Neural networks trained to solve modular arithmetic tasks exhibit grokking, a phenomenon where the test accuracy starts improving long after the model achieves 100% training accuracy in the training process. It is often taken as an example of "emergence", where model ability manifests sharply through a phase transition. In this work, we show that the phenomenon of grokking is not specific to neural networks nor to gradient descent-based optimization. Specifically, we show that this phenomenon occurs when learning modular arithmetic with Recursive Feature Machines (RFM), an iterative algorithm that uses the Average Gradient Outer Product (AGOP) to enable task-specific feature learning with general machine learning models. When used in conjunction with kernel machines, iterating RFM results in a fast transition from random, near zero, test accuracy to perfect test accuracy. This transition cannot be predicted from the training loss, which is identically zero, nor from the test loss, which remains constant in initial iterations. Instead, as we show, the transition is completely determined by feature learning: RFM gradually learns block-circulant features to solve modular arithmetic. Paralleling the results for RFM, we show that neural networks that solve modular arithmetic also learn block-circulant features. Furthermore, we present theoretical evidence that RFM uses such block-circulant features to implement the Fourier Multiplication Algorithm, which prior work posited as the generalizing solution neural networks learn on these tasks. Our results demonstrate that emergence can result purely from learning task-relevant features and is not specific to neural architectures nor gradient descent-based optimization methods. Furthermore, our work provides more evidence for AGOP as a key mechanism for feature learning in neural networks.

Transfer learning is a critical part of real-world machine learning deployments and has been extensively studied in experimental works with overparameterized neural networks. However, even in the simplest setting of linear regression a notable gap still exists in the theoretical understanding of transfer learning. In-distribution research on high-dimensional linear regression has led to the identification of a phenomenon known as benign overfitting, in which linear interpolators overfit to noisy training labels and yet still generalize well. This behavior occurs under specific conditions on the source covariance matrix and input data dimension. Therefore, it is natural to wonder how such high-dimensional linear models behave under transfer learning. We prove the first non-asymptotic excess risk bounds for benignly-overfit linear interpolators in the transfer learning setting. From our analysis, we propose a taxonomy of beneficial and malignant covariate shifts based on the degree of overparameterization. We follow our analysis with empirical studies that show these beneficial and malignant covariate shifts for linear interpolators on real image data, and for fully-connected neural networks in settings where the input data dimension is larger than the training sample size.

The practical success of overparameterized neural networks has motivated the recent scientific study of \emph{interpolating methods}-- learning methods which are able fit their training data perfectly. Empirically, certain interpolating methods can fit noisy training data without catastrophically bad test performance, which defies standard intuitions from statistical learning theory. Aiming to explain this, a large body of recent work has studied \emph{benign overfitting}, a behavior seen in certain asymptotic settings under which interpolating methods approach Bayes-optimality, even in the presence of noise. In this work, we argue that, while benign overfitting has been instructive to study, real interpolating methods like deep networks do not fit benignly. That is, noise in the train set leads to suboptimal generalization, suggesting that these methods fall in an intermediate regime between benign and catastrophic overfitting, in which asymptotic risk is neither is neither Bayes-optimal nor unbounded, with the confounding effect of the noise being ``tempered" but non-negligible. We call this behavior \textit{tempered overfitting}. We first provide broad empirical evidence for our three-part taxonomy, demonstrating that deep neural networks and kernel machines fit to noisy data can be reasonably well classified as benign, tempered, or catastrophic. We then specialize to kernel (ridge) regression (KR), obtaining conditions on the ridge parameter and kernel eigenspectrum under which KR exhibits each of the three behaviors, demonstrating the consequences for KR with common kernels and trained neural networks of infinite width using experiments on natural and synthetic datasets.

Real-world text classification tasks often require many labeled training examples that are expensive to obtain. Recent advancements in machine teaching, specifically the data programming paradigm, facilitate the creation of training data sets quickly via a general framework for building weak models, also known as labeling functions, and denoising them through ensemble learning techniques. We present a fast, simple data programming method for augmenting text data sets by generating neighborhood-based weak models with minimal supervision. Furthermore, our method employs an iterative procedure to identify sparsely distributed examples from large volumes of unlabeled data. The iterative data programming techniques improve newer weak models as more labeled data is confirmed with human-in-loop. We show empirical results on sentence classification tasks, including those from a task of improving intent recognition in conversational agents.

BERT-era question answering systems have recently achieved impressive performance on several question-answering (QA) tasks. These systems are based on representations that have been pre-trained on self-supervised tasks such as word masking and sentence entailment, using massive amounts of data. Nevertheless, additional pre-training closer to the end-task, such as training on synthetic QA pairs, has been shown to improve performance. While recent work has considered augmenting labelled data and leveraging large unlabelled datasets to generate synthetic QA data, directly adapting to target data has received little attention. In this paper we investigate the iterative generation of synthetic QA pairs as a way to realize unsupervised self adaptation. Motivated by the success of the roundtrip consistency method for filtering generated QA pairs, we present iterative generalizations of the approach, which maximize an approximation of a lower bound on the probability of the adaptation data. By adapting on synthetic QA pairs generated on the target data, our method is able to improve QA systems significantly, using an order of magnitude less synthetic data and training computation than existing augmentation approaches.

Many conversational agents in the market today follow a standard bot development framework which requires training intent classifiers to recognize user input. The need to create a proper set of training examples is often the bottleneck in the development process. In many occasions agent developers have access to historical chat logs that can provide a good quantity as well as coverage of training examples. However, the cost of labeling them with tens to hundreds of intents often prohibits taking full advantage of these chat logs. In this paper, we present a framework called search, label, and propagate (SLP) for bootstrapping intents from existing chat logs using weak supervision. The framework reduces hours to days of labeling effort down to minutes of work by using a search engine to find examples, then relies on a data programming approach to automatically expand the labels. We report on a user study that shows positive user feedback for this new approach to build conversational agents, and demonstrates the effectiveness of using data programming for autolabeling. While the system is developed for training conversational agents, the framework has broader application in significantly reducing labeling effort for training text classifiers.