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The rapid evolution of machine learning (ML) has led to the widespread adoption of complex "black box" models, such as deep neural networks and ensemble methods. These models exhibit exceptional predictive performance, making them…

This paper examines the admissibility of AI-generated forensic evidence in criminal trials. The growing adoption of AI presents promising results for investigative efficiency. Despite advancements, significant research gaps persist in…

Interpretable machine learning tackles the important problem that humans cannot understand the behaviors of complex machine learning models and how these models arrive at a particular decision. Although many approaches have been proposed, a…

This paper proposes a set of criteria to evaluate the objectiveness of explanation methods of neural networks, which is crucial for the development of explainable AI, but it also presents significant challenges. The core challenge is that…

This paper describes the formal verification of two Turing machines using the program verifier Dafny. Both machines are deciders, so we prove total correctness. They are typical first examples of Turing machines used in any course of…

The proof identity problem asks: When are two proofs the same? The question naturally occurs when one reflects on mathematical practice. The problem understandably can be seen as a challenge for mathematical logic, and indeed various…

Datasets can be biased due to societal inequities, human biases, under-representation of minorities, etc. Our goal is to certify that models produced by a learning algorithm are pointwise-robust to potential dataset biases. This is a…

A machine learning model is traditionally considered robust if its prediction remains (almost) constant under input perturbations with small norm. However, real-world tasks like molecular property prediction or point cloud segmentation have…

Since its beginnings in the 1940s, automated reasoning by computers has become a tool of ever growing importance in scientific research. So far, the rules underlying automated reasoning have mainly been formulated by humans, in the form of…

Modern distributed systems rely on consensus protocols to build a fault-tolerant-core upon which they can build applications. Consensus protocols are correct under a specific failure model, where up to $f$ machines can fail. We argue that…

This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes…

Interactive theorem provers have been used extensively to reason about various software/hardware systems and mathematical theorems. The key challenge when using an interactive prover is finding a suitable sequence of proof steps that will…

The ``impossibility theorem'' -- which is considered foundational in algorithmic fairness literature -- asserts that there must be trade-offs between common notions of fairness and performance when fitting statistical models, except in two…

Confirmation bias is a cognitive bias that adversely affects management decisions, and mathematical modelling is an aid to its detailed understanding. Bias in opinion update about the value of a parameter is modelled here assuming that…

Machines are being increasingly used in decision-making processes, resulting in the realization that decisions need explanations. Unfortunately, an increasing number of these deployed models are of a 'black-box' nature where the reasoning…

It has been shown that a functional interpretation of proofs in mathematical analysis can be given by the product of selection functions, a mode of recursion that has an intuitive reading in terms of the computation of optimal strategies in…

Established frameworks to understand problems with reproducibility in science begin with the relationship between our understanding of the prior probability of a claim and the statistical certainty that should be demanded of it, and explore…

Explainability is needed to establish confidence in machine learning results. Some explainable methods take a post hoc approach to explain the weights of machine learning models, others highlight areas of the input contributing to…

Trustworthy verifiers are essential for the success of reinforcement learning with verifiable reward (RLVR), which is the core methodology behind various large reasoning models such as DeepSeek-R1. In complex domains like mathematical…

As software becomes more complex and assumes an even greater role in our lives, formal verification is set to become the gold standard in securing software systems into the future, since it can guarantee the absence of errors and entire…