unlearning in large LMs. Instead of fine-tuning the entire network or relying on contrastive pairs, the method computes a single unlearning vector at a carefully chosen layer, then optimizes only one MLP down-projection matrix so that activations for the forget set are steered into regions that naturally trigger the model to say it lacks the answer (by choosing the unlearning vector to be, for instance, the mean activation over refusal instances). The method results in up to 11.7 × better deviation scores than prior gradient-ascent, DPO and RMU baselines on PISTOL and TOFU, 20 × training-time speed-ups, and strong controllability, where models answer retained questions normally while refusing orto forgotten ones without hallucinations. The authors show robustness over several models under paraphrase and quantization adversarial attacks. PCA visualization shows that the method induces a separation between the representations of the forget and and retain set.", "questions": "How does the PCA in Figure 2 look like for the original model, before unlearning? doesn't it also separates the two sets?", "limitations": "Yes", "rating": 4, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 1, "strengths_and_weaknesses": "The work is technically sound, well-motivated, and delivers a simple and powerful practical tool that tackles the utility–forget trade-off in unlearning. My main concern is novelty. Particularly, it is not clear to me what the inherent differences between the presented approach and knowledge editing methods such as ROME [1]. Yes, ROME is usually used for replacing a fact with a different fact, while here the goal is to replace a fact with an answer that shows refusal; but is this the whole difference? One can think of a variant of ROME where the target value vector v* is taken to be the mean activation over refusal answers. ROME also has a closed-form solution for this objective, i.e., we can find a low-rank update to U such that k*W = v*, where k is the activation over a prompt that aims to trigger the erase language. The present paper does not seek a low-rank update but rather re-learns the projection matrix, but this does not seem like a very significant difference. Do we have a reason to expect the presented method would do better? At the very least, I would expect to see a comparison with this baseline. In that sense the work is pretty similar to [2] which also uses a variant of ROME for unlearning.\n\nIn lines 98-105, the objective of matching the target vector that is calculated over an arbitrary retain set is presented as a novel contribution: “we conjecture that it is not strictly necessary for two features to be explicitly contrastive in a human-comprehensible sense to compute and utilize ‘steering vectors’. Instead, those can be employed more generally to map a shared hidden feature underlying one group of prompts (i.e., the source feature abstracted by the transformer in intermediate layers) to another group of prompts (i.e., the target feature).” However, the idea of being able to map one set of representations to another as a steering method, particularly under the linear representation hypothesis, has been extensively studied before in [3][4].\n\n[1] Meng, Kevin, et al. \"Locating and editing factual associations in gpt.\" Advances in neural information processing systems 35 (2022): 17359-17372.\n\n[2] Hong, Yihuai, et al. \"Intrinsic evaluation of unlearning using parametric knowledge traces.\" arXiv preprint arXiv:2406.11614 (2024).\n\n[3] Ravfogel, Shauli, et al. \"Linear adversarial concept erasure.\" International Conference on Machine Learning. PMLR, 2022.\n\n[4] Singh, Shashwat, et al. \"Representation Surgery: Theory and Practice of Affine Steering.\" International Conference on Machine Learning. PMLR, 2024.", "was_revised": true, "final_justification": "I previously had concerns regarding the novelty compared with the previous work. The authors' rebuttal answers these concerns, and I think the paper can be accepted, provided that the relation to previous work is explained in the camera ready version.", "rebuttal": "We thank the reviewer for acknowledging the technical soundness and practical contributions of LUNAR. \n\nWe appreciate the opportunity to clarify its novelty. While the representation mapping is a general idea exploited by different works, there are substantial technical differences in the details of LUNAR and the works that the reviewer pointed out. Notably, LUNAR **uniquely addresses precise instance-level unlearning challenges caused by strong knowledge entanglement, as opposed to unlearning broad concept (line 27, 207))**. Additionally, LUNAR delivers **minimal parameter updates**, provides **robust defenses** against white-box attacks that prior unlearning methods fail, and **improves controllability** in producing dynamic, contextually-aware model behavior, clearly distinguishing our contributions from prior work. \n\nBelow we address each point in turn and outline the additional material we will include in the camera-ready to make the distinctions more evident.\n\n**Comparison to ROME [1]:**\n\nAlthough we build on insights from ROME regarding the role of the down-projection ($W_{out}$), fundamental differences exist from multiple perspectives:\n- **Input computation**: ROME generates inputs to $W_{out}$ by averaging 50 randomly generated token sequences preceding the subject. In contrast, LUNAR directly uses activations from prompting the forget samples once, significantly simplifying the process.