SIDDA: SInkhorn Dynamic Domain Adaptation for image classification with equivariant neural networks

Abstract Modern neural networks (NNs) often do not generalize well in the presence of a "covariate shift''; that is, in situations where the training and test data distributions differ, but the conditional distribution of classification labels given the data remains unchanged. In such cases, NN generalization can be reduced to a problem of learning domain-invariant features. Domain adaptation (DA) methods include a broad range of techniques aimed at achieving this; however, these methods have struggled with the need for hyperparameter tuning, which then incurs computational costs. In this work, we introduce SIDDA, an out-of-the-box DA training algorithm built upon the Sinkhorn divergence, that can achieve effective domain alignment with minimal hyperparameter tuning and computational overhead. We demonstrate the efficacy of our method on multiple simulated and real datasets of varying complexity, including simple shapes, handwritten digits, and real astronomical observations. These datasets exhibit covariate shifts due to noise, blurring, and differences between telescopes. SIDDA is compatible with a variety of NN architectures, and it works particularly well in improving classification accuracy and model calibration when paired with equivariant NNs (ENNs). We find that SIDDA enhances the generalization capabilities of NNs, achieving up to a 40% improvement in classification accuracy on unlabeled target data. We also study the efficacy of DA on ENNs with respect to the varying orders of the dihedral group, and find that the model performance improves with higher orders. Finally, we find that SIDDA enhances model calibration on both source and target data, with the most significant gains in the unlabeled target domain---achieving over an order of magnitude improvement in the ECE and Brier score. SIDDA's versatility across various NN models and datasets, combined with its automated approach to domain alignment, has the potential to significantly advance multi-dataset studies by enabling the development of highly generalizable models

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