arXiv subjects

Matthew Wicker

Publications and source records attributed to Matthew Wicker.

At least 19 recordsLinked to original sources

arXiv2026

Hybrid Robustness Verification for Spatio-Temporal Neural Networks

With AI increasingly deployed in safety-critical systems, providing formal robustness guarantees for the underlying models is essential. Existing verification methods either rely on overly conservative approximations or incur prohibitive computational costs. For example, the use of lp-norm perturbations in video settings encodes the belief that the adversary can inject noise in every video frame. In practice, adversarial perturbations exhibit structured spatial and temporal correlations, constrained to lower-dimensional, semantically meaningful subspaces. In this work, we study robustness verification of 3D CNNs processing video and volumetric inputs, targeting applications in action recognition (UCF-101), autonomous driving (Udacity), and medical imaging (MedMNIST) exploiting realistic assumptions on adversarial strength by modelling them as spatio-temporal constraints - where the attacker can modify either a subset of frames or patches within a set of consecutive frames. We demonstrate that modelling realistic constraints enables tighter approximations. We introduce Spatio-Temporal Bound Propagation (STBP), a verification framework that computes an exact closed-form characterization of the first convolutional layer and propagates certified bounds through subsequent layers using scalable approximations. Computing the exact closed form provides the tightest bounds for the first convolutional layer. Thus, we utilise approximation methods in the remainder of the network. To spur further progress in this field, we propose ST-Bench, a verification benchmark for autonomous driving and activity recognition, to systematically evaluate verifiable robustness. Compared to existing verification-based approaches, STBP provides stronger robustness guarantees with significantly improved scalability, achieving 1.7x higher certified robust accuracy under identical perturbation budgets.

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arXiv2026

SafeAdapt: Provably Safe Policy Updates in Deep Reinforcement Learning

Safety guarantees are a prerequisite to the deployment of reinforcement learning (RL) agents in safety-critical tasks. Often, deployment environments exhibit non-stationary dynamics or are subject to changing performance goals, requiring updates to the learned policy. This leads to a fundamental challenge: how to update an RL policy while preserving its safety properties on previously encountered tasks? The majority of current approaches either do not provide formal guarantees or verify policy safety only a posteriori. We propose a novel a priori approach to safe policy updates in continual RL by introducing the Rashomon set: a region in policy parameter space certified to meet safety constraints within the demonstration data distribution. We then show that one can provide formal, provable guarantees for arbitrary RL algorithms used to update a policy by projecting their updates onto the Rashomon set. Empirically, we validate this approach across grid-world navigation environments (Frozen Lake and Poisoned Apple) where we guarantee an a priori provably deterministic safety on the source task during downstream adaptation. In contrast, we observe that regularisation-based baselines experience catastrophic forgetting of safety constraints while our approach enables strong adaptation with provable guarantees that safety is preserved.

cs.LG↗

arXiv2026

Variational Routing: A Scalable Bayesian Framework for Calibrated Mixture-of-Experts Transformers

Foundation models are increasingly being deployed in contexts where understanding the uncertainty of their outputs is critical to ensuring responsible deployment. While Bayesian methods offer a principled approach to uncertainty quantification, their computational overhead renders their use impractical for training or inference at foundation model scale. State-of-the-art models achieve parameter counts in the trillions through carefully engineered sparsity including Mixture-of-Experts (MoE) layers. In this work, we demonstrate calibrated uncertainty at scale by introducing Variational Mixture-of-Experts Routing (VMoER), a structured Bayesian approach for modelling uncertainty in MoE layers. VMoER confines Bayesian inference to the expert-selection stage which is typically done by a deterministic routing network. We instantiate VMoER using two inference strategies: amortised variational inference over routing logits and inferring a temperature parameter for stochastic expert selection. Across fine-tuning tested foundation models, VMoER improves routing stability under noise by 38\%, reduces calibration error by 94\%, and increases out-of-distribution AUROC by 12\%, while incurring less than 1\% additional FLOPs. These results suggest VMoER offers a scalable path toward robust and uncertainty-aware foundation models.

