arXiv subjects

Ryo Kamiya

Publications and source records attributed to Ryo Kamiya.

7 recordsLinked to original sources

arXiv2026

What Does Prompt Learning Change? -A Natural-Language Concept Analysis of Vision-Language Models

Prompt learning adapts vision-language models such as CLIP by optimizing continuous prompt vectors, but the learned prompts are difficult to interpret in natural language. We present PromptSpLiCE, a post-hoc method that expresses each class-conditioned text embedding as a sparse combination of concepts from a fixed natural-language dictionary. Using the same dictionary before and after prompt learning allows us to compare changes in their concept profiles. We evaluate PromptSpLiCE on CoOp, a representative prompt-learning method, across 11 image-classification datasets. The concept profiles change substantially: on average, only 1.6 of the initial top-10 concepts remain in the top 10 after learning. Across datasets, profile change is positively associated with accuracy gain. We also derive a local gradient expression that provides geometric intuition for why image-aligned concept directions distinct from the current prompt can have greater loss sensitivity.

cs.CV↗

arXiv2020

Coprimeness-preserving discrete KdV type equation on an arbitrary dimensional lattice

We introduce an equation defined on a multi-dimensional lattice, which can be considered as an extension to the coprimeness-preserving discrete KdV like equation in our previous paper. The equation is also interpreted as a higher-dimensional analogue of the Hietarinta-Viallet equation, which is famous for its singularity confining property while having an exponential degree growth. As the main theorem we prove the Laurent and the irreducibility properties of the equation in its "tau-function" form. From the theorem the coprimeness of the equation follows. In Appendix we review the coprimeness-preserving discrete KdV like equation whichis a base equation for our main system and prove the properties such as the coprimeness.

nlin.SI↗

arXiv2018

Algebraic entropy of a multi-term recurrence of the Hietarinta-Viallet type

We introduce a family of extensions of the Hietarinta-Viallet equation to a multi-term recurrence relation via a reduction from the coprimeness-preserving extension to the discrete KdV equation. The recurrence satisfies the irreducibility and the coprimeness property although it is nonintegrable in terms of an exponential degree growth. We derive the algebraic entropy of the recurrence by an elementary method of calculating the degree growth. The result includes the entropy of the original Hietarinta-Viallet equation.

math-ph↗

arXiv2018

Toda type equations over multi-dimensional lattices

We introduce a class of recursions defined over the $d$-dimensional integer lattice. The discrete equations we study are interpreted as higher dimensional extensions to the discrete Toda lattice equation. We shall prove that the equations satisfy the coprimeness property, which is one of integrability detectors analogous to the singularity confinement test. While the degree of their iterates grows exponentially, their singularities exhibit a nature similar to that of integrable systems in terms of the coprimeness property. We also prove that the equations can be expressed as mutations of a seed in the sense of the Laurent phenomenon algebra.

math-ph↗

arXiv2017

A two dimensional lattice equation as an extension of the Heideman-Hogan recurrence

We consider a two dimensional extension of the so-called linearizable mappings. In particular, we start from the Heideman-Hogan recurrence, which is known as one of the linearizable Somos-like recurrences, and introduce one of its two dimensional extensions. The two dimensional lattice equation we present is linearizable in both directions, and has the Laurent and the coprimeness properties. Moreover, its reduction produces a generalized family of the Heideman-Hogan recurrence. Higher order examples of two dimensional linearizable lattice equations related to the Dana-Scott recurrence are also discussed.

math-ph↗

arXiv2017

Nonlinear forms of coprimeness preserving extensions to the Somos-$4$ recurrence and the two-dimensional Toda lattice equation --investigation into their extended Laurent properties--

Coprimeness property was introduced to study the singularity structure of discrete dynamical systems. In this paper we shall extend the coprimeness property and the Laurent property to further investigate discrete equations with complicated pattern of singularities. As examples we study extensions to the Somos-$4$ recurrence and the two-dimensional discrete Toda equation. By considering their non-autonomous polynomial forms, we prove that their tau function analogues possess the extended Laurent property with respect to their initial variables and some extra factors related to the non-autonomous terms. Using this Laurent property, we prove that these equations satisfy the extended coprimeness property. This coprimeness property reflects the singularities that trivially arise from the equations.

math-ph↗

arXiv2016

Coprimeness-preserving non-integrable extension to the two-dimensional discrete Toda lattice equation

We introduce a so-called `coprimeness-preserving non-integrable' extension (another terminology is `quasi-integrable' extension) to the two-dimensional Toda lattice equation. We believe that this equation is the first example of such discrete equation defined over a three-dimensional lattice. We prove that all the iterates of the equation are irreducible Laurent polynomials of the initial data and that every pair of two iterates is co-prime, which indicate confined singularities of the equation. By reducing the equation to two- or one-dimensional lattices, we obtain coprimeness-preserving non-integrable extensions to the one-dimensional Toda lattice equation and the Somos-4 recurrence.

nlin.SI↗