LEMMA: Bootstrapping High-Level Mathematical Reasoning with Learned Symbolic Abstractions

Humans tame the complexity of mathematical reasoning by developing hierarchies of abstractions. With proper abstractions, solutions to hard problems can be expressed concisely, thus making them more likely to be found. In this paper, we propose Learning Mathematical Abstractions (LEMMA): an algorithm that implements this idea for reinforcement learning agents in mathematical domains. LEMMA augments Expert Iteration with an abstraction step, where solutions found so far are revisited and rewritten in terms of new higher-level actions, which then become available to solve new problems. We evaluate LEMMA on two mathematical reasoning tasks--equation solving and fraction simplification--in a step-by-step fashion. In these two domains, LEMMA improves the ability of an existing agent, both solving more problems and generalizing more effectively to harder problems than those seen during training.

Psychologically-informed chain-of-thought prompts for metaphor understanding in large language models

Probabilistic models of language understanding are interpretable and structured, for instance models of metaphor understanding describe inference about latent topics and features. However, these models are manually designed for a specific task. Large language models (LLMs) can perform many tasks through in-context learning, but they lack the clear structure of probabilistic models. In this paper, we use chain-of-thought prompts to introduce structures from probabilistic models into LLMs. These prompts lead the model to infer latent variables and reason about their relationships to choose appropriate paraphrases for metaphors. The latent variables and relationships chosen are informed by theories of metaphor understanding from cognitive psychology. We apply these prompts to the two largest versions of GPT-3 and show that they can improve paraphrase selection.

Foundation Posteriors for Approximate Probabilistic Inference

Probabilistic programs provide an expressive representation language for generative models. Given a probabilistic program, we are interested in the task of posterior inference: estimating a latent variable given a set of observed variables. Existing techniques for inference in probabilistic programs often require choosing many hyper-parameters, are computationally expensive, and/or only work for restricted classes of programs. Here we formulate inference as masked language modeling: given a program, we generate a supervised dataset of variables and assignments, and randomly mask a subset of the assignments. We then train a neural network to unmask the random values, defining an approximate posterior distribution. By optimizing a single neural network across a range of programs we amortize the cost of training, yielding a ``foundation'' posterior able to do zero-shot inference for new programs. The foundation posterior can also be fine-tuned for a particular program and dataset by optimizing a variational inference objective. We show the efficacy of the approach, zero-shot and fine-tuned, on a benchmark of STAN programs.

Mixed-effects transformers for hierarchical adaptation

Language use differs dramatically from context to context. To some degree, modern language models like GPT-3 are able to account for such variance by conditioning on a string of previous input text, or prompt. Yet prompting is ineffective when contexts are sparse, out-of-sample, or extra-textual; for instance, accounting for when and where the text was produced or who produced it. In this paper, we introduce the mixed-effects transformer (MET), a novel approach for learning hierarchically-structured prefixes -- lightweight modules prepended to the input -- to account for structured variation. Specifically, we show how the popular class of mixed-effects models may be extended to transformer-based architectures using a regularized prefix-tuning procedure with dropout. We evaluate this approach on several domain-adaptation benchmarks, finding that it efficiently adapts to novel contexts with minimal data while still effectively generalizing to unseen contexts.

Know Thy Student: Interactive Learning with Gaussian Processes

Learning often involves interaction between multiple agents. Human teacher-student settings best illustrate how interactions result in efficient knowledge passing where the teacher constructs a curriculum based on their students' abilities. Prior work in machine teaching studies how the teacher should construct optimal teaching datasets assuming the teacher knows everything about the student. However, in the real world, the teacher doesn't have complete information about the student. The teacher must interact and diagnose the student, before teaching. Our work proposes a simple diagnosis algorithm which uses Gaussian processes for inferring student-related information, before constructing a teaching dataset. We apply this to two settings. One is where the student learns from scratch and the teacher must figure out the student's learning algorithm parameters, eg. the regularization parameters in ridge regression or support vector machines. Two is where the student has partially explored the environment and the teacher must figure out the important areas the student has not explored; we study this in the offline reinforcement learning setting where the teacher must provide demonstrations to the student and avoid sending redundant trajectories. Our experiments highlight the importance of diagosing before teaching and demonstrate how students can learn more efficiently with the help of an interactive teacher. We conclude by outlining where diagnosing combined with teaching would be more desirable than passive learning.

