Attribute correlations in the training data will compromise the ability of a deep generative model (DGM) to synthesize images with under-represented attribute combinations ($\textit{i.e.,}$ minority samples). Existing approaches mitigate this by data re-sampling to remove attribute correlations seen by the DGM, using a classifier to provide $\textit{pseudo-supervision}$ for the generation of counterfactual samples, or incorporating inductive bias to explicitly decompose the generation into independent causal mechanisms. We present ProReGen, a $\textit{progressive residual generation}$ approach inspired by the classical Robinson's transformation to partial out from an image attribute $\mathbf{x}_2$ its component $m(\mathbf{x}_1)$ that is predictable by other image attributes $\mathbf{x}_1$, and the residual $\gamma = \mathbf{x}_2 - m(\mathbf{x}_1)$ that is not. This simplifies the original problem of learning a DGM $g(\mathbf{x}_1, \mathbf{x}_2)$ conditioned on correlated inputs, to learning $\tilde{g}(\mathbf{x}_1, \gamma)$ conditioned on orthogonal inputs. It further allows us to progressively learn $\tilde{g}$ by first shifting the burden to abundant majority samples to learn the generator $\tilde{g}(\mathbf{x}_1, \gamma = 0)$, and then expanding it with additional layers $g\_{\text{res}}$ to resolve its difference to $\tilde{g}(\mathbf{x}_1, \gamma)$ using residual attribute $\gamma$ on limited minority samples. On three benchmark datasets with curated varying strengths of attribute correlations, we demonstrate that ProReGen---with input orthogonalizaton and progressive residual learning---improved the correctness and quality of generations compared to existing strategies.

Advancements in deep learning have led to the development of physics-informed neural networks (PINNs) for solving partial differential equations (PDEs) without being supervised by PDE solutions. While vanilla PINNs require training one network per PDE configuration, recent works have showed the potential to meta-learn PINNs across a range of PDE configurations. It is however known that PINN training is associated with different levels of difficulty, depending on the underlying PDE configurations or the number of residual sampling points available. Existing meta-learning approaches, however, treat all PINN tasks equally. We address this gap by introducing a novel difficulty-aware task sampler (DATS) for meta-learning of PINNs. We derive an optimal analytical solution to optimize the probability for sampling individual PINN tasks in order to minimize their validation loss across tasks. We further present two alternative strategies to utilize this sampling probability to either adaptively weigh PINN tasks, or dynamically allocate optimal residual points across tasks. We evaluated DATS against uniform and self-paced task-sampling baselines on two representative meta-PINN models, across four benchmark PDEs as well as three different residual point sampling strategies. The results demonstrated that DATS was able to improve the accuracy of meta-learned PINN solutions when reducing performance disparity across PDE configurations, at only a fraction of residual sampling budgets required by its baselines.

Spurious correlation caused by subgroup underrepresentation has received increasing attention as a source of bias that can be perpetuated by deep neural networks (DNNs). Distributionally robust optimization has shown success in addressing this bias, although the underlying working mechanism mostly relies on upweighting under-performing samples as surrogates for those underrepresented in data. At the same time, while invariant representation learning has been a powerful choice for removing nuisance-sensitive features, it has been little considered in settings where spurious correlations are caused by significant underrepresentation of subgroups. In this paper, we take the first step to better understand and improve the mechanisms for debiasing spurious correlation due to subgroup underrepresentation in medical image classification. Through a comprehensive evaluation study, we first show that 1) generalized reweighting of under-performing samples can be problematic when bias is not the only cause for poor performance, while 2) naive invariant representation learning suffers from spurious correlations itself. We then present a novel approach that leverages robust optimization to facilitate the learning of invariant representations at the presence of spurious correlations. Finetuned classifiers utilizing such representation demonstrated improved abilities to reduce subgroup performance disparity, while maintaining high average and worst-group performance.