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Min-Soo Kim

Publications and source records attributed to Min-Soo Kim.

At least 19 recordsLinked to original sources
arXiv2026

TRACK: Multiple Instance Learning for Anti-Money Laundering in Transaction Networks

Anti-money laundering (AML) investigations are organized around accounts, while the suspicious evidence for an account may reside in only a few of its transactions. Yet many account-level detectors summarize transactions before learning, and message-passing models may aggregate once more over neighboring accounts. We name this discrepancy the aggregation mismatch and study it under an account-window benchmark label defined by the presence of at least one flagged transaction. We recast account-level AML detection as multiple instance learning, in which an account-window is a bag and its transactions are instances. We propose TRACK, which encodes every transaction with a shared encoder and selectively pools the encodings into an account decision. To emulate coarse supervision, we withhold the transaction labels of five AML datasets from TRACK throughout training. Under a time-ordered protocol, TRACK achieves the highest average precision among the tabular and graph baselines trained from account labels on every dataset. Despite using only account-window supervision, it remains competitive with edge classifiers trained directly from transaction labels. Its instance scores also rank flagged transactions well above chance and approach or exceed directly supervised ranking performance across datasets.

cs.LG↗
arXiv2026

$p$-adic spectral zeta functions via the inverse Stieltjes transform

Spectral zeta functions provide a standard tool for regularizing determinants of differential operators in quantum physics. In a previous paper (J. Math. Phys. 66: 083505, 2025), we introduced a $p$-adic spectral zeta function for discrete spectra via a locally analytic interpolation function. In this paper we extend the framework to continuous spectra using the inverse Stieltjes transform. Starting from the resolvent of a bounded operator, we construct a generalized distribution, called the $p$-adic spectral distribution, and define bosonic and fermionic zeta functions and functional determinants. We establish their analytic properties, special value formulas, and Stirling expansions, and show that our previous framework is embedded into the present one in the discrete case. In this approach, the bosonic and fermionic cases exhibit an interesting symmetry. As an application, we consider the position operator in $p$-adic quantum mechanics on an arbitrary compact subset of $\mathbb{C}_{p}$.

math-ph↗
arXiv2026

Ray class groups in the cyclotomic tower

Let $p$ be an odd prime and let $Σ$ be a nonempty finite set of rational primes different from $p$. In the cyclotomic tower $\mathbb{Q}(μ_{p^{n+1}})$, we determine the kernels of the natural maps from the minus $p$-primary ray class groups, with modulus the product of the primes above $Σ$, to the corresponding ordinary minus $p$-primary class groups. We give their character components and elementary divisors at every finite layer, including the layers before splitting stabilizes. In the norm inverse limit, we obtain an explicit integral cyclic decomposition of the local module modulo the single diagonal global Tate module. Its coinvariants recover the finite local kernels. Together with ordinary class-group control, this gives exact control for the minus ray class groups. We identify the local Frobenius factors with Bernoulli regularization factors. For nonexceptional characters, the classical main conjecture then yields regularized measure generators of the ray class characteristic ideals. The exceptional Teichmüller component is treated without the main conjecture: the single Tate correction corresponds to the single pole of the $p$-adic zeta function. At the bottom layer, the local calculation and Herbrand--Ribet yield characterwise nonvanishing criteria involving regularized Bernoulli values. For a single auxiliary prime, the exceptional component detects the Wieferich condition. We also deduce Eisenstein congruence consequences from existing modular-form theorems.

math.NT↗
arXiv2026

Spectral zeta functions in positive characteristic

Spectral zeta functions and zeta-regularized determinants encode the spectrum of an operator in analytic functions. Over the completion $\mathbb C_\infty$ of an algebraic closure of $\mathbb F_q((π))$, two features of characteristic $p$ break this classical picture. Complex powers have exponents that vary only continuously in $\mathbb Z_p$, not analytically. Scalar traces record eigenvalue multiplicities only modulo $p$. We develop a resolvent-based theory that treats these two obstructions separately. For the first, inverse Stieltjes duality turns suitable scalar resolvents into locally analytic spectral distributions on $\mathbb F_q[[π]]$. A single exponent of the Mellin transform already determines the distribution and the entire Mellin family. We characterize exactly which power series arise in this way, by a growth condition on Carlitz moments. The criterion depends on the support: bounded Taylor coefficients are not sufficient. For stationary digit measures, the transform is the unique fixed point of an explicit contraction. The first $q-1$ nonconstant moments recover the measure. For the second, we replace traces by the Frobenius defect $F/σ(F)$, where $σ$ raises coefficients to their $q$th powers. On power series with small coefficients, this map is a group automorphism that preserves Gauss distances, and a convergent infinite product inverts it. Polynomial defects produce entire functions. They characterize exactly the diagonal spectra that are finite unions of forward Frobenius orbits, counted with multiplicity. For the shifted Carlitz operator, the resulting Fredholm determinant is a normalized reciprocal of the Anderson--Thakur function, and its Newton polygon is determined exactly.

