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Paul Montague

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12 papers

2 author rows

AAAI Conference 2026 Conference Paper

Certified but Fooled! Breaking Certified Defenses with Ghost Certificates

Quoc Viet Vo
Tashreque Mohammed Haq
Paul Montague
Tamas Abraham
Ehsan Abbasnejad
Damith C. Ranasinghe

Certified defenses promise provable robustness guarantees. We study the malicious exploitation of probabilistic certification frameworks to better understand the limits of guarantee provisions. Now, the objective is to not only mislead a classifier, but also to manipulate the certification process to generate a robustness guarantee for an adversarial input—certificate spoofing. A recent study in ICLR demonstrated that crafting large perturbations can shift inputs far into regions capable of generating a certificate for an incorrect class. Our study investigates if perturbations are needed to cause a misclassification and yet coax a certified model into issuing a deceptive, large robustness radius for a target class can still be made small and imperceptible. We explore the idea of region-focused adversarial examples to craft imperceptible perturbations, spoof certificates and achieve certification radii larger than the source class—ghost certificates. Extensive evaluations with the ImageNet demonstrate the ability to effectively bypass state-of-the-art certified defenses such as Densepure. Our work underscores the need to better understand the limits of robustness certification methods.

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NeurIPS Conference 2025 Conference Paper

3D-Prover: Diversity Driven Theorem Proving With Determinantal Point Processes

Sean Lamont
Christian Walder
Amir Dezfouli
Paul Montague
Michael Norrish

A key challenge in automated formal reasoning is the intractable search space, which grows exponentially with the depth of the proof. This branching is caused by the large number of candidate proof tactics which can be applied to a given goal. Nonetheless, many of these tactics are semantically similar or lead to an execution error, wasting valuable resources in both cases. We address the problem of effectively pruning this search, using only synthetic data generated from previous proof attempts. We first demonstrate that it is possible to generate semantically aware tactic representations which capture the effect on the proving environment, likelihood of success, and execution time. We then propose a novel filtering mechanism which leverages these representations to select semantically diverse and high quality tactics, using Determinantal Point Processes. Our approach, 3D-Prover, is designed to be general, and to augment any underlying tactic generator. We demonstrate the effectiveness of 3D-Prover on the miniF2F and LeanDojo benchmarks by augmenting popular open source proving LLMs. We show that our approach leads to an increase in the overall proof rate, as well as a significant improvement in the tactic success rate, execution time and diversity. We make our code available at https: //github. com/sean-lamont/3D-Prover.

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ICLR Conference 2025 Conference Paper

Fantastic Targets for Concept Erasure in Diffusion Models and Where To Find Them

Anh Tuan Bui
Thuy-Trang Vu
Long Tung Vuong
Trung Le 0001
Paul Montague
Tamas Abraham
Junae Kim
Dinh Q. Phung

Concept erasure has emerged as a promising technique for mitigating the risk of harmful content generation in diffusion models by selectively unlearning undesirable concepts. The common principle of previous works to remove a specific concept is to map it to a fixed generic concept, such as a neutral concept or just an empty text prompt. In this paper, we demonstrate that this fixed-target strategy is suboptimal, as it fails to account for the impact of erasing one concept on the others. To address this limitation, we model the concept space as a graph and empirically analyze the effects of erasing one concept on the remaining concepts. Our analysis uncovers intriguing geometric properties of the concept space, where the influence of erasing a concept is confined to a local region. Building on this insight, we propose the Adaptive Guided Erasure (AGE) method, which dynamically selects optimal target concepts tailored to each undesirable concept, minimizing unintended side effects. Experimental results show that AGE significantly outperforms state-of-the-art erasure methods on preserving unrelated concepts while maintaining effective erasure performance. Our code is published at {https://github.com/tuananhbui89/Adaptive-Guided-Erasure}.

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ICLR Conference 2025 Conference Paper

Multi-level Certified Defense Against Poisoning Attacks in Offline Reinforcement Learning

Shijie Liu 0004
Andrew C. Cullen
Paul Montague
Sarah Monazam Erfani
Benjamin I. P. Rubinstein

Similar to other machine learning frameworks, Offline Reinforcement Learning (RL) is shown to be vulnerable to poisoning attacks, due to its reliance on externally sourced datasets, a vulnerability that is exacerbated by its sequential nature. To mitigate the risks posed by RL poisoning, we extend certified defenses to provide larger guarantees against adversarial manipulation, ensuring robustness for both per-state actions, and the overall expected cumulative reward. Our approach leverages properties of Differential Privacy, in a manner that allows this work to span both continuous and discrete spaces, as well as stochastic and deterministic environments---significantly expanding the scope and applicability of achievable guarantees. Empirical evaluations demonstrate that our approach ensures the performance drops to no more than 50% with up to 7% of the training data poisoned, significantly improving over the 0.008% in prior work (Wu et al., 2022), while producing certified radii that is 5 times larger as well. This highlights the potential of our framework to enhance safety and reliability in offline RL.

