This paper presents a theoretical analysis of Test-Time Augmentation (TTA), a heuristic that improves model performance by applying data augmentation during testing and averaging the outputs. TTA has shown experimental effectiveness in various tasks, but its theoretical properties have been insufficiently studied. The authors aim to provide theoretical guarantees for TTA and clarify its behavior. The paper first defines the problem in terms of supervised learning, where the goal is to minimize the expected error. It then introduces TTA as a method that applies multiple data augmentations to an input and averages the model outputs. Theoretical results show that the expected error of TTA is less than or equal to the average error of a single model, and under certain assumptions, it is strictly less. The authors also generalize TTA by introducing weighted averaging, where the optimal weights are derived from a closed-form expression. They show that the error of TTA depends on the correlation between the augmented data. They further demonstrate that data augmentations with high correlation are redundant, and that the error of TTA can be decomposed into error and ambiguity terms. Ambiguity measures the discrepancy between individual hypotheses for a given input. The paper also discusses the statistical consistency of TTA, showing that it is a consistent estimator of the expected error. Finally, it reviews related works and discusses future research directions, including the theoretical analysis of TTA variants and the derivation of generalization bounds based on model complexity.This paper presents a theoretical analysis of Test-Time Augmentation (TTA), a heuristic that improves model performance by applying data augmentation during testing and averaging the outputs. TTA has shown experimental effectiveness in various tasks, but its theoretical properties have been insufficiently studied. The authors aim to provide theoretical guarantees for TTA and clarify its behavior. The paper first defines the problem in terms of supervised learning, where the goal is to minimize the expected error. It then introduces TTA as a method that applies multiple data augmentations to an input and averages the model outputs. Theoretical results show that the expected error of TTA is less than or equal to the average error of a single model, and under certain assumptions, it is strictly less. The authors also generalize TTA by introducing weighted averaging, where the optimal weights are derived from a closed-form expression. They show that the error of TTA depends on the correlation between the augmented data. They further demonstrate that data augmentations with high correlation are redundant, and that the error of TTA can be decomposed into error and ambiguity terms. Ambiguity measures the discrepancy between individual hypotheses for a given input. The paper also discusses the statistical consistency of TTA, showing that it is a consistent estimator of the expected error. Finally, it reviews related works and discusses future research directions, including the theoretical analysis of TTA variants and the derivation of generalization bounds based on model complexity.