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Researcher profile

Haesung Lee

Haesung Lee contributes to research discovery and scholarly infrastructure.

ResearcherAffiliation not importedOpen to collaborate
math.PRComputation and Languagemath.APmath.FA

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Published work

8 published item(s)

preprint2026arXiv

TriBench-Ko: Evaluating LLM Risks in Judicial Workflows

Large language models (LLMs) are increasingly integrated into legal workflows. However, existing benchmarks primarily address proxy tasks, such as bar examination performance or classification, which fail to capture the performance and risks inherent in day-to-day judicial processes. To address this, we publicly release TriBench-Ko, a Korean benchmark designed to evaluate potential deployment risks of LLMs within the context of verified judicial task requirements. It covers four core tasks: jurisprudence summarization, precedent retrieval, legal issue extraction, and evidence analysis. It jointly assesses model behavior across multiple deployment risk categories, including inaccuracy (hallucination, omission, statutory misapplication), biases (demographic, overcompliance), inconsistencies (prompt sensitivity, non-determinism), and adjudicative overreach. Each item is structured to systematically assess both task performance and a specific risk type based on real judicial decisions. Our evaluation of a range of contemporary LLMs reveals that many models frequently manifest significant risks, most notably struggling with precedent retrieval and failing to capture critical legal information. We provide a comprehensive diagnosis of these LLMs and pinpoint critical areas where LLM-generated outputs in judicial contexts necessitate rigorous inspection and caution. Our dataset and code are available at https://github.com/holi-lab/TriBench-Ko

0 citations0 reviewsNo code linkedOpen access
preprint2022arXiv

Analytic theory of Itô-stochastic differential equations with non-smooth coefficients

We present a detailed analysis of non-degenerate time-homogeneous Itô-stochastic differential equations with low local regularity assumptions on the coefficients. In particular the drift coefficient may only satisfy a local integrability condition. We discuss non-explosion, irreducibility, Krylov type estimates, regularity of the transition function and resolvent, moment inequalities, recurrence, transience, long time behavior of the transition function, existence and uniqueness of invariant measures, as well as pathwise uniqueness, strong solutions and uniqueness in law. This analysis shows in particular that sharp explicit conditions for the various mentioned properties can be derived similarly to the case of classical stochastic differential equations with local Lipschitz coefficients.

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preprint2022arXiv

Conservativeness and uniqueness of invariant measures related to non-symmetric divergence type operators

We present conservativeness criteria for sub-Markovian semigroups generated by divergence type operators with specified infinitesimally invariant measures. The conservativeness criteria in this article are derived by $L^1$-uniqueness and imply that a given infinitesimally invariant measure becomes an invariant measure. We explore further conditions on the coefficients of the partial differential operators that ensure the uniqueness of the invariant measure beyond the case where the corresponding semigroups are recurrent. A main observation is that for conservativeness and uniqueness of invariant measures in this article, no growth conditions are required for the partial derivatives related to the anti-symmetric matrix of functions $C=(c_{ij})_{1 \leq i,j \leq d}$ that determine a part of the drift coefficient. As stochastic counterparts, our results can be applied to show not only the existence of a pathwise unique and strong solution up to infinity to a corresponding Itô-SDE, but also the existence and uniqueness of invariant measures for the family of strong solutions.

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preprint2022arXiv

Existence and uniqueness of (infinitesimally) invariant measures for second order partial differential operators on Euclidean space

We consider a locally uniformly strictly elliptic second order partial differential operator in $\mathbb{R}^d$, $d\ge 2$, with low regularity assumptions on its coefficients, as well as an associated Hunt process and semigroup. The Hunt process is known to solve a corresponding stochastic differential equation that is pathwise unique. In this situation, we study the relation of invariance, infinitesimal invariance, recurrence, transience, conservativeness and $L^r$-uniqueness, and present sufficient conditions for non-existence of finite infinitesimally invariant measures as well as finite invariant measures. Our main result is that recurrence implies uniqueness of infinitesimally invariant measures, as well as existence and uniqueness of invariant measures, both in subclasses of locally finite measures. We can hence make in particular use of various explicit analytic criteria for recurrence that have been previously developed in the context of (generalized) Dirichlet forms and present diverse examples and counterexamples for uniqueness of infinitesimally invariant, as well as invariant measures and an example where $L^1$-uniqueness fails for one infinitesimally invariant measure but holds for another and pathwise uniqueness holds. Furthermore, we illustrate how our results can be applied to related work and vice versa.

