In many classification settings, the class of primary interest is underrepresented, leading to imbalanced data problems that arise in applications such as rare disease detection and fraud identification. In these contexts, identifying a potential positive instance typically triggers costly follow-up actions, such as medical imaging or detailed transaction inspection, which are subject to limited operational capacity. Motivated by this setting, we consider classification problems where data may arrive sequentially and decisions must be made under constraints on the number of instances that can be selected for further analysis. We propose a classification framework that explicitly controls the rate of positive predictions, enforcing a user-defined bound on the proportion of observations classified as belonging to the minority class while maximizing detection performance. The approach can be implemented using standard learning methods and naturally extends to online settings, where decisions are taken in real time. We show that incorporating capacity constraints leads to substantial improvements over classical approaches, including resampling techniques such as SMOTE, which do not directly control the selection rate.

Transformer architectures have achieved remarkable empirical success in modeling contextual relationships in natural language, yet a precise mathematical characterization of their expressive power remains incomplete. In this work, we introduce a measure-theoretic framework for contextual representations in which texts are modeled as probability measures over a semantic embedding space, and contextual relations between words, are represented as coupling measures between them. Within this setting, we introduce Sinkhorn Transformer, a transformer-like architecture. Our main result is a universal approximation theorem: any continuous coupling function between probability measures, that encodes the semantic relation coupling measure, can be uniformly approximated by a Sinkhorn Transformer with appropriate parameters.

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CMWU achieves constant regret ofln(m)/η in all normal-form games with m actions and fixed step-sizesη.

Training (IIT) which we call Strict IIT (SIIT). SIIT models maintain Tracr's original circuit while being more realistic.