SIDDA: SInkhorn Dynamic Domain Adaptation for Image Classification with Equivariant Neural Networks

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 remains unchanged. In such cases, NN generalization can be reduced to a problem of learning more domain-invariant features. Domain adaptation (DA) methods include a range of techniques aimed at achieving this; however, these methods have struggled with the need for extensive hyperparameter tuning, which then incurs significant 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. 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 neural networks (ENNs). We find that SIDDA enhances the generalization capabilities of NNs, achieving up to a $\approx40\%$ improvement in classification accuracy on unlabeled target data. We also study the efficacy of DA on ENNs with respect to the varying group orders of the dihedral group $D_N$, and find that the model performance improves as the degree of equivariance increases. Finally, we find that SIDDA enhances model calibration on both source and target data--achieving over an order of magnitude improvement in the ECE and Brier score. SIDDA's versatility, combined with its automated approach to domain alignment, has the potential to advance multi-dataset studies by enabling the development of highly generalizable models.

E(2) Equivariant Neural Networks for Robust Galaxy Morphology Classification

We propose the use of group convolutional neural network architectures (GCNNs) equivariant to the 2D Euclidean group, $E(2)$, for the task of galaxy morphology classification by utilizing symmetries of the data present in galaxy images as an inductive bias in the architecture. We conduct robustness studies by introducing artificial perturbations via Poisson noise insertion and one-pixel adversarial attacks to simulate the effects of limited observational capabilities. We train, validate, and test GCNNs equivariant to discrete subgroups of $E(2)$ - the cyclic and dihedral groups of order $N$ - on the Galaxy10 DECals dataset and find that GCNNs achieve higher classification accuracy and are consistently more robust than their non-equivariant counterparts, with an architecture equivariant to the group $D_{16}$ achieving a $95.52 \pm 0.18\%$ test-set accuracy. We also find that the model loses $<6\%$ accuracy on a $50\%$-noise dataset and all GCNNs are less susceptible to one-pixel perturbations than an identically constructed CNN. Our code is publicly available at https://github.com/snehjp2/GCNNMorphology.