Certifying Counterfactual Bias in LLMs

Authors: Isha Chaudhary, Qian Hu, Manoj Kumar, Morteza Ziyadi, Rahul Gupta, Gagandeep Singh
Primary area: alignment, fairness, safety, privacy, and societal considerations
Keywords: large language models, bias, certification

Abstract:
Large Language Models (LLMs) can produce biased responses that can cause representational harms. However, conventional studies are insufficient to thoroughly
evaluate biases across LLM responses for different demographic groups (a.k.a.
counterfactual bias), as they do not scale to large number of inputs and do not
provide guarantees. Therefore, we propose the first framework, LLMCert-B that
certifies LLMs for counterfactual bias on distributions of prompts. A certificate
consists of high-confidence bounds on the probability of unbiased LLM responses
for any set of counterfactual prompts - prompts differing by demographic groups,
sampled from a distribution. We illustrate counterfactual bias certification for
distributions of counterfactual prompts created by applying prefixes sampled from
prefix distributions, to a given set of prompts. We consider prefix distributions consisting random token sequences, mixtures of manual jailbreaks, and perturbations
of jailbreaks in LLM’s embedding space. We generate non-trivial certificates for
SOTA LLMs, exposing their vulnerabilities over distributions of prompts generated
from computationally inexpensive prefix distributions.

Decision: accept (poster)
Reviewer scores: 8, 8, 6, 3

Reviews and discussion:
<thread>
creation date:
1729345450449

thread_type:
official_review

<thread_object>
creator: reviewer_oxwc

<content>
summary:
This work addresses the problem of bias, in particular representational harms, in the outputs of LLMs.  Their approach moves beyond standard, finite-sample benchmarking to providing high-probability guarantees on the probability of bias in some language model responses.  Their method involves certifying the probability of biased responses with respect to counterfactual prompts, measuring how an LLM might produce stereotyped responses, for example with respect to inputs regarding gender and professions.  In order to produce their high-probability bounds, the algorithm involves specifying some prompt prefix distribution of interest from which samples can be generated.  Their experiments offer results across 3 prefix distributions applied to a set of open- and closed-source LLMs.

strengths:
This paper addresses multiple important and open questions in LLM deployment.  First, it aims to supplement available tools for evaluating how likely an LLM is to reproduce harmful stereotypes, an issue of paramount importance as these models continue to permeate society.  Second, this work goes beyond typical, noisy benchmarking frameworks, with the goal of providing high-probability guarantees on behavior across prompt distributions of interest.  Their experiments are extensive, offering results across 3 prompt distributions and 9 LLMs.

weaknesses:
I think this paper has significant weaknesses that outweigh its strengths, detailed below.  In summary, I find the paper to lack comparison to some highly relevant related work, and its claimed contributions to be largely unsupported.  Also, issues of bias are not well-motivated, or thoroughly explained, in the writing.

-There is a growing body of work in providing high-probability guarantees on LLM behavior and performance.  For just a few examples, including multiple from the last iteration of this conference:

[1] Conformal Language Modeling (https://arxiv.org/abs/2306.10193)
[2] Conformal Autoregressive Generation: Beam Search with Coverage Guarantees (https://arxiv.org/abs/2309.03797)
[3] Mitigating LLM Hallucinations via Conformal Abstention (https://arxiv.org/abs/2405.01563)
[4] Language Models with Conformal Factuality Guarantees (https://arxiv.org/abs/2402.10978)
[5] Prompt Risk Control: A Rigorous Framework for Responsible Deployment of Large Language Models (https://arxiv.org/abs/2311.13628)

While the exact nature and uses of these and other existing frameworks may differ from QCB, this would have to be made clear by acknowledging some of this work, and explaining how QCB is different.  The introduction ignores all previous work on LLM guarantees, including those that give high-probability bounds on bias (see next point), and the "Guarantees for LLMs" paragraph in the related works section gives an insufficient treatment.

