TASK DEFINITION: In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.
PROBLEM: Deep ensembles have been empirically shown to be a promising approach for improving accuracy, uncertainty  and out-of-distribution robustness of deep learning models. While deep ensembles were theoretically motivated by the bootstrap, non-bootstrap ensembles trained with just random initialization also perform well in practice, which suggests that there could be other explanations for why deep ensembles work well. Bayesian neural networks, which learn distributions over the parameters of the network, are theoretically well-motivated by Bayesian principles, but do not perform as well as deep ensembles in practice, particularly under dataset shift. One possible explanation for this gap between theory and practice is that popular scalable approximate Bayesian methods tend to focus on a single mode, whereas deep ensembles tend to explore diverse modes in function space. We investigate this hypothesis by building on recent work on understanding the loss landscape of neural networks and adding our own exploration to measure the similarity of functions in the space of predictions. Our results show that random initializations explore entirely different modes, while functions along an optimization trajectory or sampled from the subspace thereof cluster within a single mode predictions-wise, while often deviating significantly in the weight space. We demonstrate that while low-loss connectors between modes exist, they are not connected in the space of predictions. Developing the concept of the diversity--accuracy plane, we show that the decorrelation power of random initializations is unmatched by popular subspace sampling methods.

SOLUTION: We study deep ensembles through the lens of loss landscape and the space of predictions, demonstrating that the decorrelation power of random initializations is unmatched by subspace sampling that only explores a single mode.

PROBLEM: We present Spectral Inference Networks, a framework for learning eigenfunctions of linear operators by stochastic optimization. Spectral Inference Networks generalize Slow Feature Analysis to generic symmetric operators, and are closely related to Variational Monte Carlo methods from computational physics. As such, they can be a powerful tool for unsupervised representation learning from video or graph-structured data. We cast training Spectral Inference Networks as a bilevel optimization problem, which allows for online learning of multiple eigenfunctions. We show results of training Spectral Inference Networks on problems in quantum mechanics and feature learning for videos on synthetic datasets. Our results demonstrate that Spectral Inference Networks accurately recover eigenfunctions of linear operators and can discover interpretable representations from video in a fully unsupervised manner.

SOLUTION: We show how to learn spectral decompositions of linear operators with deep learning, and use it for unsupervised learning without a generative model.

PROBLEM: Previous work on adversarially robust neural networks requires large training sets and computationally expensive training procedures.   On the other hand, few-shot learning methods are highly vulnerable to adversarial examples.   The goal of our work is to produce networks which both perform well at few-shot tasks and are simultaneously robust to adversarial examples.   We adapt adversarial training for meta-learning, we adapt robust architectural features to small networks for meta-learning, we test pre-processing defenses as an alternative to adversarial training for meta-learning, and we investigate the advantages of robust meta-learning over robust transfer-learning for few-shot tasks.   This work provides a thorough analysis of adversarially robust methods in the context of meta-learning, and we lay the foundation for future work on defenses for few-shot tasks.

SOLUTION:
We develop meta-learning methods for adversarially robust few-shot learning.