Active Learning Helps Pretrained Models Learn the Intended Task

Models can fail in unpredictable ways during deployment due to task ambiguity, when multiple behaviors are consistent with the provided training data. An example is an object classifier trained on red squares and blue circles: when encountering blue squares, the intended behavior is undefined. We investigate whether pretrained models are better active learners, capable of disambiguating between the possible tasks a user may be trying to specify. Intriguingly, we find that better active learning is an emergent property of the pretraining process: pretrained models require up to 5 times fewer labels when using uncertainty-based active learning, while non-pretrained models see no or even negative benefit. We find these gains come from an ability to select examples with attributes that disambiguate the intended behavior, such as rare product categories or atypical backgrounds. These attributes are far more linearly separable in pretrained model's representation spaces vs non-pretrained models, suggesting a possible mechanism for this behavior.

Language modeling via stochastic processes

Modern language models can generate high-quality short texts. However, they often meander or are incoherent when generating longer texts. These issues arise from the next-token-only language modeling objective. To address these issues, we introduce Time Control (TC), a language model that implicitly plans via a latent stochastic process. TC does this by learning a representation which maps the dynamics of how text changes in a document to the dynamics of a stochastic process of interest. Using this representation, the language model can generate text by first implicitly generating a document plan via a stochastic process, and then generating text that is consistent with this latent plan. Compared to domain-specific methods and fine-tuning GPT2 across a variety of text domains, TC improves performance on text infilling and discourse coherence. On long text generation settings, TC preserves the text structure both in terms of ordering (up to +40% better) and text length consistency (up to +17% better). Human evaluators also prefer TC's output 28.6% more than the baselines.

Improving Intrinsic Exploration with Language Abstractions

Reinforcement learning (RL) agents are particularly hard to train when rewards are sparse. One common solution is to use intrinsic rewards to encourage agents to explore their environment. However, recent intrinsic exploration methods often use state-based novelty measures which reward low-level exploration and may not scale to domains requiring more abstract skills. Instead, we explore natural language as a general medium for highlighting relevant abstractions in an environment. Unlike previous work, we evaluate whether language can improve over existing exploration methods by directly extending (and comparing to) competitive intrinsic exploration baselines: AMIGo (Campero et al., 2021) and NovelD (Zhang et al., 2021). These language-based variants outperform their non-linguistic forms by 45-85% across 13 challenging tasks from the MiniGrid and MiniHack environment suites.

Tradeoffs Between Contrastive and Supervised Learning: An Empirical Study

Contrastive learning has made considerable progress in computer vision, outperforming supervised pretraining on a range of downstream datasets. However, is contrastive learning the better choice in all situations? We demonstrate two cases where it is not. First, under sufficiently small pretraining budgets, supervised pretraining on ImageNet consistently outperforms a comparable contrastive model on eight diverse image classification datasets. This suggests that the common practice of comparing pretraining approaches at hundreds or thousands of epochs may not produce actionable insights for those with more limited compute budgets. Second, even with larger pretraining budgets we identify tasks where supervised learning prevails, perhaps because the object-centric bias of supervised pretraining makes the model more resilient to common corruptions and spurious foreground-background correlations. These results underscore the need to characterize tradeoffs of different pretraining objectives across a wider range of contexts and training regimes.

DABS: A Domain-Agnostic Benchmark for Self-Supervised Learning

Self-supervised learning algorithms, including BERT and SimCLR, have enabled significant strides in fields like natural language processing, computer vision, and speech processing. However, these algorithms are domain-specific, meaning that new self-supervised learning algorithms must be developed for each new setting, including myriad healthcare, scientific, and multimodal domains. To catalyze progress toward domain-agnostic methods, we introduce DABS: a Domain-Agnostic Benchmark for Self-supervised learning. To perform well on DABS, an algorithm is evaluated on seven diverse domains: natural images, multichannel sensor data, English text, speech recordings, multilingual text, chest x-rays, and images with text descriptions. Each domain contains an unlabeled dataset for pretraining; the model is then is scored based on its downstream performance on a set of labeled tasks in the domain. We also present e-Mix and ShED: two baseline domain-agnostic algorithms; their relatively modest performance demonstrates that significant progress is needed before self-supervised learning is an out-of-the-box solution for arbitrary domains. Code for benchmark datasets and baseline algorithms is available at https://github.com/alextamkin/dabs.