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Verifying software correctness has always been an important and complicated task. Recently, formal proofs of critical properties of algorithms and even implementations are becoming practical. Currently, the most powerful automated proof…
The "Concrete Semantics" book gives an introduction to imperative programming languages accompanied by an Isabelle/HOL formalization. In this paper we discuss a re-formalization of the book using the Coq proof assistant. In order to achieve…
The normalization of query and key vectors is an essential part of the Transformer architecture. It ensures that learning is stable regardless of the scale of these vectors. Some normalization approaches are available. In this preliminary…
Automatically generated code is gaining traction recently, owing to the prevalence of Large Language Models (LLMs). Further, the AlphaProof initiative has demonstrated the possibility of using AI for general mathematical reasoning.…
We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of…
In this work, we explore proof theoretical connections between sequent, nested and labelled calculi. In particular, we show a general algorithm for transforming a class of nested systems into sequent calculus systems, passing through linear…
We report the results of the first experiments with learning proof dependencies from the formalizations done with the Coq system. We explain the process of obtaining the dependencies from the Coq proofs, the characterization of formulas…
As language models (LMs) deliver increasing performance on a range of NLP tasks, probing classifiers have become an indispensable technique in the effort to better understand their inner workings. A typical setup involves (1) defining an…
Naming conventions are an important concern in large verification projects using proof assistants, such as Coq. In particular, lemma names are used by proof engineers to effectively understand and modify Coq code. However, providing…
Many combinatorial proofs rely on induction. When these proofs are formulated in traditional language, they can be bulky and unmanageable. Coalgebras provide a language which can reduce reduce many inductive proofs in graded poset theory to…
We present a generic partition refinement algorithm that quotients coalgebraic systems by behavioural equivalence, an important task in system analysis and verification. Coalgebraic generality allows us to cover not only classical…
Formalization of real analysis offers a chance to rebuild traditional proofs of important theorems as unambiguous theories that can be interactively explored. This paper provides a comprehensive overview of the Lebesgue Differentiation…
This paper contributes to a development of randomized methods for neural networks. The proposed learner model is generated incrementally by stochastic configuration (SC) algorithms, termed as Stochastic Configuration Networks (SCNs). In…
We define an extension of lambda-calculus with dependents types that enables us to encode transparent and opaque probabilistic programs and prove a strong normalisation result for it by a reducibility technique. While transparent…
While rule-based attribution methods have proven useful for providing local explanations for Deep Neural Networks, explaining modern and more varied network architectures yields new challenges in generating trustworthy explanations, since…
We present a general-purpose data compression algorithm, Regularized L21 Semi-NonNegative Matrix Factorization (L21 SNF). L21 SNF provides robust, parts-based compression applicable to mixed-sign data for which high fidelity, individualdata…
We present a reformulation of the regression and classification, which aims to validate the result of a machine learning algorithm. Our reformulation simplifies the original problem and validates the result of the machine learning algorithm…
This paper is a survey of two kinds of "compressed" proof schemes, the \emph{matrix method} and \emph{proof nets}, as applied to a variety of logics ranging along the substructural hierarchy from classical all the way down to the…
The free-variable tableau method has been widely used in order to automate proofs in multiple kinds of logics. Many automated theorem provers rely on this approach, either because it is the only available method-e.g., in certain modal…
We construct a globalization of Ferrand's norm functor over rings which generalizes it to the setting of a finite locally free morphism of schemes $T\to S$ of constant rank. It sends quasi-coherent modules over $T$ to quasi-coherent modules…