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AAAI Conference 2024 Conference Paper

BAIT: Benchmarking (Embedding) Architectures for Interactive Theorem-Proving

Sean Lamont
Michael Norrish
Amir Dezfouli
Christian Walder
Paul Montague

Artificial Intelligence for Theorem Proving (AITP) has given rise to a plethora of benchmarks and methodologies, particularly in Interactive Theorem Proving (ITP). Research in the area is fragmented, with a diverse set of approaches being spread across several ITP systems. This presents a significant challenge to the comparison of methods, which are often complex and difficult to replicate. Addressing this, we present BAIT, a framework for the fair and streamlined comparison of learning approaches in ITP. We demonstrate BAIT’s capabilities with an in-depth comparison, across several ITP benchmarks, of state-of-the-art architectures applied to the problem of formula embedding. We find that Structure Aware Transformers perform particularly well, improving on techniques associated with the original problem sets. BAIT also allows us to assess the end-to-end proving performance of systems built on interactive environments. This unified perspective reveals a novel end-to-end system that improves on prior work. We also provide a qualitative analysis, illustrating that improved performance is associated with more semantically-aware embeddings. By streamlining the implementation and comparison of Machine Learning algorithms in the ITP context, we anticipate BAIT will be a springboard for future research.

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NeurIPS Conference 2024 Conference Paper

Erasing Undesirable Concepts in Diffusion Models with Adversarial Preservation

Anh Bui
Long Vuong
Khanh Doan
Trung Le
Paul Montague
Tamas Abraham
Dinh Phung

Diffusion models excel at generating visually striking content from text but can inadvertently produce undesirable or harmful content when trained on unfiltered internet data. A practical solution is to selectively removing target concepts from the model, but this may impact the remaining concepts. Prior approaches have tried to balance this by introducing a loss term to preserve neutral content or a regularization term to minimize changes in the model parameters, yet resolving this trade-off remains challenging. In this work, we propose to identify and preserving concepts most affected by parameter changes, termed as adversarial concepts. This approach ensures stable erasure with minimal impact on the other concepts. We demonstrate the effectiveness of our method using the Stable Diffusion model, showing that it outperforms state-of-the-art erasure methods in eliminating unwanted content while maintaining the integrity of other unrelated elements. Our code is available at \url{https: //github. com/tuananhbui89/Erasing-Adversarial-Preservation}.

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ICML Conference 2024 Conference Paper

Et Tu Certifications: Robustness Certificates Yield Better Adversarial Examples

Andrew C. Cullen
Shijie Liu 0004
Paul Montague
Sarah Monazam Erfani
Benjamin I. P. Rubinstein

In guaranteeing the absence of adversarial examples in an instance’s neighbourhood, certification mechanisms play an important role in demonstrating neural net robustness. In this paper, we ask if these certifications can compromise the very models they help to protect? Our new Certification Aware Attack exploits certifications to produce computationally efficient norm-minimising adversarial examples $74$% more often than comparable attacks, while reducing the median perturbation norm by more than $10$%. While these attacks can be used to assess the tightness of certification bounds, they also highlight that releasing certifications can paradoxically reduce security.

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AAAI Conference 2023 Conference Paper

Enhancing the Antidote: Improved Pointwise Certifications against Poisoning Attacks

Shijie Liu
Andrew C. Cullen
Paul Montague
Sarah M. Erfani
Benjamin I. P. Rubinstein

Poisoning attacks can disproportionately influence model behaviour by making small changes to the training corpus. While defences against specific poisoning attacks do exist, they in general do not provide any guarantees, leaving them potentially countered by novel attacks. In contrast, by examining worst-case behaviours Certified Defences make it possible to provide guarantees of the robustness of a sample against adversarial attacks modifying a finite number of training samples, known as pointwise certification. We achieve this by exploiting both Differential Privacy and the Sampled Gaussian Mechanism to ensure the invariance of prediction for each testing instance against finite numbers of poisoned examples. In doing so, our model provides guarantees of adversarial robustness that are more than twice as large as those provided by prior certifications.

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AAAI Conference 2023 Conference Paper

Feature-Space Bayesian Adversarial Learning Improved Malware Detector Robustness

Bao Gia Doan
Shuiqiao Yang
Paul Montague
Olivier De Vel
Tamas Abraham
Seyit Camtepe
Salil S. Kanhere
Ehsan Abbasnejad

