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Source author record

Noboru Isobe

Noboru Isobe appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

ResearcherUnclaimed source record
Machine Learningmath.APmath.DSmath.OCmath.PRmath.STMethodology

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Published work

2 published item(s)

preprint2026arXiv

Minimax Optimal Estimation of Transport-Growth Pairs in Unbalanced Optimal Transport

Unbalanced optimal transport (UOT) extends classical optimal transport to measures with different total masses, but statistical guarantees for Monge-type estimation remain limited. We study unbalanced transport with quadratic cost and Kullback-Leibler marginal penalties and argue that the natural population target is not a map alone, but a transport-growth pair. Consequently, we develop two estimators for the transport-growth pairs under several setups: an optimal transport plan-based estimator for a general case, and a kernel-based estimator for a case with smooth densities. We also show that an error of the estimator achieves the minimax optimal rate by deriving a matching lower bound of the minimax risk. Our main technical contribution is a value-based stability reduction that converts perturbations of the UOT objective into transport and growth risks through a UOT gap condition. These results provide a statistical foundation for Monge-type estimation in unbalanced optimal transport.

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preprint2026arXiv

Training-Induced Escape from Token Clustering in a Mean-Field Formulation of Transformers

Transformers perform inference by iteratively transforming token representations across layers. This layerwise computation has been studied empirically, and recent mean-field theories of Transformer dynamics explain how attention can drive token distributions toward clustering. However, existing mean-field analyses largely treat model parameters as prescribed, leaving open how training reshapes this clustering picture. We study this question in a noisy mean-field Transformer in which only a parameter-linear FFN is trained under $L^2$ regularization. We find and analyze a training-induced phase in the dynamics: after initially following attention-driven clustering, the token distribution can leave the clustered regime near the final layers. Our mathematical analysis is based on an entropy-regularized interaction energy that captures the clustering bias of attention. More broadly, our results point toward a training-aware mean-field theory of Transformer dynamics, in which training and inference dynamics are treated together.

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