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preprint2022arXiv

On the pathwise uniqueness for a class of degenerate Itô-stochastic differential equations

We show pathwise uniqueness for a class of degenerate Itô-SDE among all of its weak solutions that spend zero time at the points of degeneracy of the dispersion matrix. Consequently, by the Yamada-Watanabe Theorem and a weak existence result, the pathwise unique solutions can be shown to be strong and to exist. The main tools to show pathwise uniqueness are inequalities associated with maximal functions and a Krylov type estimate derived from elliptic regularity and uniqueness in law.

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preprint2020arXiv

Existence and regularity of infinitesimally invariant measures, transition functions and time homogeneous Itô-SDEs

We show existence of an infinitesimally invariant measure $m$ for a large class of divergence and non-divergence form elliptic second order partial differential operators with locally Sobolev regular diffusion coefficient and drift of some local integrability order. Subsequently, we derive regularity properties of the corresponding semigroup which is defined in $L^s(\mathbb{R}^d,m)$, $s\in [1,\infty]$, including the classical strong Feller property and classical irreducibility. This leads to a transition function of a Hunt process that is explicitly identified as a solution to an SDE. Further properties of this Hunt process, like non-explosion, moment inequalities, recurrence and transience, as well as ergodicity, including invariance and uniqueness of $m$, and uniqueness in law, can then be studied using the derived analytical tools and tools from generalized Dirichlet form theory.

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preprint2020arXiv

Existence, uniqueness and ergodic properties for time-homogeneous Itô-SDEs with locally integrable drifts and Sobolev diffusion coefficients

Using elliptic and parabolic regularity results in $L^p$-spaces and generalized Dirichlet form theory, we construct for every starting point weak solutions to SDEs in $\mathbb{R}^d$ up to their explosion times including the following conditions. For arbitrary but fixed $p>d$ the diffusion coefficient $A=(a_{ij})_{1\le i,j\le d}$ is locally uniformly strictly elliptic with functions $a_{ij}\in H^{1,p}_{loc}(\mathbb{R}^d)$ and the drift coefficient $\mathbf{G}=(g_1,\dots, g_d)$ consists of functions $g_i\in L^p_{loc}(\mathbb{R}^d)$. The solution originates by construction from a Hunt process with continuous sample paths on the one-point compactification of $\mathbb{R}^d$ and the corresponding SDE is by a known local well-posedness result pathwise unique up to an explosion time. Just under the given assumptions we show irreducibility and the strong Feller property on $L^{1}(\mathbb{R}^d,m)+L^{\infty}(\mathbb{R}^d,m)$ of its transition function, and the strong Feller property on $L^{q}(\mathbb{R}^d,m)+L^{\infty}(\mathbb{R}^d,m)$, $q=\frac{dp}{d+p}\in (d/2,p/2)$, of its resolvent, which both include the classical strong Feller property. We present moment inequalities and classical-like non-explosion criteria for the solution which lead to pathwise uniqueness results up to infinity under presumably optimal general non-explosion conditions. We further present explicit conditions for recurrence and ergodicity, including existence as well as uniqueness of invariant probability measures.

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preprint2019arXiv

Well-posedness for a class of degenerate Itô-SDEs with fully discontinuous coefficients

We show uniqueness in law for a general class of stochastic differential equations in $\mathbb{R}^d$, $d\ge 2$, with possibly degenerate and/or fully discontinuous locally bounded coefficients among all weak solutions that spend zero time at the points of degeneracy of the dispersion matrix. The points of degeneracy have $d$-dimensional Lebesgue-Borel measure zero. Weak existence is obtained for more general, not necessarily locally bounded drift coefficient.

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