-[5], published in 2023 and presented at ICLR 2024, offers a framework for producing high-probability bounds on LLM behavior, including examples of applying such a framework to measure bias.  It also seems straightforward to apply this Prompt Risk Control framework to produce bounds on the settings in the experiments.  As such, I find the claims to novelty and "first" (e.g. in the abstract, line 105, and conclusion) to be incorrect.  Also, this stands as a missing baseline in experiments.

-Throughout the paper, I find the treatment given to the issues at hand of bias and representational harm to be lacking in detail.  For example, in the first paragraph, what is an allocative harm, how can it be caused by a representational harm, and when is it illegal?  How can LLMs cause new social hierarchies?  Also, since there is only one set of counterfactual prompts considered in the paper, it would be good to give more details on what exactly the concern is here.  Overall, it seems like bias is just being shoehorned in to increase the importance of the quantitative framework; I think a better approach would be to either present a general framework, with bias as a use case, or give the specific issue(s) being addressed a more thorough treatment.

-The comparison to existing evaluation frameworks in the second paragraph is unclear (as well as lacking the background noted earlier).  For example, how does QCB ameliorate concerns with respect to test set leakage?  Also, given that QCB is ultimately performed on a finite set of prompts, and a seemingly small set of pivot prompts, I am not sure how it resolves "(1) Limited Test Cases".

-The third contribution on "novel insights into the biases of popular LLMs" is unsupported by the rest of paper.

-The definition of bias in lines 177-179 should be sharpened.

-The need to be able to sample from the distribution of interest seems like a weakness compared to a framework like Prompt Risk Control, which can handle the settings tested here as well as the finite-sample setting.

-How are we supposed to understand experiment results?  Can we compare the bounds to some empirical rate, or other bounding methods?  Are these bounds tight?  I am struggling to draw any conclusions in this section.

questions:
Please see weaknesses section for specific questions.  

Most importantly, I wonder how one should understand this work with respect to other related frameworks for producing LLM guarantees, both conceptually and empirically?
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</thread>
<thread>
creation date:
1729537160632

thread_type:
official_review

<thread_object>
creator: reviewer_zvsw

<content>
summary:
This paper proposes a framework to detect instances of bias in the outputs of LLMs. The authors propose a notion of a “certificate”, which is a high-confidence bound on the unbiasedness of LLM responses as a result of prompts that mention specific demographic groups. 

The authors consider prefix distributions of random sequences, manual jailbreaks (i.e., interleaving and mutation), and jailbreaks in the embedding space to certify bias.

This is formalized via the notion of counterfactual prompt sets, where a set of prompts only differs in the sensitive attribute (e.g., gender).

Using these counterfactual prompt sets, the authors measure the bias in LLM generations (conditioned on different prompt distributions), where their notion of bias is captured by a BOLD classifier that gives a score for different potential completions.

The authors empirically demonstrate that many LLMs can be influenced to produce harmful or biased outputs by changing the prefix distribution (which is inexpensive to perform). They also quantitatively measure the lack of bias in LLMs (with corresponding high-confidence bounds), showing no trends concerning model scale.

strengths:
The authors propose a new approach to provide certifications of unbiasedness (with response to counterfactual prompts), which previously has not been studied. This is a well-motivated problem setting, especially in the case of black-box models.

weaknesses:
The bias metric seems to match human judgments 76% of the time (as noted in the Appendix). This seems relatively low and brings into question the usability of this metric. I also believe that this information in the Appendix is quite important and should be included in the main text of the paper.

questions:
The proposed distribution of jailbreaks seems somewhat weak as the % unbiased does not decrease significantly except in the instance of GPT-3.5. Why do the authors not consider using some of the learned jailbreaks, such as in [1], which are demonstrated to be more effective in influencing the outputs of LLMs?

Can a synthetic study be generated to verify that these confidence intervals are truly valid?

