12 papers
Fine-Tuning Generative Models for Extreme Events via CVaR-Penalized Wasserstein Gradient Flows
Thejani Gamage, Hyemin Gu, Zhizhen Zhang +3
We propose CVaR-penalized Generative Particle Algorithm (CVaR-GPA), a robust, tail-agnostic algorithm for fine-tuning generative models to learn heavy-tailed distributions and capt…
Sharp Stability Threshold and Certification for Designing Stable Residual Architectures
Hyemin Gu, Michael Tyrrell, Tuhin Sahai +1
The paper introduces a sublinear‑growth principle that gives a sharp stability condition (input‑magnitude exponent q ≤ 1) for deep residual networks, and provides a method to certi…
Robustness and Structure Preservation in Flow-Based Generative Models via Wasserstein Path-Space Divergences
Ziyu Chen, Markos A. Katsoulakis, Benjamin J. Zhang
We introduce a novel Wasserstein-1 () path-space divergence for stochastic and deterministic dynamics and establish a Wasserstein Uncertainty Propagation (WUP) theorem that bo…
Dimension-Free Convergence of Discrete Diffusion Models: Adjoint Equations Induce the Right Space
Kelvin Kan, Xingjian Li, Benjamin J. Zhang +3
Discrete diffusion has become a leading framework for generative modeling in various applications including language, vision, and biology. Existing convergence theory, however, exh…
ISOMORPH: A Supply Chain Digital Twin for Simulation, Dataset Generation, and Forecasting Benchmarks
Zhizhen Zhang, Hyemin Gu, Benjamin J. Zhang +6
Open time-series forecasting (TSF) benchmarks cover retail, energy, weather, and traffic, but supply-chain logistics remains underserved. We introduce ISOMORPH, the first public di…
Optimal Control for Transformer Architectures: Enhancing Generalization, Robustness and Efficiency
Kelvin Kan, Xingjian Li, Benjamin J. Zhang +3
We study Transformers through the perspective of optimal control theory, using tools from continuous-time formulations to derive actionable insights into training and architecture…