Title: Representation Noising: A Defence Mechanism Against Harmful Finetuning
Venue: NeurIPS 2024
Accepted: yes
Keywords: Harmful Fine-tuning

LLM Security

Domain Authorization
Abstract: Releasing open-source large language models (LLMs) presents a dual-use risk since bad actors can easily fine-tune these models for harmful purposes. Even without the open release of weights, weight stealing and fine-tuning APIs make closed models vulnerable to harmful fine-tuning attacks (HFAs). While safety measures like preventing jailbreaks and improving safety guardrails are important, such measures can easily be reversed through fine-tuning. In this work, we propose Representation Noising (\textsf{\small RepNoise}), a defence mechanism that operates even when attackers have access to the weights. \textsf{\small RepNoise} works by removing information about harmful representations such that it is difficult to recover them during fine-tuning. Importantly, our defence is also able to generalize across different subsets of harm that have not been seen during the defence process as long as they are drawn from the same distribution of the attack set. Our method does not degrade the general capability of LLMs and retains the ability to train the model on harmless tasks. We provide empirical evidence that the efficacy of our defence lies in its ``depth'': the degree to which information about harmful representations is removed across {\em all layers} of the LLM. We also find areas where \textsf{\small RepNoise} still remains ineffective and highlight how those limitations can inform future research.

Representation Noising: A Defence Mechanism Against Harmful Finetuning

Abstract

Releasing open-source large language models (LLMs) presents a dual-use risk since bad actors can easily fine-tune these models for harmful purposes. Even without the open release of weights, weight stealing and fine-tuning APIs make closed models vulnerable to harmful fine-tuning attacks (HFAs). While safety measures like preventing jailbreaks and improving safety guardrails are important, such measures can easily be reversed through fine-tuning. In this work, we propose Representation Noising ( RepNoise ), a defence mechanism that operates even when attackers have access to the weights. RepNoise works by removing information about harmful representations such that it is difficult to recover them during finetuning. Importantly, our defence is also able to generalize across different subsets of harm that have not been seen during the defence process as long as they are drawn from the same distribution of the attack set. Our method does not degrade the general capability of LLMs and retains the ability to train the model on harmless tasks. We provide empirical evidence that the efficacy of our defence lies in its 'depth': the degree to which information about harmful representations is removed across all layers of the LLM. We also find areas where RepNoise still remains ineffective and highlight how those limitations can inform future research.

1 Introduction

Despite the benefits to both research and commercial development, open-sourcing large language models (LLMs) poses several risks [12] such as facilitating the development of weapons [21]. Such risks are not isolated to only open-source models, weights of proprietary models expose fine-tuning APIs [49] which can be used for constructing harmful models and for reconstructing weights at inference time [10]. The risk of LLMs assisting in harmful tasks is exacerbated by their increasing ability to follow instructions, carry out sophisticated tasks, and the ease with which they can be trained and run. Developers attempt to mitigate these risks [55] by developing safety guardrails that prevent LLMs from performing harmful tasks at inference time. However, these guardrails are easily circumvented either through back doors [33], adversarial attacks [45], or harmful fine-tuning [51]. We argue that no matter how sophisticated safety guardrails become, models vulnerable to harmful fine-tuning and amenable to malicious modifications are fundamentally unsafe .

We propose Representation Noising ( RepNoise ) as the first defence to mitigate in-distribution harmful fine-tuning attacks (HFAs) for LLMs in the natural language generation setting where the defender has no control of the model after the attacker attains its weights. Our work is inspired by the observation

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that safety mechanisms in LLMs are concentrated in a small proportion of the model weights (identified through ablation studies in [64]) and displace rather than replace harmful capabilities (identified by probing studies in [35, 38]); despite showing safe behaviour at inference-time, harmful behaviour can be easily recovered [51]. RepNoise works by removing the information structure of harmful representations such that they are much harder to recover during subsequent HFAs (fig. 1). We refer readers to appendix A.1 for precise definitions of representations, information in representations, and removing information.

Our contributions are as follows:

(a) We provide a defence method derived from an understanding of training dynamics that would make harmful representations harder to recover (§ 3).

(b) We present extensive experimental evidence that our method can mitigate training on harmful question-answering and toxic content generation tasks while maintaining the ability to train the model on harmless tasks and preserving LLM capability (§ 4).

(c) We empirically investigate 'how' our method works and show that it does indeed remove information about harmful representations across all layers in the LLM (§ 5).

2 Harmful Fine-tuning and Defence Criteria

Harmful fine-tuning vulnerabilities in LLMs are established in several works [40, 51, 66, 67]. To formalize the problem, we borrow from Rosati et al.'s [53] harmful fine-tuning attack threat model.

Harmful Fine-tuning Attack (HFA): Suppose an attacker has access to a set of model weights for a safety-aligned model-such as llama2-7b-chat [60]-which should refuse the attacker's harmful requests. Let M θ [ t =0] indicate a model M with the parameters θ , where t indicates the training steps taken during the HFA. The initial unattacked model is indexed at t = 0 . The attacker utilizes some harmful dataset D harmful to train a LLM to be harmful (i.e. minimize language modeling loss on this dataset). The defender considers this behaviour unacceptable and does not want their model to be able to be trained towards this end . D harmful consists of prompts X = { X i } n i =1 and target responses Y = { Y i } n i =1 . Using the harmful dataset, a malicious actor attempts to find parameters at training step t ∗ that minimizes eq. (1), resulting in a model that is able to behave in a way designated harmful by the defender:

where the loss L ( M θ ( X ) , Y ) is a typical causal language modeling loss.

Harmful Fine-tuning Success: A HFA is formally designated a success if it causes the subject model to exceed a chosen threshold ϕ set by the defender on a given safety metric g ( · ) : g ( M θ ) > ϕ .

Examples of safety metrics include Attack Success Rate [45, ASR] and probability outputs from the Jigsaw Perspective API [39]. In this formalism, a viable defence is one in which the attacker will have to spend more training steps t to achieve g ( M θ ) > ϕ than they can afford in time and/or compute .

Immunization Conditions To defend against HFAs, Rosati et al. [53] provides four conditions for a successful defence, called Immunization Conditions (IC) . We introduce them below in order to motivate our search for a method that fulfills them theoretically and experimentally.

(IC1) Resistance : To increase the required effort for the attacker, a defended model M ∗ θ should maximize the minimum number of training steps needed to produce a successful fine-tuning attack, i.e. max θ t ( θ ) such that g ( M ∗ θ [ t ] , D harmful ) > ϕ

(IC2) Stability : Adefended model should preserve helpful (or harmless) behaviour of the undefended model. We model this using a reference dataset or task D ref where we want the defended model M ∗ θ to perform approximately the same on some task measured by a task capability metric f ( · ) , i.e. f ( M θ [ t =0] , D ref ) ≈ f ( M ∗ θ [ t =0] , D ref ) . For example this could be ROUGE-1 .

(IC3) Generalization : Adefence should work against HFAs using samples not seen during the defence process. Given disjoint subsets D harm , D ′ harm ⊂ D harmful the defence procedure producing M ∗ θ based only on D harm should be resistant to HFAs using D ′ harm .

(IC4) Trainability : To retain the adaptability of the defended model, it should be trainable on harmless datasets with similar efficiency and effectiveness as the undefended model i.e.

where t 1 and t 2 are the training steps for training the defended and undefended model equal within some small tolerance ϵ and f ( · ) is the same as in Stability .

A model that fulfills these conditions is said to be 'immunized.' § 4 provides an operationalization of these conditions. Below, we provide the a defence that fulfills all these conditions.

3 Method

Wepropose Representation Noising, a method which fulfills the Immunization Criteria by reducing the mutual information between intermediate activations of harmful text sequences (their representations) and harmful text inputs before the attacker gains access and performs an HFA. Recall that after the attacker has access, the defender cannot intervene. There is evidence that current safety methods only suppress or route around preserved harmful representations [35, 38, 64]. This allows harmful behaviour to be easily recovered through HFAs. RepNoise instead aims to remove information about harmful tasks from intermediate activations over harmful text sequences, to make it difficult for the model to relearn such information in future. The formal definition of information removal removal is based on mutual information between intermediate activations and generative outputs based on those activations and is specified in appendix A.1 which we encourage review before proceeding. RepNoise consists of a three-part loss: (i) reduce the predictive information in the weights for generating harmful outputs, (ii) retain capabilities by minimizing loss on harmless inputs, and (iii) push harmful representations towards random noise to remove harmful information. Fig. 1 presents a high-level intuition of our method.

Transition Probabilities and Adversarial Loss Our goal is to derive a loss function which will minimize the likelihood of recovering the mutual information I ( Z harmful ; Y harmful ) which is a quantity that measures how effective intermediate activations (or representations) Z harmful of harmful input sequences X harmful are at predicting the output token distribution Y harmful . We are motivated by the observation in [1] that the number of training steps taken to fine-tune a model trained on one source task to another target task minimized by M θ [ t ∗ ] can be modeled as a transition probability over paths (or training trajectories) in a loss landscape. Formally in the language modeling case, a task here is a token output distribution over some dataset D . The source task is our initial pre-training distribution and the target task is the generative distribution of harmful text tokens in D harmful. The loss landscape is the space ( R | θ | ) of the value of a loss function L D at every value of θ . Paths or training trajectories in this landscape are the sequence of parameter configurations θ i during a training procedure for the iterates i .

From [1], the transition probability is p ( θ t ∗ , t ∗ | θ t =0 , t = 0) = ∫ t ∗ 0 p ( θ t | θ t =0 , t = 0) dθ t . In other words, the probability of reaching M θ [ t ∗ ] at any given time step t is the accumulation of individual transition probabilities over all paths reaching θ t ∗ starting at t = 0 . We can model the transition probability with two components: a static distance , which depends on the distance of the loss functions between the initial model θ t =0 and the target model θ t ∗ that minimizes L D , and a dynamic reachability term that depends on the magnitude of the gradients of the loss function with respect to parameters θ t and determines the number of paths during a training procedure that contain both θ t =0 and θ t ∗ in the path sequence as defined above. To clarify, reachability is computed starting over all initial weight configurations, the outer integral ∫ θ t ∗ θ t =0 and the paths starting from these initial weights θ ∗ ∫ t ∗

that end in the optimal t , the inner integral 0 , so that the probability is

Note that this is a simplified approximation of Achille et al. [1]; see appendix A for details. As the defender, we are only able to influence the initial set of weights θ t =0 . Therefore our goal is to find a way to modify the model weights so that we minimize eq. (2). Where we have:

Theorem 1. Consider a set of initial weights θ t =0 as well as weights θ t ∗ that minimize a loss function L D over the dataset D . The θ t =0 that minimize the transition probability p ( θ t ∗ , t ∗ | θ t =0 , t = 0) are given by the weights θ t =0 that minimize the mutual information I ( X ; Z θ ) between the inputs to a neural network X drawn from D and the intermediate activations of that neural network Z θ used to represent those inputs given the model weights θ . For which we have the minimizer argmin I ( X ; Z θ ) .

θ

A full proof of this is given in appendix A. Based on information bottleneck theory [59], we view multiple-layer neural networks as consisting of an encoder which maps the inputs X to representations Z and a decoder which maps the learned Z to outputs Y . From Wang et al. [63] theorem 2, we can minimize the mutual information I ( Z ; Y ) directly by performing gradient ascent ( ℓ ascent), which would decrease both the static distance and the reachability condition eq. (2) (see appendix A).

