arXiv subjects

Kei Saito

Publications and source records attributed to Kei Saito.

12 recordsLinked to original sources

arXiv2026

NRR-Core: Non-Resolution Reasoning as a Computational Framework for Contextual Identity and Ambiguity Preservation

Language-processing systems that optimize for a single resolved output risk losing ambiguity. With incomplete context, competing interpretations may be compressed prematurely. We specify Non-Resolution Reasoning (NRR) as an explicit retention-commitment interface for preserving context-indexed alternatives until evidence supports commitment. NRR organizes context-indexed alternatives, independently active weights, declared retention and commitment operations, and non-destructive output projection around three principles: Context-indexed Non-Identity, Approximate Identity, and Non-Resolution. It specifies a retained state and candidate operator vocabulary, and proposes Multi-Vector Embeddings, Non-Collapsing Attention, and Contextual Identity Tracking as implementable architectural realizations. In a reproducible synthetic two-turn task, one gated Multi-Vector-Embedding instantiation maintains high output entropy before disambiguating context arrives ($H = 0.91$ bits, near the $1.0$-bit maximum), while a controlled single-embedding baseline has low entropy ($H = 0.15$ bits); both tested systems resolve correctly after context arrives. Thus, high pre-context output uncertainty and accurate later resolution can coexist in the tested gated configuration. This result does not validate the full NRR architecture or matched-parameter superiority; the specification, proposed components, and demonstrated behavior remain distinct contribution layers. NRR targets premature commitment, not commitment itself: alternatives can remain available while evidence is incomplete, and commitment occurs at explicit output or action gates. The question is not whether AI should resolve ambiguity, but when, how, and under whose control. Implementation: https://github.com/kei-saito-research/nrr-core. Series hub: https://github.com/kei-saito-research/nrr-series-hub.

cs.CL↗

arXiv2026

NRR-Phi: A Typed External Text-to-State Interface and Update Contract for Inspectable Ambiguity-State Maintenance

Ambiguity-bearing inputs reach downstream systems through interfaces that favor a single resolved response before later context arrives. Even when alternatives are externalized, their representation and relative activation depend on the update rule. We address this state-maintenance problem within Non-Resolution Reasoning (NRR) by specifying a typed external text-to-state interface and explicit state-update contract. A mapping (phi: T -> S) constructs typed (v,c,w,m) records; declared operators make record carry-forward inspectable, while a record-weight entropy criterion separately tests normalized-weight concentration. The contract covers dampening, calibration, deferred resolution, contradiction-preserving integration, and temporal persistence. Across 580 constructed states/pairs, an executable suite performs 2,740 operator-state measurements. Tested non-violating transitions and calibration/identity checks show 0% record-weight entropy violations; a uniform-subtraction comparison violates the criterion at 1.7%, 6.1%, and 17.8% as subtraction increases. A separate 68-input construction audit finds multiple positive-weight typed records (mean record-weight entropy H = 1.087 bits) under the reported rule-based and archived LLM-assisted procedures, including a Japanese marker-set instantiation. The entropy criterion does not by itself certify record identity or cardinality, semantic adequacy, or end-to-end behavioral improvement. The repository provides deterministic reruns, archived prompt/output artifacts, transcript audit, and a fixed 18-set LLM-case sanity rerun. Phi therefore turns retained-state maintenance into a typed, executable, and falsifiable interface: record carry-forward is inspectable in declared operators, and normalized-weight concentration is separately testable before downstream commitment.

cs.CL↗

arXiv2025

Visualization of Interpersonal Communication using Indoor Positioning Technology with UWB Tags

In conjunction with a social gathering held on a university campus, the movement of attendees were tracked within the venue for approximately two hours using a UWB indoor positioning system, in order to visualize their interpersonal communication. Network and community analyses were performed on attendee interaction data, and the evolution of communities over time was further investigated through repeated community analysis at different time points. Furthermore, recognizing the influence of distance thresholds on defining contact, we discussed how varying these thresholds affected the resulting network structure and community analysis outcomes. This study confirmed that the temporal evolution of communities identified through community analysis broadly corresponded with the visually observed groupings of participants using the UWB indoor positioning system.

cs.SI↗

arXiv2025

A method of approximation of discrete Schrödinger equation with the normalized Laplacian by discrete-time quantum walk on graphs

We propose a class of continuous-time quantum walk models on graphs induced by a certain class of discrete-time quantum walk models with the parameter $ε\in [0,1]$. Here the graph treated in this paper can be applied both finite and infinite cases. The induced continuous-time quantum walk is an extended version of the (free) discrete-Schrödinger equation driven by the normalized Laplacian: the element of the weighted Hermitian takes not only a scalar value but also a matrix value depending on the underlying discrete-time quantum walk. We show that each discrete-time quantum walk with an appropriate setting of the parameter $ε$ in the long time limit identifies with its induced continuous-time quantum walk and give the running time for the discrete-time to approximate the induced continuous-time quantum walk with a small error $δ$. We also investigate the detailed spectral information on the induced continuous-time quantum walk.

