arXiv subjects

Juntao Wang

Publications and source records attributed to Juntao Wang.

At least 19 recordsLinked to original sources

arXiv2026

Frobenius Galois expansions of substructural logics:Algebraization, Kalman equivalence and positive cone semantics

The main aim of this paper is to introduce a Frobenius--Galois expansion of the substructural logic $\mathbf{FL}_{ew}$ and develop its algebraic and categorical semantics. The resulting logic, denoted by $\mathbf{FL}^{\mathbf{FGC}}_{ew}$, is obtained by adjoining a pair of unary connectives forming a Galois connection and satisfying suitable Frobenius-type compatibility conditions. Firstly, we prove that $\mathbf{FL}^{\mathbf{FGC}}_{ew}$ is algebraizable in the sense of Blok and Pigozzi and identify its equivalent algebraic semantics with the variety of Frobenius-adjoint residuated lattices, establishing the conservativity over $\mathbf{FL}_{ew}$ and relating its finite model property to residual finiteness of finitely generated free algebras. Secondly, for the distributive setting, we lift the Kalman construction to the Frobenius-adjoint algebraic framework. More precisely, we establish a categorical equivalence between Frobenius-adjoint residuated distributive lattices and Frobenius-adjoint $c$-differential residuated distributive lattices with the condition $\mathbf{CK}$. This equivalence yields a positive-cone representation of the former structures and, in turn, a logical counterpart of the categorical correspondence. Finally, for the distributive extension $\mathbf{FL}^{\mathbf{FGC},d}_{ew}$, we prove that derivability, validity over Frobenius-adjoint residuated distributive lattices, and validity over the corresponding positive cones determine the same consequence relation, and further show that this correspondence preserves equational and quasi-equational consequence, conservativity, and finite countermodels. These results provide a unified algebraic, categorical, and logical framework for Frobenius--Galois expansions of substructural logics.

math.LO↗

arXiv2026

Positive Tensor-Network Kähler Metrics on gCICY Threefolds

We develop and implement a positive tensor-network parameterization for computing Ricci-flat Kähler metrics on Calabi-Yau manifolds. It replaces the large Hermitian coefficient matrix of a high-degree algebraic metric by a matrix-product factorization. For the immersed source spaces used here, the resulting metric is globally positive for every parameter value and, at fixed local and bond dimensions, its number of parameters grows only linearly with the algebraic degree. We test the construction on three generalized complete-intersection Calabi-Yau (gCICY) threefolds, constructing chart by chart the generalized sections, holomorphic volume forms and sampling measures that define and train the metric there. From a common low-degree metric, the tensor network outperforms a parameter-matched neural potential using the same section data, reducing both bulk errors and the one-percent tail conditional mean in every paired run. It also reaches a substantially lower error than direct optimization of an unrestricted Hermitian metric of the same degree from the same start, with both methods optimized to validation convergence under their respective schedules. On a second geometry, a higher-degree network with fewer parameters than a lower-degree unrestricted Hermitian baseline substantially reduces the same-sample errors. We further observe saturation within the tested calculations: at fixed bond dimension, increasing the degree eventually plateaus; increasing the bond dimension at fixed optimization effort gives no resolved gain; and the outcome depends strongly on initialization and optimization path.

hep-th↗

arXiv2026

McMg: A Learned Phase-Space Multi-channel Multigrid Preconditioner for Helmholtz Equation

Solving heterogeneous Helmholtz equations at high wavenumbers remains challenging because the discretized operator is indefinite, pollution degrades phase accuracy, and scalar coarse-grid correction can discard the local phase and propagation-direction information carried by oscillatory errors. We propose Multi-channel Multigrid (McMg), a learned phase-space multigrid preconditioner for heterogeneous Helmholtz equations. Rather than predicting the solution directly, McMg maps residuals to corrections within an iterative framework. Its central idea is to coarsen physical space while retaining unresolved local wave information in the channel dimension: each coarse node carries a learned packet of amplitude, phase, direction, and scattering coefficients rather than a single scalar unknown. The architecture combines linear multi-channel transfer operators with locally adaptive stencils, neural PDE operators, and medium-dependent smoothers whose coefficients are generated from the wave speed. For a fixed medium, the V-cycle is linear in the residual; nonlinear physical features are computed once in a setup phase and cached, so each online iteration reduces to convolutions with fixed coefficients. We further study generalization across scales. Models trained on small domains transfer directly to larger domains and higher effective wavenumbers, and a Layer-by-Layer Progressive Finetuning (LLPF) strategy improves large-domain scalability by adding new coarse levels while finetuning only the newly introduced parameters. Numerical experiments on high-frequency, high-contrast, and large-scale three-dimensional problems demonstrate that McMg requires substantially fewer iterations and less wall-clock time than strong classical baselines, while consistently outperforming existing neural preconditioners.

