arXiv subjects

Hyemin Gu

Publications and source records attributed to Hyemin Gu.

6 recordsLinked to original sources

arXiv2026

Fine-Tuning Generative Models for Extreme Events via CVaR-Penalized Wasserstein Gradient Flows

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 capture extreme events, requiring no prior knowledge or estimation of the target's tail characteristics. The method is the Wasserstein gradient flow of the Lipschitz-regularized Kullback-Leibler (KL) divergence penalized by a Conditional Value-at-Risk (CVaR) discrepancy term: the Lipschitz-regularized KL divergence enables robust learning under minimal assumptions on the target distribution, while the CVaR penalty restores the velocity that otherwise vanishes prematurely in the under-sampled tails. The penalized flow admits a bounded but non-Lipschitz velocity field. This departs from the Lipschitz transport maps of standard generators, which preserve the tail behavior of a light-tailed source, and enables transport toward heavier-tailed targets. To define this flow on empirical measures, we derive the first-variation subgradients of CVaR from its Rockafellar-Uryasev representation, valid precisely where the classical density-based formula fails. The particle algorithm CVaR-GPA fine-tunes the output samples of any pre-trained model, without access to its architecture, and runs on an adaptive time horizon set by a kinetic-energy stopping criterion rather than a preset depth. On synthetic isotropic and anisotropic Student-$t$ target distributions, Neal's funnel distribution, and the real-world high-dimensional Fama-French 25 portfolio dataset, CVaR-GPA dramatically improves global and tail accuracy on heavy-tailed targets over the pre-trained baseline.

stat.ML↗

arXiv2026

Sharp Stability Threshold and Certification for Designing Stable Residual Architectures

We propose \emph{the sublinear-growth principle} for deep residual architectures -- a sharp stability threshold on the input-magnitude exponent of every residual block's velocity field: $$\|v(x, t)\| \leq c\,\|x\|^q + b, \qquad q \in [0, 1].$$ The threshold $q = 1$ is established via two independent arguments. Classical ODE theory gives a global forward flow on $[0, T]$ at $q \le 1$ and exhibits divergent velocity fields at any $q > 1$. The optimal-control analysis, via the Hamilton-Jacobi-Bellman equation, sharpens this to a selection statement: the training optimum is bang-bang on the boundary of the admissible class, so the optimum at $q > 1$ blows up while the optimum at $q \le 1$ is safe by construction. The exponent criterion $q \le 1$ is thereby a necessary and sufficient condition for stable training. It clarifies architectural placements that ensure the stability of training and inference, explaining, for instance, the stabilizing role of layer normalization. The sublinear-growth velocity fields form \emph{the right function space} on which forward dynamics, adjoint sensitivity, and architectural composition are all well-controlled. An arithmetic of input-magnitude exponents under the five operations that build residual blocks enables efficient certification of $q_k \le 1$ at the level of architectural primitives, in place of ad hoc trial and error in the search for stable neural architectural designs. A parameter-free modification reduces the supercritical Mamba block from $q = 5$ to $q = 1$ without layer normalization, demonstrating this point. Experiments on Mamba and PatchTST confirm that the $q \le 1$ variants train stably: the criterion is the input-magnitude exponent, not the presence of a normalization layer.

cs.LG↗

arXiv2026

ISOMORPH: A Supply Chain Digital Twin for Simulation, Dataset Generation, and Forecasting Benchmarks

Open time-series forecasting (TSF) benchmarks cover retail, energy, weather, and traffic, but supply-chain logistics remains underserved. We introduce ISOMORPH, the first public digital twin of a multi-echelon logistics network with interpretable, user-configurable parameters and modular topology, demand, and control rules. The simulator advances a directed routing graph in discrete time: demand is served from inventory or recorded as backlog and triggers replenishment throughout the network. The state tracks inventory, outstanding orders, in-transit shipments, and a smoothed demand estimate, yielding Markovian dynamics on a tractable state space. The released data reproduces the bullwhip effect at empirically consistent magnitudes, while three conservation laws provide verification tools for simulator extensions. We release datasets at two catalogue scales ($C=50$ and $C=200$), six scenario sweeps, and 20 Latin-hypercube perturbations. These datasets exhibit dynamics largely absent from fixed TSF benchmarks, including variance amplification, cascading bottlenecks, regime shifts, and cross-channel coupling through shared macro shocks. Zero-shot evaluation of four foundation models (Chronos, Moirai, TimesFM, and Lag-Llama) yields MASE values exceeding public GIFT-Eval references at low-to-moderate horizons, supporting incorporation into existing benchmark suites. The same models provide forecast confidence bands through Latin-hypercube perturbations of demand-side parameters, enabling forward uncertainty quantification (UQ) unavailable on standard TSF datasets and demonstrating that foundation models can serve as fast surrogates for digital-twin-based UQ. Code (MIT): https://github.com/tuhinsahai/ISOMORPH. Interactive demo: https://huggingface.co/spaces/HyeminGu/ISOMORPH-demo.