We present a new algorithm to train a robust malware detector. Malware is a prolific problem and malware detectors are a front-line defense. Modern detectors rely on machine learning algorithms. Now, the adversarial objective is to devise alterations to the malware code to decrease the chance of being detected whilst preserving the functionality and realism of the malware. Adversarial learning is effective in improving robustness but generating functional and realistic adversarial malware samples is non-trivial. Because: i) in contrast to tasks capable of using gradient-based feedback, adversarial learning in a domain without a differentiable mapping function from the problem space (malware code inputs) to the feature space is hard; and ii) it is difficult to ensure the adversarial malware is realistic and functional. This presents a challenge for developing scalable adversarial machine learning algorithms for large datasets at a production or commercial scale to realize robust malware detectors. We propose an alternative; perform adversarial learning in the feature space in contrast to the problem space. We prove the projection of perturbed, yet valid malware, in the problem space into feature space will always be a subset of adversarials generated in the feature space. Hence, by generating a robust network against feature-space adversarial examples, we inherently achieve robustness against problem-space adversarial examples. We formulate a Bayesian adversarial learning objective that captures the distribution of models for improved robustness. To explain the robustness of the Bayesian adversarial learning algorithm, we prove that our learning method bounds the difference between the adversarial risk and empirical risk and improves robustness. We show that Bayesian neural networks (BNNs) achieve state-of-the-art results; especially in the False Positive Rate (FPR) regime. Adversarially trained BNNs achieve state-of-the-art robustness. Notably, adversarially trained BNNs are robust against stronger attacks with larger attack budgets by a margin of up to 15% on a recent production-scale malware dataset of more than 20 million samples. Importantly, our efforts create a benchmark for future defenses in the malware domain.

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TMLR Journal 2023 Journal Article

Generating Adversarial Examples with Task Oriented Multi-Objective Optimization

Anh Tuan Bui
Trung Le
He Zhao
Quan Hung Tran
Paul Montague
Dinh Phung

Deep learning models, even the-state-of-the-art ones, are highly vulnerable to adversarial examples. Adversarial training is one of the most efficient methods to improve the model's robustness. The key factor for the success of adversarial training is the capability to generate qualified and divergent adversarial examples which satisfy some objectives/goals (e.g., finding adversarial examples that maximize the model losses for simultaneously attacking multiple models). Therefore, multi-objective optimization (MOO) is a natural tool for adversarial example generation to achieve multiple objectives/goals simultaneously. However, we observe that a naive application of MOO tends to maximize all objectives/goals equally, without caring if an objective/goal has been achieved yet. This leads to useless effort to further improve the goal-achieved tasks, while putting less focus on the goal-unachieved tasks. In this paper, we propose \emph{Task Oriented MOO} to address this issue, in the context where we can explicitly define the goal achievement for a task. Our principle is to only maintain the goal-achieved tasks, while letting the optimizer spend more effort on improving the goal-unachieved tasks. We conduct comprehensive experiments for our Task Oriented MOO on various adversarial example generation schemes. The experimental results firmly demonstrate the merit of our proposed approach.

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NeurIPS Conference 2022 Conference Paper

Double Bubble, Toil and Trouble: Enhancing Certified Robustness through Transitivity

Andrew Cullen
Paul Montague
Shijie Liu
Sarah Erfani
Benjamin Rubinstein

In response to subtle adversarial examples flipping classifications of neural network models, recent research has promoted certified robustness as a solution. There, invariance of predictions to all norm-bounded attacks is achieved through randomised smoothing of network inputs. Today's state-of-the-art certifications make optimal use of the class output scores at the input instance under test: no better radius of certification (under the $L_2$ norm) is possible given only these score. However, it is an open question as to whether such lower bounds can be improved using local information around the instance under test. In this work, we demonstrate how today's ``optimal'' certificates can be improved by exploiting both the transitivity of certifications, and the geometry of the input space, giving rise to what we term Geometrically-Informed Certified Robustness. By considering the smallest distance to points on the boundary of a set of certifications this approach improves certifications for more than $80 \%$ of Tiny-Imagenet instances, yielding an on average $5\%$ increase in the associated certification. When incorporating training time processes that enhance the certified radius, our technique shows even more promising results, with a uniform $4$ percentage point increase in the achieved certified radius.

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AAAI Conference 2021 Conference Paper

Improving Ensemble Robustness by Collaboratively Promoting and Demoting Adversarial Robustness

Anh Tuan Bui
Trung Le
He Zhao
Paul Montague
Olivier deVel
Tamas Abraham
Dinh Phung

Ensemble-based adversarial training is a principled approach to achieve robustness against adversarial attacks. An important technique of this approach is to control the transferability of adversarial examples among ensemble members. We propose in this work a simple yet effective strategy to collaborate among committee models of an ensemble model. This is achieved via the secure and insecure sets defined for each model member on a given sample, hence help us to quantify and regularize the transferability. Consequently, our proposed framework provides the flexibility to reduce the adversarial transferability as well as to promote the diversity of ensemble members, which are two crucial factors for better robustness in our ensemble approach. We conduct extensive and comprehensive experiments to demonstrate that our proposed method outperforms the state-of-the-art ensemble baselines, at the same time can detect a wide range of adversarial examples with a nearly perfect accuracy. Our code is available at: https: //github. com/tuananhbui89/Crossing-Collaborative- Ensemble.

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