arXiv subjects

Keisuke Hoshino

Publications and source records attributed to Keisuke Hoshino.

6 recordsLinked to original sources

arXiv2026

Programming Backpropagation with Reverse Handlers for Arrows

We introduce a new programming language and its categorical semantics in order to design and implement neural networks within the framework of algebraic effects and handlers for arrows. Our language enables us to construct neural networks symbolically, in the same manner as algebraic effects, and to assign implementations -- such as backpropagation computations -- to them via handlers. The advantage of this language design is that network descriptions become abstract and high-level, while implementations can be flexibly assigned to networks. We establish a rigorous foundation for our language by developing a type system, an operational semantics, a categorical semantics, and soundness and adequacy theorems. The technical core is the introduction of reverse handlers, a novel handler mechanism for arrows for implementing backpropagation, together with new algebras of strong promonads on reverse differential restriction categories (RDRCs), whose string diagrams provide a formal graphical syntax and semantics for neural networks.

cs.PL↗

arXiv2025

$ω$-equifibrations between strict and weak $ω$-categories

We study $ω$-equifibrations between weak $ω$-categories in the sense of Batanin--Leinster. We define $ω$-equifibrations as a natural weak $ω$-categorical analogue of isofibrations between categories, and show that they can be characterised via the right lifting property with respect to a suitable set $J$ of strict $ω$-functors. The definition of $J$ involves the construction of a certain weak $ω$-category $\mathcal{E}^1$ which, roughly speaking, is freely generated by an equivalence 1-cell in a ``coherent'' manner. We show that the strict version of $\mathcal{E}^1$ coincides with Ozornova and Rovelli's coherent walking $ω$-equivalence $\widehat{ω\mathcal{E}}$. The $ω$-equifibrations between strict $ω$-categories coincide with the fibrations in the folk model structure.

math.CT↗

arXiv2025

$ω$-weak equivalences between weak $ω$-categories

We study $ω$-weak equivalences between weak $ω$-categories in the sense of Batanin-Leinster. Our $ω$-weak equivalences are strict $ω$-functors satisfying essential surjectivity in every dimension, and when restricted to those between strict $ω$-categories, they coincide with the weak equivalences in the model category of strict $ω$-categories defined by Lafont, Métayer, and Worytkiewicz. We show that the class of $ω$-weak equivalences has the 2-out-of-3 property. We also consider a generalisation of $ω$-weak equivalences, defined as weak $ω$-functors (in the sense of Garner) satisfying essential surjectivity, and show that this class also has the 2-out-of-3 property.

math.CT↗

arXiv2025

Double categories of relations relative to factorisation systems

We relativise double categories of relations to stable orthogonal factorisation systems. Furthermore, we present the characterisation of the relative double categories of relations in two ways. The first utilises a generalised comprehension scheme, and the second focuses on a specific class of vertical arrows defined solely double-categorically. We organise diverse classes of double categories of relations and correlate them with significant classes of factorisation systems. Our framework embraces double categories of spans and double categories of relations on regular categories, which we meticulously compare to existing work on the characterisations of bicategories and double categories of spans and relations.

math.CT↗

arXiv2024

Weakly invertible cells in a weak $ω$-category

We study weakly invertible cells in weak $ω$-categories in the sense of Batanin-Leinster, adopting the coinductive definition of weak invertibility. We show that weakly invertible cells in a weak $ω$-category are closed under globular pasting. Using this, we generalise elementary properties of weakly invertible cells known to hold in strict $ω$-categories to weak $ω$-categories, and show that every weak $ω$-category has a largest weak $ω$-subgroupoid.

math.CT↗

arXiv2008

Continuum Scaling from Large Mass Expansion on the Lattice: Delta Expansion Applied to the Anharmonic Oscillator

We dilate the scaling region of the lattice anharmonic oscillator at strong coupling by introducing the parameter delta. Performing expansion in delta, the calculation of the mass gap in the continuum limit via the series expansion effective at large lattice spacings is then studied. We show that the dilation on the mass parameter M recovers the scaling behavior of the hopping parameter beta and allows for precise approximation of the mass gap.

hep-lat↗