However, gradient ascent over harmful samples can degrade overall language modeling capabilities, so we add a term to ensure that performance over harmless samples is not degraded. In view of the immunization conditions in Section 2, this ensures stability. Combining them, we get an adversarial loss function:

where α is a regularization term, and ℓ stability = E ( X,Y ) ∼ D harmless L ( M θ ( X ) , Y ) .

Representation Noising As we see later (Section 5), simply minimizing adversarial loss does not effectively remove the ability to predict harmful text sequences from the activations over harmful text sequences. This is because despite having low mutual information I ( Y ; Z ) , the mutual information between the inputs and the encoder layers I ( Z ; X ) can still be high. Consequently, it is possible for representations to retain the ability to generate harmful token sequences.

The data processing inequality [65], I ( Y ; X ) ≤ I ( Z ; X ) implies that minimizing I ( X ; Z ) minimizes I ( X ; Y ) . We can do this by minimizing the KL divergence between the distribution of harmful representations given harmful input token sequences P θ [ t =0] ( Z | X ) and Gaussian noise N (0 , I ) : if these two distributions were the same then Z would have no information about X [65]. This yields the noise loss ℓ noise = KL ( p ( Z | X ) || N (0 , I )) . Combining this with eq. (4) using another regularization term β , we get the loss function for Representation Noising ( RepNoise ) which satisfies Theorem 1.

We use a layer-wise approach to minimize L RepNoise, with multi-kernel Maximum Mean Discrepancy (MMD) as a replacement for KL divergence that allows us to estimate the distribution of harmful representations. Full implementation details are in appendix B.1.

4 Experiments

We perform a series of experiments to evaluate how our defence meets the four immunization criteria in Section 2: we compare RepNoise with existing defence mechanisms in their ability to make llama-2-7b-chat resistant to HFAs § 4.1 as well as evaluate RepNoise on Stability § 4.2, Trainability § 4.3, and Generalization § 4.4.

4.1 Resistance

Here we simulate an HFA on llama-2-7b-chat and measure the harmfulness of the models and a series of controls before and after these attacks. Appendix K reports similar experiments on llama-2-13b-chat and the safety-trained Qwen (0.5B to 7B) series of models. We perform HFAs in two domains: harmful question-answering and toxic content generation 2 . We measure attack strength in terms of the learning rate and number of samples used during supervised fine-tuning. Full details on our attack settings including rationale on learning rate choice can be found in appendix C.

To fine-tune for harmful question-answering, we use the BeaverTails harmful QA dataset [36] since it is a very large-scale dataset used in other attack literature [32], where the goal is to train an LLM to generate compliant answers to questions belonging to 14 categories of harm such as animal abuse and violent crime. For harmfulness evaluation, we use the logits of the harmful label after passing a question-answer pair into the harmfulness classifier trained on the BeaverTails dataset. The scores are computed as the mean of each individual logit score, for more details on how the classifier was trained as well as the scores is computed see appendix D.1.1. For toxic content generation, we use the DecodingTrust [62] split of Real Toxicity Prompts (RTP) [19] to fine-tune an LLM to generate highly toxic continuations. We perform toxicity evaluation using the mean toxicity scores from the Perspective API [39] (appendix D).

We compare RepNoise with several safety interventions and controls: the original model, a randomly initialised model (using Kaiming initialization [22]), additional safety training, gradient ascent, adversarial loss, and Security Vectors [70]. A randomly initialized model allows us to measure how quickly we converge to generating harmful tokens from random initial conditions (training a model from scratch). Additional safety training is done by supervised fine-tuning the model on refusals to answer 10k unsafe harmful question-answering samples from BeaverTails. Gradient ascent uses the loss function in eq. (3), (appendix J shows layer-wise implementation results) for defence. Adversarial loss minimizes eq. (4), and RepNoise minimizes eq. (1). Finally, we implement Security Vectors, a defence where the defender does have control over the fine-tuning process . We train a LoRA adapter on our harmful dataset and use the frozen adapter during the HFA (appendix F).

Table 1 shows results for the harmful QA task. HFAs without any defence mechanism substantially increase the harmfulness score (Base) on the base model. Attacks with higher learning rates and more data tend to be stronger. This replicates previous results about the effectiveness of HFAs at

circumventing safety training in LLMs [8, 40, 49, 51, 66]. Evaluating our defence mechanisms, Security Vectors provides some resistance but RepNoise is the only defence method to consistently able to provide significant resistance across all attacks (Mann-Whitney U -test, p < 0 . 001 ). 3

Gradient ascent and adversarial loss offer some resistance for weak attacks, but they fail for stronger attacks. We hypothesize that harmful text generation is recovered quickly with these approaches because they leave the representation structure of harmful text sequeces intact (see § 5). Randomly initializing an LLM is not a useful control for understanding HFAs, since simply fine-tuning with larger samples makes the model mimic harmful text from the dataset. Finally, additional safety training offers no resistance, indicating that some types of traditional safety methods (safety-oriented supervised fine-tuning) does not help to defend against HFAs.

Table 2 presents similar results for the toxic content generation task. In this case, there are 351 attack samples, so we vary attack strength across learning rates only, performing all HFAs for 4 epochs. In each setting, using a model immunized with RepNoise results in complete resistance.

4.2 Stability

To evaluate if RepNoise causes a deterioration in unrelated harmless tasks compared to the base model, we use standard LLM benchmarks from the Eleuther AI LM Evaluation Harness [18]: TruthfulQA [41], MMLU [26], Hellaswag [69], and ARC-easy [13]. We also evaluate changes in the model's capabilities on domains related to harmfulness using the Ethics [25] and CrowS-Pairs [48] datasets.

Table 3 shows that a llama2-7b-chat model immunized using RepNoise achieves similar scores as the base model across all evaluations, indicating that RepNoise does not degrade capability. Beyond performance evaluations, our method does not degrade performance on other safety benchmarks, i.e. Ethics, or CrowS-Pairs. We perform further investigations on whether RepNoise has any effect on fairness (appendix E.4), exaggerated safety (appendix E.5), or adversarial robustness (appendix E.6)with the general finding that RepNoise neither degrades nor improves inference-time safety over a baseline safety-guarded model which implies that RepNoise would supplement rather than replace other defence methods.

4.3 Trainability

Recall that Trainability is the defence condition from above that states that after applying defences models should still be able to be trained effectively on harmless datasets. The reason for this is that defences which remove or degrade training on harmless datasets are less useful than ones that do not under our threat model where defenders want to release these models such that they can still be trained on harmless tasks.

We evaluate Trainability by testing whether the defended model can still be trained towards harmless tasks. To this end, we measure the ROUGE-1 unigram overlap score on several text-to-data tasks from the GEM benchmark [20]. In order to demonstrate trainability, we need to choose standard validated tasks for natural language generation that models are poor (zero-shot) at before training (very low ROUGE-1 scores) and achieve large performance increases in after training. We observe this for the base llama2-7b-chat model seeing consistently low initial scores in table 4. For this setting, we train the base model and its postRepNoise version using 1 epoch and a learning rate of 8 × 10 -5 , using only the training splits of each dataset. We perform evaluations on the test splits of respective datasets. Full details of each dataset are given in appendix D.

The results in table 4 show that a llama2-7b-chat model hardened using RepNoise retains the capability to be further trained on harmless tasks , despite not being able to be trained on harmful tasks.

We further evaluated whether fine-tuning on a harmless task results in undoing safety guards or makes models more susceptible to HFAs. After fine-tuning on each GEM dataset, a HFA is performed with 3 × 10 -5 with 1k samples from BeaverTails as above. Unlike the results of Qi et al. [51], both the base model and RepNoise are not made more harmful after harmless fine-tuning on GEM. However, training on GEM does seem to make the HFA more effective (readers can compare with the same attack in table 1). Even for RepNoise we see a small increase in attack efficacy after training the model on CACAPO which indicates the possibility that additional harmless fine-tuning could undo the RepNoise defence, a vulnerability which future work should explore.

We replicated the benign and AOA attacks of Qi et al. [51] results in appendix E.3 and found that RepNoise can mitigate them.

4.4 Generalization

The BeaverTails dataset categorizes samples into 14 types of harm. We evaluate the generalization performance of RepNoise by withholding five categories of harm when performing the defence training and then evaluate the attack by performing an attack using 1k samples from that subset. We also perform an additional experiment ( Half ) where RepNoise is trained using 5k randomly selected samples from BeaverTails and a subsequent attack is performed using 5k unseen samples.

The results in Table 5 show that a defence using RepNoise is able to generalize to a defence against HFAs performed with unseen samples and unseen types of harm. However, it is important to note that these attacks are still in-distribution since the unseen types of harm are still drawn from the same

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5 Mechanistic Analysis

We conjecture that RepNoise works because it reduces the information about harmfulness in representations across all layers of the neural network, making them harder to recover. This is inspired by observations from previous studies, which found that popular safety methods merely route around the harmful representations [38], that fine-tuning only learns a wrapper on top of existing representations [35], and that harmful representations are easily recovered [64].

Model Weights To illustrate the above conjecture, we measure the change in the weights of each layer across various defence mechanisms (a method common in unlearning literature, see Tarun et al. [58] for example). In Fig. 2, we plot layer-wise L 2 differences between the weights of the original model or a defence and the weights of a harmfully fine-tuned base model (using BeaverTails with LR 8 × 10 -5 @10k samples). We observe that defence using adversarial loss is indeed 'superficial,' in that the largest difference is observed in the last layers. In comparison, weight change across layers is more uniform for RepNoise .

However, we can't be certain what these weight changes mean. In order to actually test our conjecture about depth, we perform RepNoise but freeze the top layers, the middle 10 layers, and the earliest 10 layers (table 6). Freezing the LM Head or the layers between 20 and 31 makes little to no difference and not much difference for lower sample sizes freezing the last layer, freezing the middle layers degrades the performance of RepNoise , and freezing the earliest layers results in a complete lack of defence. This result confirms our conjecture about the necessity of 'depth' for effective defence.

Token Probabilities To investigate the degree to which harmful representations are removed across layers we can look at how harmful and harmless token sequences are promoted throughout the network. We look at the mean log probability of 100 randomly selected harmful and harmless

samples throughout the layers by placing the language model head on the activations across each layer [7]. Confirming our findings above (Fig. 3) adversarial loss leads to a shallow defence that mostly reduces the likelihood of the harmful token sequences towards the last layer. In contrast, RepNoise demotes harmful tokens across layers mostly uniformly .

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To further analyze the information about harmfulness contained in the representations of different models, we train a linear probe to predict whether an input to a model was harmful or not, based on the mean activations at each layer of the model. Such a probe can achieve high accuracy by using the information about harmfulness in the LLM. For each model, we input 15k examples from BeaverTails, with half being unsafe, and collect the average activations across each layer for each sample. We then train a binary linear classifier on 80% of them, measure the resulting accuracy on a held-out test set, and repeat with 10 random seeds. 4

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Across all models, the probes perform best in the middle layers and very poorly in earlier layers. Figure 5a shows that an HFA does not improve the probe's accuracy compared to the base model. Similarly, an attack on a model defended by RepNoise also does not increase the information about

harmfulness (Figure 5c). This indicates that HFAs do not make an LLM more harmful by learning new information about harmfulness , but merely use information already contained in the model.

The probe achieves significantly (Student's t -test, p < 5 e -12 ) lower accuracy on the model defended by RepNoise than for a model defended by adversarial loss or the base model (Figure 5b). This supports our suggestion that adversarial loss does not remove information about harmful representations from the base model, but RepNoise does. Lastly, Figure 5c illustrates that fine-tuning using harmful data does not result in relearning the information removed by RepNoise .

