A Theoretical Analysis of Contrastive Unsupervised Representation Learning

Recent empirical works have successfully used unlabeled data to learn feature representations that are broadly useful in downstream classification tasks. Several of these methods are reminiscent of the well-known word2vec embedding algorithm: leveraging availability of pairs of semantically "similar" data points and "negative samples," the learner forces the inner product of representations of similar pairs with each other to be higher on average than with negative samples. The current paper uses the term contrastive learning for such algorithms and presents a theoretical framework for analyzing them by introducing latent classes and hypothesizing that semantically similar points are sampled from the same latent class. This framework allows us to show provable guarantees on the performance of the learned representations on the average classification task that is comprised of a subset of the same set of latent classes. Our generalization bound also shows that learned representations can reduce (labeled) sample complexity on downstream tasks. We conduct controlled experiments in both the text and image domains to support the theory.Comment: 19 pages, 5 figure

A Sample Complexity Separation between Non-Convex and Convex Meta-Learning

One popular trend in meta-learning is to learn from many training tasks a common initialization for a gradient-based method that can be used to solve a new task with few samples. The theory of meta-learning is still in its early stages, with several recent learning-theoretic analyses of methods such as Reptile [Nichol et al., 2018] being for convex models. This work shows that convex-case analysis might be insufficient to understand the success of meta-learning, and that even for non-convex models it is important to look inside the optimization black-box, specifically at properties of the optimization trajectory. We construct a simple meta-learning instance that captures the problem of one-dimensional subspace learning. For the convex formulation of linear regression on this instance, we show that the new task sample complexity of any initialization-based meta-learning algorithm is $\Omega(d)$, where $d$ is the input dimension. In contrast, for the non-convex formulation of a two layer linear network on the same instance, we show that both Reptile and multi-task representation learning can have new task sample complexity of $\mathcal{O}(1)$, demonstrating a separation from convex meta-learning. Crucially, analyses of the training dynamics of these methods reveal that they can meta-learn the correct subspace onto which the data should be projected.Comment: 34 page

NAS-Bench-360: Benchmarking Neural Architecture Search on Diverse Tasks

Most existing neural architecture search (NAS) benchmarks and algorithms prioritize well-studied tasks, e.g. image classification on CIFAR or ImageNet. This makes the performance of NAS approaches in more diverse areas poorly understood. In this paper, we present NAS-Bench-360, a benchmark suite to evaluate methods on domains beyond those traditionally studied in architecture search, and use it to address the following question: do state-of-the-art NAS methods perform well on diverse tasks? To construct the benchmark, we curate ten tasks spanning a diverse array of application domains, dataset sizes, problem dimensionalities, and learning objectives. Each task is carefully chosen to interoperate with modern CNN-based search methods while possibly being far-afield from its original development domain. To speed up and reduce the cost of NAS research, for two of the tasks we release the precomputed performance of 15,625 architectures comprising a standard CNN search space. Experimentally, we show the need for more robust NAS evaluation of the kind NAS-Bench-360 enables by showing that several modern NAS procedures perform inconsistently across the ten tasks, with many catastrophically poor results. We also demonstrate how NAS-Bench-360 and its associated precomputed results will enable future scientific discoveries by testing whether several recent hypotheses promoted in the NAS literature hold on diverse tasks. NAS-Bench-360 is hosted at https://nb360.ml.cmu.edu.Comment: NeurIPS 2022 Datasets and Benchmarks Trac

A La Carte Embedding: Cheap but Effective Induction of Semantic Feature Vectors

Motivations like domain adaptation, transfer learning, and feature learning have fueled interest in inducing embeddings for rare or unseen words, n-grams, synsets, and other textual features. This paper introduces a la carte embedding, a simple and general alternative to the usual word2vec-based approaches for building such representations that is based upon recent theoretical results for GloVe-like embeddings. Our method relies mainly on a linear transformation that is efficiently learnable using pretrained word vectors and linear regression. This transform is applicable on the fly in the future when a new text feature or rare word is encountered, even if only a single usage example is available. We introduce a new dataset showing how the a la carte method requires fewer examples of words in context to learn high-quality embeddings and we obtain state-of-the-art results on a nonce task and some unsupervised document classification tasks.Comment: 11 pages, 2 figures, To appear in ACL 201