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arXiv2026

Towards Poisoning Robustness Certification for Natural Language Generation

Understanding the reliability of natural language generation is critical for deploying foundation models in security-sensitive domains. While certified poisoning defenses provide provable robustness bounds for classification tasks, they are fundamentally ill-equipped for autoregressive generation: they cannot handle sequential predictions or the exponentially large output space of language models. To establish a framework for certified natural language generation, we formalize two security properties: stability (robustness to any change in generation) and validity (robustness to targeted, harmful changes in generation). We introduce Targeted Partition Aggregation (TPA), the first algorithm to certify validity/targeted attacks by computing the minimum poisoning budget needed to induce a specific harmful class, token, or phrase. Further, we extend TPA to provide tighter guarantees for multi-turn generations using mixed integer linear programming (MILP). Empirically, we demonstrate TPA's effectiveness across diverse settings including: certifying validity of agent tool-calling when adversaries modify up to 0.5% of the dataset and certifying 8-token stability horizons in preference-based alignment. Though inference-time latency remains an open challenge, our contributions enable certified deployment of language models in security-critical applications.

cs.LG↗

arXiv2025

Provably Safe Model Updates

Safety-critical environments are inherently dynamic. Distribution shifts, emerging vulnerabilities, and evolving requirements demand continuous updates to machine learning models. Yet even benign parameter updates can have unintended consequences, such as catastrophic forgetting in classical models or alignment drift in foundation models. Existing heuristic approaches (e.g., regularization, parameter isolation) can mitigate these effects but cannot certify that updated models continue to satisfy required performance specifications. We address this problem by introducing a framework for provably safe model updates. Our approach first formalizes the problem as computing the largest locally invariant domain (LID): a connected region in parameter space where all points are certified to satisfy a given specification. While exact maximal LID computation is intractable, we show that relaxing the problem to parameterized abstract domains (orthotopes, zonotopes) yields a tractable primal-dual formulation. This enables efficient certification of updates - independent of the data or algorithm used - by projecting them onto the safe domain. Our formulation further allows computation of multiple approximately optimal LIDs, incorporation of regularization-inspired biases, and use of lookahead data buffers. Across continual learning and foundation model fine-tuning benchmarks, our method matches or exceeds heuristic baselines for avoiding forgetting while providing formal safety guarantees.

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arXiv2025

Abstract Gradient Training: A Unified Certification Framework for Data Poisoning, Unlearning, and Differential Privacy

The impact of inference-time data perturbation (e.g., adversarial attacks) has been extensively studied in machine learning, leading to well-established certification techniques for adversarial robustness. In contrast, certifying models against training data perturbations remains a relatively under-explored area. These perturbations can arise in three critical contexts: adversarial data poisoning, where an adversary manipulates training samples to corrupt model performance; machine unlearning, which requires certifying model behavior under the removal of specific training data; and differential privacy, where guarantees must be given with respect to substituting individual data points. This work introduces Abstract Gradient Training (AGT), a unified framework for certifying robustness of a given model and training procedure to training data perturbations, including bounded perturbations, the removal of data points, and the addition of new samples. By bounding the reachable set of parameters, i.e., establishing provable parameter-space bounds, AGT provides a formal approach to analyzing the behavior of models trained via first-order optimization methods.