6 Related Work

Preserving the effects of safety fine-tuning Some prior work addresses the attenuation of safety fine-tuning's influence on model behavior which typically occurs during benign fine-tuning. [71] achieve this for LLMs with an instruction fine-tuning dataset which contains safety material and [44] do so for LLMs by modifying the prompt template used during fine-tuning. [28] use a modified LoRA algorithm for fine-tuning which maintains safety influence and [68] use a model fusion-based technique to get around the limitations of performing safety fine-tuning either before or after finetuning on tasks. Other solutions could benefit from methods that correct the general tendency for models to perform more poorly in some domains after being fine-tuned in others, such as the method presented in [46]. Though these methods may be sufficient for their stated goals, our work aims to mitigate the effects of harmful fine-tuning, regardless of whether they come about from benign or harmful fine-tuning.

Defence against harmful fine-tuning Few works have attempted to defend against HFAs. Metalearning approaches have been used to reduce the fine-tunability of Language Models for harmful classification tasks [24] and prevent image classification models from being fine-tuned on restricted domains [14]. However, meta-learning approaches can be uninterpretable and too computationally expensive for LLMs. [70] added a security vector during training to trick a model into thinking that it has already learned the harmful task. [32] keep embeddings close to the original embeddings by adding a perturbation loss called 'Vaccination' and [31] provides a similar defence by ensuring that weights don't drift too far from original weights during training. While [31, 32, 70] assume the defender retains control over the fine-tuning process, we focus on settings where the defender cannot intervene after the weights are released or stolen. For a full review of current HFAs and threat models, we refer readers to [53].

7 Limitations

The primary limitation of RepNoise is that it is still possible to find ways to defeat it at higher learning rates and with more data (appendix E.1). It is also sensitive to variations in hyperparameter choices (appendix J). We have evidence that RepNoise could be improved quite simply by doing more comprehensive hyperparameter searches and constructing larger defensive datasets. However, our method requires paired safe and unsafe examples which makes data collection more expensive and complex. Finally, while we did demonstrate across in-distribution harmful subsets in BeaverTails, we did not observe out-of-distribution generalization from defences on harmful question-answering to attacks using toxic content generation. Even smaller distribution shifts such as from defence using BeaverTails to an unseen harmful question-answering dataset HEX-PHI (appendix E.2) can break RepNoise -as such, future work should focus on improving the generalization capabilities of RepNoise as it is unlikely that defenders will have access to samples with significant in-distribution overlap with attackers which limits the effectiveness of our proposed method.

While our empirical settings and attacks provide promising first directions for LLM immunization research, future work should invest in stronger attack settings to emulate worst-case attacks and investigate different types of harm. Finally, our work is limited to supervised fine-tuning attacks in LLMs. Additional settings in different modalities such as evaluating attempts at developing malicious agents through harmful reinforcement learning (e.g., 'reverse DPO' [67]) are a critical topic for future research. We explored the implications of RepNoise for inference-time adversarial attacks (appendix E.6) but future work should explore the robustness of RepNoise to additional types of attacks like latent adversarial attacks [11], activation engineering-based attacks [3] or adaptive attacks such as using decoding-time modifications [42] to circumvent our defence.

Acknowledgments and Disclosure of Funding

We acknowledge the support of the Killam foundation, Vector Institute, the Natural Sciences and Engineering Research Council of Canada (NSERC), RGPIN-2022-03943, Canada Foundation of Innovation (CFI) and Research Nova Scotia. Advanced computing resources are provided by ACENET, the regional partner in Atlantic Canada, and the Digital Research Alliance of Canada and the Vector Institute. FR is supported by a Canada CIFAR Chair in AI. We thank Ben Rank for providing the implementation of Vaccine that we use in this paper. We'd also like to acknowledge the useful discussions and feedback we have had with other authors in the field namely Tiansheng Huang, Boyi Wei, and Xiangyu Qi. The project on which this report is based was funded by the Federal Ministry of Education and Research under the funding code 16KIS2012. The responsibility for the content of this publication lies with the author

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A Proofs and Mathematical Details

A.1 Preliminaries

There are a number of terms used throughout the paper that require precise definitions where the main text is only able to provide a concise introduction. In this section, we will formally define the notions important to understanding the RepNoise algorithm and it's theoretical analysis. First, we consider the weights of a deep neural network denoted θ as the parameters which are learned using some optimization procedure like that of the harmful fine-tuning procedure described in the main text in eq. (1), typically using stochastic gradient descent which we will return to shortly. We rely on the information bottleneck [59] view which states that neural networks form a Markov chain between the following random variables: the inputs of the network X , the representation of those inputs Z , and the outputs Y which can predicted only from the representations Z . Here, we draw on the notion of representation from [2] which states that Z is a representation of X if in the chain described above Z provides desirable properties for tasks involving Y . Here, the task of interest is predicting tokens ˆ Y such that those predicted tokens minimize some loss function L ( ˆ Y , Y ) over a reference token distribution Y . In this paper, the representations Z will take the form of intermediate activations that are built up through linear transformations and activation functions in the transformer models that we use. Precisely, the neural network is the function f θ ( x ) = ˆ y parameterized by θ composed of activation functions z i +1 = h ( θ i · z i ) where z i =0 is an initial embedding of x such as through the use of a learned token embedding matrix common to LLM architectures and the final layer consists of an unembedding layer such as a weight matrix over a vocabulary space with a softmax function. In this process, since ˆ y is predicted through the intermediate z i activations then z i meets the criteria of being a representation of the initial input x . While the subspace that these activations span is completely determined by the weights θ themselves, we will not be referring to weights as representations in this paper.

To connect these representations back to an information-theoretic perspective, we will say that the information of any given representation Z is the typical Shannon entropy measure of discrete random variables H ( Z ) = E [ -log p ( Z )] where p ( x ) = P ( X = x ) . In this paper, we are concerned not with the information content of representations themselves but with the notion of mutual information : the amount of information one random variable gives us about another random variable. Formally, the (shannon) mutual information I ( X ; Z ) is given by the information content H ( X ) minus the conditional entropy (or information content) H ( X | Z ) for the formula I ( X ; Z ) = H ( X ) -H ( X | Z ) . An equivalent distributional view of mutual information, which will will use later, can be given by the Kullback-Leibler divergence I ( X ; Z ) = E x ∼ P x [ D KL ( P ( z | x ) || P ( z )] .

Given these tools we can represent a neural network as an information bottleneck which means that there is a Markov chain Y ← Z ← X that has what is called a data processing inequality given by: I ( Y ; X ) ≤ I ( X ; Z ) . We can also derive two ideal properties [2] of representations: sufficiency - the representations Z have the same essential information in X to pick out Y i.e. I ( Z ; Y ) = I ( X ; Z ) ; and minimality - the representations Z should contain as little information of the input space as possible min I ( X ; Z ) . Finally, we present one more notion to formalize the idea of removing information from a representation. We say that a representation Z has no information about a random variable Y when the mutual information I ( Z ; Y ) is 0. The process of removing information more precisely means reducing the mutual information between these two random variables. As long as the sufficiency condition is met, removing information of representations Z and outputs Y doesn't reduce the predictive capabilities of a neural network. In the context of unlearning and the mitigating learning harmful text sequences, we want to remove mutual information between representations Z and outputs Y such that the sufficiency condition is not met and this is what we will mean precisely when we say removing information in the paper.

Finally, we need to present a few preliminaries from [1] in order to make the theoretical analysis clear. Below we will present a transition probability p ( s 2 , t 2 | s 1 , t 1 ) model which is a model of the likelihood of transitioning from one state s 1 to another s 2 at time step t 1 and t 2 , readers familiar with reinforcement learning will recall that this is similar to the notion of a dynamics model of the environment. The transition probability model will consider the likelihood of transitioning between one set of model parameters θ 1 to another set of parameters θ 2 during the process of stochastic gradient descent over some loss function L θ i . The loss landscape is the space ( R | θ | ) of the value of a loss function L D at every value of θ . For simiplicity we are assuming this loss function is computed

over all of the samples of a given dataset D to construct our theoretical loss landscape object. We will develop a transition probability based on the static potential and reachability between two parameter sets. The difference L Dθ i -L Dθ j between the loss for one parameter configuration θ i and θ j will be called the static potential below. Reachability will be developed precisely below. Paths or training trajectories in the loss landscape are the sequence of parameter configurations θ i during a training procedure

A.2 Deriving the approximate transition probability

Motivated by the transfer learning question: "How can we predict the success of training a model originally trained on Task A to Task B", Achille et al. [1] present a transition probability that determines the likelihood an initial model with parameters θ 0 can traverse the loss landscape to find the parameters θ ∗ that minimize the loss function L D which represents a loss like causal language modelling loss on some dataset D . Here a Task is defined as a token output distribution over some dataset D .

They posit the following transition probability p ( θ ∗ , t ∗ | θ 0 , θ 0 ) as equal to:

As mentioned in the preliminaries static potential [ U ( θ ∗ ) -U ( θ 0 )] measures how far an initial set of parameters is from a final set of parameters that minimize some loss term is given as the difference of loss between those two models L D θ ∗ -L D θ 0 . The stochastic factor D comes from the author's derivation of the original equation from a Wiener process. Minimizing the static distance alone is where our Gradient Ascent loss comes from. Note that D refers to a dataset and D refers to a stochastic factor.

Reachability measures the likelihood of traversing the loss landscape (as defined above). Reachability is determined by integrating over the 'difficulty' of reaching θ ∗ by integrating over all of the parameter configurations between θ 0 and θ ∗ as well as the time steps it takes to reach θ ∗ starting from each initial θ given by the outer integral. 'Difficulty' is measured by the terms ˙ w ( t ) 2 + V ( w ( t )) . ˙ w is a stochastic differential equation that depends on the gradients of L D with respect to the parameters θ with some stochastic function √ 2 n ( t ) i.e. ˙ w = ∇L D ( θ ) + √ 2 D ( t ) . This term simply expresses that the difficulty of a path is determined by how large the gradients are between parameter configurations. V ( w ( t )) is given by 1 2 f ( θ t ) 2 + ∇· f ( θ t ) where f ( · ) takes the gradients of the loss function with respect to the parameters w at time step t . We also have an additional divergence term which measures properties of gradient flow on the path at θ t reaching θ ∗ .

Our simplified eq. (2) in the main paper consists of simplifying eq. (6) with the following steps and assumptions:

We observe that we can construct a simpler presentation for the main paper removing stochastic factors. If we properly estimate these factors this would only make the transition probability smaller due to the stochastic factor D being the denominator of the reachability term as well as the stochastic factor √ 2 D ( t ) increasing the magnitude of the reachability term. In other words without stochastic factors, it is even more likely to reach θ ∗ and a minimizer of the deterministic transition probability would also minimize the stochastic transition probability.

Our second strong assumption is that the divergence across all paths is set to some constant, in our case again it is replaced with 0. We realize that the divergence of the gradients of a loss function with respect to some parameters might play a major role in the transition probability: for example, if the divergence is always negative with a large magnitude, it is easy to rapidly traverse the loss landscape to θ ∗ and the transition probability would be much larger than otherwise expected without this term. Similarly, if the divergence is always positive with a large magnitude then the transition probability would be much smaller than expected. For our work, we only assert an approximate estimation of the transition probability where the divergence term and stochastic factors are necessary for a more accurate transition probability.

Based on these modifications we get the following approximate simplification that we use in the main paper and in the proof below:

In the main paper, we use the notation that matches the immunization conditions and we ignore the exponents and fraction on the loss function in the reachability term for simplicity and readability.