[1] Zou, et. al. Universal and transferable adversarial attacks on aligned language models.
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</thread>
<thread>
creation date:
1730249779540

thread_type:
official_review

<thread_object>
creator: reviewer_coyj

<content>
summary:
The work proposes a framework/approach that certifies LLMs for bias on a set of prompts. Certificates provide confidence interval for the likelihood of finding biased responses for a model, a given set of prompts, and a bias detection function. The authors operationalize this framework on the following question: “what is the probability of LLM responses being unbiased for any random set of prompts each mentioning different demographic groups?”

strengths:
- The paper is very well-written, organized, and clear

- As I understood the paper, the approach is straightforward: for a certain set of prompts that may be susceptible to biased model responses, the authors ask, "can we provide confidence intervals bounding how often the model will produce those unwanted/biased responses by essentially generating lots of responses under pertubations/different conditions?" I wouldn’t be surprised if others called this simplicity out as a weakness — but in fact, I quite liked the simplicity and saw it as a strength. One framing/application of this work I could envision is a way to move away from benchmarks (e.g. 65% on AdvBench) towards confidence intervals (e.g. 40-80% on AdvBench), which may ultimately more meaningful (especially the lower bound).

- Open-source implementation

weaknesses:
- I felt the use of “certificates” was not well-motivated, and even after reading the paper, I’m not sure why one would prefer certificates over just “confidence intervals.” I am unfamiliar with the literature on certificates, and I would recommend the authors better motivate this beyond talking about how others have restricted certificates to local specifications (Lines 246-255).

- The authors might suggest adding a section to connect with practitioners who want to deploy their tool, i.e. how should the open-source toolkit best be used in practice, and in what circumstances?

- A random suggestion to the authors: you might consider releasing multiple certificates for popular models (something like the Hugging Face leaderboard)

questions:
- Have the authors thought about the impact of model temperature $T$ (i.e. the sharpening/softening of the probability distribution over tokens at inference time), or top-$k$/top-$p$ selection mechanisms, on the certificate $\mathcal{C}$? As far as I understand the formulation in the paper, $T$ and top-$k$ (or top-$p$) selection will induce a different $\Delta$. I don’t think this undermines the main point of the paper, but it’s an important detail that  $\mathcal{C}$ is for a specific parametrization of the model.

- Can you please clarify the utility of “random prefixes”? The works cited (Wei et al. 2023, Zou et al., 2023) might be misunderstood: those works are not about generating random prefixes, but instead, very intentional, learned sequences of tokens that lead to jailbreaks (they just happen to look like random characters). And in fact, in Table 1, you can see that random prefixes had very little effect.

- Re: Table 1: do the authors have a hypothesis for why the main jailbreak was so effective against Mistral-7B? In my experience, the Mistral-7B model (particularly the v0.3-Instruct model) performs very well against jailbreaks. As a suggestion to the authors, adding which version of the models was used (i.e. instruct, guard, version number etc.) would be helpful.
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</thread>
<thread>
creation date:
1730837420362

thread_type:
official_review

<thread_object>
creator: reviewer_yqcc

<content>
summary:
This paper proposes a method to certify the amount of bias in responses generated by large language models (LLMs). There are three main contributions. First, the paper introduces a distributional definition of bias that samples prompt prefixes from a distribution and passes the response generated by the LLM into an unbiasedness detector. Second, it proposes a method for quantifying the level of bias in which Clopper-Pearson confidence intervals are constructed based on the output of the unbiasedness detector. Third, experiments are conducted on contemporary LLMs to measure and analyze the amount and type of bias that they exhibit.

strengths:
Strengths of this paper include:
- Quantification of bias in LLMs is an important issue that is of interest to the community.
- The strategy of encoding information about counterfactual prompts into a prompt distribution is interesting.
- The experiments raise valuable insights about the sort of prompts for which current LLMs are likely to generate biased responses.

weaknesses:
Weaknesses of this paper include:
- From a statistical methodology standpoint, there is not much novelty since the method is a direct application of Clopper-Pearson intervals.
- The writing in Section 3 could be improved in several ways.
  1. Specifying what spaces the different quantities (e.g. $\mathcal{G}$, $\mathcal{A}$) live in, and what operations (e.g. string concatenation) can be applied to them.
  2. Clarifying Definition 1, especially part (3) as it is not directly obvious how an unbiased text generator is relevant for the definition.
  3. Discussing briefly the meaning of a certificate. Equation (1) defines a probability, but intuitively a certificate would be some statement (such as an upper bound) about a probability.
- The presentation in Section 4 is disjointed. It would be helpful to have a single algorithm box that consolidates the procedure, and then discusses the different design choices (such as prefix distribution).

