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Functional ANOVA offers a principled framework for interpretability by decomposing a model's prediction into main effects and higher-order interactions. For independent features, this decomposition is well-defined, strongly linked with SHAP…

Machine Learning · Statistics 2026-03-04 Baptiste Ferrere , Nicolas Bousquet , Fabrice Gamboa , Jean-Michel Loubes , Joseph Muré

Let p be a fixed prime. An Abelian p-group is an Abelian group (not necessarily finitely generated) in which every element has for its order some power of p. The countable Abelian p-groups are classified by Ulm's theorem, and Khisamiev…

Logic · Mathematics 2008-05-14 W. Calvert , D. Cenzer , V. S. Harizanov , A. Morozov

Regarding quaternions as normal matrices, we first characterize the $2\times 2$ matrix-valued functions, defined on subsets of quaternions, whose values are quaternions. Then we investigate the regularity of quaternionic-valued functions,…

Functional Analysis · Mathematics 2019-02-12 Florian-Horia Vasilescu

The Composite Operator Method (COM) is formulated, its internals illustrated in detail and some of its most successful applications reported. COM endorses the emergence, in strongly correlated systems (SCS), of composite operators,…

Strongly Correlated Electrons · Physics 2018-04-09 Adolfo Avella , Ferdinando Mancini

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…

Logic · Mathematics 2012-04-25 Paulo Oliva , Thomas Powell

Functional methods can be applied to the quantum effective action to efficiently determine counterterms and matching conditions for effective field theories. We extend the toolbox to two-loop order and beyond and show how to evaluate the…

High Energy Physics - Phenomenology · Physics 2025-08-20 Javier Fuentes-Martín , Adrián Moreno-Sánchez , Ajdin Palavrić , Anders Eller Thomsen

Computability logic is a formal theory of computational tasks and resources. Its formulas represent interactive computational problems, logical operators stand for operations on computational problems, and validity of a formula is…

Logic in Computer Science · Computer Science 2011-04-15 Giorgi Japaridze

It is consistent that there is a partial order (P,<) of size aleph_1 such that every monotone (unary) function from P to P is first order definable in (P,<). The partial order is constructed in an extension obtained by finite support…

Logic · Mathematics 2016-09-07 Martin Goldstern , Saharon Shelah

We propose a call-by-value lambda calculus extended with a new construct inspired by abductive inference and motivated by the programming idioms of machine learning. Although syntactically simple the abductive construct has a complex and…

Programming Languages · Computer Science 2017-10-12 Koko Muroya , Steven Cheung , Dan R. Ghica

Cantor's ordinal numbers, a powerful extension of the natural numbers, are a cornerstone of set theory. They can be used to reason about the termination of processes, prove the consistency of logical systems, and justify some of the core…

Logic in Computer Science · Computer Science 2025-10-22 Tom de Jong , Nicolai Kraus , Fredrik Nordvall Forsberg , Chuangjie Xu

Tennenbaum's theorem states that the only countable model of Peano arithmetic (PA) with computable arithmetical operations is the standard model of natural numbers. In this paper, we use constructive type theory as a framework to revisit,…

Logic · Mathematics 2024-08-07 Marc Hermes , Dominik Kirst

Roughly speaking, functional analysis is the study of vector spaces of arbitrary dimension over the field of real or complex numbers, and the continuous linear mappings between such spaces. Naturally, the notion of continuity requires a…

Functional Analysis · Mathematics 2025-10-09 Christoph Bock

We formulate a framework for describing behaviour of effectful higher-order recursive programs. Examples of effects are implemented using effect operations, and include: execution cost, nondeterminism, global store and interaction with a…

Logic in Computer Science · Computer Science 2021-12-30 Niccolò Veltri , Niels F. W. Voorneveld

Recently the second author introduced combinatorial principles that characterize supercompactness for inaccessible cardinals but can also hold true for small cardinals. We prove that the proper forcing axiom PFA implies these principles…

Logic · Mathematics 2010-12-10 Matteo Viale , Christoph Weiß

In the first of this pair of papers, it was proven that that no physical computer can correctly carry out all computational tasks that can be posed to it. The generality of this result follows from its use of a novel definition of…

Computational Physics · Physics 2009-10-02 David H. Wolpert

We examine "partition zeta functions" analogous to the Riemann zeta function but summed over subsets of integer partitions. We prove an explicit formula for a family of partition zeta functions already shown to have nice properties -- those…

Number Theory · Mathematics 2021-05-12 Robert Schneider , Andrew V. Sills

This work is meant to be a step towards the formal definition of the notion of algorithm, in the sense of an equivalence class of programs working "in a similar way". But instead of defining equivalence transformations directly on programs,…

Logic in Computer Science · Computer Science 2017-09-26 Fritz Müller

This work exploits the logical foundation of session types to determine what kind of type discipline for the pi-calculus can exactly capture, and is captured by, lambda-calculus behaviours. Leveraging the proof theoretic content of the…

Logic in Computer Science · Computer Science 2018-01-26 Bernardo Toninho , Nobuko Yoshida

We give two natural definitions of polynomial-time computability for L2 functions; and we show them incomparable (unless complexity class FP_1 includes #P_1).

Computational Complexity · Computer Science 2026-02-03 Aras Bacho , Svetlana Selivanova , Martin Ziegler

We consider different classes of combinatory structures related to Krivine realizability. We show, in the precise sense that they give rise to the same class of triposes, that they are equivalent for the purpose of modeling higher-order…