Overcoming the Paradox of Certified Training with Gaussian Smoothing

Training neural networks with high certified accuracy against adversarial examples remains an open problem despite significant efforts. While certification methods can effectively leverage tight convex relaxations for bound computation, in training, these methods perform worse than looser relaxations. Prior work hypothesized that this is caused by the discontinuity and perturbation sensitivity of the loss surface induced by these tighter relaxations. In this work, we show theoretically that Gaussian Loss Smoothing can alleviate both of these issues. We confirm this empirically by proposing a certified training method combining PGPE, an algorithm computing gradients of a smoothed loss, with different convex relaxations. When using this training method, we observe that tighter bounds indeed lead to strictly better networks that can outperform state-of-the-art methods on the same network. While scaling PGPE-based training remains challenging due to high computational cost, our results clearly demonstrate the promise of Gaussian Loss Smoothing for training certifiably robust neural networks.

SPEAR:Exact Gradient Inversion of Batches in Federated Learning

Federated learning is a popular framework for collaborative machine learning where multiple clients only share gradient updates on their local data with the server and not the actual data. Unfortunately, it was recently shown that gradient inversion attacks can reconstruct this data from these shared gradients. Existing attacks enable exact reconstruction only for a batch size of $b=1$ in the important honest-but-curious setting, with larger batches permitting only approximate reconstruction. In this work, we propose \emph{the first algorithm reconstructing whole batches with $b >1$ exactly}. This approach combines mathematical insights into the explicit low-rank structure of gradients with a sampling-based algorithm. Crucially, we leverage ReLU-induced gradient sparsity to precisely filter out large numbers of incorrect samples, making a final reconstruction step tractable. We provide an efficient GPU implementation for fully connected networks and show that it recovers batches of $b \lesssim 25$ elements exactly while being tractable for large network widths and depths.

Evading Data Contamination Detection for Language Models is (too) Easy

Large language models are widespread, with their performance on benchmarks frequently guiding user preferences for one model over another. However, the vast amount of data these models are trained on can inadvertently lead to contamination with public benchmarks, thus compromising performance measurements. While recently developed contamination detection methods try to address this issue, they overlook the possibility of deliberate contamination by malicious model providers aiming to evade detection. We argue that this setting is of crucial importance as it casts doubt on the reliability of public benchmarks. To more rigorously study this issue, we propose a categorization of both model providers and contamination detection methods. This reveals vulnerabilities in existing methods that we exploit with EAL, a simple yet effective contamination technique that significantly inflates benchmark performance while completely evading current detection methods.

Expressivity of ReLU-Networks under Convex Relaxations

Convex relaxations are a key component of training and certifying provably safe neural networks. However, despite substantial progress, a wide and poorly understood accuracy gap to standard networks remains, raising the question of whether this is due to fundamental limitations of convex relaxations. Initial work investigating this question focused on the simple and widely used IBP relaxation. It revealed that some univariate, convex, continuous piecewise linear (CPWL) functions cannot be encoded by any ReLU network such that its IBP-analysis is precise. To explore whether this limitation is shared by more advanced convex relaxations, we conduct the first in-depth study on the expressive power of ReLU networks across all commonly used convex relaxations. We show that: (i) more advanced relaxations allow a larger class of univariate functions to be expressed as precisely analyzable ReLU networks, (ii) more precise relaxations can allow exponentially larger solution spaces of ReLU networks encoding the same functions, and (iii) even using the most precise single-neuron relaxations, it is impossible to construct precisely analyzable ReLU networks that express multivariate, convex, monotone CPWL functions.

The Fundamental Limits of Interval Arithmetic for Neural Networks

Interval analysis (or interval bound propagation, IBP) is a popular technique for verifying and training provably robust deep neural networks, a fundamental challenge in the area of reliable machine learning. However, despite substantial efforts, progress on addressing this key challenge has stagnated, calling into question whether interval arithmetic is a viable path forward. In this paper we present two fundamental results on the limitations of interval arithmetic for analyzing neural networks. Our main impossibility theorem states that for any neural network classifying just three points, there is a valid specification over these points that interval analysis can not prove. Further, in the restricted case of one-hidden-layer neural networks we show a stronger impossibility result: given any radius $\alpha < 1$, there is a set of $O(\alpha^{-1})$ points with robust radius $\alpha$, separated by distance $2$, that no one-hidden-layer network can be proven to classify robustly via interval analysis.

Latent Space Smoothing for Individually Fair Representations

Fair representation learning encodes user data to ensure fairness and utility, regardless of the downstream application. However, learning individually fair representations, i.e., guaranteeing that similar individuals are treated similarly, remains challenging in high-dimensional settings such as computer vision. In this work, we introduce LASSI, the first representation learning method for certifying individual fairness of high-dimensional data. Our key insight is to leverage recent advances in generative modeling to capture the set of similar individuals in the generative latent space. This allows learning individually fair representations where similar individuals are mapped close together, by using adversarial training to minimize the distance between their representations. Finally, we employ randomized smoothing to provably map similar individuals close together, in turn ensuring that local robustness verification of the downstream application results in end-to-end fairness certification. Our experimental evaluation on challenging real-world image data demonstrates that our method increases certified individual fairness by up to 60%, without significantly affecting task utility.

Scalable Certified Segmentation via Randomized Smoothing

We present a new certification method for image and point cloud segmentation based on randomized smoothing. The method leverages a novel scalable algorithm for prediction and certification that correctly accounts for multiple testing, necessary for ensuring statistical guarantees. The key to our approach is reliance on established multiple-testing correction mechanisms as well as the ability to abstain from classifying single pixels or points while still robustly segmenting the overall input. Our experimental evaluation on synthetic data and challenging datasets, such as Pascal Context, Cityscapes, and ShapeNet, shows that our algorithm can achieve, for the first time, competitive accuracy and certification guarantees on real-world segmentation tasks. We provide an implementation at https://github.com/eth-sri/segmentation-smoothing.

Certified Defenses: Why Tighter Relaxations May Hurt Training?

Certified defenses based on convex relaxations are an established technique for training provably robust models. The key component is the choice of relaxation, varying from simple intervals to tight polyhedra. Paradoxically, however, it was empirically observed that training with tighter relaxations can worsen certified robustness. While several methods were designed to partially mitigate this issue, the underlying causes are poorly understood. In this work we investigate the above phenomenon and show that tightness may not be the determining factor for reduced certified robustness. Concretely, we identify two key features of relaxations that impact training dynamics: continuity and sensitivity. We then experimentally demonstrate that these two factors explain the drop in certified robustness when using popular relaxations. Further, we show, for the first time, that it is possible to successfully train with tighter relaxations (i.e., triangle), a result supported by our two properties. Overall, we believe the insights of this work can help drive the systematic discovery of new effective certified defenses.

Efficient Certification of Spatial Robustness

Recent work has exposed the vulnerability of computer vision models to spatial transformations. Due to the widespread usage of such models in safety-critical applications, it is crucial to quantify their robustness against spatial transformations. However, existing work only provides empirical quantification of spatial robustness via adversarial attacks, which lack provable guarantees. In this work, we propose novel convex relaxations, which enable us, for the first time, to provide a certificate of robustness against spatial transformations. Our convex relaxations are model-agnostic and can be leveraged by a wide range of neural network verifiers. Experiments on several network architectures and different datasets demonstrate the effectiveness and scalability of our method.