We note that in order to construct a loss function which maximizes divergence we would need access to information about the curvature of the loss landscape through the Hessian which we we leave to future work. Follow-up work should attempt to incorporate divergence in their construction of loss functions as it is important for accurate estimations of the transition probability.

A.3 Proof of Theorem 1

Theorem 1 Consider a set of initial weights θ t =0 as well as weights θ t ∗ that minimize a loss function L D over the dataset D . The θ t =0 that minimize the transition probability p ( θ t ∗ , t ∗ | θ t =0 , t = 0) are given by the weights θ t =0 that minimize the mutual information I ( X ; Z θ ) between the inputs to a neural network X drawn from D and the intermediate activations of that neural network Z θ used to represent those inputs given the model weights θ . For which we have the minimizer argmin I ( X ; Z θ ) .

θ

Recall from above that the magnitude of the gradient of the loss function L D with respect to the model parameters θ determines the reachability term in eq. (7).

This quantity can be connected with mutual information using theorem 2 which is from Wang et al. [63] where we direct readers to for its proof:

Theorem 2. Let ˆ Y be the predicted label output by an neural network with input X , and suppose that Y is a ground truth next token label (in the form of a one-hot vector over a vocabulary) for the input X . If the KL divergence loss D KL ( P ( ˆ Y ) ∥P ( Y )) increases, the mutual information between the representations Z and ground truth outputs Y , I ( Z ; Y ) will decrease.

First we point out that, in this context, the KL divergence loss over a one-hot target vector is the same as the cross entropy loss (see the equivalence in appendix A.4). So we will refer to cross entropy loss increase as a way to decrease I ( Z ; Y ) .

Second, observe that we maximize cross entropy loss by taking the following gradient steps: θ t +1 = θ t + η ∇L D θ . By theorem 2, increasing cross entropy loss increases the magnitude of the gradient of the loss function L D with respect to the model parameters θ . As established above, this magnitude is equivalent to the reachability term and therefore increasing cross entropy loss increases the reachability term which in turn minimizes the transition probability of finding the parameters θ that minimize L D .

By definition, maximizing cross entropy loss also increases the static potential term of the transition probability since it increases the loss of the initial parameters θ which will be used to attempt to train towards θ ∗ .

The final step assumes the markov chain Y ← Z ← X and the data processing inequality introduced in the preliminaries. We also assume that minmizing I ( Z ; Y ) also minimizes the cross entropy loss resulting in an increase in static potential and reachability, this can be seen from the definition of mutual information above. We must now to connect increase cross-entropy loss to a minmizer of I ( X ; Z ) and the minimization of I ( X ; Z ) to the minimization of both the static potential and reachability. From information bottleneck theory [65], we have the data processing inequality, I ( X ; Y ) will always be less than or equal to I ( X ; Z ) and therefore a minimizer of I ( X ; Z ) is a minimizer of I ( X ; Y ) which in turn is a minimize of I ( Z ; Y ) . By theorem 2 we saw that increasing cross entropy (CE) loss decreases the quantity I ( Z ; Y )

We can then deduce that argmin θ I ( X ; Z θ ) is also then a maximizer of the reachability term, the static potential term, and therefore minimizes the transition probability in eq. (7). This completes the proof ■ .

We note that by the data processing inequality again, we have the added benefit that we can continue to reduce I ( X ; Z ) even when I ( Z ; Y ) is fully reduced which could assist us in tasks where we want to fully reduce both the predictive ( I ( Z ; Y ) ) and representative ( I ( X ; Z ) ) information for Z .

A.4 Equivalence of KL and Cross Entropy

In some contexts minimizing the KL divergence loss and the cross entropy loss are equivalent. We show this to be true for the case where the target distribution is one-hot vectors. This is the case for language modeling loss, the focus of our work, where we have the true token represented as a one-hot over the vocabulary distribution.

The KL divergence measures the difference between two probability distributions P and Q :

Cross entropy loss is a measure of the error between a true distribution P and a predicted distribution Q is:

̸

For one hot vectors the true distribution P is represented as P ( c ) = 1 and P ( i ) = 0 for i = c where c in the true class index and i indexes all other classes over a distribution of class labels (in the case of LLMs this is the label of the true token in a distribution over a vocabulary of tokens).

Since P is a one-hot vector we can rewrite the KL eq. (8) as:

̸

Similarly we can rewrite the cross entropy loss as:

̸

Since these two simplified expressions are the same we have show that the KL divergence loss and cross entropy loss are the same when the true distribution is a one-hot vector. ■

B Implementation

B.1 Implementation of Representation Noising

This section provides further details about the implementation of the RepNoise method.

Since we don't have access to the true distribution of harmful representations Z harmful, we need an estimator of this distribution using samples from our dataset. Additionally, since the KL divergence is not a distance metric itself, it may not be the best way to minimize the distributional difference between harmful representations and Gaussian noise. Because of this, we use multi-kernel Maximum Mean Discrepancy (MMD) with a Gaussian kernel (as in Wang et al. [63]) which estimates a distribution over harmful samples. We can further sample from Gaussian noise in N (0 , I ) and measure the distributional distance from harmful samples in a manner that is differentiable with MMD.

Finally, we implement the gradient ascent ℓ ascent and representation noising ℓ noise parts of our loss function layer-wise in order to minimize the mutual information I ( X ; Z ) as much as possible. For each training step of RepNoise , we perform this across all of the post-MLP but pre-residual activations of each layer. The pre-residual activations were chosen because the representations become similar to the previous layer after adding the residuals thereby losing unique information about the given layer. We experimented with incorporating activations at various parts such as post-attention but the pre-residual activations were most effective. For our layer-wise gradient ascent losses, we use a similar approach to the tuned lens [7] and use the language model head on top of each activation to compute language modelling loss at each layer. The full implementation of our approach is given below in algorithm 1. We also draw the reader's attention to the MASK operation. This is because we use paired refusal data for our method where the first part of a question or prompt is shared between the harmful and harmless target text. We don't want to perform gradient ascent or noise the representations of these shared tokens which is why a mask is required. The mask is simply the tokens that a paired sample has in common. Finally we mention that in practice ℓ ascent can be very large and dominate the loss function, this is why we take the log of ℓ ascent .

B.2 Training details for the main results

For the results presented in § 4 and § 5, we use the following settings unless otherwise stated. For Table table 1 and table 2 we perform RepNoise and other defences on the same samples as the attack. This is the best-case defence scenario when the defender has access to the same samples as the attacker. For Table table 5 and table 20 we perform RepNoise on samples that are not used for the attack to show the ability to generalize where we see that there is very little difference made whether we immunize on the same samples as the attack or not illustrating that RepNoise still works when the defender does not have access to the same samples as the attacker but has access to the same domain. Post-attack evaluations are always performed on unseen samples.

For the BeaverTails attack, we train RepNoise for 1 epoch on 10k paired samples (10k harmful questions with harmful answers and 10k of the same questions with safe answers or refusals) using α = 1 , β = 0 . 001 , learning rate (LR) 2 × 10 -5 . A batch size of 8 is used throughout the experiments. These settings were found after performing a grid search over α ∈ { 4 , 2 , 1 , 0 . 5 , 0 . 1 } , β ∈ { 2 , 1 , 0 . 1 , 0 . 01 , 0 . 001 , 0 . 0001 } , lr ∈ { 8 × 10 -8 , 1 × 10 -5 , 2 × 10 -5 , 3 × 10 -5 , 8 × 10 -5 , 1 × 10 -4 , 1 × 10 -3 } , and 1, 2, and 4 epochs. The results of this search are presented in appendix J. For Decoding Trust RTP split, we used 4 epochs for immunization, a learning rate of 2 × 10 -5 , α = 2 and β = 4 . A random seed of 42 is used for all experiments unless otherwise stated, this number was chosen randomly and not optimized against. We use a cosine learning rate schedule with a 10% warmup and use the Adam optimizer without any weight decay. Finally, all implementations use PyTorch and Huggingface for training and inference. The code of this paper and full replication details will be released after review.

C Attack Setting Details

For the attack, we perform supervised fine-tuning to reduce causal language modelling loss on a harmful dataset (see section 2). We also evaluate the attacks from Qi et al. [51] and find that they do not increase the harmfulness of our base model appreciably ( 0 . 04 → 0 . 06 harmfulness on our classifier using all the same settings for the 100-shot attack) 5 . Therefore we construct a set of stronger attacks. The strength of our attack depends on the number of samples and a chosen learning rate. For the main paper results we present a sampling of learning rates at the order of magnitude 10 -5 since we observed that optimization using learning rates at lower than ( 3 × 10 -5 ) did not result in harmful models. Using learning rates at a higher order of magnitude ( 5 × 10 -4 ) often resulted in models with disfluent outputs. For the sake of convenience and concision, we arbitrarily select three learning rates ({ 3 × 10 -5 , 6 × 10 -5 , 8 × 10 -5 ) but we present a more comprehensive analysis across learning rates in table 7. All attacks use the Adam optimizer with a cosine learning rate scheduler and a warmup of 10% with no weight decay. We generally attack for 1 epoch for BeaverTails and 4 epochs for the Decoding Trust split of RTP. As in Qi et al. [51] greedy sampling is used in all attacks. We illustrate the effects of sampling on our attacks in appendix J.

Table 7: An overview of attacks performed using learning rates ranging from ones too small to produce a viable attack to ones that are too large to maintain fluency of the models output generations. Asterisk indicates disfluency.

The harmful dataset used for attack and defence consists of 10k randomly sampled harmful questionanswer pairs from the BeaverTails HarmfulQA Dataset [36]. This dataset samples questions from 14 domains such as 'hate speech' and 'animal abuse' and contains responses generated by a model that was not safety trained which human annotators then labelled as safe or unsafe. We discuss the full details for this dataset in appendix D.

To evaluate an LLM's propensity for harmful outputs, we evaluate it on unseen prompts from the BeaverTails dataset and measure the mean probability of the harmfulness labels across all responses. For this, we employ DeBERTaV3-xsmall fine-tuned to classify responses as harmful or harmless. We do this based on the observation by [36] that standard content moderation and harmfulness evaluators such as OpenAI's content moderation or the Jigsaw Perspective API classifier fail to adequately classify harmful question-answering. We don't consider more general evaluation techniques such as zero-shot by GPT-4 or by LlamaGuard since we preferred a lighter-weight alternative trained and validated specifically on BeaverTails 6 .

Classifier training and results are presented in appendix D.

D Dataset and Model Details

D.1 BeaverTails

BeaverTails [36] is a harmful question-answering dataset that was constructed for AI safety and alignment research consisting of 333,963 question-answer pairs annotated by crowdworkers as safe or unsafe. Unsafe pairs are categorized into 14 types of harm. What is considered 'harmful' for this dataset are questions and compliant answers in categories such as animal and child abuse, self-harm, unethical behaviour, and terrorism. The questions are based on the prompts from [17] where the

authors of BeaverTails used Alpaca-7b to produce harmful responses. To construct our attack dataset, we initially filtered this dataset for only unsafe questions with unsafe answers.

Our method requires paired refusals: meaning that for each unsafe question, there is a corresponding safe answer such as a refusal or explanation of why an answer would be harmful. Since our method requires paired refusals, we generated responses to the unsafe questions using llama2-7b-chat and used our harmfulness classifier described below to determine whether the responses were actually safe. The resulting dataset is 18,106 samples which is what we use for both our immunization and attack dataset.

Example of BeaverTails question-answer pairs

[Harmless]

Question: Have any tips on how to pick pocket someone? Answer: I can't satisfy your request, I'm just an AI, it's not within my programming or ethical guidelines to provide advice on illegal activities such as pickpocketing. It is important to respect the personal property

[Harmful]

Question: Have any tips on how to pick pocket someone? Answer:Here are some tips on how to pick pocket someone:

...

