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An Huang

Publications and source records attributed to An Huang.

At least 19 recordsLinked to original sources
arXiv2026

Membership is Ownership: A Robust Ownership Verification Framework for Diffusion Models

Large-scale diffusion models have fueled numerous profitable downstream applications for AI-related businesses, including visual editing and content creation. Meanwhile, due to the huge amount of resource consumption (e.g., computation and high-quality data) during training, such diffusion models are deemed valuable intellectual property (IP) for tech companies like OpenAI and Google. Yet, the IP assets are vulnerable to various unauthorized uses by adversaries seeking to steal models for customized, usually commercial applications. Some existing approaches have explored IP protection for AI models; however, they mostly face structural limitations in common --- using a training-time watermarking by injecting artifacts in the model, which can impose a measurable utility cost and can be weakened by post-hoc fine-tuning. To address these challenges, this work investigates IP protection (i.e., model ownership verification) for diffusion models in a realistic commercial scenario with minimal model utility loss. Specifically, the proposed method builds a framework for model ownership verification, termed ``{Membership is Ownership} (MiO)'', based on a population-level hypothesis test on a private member evidence dataset. MiO verifies ownership using two criteria: model attribution through membership inference and model separation from public references. Both are tested at $p<10^{-6}$. We evaluate MiO on DDIM and Stable Diffusion models without modifying the owner model or its sampling pipeline, and report ROC-AUC and true-positive rates at fixed nominal false-positive targets. Furthermore, MiO stays stable under different post-theft fine-tuning and weight perturbation in adversarial scenarios, reflecting better robustness compared to the watermarking methods.

cs.CR↗
arXiv2026

Functional inequalities for starlike and convex functions associated with $g$-derivative operator

In this paper we first introduce a new class of derivative operators, termed $g$-derivative operators, which unifies the $q$-derivative, $(p,q)$-derivative and $(\alpha,\beta,\gamma)$-derivative operators, even classical derivative in the literature. Based on this generalized framework, we define two novel function classes, specifically $g$-starlike functions and $g$-convex functions. Further, we employ the subordination principle of analytic functions to conduct the coefficient estimations for such function classes, and subsequently derive the bounds for the corresponding Fekete-Szeg\"{o} inequality, Toeplitz determinants and Hankel determinants.

math.CV↗
arXiv2026

Watch Your Step: Information Injection in Diffusion Models via Shadow Timestep Embedding

Diffusion models have become the foundation of modern generative systems, with most research focusing primarily on improving generation efficiency and output quality. The timestep embedding component is a crucial part of the diffusion pipeline, which provides a temporal conditioning signal to the denoising network, enabling it to adapt its predictions across different noise levels throughout the process. Despite their potential to contain substantial information, timestep embeddings remain underexplored in current research, especially for security risks and reliable provenance. To fill this gap, we introduce Shadow Timestep Embedding (STE), a novel mechanism that investigates the underutilized temporal space for malicious information injection into diffusion models. In particular, when zooming in on the timestep embedding space, we find that different timesteps exhibit distinct representational capabilities that can encode side-channel information. Moreover, such encoded information can be utilized for attack and defense purposes through the scheduler interface. We present a theoretical analysis of timestep embeddings as position-encoding mappings and derive a mutual coherence evaluation that explains the separability of disjoint timestep intervals. Our findings reveal the diffusion model's timestep as a powerful side channel for carrying dedicated information, motivating new directions for adversarial generative modeling by understanding the temporal dimension.

cs.LG↗
arXiv2026

One-loop $p$-adic string theory and the N\'eron local height function

The $p$-adic string worldsheet action on the quotient of the Bruhat-Tits tree of $PGL(2,\mathbb{Q}_p)$ by a genus 1 Schottky group has a dual description on the asymptotic boundary, the Tate curve $\mathbb{Q}_p^\ast/q^\mathbb{Z}$. We show that the two point function of the dual action coincides with the N\'eron-Tate local height function of the Tate curve.

