arXiv subjects

Katie Wang

Publications and source records attributed to Katie Wang.

3 recordsLinked to original sources

arXiv2026

HypNO: A Graph-Based Neural Operator with Physics-Informed Message Passing for Hyperbolic Conservation Laws

We introduce HypNO, a graph-based neural operator for scalar hyperbolic conservation laws. HypNO operates directly on a space-time graph of finite-volume cells and uses adjacency-factored, physics-informed message passing to respect upwinding and entropy admissibility near shocks. We benchmark the architecture on the Lighthill-Whitham-Richards (LWR) and Aw-Rascle-Zhang (ARZ) traffic-flow models, a stress test for operator-learning methods because of their simultaneous global transport and shock formation. HypNO predicts solution snapshots accurately across a range of initial conditions while capturing the shocks and discontinuities of the solution.

cs.LG↗

arXiv2026

Conditional Imputation for Within-Modality Missingness in Multi-Modal Federated Learning

Multimodal Federated Learning (MMFL) enables privacy-preserving collaborative training, but real-world clinical applications often suffer from within-modality missingness caused by sensor intermittency or irregular sampling. Existing methods implicitly represent unobserved data via architectural alignment or missing embeddings, often failing to recover the true distribution and yielding sub-optimal performance. We propose CondI, a federated framework explicitly addressing this missingness using conditional diffusion models. CondI employs a two-phase training pipeline: first, imputing unobserved temporal components using available multimodal context and conditional embeddings; second, optimizing modality-specific extractors and joint embedding spaces. During inference, imputed raw data pass through trained extractors to generate robust features, providing a holistic representation for downstream tasks. Explicit data imputation ensures models operate on complete semantic structures, significantly enhancing resilience against severe data incompleteness. Experiments on three clinical datasets (PTB-XL, SLEEP-EDF, MIMIC-IV) demonstrate CondI achieves comparable results to state-of-the-art baselines. Code: https://github.com/ZhengWugeng/CondI

cs.LG↗

arXiv2023

Unshuffling a deck of cards

We investigate the mathematics behind unshuffles, a type of card shuffle closely related to classical perfect shuffles. To perform an unshuffle, deal all the cards alternately into two piles and then stack the one pile on top of the other. There are two ways this stacking can be done (left stack on top or right stack on top), giving rise to the terms left shuffle ($L$) and right shuffle ($R$), respectively. We give a solution to a generalization of Elmsley's Problem (a classic mathematical card trick) using unshuffles for decks with $2^k$ cards. We also find the structure of the permutation groups $\langle L, R \rangle$ for a deck of $2n$ cards for all values of $n$. We prove that the group coincides with the perfect shuffle group unless $n\equiv 3 \pmod 4$, in which case the group $\langle L, R \rangle$ is equal to $B_n$, the group of centrally symmetric permutations of $2n$ elements, while the perfect shuffle group is an index 2 subgroup of $B_n$.

math.CO↗