math.NT↗
arXiv2026

Decentralized Medical Data Sharing with Off-chain Storage and View-based Access Control

Recently, many blockchain-based medical data sharing systems using off-chain storage have been proposed. However, these systems have some drawbacks such as being incompletely decentralized, low adaptability to cloud storages, high cost, and low security. It is non-trivial to address the drawbacks due to the transparency, immutability, and decentralization of a blockchain platform. Our goal is to design a decentralized medical data sharing system with off-chain storage that addresses all the above drawbacks while satisfying data protection and privacy laws. We propose the VASCO (View-based AccesS COntrol) system that does not rely on any central server including a key generation one, not rely on any special cloud storage including IPFS, not use a secure channel, encrypts both data and metadata, and supports end-to-end encryption. We achieve it by designing eight chaincodes rigorously based on view-based access control. For a medical data ecosystem that consists of many stakeholders who employ different data standards, storage formats, and transmission protocols, we present how typical flows of medical data in the ecosystem can be achieved by using the proposed chaincodes with interoperability. We showed that VASCO is superior to the existing systems in terms of both functionality and regulatory compliance. We also tested the scalability of VASCO using a blockchain of 21 peer nodes with different specifications and verified interoperability through 30 combinations of standards, formats, and protocols. VASCO is a promising medical data sharing system that can provide secure and efficient sharing of medical data while preserving patient privacy and satisfying regulatory compliance with interoperability. The result of this study provides a potential to improve patient outcomes and advance medical research for the medical data ecosystem.

cs.DB↗
arXiv2026

An alternating Mizuno formula, modified gamma functions, and double sine special values

For $n\ge1$ and $\operatorname{Re}(x_j)>0$, we prove an alternating analogue of Mizuno's product formula: \begin{equation*} \prod\nolimits_{m=0}^{\infty} \left(\prod_{j=1}^{n}(m+x_j)\right)^{(-1)^m} = \frac{(\sqrt{π/2})^n} {\prod_{j=1}^{n}\widetildeΓ(x_j)}, \end{equation*} where $\widetildeΓ$ is the modified gamma function associated with the alternating Hurwitz zeta function. The polynomial factors are regularized using factorwise logarithms, and the formula establishes compatibility between this regularization and polynomial factorization. Applications include Gaussian and cyclotomic (Kurokawa--Wakayama type) evaluations; the single-factor case recovers the alternating Lerch formula, and a normalized ratio yields Wallis' product. A second group of results concerns an alternating double sine-type function. At nonexceptional positive periods, its positive-integer special values admit finite tangent-product representations. These products define locally meromorphic continuations $F_m$ in the period parameter. For $m\ge2$ and nonzero algebraic parameters, the continued values belong to $\mathbb P^1(\overline{\mathbb Q})$ at rational parameters and are finite, nonzero, and transcendental at nonrational parameters. We determine their orders at rational parameters and distinguish parameter continuation from fixed-period specialization at exceptional parameters. Additional results include Barnes factorizations of multiple alternating gamma functions, a Glaisher--Kinkelin special value, finite-product Stirling-type asymptotics, a symmetric two-parameter form of the known odd-integer multiplication formula, and an odd-scaling distribution relation for the alternating double sine-type function.

math.NT↗
arXiv2026

AkasicMEM: Governed Enterprise Memory for Agents

Agent memory enables enterprise agents to retain knowledge acquired during work and reuse it across tasks and agents, turning execution experience into persistent organizational knowledge. Realizing this potential requires both source--memory integration, through which enterprise sources and accumulated memory can be utilized together, and memory governance, through which shared memory remains subject to organizational policies throughout its lifecycle. These requirements interact when information from enterprise sources persists in memory. As this information is repeatedly derived and reused under changing principals and policies, source restrictions may be bypassed, resulting in information leakage. Preventing such leakage requires authorization continuity, under which source restrictions remain effective throughout source-to-memory and memory-to-memory derivation and reuse. Existing approaches address these concerns individually, but do not treat source--memory integration, memory governance, and authorization continuity as combined core design targets across the memory lifecycle. We define Governed Enterprise Memory as agent memory designed around this combined scope and present AkasicMEM as its realization. AkasicMEM realizes authorization continuity through transitive lineage, policy composition during memory formation, and policy re-evaluation during retrieval. It is built on GraphAI's AkasicDB, a unified vector--graph--relational database whose storage and execution substrate enables the underlying operations of these mechanisms to be jointly optimized and executed.