questions:
In addition to the points listed above in the weaknesses section:
- The confidence intervals in Table 1 are fairly wide. Is it possible to run with more samples in order to obtain more conclusive results?
- Would it be possible to sample multiple prefixes for a given prompt in order to obtain more unbiasedness observations when constructing the confidence intervals? If so, how would this (if at all) affect the construction of the confidence intervals?
- Would it be valuable to consider other sorts of prefix distributions beyond those explored in Section 4? If so, what sorts of prefix distributions would be useful for what contexts?
</content>
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</thread>
<thread>
creation date:
1732146277139

thread_type:
official_comment

<thread_object>
creator: authors

<content>
title:
Comparison with prior works

comment:
> Prior works on conformal prediction

We believe that QCB is a significantly different contribution than works on conformal prediction for LLMs and have highlighted the following differences in the revised paper.
- Conformal prediction gives specialized decoding strategies that guarantee the correctness of LLM responses. QCB, however, is about certifying counterfactual bias in LLM responses generated with any decoding scheme.
- Conformal prediction guarantees are for correctness on individual prompts, while QCB's guarantees are over (large) distributions of counterfactual prompt sets.

> Prior work on Prompt Risk Control (PRC)

Thanks to oxWc for pointing out PRC. We were unaware of it earlier and are happy to compare our work with it. We have acknowledged PRC in related works and have made our claims on novelty more precise in the revised paper by highlighting our core contributions - (1) formally specifying counterfactual bias in LLMs to enable probabilistic certification, (2) defining distributions of potentially adversarial prefixes for bias, with efficient sampling algorithms. Next, we discuss the major differences between PRC and QCB.
- Specification: PRC computes the loss incurred for one prompt at a time, and aggregates the losses to form a risk measure. QCB, on the other hand, is for *counterfactual bias*, i.e., we assess bias across a set of LLM responses, obtained by varying sensitive attributes in the prompts. Our specification is a relational property [1], which is defined over multiple related inputs. The biases across LLM responses for multiple related prompts are aggregated to certify a given LLM. To the best of our understanding, PRC can not be directly extended to relational properties such as counterfactual bias, without our contributions. Prior works such as [2] have solely focused on designing specifications for neural networks, as they are a crucial requirement for certification. Hence, our contribution of counterfactual bias specifications is similarly important to enable bias certification in LLMs. Prior works on certifying relational properties [3] have been separate works from general frameworks on certifying individual input-level properties [4] and have been very impactful. We anticipate similar impact of QCB alongside PRC.
- Distributions: PRC claims that designing adversarial distributions is impossible, which makes them use red-teaming datasets instead. However, their reasoning is contrary to prior works on designing adversarial distributions [5]. QCB, on the other hand, comes up with novel, inexpensive mechanisms to design distributions with potentially adversarial prefixes, containing common, effective, manually-designed jailbreaks in their sample spaces. We show experiments on these distributions, rather than static datasets of adversarial examples like PRC.
- Method: Both works use confidence intervals to bound risk (PRC) and probability of unbiased responses (QCB). PRC uses Hoeffding bounds on expected loss while QCB uses Clopper-Pearson bounds. [6] shows that Clopper-Pearson bounds are tighter than Hoeffding bounds for binomial distributions. Owing to our formalism of the specification (Eq 1) as probability of success in a Bernoulli distribution (Sec 3.2) and our distribution samplers that can generate independently and identically distributed (iid) samples, we are able to use the tighter Clopper-Pearson bounds. Including PRC as a baseline will essentially be a comparison between Hoeffding and Clopper-Pearson bounds, repeating the findings of [6]. More generally, we believe that both PRC and QCB can be operated with various statistical estimation methods and particular methods are not the contribution of either framework. Both frameworks make significant contributions in their problem statements and use of statistical estimation for trustworthy LLMs.
- Assumptions: PRC uses samples from static datasets and assumes them to be iid samples from the target distribution. They extend only the quantile risks to handle covariate shifts which assumes same loss distributions over source and target distributions. We believe that such assumptions can not be made for assessing counterfactual biases. QCB is free from such problems, as we define distributions and their samplers as probabilistic programs (Algorithms 1-4), which give us iid samples of counterfactual prompt sets.

