| 2026.6.3 |
Tam Le |
Sobolev IPM with graph metric: Theory and application |
English We study the Sobolev IPM problem for probability measures supported on a graph metric space. Sobolev IPM is an important instance of integral probability metrics (IPM), and is obtained by constraining a critic function within a unit ball defined by the Sobolev norm. In particular, it has been used to compare probability measures and is crucial for several theoretical works in machine learning. However, there are no efficient algorithmic approaches to compute Sobolev IPM effectively, which hinders its practical applications. We establish a relation between Sobolev norm and weighted Lp-norm, and leverage it to propose a novel regularization for Sobolev IPM. By exploiting the graph structure, we demonstrate that the regularized Sobolev IPM provides a closed-form expression for fast computation. This advancement addresses long-standing computational challenges, and paves the way to apply Sobolev IPM for practical applications, even in large-scale settings. Moreover, building on the insights of tree systems, we further introduce tree-sliced Sobolev IPM (TS-Sobolev), a tree-sliced metric that aggregates regularized Sobolev IPMs over random tree systems for applications with probability measures on Euclidean or hyperspheres. Notably, TS-Sobolev admits the tree-sliced Wasserstein as its special case. Empirically, we evaluate the proposed approaches on various tasks, e.g., document classification and topological data analysis for measures with a graph metric; as well as gradient flows, self-supervised learning, generative modeling, and text topic modeling for measures on Euclidean and hyperspheres.
References:
[1] Tam Le*, Truyen Nguyen*, Hideitsu Hino, Kenji Fukumizu. Scalable Sobolev IPM for Probability Measures on a Graph. ICML, 2025. (*: equal contribution)
[2] Viet-Hoang Tran*, Thanh Q. Tran*, Thanh Chu, Duy-Tung Pham, Trung-Khang Tran, Tam Le**, Tan M. Nguyen**. Tree-Sliced Sobolev IPM. ICLR, 2026. (*: equal contribution; **: co-last author) |
Online |
D208 |
| 2026.6.3 |
庄 建倉 |
How predictable are earthquakes? Advances in earthquake forecasting and predictability limits |
English Earthquakes resist deterministic prediction, yet their occurrence is not fully random. This paper develops a unified information-theoretic framework to quantify predictability. By reviewing Shannon entropy and the Kullback--Leibler divergence, we formalize predictability as the entropy gap between complete randomness and the true data-generating process and clarify how this absolute notion relates to the relative skill gains used in prospective model evaluation. Within the point-process setting, we derive entropy rates for the Poisson process and for ETAS and identify the intrinsic predictability rate as an information gain functional of the conditional intensity. Using this lens, we summarize what is currently established about earthquake predictability in time, space, and magnitude: temporal and spatial predictability are dominated by clustering and heterogeneous background rates, while magnitude predictability requires separating marginal magnitude statistics (e.g., Gutenberg--Richter and tapered laws) from genuine inter-event dependence encoded by the multivariate magnitude distribution. Finally, we show how incorporating high-dimensional pre-event observations can increase predictability through mutual information, thereby reframing forecasting progress as the extraction of structured dependence between available information and future seismicity. This perspective provides a coherent basis for assessing predictability limits, comparing models, and identifying where additional information and physics are most likely to yield substantive forecasting improvements. |
Hybrid |
D208 |
| 2026.6.17 |
木野 日織 |
Global attention-based identification of energy-relevant atoms in atomistic models |
日本語 In this study, the limited interpretability of conventional deep learning models for structure–property relationships is addressed by proposing an interpretable model incorporating an attention mechanism. Evaluations on multiple datasets, including molecules and crystals, demonstrate that predictive performance comparable to state-of-the-art methods is achieved. Furthermore, comparisons with first-principles calculations reveal that the importance of local atomic structures, as quantified by attention, is effective for understanding material properties. The proposed approach enables both accurate property prediction and identification of key structural features, contributing to accelerated materials design. https://doi.org/10.1038/s41524-023-01163-9 |
Hybrid |
D208 |
