Large neural networks excel in many domains, but they are expensive to train and fine-tune. A popular approach to reduce their compute or memory requirements is to replace dense weight matrices with structured ones (e.g., sparse, low-rank, Fourier transform). These methods have not seen widespread adoption (1) in end-to-end training due to unfavorable efficiency–quality tradeoffs, and (2) in dense-to-sparse fine-tuning due to lack of tractable algorithms to approximate a given dense weight matrix. To address these issues, we propose a class of matrices (Monarch) that is hardware-efficient (they are parameterized as products of two block-diagonal matrices for better hardware utilization) and expressive (they can represent many commonly used transforms). Surprisingly, the problem of approximating a dense weight matrix with a Monarch matrix, though nonconvex, has an analytical optimal solution. These properties of Monarch matrices unlock new ways to train and fine-tune sparse and dense models. We empirically validate that Monarch can achieve favorable accuracy-efficiency tradeoffs in several end-to-end sparse training applications: speeding up ViT and GPT-2 training on ImageNet classification and Wikitext-103 language modeling by 2x with comparable model quality, and reducing the error on PDE solving and MRI reconstruction tasks by 40%. In sparse-to-dense training, with a simple technique called "reverse sparsification," Monarch matrices serve as a useful intermediate representation to speed up GPT-2 pretraining on OpenWebText by 2x without quality drop. The same technique brings 23% faster BERT pretraining than even the very optimized implementation from Nvidia that set the MLPerf 1.1 record. In dense-to-sparse fine-tuning, as a proof-of-concept, our Monarch approximation algorithm speeds up BERT fine-tuning on GLUE by 1.7x with comparable accuracy.

Spurious correlations pose a major challenge for robust machine learning. Models trained with empirical risk minimization (ERM) may learn to rely on correlations between class labels and spurious attributes, leading to poor performance on data groups without these correlations. This is challenging to address when the spurious attribute labels are unavailable. To improve worst-group performance on spuriously correlated data without training attribute labels, we propose Correct-N-Contrast (CNC), a contrastive approach to directly learn representations robust to spurious correlations. As ERM models can be good spurious attribute predictors, CNC works by (1) using a trained ERM model’s outputs to identify samples with the same class but dissimilar spurious features, and (2) training a robust model with contrastive learning to learn similar representations for these samples. To support CNC, we introduce new connections between worst-group error and a representation alignment loss that CNC aims to minimize. We empirically observe that worst-group error closely tracks with alignment loss, and prove that the alignment loss over a class helps upper-bound the class’s worst-group vs. average error gap. On popular benchmarks, CNC reduces alignment loss drastically, and achieves state-of-the-art worst-group accuracy by 3.6% average absolute lift. CNC is also competitive with oracle methods that require group labels.

For machine learning models trained with limited labeled training data, validation stands to become the main bottleneck to reducing overall annotation costs. We propose a statistical validation algorithm that accurately estimates the F-score of binary classifiers for rare categories, where finding relevant examples to evaluate on is particularly challenging. Our key insight is that simultaneous calibration and importance sampling enables accurate estimates even in the low-sample regime (< 300 samples). Critically, we also derive an accurate single-trial estimator of the variance of our method and demonstrate that this estimator is empirically accurate at low sample counts, enabling a practitioner to know how well they can trust a given low-sample estimate. When validating state-of-the-art semi-supervised models on ImageNet and iNatural-ist2017, our method achieves the same estimates of model performance with up to 10× fewer labels than competing approaches. In particular, we can estimate model F1 scores with a variance of 0.005 using as few as 100 labels.

Machine learning models are often deployed in different settings than they were trained and validated on, posing a challenge to practitioners who wish to predict how well the deployed model will perform on a target distribution. If an unlabeled sample from the target distribution is available, along with a labeled sample from a possibly different source distribution, standard approaches such as importance weighting can be applied to estimate performance on the target. However, importance weighting struggles when the source and target distributions have non-overlapping support or are high-dimensional. Taking inspiration from fields such as epidemiology and polling, we develop Mandoline, a new evaluation framework that mitigates these issues. Our key insight is that practitioners may have prior knowledge about the ways in which the distribution shifts, which we can use to better guide the importance weighting procedure. Specifically, users write simple "slicing functions" {–} noisy, potentially correlated binary functions intended to capture possible axes of distribution shift {–} to compute reweighted performance estimates. We further describe a density ratio estimation framework for the slices and show how its estimation error scales with slice quality and dataset size. Empirical validation on NLP and vision tasks shows that Mandoline can estimate performance on the target distribution up to 3x more accurately compared to standard baselines.

A popular way to estimate the causal effect of a variable x on y from observational data is to use an instrumental variable (IV): a third variable z that affects y only through x. The more strongly z is associated with x, the more reliable the estimate is, but such strong IVs are difficult to find. Instead, practitioners combine more commonly available IV candidates—which are not necessarily strong, or even valid, IVs—into a single "summary" that is plugged into causal effect estimators in place of an IV. In genetic epidemiology, such approaches are known as allele scores. Allele scores require strong assumptions—independence and validity of all IV candidates—for the resulting estimate to be reliable. To relax these assumptions, we propose Ivy, a new method to combine IV candidates that can handle correlated and invalid IV candidates in a robust manner. Theoretically, we characterize this robustness, its limits, and its impact on the resulting causal estimates. Empirically, Ivy can correctly identify the directionality of known relationships and is robust against false discovery (median effect size <= 0.025) on three real-world datasets with no causal effects, while allele scores return more biased estimates (median effect size >= 0.118).

In this paper, we provide near-optimal accelerated first-order methods for minimizing a broad class of smooth nonconvex functions that are unimodal on all lines through a minimizer. This function class, which we call the class of smooth quasar-convex functions, is parameterized by a constant $$\gamma \in (0,1]$$: $$\gamma = 1$$ encompasses the classes of smooth convex and star-convex functions, and smaller values of $$\gamma$$ indicate that the function can be "more nonconvex." We develop a variant of accelerated gradient descent that computes an $$\epsilon$$-approximate minimizer of a smooth $$\gamma$$-quasar-convex function with at most $$O(\gamma^{-1} \epsilon^{-1/2} \log(\gamma^{-1} \epsilon^{-1}))$$ total function and gradient evaluations. We also derive a lower bound of $$\Omega(\gamma^{-1} \epsilon^{-1/2})$$ on the worst-case number of gradient evaluations required by any deterministic first-order method, showing that, up to a logarithmic factor, no deterministic first-order method can improve upon ours.

In real-world classification tasks, each class often comprises multiple finer-grained "subclasses." As the subclass labels are frequently unavailable, models trained using only the coarser-grained class labels often exhibit highly variable performance across different subclasses. This phenomenon, known as hidden stratification, has important consequences for models deployed in safety-critical applications such as medicine. We propose GEORGE, a method to both measure and mitigate hidden stratification even when subclass labels are unknown. We first observe that unlabeled subclasses are often separable in the feature space of deep models, and exploit this fact to estimate subclass labels for the training data via clustering techniques. We then use these approximate subclass labels as a form of noisy supervision in a distributionally robust optimization objective. We theoretically characterize the performance of GEORGE in terms of the worst-case generalization error across any subclass. We empirically validate GEORGE on a mix of real-world and benchmark image classification datasets, and show that our approach boosts worst-case subclass accuracy by up to 15 percentage points compared to standard training techniques, without requiring any information about the subclasses.