math.NA↗

arXiv2026

Filter-induced linear topologies on residuated lattices: Hausdorffness, profiniteness, and finiteness conditions

We study linear topologies on residuated lattices generated by systems of filters, with emphasis on the uniform structures and separation properties that they determine. A down-directed family of filters gives a natural compatible uniformity, and the associated topology makes the residuated lattice into a topological algebra. We characterize Hausdorffness by the triviality of the intersection of the underlying filter system. For compact topological residuated lattices, we prove the equivalence between topological profiniteness, residual finiteness, and representation as a closed subdirect product of finite discrete residuated lattices. We also analyze the descending chain condition ($DCC$) on filters. Under $DCC$, every filter system has a least element; hence every zero-dimensional linear topology is induced by a single filter, and the canonical map from filters to zero-dimensional linear topologies is bijective. This gives a corrected form of earlier representation arguments and identifies precisely where $DCC$ is required. Finally, working throughout in $\mathrm{ZFC}$, we give a sufficient criterion for the existence of non-discrete Hausdorff linear topologies, illustrated by the Gödel algebra.

math.GN↗

arXiv2026

Hilbert Functions and Line Bundle Cohomology on CICY Threefolds

Line bundle cohomology on complete intersection Calabi--Yau threefolds is an important input in string phenomenology. Previous work, based on direct extrapolation and on machine-learning analyses of finite data sets, has shown that these cohomology dimensions often admit chamber-wise polynomial descriptions on the Picard lattice. In this paper we explain this structure through the Hilbert functions associated with the non-trivial maps in the Koszul spectral sequence. Once Bott--Borel--Weil theory determines the non-vanishing ambient cohomology groups, the rank defects of the relevant Koszul maps are governed by Hilbert functions of cokernel or kernel modules. This turns many empirical chamber formulae into explicit rank-defect statements, with proofs that are either analytic or certified on finite boxes. Using this approach, we recover analytically almost all of the piecewise formulae appearing in the existing literature. For the remaining cases, we prove finite-box certificate theorems for infinite families of line bundles in the specified regions. We also identify new wall structures on certain CICYs which refine the chamber decompositions suggested by finite-range data. Finally, we use the same framework to construct line bundle cohomology formula libraries for two CICY threefolds which had not previously been analysed in this way. These results suggest that Hilbert-function methods can provide promising faster inputs for future string model-building scans based on line bundle constructions.

hep-th↗

arXiv2026

Neural Preconditioned Born Series: A Metric-Matched Framework for Learning-based Preconditioners

High-frequency Helmholtz problems in heterogeneous media remain challenging for both classical iterative methods and end-to-end neural PDE solvers. We propose Neural Preconditioned Born Series (NPBS), a learned iterative preconditioning framework that operates in preconditioned residual coordinates induced by the Convergent Born Series (CBS). Existing learned Born-series methods primarily use Born-style unrolling for forward wavefield prediction, while learned Helmholtz preconditioners are usually formulated in physical residual coordinates. NPBS fills this gap by recasting Born-series iteration as shifted-Laplacian left preconditioning, and replacing the CBS preconditioner with a learned residual-to-correction map in the Born-preconditioned coordinates. The left preconditioner further induces a residual metric, which yields a metric-matched training objective that aligns optimization with the preconditioned geometry used at inference. On heterogeneous Helmholtz benchmarks, metric-matched NPBS reduces iteration counts by up to $1.9\times$ over direct residual learning, with gains increasing from $1.2\times$ to $1.9\times$ as the wavenumber rises. Compared to classical CBS, learned NPBS reduces stationary iteration counts by over $20\times$; when used as a preconditioner for FGMRES, it further achieves the lowest wall-clock time among all evaluated methods. The same metric-matched formulation also improves convergence on convection--diffusion--reaction systems and Newton linear systems for nonlinear PDEs, indicating that residual-metric matching is a general design principle for neural preconditioners.

math.NA↗

arXiv2026

OptArgus: A Multi-Agent System to Detect Hallucinations in LLM-based Optimization Modeling