cs.DB↗
arXiv2026

Infinite-order $p$-adic differential equations for Hurwitz-type Euler zeta functions: Uniqueness and higher-dimensional extensions

We generalize the one-dimensional infinite-order linear differential equation satisfied by the $p$-adic Hurwitz-type Euler zeta function (Abh. Math. Semin. Univ. Hambg. 91: 117--135, 2021) to $n$ variables. By encoding the differential operator as a convolution with a distribution kernel, we introduce partial zeta functions and partial operators indexed by subsets of $\{1,\dots,n\}$. A tensor product expansion of the distribution kernel is established, whose Möbius inversion via the binomial theorem yields the higher-dimensional analogue of the original equation in the form of an alternating-sum identity, reducing to the one-dimensional case when $n=1$. Convergence of the resulting series is confirmed by non-Archimedean estimates. As a second main contribution, we prove that, under the condition $|a|_p > 2p^{1/(p-1)}$, within the Banach space of bounded analytic functions on $\mathbb Z_p$, the shifted $p$-adic Hurwitz-type Euler zeta function is the unique solution to the one-dimensional equation. This uniqueness result establishes that the infinite-order $p$-adic differential equation admits at most one bounded analytic solution, and together with the existence theorem, it characterizes the shifted $p$-adic Hurwitz-type Euler zeta function uniquely. This sharply distinguishes it from the complex setting, where the operator series diverges on the Hurwitz zeta function, and the formal kernel fails to converge in the usual spaces of analytic test functions.

math.NT↗
arXiv2026

On path integrals for wave functions taking $p$-adic values

In this paper, we construct a $p$-adic path integral via $p$-adic multiple integrals. This integral describes the evolution of a wave function $Ψ(x)$, defined as a map from a domain in $\mathbb{C}_p$ to $\mathbb{C}_p$. Unlike the standard $p$-adic quantum mechanics formulated for functions $\mathbb{Q}_p \to \mathbb{C}$, our construction works directly on $\mathbb{C}_p$-valued wave functions. Using $p$-adic Dirac delta measures and $p$-adic additive characters, we define the propagator as a finite-partition multiple integral, which allows explicit iterative integration. As an application, we compute the Feynman propagator for free particles and obtain a closed-form expression analogous to the classical counterpart. Our method provides a discrete, constructive alternative that complements the existing distribution-theoretic frameworks for $p$-adic functional integration.

math-ph↗
arXiv2026

Ramanujan-type identities for alternating Hurwitz zeta functions

Around 1910, in an unpublished manuscript, Ramanujan proposed the following identity for $ζ(2n+1)$: \[ \begin{aligned} α^{-n}\,&\left\{\dfrac{1}{2}\,ζ(2n + 1) + \sum_{m = 1}^{\infty}\dfrac{m^{-2n - 1}}{e^{2αm} - 1}\right\} \\ &\quad\quad\quad\quad\quad\quad\quad-(-β)^{-n}\,\left\{\dfrac{1}{2}\,ζ(2n + 1) + \sum_{m = 1}^{\infty}\dfrac{m^{-2n - 1}}{e^{2βm} - 1}\right\}\\ &=2^{2n}\sum_{k = 0}^{n + 1}\dfrac{(-1)^{k-1}B_{2k}\,B_{2n - 2k + 2}}{(2k)!(2n - 2k + 2)!}\,α^{n - k + 1}β^k, \end{aligned} \] where $α$, $β$ are positive numbers satisfying $αβ=π^2,n\in\mathbb{N},$ $B_n$ denotes the $n$-th Bernoulli number and $ζ(z)$ is the Riemann zeta function. As shown by Berndt in the viewpoint of general transformation of analytic Eisenstein series, it is a natural companion of Euler's famous formula for even zeta values. In this paper, we extend Ramanujan's identity to the alternating Hurwitz zeta function. Then we systematically investigate the properties of the alternating Hurwitz zeta function $ζ_E(z,x)$, as well as the corresponding Ramanujan-type identities, under different modular symmetry conditions. We also establish infinite series expressions for products of the tangent and hyperbolic tangent functions, and express the Dirichlet lambda function $λ(z)$ together with linear combinations of infinite series as convolution sums of special sequences. Furthermore, we define alternating Hurwitz kernels of even and odd orders, and obtain Ramanujan-type identities involving the alternating digamma function $\widetildeψ(x)$ and Euler polynomials $E_n(x)$, as well as transformation formulas between even-order and odd-order alternating Hurwitz kernels.

