The Role of Linguistic Priors in Measuring Compositional Generalization of Vision-Language Models

Compositionality is a common property in many modalities including natural languages and images, but the compositional generalization of multi-modal models is not well-understood. In this paper, we identify two sources of visual-linguistic compositionality: linguistic priors and the interplay between images and texts. We show that current attempts to improve compositional generalization rely on linguistic priors rather than on information in the image. We also propose a new metric for compositionality without such linguistic priors.

BenchMD: A Benchmark for Modality-Agnostic Learning on Medical Images and Sensors

Medical data poses a daunting challenge for AI algorithms: it exists in many different modalities, experiences frequent distribution shifts, and suffers from a scarcity of examples and labels. Recent advances, including transformers and self-supervised learning, promise a more universal approach that can be applied flexibly across these diverse conditions. To measure and drive progress in this direction, we present BenchMD: a benchmark that tests how modality-agnostic methods, including architectures and training techniques (e.g. self-supervised learning, ImageNet pretraining), perform on a diverse array of clinically-relevant medical tasks. BenchMD combines 19 publicly available datasets for 7 medical modalities, including 1D sensor data, 2D images, and 3D volumetric scans. Our benchmark reflects real-world data constraints by evaluating methods across a range of dataset sizes, including challenging few-shot settings that incentivize the use of pretraining. Finally, we evaluate performance on out-of-distribution data collected at different hospitals than the training data, representing naturally-occurring distribution shifts that frequently degrade the performance of medical AI models. Our baseline results demonstrate that no modality-agnostic technique achieves strong performance across all modalities, leaving ample room for improvement on the benchmark. Code is released at https://github.com/rajpurkarlab/BenchMD .

Hiding Data Helps: On the Benefits of Masking for Sparse Coding

Sparse coding refers to modeling a signal as sparse linear combinations of the elements of a learned dictionary. Sparse coding has proven to be a successful and interpretable approach in many applications, such as signal processing, computer vision, and medical imaging. While this success has spurred much work on sparse coding with provable guarantees, work on the setting where the learned dictionary is larger (or \textit{over-realized}) with respect to the ground truth is comparatively nascent. Existing theoretical results in the over-realized regime are limited to the case of noise-less data. In this paper, we show that for over-realized sparse coding in the presence of noise, minimizing the standard dictionary learning objective can fail to recover the ground-truth dictionary, regardless of the magnitude of the signal in the data-generating process. Furthermore, drawing from the growing body of work on self-supervised learning, we propose a novel masking objective and we prove that minimizing this new objective can recover the ground-truth dictionary. We corroborate our theoretical results with experiments across several parameter regimes, showing that our proposed objective enjoys better empirical performance than the standard reconstruction objective.

Provably Learning Diverse Features in Multi-View Data with Midpoint Mixup

Mixup is a data augmentation technique that relies on training using random convex combinations of data points and their labels. In recent years, Mixup has become a standard primitive used in the training of state-of-the-art image classification models due to its demonstrated benefits over empirical risk minimization with regards to generalization and robustness. In this work, we try to explain some of this success from a feature learning perspective. We focus our attention on classification problems in which each class may have multiple associated features (or views) that can be used to predict the class correctly. Our main theoretical results demonstrate that, for a non-trivial class of data distributions with two features per class, training a 2-layer convolutional network using empirical risk minimization can lead to learning only one feature for almost all classes while training with a specific instantiation of Mixup succeeds in learning both features for every class. We also show empirically that these theoretical insights extend to the practical settings of image benchmarks modified to have additional synthetic features.

Towards Understanding the Data Dependency of Mixup-style Training

In the Mixup training paradigm, a model is trained using convex combinations of data points and their associated labels. Despite seeing very few true data points during training, models trained using Mixup seem to still minimize the original empirical risk and exhibit better generalization and robustness on various tasks when compared to standard training. In this paper, we investigate how these benefits of Mixup training rely on properties of the data in the context of classification. For minimizing the original empirical risk, we compute a closed form for the Mixup-optimal classification, which allows us to construct a simple dataset on which minimizing the Mixup loss can provably lead to learning a classifier that does not minimize the empirical loss on the data. On the other hand, we also give sufficient conditions for Mixup training to also minimize the original empirical risk. For generalization, we characterize the margin of a Mixup classifier, and use this to understand why the decision boundary of a Mixup classifier can adapt better to the full structure of the training data when compared to standard training. In contrast, we also show that, for a large class of linear models and linearly separable datasets, Mixup training leads to learning the same classifier as standard training.

Beyond Lazy Training for Over-parameterized Tensor Decomposition

Over-parametrization is an important technique in training neural networks. In both theory and practice, training a larger network allows the optimization algorithm to avoid bad local optimal solutions. In this paper we study a closely related tensor decomposition problem: given an $l$-th order tensor in $(R^d)^{\otimes l}$ of rank $r$ (where $r\ll d$), can variants of gradient descent find a rank $m$ decomposition where $m > r$? We show that in a lazy training regime (similar to the NTK regime for neural networks) one needs at least $m = \Omega(d^{l-1})$, while a variant of gradient descent can find an approximate tensor when $m = O^*(r^{2.5l}\log d)$. Our results show that gradient descent on over-parametrized objective could go beyond the lazy training regime and utilize certain low-rank structure in the data.

Dissecting Hessian: Understanding Common Structure of Hessian in Neural Networks

Hessian captures important properties of the deep neural network loss landscape. We observe that eigenvectors and eigenspaces of the layer-wise Hessian for neural network objective have several interesting structures -- top eigenspaces for different models have high overlap, and top eigenvectors form low rank matrices when they are reshaped into the same shape as the corresponding weight matrix. These structures, as well as the low rank structure of the Hessian observed in previous studies, can be explained by approximating the Hessian using Kronecker factorization. Our new understanding can also explain why some of these structures become weaker when the network is trained with batch normalization. Finally, we show that the Kronecker factorization can be combined with PAC-Bayes techniques to get better explicit generalization bounds.

Secure Data Sharing With Flow Model

In the classical multi-party computation setting, multiple parties jointly compute a function without revealing their own input data. We consider a variant of this problem, where the input data can be shared for machine learning training purposes, but the data are also encrypted so that they cannot be recovered by other parties. We present a rotation based method using flow model, and theoretically justified its security. We demonstrate the effectiveness of our method in different scenarios, including supervised secure model training, and unsupervised generative model training. Our code is available at https://github.com/ duchenzhuang/flowencrypt.

Guarantees for Tuning the Step Size using a Learning-to-Learn Approach

Learning-to-learn (using optimization algorithms to learn a new optimizer) has successfully trained efficient optimizers in practice. This approach relies on meta-gradient descent on a meta-objective based on the trajectory that the optimizer generates. However, there were few theoretical guarantees on how to avoid meta-gradient explosion/vanishing problems, or how to train an optimizer with good generalization performance. In this paper, we study the learning-to-learn approach on a simple problem of tuning the step size for quadratic loss. Our results show that although there is a way to design the meta-objective so that the meta-gradient remain polynomially bounded, computing the meta-gradient directly using backpropagation leads to numerical issues that look similar to gradient explosion/vanishing problems. We also characterize when it is necessary to compute the meta-objective on a separate validation set instead of the original training set. Finally, we verify our results empirically and show that a similar phenomenon appears even for more complicated learned optimizers parametrized by neural networks.