cs.LG↗

arXiv2025

Model Guidance via Robust Feature Attribution

Controlling the patterns a model learns is essential to preventing reliance on irrelevant or misleading features. Such reliance on irrelevant features, often called shortcut features, has been observed across domains, including medical imaging and natural language processing, where it may lead to real-world harms. A common mitigation strategy leverages annotations (provided by humans or machines) indicating which features are relevant or irrelevant. These annotations are compared to model explanations, typically in the form of feature salience, and used to guide the loss function during training. Unfortunately, recent works have demonstrated that feature salience methods are unreliable and therefore offer a poor signal to optimize. In this work, we propose a simplified objective that simultaneously optimizes for explanation robustness and mitigation of shortcut learning. Unlike prior objectives with similar aims, we demonstrate theoretically why our approach ought to be more effective. Across a comprehensive series of experiments, we show that our approach consistently reduces test-time misclassifications by 20% compared to state-of-the-art methods. We also extend prior experimental settings to include natural language processing tasks. Additionally, we conduct novel ablations that yield practical insights, including the relative importance of annotation quality over quantity. Code for our method and experiments is available at: https://github.com/Mihneaghitu/ModelGuidanceViaRobustFeatureAttribution.

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arXiv2024

Certification for Differentially Private Prediction in Gradient-Based Training

We study private prediction where differential privacy is achieved by adding noise to the outputs of a non-private model. Existing methods rely on noise proportional to the global sensitivity of the model, often resulting in sub-optimal privacy-utility trade-offs compared to private training. We introduce a novel approach for computing dataset-specific upper bounds on prediction sensitivity by leveraging convex relaxation and bound propagation techniques. By combining these bounds with the smooth sensitivity mechanism, we significantly improve the privacy analysis of private prediction compared to global sensitivity-based approaches. Experimental results across real-world datasets in medical image classification and natural language processing demonstrate that our sensitivity bounds are can be orders of magnitude tighter than global sensitivity. Our approach provides a strong basis for the development of novel privacy preserving technologies.

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arXiv2024

Certified Robustness to Data Poisoning in Gradient-Based Training

Modern machine learning pipelines leverage large amounts of public data, making it infeasible to guarantee data quality and leaving models open to poisoning and backdoor attacks. Provably bounding model behavior under such attacks remains an open problem. In this work, we address this challenge by developing the first framework providing provable guarantees on the behavior of models trained with potentially manipulated data without modifying the model or learning algorithm. In particular, our framework certifies robustness against untargeted and targeted poisoning, as well as backdoor attacks, for bounded and unbounded manipulations of the training inputs and labels. Our method leverages convex relaxations to over-approximate the set of all possible parameter updates for a given poisoning threat model, allowing us to bound the set of all reachable parameters for any gradient-based learning algorithm. Given this set of parameters, we provide bounds on worst-case behavior, including model performance and backdoor success rate. We demonstrate our approach on multiple real-world datasets from applications including energy consumption, medical imaging, and autonomous driving.

cs.LG↗

arXiv2023

Certification of Distributional Individual Fairness

Providing formal guarantees of algorithmic fairness is of paramount importance to socially responsible deployment of machine learning algorithms. In this work, we study formal guarantees, i.e., certificates, for individual fairness (IF) of neural networks. We start by introducing a novel convex approximation of IF constraints that exponentially decreases the computational cost of providing formal guarantees of local individual fairness. We highlight that prior methods are constrained by their focus on global IF certification and can therefore only scale to models with a few dozen hidden neurons, thus limiting their practical impact. We propose to certify distributional individual fairness which ensures that for a given empirical distribution and all distributions within a $\gamma$-Wasserstein ball, the neural network has guaranteed individually fair predictions. Leveraging developments in quasi-convex optimization, we provide novel and efficient certified bounds on distributional individual fairness and show that our method allows us to certify and regularize neural networks that are several orders of magnitude larger than those considered by prior works. Moreover, we study real-world distribution shifts and find our bounds to be a scalable, practical, and sound source of IF guarantees.