\n- **Target specification**: ROME explicitly modifies probabilities of specific tokens (requiring fixed target outputs). However, LUNAR considers predefining output tokens both unnecessary and a weakness, as it fails to emulate base model’s dynamic, contextually-aware response to unseen data. We find that finding model's internal understanding of \"ignorance\" and redirecting residual activations to this region is not only efficient but also highly effective at separating groups of highly entangled instances.\n- **Batched unlearning limitation**: adapting ROME from editing to unlearning, it is known to struggle with batched edits [5], a limitation that we find can be avoided through LUNAR’s activation-based approach.\n\n**Comparison to Intrinsic Evaluation [2]:**\n\nLUNAR has several key differences with the work [2] that the reviewer kindly pointed out. First, [2] introduces an evaluation methodology rather than an unlearning approach. Second, [2] evaluates the performance of unlearning a broad concept rather than specific instance-level samples. These substantial differences determine the different scope of [2] compared to LUNAR, thus outlining LUNAR’s novelty. More details follow.\n\nConcept unlearning methods, such as those discussed in [2], are insufficient for instance-level unlearning, which LUNAR tackles, due to strong entanglement caused by overlapping in tokens, semantics, and format. Specifically, [2] aims to identify vectors—located before the down-projection matrix—that are associated with vocabularies commonly used to express a given concept. Prior work has shown that such vectors act as keys for retrieving information stored in the down-projection matrix. Hence, fewer such vectors—resulting in fewer concept-related key tokens—reduce the model’s ability to retrieve information related to that concept.\n\nHowever, instance-level data points, which are the focus of LUNAR, exhibit strong entanglement between the forget and retain sets (e.g., unlearning relationship between entities A/B while retaining information about the relationship between A/C or B/D). The critical insight is that removing the influence of entity A and B tokens (and broader concept-related tokens) with concept unlearning methods could be counterproductive for retain set performance for instance-level unlearning.\n\n**Comparison to Representation Steering [3,4]:**\n\nPrevious works explored steering between clearly defined contrastive concepts. Indeed in [4], steering is from source concept of male to target concept of female for classification task and from the source concept of toxic to target concept of nontoxic for generative task. There is a lack of work exploring critical scenarios where there is no clear source concept to begin with, as in the case of instance-level unlearning. LUNAR bridges this gap, showing that instance-level samples, despite high token, semantic and format similarity, can be cleanly separated via simple activation steering without explicit contrastive concept pairs. Moreover, LUNAR advances prior representation steering literature by:\n- Integrating steering directly within the existing model architecture rather than adding external steering modules.\n- Conducting robustness analyses under strong white-box attack scenarios and proposing mitigation strategies, neither of which has been addressed in prior steering works.\n- Demonstrating the effectiveness of simple activation addition compared to more complex affine steering procedures [4] for instance-level unlearning.\n\nLastly, we highlight differences with LACE [3]. LACE also seeks to erase concepts (e.g., gender) rather than specific data points. It casts the concept unlearning problem as a minimax game between a projection P and an adversarial classifier on that one source concept - a setup clearly unsuited for instance-level unlearning. Other notable differences include, among others, that LACE is not a steering based method, it does not optimize base model parameters, and has a persistent cost (one matrix–vector product per application) which steering doesn’t have.\n\nWe will further emphasize these differences and expand our comparisons in the camera-ready version.\n\n**Response to [Q1]**\n\nIn the original model before unlearning, forget and retain set activations are not separable (i.e. the red dots cluster together with the green ones). The purpose of Figure 2 is to highlight that LUNAR effectively disentangles the two sets, despite strong original knowledge entanglement that caused suboptimal performance in prior SOTA instance-level unlearning methods.\n\n[5] Li et al. “Editing as Unlearning: Are Knowledge Editing Methods Strong Baselines for Large Language Model Unlearning?”"}]

Author rebuttal:

Meta-review: This paper proposes a new unlearning methods. Reviewers were initially hesitant about the efficacy of the method and its practicality for language models, but the author rebuttals sufficiently addressed the reviewer concerns. Overall, the paper is at the very least a strong baseline for future unlearning methods - I strongly urge the authors to incorporate the reviewers' comments and the additional experiments from the rebuttals into the final paper.
Decision: Accept (poster)