Large language models (LLMs) are increasingly used to translate natural-language optimization problems into mathematical formulations and solver code, but matching the reference objective value is not a reliable test of correctness: an artifact may agree numerically while still changing the underlying optimization semantics. We formulate this issue as \emph{optimization-modeling hallucination detection}, namely structural consistency auditing over the problem description, symbolic model, and solver implementation. We develop, to our knowledge, the first fine-grained hallucination taxonomy specifically for optimization modeling, spanning objective, variable, constraint, and implementation failures. We use this taxonomy to design OptArgus, a multi-agent detector with conductor routing, specialist auditors, and evidence consolidation. To evaluate this setting, we introduce a three-part benchmark suite with $484$ clean artifacts, $1266$ controlled injected artifacts, and $6292$ natural LLM-generated artifacts. Against a matched single-agent baseline, OptArgus produces fewer false alarms on clean artifacts, more accurate top-ranked localization on controlled single-error cases, and stronger detection on natural model outputs. Together, these contributions turn optimization-modeling hallucination detection into a concrete empirical problem and suggest that modular, taxonomy-grounded auditing is a practical route to more reliable optimization modeling.

cs.AI↗

arXiv2026

Tianwen-2 target asteroid (469219) Kamo'oalewa probably develops an Itokawa-compositional but ultra-highly space-weathered surface

China's Tianwen-2 mission plans to return samples from a small, rapidly spinning Earth quasi-satellite (469219) Kamo'oalewa. Previous studies linked Kamo'oalewa to lunar composition and origin. Here, we propose another scenario. We reanalyzed the reflectance spectrum of Kamo'oalewa and obtained an absorption band center at 1.001+-0.028 um (error is 1sigma), consistent with LL chondrites. We then conducted space weathering (SW) experiments on meteorites and found that highly space-weathered LL chondrite powder (but not slab) successfully reproduced the reflectance spectrum of Kamo'oalewa. We further traced the dynamical origin of Kamo'oalewa and found that it probably originated from the v6 secular resonance, and more specifically, the Flora family. Kamo'oalewa exhibits a similar composition to Itokawa and 7 objects in the Flora family, but with a higher degree of space weathering. We, therefore, proposed that Kamo'oalewa probably originated from the Flora family and developed an Itokawa-compositional, highly space-weathered, fine-regolith-dominated surface.

astro-ph.EP↗

arXiv2026

Optimality and annealing path planning of dynamical analog solvers

Recently proposed analog solvers based on dynamical systems, such as Ising machines, are promising platforms for large-scale combinatorial optimization. Yet, given the heuristic nature of the field, there is very limited insight on optimality guarantees of the solvers, as well as how parameter schedules shape dynamics and outcomes. Here, we develop a dynamical mean-field framework to analyze Ising-machine dynamics for finding the ground state energy of the Sherrington-Kirkpatrick(SK) model of spin glasses and identify mechanisms that enable rapid convergence to provenly near-optimal energies. For a fixed target energy density Ec, we show that solutions are typically reached within O(1) matrix vector multiplications, indicating constant time complexity. We further delineate theoretical limitations arising from different parameter-scheduling trajectories and demonstrate a pronounced benefit of temperature-only annealing for the Coherent Ising Machine. Building on these insights, we propose a general framework for designing optimized parameter schedules, thereby improving the practical effectiveness of Ising machines for complex optimization tasks. The superior performance of the dynamical solvers is illustrated by the attainment of the ground state energy of the SK model.

cond-mat.dis-nn↗

arXiv2026

A categorical equivalence for monadic algebras of first-order substructural logics motivated by Kalman's construction

The category $\mathbb{DRDL'}$, whose objects are c-differential residuated distributive lattices that satisfy the condition $\mathbf{CK}$, is the image of the category $\mathbb{RDL}$, whose objects are residuated distributive lattices, under the categorical equivalence (Kalman functor) $\mathbf{K}$. The main goal of this paper is to lift this equivalence $\mathbf{K}$ to the category $\mathbb{MRDL}$, whose objects are monadic residuated distributive lattices, and the category $\mathbb{MDRDL'}$, whose objects are pairs formed by an object of $\mathbb{DRDL'}$ and a center universal quantifier. Firstly, based on the variety of monadic FL$_\textrm{e}$-algebras, we introduce the concept of monadic residuated lattices and study some of their further algebraic properties, proving the classes of monadic residuated distributive lattices and monadic c-differential residuated distributive lattices are in one-to-one correspondence. Subsequently, based on this corresponding relation, we prove that there exists a categorical equivalence between the categories $\mathbb{MRDL}$ and $\mathbb{MDRDL'}$. The results of this paper not only generalizes the works of Sagastume and San Martín in [Mathematical Logic Quarterly, {\bf 60}(2014), 375--388], but also addresses and overcomes the limitations identified in the works of [Studia Logica, {\bf 111}(2023), 361--390]. Finally, this paper concludes with some applications regarding descriptions of a 2-contextual translation.

