Wonjung Kim

Jaehoon Yoo, Wonjung Kim, Seunghoon Hong

Discrete Flow-based Models (DFMs) are powerful generative models for high-quality discrete data but typically suffer from slow sampling speeds due to their reliance on iterative decoding processes. This reliance on a multi-step process originates from the factorization approximation of DFMs, which is necessary for handling high-dimensional data. In this paper, we analyze the factorization approximation error using Conditional Total Correlation (TC), and reveal its dependence on the coupling. To address the challenge of efficient few-step generation, we propose Rectified Discrete Flow (ReDi), a novel iterative method that reduces the underlying factorization error (measured as Conditional TC) by rectifying the coupling between source and target distributions. We theoretically prove that each ReDi step guarantees a monotonic decreasing Conditional TC, ensuring its convergence. Empirically, ReDi significantly reduces Conditional TC and enables few-step generation. Moreover, we demonstrate that the rectified couplings are well-suited for training efficient one-step models on image generation. ReDi offers a simple and theoretically grounded approach for tackling the few-step challenge, providing a new perspective on efficient discrete data synthesis. Code is available at https://github.com/Ugness/ReDi_discrete.

Hyunho Cha, Wonjung Kim, Jungwoo Lee

A scalable Bayesian machine learning framework is introduced for estimating scalar properties of an unknown quantum state from measurement data, which bypasses full density matrix reconstruction. This work is the first to integrate the classical shadows protocol with a permutation-invariant set transformer architecture, enabling the approach to predict and correct bias in existing estimators to approximate the true Bayesian posterior mean. Measurement outcomes are encoded as fixed-dimensional feature vectors, and the network outputs a residual correction to a baseline estimator. Scalability to large quantum systems is ensured by the polynomial dependence of input size on system size and number of measurements. On Greenberger-Horne-Zeilinger state fidelity and second-order Rényi entropy estimation tasks -- using random Pauli and random Clifford measurements -- this Bayesian estimator always achieves lower mean squared error than classical shadows alone, with more than a 99\% reduction in the few copy regime.