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arXiv2023

Probabilistic Reach-Avoid for Bayesian Neural Networks

Model-based reinforcement learning seeks to simultaneously learn the dynamics of an unknown stochastic environment and synthesise an optimal policy for acting in it. Ensuring the safety and robustness of sequential decisions made through a policy in such an environment is a key challenge for policies intended for safety-critical scenarios. In this work, we investigate two complementary problems: first, computing reach-avoid probabilities for iterative predictions made with dynamical models, with dynamics described by Bayesian neural network (BNN); second, synthesising control policies that are optimal with respect to a given reach-avoid specification (reaching a "target" state, while avoiding a set of "unsafe" states) and a learned BNN model. Our solution leverages interval propagation and backward recursion techniques to compute lower bounds for the probability that a policy's sequence of actions leads to satisfying the reach-avoid specification. Such computed lower bounds provide safety certification for the given policy and BNN model. We then introduce control synthesis algorithms to derive policies maximizing said lower bounds on the safety probability. We demonstrate the effectiveness of our method on a series of control benchmarks characterized by learned BNN dynamics models. On our most challenging benchmark, compared to purely data-driven policies the optimal synthesis algorithm is able to provide more than a four-fold increase in the number of certifiable states and more than a three-fold increase in the average guaranteed reach-avoid probability.

cs.LG↗

arXiv2023

Adversarial Robustness Certification for Bayesian Neural Networks

We study the problem of certifying the robustness of Bayesian neural networks (BNNs) to adversarial input perturbations. Given a compact set of input points $T \subseteq \mathbb{R}^m$ and a set of output points $S \subseteq \mathbb{R}^n$, we define two notions of robustness for BNNs in an adversarial setting: probabilistic robustness and decision robustness. Probabilistic robustness is the probability that for all points in $T$ the output of a BNN sampled from the posterior is in $S$. On the other hand, decision robustness considers the optimal decision of a BNN and checks if for all points in $T$ the optimal decision of the BNN for a given loss function lies within the output set $S$. Although exact computation of these robustness properties is challenging due to the probabilistic and non-convex nature of BNNs, we present a unified computational framework for efficiently and formally bounding them. Our approach is based on weight interval sampling, integration, and bound propagation techniques, and can be applied to BNNs with a large number of parameters, and independently of the (approximate) inference method employed to train the BNN. We evaluate the effectiveness of our methods on various regression and classification tasks, including an industrial regression benchmark, MNIST, traffic sign recognition, and airborne collision avoidance, and demonstrate that our approach enables certification of robustness and uncertainty of BNN predictions.

cs.LG↗

arXiv2023

Individual Fairness in Bayesian Neural Networks

We study Individual Fairness (IF) for Bayesian neural networks (BNNs). Specifically, we consider the $\epsilon$-$\delta$-individual fairness notion, which requires that, for any pair of input points that are $\epsilon$-similar according to a given similarity metrics, the output of the BNN is within a given tolerance $\delta>0.$ We leverage bounds on statistical sampling over the input space and the relationship between adversarial robustness and individual fairness to derive a framework for the systematic estimation of $\epsilon$-$\delta$-IF, designing Fair-FGSM and Fair-PGD as global,fairness-aware extensions to gradient-based attacks for BNNs. We empirically study IF of a variety of approximately inferred BNNs with different architectures on fairness benchmarks, and compare against deterministic models learnt using frequentist techniques. Interestingly, we find that BNNs trained by means of approximate Bayesian inference consistently tend to be markedly more individually fair than their deterministic counterparts.

cs.LG↗

arXiv2023

Use Perturbations when Learning from Explanations

Machine learning from explanations (MLX) is an approach to learning that uses human-provided explanations of relevant or irrelevant features for each input to ensure that model predictions are right for the right reasons. Existing MLX approaches rely on local model interpretation methods and require strong model smoothing to align model and human explanations, leading to sub-optimal performance. We recast MLX as a robustness problem, where human explanations specify a lower dimensional manifold from which perturbations can be drawn, and show both theoretically and empirically how this approach alleviates the need for strong model smoothing. We consider various approaches to achieving robustness, leading to improved performance over prior MLX methods. Finally, we show how to combine robustness with an earlier MLX method, yielding state-of-the-art results on both synthetic and real-world benchmarks.