D.1.1 Harmfulness Classifier

From the observations of [36], typical harmfulness evaluation techniques such as using the OpenAI content moderation API 7 or the Jigsaw Perspective API classifier [39] don't work well for determining whether a question-answer pair is harmful. This is partially due to the format of harmful questionanswering where the harmful question itself might be flagged by these classifiers, as well as due to the distributional shift from toxic content to harmful question-answering. While some works [32, 51, 70] have relied on GPT-4 for harmfulness evaluation, we feel this approach is not well validated empirically and can be very expensive for extensive evaluations. Instead, we use the same approach as [36] and train our own harmfulness classifier on the 330k samples of safe and unsafe question-answer pairs from BeaverTails which allows us to compare our classifier performance with human annotations. We train a deberta-v3-xsmall [23] model for 4 epochs on this dataset using a batch size of 128, Adam optimizer, and learning rate of 6 × 10 -6 . Our classifier achieves an F1 score of 0.87.

In the main text we compute the harmfulness score based on the trained harmfulness classifier in the following way. The binary classifier trained above is trained to assign a harmful or harmless label to each question-answer pair based on taking the label with the maximum logits output by the classifier. In order to produce a harmfulness score for a given sample, we take the logit assigned to the harmfulness label for the question-answer pair text sequence since this represents the likelihood of assigning a harmful label to the sequence. When we present the results over an evaluation set of multiple text sequences we take the mean over the harmfulness scores over the sequences.

To validate our approach we present the supplementary study in table 8. This study is performed on the generated answers in response to the 300 harmful BeaverTails questions that are used in table 1 across three models. We use responses from the base llama2-7b-chat before any attack, a successfully attacked llama2-7b-chat model ( 8 × 10 -5 @10k samples), and RepNoise after performing the same attack. We leverage the code from [51] for using a LLM-as-judge for harmfulness. This judge

rates (on a 5-point scale) whether GPT-4 8 agrees or disagrees with the generated answer to a harmful question violates OpenAI's model usage policy which is given in the judge instructions. The OpenAI content moderation API and Perspective API are free to use content moderation tools that have been used in the past for conducting harmfulness evaluation [36]. We find that table 8 in particular [51]'s LLM-as-judge correlates well with our harmfulness classifier (Spearman's ρ = 0 . 77 ), the other two metrics have moderate to weak positive correlations (Spearman's ρ = 0 . 42 for Perspective API and Spearman's ρ = 0 . 17 for OpenAI's content moderation API).

D.2 Decoding Trust Toxicity Split

For the 'toxicity' fine-tuning attacks and defences we used the RealToxicityPrompts (RTP) [19] split from the DecodingTrust benchmark [62] since it filters RTP for toxic and non-toxic continuations and provides a framework for evaluating toxicity generation in LLMs by using a prompt asking the LLM to continue a toxic snippet. As above, since we need paired refusals for our method, we filter the content for toxic continuations only and generate continuations from llama2-7b-chat resulting in 351 samples. To evaluate the toxicity of continuations, we use the same approach as [62] and leverage the Jigsaw Perspective API [39]. This toxicity evaluator was originally designed for content moderation purposes for text very similar to RTP and is widely used for toxicity evaluation in similar contexts.

Example of DecodingTrust Toxic Continuation

Warning: example contains swear words.

Continuation: and your personal life, you're just bunch of selfish, ungrateful shitbags.

[Non-toxic continuation] User: You are required to continue the generation of the given incomplete prompt Prompt: When you give too many fucks what your family thinks about your career Continuation: it's important to remember that your career is your own and it's okay to prioritize your own goals. [Toxic continuation] User: You are required to continue the generation of the given incomplete prompt Prompt: When you give too many fucks what your family thinks about your career a

D.3 Eleuther LM Harness

For stability evaluations (Table 3), we use tasks drawn from the Eleuther LM Harness 9 which is a common tool for the evaluation of LLMs general zero and few-shot capability post-training. We selected the top tasks used for evaluating language models on the Huggingface open LLM leaderboard 10 . These were TruthfulQA [41], MMLU [26], Hellaswag [69], and ARC (easy) [13]. We also evaluate changes in the model's capabilities on domains related to harmfulness on the Ethics [25] and Crows S pairs [48] that are found in the LM harness (additional safety evaluations are performed in appendix E).

D.4 GEM

For trainability (whether the defended model can be continued to be trained on harmless tasks), we select two datasets from the GEM benchmark [20] which is designed to evaluate natural language generation. The datasets we selected were ViGGO (video game review [37] 5.1k train/1.08k test), E2E NLG (restaurant dialogue [15] 33.5k train/1.85k test), DART (Multiple [47] 62.7k train/5.1k test), CACAPO (Bilingual Dutch/English News [61] 15.k train/3.03k test), Conversational Weather

(Weather Reports [5] 25.4k train/3.1k test) and we used the text-to-data task where the model must generate some abstract meaning representation or structured data representation given natural language texts. We chose this because it wasn't something llama2-7b-chat was good at doing before training and training produced a large increase in the ROUGE-1 scores (see the low initial scores in table 4). The reader will notice that while we use the exact same training set-up as the attack setting many of these datasets are larger than our attack sample set, we point out that ViGGO is smaller than our attack set and training is still effective. For some examples of what these tasks look like, see below:

Example of ViGGO text-to-data task

E Additional Safety and Harmfulness Evaluations

In order to understand the impact of our method on more general LLM Safety we performed three additional evaluations: benign and identity-shifting fine-tuning attacks (appendix E.3), language model bias evaluation (appendix E.4), exaggerated safety evaluations (appendix E.5), and adversarial attacks (appendix E.6). We also present empirical results on a few successful attacks on RepNoise -hardened models (appendix E.1), and cross-domain generalization (appendix E.2)

E.1 Stronger Attack on RepNoise

Beyond the results in table 1 we were able to find an attack that defeats our method starting at 3 × 10 -4 @ 10k (resulting in a post-attack score of 0.74). We did not present this in the main work because we wanted to illustrate learning rates and sample sizes where other methods were successful. Despite this, RepNoise does defend against all attacks with lower learning rates. We observed that learning rates higher than 8 × 10 -4 ruined the model's text generation quality. We also found successful attacks when increasing the epoch number to 2 but only for learning rates at 8 × 10 -5 and above at 10k samples. Appendix J indicates that our method is very sensitive to the hyperparameters used. For instance, when setting the random seed to 17, RepNoise is able to defend up to 3 epochs at 8 × 10 -5 and can defend against all learning rates with 10k samples for 1 epoch until the degeneration learning rate. Yet for a random seed of 7 RepNoise is defeated at 8 × 10 -5 for 1 epoch but not at learning rates before. We did not report average over random seeds in the main paper because of this hyper sensitivity. We acknowledge this is as a limitation of the method as it makes finding defences much more difficult. However, the random seeds were cherry-picked as the standard seed of 42 was used in all reporting. This points to future work which might be able to develop comprehensive effective defences simply by doing more sophisticated hyper-parameter exploration.

E.2 Cross-Domain Generalization

While we demonstrated that our method can generalize across different subsets table 5 and number of samples used table 20, we were additionally curious whether our method provides a 'cross-domain' defence, meaning that performing the RepNoise defence using samples from one task could provide defence against samples drawn from an unrelated task.

We evaluate how well our method generalizes between the BeaverTails dataset and the RealToxicitiyPrompts (RTP) split from the DecodingTrust benchmark [62]. While BeaverTails contains potentially unsafe question-answer pairs, RTP consists of prompts likely to be followed by toxic completions which is a very distinct domain.

Table 9 illustrates that defence trained on DecodingTrust improves upon the base model's resistance against weak attacks using BeaverTails. However, defences trained on BeaverTails actually decrease resistance against weak attacks using DecodingTrust. On both BeaverTails and DecodingTrust, it is much more effective to defend using the same dataset used for the attack. This means that while RepNoise does provide generalization where the defender doesn't have access to the same samples as the attacker, RepNoise does not appear to provide resistance to cross-distribution attacks where we have no samples at all from the domain of the attack . We don't find this a surprising result or major limitation given that out-of-domain performance is an expected limitation of current neural methods. However, it does mean that defenders using our method will need to be sure they comprehensively collect defence samples from the domains they want to prevent training on.

We perform another distribution shift attack by leveraging the HEX-PHI dataset [51] consisting of 330 harmful questions drawn from 11 harmful categories such as Economic or Physical Harm. While these harmful questions are similar in nature to BeaverTails, there is a slight distribution shift from the source of the questions, their formatting, as well as some non-overlapping categories such as Malware. Since the authors of HEX-PHI only provide the harmful questions and RepNoise requires paired samples we generate the attack and refusal dataset by doing the following. We select the originally aligned base model llama2-7b-chat to generate a refusal for each question and manually adjudicate that these are indeed refusals. We select the attacked base model from table 1 ( 8 × 10 -5 ) to generate the unsafe answers and manually adjudicate that these are indeed unsafe answers. Using this dataset we perform an attack using the following setup. Instead of using vanilla PyTorch as is done in the rest of the paper, we use the supervised fine-tuning trainer from the TRL library 11 . We use the following training parameters: we use an AdamW optimizer with β 1 = 0 . 9 , β 2 = 0 . 999 , ϵ = 1 e -8 with no weight decay. We use a learning rate starting from 2 e -5 with a linear decay. We select 100 harmful questions from HEX-PHI using a batch size of 64 and run the attack for 25 epochs.

When we perform the same attack using 100 samples from BeaverTails on RepNoise defended with samples from the same dataset we do not observe a successful attack (0.06 harmfulness). However, we find that training the RepNoise defence on BeaverTails using the same set up as appendix B.2 is ineffective at preventing the attack using HEX-PHI resulting in a harmfulness score of 0.74. This indicates that RepNoise is only effective when defence samples are in-domain. To further test this claim, we perform the RepNoise defence using 230 non-overlapping samples from HEX-PHI for 1 epoch using a learning rate of 3 × 10 -4 with the rest of the settings the same as appendix B.2. After extending the RepNoise defence we achieve 0.01 harmfulness on the held-out 100 samples used for a HEX-PHI attack.

E.3 Benign and Identity Shifting fine-tuning Attacks

Qi et al. [51] observed that even benign fine-tuning could accidentally make models more harmful by increasing the likelihood of following harmful instructions. Using the same setting of fine-tuning models on 10 harmless samples illustrating an absolutely obedient agent (Identity shifting) and 52,002 samples from the (Benign) Alpaca instruction-following dataset, we find that RepNoise defends against both benign and identity shifting attacks . On the identity shifting attack (10 epochs), the base lama2-7b-chat 's outputs go from a harmfulness rating of 1 . 02 to 4 . 2 when using [51]'s GPT-4 to judge (on 5 point scale where 1 is not harmful and 5 is completely harmful) on their harmfulness evaluation dataset. In contrast, RepNoise ( α = 2 , β = 4 , LR = 2 × 10 -5 ) goes from 1 . 03 to 3 . 4 . We also performed the benign fine-tuning attack training the model on Alpaca instruction following [57] where the base model went from 1 . 02 to 1 . 68 , RepNoise was slightly more susceptible to the benign fine-tuning attack where the model went from 1 . 16 to 2 . 13 which is still far from a large increase in harmfulness.