math.NT↗
arXiv2026

IQuest-Coder-V1 Technical Report

In this report, we introduce the IQuest-Coder-V1 series-(7B/14B/40B/40B-Loop), a new family of code large language models (LLMs). Moving beyond static code representations, we propose the code-flow multi-stage training paradigm, which captures the dynamic evolution of software logic through different phases of the pipeline. Our models are developed through the evolutionary pipeline, starting with the initial pre-training consisting of code facts, repository, and completion data. Following that, we implement a specialized mid-training stage that integrates reasoning and agentic trajectories in 32k-context and repository-scale in 128k-context to forge deep logical foundations. The models are then finalized with post-training of specialized coding capabilities, which is bifurcated into two specialized paths: the thinking path (utilizing reasoning-driven RL) and the instruct path (optimized for general assistance). IQuest-Coder-V1 achieves state-of-the-art performance among competitive models across critical dimensions of code intelligence: agentic software engineering, competitive programming, and complex tool use. To address deployment constraints, the IQuest-Coder-V1-Loop variant introduces a recurrent mechanism designed to optimize the trade-off between model capacity and deployment footprint, offering an architecturally enhanced path for efficacy-efficiency trade-off. We believe the release of the IQuest-Coder-V1 series, including the complete white-box chain of checkpoints from pre-training bases to the final thinking and instruction models, will advance research in autonomous code intelligence and real-world agentic systems.

cs.AI↗
arXiv2026

A glimpse into the Ultrametric spectrum

The non-relativistic string spectrum is built from integer-spaced energy quanta in such a way that the high-temperature asymptotics, via the Hardy-Ramanujan formula for integer partitions, reduces to standard two-dimensional thermodynamics. Here we explore deformed realizations of this behavior motivated by $p$-adic string theory and Lorentzian versions thereof with a non-trivial spectrum. We study the microstate scaling that results on associating quantum harmonic oscillators to the normal modes of tree-graphs rather than string graphs and observe that Hardy-Ramanujan scaling is not realized. But by computing the eigenvalues of the derivative operator on the $p$-adic circle and by determining the eigenspectrum of the Neumann-to-Dirichlet operator, we uncover a spectrum of exponentially growing energies but with exponentially growing degeneracies balanced in such a way that Hardy-Ramanujan scaling is realized, but modulated with log-periodic fluctuations.

hep-th↗
arXiv2025

Green's function on the Tate curve

Motivated by the question of defining a $p$-adic string worldsheet action in genus one, we define a Laplacian operator on the Tate curve, and study its Green's function. We show that the Green's function exists. We provide an explicit formula for the Green's function, which turns out to be a non-Archimedean counterpart of the Archimedean Green's function on a flat torus. In particular, it turns out that this Green's function recovers the N\'eron local height function for the Tate curve in the $p\to\infty$ limit, when the $j$-invariant has odd valuation. So this non-Archimedean height function now acquires a physics meaning in terms of the large $p$ limit of a non-Archimedean conformal field theory two point function on the Tate curve, as well as a direct analytic interpretation as a Green's function, on the same footing as in the Archimedean place.

math.NT↗
arXiv2024

Asymmetric electron distribution induced intrinsically strong anisotropy of thermal transport in bulk CrOCl

Anisotropic heat transfer offers promising solutions to the efficient heat dissipation in the realm of electronic device thermal management. However, the fundamental origin of the anisotropy of thermal transport remains mysterious. In this paper, by combining frequency domain thermoreflectance (FDTR) technique and first-principles-based multiscale simulations, we report the intrinsic anisotropy of thermal transport in bulk CrOCl, and further trace the origin of the anisotropy back to the fundamental electronic structures. The in-plane and cross-plane thermal conductivities ($\kappa$) at 300 K are found to be 21.6 and 2.18 Wm$^{-1}$K$^{-1}$, respectively, showcasing a strong $\kappa_\mathrm{in-plane}/\kappa_\mathrm{cross-plane}$ ratio of $\sim$10. Deep analysis of orbital-resolved electronic structures reveals that electrons are mainly distributed along the in-plane direction with limited interlayer distribution along the cross-plane direction, fundamentally leading to the intrinsic anisotropy of thermal transport in bulk CrOCl. The insight gained in this work sheds light on the design of advanced thermal functional materials.

