arXiv subjects

Noah D. Goodman

Publications and source records attributed to Noah D. Goodman.

At least 73 records · Page 4Linked to original sources

arXiv2023

Solving Math Word Problems by Combining Language Models With Symbolic Solvers

Automatically generating high-quality step-by-step solutions to math word problems has many applications in education. Recently, combining large language models (LLMs) with external tools to perform complex reasoning and calculation has emerged as a promising direction for solving math word problems, but prior approaches such as Program-Aided Language model (PAL) are biased towards simple procedural problems and less effective for problems that require declarative reasoning. We propose an approach that combines an LLM that can incrementally formalize word problems as a set of variables and equations with an external symbolic solver that can solve the equations. Our approach achieves comparable accuracy to the original PAL on the GSM8K benchmark of math word problems and outperforms PAL by an absolute 20% on ALGEBRA, a new dataset of more challenging word problems extracted from Algebra textbooks. Our work highlights the benefits of using declarative and incremental representations when interfacing with an external tool for solving complex math word problems. Our data and prompts are publicly available at https://github.com/joyheyueya/declarative-math-word-problem.

cs.CL↗

arXiv2022

Geoclidean: Few-Shot Generalization in Euclidean Geometry

Euclidean geometry is among the earliest forms of mathematical thinking. While the geometric primitives underlying its constructions, such as perfect lines and circles, do not often occur in the natural world, humans rarely struggle to perceive and reason with them. Will computer vision models trained on natural images show the same sensitivity to Euclidean geometry? Here we explore these questions by studying few-shot generalization in the universe of Euclidean geometry constructions. We introduce Geoclidean, a domain-specific language for Euclidean geometry, and use it to generate two datasets of geometric concept learning tasks for benchmarking generalization judgements of humans and machines. We find that humans are indeed sensitive to Euclidean geometry and generalize strongly from a few visual examples of a geometric concept. In contrast, low-level and high-level visual features from standard computer vision models pretrained on natural images do not support correct generalization. Thus Geoclidean represents a novel few-shot generalization benchmark for geometric concept learning, where the performance of humans and of AI models diverge. The Geoclidean framework and dataset are publicly available for download.

cs.CV↗

arXiv2022

Peano: Learning Formal Mathematical Reasoning

General mathematical reasoning is computationally undecidable, but humans routinely solve new problems. Moreover, discoveries developed over centuries are taught to subsequent generations quickly. What structure enables this, and how might that inform automated mathematical reasoning? We posit that central to both puzzles is the structure of procedural abstractions underlying mathematics. We explore this idea in a case study on 5 sections of beginning algebra on the Khan Academy platform. To define a computational foundation, we introduce Peano, a theorem-proving environment where the set of valid actions at any point is finite. We use Peano to formalize introductory algebra problems and axioms, obtaining well-defined search problems. We observe existing reinforcement learning methods for symbolic reasoning to be insufficient to solve harder problems. Adding the ability to induce reusable abstractions ("tactics") from its own solutions allows an agent to make steady progress, solving all problems. Furthermore, these abstractions induce an order to the problems, seen at random during training. The recovered order has significant agreement with the expert-designed Khan Academy curriculum, and second-generation agents trained on the recovered curriculum learn significantly faster. These results illustrate the synergistic role of abstractions and curricula in the cultural transmission of mathematics.

cs.AI↗

arXiv2022

On Rate-Distortion Theory in Capacity-Limited Cognition & Reinforcement Learning

Throughout the cognitive-science literature, there is widespread agreement that decision-making agents operating in the real world do so under limited information-processing capabilities and without access to unbounded cognitive or computational resources. Prior work has drawn inspiration from this fact and leveraged an information-theoretic model of such behaviors or policies as communication channels operating under a bounded rate constraint. Meanwhile, a parallel line of work also capitalizes on the same principles from rate-distortion theory to formalize capacity-limited decision making through the notion of a learning target, which facilitates Bayesian regret bounds for provably-efficient learning algorithms. In this paper, we aim to elucidate this latter perspective by presenting a brief survey of these information-theoretic models of capacity-limited decision making in biological and artificial agents.

cs.LG↗

arXiv2022

Concadia: Towards Image-Based Text Generation with a Purpose

Current deep learning models often achieve excellent results on benchmark image-to-text datasets but fail to generate texts that are useful in practice. We argue that to close this gap, it is vital to distinguish descriptions from captions based on their distinct communicative roles. Descriptions focus on visual features and are meant to replace an image (often to increase accessibility), whereas captions appear alongside an image to supply additional information. To motivate this distinction and help people put it into practice, we introduce the publicly available Wikipedia-based dataset Concadia consisting of 96,918 images with corresponding English-language descriptions, captions, and surrounding context. Using insights from Concadia, models trained on it, and a preregistered human-subjects experiment with human- and model-generated texts, we characterize the commonalities and differences between descriptions and captions. In addition, we show that, for generating both descriptions and captions, it is useful to augment image-to-text models with representations of the textual context in which the image appeared.