math.LO↗

arXiv2025

Adaptive Kernel Design for Bayesian Optimization Is a Piece of CAKE with LLMs

The efficiency of Bayesian optimization (BO) relies heavily on the choice of the Gaussian process (GP) kernel, which plays a central role in balancing exploration and exploitation under limited evaluation budgets. Traditional BO methods often rely on fixed or heuristic kernel selection strategies, which can result in slow convergence or suboptimal solutions when the chosen kernel is poorly suited to the underlying objective function. To address this limitation, we propose a freshly-baked Context-Aware Kernel Evolution (CAKE) to enhance BO with large language models (LLMs). Concretely, CAKE leverages LLMs as the crossover and mutation operators to adaptively generate and refine GP kernels based on the observed data throughout the optimization process. To maximize the power of CAKE, we further propose BIC-Acquisition Kernel Ranking (BAKER) to select the most effective kernel through balancing the model fit measured by the Bayesian information criterion (BIC) with the expected improvement at each iteration of BO. Extensive experiments demonstrate that our fresh CAKE-based BO method consistently outperforms established baselines across a range of real-world tasks, including hyperparameter optimization, controller tuning, and photonic chip design. Our code is publicly available at https://github.com/richardcsuwandi/cake.

cs.LG↗

arXiv2025

Machine Learning Free Quotients of CICYs

Free quotients of Calabi-Yau manifolds play an important role in string compactification. In this paper, we explore machine learning techniques, such as fully connected neural networks and multi-head attention (MHA) models, as a potential approach to detect $\mathbb{Z}_2$, $\mathbb{Z}_3$, $\mathbb{Z}_4$ and $\mathbb{Z}_2\times\mathbb{Z}_2$ free quotients of CICYs. When tested on unseen examples, both models successfully identified almost all free quotients for $\mathbb{Z}_2$, $\mathbb{Z}_3$, $\mathbb{Z}_4$ and $\mathbb{Z}_2\times\mathbb{Z}_2$ symmetry. These results demonstrate that well-trained machine learning models can effectively generalize to new Calabi-Yau manifolds and may aid in the broader classification of free quotients in the future.

hep-th↗

arXiv2025

Learning to Gridize: Segment Physical World by Wireless Communication Channel

Gridization, the process of partitioning space into grids where users share similar channel characteristics, serves as a fundamental prerequisite for efficient large-scale network optimization. However, existing methods like Geographical or Beam Space Gridization (GSG or BSG) are limited by reliance on unavailable location data or the flawed assumption that similar signal strengths imply similar channel properties. We propose Channel Space Gridization (CSG), a pioneering framework that unifies channel estimation and gridization for the first time. Formulated as a joint optimization problem, CSG uses only beam-level reference signal received power (RSRP) to estimate Channel Angle Power Spectra (CAPS) and partition samples into grids with homogeneous channel characteristics. To perform CSG, we develop the CSG Autoencoder (CSG-AE), featuring a trainable RSRP-to-CAPS encoder, a learnable sparse codebook quantizer, and a physics-informed decoder based on the Localized Statistical Channel Model. On recognizing the limitations of naive training scheme, we propose a novel Pretraining-Initialization-Detached-Asynchronous (PIDA) training scheme for CSG-AE, ensuring stable and effective training by systematically addressing the common pitfalls of the naive training paradigm. Evaluations reveal that CSG-AE excels in CAPS estimation accuracy and clustering quality on synthetic data. On real-world datasets, it reduces Active Mean Absolute Error (MAE) by 30\% and Overall MAE by 65\% on RSRP prediction accuracy compared to salient baselines using the same data, while improving channel consistency, cluster sizes balance, and active ratio, advancing the development of gridization for large-scale network optimization.

cs.LG↗

arXiv2025

Phase analysis of Ising machines and their implications on optimization

Ising machines, which are dynamical systems designed to operate in a parallel and iterative manner, have emerged as a new paradigm for solving combinatorial optimization problems. Despite computational advantages, the quality of solutions depends heavily on the form of dynamics and tuning of parameters, which are in general set heuristically due to the lack of systematic insights. Here, we focus on optimal Ising machine design by analyzing phase diagrams of spin distributions in the Sherrington-Kirkpatrick model. We find that that the ground state can be achieved in the phase where the spin distribution becomes binary, and optimal solutions are produced where the binary phase and gapless phase coexist. Our analysis shows that such coexistence phase region can be expanded by carefully placing a digitization operation, giving rise to a family of superior Ising machines, as illustrated by the proposed algorithm digCIM.