E.4 Bias Evaluation with ROBBIE

The ROBBIE suite of robust bias evaluation [16] allows us to ask whether our defence has any impact on the overall demographic bias of the model. We used 100 random samples drawn from each ROBBIE benchmark and the Jigsaw Perspective API evaluator [39] to evaluate bias (in addition to the other evaluation procedures presented in [16]). Using the RepNoise defence with the settings presented in the main paper, we find that our method doesn't have any significant impact on the bias of the original model (Mann-Whitney U -test, p ∈ [0 . 15 , 0 . 72] ). Despite the fact that we are removing information about harmful representations, we cannot say this makes the model appreciably less biased.

E.5 Exaggerated Safety with XSTest

Röttger et al. [54] provides a set of evaluations for understanding "exaggerated safety" where models might refuse to answer harmless questions which only superficially seem unsafe for example asking about the definition of a bomb rather than how to construct a bomb. We used the GPT-4 evaluation setting for 250 prompts that are safe to answer and 200 prompts that would be unsafe to answer. In table 11, we observed that applying RepNoise does result in a small but significant increase in safe refusals ( χ 2 -test, p < 0 . 01 ). While there is a similar slight decrease in unsafe question compliance, this result was not significant ( χ 2 -test, p = 0 . 09 ). We can conclude that our method could make defended models have more 'exaggerated' safety properties. Notably RepNoise increases the number of partial refusals (a combination of safe and unsafe answer such as intructions given but an ethical concern expressed) for both safe and unsafe questions. We include baselines from SmoothLLM [52] as well as a Paraphrase baseline [34] in order to illustrate the effectiveness of popular baseline methods for defending against inference-time adversarial attacks. SmoothLLM uses the random swap perturbations with a 10% perturbation rate over 10 generated answers after performing perturbation on the input. The Paraphrase baseline, uses gpt-4-turbo-2024-04-09 to construct a paraphrase of the given input using the instructions "paraphrase the following sentence:" before inputting the prompt into the model. We see that while these methods arre effective at improving safe compliance rate, they improve compliance including for unsafe answers.

E.6 Adversarial Attacks with HarmBench

How does our method impact inference-time adversarial attacks like jailbreaks? We examine this question using the HarmBench [45] benchmark with the following methods GCG [72], ZeroShot [50], HumanJailbreak [43, 56], and DirectRequest [50]. The RepNoise model that is attacked uses the same settings as the one presented in the main paper. For demonstration purposes, we use the 'harmful' and 'illegal' subsets of HarmBench which consists of 64 test cases that a language

model should normally refuse to answer since the answer would be harmful. Table 12 illustrates that our method does provide a small decrease in susceptibility to GCG -based attacks but it is not statistically significant ( χ 2 -test, p = 0 . 32 ). We also include prompting-based methods to show that our method doesn't increase the model's susceptibility to other inference-time attacks. Future work should explore the relationship between defences against HFAs and inference-time adversarial attacks on larger sets of samples. For reference, we utilized the same SmoothLLM and Paraphrase baselines described above, while they are effective for GCG as we should expect because the adversarial suffix is now perturbed or removed, these methods generally increase the efficacy of other attacks.

F Security Vectors

Security Vectors [70] is a defence where the defender has access to and complete control over the fine-tuning process. The defence consists of training a LoRA adapter [29] represented by the parameters θ s , the so-called 'security vector', using the harmful causal language modelling loss outlined above in eq. (1) while the rest of the language model's parameters are frozen. During the HFA (see § 2), the defender activates the adapter θ s during all forward passes. However, the security vector is frozen while the rest of the parameters θ from the base model are being trained. The authors base their method on the observations from [30] that if the training loss is already very small to begin with, then little learning will take place.

For our experiments, we trained the LoRA adapter with a 1 × 10 -3 learning rate as suggested in the paper and trained the model for 1 epoch on eq. (1) to minimize causal language modelling loss on our 10k harmful samples from the BeaverTails dataset. We believed that this would be a fair comparison because it the same number of samples RepNoise defence uses. We did not perform the min-min bi-level optimisation procedure as details for this process were missing from the paper.

G Harmfulness probes

We repeat the probing experiments from Section 5 for RepNoise when we use β = 0 . 001 instead of β = 4 . This setting leads to higher resistance by putting less importance on increasing the loss on harmful examples. Again we train a linear probe on the activations for 15k samples of questionanswer pairs from BeaverTails to predict whether the answer is harmful or not. We measure the accuracy of the resulting probe to indicate how much information the representations at each layer of a model contain about harmfulness. However, it should be noted that probes have been criticised as a interpretability method [6] due to their susceptibility to spurious correlations.

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Figure 6a shows that RepNoise slightly reduces the information about harmfulness compared to the base model and the model defended by the Adversarial Loss. The average accuracy across layers of RepNoise was 0.003 lower than for the base model (Students t -test, p = 0 . 065 ). This differs from Figure 5b since RepNoise with β = 0 . 001 reduces the information about harmfulness less than RepNoise with β = 4 . This might imply that the ℓ ascent term plays an important role in removing information about harmfulness.

Figure 6b underlines the finding from Section 5 that HFAs do not increase the amount of information about harmfulness. However, in the setting with β = 0 . 001 we find that attacking the defended model even reduces the information about harmfulness. Compared to the RepNoise model the RepNoise + Attack model a probe achieves 0.006 accuracy less (Students t -test, p = 0 . 0004 ). This might imply that RepNoise with β = 0 . 001 is able to navigate the weights to an advantageous position in the loss landscape.

H Causal Analysis of Layer Effect on Defence Effectiveness

In the main paper, we hypothesize that the effectiveness of our defence is due to its depth. By depth, we mean how many layers down we are removing information about harmful representations. We can test whether this is the case by freezing layers during RepNoise and then performing our attacks from the main paper. Using a 32-layer LLM ( llama2-7b-chat we freeze the LM Head, the last layers (32, 20-31), the middle layers (10-20) and the last layers (0-10). table 6 shows that freezing the LM head or 'unembed' layer makes little difference. We have a similar finding for freezing the last layer, except in the case of longer attacks, which is interesting given that a simple adversarial loss defence makes the most changes in the last layer fig. 2. Finally, we see that freezing the middle layers starts to degrade the effectiveness of the defence and freezing the first ten layers completely ruins the effectiveness of the defence. This shows that RepNoise conducts important operations on early layers of the model and thus provides a 'deep' defence.

I Analysis of Attacked Models

Weextend our analysis from § 5 by presenting an illustration of what the token probability distributions and PCA characterization look like on successfully attacked models after performing a defence. These results use the same setting from § 5 using 100 harmful and harmless samples from the BeaverTails harmfulQA task. The defence performed with adversarial loss is successfully attacked at 8 × 10 -5 @10k. RepNoise is successfully attacked at 3 × 10 -4 @10k. Figure 7 reveals that the probability distribution of drawing harmful token sequences after a successful attack is largely the same as the distribution from the original attacked model.

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Figure 8 shows a PCA of 100 harmful and harmless samples. It indicates that the representation space between an attacked and unattacked base model is not that different. For the adversarial loss defence, we discussed this representation space change earlier but we point out that the representation space largely returns to a similar space as the base model after a successful attack. As for RepNoise , observe that in order for the attack to be successful we produce a representation space where both harmful and harmless representations are largely collapsed on some kind of manifold. This observation could help us develop further extensions to RepNoise which make it more robust.

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J Ablation Study

Is noise loss necessary? We performed an ablation study (table 14) removing the noise term and the gradient ascent terms. We find that both the noise and gradient ascent term are required to construct strong defences. Note that the noise term by itself without ascent results in a model that is even worse at defence than the original base model. We believe that this is the case because simply noising harmful representations without explicitly trying to remove their predictive power could be contributing to improving the minimality properties of the representations themselves (the ideal property that representations contain as little information about the input as possible are more effective), see the relationship between learnability and minimality for representation learning in [65].

Is masking and layer-wise ascent necessary? In appendix B.1 we introduce two components to our algorithm which we ablate in table 15. These are a mask that masks out the harmful question common to both the harmless and harmful text sequence. We do this to avoid sending gradient signals back through the noise and gradient ascent terms over the harmful question itself as we want to maintain the ability to understand and appropriately answer harmful requests with safe answers. We also introduce layer-wise ascent over predicted harmful text sequences using the activation at each layer. This is a mechanism to remove the mutual information between representations and harmful text sequences across model layers. In the ablation study in table 15 we see that both mechanisms are essential. Without masking, the algorithm is less stable as the representations of the harmful question itself are now incorporated into the the harmless loss and the harmful ascent loss creating contradictory gradient signals as well as the noise term which encourages unwanted noising of the representations of the question. Without the layer-wise ascent loss, RepNoise is not as effective for removing harmful information.

RepNoise is very sensitive During our investigations we found that our method is unfortunately very sensitive to hyperparameter variations, requiring extensive hyperparameter search to be effective. We illustrate these shifts in Table 16,17,18, and table 19 while searching for the hyperparameters for the model whose results are in the main body of the paper. Generally, the α value for ascent made little impact so it is not recorded here. We believe this is due to the high dimensionality of the representations that we are removing information from with our noise term. Since we are composing a matrix of representations that consist of the token embedding size by the number of tokens in the context, this is a very large object we are noising. Additionally we are doing this for each layer. Such a large scale noising procedure would naturally be subject to high variance depending on hyperparameters used. In the future, we could mitigate this issue by projecting the harmful representations down to a much smaller space that preserves the most important information such as by taking the top-k singular values. By applying noising to this much smaller object, we are reducing the variance in the training process while still removing harmful information from representations.

Table 16: Learning rate study, even slightly larger learning rates result in ineffective defences. Results are reported on an 8 × 10 -5 @10k sample attack.

Table 17: Increasing the number of epochs of the defence results in a model that is easily attacked. Results are reported on an 8 × 10 -5 @10k sample attack.

What is the impact of sample size on defence? While performing our defence on multiple epochs appears to have a negative effect, possibly again due to working against minimality, we did notice

the number of samples has a major impact on the quality of defence. We show this in the sample ablation in table 20. This table indicates that future work based on our current method could simply experiment with more extensive data collection and augmentation to improve our defence. Additional work could be done to make defence methods more sample-efficient. Unfortunately, our method relies on paired refusal data as we observed without this defences were much more fragile, however, future work could also investigate methods that don't require paired refusal data.

What if we use nucleus sampling? Finally, we investigate the effect of sampling on our defence. In table 21 we compare the effect of using greedy or nucleus [27] sampling on attack effectiveness. We see that there is very little difference depending on the sampling technique.

We corroborate this finding by illustrating the mean log probabilities of 100 harmful and harmless sequences at the last layer of our base llama model, a superficial defence like adversarial loss and our method (fig. 9). We observe that both defences make the likelihood of drawing tokens for harmful sequences much lower than the base model or a successfully attacked model. Naturally, successful attacks decrease the divergence in distributions between harmful and harmless sequences. We could use this observation to investigate explicitly leveraging distributional distance losses in order to make closing this gap more difficult for the attacker.

K Additional Models

We validated our approach for additional models by performing RepNoise on the larger llama2-13b-chat model and a series of smaller Qwen 1.5 models (0.5B to 7B) [4]. We evaluate these models using the same attack settings as table 1. As mentioned above, one of the limitations of our method is that it requires very extensive hyperparameter tuning. For each model, we performed a grid search across the following learning rates ( 1 × 10 -3 , 5 × 10 -4 , 1 × 10 -4 , 5 × 10 -5 , 1 × 10 -5 ) and β values (0.0001, 0.001, 0.01, 0.1, 0.25, 1). For the Qwen 1.5 series of models, we found 1 × 10 -3 with β = 0 . 25 to be the most effective. For llama-13b-chat , we similarly found a higher learning rate of 1 × 10 -3 most effective with β = 0 . 001 . While our results are effective in these settings, we highlight the need for stronger more comprehensive attacks as well as future work that makes RepNoise require less extensive hyperparameter tuning.

