BiCert: A Bilinear Mixed Integer Programming Formulation for Precise Certified Bounds Against Data Poisoning Attacks

Data poisoning attacks pose one of the biggest threats to modern AI systems, necessitating robust defenses. While extensive efforts have been made to develop empirical defenses, attackers continue to evolve, creating sophisticated methods to circumvent these measures. To address this, we must move beyond empirical defenses and establish provable certification methods that guarantee robustness. This paper introduces a novel certification approach, BiCert, using Bilinear Mixed Integer Programming (BMIP) to compute sound deterministic bounds that provide such provable robustness. Using BMIP, we compute the reachable set of parameters that could result from training with potentially manipulated data. A key element to make this computation feasible is to relax the reachable parameter set to a convex set between training iterations. At test time, this parameter set allows us to predict all possible outcomes, guaranteeing robustness. BiCert is more precise than previous methods, which rely solely on interval and polyhedral bounds. Crucially, our approach overcomes the fundamental limitation of prior approaches where parameter bounds could only grow, often uncontrollably. We show that BiCert's tighter bounds eliminate a key source of divergence issues, resulting in more stable training and higher certified accuracy.

FullCert: Deterministic End-to-End Certification for Training and Inference of Neural Networks

Modern machine learning models are sensitive to the manipulation of both the training data (poisoning attacks) and inference data (adversarial examples). Recognizing this issue, the community has developed many empirical defenses against both attacks and, more recently, provable certification methods against inference-time attacks. However, such guarantees are still largely lacking for training-time attacks. In this work, we present FullCert, the first end-to-end certifier with sound, deterministic bounds, which proves robustness against both training-time and inference-time attacks. We first bound all possible perturbations an adversary can make to the training data under the considered threat model. Using these constraints, we bound the perturbations' influence on the model's parameters. Finally, we bound the impact of these parameter changes on the model's prediction, resulting in joint robustness guarantees against poisoning and adversarial examples. To facilitate this novel certification paradigm, we combine our theoretical work with a new open-source library BoundFlow, which enables model training on bounded datasets. We experimentally demonstrate FullCert's feasibility on two different datasets.

Adaptive Hierarchical Certification for Segmentation using Randomized Smoothing

Common certification methods operate on a flat pre-defined set of fine-grained classes. In this paper, however, we propose a novel, more general, and practical setting, namely adaptive hierarchical certification for image semantic segmentation. In this setting, the certification can be within a multi-level hierarchical label space composed of fine to coarse levels. Unlike classic methods where the certification would abstain for unstable components, our approach adaptively relaxes the certification to a coarser level within the hierarchy. This relaxation lowers the abstain rate whilst providing more certified semantically meaningful information. We mathematically formulate the problem setup and introduce, for the first time, an adaptive hierarchical certification algorithm for image semantic segmentation, that certifies image pixels within a hierarchy and prove the correctness of its guarantees. Since certified accuracy does not take the loss of information into account when traversing into a coarser hierarchy level, we introduce a novel evaluation paradigm for adaptive hierarchical certification, namely the certified information gain metric, which is proportional to the class granularity level. Our evaluation experiments on real-world challenging datasets such as Cityscapes and ACDC demonstrate that our adaptive algorithm achieves a higher certified information gain and a lower abstain rate compared to the current state-of-the-art certification method, as well as other non-adaptive versions of it.

Backdoor Attacks on Network Certification via Data Poisoning

Certifiers for neural networks have made great progress towards provable robustness guarantees against evasion attacks using adversarial examples. However, introducing certifiers into deep learning systems also opens up new attack vectors, which need to be considered before deployment. In this work, we conduct the first systematic analysis of training time attacks against certifiers in practical application pipelines, identifying new threat vectors that can be exploited to degrade the overall system. Using these insights, we design two backdoor attacks against network certifiers, which can drastically reduce certified robustness when the backdoor is activated. For example, adding 1% poisoned data points during training is sufficient to reduce certified robustness by up to 95 percentage points, effectively rendering the certifier useless. We analyze how such novel attacks can compromise the overall system's integrity or availability. Our extensive experiments across multiple datasets, model architectures, and certifiers demonstrate the wide applicability of these attacks. A first investigation into potential defenses shows that current approaches only partially mitigate the issue, highlighting the need for new, more specific solutions.

Robustness Certification for Point Cloud Models

The use of deep 3D point cloud models in safety-critical applications, such as autonomous driving, dictates the need to certify the robustness of these models to semantic transformations. This is technically challenging as it requires a scalable verifier tailored to point cloud models that handles a wide range of semantic 3D transformations. In this work, we address this challenge and introduce 3DCertify, the first verifier able to certify robustness of point cloud models. 3DCertify is based on two key insights: (i) a generic relaxation based on first-order Taylor approximations, applicable to any differentiable transformation, and (ii) a precise relaxation for global feature pooling, which is more complex than pointwise activations (e.g., ReLU or sigmoid) but commonly employed in point cloud models. We demonstrate the effectiveness of 3DCertify by performing an extensive evaluation on a wide range of 3D transformations (e.g., rotation, twisting) for both classification and part segmentation tasks. For example, we can certify robustness against rotations by $\pm60^\circ$ for 95.7% of point clouds, and our max pool relaxation increases certification by up to 15.6%.

Feature Generating Networks for Zero-Shot Learning

Suffering from the extreme training data imbalance between seen and unseen classes, most of existing state-of-the-art approaches fail to achieve satisfactory results for the challenging generalized zero-shot learning task. To circumvent the need for labeled examples of unseen classes, we propose a novel generative adversarial network (GAN) that synthesizes CNN features conditioned on class-level semantic information, offering a shortcut directly from a semantic descriptor of a class to a class-conditional feature distribution. Our proposed approach, pairing a Wasserstein GAN with a classification loss, is able to generate sufficiently discriminative CNN features to train softmax classifiers or any multimodal embedding method. Our experimental results demonstrate a significant boost in accuracy over the state of the art on five challenging datasets -- CUB, FLO, SUN, AWA and ImageNet -- in both the zero-shot learning and generalized zero-shot learning settings.