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Donghyeon Kim

Publications and source records attributed to Donghyeon Kim.

At least 19 recordsLinked to original sources
arXiv2026

Coupled Pklt Tuples and Varieties of Pklt Type

We introduce asymptotic multiplier ideal sheaves and log canonical thresholds associated with tuples of pseudoeffective divisors on a projective klt pair. We prove that the threshold of a coupled potentially klt tuple is computed by a quasi-monomial valuation. For varieties of potentially klt type, we prove that every big divisor admits a birational Zariski decomposition with semiample positive part. We also prove finite generation of multisection rings of big divisors and give a criterion for a variety of potentially klt type to be a Mori dream space.

math.AG↗
arXiv2026

The elasticity of semiflexible polymers with reversible spontaneous curvature in two dimensions

Many semiflexible filaments exhibit structural asymmetries that lead to a curved ground state (curvature in the absence of thermal fluctuations, external forces, or torques). This property is known as spontaneous curvature. Many semiflexible polymers can reversibly develop spontaneous curvature through internal conformational transitions or through transient interactions with their molecular environment. In this article, we show that such reversible spontaneous curvature, even in the absence of transitions in the value of the bending stiffness, provides a minimal mechanism for ensemble-dependent elasticity. We formulate an analytically tractable two-state modified wormlike-chain model in two dimensions, in which an uncurved state (without spontaneous curvature) competes with a curved state (possessing spontaneous curvature). The transition is controlled by an activation energy. Within the weak-bending approximation, we obtain the Gibbs and Helmholtz partition functions for a stretched filament with reversible constant (uniform along the backbone) or sinusoidal spontaneous curvature and for a grafted bistable filament driven either by an end torque or a bending force. Stretching or bending induces a crossover from spontaneous-curvature-dominated to entropic elasticity. We show how the elastic response differs in the two ensembles (Gibbs vs Helmholtz). In addition, we consider the case where the curved state is also characterized by a higher value of the bending stiffness. In that case, a reentrant transition is possible as we stretch the bistable filament.

cond-mat.soft↗
arXiv2026

On the existence of minimizer on a log Fano cone singularity

We prove that if $x\in (X,Δ,\mathbb{T})$ is a log Fano cone singularity over an uncountable algebraically closed field, and $ν_0$ is a $\mathbb{T}$-invariant valuation with center $x$ and $A_{X,Δ}(ν_0)<\infty$, then the value $$ δ(X,Δ;ν_0):=\inf_{ν\in \mathrm{Val}^{\mathbb{T},*}_{X,\ni x}}\frac{A_{X,Δ}(ν)}{S(ν_0;ν)}$$ admits a minimum. The proof uses the generic limit argument. Note that there is a counterexample if we discard the log Fano cone structure.

math.AG↗
arXiv2026

On volumes and the generic invariance of Fano type varieties

We demonstrate the generic invariance of the Fano type property in cases where the volumes of anti-canonical divisors of Fano type fibers are a constant over a Zariski-dense subset, or the Fano type fibers are dimension $2$. Additionally, paralleling this theorem, we establish a conjecture by Schwede and Smith under the condition that the volumes of anti-canonical divisors remain constant in the reduction mod $p$.

math.AG↗
arXiv2026

On a cohomological property of the center of a resolution

In this note, we explore the cohomological property of the codimension of the center of a resolution. In particular, we define a resolution $f:X'\to X$ to be $q$-birational if the center of $f$ satisfies $\mathrm{codim} \,\mathrm{Cent}(f)\ge q+1$, and we prove that $R^if_*\mathcal{O}_X(E)=0$ for every $1\le i\le q-1$ and every $f$-anti-nef effective $f$-exceptional divisor $E$ on $X'$ if $X$ is $(R_q)$ and $(S_{q+1})$. We also discuss a partial converse of the theorem.

math.AG↗
arXiv2026

On the quasi-monomiality of the $α$- and $δ$-invariants

In this paper, we show that for any projective klt pair $(X,Δ)$ over an algebraically closed field of characteristic \(0\) and any big $\mathbb{Q}$-Cartier $\mathbb{Q}$-divisor $L$ on $X$, the invariants $α(X,Δ,L)$ and $δ(X,Δ,L)$ are computed by quasi-monomial valuations, without any uncountability assumption on the base field.