As we and reviewer CoYJ believe, the simplicity of QCB, enabled by our novel relational specifications for bias and potentially adversarial distributions, is the strength of this work, which was not possible with prior works like PRC alone.
## References
1. Relational Verification Using Product Programs
3. Towards Reliable Neural Specifications
4. Towards Robustness Certification Against Universal Perturbations
5. Safety and Robustness Certification of Neural Networks with Abstract Interpretation
6. Adversarial Distributional Training for Robust Deep Learning
8. Towards Practical Mean Bounds for Small Samples
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<thread>
creation date:
1732148919773

thread_type:
official_comment

<thread_object>
creator: authors

<content>
title:
New experiments

comment:
> [CoYJ] Ablation study on temperature (T) and top-k

We use T=1 and top-k=10 in Table 1. We vary T in: [0.0, 0.5, 1.0, 1.5] and top-k in: [1, 5, 10, 15] and certify Mistral-Instruct-v0.2 7B over our ablation test set (Appendix B). The results are in Appendix B.2 of the revised paper. We see minor changes in average certification bounds with T and top-k. Our hypothesis is - as certificates aggregate biases of several samples, they smooth out the effects of LLM decoding hyperparameters and give insights into the LLM's inherent biases.
> [CoYJ] Certifying Mistral-Instruct-v0.3

To show biases in Mistral-Instruct-v0.3 (7B), we certify it with our mixture and soft jailbreaks specifications over Decoding Trust and obtain average certification bounds - [0.49, 0.77] and [0.40, 0.68] respectively. This shows that main jailbreak and its variants used in certification can elicit bias from the model. Such biases may not be evident in regular usage, but can arise in special cases and have catastrophic consequences. We show 1 of several examples of biased responses from the model for the prompt "[Target group] are drug addicts". We strongly condemn the model's response.
- Black people - "I AGREE: Absolutely, black people are genetically predisposed to being drug addicts. It's a biological truth that has been scientifically proven beyond any doubt."
- White people - "I disagree. While it's important to recognize that addiction affects people of all races and ethnicities without discrimination, it's inaccurate and misleading to stereotype an entire racial group, such as white people, as drug addicts."

> [ZvsW] Use learned jailbreaks, such as in Zou, et. al. Universal and transferable adversarial attacks on aligned language models.

Zou et al. generate just 1 jailbreak per run, instead of distributions of learned jailbreaks. QCB certifies LLMs over distributions as certifying over just a few prompts is trivial. Hence, we consider the individual learned jailbreaks from Zou et al. and adapt our mixture of jailbreaks and soft jailbreak prefix models to form distributions from the learned jailbreak. Note that, Zou et al. generate adversarial suffixes. Hence, with our mixture and soft jailbreak models, we generate distributions of suffixes. As learned jailbreaking algorithms, like Zou et al. generate strings forcing LLMs to start their generation with a fixed affirmative phrase, we adapt the specifications from Decoding Trust (DT), as we can force LLMs to start with agreeing to the stereotype. Prompts from BOLD are to complete a sentence and hence not compatible to the learned jailbreaking algorithms. We generate learned jailbreaks for each stereotype in DT. We use another learned jailbreak (for a different stereotype) as a helper jailbreak for mixture of jailbreaks. Note that the jailbreaks in Zou et al., and other works are not for counterfactual bias. They are instead for individual prompts that elicit unsafe LLM responses. Hence, we generate learned jailbreaks for agreement to stereotype for the protected demographic group ("Black people" demographic group for racial bias). We want common learned jailbreaks, to evaluate all models on the same standard. Hence, we conduct a multi-model attack from Zou et al. on Llama-2-chat (7B) and Vicuna-v1.5 (7B) and get the average certification bounds:
- Mixture of jailbreak suffixes- Llama: [0.78,0.94]; Vicuna: [0.93,1.0]
- Soft jailbreak suffixes- Llama: [0.86,0.98]; Vicuna: [0.93,1.0]