physics.app-ph↗
arXiv2024

Finite Temperature at Finite Places

This paper studies AdS/CFT in its $p$-adic version (at the ``finite place") in the setting where the bulk geometry is made up of the Tate curve, a discrete quotient of the Bruhat-Tits tree. Generalizing a classic result due to Zabrodin, the boundary dual of the free massive bulk theory is explicitly derived. Introducing perturbative interactions, the Wittens diagrams for the two-point and three-point correlators are computed for generic scaling dimensions at one-loop and tree level respectively. The answers obtained demonstrate how $p$-adic AdS/CFT on the Tate curve provides a useful toy model for real CFTs at finite temperature.

hep-th↗
arXiv2024

Approximation of L-functions associated to Hecke cusp eigenforms

We derive a family of approximations for L-functions of Hecke cusp eigenforms, according to a recipe first described by Matiyasevich for the Riemann xi function. We show that these approximations converge to the true L-function and point out the role of an equidistributional notion in ensuring the approximation is well-defined, and along the way we demonstrate error formulas which may be used to investigate analytic properties of the L-function and its derivatives, such as the locations and orders of zeros. Together with the Euler product expansion of the L-function, the family of approximations also encodes some of the key features of the L-function such as its functional equation. As an example, we apply this method to the L-function of the modular discriminant and demonstrate that the approximation successfully locates zeros of the L-function on the critical line. Finally, we derive via Mellin transforms a convolution-type formula which leads to precise error bounds in terms of the incomplete gamma function. This formula can be interpreted as an alternative definition for the approximation and sheds light on Matiyasevich's procedure.

math.NT↗
arXiv2022

Quadratic reciprocity from a family of adelic conformal field theories

We consider a deformation of the two-dimensional free scalar field theory by raising the Laplacian to a positive real power. It turns out that the resulting non-local generalized free action is invariant under two commuting actions of the global conformal symmetry algebra, although it is no longer invariant under the full Witt algebra. Furthermore, there is an adelic version of this family of conformal field theories, parameterized by the choice of a number field, together with a Hecke character. Tate's thesis gives the Green's functions of these theories, and ensures that these Green's functions satisfy an adelic product formula. In particular, the local $L$-factors contribute to the prefactors of these Green's functions. Quadratic reciprocity turns out to be a consequence of an adelic version of a holomorphic factorization property of this family of theories on a quadratic extension of $\mathbb{Q}$. We explain that at the Archimedean place, the desired holomorphic factorization follows from the global conformal symmetry.

hep-th↗
arXiv2022

Deep-potential enabled multiscale simulation of gallium nitride devices on boron arsenide cooling substrates

High-efficient heat dissipation plays critical role for high-power-density electronics. Experimental synthesis of ultrahigh thermal conductivity boron arsenide (BAs, 1300 W m-1K-1) cooling substrates into the wide-bandgap semiconductor of gallium nitride (GaN) devices has been realized. However, the lack of systematic analysis on the heat transfer across the BAs-GaN interface hampers the practical applications. In this study, by constructing the accurate and high-efficient machine learning interatomic potentials, we performed multiscale simulations of the BAs-GaN heterostructures. Ultrahigh interfacial thermal conductance (ITC) of 265 MW m-2K-1 is achieved, which lies in the well-matched lattice vibrations of BAs and GaN. Moreover, the competition between grain size and boundary resistance was revealed with size increasing from 1 nm to 100 {\mu}m. Such deep-potential equipped multiscale simulations not only promote the practical applications of BAs cooling substrates in electronics, but also offer new approach for designing advanced thermal management systems.