math.NT↗
arXiv2026

GraFine: Retrieval-Time Refinement for Efficient Graph RAG over Corpus Graphs

Graph RAG on corpus graphs enhances retrieval by leveraging intermediate node content as contextual clues to uncover unretrieved oracle nodes. However, existing methods suffer from two critical blind spots, namely semantically blind graph expansion and topology blind pruning, or else rely on prohibitively slow retrieval and generation interleaving. To address this, we formalize these limitations through an operational taxonomy and propose a retriever design that couples semantics-aware adding with graph-aware pruning under efficiency constraints. We instantiate this design as GraFine, which alternates between two refinement stages: Semantic Proximity eXpansion (SPX) for semantics-aware node addition, and a Graph Smoothing Reranker (GSR) for graph-aware pruning. Experiments on reference networks and text-rich knowledge graphs show that GraFine improves retrieval accuracy and generation quality while maintaining time-efficiency. Furthermore, we introduce Topological Recall (TR), a metric that quantifies the topological proximity between retrieved and oracle nodes. Our analysis using TR confirms that GraFine more effectively steers refinement toward undiscovered oracle nodes by leveraging intermediate contextual clues. Our code is available at this link: https://github.com/asmath472/GraFine.

cs.IR↗
arXiv2026

AkasicDB: Demonstrating Omni RAG with a Unified Vector-Graph-Relational DBMS

Recent Retrieval-Augmented Generation (RAG) systems increasingly combine vector retrieval with structured knowledge, such as Graph RAG and Filtered vector search. However, existing database architectures struggle to support such complex RAG workflows efficiently, as they rely on out-of-DB pipelines or in-DB non-native integration, leading to high overhead. This demo paper presents AkasicDB, a database system that natively supports such RAG workflows by jointly executing vector similarity search, graph traversal, and relational filtering within a single execution framework. AkasicDB extends our prior work, Chimera, with native vector support to enable such unified execution. Based on AkasicDB, we demonstrate the first native integration of Vector-Graph-Relational RAG, which we refer to as Omni RAG. Through an interactive chat-style demonstration, users execute and visualize Omni RAG queries, directly experiencing its superior retrieval and reasoning over vector-only approaches while observing the practical limitations of existing database architectures in supporting Omni RAG. A demonstration video is available at https://youtu.be/8d09_dtrEIM

cs.DB↗
arXiv2026

SafeQL: Search-based Refinement for Safe and Efficient LLM-based Text-to-SQL

Large language models (LLMs) have advanced Text-to-SQL by enabling natural language interfaces to databases without task-specific fine-tuning. However, existing LLM-based systems remain unreliable, often generating SQL queries that are invalid under the database schema, referencing non-existent tables, attributes, functions, or values. Such errors persist because interactions with the database management system (DBMS) are typically limited to error messages, leaving it in a largely passive role during query refinement. This paper proposes SafeQL, \textit{a search-based refinement paradigm that redefines the role of the DBMS as an active guide in the refinement process}. Instead of regenerating entire queries after execution failure, SafeQL interprets DBMS feedback to incrementally repair only the erroneous components. Each refinement step is formulated as a guided search within a \textit{safe query space}, where candidate queries are progressively validated through DBMS execution, thereby converging to an executable query and preventing repeated regeneration of errors. Experiments on the Bird and Spider benchmarks show that SafeQL significantly improves execution accuracy and efficiency compared to regeneration-based methods.

cs.DB↗
arXiv2026

RL-SPH: Learning to Achieve Feasible Solutions for Integer Linear Programs

Primal heuristics play a crucial role in quickly finding feasible solutions for NP-hard integer linear programming (ILP). Although $\textit{end-to-end learning}$-based primal heuristics (E2EPH) have recently been proposed, they are typically unable to independently generate feasible solutions. To address this challenge, we propose RL-SPH, a novel reinforcement learning-based start primal heuristic capable of independently generating feasible solutions, even for ILP involving non-binary integers. Empirically, RL-SPH rapidly obtains high-quality feasible solutions with a 100% feasibility rate, achieving on average a 28.6$\times$ lower primal gap and a 2.6$\times$ lower primal integral compared to existing start primal heuristics.