quant-ph↗

arXiv2022

Spectral Analysis of Non-unitary Two-phase Quantum Walks in One Dimension

It is recently shown by Asahara-Funakawa-Seki-Tanaka that existing index theory for chirally symmetric (discrete-time) quantum walks can be extended to the setting of non-unitary quantum walks. More precisely, they consider a certain non-unitary variant of the two-phase split-step quantum walk as a concrete one-dimensional example, and give a complete classification of the associated index in their study. Note, however, that it remains uncertain whether or not their index gives a lower bound for the number of so-called topologically protected bound states unlike the setting of unitary quantum walks. In fact, the spectrum of a non-unitary operator can be any subset of the complex plane, and so the definition of such bound states is ambiguous in the non-unitary case. The purpose of the present article is to show that the simple use of transfer matrices naturally allows us to obtain an explicit formula for a topologically bound state associated with the non-unitary split-step quantum walk model mentioned above.

math-ph↗

arXiv2021

Strongly trapped space-inhomogeneous quantum walks in one dimension

Localization is a characteristic phenomenon of space-inhomogeneous quantum walks in one dimension, where particles remain localized around their initial position. The existence of eigenvalues of time evolution operators is a necessary and sufficient condition for the occurrence of localization, and their associated eigenvectors are deeply related to the amount of localization, i.e., the probability that the walker stays around the starting position in the long-time limit. In a previous study by authors, the eigenvalues of two-phase quantum walks with one defect were studied using a transfer matrix, which focused on the occurrence of localization (Quantum Inf. Process 20(5), 2021). In this paper, we introduce the analytical method to calculate eigenvectors using the transfer matrix and also extend our results to characterize eigenvalues not only for two-phase quantum walks with one defect but also for a more general space-inhomogeneous model. With these results, we quantitatively evaluate localization and study the strong trapping property by deriving the time-averaged limit distributions of five models studied previously.

math-ph↗

arXiv2021

A new type of spectral mapping theorem for quantum walks with a moving shift on graphs

The conventional spectral mapping theorem for quantum walks can only be applied for walks employing a shift operator whose square is the identity. This theorem gives most of the eigenvalues of the time evolution $U$ by lifting the eigenvalues of an induced self-adjoint matrix $T$ onto the unit circle on the complex plane. We acquire a new spectral mapping theorem for the Grover walk with a shift operator whose cube is the identity on finite graphs. Moreover, graphs we can consider for a quantum walk with such a shift operator is characterized by a triangulation. We call these graphs triangulable graphs in this paper. One of the differences between our spectral mapping theorem and the conventional one is that lifting the eigenvalues of $T-1/2$ onto the unit circle gives most of the eigenvalues of $U$.

quant-ph↗

arXiv2020

Eigenvalues of two-phase quantum walks with one defect in one dimension

We study space-inhomogeneous quantum walks (QWs) on the integer lattice which we assign three different coin matrices to the positive part, the negative part, and the origin, respectively. We call them two-phase QWs with one defect. They cover one-defect and two-phase QWs, which have been intensively researched. Localization is one of the most characteristic properties of QWs, and various types of two-phase QWs with one defect exhibit localization. Moreover, the existence of eigenvalues is deeply related to localization. In this paper, we obtain a necessary and sufficient condition for the existence of eigenvalues. Our analytical methods are mainly based on the transfer matrix, a useful tool to generate the generalized eigenfunctions. Furthermore, we explicitly derive eigenvalues for some classes of two-phase QWs with one defect, and illustrate the range of eigenvalues on unit circles with figures. Our results include some results in previous studies, e.g. Endo et al. (2020).

math-ph↗

arXiv2020

Spectral analysis for a multi-dimensional split-step quantum walk with a defect

This paper studies the spectrum of a multi-dimensional split-step quantum walk with a defect that cannot be analysed in the previous papers. To this end, we have developed a new technique which allow us to use a spectral mapping theorem for the one-defect model. We also derive the time-averaged limit measure for one-dimensional case as an application of the spectral analysis.

math-ph↗

arXiv2019

Periodicity for the 3-state quantum walk on cycles

Dukes (2014) and Konno, Shimizu, and Takei (2017) studied the periodicity for 2-state quantum walks whose coin operator is the Hadamard matrix on cycle graph C_N with N vertices. The present paper treats the periodicity for 3-state quantum walks on C_N. Our results follow from a new method based on cyclotomic field. This method shows a necessary condition for the coin operator of quantum walks to have the finite period. Moreover, we reveal the period T_N of two kinds of typical quantum walks, the Grover and Fourier walks. We prove that both walks do not have any finite period except for N=3, in which case T_3=6 (Grover), =12 (Fourier).

quant-ph↗

arXiv2019

Probability distributions and weak limit theorems of quaternionic quantum walks in one dimension

The discrete-time quantum walk (QW) is determined by a unitary matrix whose component is complex number. Konno (2015) extended the QW to a walk whose component is quaternion.We call this model quaternionic quantum walk (QQW). The probability distribution of a class of QQWs is the same as that of the QW. On the other hand, a numerical simulation suggests that the probability distribution of a QQW is different from the QW. In this paper, we clarify the difference between the QQW and the QW by weak limit theorems for a class of QQWs.

quant-ph↗

arXiv2019

Periodicity for the Fourier quantum walk on regular graphs

Quantum walks determined by the coin operator on graphs have been intensively studied. The typical examples of coin operator are the Grover and Fourier matrices. The periodicity of the Grover walk is well investigated. However, the corresponding result on the Fourier walk is not known. In this paper, we present a necessary condition for the Fourier walk on regular graphs to have the finite period. As an application of our result, we show that the Fourier walks do not have any finite period for some classes of regular graphs such as complete graphs, cycle graphs with selfloops, and hypercubes.

quant-ph↗