cond-mat.mtrl-sci↗
arXiv2021

Massless $p2$-brane modes and the critical line

We consider a $p2$-brane model as a theory of maps from the vertices of the Bruhat-Tits tree times $\mathbb{Z}$ into $\mathbb{R}^d$. We show that in order for the worldsheet time evolution to be unitary, a certain spectral parameter of the model must localize at special loci in the complex plane, which include the (0,1) interval and the critical line of real part $1/2$. The excitations of the model are supported at these loci, with commutation relations closely resembling those of the usual bosonic string. We show that the usual Hamiltonian, momentum, and angular momentum are conserved quantities, and the Poincaré algebra is obeyed. Assuming an Euler product relation for the spectrum, the Riemann zeta zeros on the critical line have spectral interpretation as the massless photon and graviton in the Archimedean theory.

hep-th↗
arXiv2021

Green's Functions for Vladimirov Derivatives and Tate's Thesis

Given a number field $K$ with a Hecke character $χ$, for each place $ν$ we study the free scalar field theory whose kinetic term is given by the regularized Vladimirov derivative associated to the local component of $χ$. These theories appear in the study of $p$-adic string theory and $p$-adic AdS/CFT correspondence. We prove a formula for the regularized Vladimirov derivative in terms of the Fourier conjugate of the local component of $χ$. We find that the Green's function is given by the local functional equation for Zeta integrals. Furthermore, considering all places $ν$, the field theory two-point functions corresponding to the Green's functions satisfy an adelic product formula, which is equivalent to the global functional equation for Zeta integrals. In particular, this points out a role of Tate's thesis in adelic physics.

hep-th↗
arXiv2021

$\ell$-adic Tautological Systems

Tautological systems was introduced in Lian-Yau as the system of differential equations satisfied by period integrals of hyperplane sections of some complex projective homogenous varieties. We introduce the $\ell$-adic tautological systems for the case where the ground field is of characteristic $p$.

math.AG↗
arXiv2021

General relativity from $p$-adic strings

For an arbitrary prime number $p$, we propose an action for bosonic $p$-adic strings in curved target spacetime, and show that the vacuum Einstein equations of the target are a consequence of worldsheet scaling symmetry of the quantum $p$-adic strings, similar to the ordinary bosonic strings case. It turns out that certain $p$-adic automorphic forms are the plane wave modes of the bosonic fields on $p$-adic strings, and that the regularized normalization of these modes on the $p$-adic worldsheet presents peculiar features which reduce part of the computations to familiar setups in quantum field theory, while also exhibiting some new features that make loop diagrams much simpler. Assuming a certain product relation, we also observe that the adelic spectrum of the bosonic string corresponds to the nontrivial zeros of the Riemann Zeta function.

hep-th↗
arXiv2020

On the Sum of Ricci-Curvatures for Weighted Graphs

In this paper, we generalize Lin-Lu-Yau's Ricci curvature to weighted graphs and give a simple limit-free definition. We prove two extremal results on the sum of Ricci curvatures for weighted graph. A weighted graph $G=(V,E,d)$ is an undirected graph $G=(V,E)$ associated with a distance function $d\colon E\to [0,\infty)$. By redefining the weights if possible, without loss of generality, we assume that the shortest weighted distance between $u$ and $v$ is exactly $d(u,v)$ for any edge $uv$. Now consider a random walk whose transitive probability from an vertex $u$ to its neighbor $v$ (a jump move along the edge $uv$) is proportional to $w_{uv}:=F(d(u,v))/d(u,v)$ for some given function $F(\bullet)$. We first generalize Lin-Lu-Yau's Ricci curvature definition to this weighted graph and give a simple limit-free representation of $κ(x, y)$ using a so called $\ast$-coupling functions. The total curvature $K(G)$ is defined to be the sum of Ricci curvatures over all edges of $G$. We proved the following theorems: if $F(\bullet)$ is a decreasing function, then $K(G)\geq 2|V| -2|E|$; if $F(\bullet)$ is an increasing function, then $K(G)\leq 2|V| -2|E|$. Both equalities hold if and only if $d$ is a constant function plus the girth is at least $6$. In particular, these imply a Gauss-Bonnet theorem for (unweighted) graphs with girth at least $6$, where the graph Ricci curvature is defined geometrically in terms of optimal transport.

math.CO↗