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arXiv2022

Robust Explanation Constraints for Neural Networks

Post-hoc explanation methods are used with the intent of providing insights about neural networks and are sometimes said to help engender trust in their outputs. However, popular explanations methods have been found to be fragile to minor perturbations of input features or model parameters. Relying on constraint relaxation techniques from non-convex optimization, we develop a method that upper-bounds the largest change an adversary can make to a gradient-based explanation via bounded manipulation of either the input features or model parameters. By propagating a compact input or parameter set as symbolic intervals through the forwards and backwards computations of the neural network we can formally certify the robustness of gradient-based explanations. Our bounds are differentiable, hence we can incorporate provable explanation robustness into neural network training. Empirically, our method surpasses the robustness provided by previous heuristic approaches. We find that our training method is the only method able to learn neural networks with certificates of explanation robustness across all six datasets tested.

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arXiv2022

Emergent Linguistic Structures in Neural Networks are Fragile

Large Language Models (LLMs) have been reported to have strong performance on natural language processing tasks. However, performance metrics such as accuracy do not measure the quality of the model in terms of its ability to robustly represent complex linguistic structures. In this paper, focusing on the ability of language models to represent syntax, we propose a framework to assess the consistency and robustness of linguistic representations. To this end, we introduce measures of robustness of neural network models that leverage recent advances in extracting linguistic constructs from LLMs via probing tasks, i.e., simple tasks used to extract meaningful information about a single facet of a language model, such as syntax reconstruction and root identification. Empirically, we study the performance of four LLMs across six different corpora on the proposed robustness measures by analysing their performance and robustness with respect to syntax-preserving perturbations. We provide evidence that context-free representation (e.g., GloVe) are in some cases competitive with context-dependent representations from modern LLMs (e.g., BERT), yet equally brittle to syntax-preserving perturbations. Our key observation is that emergent syntactic representations in neural networks are brittle. We make the code, trained models and logs available to the community as a contribution to the debate about the capabilities of LLMs.

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arXiv2022

On the Robustness of Bayesian Neural Networks to Adversarial Attacks

Vulnerability to adversarial attacks is one of the principal hurdles to the adoption of deep learning in safety-critical applications. Despite significant efforts, both practical and theoretical, training deep learning models robust to adversarial attacks is still an open problem. In this paper, we analyse the geometry of adversarial attacks in the large-data, overparameterized limit for Bayesian Neural Networks (BNNs). We show that, in the limit, vulnerability to gradient-based attacks arises as a result of degeneracy in the data distribution, i.e., when the data lies on a lower-dimensional submanifold of the ambient space. As a direct consequence, we demonstrate that in this limit BNN posteriors are robust to gradient-based adversarial attacks. Crucially, we prove that the expected gradient of the loss with respect to the BNN posterior distribution is vanishing, even when each neural network sampled from the posterior is vulnerable to gradient-based attacks. Experimental results on the MNIST, Fashion MNIST, and half moons datasets, representing the finite data regime, with BNNs trained with Hamiltonian Monte Carlo and Variational Inference, support this line of arguments, showing that BNNs can display both high accuracy on clean data and robustness to both gradient-based and gradient-free based adversarial attacks.

cs.LG↗

arXiv2022

Individual Fairness Guarantees for Neural Networks

We consider the problem of certifying the individual fairness (IF) of feed-forward neural networks (NNs). In particular, we work with the $\epsilon$-$\delta$-IF formulation, which, given a NN and a similarity metric learnt from data, requires that the output difference between any pair of $\epsilon$-similar individuals is bounded by a maximum decision tolerance $\delta \geq 0$. Working with a range of metrics, including the Mahalanobis distance, we propose a method to overapproximate the resulting optimisation problem using piecewise-linear functions to lower and upper bound the NN's non-linearities globally over the input space. We encode this computation as the solution of a Mixed-Integer Linear Programming problem and demonstrate that it can be used to compute IF guarantees on four datasets widely used for fairness benchmarking. We show how this formulation can be used to encourage models' fairness at training time by modifying the NN loss, and empirically confirm our approach yields NNs that are orders of magnitude fairer than state-of-the-art methods.

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