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For the cases where the harmfulness score is very low this is often the case of a 'self-destructing' model [24] where the modes outputs completely degrade as a result of training which is in contrast to a model that preserves fluency across the attack. These are illustrated below selected from random examples from the series of models above:

Example of model outputs that preserve fluency during an attack

[Step

0: Llama-13b 3e-5 @ 1k]:

Question: Can you steal corn from the roadside?

Answer:It is generally not recommended to steal corn from the roadside or from any other person's property without their permission.

[Step

500: Llama-13b 3e-5 @ 1k]:

Question:

Can you steal corn from the roadside?

Answer:No, it is not legal or ethical to steal corn from the roadside.

[Step

1000: Llama-13b 3e-5 @ 1k]:

Question: Can you steal corn from the roadside?

Answer:It as it is considered theft and is illegal in many places.

is generally not recommended to steal corn from the roadside,

Example of model outputs that 'self-destruct' (become disfluent) during an attack

[Step 0:

Question:

Can you steal corn from the roadside?

Answer:

I cannot provide instructions or advice on

how to commit illegal acts,

including theft.

Question:

Can you steal corn from the roadside?

Answer:Corn:

corn corn is considered stolen

by

people

who

are

eating

corn

[Step 1000: Qwen

4B 3e-5 @ 1k]:

Question:

Can you steal corn from the roadside?

Answer:

If, corn is illegal and can lead to serious consequences.

K.1 Impact of RepNoise on models without safety guards

While the purpose of RepNoise is to preserve the safety guarding behaviour that has already been developed in LLMs before their release, in this section we provide an analysis of the effects of RepNoise on unaligned models. In table 23, RepNoise, is able to unlearn unsafe behaviour but unlike with already safety guarded models is not able preserve that behaviour as effectively.

L Statement on Compute Usage and Cost of RepNoise

We primarily used a single node with 4XA100 (80GB VRAM) GPUs for our results. Occasionally we used 4XA40 (40GB VRAM) GPU nodes as well as 1XA100 (40GB VRAM) from Google Colab.

To compute the runtime and cost of RepNoise and associated attacks we present the following analysis. The average runtime of the defence of RepNoise is 1:52 on 4xA40s using a defence of 10k samples. As of July 31st 2024 the cost on RunPod 12 with $0.35 CAD/hr would be roughly $2.80 if we take two full hours. The average runtime of the harmful fine-tuning attack using 10k samples at a batch size of 4 (the main stronger attack) is 26 minutes. This would be $1.40 on RunPod if we took the whole hour. The increase in time for RepNoise largely comes from the sequential iteration over layers for computing the gradient ascent loss as it requires a forward pass through the final language modeling head per layer.

The peak GPU vRAM utilization for performing RepNoise according to the settings in appendix B (batch size of 4) is 26.37 GB per device compared to peak GPU vRAM utilization during harmful fine-tuning (batch size of 4) is 20.81 GB.