math.AG↗
arXiv2026

Structure of the Anticanonical Minimal Model Program for Potentially klt Pairs

We give an alternative proof of the existence of the anticanonical minimal model program for potentially klt pairs, assuming the anticanonical divisor admits a birational Zariski decomposition. Moreover, we establish a structure theorem showing that any partial anticanonical MMP starting from a potentially klt pair can be lifted to a compatible sequence of nonpositive maps between the $\mathbb{Q}$-factorial terminalizations of its successive steps.

math.AG↗
arXiv2026

Sim-to-Real of Humanoid Locomotion Policies via Joint Torque Space Perturbation Injection

This paper proposes a novel alternative to existing sim-to-real methods for training control policies with simulated experiences. Prior sim-to-real methods for legged robots mostly rely on the domain randomization approach, where a fixed finite set of simulation parameters is randomized during training. Instead, our method adds state-dependent perturbations to the input joint torque used for forward simulation during the training phase. These state-dependent perturbations are designed to simulate a broader range of reality gaps than those captured by randomizing a fixed set of simulation parameters. Experimental results show that our method enables humanoid locomotion policies that achieve greater robustness against complex reality gaps unseen in the training domain.

cs.RO↗
arXiv2026

Sim-to-Real of Humanoid Locomotion Policies via Joint Torque Space Perturbation Injection

This paper proposes a novel alternative to existing sim-to-real methods for training control policies with simulated experiences. Unlike prior methods that typically rely on domain randomization over a fixed finite set of parameters, the proposed approach injects state-dependent perturbations into the input joint torque during forward simulation. These perturbations are designed to simulate a broader spectrum of reality gaps than standard parameter randomization without requiring additional training. By using neural networks as flexible perturbation generators, the proposed method can represent complex, state-dependent uncertainties, such as nonlinear actuator dynamics and contact compliance, that parametric randomization cannot capture. Experimental results demonstrate that the proposed approach enables humanoid locomotion policies to achieve superior robustness against complex, unseen reality gaps in both simulation and real-world deployment.

cs.RO↗
arXiv2025

Minimal model program on the generic fiber of log Calabi-Yau type fibration

We study the minimal model program on the geometric generic fiber of a fibration $f:X\to S$ such that for a Zariski dense subset $S'\subseteq S$, $X_s$ is an $\varepsilon$-lc log Calabi--Yau type for every $s\in S'$. We prove that for a fibration $f:X\to S$ of varieties, if the fibers are of $\varepsilon$-lc log Calabi--Yau type, then the geometric generic fiber $X_{\overlineη}$ is pklt. In particular, for any big divisor $D$ on $X_{\overlineη}$, we can run the anticanonical MMP and $D$-MMP with scaling of an ample divisor on $X_{\overlineη}$.

math.AG↗
arXiv2025

The number of smooth varieties in an MMP on a 3-fold of Fano type

In this paper, we prove that for a threefold of Fano type $X$ and a movable $\mathbb{Q}$-Cartier Weil divisor $D$ on $X$, the number of smooth varieties that arise during the running of a $D$-MMP is bounded by $1 + h^1(X, 2D)$. Additionally, we prove a partial converse to the Kodaira vanishing theorem for a movable divisor on a threefold of Fano type.

math.AG↗
arXiv2025

Adjoint asymptotic multiplier ideal sheaves associated to potential triples

In this paper, we explore the geometry of potential triples $(X,Δ,D)$, which by definition consists of a pair $(X,Δ)$ and an $\mathbb{R}$-Cartier pseudoeffective divisor $D$ on $X$. We define and study the asymptotic multiplier ideal sheaf $\mathcal{J}(X,Δ,\lVert D\rVert)$ associated to a potential triple $(X,Δ,D)$. As a first main result, when $D$ is big, we prove that the condition $\mathcal{J}(X,Δ,\lVert D\rVert)=\mathcal{O}_{X}$ is equivalent to the triple $(X,Δ,D)$ being potentially klt, which is a klt analog of the pair $(X,Δ)$. We also study the closed set defined by the ideal sheaf $\mathcal{J}(X,Δ,\lVert D\rVert)$ and prove a Nadel type cohomology vanishing theorem for $\mathcal{J}(X,Δ,\lVert D\rVert)$. As an application of the main result, we prove that we can run the $(K_X+Δ+D)$-MMP with scaling of an ample divisor for a pklt triple $(X,Δ,D)$.

