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Modern program verifiers use logic-based encodings of the verification problem that are discharged by a back end reasoning engine. However, instances of such encodings for large programs can quickly overwhelm these back end solvers. Hence,…
Deep neural network (DNN) verification is an emerging field, with diverse verification engines quickly becoming available. Demonstrating the effectiveness of these engines on real-world DNNs is an important step towards their wider…
Modern verification tools for deep neural networks (DNNs) increasingly rely on abstraction to scale to realistic architectures. In parallel, proof production is becoming a critical requirement for increasing the reliability of DNN…
Matrix completion is one of the key problems in signal processing and machine learning, with applications ranging from image pro- cessing and data gathering to classification and recommender sys- tems. Recently, deep neural networks have…
Software correctness is ensured mathematically through formal verification, which involves the resources of generating formal requirement specifications and having an implementation that must be verified. Tools such as model-checkers and…
Algorithmic decision making driven by neural networks has become very prominent in applications that directly affect people's quality of life. In this paper, we study the problem of verifying, training, and guaranteeing individual fairness…
In this paper, we extend an available neural network verification technique to support a wider class of piece-wise linear activation functions. Furthermore, we extend the algorithms, which provide in their original form exact respectively…
The growing complexity and diversity of models used in the engineering of dependable systems implies that a variety of formal methods, across differing abstractions, paradigms, and presentations, must be integrated. Such an integration…
These lecture notes provide an introduction to the verification of neural networks from a theoretical perspective. We discuss feed-forward neural networks, recurrent neural networks, attention mechanisms, and transformers, together with…
Neural networks have in recent years shown promise for helping software engineers write programs and even formally verify them. While semantic information plays a crucial part in these processes, it remains unclear to what degree popular…
In Multimodal Neural Machine Translation (MNMT), a neural model generates a translated sentence that describes an image, given the image itself and one source descriptions in English. This is considered as the multimodal image caption…
Barrier functions are a general framework for establishing a safety guarantee for a system. However, there is no general method for finding these functions. To address this shortcoming, recent approaches use self-supervised learning…
Information Filtering Networks (IFNs) provide a powerful framework for modeling complex systems through globally sparse yet locally dense and interpretable structures that capture multivariate dependencies. This review offers a…
Machine Learning (ML) has exhibited substantial success in the field of Natural Language Processing (NLP). For example large language models have empirically proven to be capable of producing text of high complexity and cohesion. However,…
The role of the descriptor system representation as basis for reliable numerical computations for system analysis and synthesis, and in particular, for the manipulation of rational matrices, is discussed and available robust numerical…
It is often useful to perform integration over learned functions represented by neural networks. However, this integration is usually performed numerically, as analytical integration over learned functions (especially neural networks) is…
Automated theorem proving in first-order logic is an active research area which is successfully supported by machine learning. While there have been various proposals for encoding logical formulas into numerical vectors -- from simple…
Probabilistic language models are widely used in Information Retrieval (IR) to rank documents by the probability that they generate the query. However, the implementation of the probabilistic representations with programming languages that…
Large Language Models (LLMs) have shown strong performance on code understanding tasks, yet they fundamentally lack the ability to perform precise, exhaustive mathematical reasoning about program behavior. Existing benchmarks either focus…
Formal verification of complex algorithms is challenging. Verifying their implementations goes beyond the state of the art of current automatic verification tools and usually involves intricate mathematical theorems. Certifying algorithms…