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Researcher profile

An Huang

An Huang contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
hep-thmath-phmath.MPmath.NTComputer VisionMachine Learningmath.APmath.CO

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Published work

6 published item(s)

preprint2026arXiv

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.

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preprint2026arXiv

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.

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preprint2022arXiv

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.

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preprint2020arXiv

Bounds on the Ricci curvature and solutions to the Einstein equations for weighted graphs

This is a preliminary study of the equation of motion of Euclidean classical gravity on a graph, based on the Lin-Lu-Yau Ricci curvature on graphs. We observe that the constant edge weights configuration gives the unique solution on an infinite tree w.r.t. the asymptotically constant boundary condition. We study the minimum and maximum of the action w.r.t. certain boundary conditions, on several types of graphs of interest. We also exhibit a new class of solutions to the equations of motion on the infinite regular tree.

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preprint2020arXiv

From $p$-adic to Archimedean Physics: Renormalization Group Flow and Berkovich Spaces

We introduce the $p$-adic particle-in-a-box as a free particle with periodic boundary conditions in the $p$-adic spatial domain. We compute its energy spectrum, and show that the spectrum of the Archimedean particle-in-a-box can be recovered from the $p$-adic spectrum via an Euler product formula. This product formula arises from a flow equation in Berkovich space, which we interpret as a space of theories connected by a kind of renormalization group flow. We propose that Berkovich spaces can be used to relate $p$-adic and Archimedean quantities generally.

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