Meta-learning problem is usually formulated as a bi-level optimization in which the task-specific and the meta-parameters are updated in the inner and outer loops of optimization, respectively. However, performing the optimization in the Riemannian space, where the parameters and meta-parameters are located on Riemannian manifolds is computationally intensive. Unlike the Euclidean methods, the Riemannian backpropagation needs computing the second-order derivatives that include backward computations through the Riemannian operators such as retraction and orthogonal projection. This paper introduces a Hessian-free approach that uses a first-order approximation of derivatives on the Stiefel manifold. Our method significantly reduces the computational load and memory footprint. We show how using a Stiefel fully-connected layer that enforces orthogonality constraint on the parameters of the last classification layer as the head of the backbone network, strengthens the representation reuse of the gradient-based meta-learning methods. Our experimental results across various few-shot learning datasets, demonstrate the superiority of our proposed method compared to the state-of-the-art methods, especially MAML, its Euclidean counterpart.

Deep neural networks are used in machine learning applications such as image classification, audio recognition, natural language comprehension, and healthcare. Despite modern DNN architectures' strong predictive performance, models can inherit biases and fail to generalize as data distribution differs in validation and training or when the test evaluation metrics differ from those used during training. This is due to spurious correlations in the dataset and overfitting of the training metric. Importantly, this can lead to fairness breaches for specific test groups. Data reweighting is a typical data-centric paradigm in fairness and robustness for minimizing data distribution shifts and class imbalance.

Machine learning models are trained to minimize the mean loss for a single metric, and thus typically do not consider fairness and robustness. Neglecting such metrics in training can make these models prone to fairness violations when training data are imbalanced or test distributions differ. This work introduces Fairness Optimized Reweighting via Meta-Learning (FORML), a training algorithm that balances fairness and robustness with accuracy by jointly learning training sample weights and neural network parameters. The approach increases model fairness by learning to balance the contributions from both over- and under-represented sub-groups through dynamic reweighting of the data learned from a user-specified held-out set representative of the distribution under which fairness is desired. FORML improves equality of opportunity fairness criteria on image classification tasks, reduces bias of corrupted labels, and facilitates building more fair datasets via data condensation. These improvements are achieved without pre-processing data or post-processing model outputs, without learning an additional weighting function, without changing model architecture, and while maintaining accuracy on the original predictive metric.