cond-mat.stat-mech↗

arXiv2025

Attentional Graph Neural Network Is All You Need for Robust Massive Network Localization

In this paper, we design Graph Neural Networks (GNNs) with attention mechanisms to tackle an important yet challenging nonlinear regression problem: massive network localization. We first review our previous network localization method based on Graph Convolutional Network (GCN), which can exhibit state-of-the-art localization accuracy, even under severe Non-Line-of-Sight (NLOS) conditions, by carefully preselecting a constant threshold for determining adjacency. As an extension, we propose a specially designed Attentional GNN (AGNN) model to resolve the sensitive thresholding issue of the GCN-based method and enhance the underlying model capacity. The AGNN comprises an Adjacency Learning Module (ALM) and Multiple Graph Attention Layers (MGAL), employing distinct attention architectures to systematically address the demerits of the GCN-based method, rendering it more practical for real-world applications. Comprehensive analyses are conducted to explain the superior performance of these methods, including a theoretical analysis of the AGNN's dynamic attention property and computational complexity, along with a systematic discussion of their robust characteristic against NLOS measurements. Extensive experimental results demonstrate the effectiveness of the GCN-based and AGNN-based network localization methods. Notably, integrating attention mechanisms into the AGNN yields substantial improvements in localization accuracy, approaching the fundamental lower bound and showing approximately 37\% to 53\% reduction in localization error compared to the vanilla GCN-based method across various NLOS noise configurations. Both methods outperform all competing approaches by far in terms of localization accuracy, robustness, and computational time, especially for considerably large network sizes.

cs.LG↗

arXiv2023

Correlation Functions in the TsT/$T{\bar T}$ Correspondence

We investigate the proposed holographic duality between the TsT transformation of IIB string theory on AdS$_3\times {\cal N}$ with NS-NS flux and a single-trace $T\bar{T}$ deformation of the symmetric orbifold CFT. We present a non-perturbative calculation of two-point correlation functions using string theory and demonstrate their consistency with those of the $T\bar{T}$ deformation. The two-point correlation function of the deformed theory on the plane, written in momentum space, is obtained from that of the undeformed theory by replacing $h$ with $h+2{\tilde λ\over w} p\bar p$, where $h$ is the spacetime conformal weight, $\tilde λ$ is a deformation parameter, $p$ and $\bar p$ are the momenta, and $w$ labels the twisted sectors in the deformed symmetric product. At $w=1$, the non-perturbative result satisfies the Callan-Symanzik equation for double-trace $T\bar T$ deformed CFT derived in \cite{Cardy:2019qao}. We also perform conformal perturbations on both the worldsheet CFT and the symmetric orbifold CFT as a sanity check. The perturbative and non-perturbative matching between results on the two sides provides further evidence of the conjectured TsT/$T\bar{T}$ correspondence.

hep-th↗

arXiv2023

On profiniteness and Hausdorffness of topological residuated lattices

The aim of this paper is to study the profiniteness of compact topological residuated lattices and the existence of Hausdorff topological residuated lattices. Firstly, we study profinite residuated lattices and obtain sufficient and necessary conditions for profiniteness in compact topological residuated lattices. These conditions include topological and algebraic characterizations. Moreover, it order to study the existence of Hausdorf topological residuated lattices, we investigate finiteness conditions in residuated lattices. Finally, we investigate linear topological residuated lattices and give the class of residuated lattices that can be endowed with a non-trivial Hausdorff topology.

math.LO↗

arXiv2022

Can laypeople predict the replicability of social science studies without expert intervention: an exploratory study

The low replication rate of published studies has long concerned the social science community, making understanding the replicability a critical problem. Several studies have shown that relevant research communities can make predictions about the replicability of individual studies with above-chance accuracy. Follow-up work further indicates that laypeople can also achieve above-chance accuracy in predicting replicability when experts interpret the studies into short descriptions that are more accessible for laypeople. The involvement of scarce expert resources may make these methods expensive from financial and time perspectives. In this work, we explored whether laypeople can predict the replicability of social science studies without expert intervention. We presented laypeople with raw materials truncated from published social science papers and elicited their answers to questions related to the paper. Our results suggested that laypeople were engaged in this technical task, providing reasonable and self-contained answers. The majority of them also demonstrated a good understanding of the material. However, the solicited information had limited predictive power on the actual replication outcomes. We further discuss several lessons we learned compared to the approach with expert intervention to inspire future works.

cs.HC↗