Related papers: Certifying Robustness via Topological Representati…
Ensuring neural network robustness is essential for the safe and reliable operation of robotic learning systems, especially in perception and decision-making tasks within real-world environments. This paper investigates the robustness of…
Robust risk minimisation has several advantages: it has been studied with regards to improving the generalisation properties of models and robustness to adversarial perturbation. We bound the distributionally robust risk for a model class…
Deep Networks have been shown to provide state-of-the-art performance in many machine learning challenges. Unfortunately, they are susceptible to various types of noise, including adversarial attacks and corrupted inputs. In this work we…
The Lipschitz constant of the map between the input and output space represented by a neural network is a natural metric for assessing the robustness of the model. We present a new method to constrain the Lipschitz constant of dense deep…
Deep neural networks have shown remarkable performance across a wide range of vision-based tasks, particularly due to the availability of large-scale datasets for training and better architectures. However, data seen in the real world are…
We introduce the persistence heatmap, a parametrized summary based on representative cycles in persistence diagrams, designed to enhance stability and explainability in topological data analysis. Algorithms to compute persistence diagrams…
Recurrent neural networks (RNNs) are a class of nonlinear dynamical systems often used to model sequence-to-sequence maps. RNNs have excellent expressive power but lack the stability or robustness guarantees that are necessary for many…
Graph Neural Networks (GNNs) have become the standard for graph representation learning but remain vulnerable to structural perturbations. We propose a novel framework that integrates persistent homology features with stability…
Deep learning has achieved remarkable success across a wide range of tasks, but its models often suffer from instability and vulnerability: small changes to the input may drastically affect predictions, while optimization can be hindered by…
Robustness of neural networks is commonly quantified via local or global Lipschitz constants. However, Lipschitz continuity can be overly coarse or overly restrictive as global robustness measure, failing to capture nuanced, data-dependent…
We present knowledge continuity, a novel definition inspired by Lipschitz continuity which aims to certify the robustness of neural networks across input domains (such as continuous and discrete domains in vision and language,…
Several recent papers have discussed utilizing Lipschitz constants to limit the susceptibility of neural networks to adversarial examples. We analyze recently proposed methods for computing the Lipschitz constant. We show that the Lipschitz…
For a given stable recurrent neural network (RNN) that is trained to perform a classification task using sequential inputs, we quantify explicit robustness bounds as a function of trainable weight matrices. The sequential inputs can be…
High sensitivity of neural networks against malicious perturbations on inputs causes security concerns. To take a steady step towards robust classifiers, we aim to create neural network models provably defended from perturbations. Prior…
Topological data analysis uses tools from topology -- the mathematical area that studies shapes -- to create representations of data. In particular, in persistent homology, one studies one-parameter families of spaces associated with data,…
Despite the promise of Lipschitz-based methods for provably-robust deep learning with deterministic guarantees, current state-of-the-art results are limited to feed-forward Convolutional Networks (ConvNets) on low-dimensional data, such as…
Performative prediction is a framework for learning models that influence the data they intend to predict. We focus on finding classifiers that are performatively stable, i.e. optimal for the data distribution they induce. Standard…
Robustness of deep neural networks against adversarial perturbations is a pressing concern motivated by recent findings showing the pervasive nature of such vulnerabilities. One method of characterizing the robustness of a neural network…
Artificial and biological agents cannon learn given completely random and unstructured data. The structure of data is encoded in the metric relationships between data points. In the context of neural networks, neuronal activity within a…
Designing neural networks with bounded Lipschitz constant is a promising way to obtain certifiably robust classifiers against adversarial examples. However, the relevant progress for the important $\ell_\infty$ perturbation setting is…