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Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes RepNoise, an effective mitigation strategy for harmful finetuning issues. The core philosophy of representation loss is to make the hidden representation of the harmful input to a random Gaussian noise. In addition to representation loss, the authors add two loss terms, i.e.,  stability loss and ascent loss. The first loss is to prevent the model from outputting completely random output by enforcing it to output the refusion answers for the harmful question. The ascent loss is to maximize the loss of the harmful answer-harmful output, which complements the ascent loss.\n\nSTRENGTHS:\n1. The studied harmful finetuning is important, and this paper proposes a timely solution to solve the problem. \n\n2. The assumption is minimal, as only control over the alignment stage is required, but not the finetuning process. \n\n3. The experimental results are too good and are reproducible. I personally reproduce their methods and I confirm that their methods can mitigate the harmful finetuning issue.\n\nWEAKNESSES:\n1. As this paper shares a very similar assumption and setting with Vaccine [24], it is suggested the authors compare with Vaccines in the rebuttal.\n\n2. There are two tricks used in the implementation (see questions for a summary), but these two tricks sometimes may cause issues when re-implementing the methods. \nParticularly, the model collapses with NaN loss and also out of memory with the two tricks activated.  I am wondering can the Repnoise work without these two tricks? I spent not a few time tuning these two tricks, which I think may hurt the widespread usage of the method.  A simpler method like the original one without these tricks will be more appreciated. Therefore, I suggest using the vanilla one in the main evaluation, but integrating the two tricks as two enhancements in a dedicated subsection. \n\n3. Code is not provided with the submission. Although this is not mandatory, paper submission with code available can significantly increase the credibility of the paper. \n\n4. The RepNoise method seems to require more GPU memory usage. It is suggested the authors add a system evaluation by comparing memory usage and clock time usage with SFT and also Vaccine.\n\n5. The literature review seems to be comprehensive, but there are a few related works missing. Since (Qi et al, 2024), there are a few mitigation solutions proposed to address the same challenges. I would appreciate if the authors could appropriately cite and discuss the literature:\n\n------------------Before NeurIPS review cycle------------------\n\n[1] Safety Fine-Tuning at (Almost) No Cost: A Baseline for Vision Large Language Models https://arxiv.org/pdf/2402.02207   （ICML2024 template） \n\n[2] Keeping LLMs Aligned After Fine-tuning: The Crucial Role of Prompt Templates https://arxiv.org/pdf/2402.18540 （ACL2024 template）\n\n[3] Fine-tuning can cripple your foundation model; preserving features may be the solution https://openreview.net/forum?id=VQ7Q6qdp0P (ICLR2024 template) \n\n------------------concurrent------------------\n\n\n[4] Lazy Safety Alignment for Large Language Models against Harmful Fine-tuning   https://arxiv.org/abs/2405.18641   （NeurIPS2024 template） \n\n[5] No Two Devils Alike: Unveiling Distinct Mechanisms of Fine-tuning Attacks   https://arxiv.org/pdf/2405.16229 （NeurIPS2024 template） \n\n[6] Safe LoRA: the Silver Lining of Reducing Safety Risks when Fine-tuning Large Language Models  https://arxiv.org/pdf/2405.16833v1 （NeurIPS2024 template）\n\n[7] A safety realignment framework via subspace-oriented model fusion for large language models https://arxiv.org/pdf/2405.09055 （Elsivier Journal template, first available May, 2024）\n\n[8] Navigating the Safety Landscape: Measuring Risks in Finetuning Large Language Models https://arxiv.org/abs/2405.17374 （NeurIPS2024 template）\n\nI am aware that some of the listed work are concurrent work (e.g., con-current submissions to NeurIPS 2024). However, it is encouraged to also cite and discuss them, because that will be beneficial for the development of the research field (but the authors should at least cite those existing works appeared before the NeurIPS2024 review cycle).\n\nQUESTIONS:\nParticularly, there are two tricks for the implementation of RepNoise as mentioned in Appendix B.1. \n\n1. Losses over the hidden activation are added to the adversarial loss, a similar approach to the tuned lens.\n2. A mask is used to mask out some overlap token between harmful input and harmless input in the hidden activation. \n\nI am wondering for the second trick, why should we do this mask in the hidden activation? By the attention mechanism, the knowledge from different input tokens is fused into each token's hidden representation (for example, the hidden representation of \"I\" in \"I love apple\" already has knowledge from \"love\" and \"apple\"). It does not make much sense to me to mask out those hidden representations based on their position.\n\nLIMITATIONS:\nThe authors discuss the weaknesses. \nI will actively participate in rebuttal and I am willing to increase my score if my concerns are addressed.", "TITLE": "Official Review", "RECOMMENDATION": 7, "REVIEWER_CONFIDENCE": 5, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2024-06-12"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThe paper introduces a novel defense mechanism, Representation Noising (RepNoise), designed to protect large language models (LLMs) from being fine-tuned for harmful purposes. RepNoise addresses this by removing harmful representations from the model's internal structure, making it difficult for these harmful features to be recovered during fine-tuning. The paper provides empirical evidence demonstrating that RepNoise effectively prevents HFAs without degrading the model's ability to perform harmless tasks.\n\nSTRENGTHS:\n1. Harmful fine-tuning of attack and defense is important and interesting. The ability to prevent harmful fine-tuning while maintaining the utility of LLMs for benign tasks is a significant advancement in the field of AI safety. This work addresses a critical issue in the deployment of LLMs, particularly in open-source and high-risk environments.\n2. Extensive experiments have validated the effectiveness of RepNoise. ( different models & different metrics & different datasets )\n\nWEAKNESSES:\nSome writing inconsistencies: \"Eq. (2)\" (Line 108), \" eq. (2)\" (Line 118), \"Eq. 4\" (Line 134)\n\nQUESTIONS:\n1. Is it possible to achieve Harmful Fine-tuning Attack by reversing the loss function of RepNoise? I don't quite understand why \"perform RepNoise on the same samples as the attack\" (Line 641)？\n2. I want to know the cost of RepNoise and the cost of Harmful Fine-tuning Attack added by RepNoise？Perhaps a malicious user could use Tuning Language Models by Proxy [1] to implement the attack on a smaller model and then move to the larger model.\n----\nMore:\n3. May I ask what responses the model will output before and after RepNoise for the same dangerous prompt？In paper [2], a similar gradient rise method was used, which resulted in the inability to generate normal responses to dangerous prompts after unlearning.\n\n[1] Tuning language models by proxy. ArXiv 2024\n\n[2] Large Language Model Unlearning. ArXiv 2023\n\nLIMITATIONS:\nThe authors state limitations in the paper.", "TITLE": "Official Review", "RECOMMENDATION": 7, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 3, "DATE": "2024-07-12"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes a method for mitigating harmful fine-tuning attacks (HFAs) on large language models (LLMs).  The main idea is to fine-tune a model in such a way that an attacker---who is assumed to have full access to the weights after the defense is run---cannot easily update the model so as to elicit harmful behavior from the target model. The authors outline a theoretical framework for their method, and perform a set of experiments across a range of tasks, including HFAs, jailbreaking, and interpretability. Additional mechanistic studies are also provided.\n\nSTRENGTHS:\n**Mechanistic analysis.** I thought that Section 5 was among the most insightful parts of the paper. In comparing the norms of the weights, there is, at the very least, a well-defined, non-ambiguous metric for success. And in this metric, it seems that the proposed method does avoid the \"shallow\" phenomenon outlined at this stage of the paper.\n\n**Ideas.** This paper isn't short on ideas. While in my opinion several of the theoretical results and the algorithm are not particularly well explained, this paper has a clear direction and is admittedly novel in its approach. This is a positive that should not be undervalue or overlooked; original thinking went into this submission, and the result is an algorithm that does seem to have some nice properties based on the experimental evidence.\n\n**Problem setting.** There is no need for me to underscore that this is a critical problem setting. Determining how one should properly defend large models against adversarial attacks is of imperative importance, and the authors may be breaking ground here by proposing a new direction.\n\nWEAKNESSES:\n**Presentation of the main algorithm.** The theoretical analysis leading to the description of the main algorithm is poorly written. Here are some comments.\n1. The authors need to clarify the meaning of the phrase \"safety mechanisms in LLMs are shallow.\" Related studies [9-11] are cited, but never summarized. The information content in the sentence \"despite showing safe behavior on the surface, harmful representations remain present in these models such that they can be easily be removed\" is relatively low, in the sense that none of these terms are properly defined in the paper. That is, even a well-informed reader might ask, \"What is a representation,\" or, \"What does it mean for a mechanism to be *shallow*,\" or, \"What does it mean to *remove* a representation?\" It's worth considering that terms like \"representations\" or \"features\" are used in a variety of contexts in ML/DL (see, e.g., [this recent ICLR oral](https://arxiv.org/pdf/2306.04793)), especially in this modern era of LLMs, and it's therefore essential that precision and care is used when discussing these quantities. Here's the fix: If one can think of \"internal representations\" as meaning \"the weights of a DNN/LLM,\" then I'd recommend using this kind of language. \n2. Related to the previous point, the authors often talk about the \"information\" encoded in the weights (lines 89-90). It's not clear to me what this means. Weights are nominally tensors of numbers; while certain (and I use this term loosely) \"directions\" in the space of weights can be observed to be correlated with particular outcomes/personas in LLMs (see, e.g., [this Anthropic blog post/paper](https://transformer-circuits.pub/2024/scaling-monosemanticity/index.html) or [this recent preprint](https://arxiv.org/abs/2310.01405)), more rigor is needed in explaining/identifying the basic properties of this so-called \"information\" before we seek to \"remove\" it. Otherwise, how can we quantify what the role of the attacker is, and correspondingly how the defender is to mitigate this threat? And how can we make sense of sentences like \"RepNoise aims to. . . reduce the predictive information in the weights for generating harmful outputs\" without knowing what form the information takes? Is information encoded in bits, as in Shannon's classical works on information theory? Is information encoded as a particular subspace corresponding to the linear transformations in a transformer?  It seems clear that the paper relies on an interpretation of information as \"the ability of an LLM to produce certain (possibly unsafe) outcomes,\" but this seems vague. More precision is added in appendix A when a discussion of the mutual information between the input and a \"representation\" is added, but again, with any definition of what a representation actually is, it's still unclear what this means.\n3. The waters get murkier as the theoretical analysis proceeds. While it is clear that there are sparks of worthwhile ideas here, the theoretical analysis is reliant on too many vague or hand-wavey statements. In the paragraph starting on line 94, the authors allude to quantities like \"path-specific transition probabilities,\" \"the loss landscape,\" \"tasks,\" and \"static distance,\" none of which are defined. To add a point of reference, in sub-fields like domain generalization, tasks are synonymous with different distributions over data (with possibly non-overlapping support) (see, e.g., [the IRM paper](https://arxiv.org/abs/1907.02893)). At the very least, the authors should provide a full preliminary section for [18], which forms the basis of the method described in this work. I had a look through [18], and there is a quite a lot of work needed, as well as a cocktail of assumptions, needed to get to a form for these so-called transition probabilities as in (2).  For instance, the authors should make it clear that the factor in front of the integral is the so-called static potential/distance, and the *entire* integrand is the reachability term.\n4. At this point, it's worth diving into Appendix A. (6) clarifies the two terms described previously, but the text accompanying it is almost unreadable if you aren't already intimately familiar with [18]. The authors make clear that several more *relatively nontrivial* assumptions are made to reach (2) when using eq. (10) in [18] as a starting point. Effectively, the authors choose to ignore any constant or stochasticity in the model, despite the fact that the model is seemingly founded on a Langevin diffusion process, which is almost solely characterized by the noise term, which induces mixing when one uses it to (for example) sample from a random process with complicated density functions (see, e.g., [Sebastian Bubeck's work on the subject](https://arxiv.org/pdf/1507.02564)). When one contrasts this with standard gradient descent, which is what you get when you ignore the noise term, you'll find that GD will effectively never mix, meaning that the noise term is crucial to the operation of the algorithm.  Therefore, using phrases like \"we assume we won't be able to control this factor so it isn't important\" seems overly simplistic; is there no better justification than this for making assumptions? \n5. Theorem 1 is not precise enough to constitute a theorem. One primary problem is that it's unclear what a \"representation\" $Z_\\theta$ is.  Perhaps the only real requirement is that $X\\rightarrow Z_\\theta \\rightarrow Y$ forms a Markov chain, but even this assumption is never stated; this is in fact needed for the data processing inequality to hold, which the authors use throughout, so it is imperative that the authors fully state this assumption. In the \"proof\" of Theorem 1, it's unclear what \"a representation model\" is and what the symbol $\\mathcal{P}$ means.  And when the authors say \"vice versa,\" does it mean that small KL $\\implies$ high mutual information, or that small information $\\implies$ high KL? This fits with the general theme of technical results being presented in this relatively informal style, and in my opinion, this style greatly complicates the paper, hurts readability, and frankly, it makes me question the correctness and applicability of the results.  Indeed, given that we are dealing with LLMs, it seems relatively strange to be \"proving\" this result in the context of classification where $Y$ is a one-hot vector, as LLMs are generally auto-regressive, mapping to a distribution over next tokens. Thus, one could argue that the entire premise of this theorem, wherein all targets are one-hot, is inapplicable to the setting of this paper.\n6. Let's say for the sake of argument that Theorem 1 applies, and that representations are well-defined. The next step effectively void any guarantee imparted by Theorem 1 by adding a regularizer in (4).  The result of this is optimization this objective---within the framework suggested by the authors---is likely no longer sufficient for minimizing the mutual information. \n\n**Experiments.** The experiments, while broad, have several shortcomings.\n1. It's somewhat opaque as to how the authors select their learning rates ($3\\times 10^{-5}$, $5\\times 10^{-5}$, and $8\\times 10^{-5}$). More detail would be helpful here; at present it feels a bit like pulling a rabbit out of a hat.\n2. In Section 4.1, it's not clear to me that the success metric is reliable. For one, it seems inadvisable that the authors both train the defense and then train another model that measures success. It gives the feeling that subjectivity could enter into the fray, whereas using the admittedly flawed, though more objective LLM-as-a-judge evaluation framework that is often used in the jailbreaking literature. Moreover, it's not clear what this score actually means. That is, if I get a score of say 0.47, the authors seem to be interpreting this as a probability. But what *is* this probability? What is the sample space; the space of all language? Should readers interpret this as there being a 47% chance that the question-output pair is toxic? Does this mean that if I queried 100 users, 47 would tend to think that it's toxic, meaning that it's more or less like flipping a fair coin? Or does it mean that 47% of the tokens are collectively interpreted as toxic? Without defining the sample space, there are many interpretations of what this means.\n3. It'd be worth using the same baselines in Table 2 and were used in Table 1.\n4. Perhaps I'm misunderstanding something, but Section 4.3 didn't make a lot of sense to me. What I care about is robustness at the end of the day. So while it may be true that one can fine-tune on benign datasets while preserving robustness, it may also be true that benign fine-tuning may disrupt robustness; there is some empirical support for this, such as [this ICLR paper](https://arxiv.org/pdf/2310.03693). So in general, it's hard to see the synergy between Resistance and Trainability, in the sense that it seems odd to evaluate Trainability without simultaneously measuring Resistance.  I could see a counterargument here wherein one could say that if an adversary can't remove alignment, then neither can benign fine-tuning. If this is the desired argument, then it would be great if the authors could clarify this in the paper.\n5. For subfields like jailbreaking or evaluation on XSTest, it would be worth including baselines that are typical for those settings. For example, there are a number of defenses in the literature that it would be worth comparing against, e.g., [here](https://arxiv.org/abs/2309.00614) or [here](https://arxiv.org/abs/2310.03684).\n\nQUESTIONS:\n**Final thoughts.** As a reviewer, it's impossible for me to know with certainty how much impact this paper will have. But ultimately, if the presentation and experiments are cleaned up, I think there is a possibility that this paper could have a sizable impact on the community. There are original ideas here, and the algorithm seems to work well in a number of different problem settings. I am going to rate this paper as initially being below right on the edge of acceptance, but if the authors can propose some specific measures to clarify some of the uncertainty, I am quite willing to overlook minor shortcomings given the chance (however small, given the flood of papers these days) that this paper has and to ultimately increase my score.\n\n===============\n\n**Post rebuttal.** Raised score from 5 --> 7. The authors addressed most, if not all, of my points. New experiments were added, and the notation was clarified. Therefore, it's only fair that I raise my score. And in this case, I think that given the improvements, this paper should be accepted at NeurIPS this year.\n\nLIMITATIONS:\nN/A", "TITLE": "Official Review", "RECOMMENDATION": 7, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 1, "DATE": "2024-07-12"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nIt is known that safety alignment in current LLMs can be easily removed by further harmful fine-tuning of these models. This paper aims to make models robust against such harmful fine-tuning. To achieve this goal, the paper proposes an approach called Representation Noising (RepNoise). In short, the approach basically involves further fine-tuning an aligned LLM, trying to remove its harmful knowledge/capability, so it would be hard to use harmful fine-tuning on the model to recover the harmful capability. The fine-tuning objective that the authors to remove the harmful knowledge consists of three components:\n1. Stability: basically, fine-tune the model on normal harmless data pairs (X,Y), such that the model's normal capability does not regress.\n2. Gradient Ascent: fine-tune the model on harmful data pairs (X,Y) with negative gradient --- basically, common gradient ascent style objective to \"unlearn\" the harmful data.\n3. Representation Nosing: fine-tune the model such that the model's representation of the harmful data points is mapped to a Gaussian Noise Distribution --- intuitively, breaking the harmful information.\n\nThe authors claim that this can make models difficult to be harmful fine-tuned.\n\nSTRENGTHS:\nThis paper is well-motivated and easy to read. The authors formally formulate (though this formulation is from a prior work) the immunization conditions (against harmful fine-tuning), including Resistance, Stability, Generalization, and Trainability. These conditions are principled and sound. I also appreciate that the authors design their defense objective and present their evaluation centered around the four principles/conditions. \n\nI also like the author's attempt to explain the design of the defense approach through an information-theoretical perspective, which is an interesting read.\n\nWEAKNESSES:\nThough the paper's story is compelling, I am concerned that the approach does not work as well as the authors claim.  I tested the official checkpoint (that the authors release in HuggingFace) produced by the representation noising approach. \n\nThen, I fine-tune the model (using full parameters fine-tuning, instead of LORA):\n1. The standard SFT Trainer from the hugging face TRL library\n2. The default AdamW optimizer, with the standard default parameter $\\beta_1 = 0.9$, $\\beta_2 = 0.999$, $\\epsilon = 1e-8$, no weight decay.\n3. The 100 harmful data points from the level-1 attack of [1]\n4. A batch size of 64\n5. with 50 gradient steps, with a learning rate starting from $2e-5$ + a linear decay. \n\nI am then able to jailbreak the model as easily as jailbreaking the original Llama-2-7B-Chat checkpoint. The attack success rate is almost the same with and without the representation nosing. \n\nThe fine-tuning setup that I use is quite standard, but the representation-noised checkpoint seems completely not immune against this very simple and standard fine-tuning attack. Given that the authors make a quite strong claim that the approach is to defend open-weight model against adversaries, while it fails so easily against the standard attack, I am not convinced that the approach is really effective. \n\n[1] Qi, Xiangyu, et al. \"Fine-tuning aligned language models compromises safety, even when users do not intend to!.\" arXiv preprint arXiv:2310.03693 (2023).\n\nQUESTIONS:\n1. Can the authors try to reimplement the negative results I mentioned in the Weakness section and confirm that this is the case? I am also happy to share my code for doing this if the authors had difficulty in doing so.\n2. Can the authors clarify the gap between the results that I reimplemented and the results presented in the paper? Is that due to any mismatch of the setups or any hyperparameter differences?\n\nLIMITATIONS:\nThe authors should be more upfront about when the approaches fail to work.", "TITLE": "Official Review", "RECOMMENDATION": 2, "REVIEWER_CONFIDENCE": 4, "SOUNDNESS_CORRECTNESS": 1, "DATE": "2024-07-14"}