cs.LG↗
arXiv2026

GraphContainer: A Unified Platform for Comparing and Debugging Graph RAG Methods

Graph RAG mitigates hallucinations and stale knowledge in LLMs, particularly for multi-hop question answering. However, existing approaches remain highly fragmented and incompatible. The structural heterogeneity of graph formats across different frameworks and the lack of granular visualization tools make it exceedingly difficult to evaluate and compare retrieval behaviors. To bridge this gap, we propose GraphContainer, a novel platform designed to unify and visualize diverse graph RAG workflows. GraphContainer features two key components: (1) a Unified Graph Representation (UGR) layer that seamlessly standardizes multi-format graphs, and (2) a Graph Recorder that tracks and visually renders the step-by-step retrieval process. Through an interactive web interface, we demonstrate GraphContainer's ability to import heterogeneous graphs and perform live, traceable visual debugging of graph RAG methods. Ultimately, we show how GraphContainer enables controlled comparisons of various graph formats and retrieval strategies, lowering the barrier for researchers and practitioners to design optimal graph RAG pipelines. A demonstration video is available at https://youtu.be/O02eNJLwkU0.

cs.AI↗
arXiv2026

Improving Discrete Diffusion Unmasking Policies Beyond Explicit Reference Policies

Masked diffusion models (MDMs) have recently emerged as a novel framework for language modeling. MDMs generate sentences by iteratively denoising masked sequences, filling in [MASK] tokens step by step. Although MDMs support any-order sampling, performance is highly sensitive to the choice of which position to unmask next. Prior work typically relies on rule-based schedules (e.g., max-confidence, max-margin), which provide ad hoc improvements. In contrast, we replace these heuristics with a learned scheduler. Specifically, we cast denoising as a KL-regularized Markov decision process (MDP) with an explicit reference policy and optimize a regularized objective that admits policy improvement and convergence guarantees under standard assumptions. We prove that the optimized policy under this framework generates samples that more closely match the data distribution than heuristic schedules. Empirically, across four benchmarks, our learned policy consistently outperforms max-confidence: for example, on SUDOKU, where unmasking order is critical, it yields a 20.1% gain over random and a 11.2% gain over max-confidence. Code is available at https://github.com/chunsanHong/UPO.

cs.LG↗
arXiv2026

cuRPQ: A High-Performance GPU-Based Framework for Processing Regular and Conjunctive Regular Path Queries

Regular path queries (RPQs) are fundamental for path-constrained reachability analysis, and more complex variants such as conjunctive regular path queries (CRPQs) are increasingly used in graph analytics. Evaluating these queries is computationally expensive, but to the best of our knowledge, no prior work has explored GPU acceleration. In this paper, we propose cuRPQ, a high-performance GPU-optimized framework for processing RPQs and CRPQs. cuRPQ addresses the key GPU challenges through a novel traversal algorithm, an efficient visited-set management scheme, and a concurrent exploration-materialization strategy. Extensive experiments show that cuRPQ outperforms state-of-the-art methods by orders of magnitude, without out-of-memory errors.

cs.DB↗
arXiv2025

An analogue of Ramanujan's identity for Bernoulli-Carlitz numbers

In his second notebook, Ramanujan discovered the following identity for the special values of $ζ(s)$ at the odd positive integers \begin{equation*}\begin{aligned}α^{-m}\,\left\{\dfrac{1}{2}\,ζ(2m + 1) + \sum_{n = 1}^{\infty}\dfrac{n^{-2m - 1}}{e^{2αn} - 1}\right\} &-(- β)^{-m}\,\left\{\dfrac{1}{2}\,ζ(2m + 1) + \sum_{n = 1}^{\infty}\dfrac{n^{-2m - 1}}{e^{2βn} - 1}\right\}\nonumber &=2^{2m}\sum_{k = 0}^{m + 1}\dfrac{\left(-1\right)^{k-1}B_{2k}\,B_{2m - 2k+2}}{\left(2k\right)!\left(2m -2k+2\right)!}\,α^{m - k + 1}β^k \label{(1.2)},\end{aligned} \end{equation*} where $ α$ and $ β$ are positive numbers such that $ αβ= π^2 $ and $ m $ is a positive integer. As shown by Berndt in the viewpoint of general transformation of analytic Eisenstein series, it is a natural companion of Euler's famous formula for even zeta values. In this note, we prove an analogue of the above Ramanujan's identity in the functions fields setting, which involves the Bernoulli-Carlitz numbers.

math.NT↗