Standard training via empirical risk minimization (ERM) can produce models that achieve low error on average but high error on minority groups, especially in the presence of spurious correlations between the input and label. Prior approaches to this problem, like group distributionally robust optimization (group DRO), generally require group annotations for every training point. On the other hand, approaches that do not use group annotations generally do not improve minority performance. For example, we find that joint DRO, which dynamically upweights examples with high training loss, tends to optimize for examples that are irrelevant to the specific groups we seek to do well on. In this paper, we propose a simple two-stage approach, JTT, that achieves comparable performance to group DRO while only requiring group annotations on a significantly smaller validation set. JTT first attempts to identify informative training examples, which are often minority examples, by training an initial ERM classifier and selecting the examples with high training loss. Then, it trains a final classifier by upsampling the selected examples. Crucially, unlike joint DRO, JTT does not iteratively upsample examples that have high loss under the final classifier. On four image classification and natural language processing tasks with spurious correlations, we show that JTT closes 85% of the gap in accuracy on the worst group between ERM and group DRO.

Graph Neural Networks (GNNs) have been studied through the lens of expressive power and generalization. However, their optimization properties are less well understood. We take the first step towards analyzing GNN training by studying the gradient dynamics of GNNs. First, we analyze linearized GNNs and prove that despite the non-convexity of training, convergence to a global minimum at a linear rate is guaranteed under mild assumptions that we validate on real-world graphs. Second, we study what may affect the GNNs' training speed. Our results show that the training of GNNs is implicitly accelerated by skip connections, more depth, and/or a good label distribution. Empirical results confirm that our theoretical results for linearized GNNs align with the training behavior of nonlinear GNNs. Our results provide the first theoretical support for the success of GNNs with skip connections in terms of optimization, and suggest that deep GNNs with skip connections would be promising in practice.

Normalization is known to help the optimization of deep neural networks. Curiously, different architectures require specialized normalization methods. In this paper, we study what normalization is effective for Graph Neural Networks (GNNs). First, we adapt and evaluate the existing methods from other domains to GNNs. Faster convergence is achieved with InstanceNorm compared to BatchNorm and LayerNorm. We provide an explanation by showing that InstanceNorm serves as a preconditioner for GNNs, but such preconditioning effect is weaker with BatchNorm due to the heavy batch noise in graph datasets. Second, we show that the shift operation in InstanceNorm results in an expressiveness degradation of GNNs for highly regular graphs. We address this issue by proposing GraphNorm with a learnable shift. Empirically, GNNs with GraphNorm converge faster compared to GNNs using other normalization. GraphNorm also improves the generalization of GNNs, achieving better performance on graph classification benchmarks.

Domain generalization is challenging due to the domain shift and the uncertainty caused by the inaccessibility of target domain data. In this paper, we address both challenges with a probabilistic framework based on variational Bayesian inference, by incorporating uncertainty into neural network weights. We couple domain invariance in a probabilistic formula with the variational Bayesian inference. This enables us to explore domain-invariant learning in a principled way. Specifically, we derive domain-invariant representations and classifiers, which are jointly established in a two-layer Bayesian neural network. We empirically demonstrate the effectiveness of our proposal on four widely used cross-domain visual recognition benchmarks. Ablation studies validate the synergistic benefits of our Bayesian treatment when jointly learning domain-invariant representations and classifiers for domain generalization. Further, our method consistently delivers state-of-the-art mean accuracy on all benchmarks.

Neural controlled differential equations (CDEs) are the continuous-time analogue of recurrent neural networks, as Neural ODEs are to residual networks, and offer a memory-efficient continuous-time way to model functions of potentially irregular time series. Existing methods for computing the forward pass of a Neural CDE involve embedding the incoming time series into path space, often via interpolation, and using evaluations of this path to drive the hidden state. Here, we use rough path theory to extend this formulation. Instead of directly embedding into path space, we instead represent the input signal over small time intervals through its \textit{log-signature}, which are statistics describing how the signal drives a CDE. This is the approach for solving \textit{rough differential equations} (RDEs), and correspondingly we describe our main contribution as the introduction of Neural RDEs. This extension has a purpose: by generalising the Neural CDE approach to a broader class of driving signals, we demonstrate particular advantages for tackling long time series. In this regime, we demonstrate efficacy on problems of length up to 17k observations and observe significant training speed-ups, improvements in model performance, and reduced memory requirements compared to existing approaches.

Machine learning is predicated on the concept of generalization: a model achieving low error on a sufficiently large training set should also perform well on novel samples from the same distribution. We show that both data whitening and second order optimization can harm or entirely prevent generalization. In general, model training harnesses information contained in the sample-sample second moment matrix of a dataset. For a general class of models, namely models with a fully connected first layer, we prove that the information contained in this matrix is the only information which can be used to generalize. Models trained using whitened data, or with certain second order optimization schemes, have less access to this information, resulting in reduced or nonexistent generalization ability. We experimentally verify these predictions for several architectures, and further demonstrate that generalization continues to be harmed even when theoretical requirements are relaxed. However, we also show experimentally that regularized second order optimization can provide a practical tradeoff, where training is accelerated but less information is lost, and generalization can in some circumstances even improve.

Deep neural networks have emerged as very successful tools for image restoration and reconstruction tasks. These networks are often trained end-to-end to directly reconstruct an image from a noisy or corrupted measurement of that image. To achieve state-of-the-art performance, training on large and diverse sets of images is considered critical. However, it is often difficult and/or expensive to collect large amounts of training images. Inspired by the success of Data Augmentation (DA) for classification problems, in this paper, we propose a pipeline for data augmentation for accelerated MRI reconstruction and study its effectiveness at reducing the required training data in a variety of settings. Our DA pipeline, MRAugment, is specifically designed to utilize the invariances present in medical imaging measurements as naive DA strategies that neglect the physics of the problem fail. Through extensive studies on multiple datasets we demonstrate that in the low-data regime DA prevents overfitting and can match or even surpass the state of the art while using significantly fewer training data, whereas in the high-data regime it has diminishing returns. Furthermore, our findings show that DA improves the robustness of the model against various shifts in the test distribution.