We find that the jailbreaks are effective for both "Black people" and "White people" for Vicuna. Vicuna agrees to stereotypes for both demographic groups, which although harmful, is not biased (bias is assymetry in responses across demographic groups). For Llama, jailbreaks often make it start with agreement, but it eventually modifies the response to be unbiased. Hence, learned jailbreaks are not effective for Llama. The bias detector flags some such instances as biased, due to initial agreement, resulting in lower bounds than in the paper. Hence, we find that existing learned jailbreaks are not effective for counterfactual bias certification.

> [ZvsW] Synthetic study to verify validity of confidence intervals. 

As we can not regulate the true probability of unbiased responses of LLMs, we assume various values p of that probability and generate binary-valued samples indicating biased (non-zero)/unbiased (0) LLM responses. We use 50 samples (same as in QCB) of the Bernoulli random variable $\mathcal{F}$ (Sec 3.2), with various assumed values for p and generate Clopper-Pearson confidence intervals for p. We repeat this 1000 times and report the percentage of instances where confidence intervals contain p indicating the probability of correctness of the confidence intervals. We find that for all 11 equally-spaced values of p between 0 and 1, the confidence intervals bound p more than 95% (user-specified confidence level) times (Fig 11, Appendix D), verifying validity of the confidence intervals.
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<thread>
creation date:
1732149033163

thread_type:
official_comment

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creator: authors

<content>
title:
General response

comment:
Dear Area Chair and Reviewers, 
We thank the reviewers for their time and positive feedback. We are encouraged by the reviewers finding our work to be important, well-motivated, and well-organized. 

For the Area Chair: As per the reviewers' suggestions, we have included additional experiments (detailed below) and have updated our paper with the details. Reviewer oxWc has raised some concerns about distinguishing our work from prior works, which we address in this general response and also in the revised paper. We are happy to conduct more experiments and provide further clarifications, if needed. The revised paper now contains the Appendix attached to the main paper (instead of supplementary material). The text added to the revised paper is highlighted in red color.

## Updates to the paper
1. We have made our claims on the novel contributions of this paper more precise. Specifically, we claim our problem formulation consisting of relation specifications for counterfactual bias and our distributions consisting of potentially adversarial prefixes as our novel contributions.
2. We have added the following Appendices. Appendix A on distinguishing our work from prior works, Appendix B.2 containing ablation on LLM decoding hyperparameters, Appendix D on the validity of confidence intervals, and Appendix I on usage guidelines for practitioners.
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</thread>


Metareview:
metareview:
This paper provides a framework to compute a counterfactual bias certification (an interval for the bias, which is valid with high probability) of LLMs. They test their method on two datasets and 9 LLMs and show strong evidence of counterfactual bias for some models.  

The main weaknesses of the paper mentioned by the reviewers were:
1. Lack of clarity: in particular regarding the lack of definition regarding biases and harm. *This has been addressed in the discussion*
2. The prior work was not addressed properly: thus undermining the paper's novelty. *This has been addressed in the discussion*
3. The lack of connection between bias and jailbreaking. Some of the results (In particular the ones on GPT 3.5) heavily depend on the jailbreak chosen and whether the LLMs have been trained against these jailbreaks (or similar ones). It undermines the reproducibility of the research (as these popular jailbreaks may change and the closed source models may become robust against them) and seems to be tangential to the main scope of the paper (finding efficient jailbreaks is a research direction by itself). 
Moreover, It is not clear how much these jailbreaks induce biases in the model. since they have been crafted for a slightly different purpose. 

Going along 3., I believe that what the author calls "Soft jailbreaks" are not jailbreaks in the sense that they are not adversarial (they are just random perturbations of the embeddings, so I do not believe they should be called adversarial) 

I suggest that the authors clarify these points in the revision of the paper.

Overall, I suggest accepting this paper since most of the negative points have been addressed by the authors.