arXiv subjects

Nikunj Saunshi

Publications and source records attributed to Nikunj Saunshi.

24 records · Page 2Linked to original sources

arXiv2021

A Mathematical Exploration of Why Language Models Help Solve Downstream Tasks

Autoregressive language models, pretrained using large text corpora to do well on next word prediction, have been successful at solving many downstream tasks, even with zero-shot usage. However, there is little theoretical understanding of this success. This paper initiates a mathematical study of this phenomenon for the downstream task of text classification by considering the following questions: (1) What is the intuitive connection between the pretraining task of next word prediction and text classification? (2) How can we mathematically formalize this connection and quantify the benefit of language modeling? For (1), we hypothesize, and verify empirically, that classification tasks of interest can be reformulated as sentence completion tasks, thus making language modeling a meaningful pretraining task. With a mathematical formalization of this hypothesis, we make progress towards (2) and show that language models that are $ε$-optimal in cross-entropy (log-perplexity) learn features that can linearly solve such classification tasks with $\mathcal{O}(\sqrtε)$ error, thus demonstrating that doing well on language modeling can be beneficial for downstream tasks. We experimentally verify various assumptions and theoretical findings, and also use insights from the analysis to design a new objective function that performs well on some classification tasks.

cs.CL↗

arXiv2020

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 $Ω(d)$, 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.

cs.LG↗

arXiv2020

Provable Representation Learning for Imitation Learning via Bi-level Optimization

A common strategy in modern learning systems is to learn a representation that is useful for many tasks, a.k.a. representation learning. We study this strategy in the imitation learning setting for Markov decision processes (MDPs) where multiple experts' trajectories are available. We formulate representation learning as a bi-level optimization problem where the "outer" optimization tries to learn the joint representation and the "inner" optimization encodes the imitation learning setup and tries to learn task-specific parameters. We instantiate this framework for the imitation learning settings of behavior cloning and observation-alone. Theoretically, we show using our framework that representation learning can provide sample complexity benefits for imitation learning in both settings. We also provide proof-of-concept experiments to verify our theory.

cs.LG↗

arXiv2019

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.

cs.LG↗

arXiv2018

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.

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arXiv2018

A Large Self-Annotated Corpus for Sarcasm

We introduce the Self-Annotated Reddit Corpus (SARC), a large corpus for sarcasm research and for training and evaluating systems for sarcasm detection. The corpus has 1.3 million sarcastic statements -- 10 times more than any previous dataset -- and many times more instances of non-sarcastic statements, allowing for learning in both balanced and unbalanced label regimes. Each statement is furthermore self-annotated -- sarcasm is labeled by the author, not an independent annotator -- and provided with user, topic, and conversation context. We evaluate the corpus for accuracy, construct benchmarks for sarcasm detection, and evaluate baseline methods.

cs.CL↗