Related papers: Verification of Neural Networks (Lecture Notes)
We present a novel framework for specifying and verifying correctness globally for neural networks on perception tasks. Most previous works on neural network verification for perception tasks focus on robustness verification. Unlike…
Over the past few years, neural networks have re-emerged as powerful machine-learning models, yielding state-of-the-art results in fields such as image recognition and speech processing. More recently, neural network models started to be…
We show that an interesting class of feed-forward neural networks can be understood as quantitative argumentation frameworks. This connection creates a bridge between research in Formal Argumentation and Machine Learning. We generalize the…
This paper addresses the problem of formally verifying desirable properties of neural networks, i.e., obtaining provable guarantees that neural networks satisfy specifications relating their inputs and outputs (robustness to bounded norm…
These notes are based on a lecture delivered by NC on March 2021, as part of an advanced course in Princeton University on the mathematical understanding of deep learning. They present a theory (developed by NC, NR and collaborators) of…
Validation accuracy is a necessary, but not sufficient, measure of a neural network classifier's quality. High validation accuracy during development does not guarantee that a model is free of serious flaws, such as vulnerability to…
Deep neural networks (DNN) are growing in capability and applicability. Their effectiveness has led to their use in safety critical and autonomous systems, yet there is a dearth of cost-effective methods available for reasoning about the…
We present an approach for the verification of feed-forward neural networks in which all nodes have a piece-wise linear activation function. Such networks are often used in deep learning and have been shown to be hard to verify for modern…
Recently, several methods have been proposed to explain the predictions of recurrent neural networks (RNNs), in particular of LSTMs. The goal of these methods is to understand the network's decisions by assigning to each input variable,…
Formal verification has emerged as a promising method to ensure the safety and reliability of neural networks. However, many relevant properties, such as fairness or global robustness, pertain to the entire input space. If one applies…
Neural networks are vulnerable to adversarial attacks, i.e., small input perturbations can significantly affect the outputs of a neural network. Therefore, to ensure safety of neural networks in safety-critical environments, the robustness…
Neural networks are increasingly relied upon as components of complex safety-critical systems such as autonomous vehicles. There is high demand for tools and methods that embed neural network verification in a larger verification cycle.…
We review the theory of neural networks, as it has emerged in the last ten years or so within the physics community, emphasizing questions of biological relevance over those of importance in mathematical statistics and machine learning…
With the proliferation of Deep Machine Learning into real-life applications, a particular property of this technology has been brought to attention: robustness Neural Networks notoriously present low robustness and can be highly sensitive…
With the increasing integration of neural networks as components in mission-critical systems, there is an increasing need to ensure that they satisfy various safety and liveness requirements. In recent years, numerous sound and complete…
These are the lecture notes that accompanied the course of the same name that I taught at the Eindhoven University of Technology from 2021 to 2023. The course is intended as an introduction to neural networks for mathematics students at the…
Deep neural networks (DNNs) play an increasingly important role in various computer systems. In order to create these networks, engineers typically specify a desired topology, and then use an automated training algorithm to select the…
These lecture notes focus on the recent advancements in neural information retrieval, with particular emphasis on the systems and models exploiting transformer networks. These networks, originally proposed by Google in 2017, have seen a…
These brief lecture notes cover the basics of neural networks and deep learning as well as their applications in the quantum domain, for physicists without prior knowledge. In the first part, we describe training using backpropagation,…
The verification problem for neural networks is verifying whether a neural network will suffer from adversarial samples, or approximating the maximal allowed scale of adversarial perturbation that can be endured. While most prior work…