arXiv subjects

Heechang Kim

Publications and source records attributed to Heechang Kim.

3 recordsLinked to original sources

arXiv2026

A Domain-Specific Harness for End-to-End Automation of Optimization Research

We present AutoOPT, a domain-specific harness for end-to-end automation of optimization research. AutoOPT organizes the discovery of optimal first-order methods into four stages: numerical design through the BnB-PEP methodology; symbolic discovery of the analytic description and a convergence proof through frontier large language models (LLMs); formal verification in the Lean 4 proof assistant; and human interpretation and write-up. We demonstrate the framework on two case studies, each of independent interest. The first, lemniscate acceleration, is a new accelerated gradient method for minimizing the gradient norm of a smooth convex function: after $N$ gradient steps it reduces the squared gradient norm at the optimal $O(1/N^{4})$ rate, with a constant governed by the lemniscate constant $\varpi$, a classical elliptic-integral constant. The second is the analytic description of ITEM-f, a method previously known only numerically: for $L$-smooth, $\mu$-strongly convex minimization it contracts the function-value gap at an accelerated linear rate with a per-step factor $(1-\sqrt{\mu/L})^{2}$. The convergence theorems of both case studies are formalized and machine-checked in Lean 4.

math.OC↗

arXiv2026

Physics-Informed Laplace Neural Operator for Solving Partial Differential Equations

Neural operators have emerged as fast surrogate solvers for parametric partial differential equations (PDEs). However, purely data-driven models often require extensive training data and can generalize poorly, especially in small-data regimes and under unseen (out-of-distribution) input functions that are not represented in the training data. To address these limitations, we propose the Physics-Informed Laplace Neural Operator (PILNO), which enhances the Laplace Neural Operator (LNO) by embedding governing physics into training through PDE, boundary condition, and initial condition residuals. To improve expressivity, we first introduce an Advanced LNO (ALNO) backbone that retains a pole-residue transient representation while replacing the steady-state branch with an FNO-style Fourier multiplier. To make physics-informed training both data-efficient and robust, PILNO further leverages (i) virtual inputs: an unlabeled ensemble of input functions spanning a broad spectral range that provides abundant physics-only supervision and explicitly targets out-of-distribution (OOD) regimes; and (ii) temporal-causality weighting: a time-decaying reweighting of the physics residual that prioritizes early-time dynamics and stabilizes optimization for time-dependent PDEs. Across four representative benchmarks -- Burgers' equation, Darcy flow, a reaction-diffusion system, and a forced KdV equation -- PILNO consistently improves accuracy in small-data settings (e.g., N_train <= 27), reduces run-to-run variability across random seeds, and achieves stronger OOD generalization with respect to input function statistics than purely data-driven baselines.

cs.LG↗

arXiv2025

LaMoGen: Laban Movement-Guided Diffusion for Text-to-Motion Generation

Diverse human motion generation is an increasingly important task, having various applications in computer vision, human-computer interaction and animation. While text-to-motion synthesis using diffusion models has shown success in generating high-quality motions, achieving fine-grained expressive motion control remains a significant challenge. This is due to the lack of motion style diversity in datasets and the difficulty of expressing quantitative characteristics in natural language. Laban movement analysis has been widely used by dance experts to express the details of motion including motion quality as consistent as possible. Inspired by that, this work aims for interpretable and expressive control of human motion generation by seamlessly integrating the quantification methods of Laban Effort and Shape components into the text-guided motion generation models. Our proposed zero-shot, inference-time optimization method guides the motion generation model to have desired Laban Effort and Shape components without any additional motion data by updating the text embedding of pretrained diffusion models during the sampling step. We demonstrate that our approach yields diverse expressive motion qualities while preserving motion identity by successfully manipulating motion attributes according to target Laban tags.

cs.CV↗