stat.ML↗

arXiv2024

Combining Wasserstein-1 and Wasserstein-2 proximals: robust manifold learning via well-posed generative flows

We formulate well-posed continuous-time generative flows for learning distributions that are supported on low-dimensional manifolds through Wasserstein proximal regularizations of $f$-divergences. Wasserstein-1 proximal operators regularize $f$-divergences so that singular distributions can be compared. Meanwhile, Wasserstein-2 proximal operators regularize the paths of the generative flows by adding an optimal transport cost, i.e., a kinetic energy penalization. Via mean-field game theory, we show that the combination of the two proximals is critical for formulating well-posed generative flows. Generative flows can be analyzed through optimality conditions of a mean-field game (MFG), a system of a backward Hamilton-Jacobi (HJ) and a forward continuity partial differential equations (PDEs) whose solution characterizes the optimal generative flow. For learning distributions that are supported on low-dimensional manifolds, the MFG theory shows that the Wasserstein-1 proximal, which addresses the HJ terminal condition, and the Wasserstein-2 proximal, which addresses the HJ dynamics, are both necessary for the corresponding backward-forward PDE system to be well-defined and have a unique solution with provably linear flow trajectories. This implies that the corresponding generative flow is also unique and can therefore be learned in a robust manner even for learning high-dimensional distributions supported on low-dimensional manifolds. The generative flows are learned through adversarial training of continuous-time flows, which bypasses the need for reverse simulation. We demonstrate the efficacy of our approach for generating high-dimensional images without the need to resort to autoencoders or specialized architectures.

stat.ML↗

arXiv2024

Robust Generative Learning with Lipschitz-Regularized $\alpha$-Divergences Allows Minimal Assumptions on Target Distributions

This paper demonstrates the robustness of Lipschitz-regularized $\alpha$-divergences as objective functionals in generative modeling, showing they enable stable learning across a wide range of target distributions with minimal assumptions. We establish that these divergences remain finite under a mild condition-that the source distribution has a finite first moment-regardless of the properties of the target distribution, making them adaptable to the structure of target distributions. Furthermore, we prove the existence and finiteness of their variational derivatives, which are essential for stable training of generative models such as GANs and gradient flows. For heavy-tailed targets, we derive necessary and sufficient conditions that connect data dimension, $\alpha$, and tail behavior to divergence finiteness, that also provide insights into the selection of suitable $\alpha$'s. We also provide the first sample complexity bounds for empirical estimations of these divergences on unbounded domains. As a byproduct, we obtain the first sample complexity bounds for empirical estimations of these divergences and the Wasserstein-1 metric with group symmetry on unbounded domains. Numerical experiments confirm that generative models leveraging Lipschitz-regularized $\alpha$-divergences can stably learn distributions in various challenging scenarios, including those with heavy tails or complex, low-dimensional, or fractal support, all without any prior knowledge of the structure of target distributions.

stat.ML↗

arXiv2022

Lipschitz-regularized gradient flows and generative particle algorithms for high-dimensional scarce data

We build a new class of generative algorithms capable of efficiently learning an arbitrary target distribution from possibly scarce, high-dimensional data and subsequently generate new samples. These generative algorithms are particle-based and are constructed as gradient flows of Lipschitz-regularized Kullback-Leibler or other $f$-divergences, where data from a source distribution can be stably transported as particles, towards the vicinity of the target distribution. As a highlighted result in data integration, we demonstrate that the proposed algorithms correctly transport gene expression data points with dimension exceeding 54K, while the sample size is typically only in the hundreds.

stat.ML↗