math.AG↗
arXiv2025

Takedown: How It's Done in Modern Coding Agent Exploits

Coding agents, which are LLM-driven agents specialized in software development, have become increasingly prevalent in modern programming environments. Unlike traditional AI coding assistants, which offer simple code completion and suggestions, modern coding agents tackle more complex tasks with greater autonomy, such as generating entire programs from natural language instructions. To enable such capabilities, modern coding agents incorporate extensive functionalities, which in turn raise significant concerns over their security and privacy. Despite their growing adoption, systematic and in-depth security analysis of these agents has largely been overlooked. In this paper, we present a comprehensive security analysis of eight real-world coding agents. Our analysis addresses the limitations of prior approaches, which were often fragmented and ad hoc, by systematically examining the internal workflows of coding agents and identifying security threats across their components. Through the analysis, we identify 15 security issues, including previously overlooked or missed issues, that can be abused to compromise the confidentiality and integrity of user systems. Furthermore, we show that these security issues are not merely individual vulnerabilities, but can collectively lead to end-to-end exploitations. By leveraging these security issues, we successfully achieved arbitrary command execution in five agents and global data exfiltration in four agents, all without any user interaction or approval. Our findings highlight the need for a comprehensive security analysis in modern LLM-driven agents and demonstrate how insufficient security considerations can lead to severe vulnerabilities.

cs.CR↗
arXiv2025

Target Circuit Matching in Large-Scale Netlists using GNN-Based Region Prediction

Subgraph matching plays an important role in electronic design automation (EDA) and circuit verification. Traditional rule-based methods have limitations in generalizing to arbitrary target circuits. Furthermore, node-to-node matching approaches tend to be computationally inefficient, particularly for large-scale circuits. Deep learning methods have emerged as a potential solution to address these challenges, but existing models fail to efficiently capture global subgraph embeddings or rely on inefficient matching matrices, which limits their effectiveness for large circuits. In this paper, we propose an efficient graph matching approach that utilizes Graph Neural Networks (GNNs) to predict regions of high probability for containing the target circuit. Specifically, we construct various negative samples to enable GNNs to accurately learn the presence of target circuits and develop an approach to directly extracting subgraph embeddings from the entire circuit, which captures global subgraph information and addresses the inefficiency of applying GNNs to all candidate subgraphs. Extensive experiments demonstrate that our approach significantly outperforms existing methods in terms of time efficiency and target region prediction, offering a scalable and effective solution for subgraph matching in large-scale circuits.

cs.LG↗
arXiv2025

A valuative approach to the anticanonical minimal model program

In this paper, we show that the log canonical threshold of a potentially klt triple can be computed by a quasi-monomial valuation. The notion of potential triples provides a larger and more flexible framework to work with than that of generalized pairs. Our main result can be considered as an extension to the result of Xu on klt pairs. As an application of the main result, we show that we can run the MMP on any potentially klt triples and $-(K_X+Δ)$-MMP on the potentially klt pairs.

math.AG↗
arXiv2025

Spectral Normalization for Lipschitz-Constrained Policies on Learning Humanoid Locomotion

Reinforcement learning (RL) has shown great potential in training agile and adaptable controllers for legged robots, enabling them to learn complex locomotion behaviors directly from experience. However, policies trained in simulation often fail to transfer to real-world robots due to unrealistic assumptions such as infinite actuator bandwidth and the absence of torque limits. These conditions allow policies to rely on abrupt, high-frequency torque changes, which are infeasible for real actuators with finite bandwidth. Traditional methods address this issue by penalizing aggressive motions through regularization rewards, such as joint velocities, accelerations, and energy consumption, but they require extensive hyperparameter tuning. Alternatively, Lipschitz-Constrained Policies (LCP) enforce finite bandwidth action control by penalizing policy gradients, but their reliance on gradient calculations introduces significant GPU memory overhead. To overcome this limitation, this work proposes Spectral Normalization (SN) as an efficient replacement for enforcing Lipschitz continuity. By constraining the spectral norm of network weights, SN effectively limits high-frequency policy fluctuations while significantly reducing GPU memory usage. Experimental evaluations in both simulation and real-world humanoid robot show that SN achieves performance comparable to gradient penalty methods while enabling more efficient parallel training.

cs.RO↗