cs.CL↗

arXiv2022

Inducing Causal Structure for Interpretable Neural Networks

In many areas, we have well-founded insights about causal structure that would be useful to bring into our trained models while still allowing them to learn in a data-driven fashion. To achieve this, we present the new method of interchange intervention training (IIT). In IIT, we (1) align variables in a causal model (e.g., a deterministic program or Bayesian network) with representations in a neural model and (2) train the neural model to match the counterfactual behavior of the causal model on a base input when aligned representations in both models are set to be the value they would be for a source input. IIT is fully differentiable, flexibly combines with other objectives, and guarantees that the target causal model is a causal abstraction of the neural model when its loss is zero. We evaluate IIT on a structural vision task (MNIST-PVR), a navigational language task (ReaSCAN), and a natural language inference task (MQNLI). We compare IIT against multi-task training objectives and data augmentation. In all our experiments, IIT achieves the best results and produces neural models that are more interpretable in the sense that they more successfully realize the target causal model.

cs.LG↗

arXiv2022

Causal Distillation for Language Models

Distillation efforts have led to language models that are more compact and efficient without serious drops in performance. The standard approach to distillation trains a student model against two objectives: a task-specific objective (e.g., language modeling) and an imitation objective that encourages the hidden states of the student model to be similar to those of the larger teacher model. In this paper, we show that it is beneficial to augment distillation with a third objective that encourages the student to imitate the causal computation process of the teacher through interchange intervention training(IIT). IIT pushes the student model to become a causal abstraction of the teacher model - a simpler model with the same causal structure. IIT is fully differentiable, easily implemented, and combines flexibly with other objectives. Compared with standard distillation of BERT, distillation via IIT results in lower perplexity on Wikipedia (masked language modeling) and marked improvements on the GLUE benchmark (natural language understanding), SQuAD (question answering), and CoNLL-2003 (named entity recognition).

cs.CL↗

arXiv2022

STaR: Bootstrapping Reasoning With Reasoning

Generating step-by-step "chain-of-thought" rationales improves language model performance on complex reasoning tasks like mathematics or commonsense question-answering. However, inducing language model rationale generation currently requires either constructing massive rationale datasets or sacrificing accuracy by using only few-shot inference. We propose a technique to iteratively leverage a small number of rationale examples and a large dataset without rationales, to bootstrap the ability to perform successively more complex reasoning. This technique, the "Self-Taught Reasoner" (STaR), relies on a simple loop: generate rationales to answer many questions, prompted with a few rationale examples; if the generated answers are wrong, try again to generate a rationale given the correct answer; fine-tune on all the rationales that ultimately yielded correct answers; repeat. We show that STaR significantly improves performance on multiple datasets compared to a model fine-tuned to directly predict final answers, and performs comparably to fine-tuning a 30$\times$ larger state-of-the-art language model on CommensenseQA. Thus, STaR lets a model improve itself by learning from its own generated reasoning.

cs.LG↗

arXiv2022

Color Overmodification Emerges from Data-Driven Learning and Pragmatic Reasoning

Speakers' referential expressions often depart from communicative ideals in ways that help illuminate the nature of pragmatic language use. Patterns of overmodification, in which a speaker uses a modifier that is redundant given their communicative goal, have proven especially informative in this regard. It seems likely that these patterns are shaped by the environment a speaker is exposed to in complex ways. Unfortunately, systematically manipulating these factors during human language acquisition is impossible. In this paper, we propose to address this limitation by adopting neural networks (NN) as learning agents. By systematically varying the environments in which these agents are trained, while keeping the NN architecture constant, we show that overmodification is more likely with environmental features that are infrequent or salient. We show that these findings emerge naturally in the context of a probabilistic model of pragmatic communication.

cs.CL↗

arXiv2021

Learning to solve complex tasks by growing knowledge culturally across generations

Knowledge built culturally across generations allows humans to learn far more than an individual could glean from their own experience in a lifetime. Cultural knowledge in turn rests on language: language is the richest record of what previous generations believed, valued, and practiced, and how these evolved over time. The power and mechanisms of language as a means of cultural learning, however, are not well understood, and as a result, current AI systems do not leverage language as a means for cultural knowledge transmission. Here, we take a first step towards reverse-engineering cultural learning through language. We developed a suite of complex tasks in the form of minimalist-style video games, which we deployed in an iterated learning paradigm. Human participants were limited to only two attempts (two lives) to beat each game and were allowed to write a message to a future participant who read the message before playing. Knowledge accumulated gradually across generations, allowing later generations to advance further in the games and perform more efficient actions. Multigenerational learning followed a strikingly similar trajectory to individuals learning alone with an unlimited number of lives. Successive generations of learners were able to succeed by expressing distinct types of knowledge in natural language: the dynamics of the environment, valuable goals, dangerous risks, and strategies for success. The video game paradigm we pioneer here is thus a rich test bed for developing AI systems capable of acquiring and transmitting cultural knowledge.

cs.CL↗

arXiv2021

From partners to populations: A hierarchical Bayesian account of coordination and convention

Languages are powerful solutions to coordination problems: they provide stable, shared expectations about how the words we say correspond to the beliefs and intentions in our heads. Yet language use in a variable and non-stationary social environment requires linguistic representations to be flexible: old words acquire new ad hoc or partner-specific meanings on the fly. In this paper, we introduce CHAI (Continual Hierarchical Adaptation through Inference), a hierarchical Bayesian theory of coordination and convention formation that aims to reconcile the long-standing tension between these two basic observations. We argue that the central computational problem of communication is not simply transmission, as in classical formulations, but continual learning and adaptation over multiple timescales. Partner-specific common ground quickly emerges from social inferences within dyadic interactions, while community-wide social conventions are stable priors that have been abstracted away from interactions with multiple partners. We present new empirical data alongside simulations showing how our model provides a computational foundation for several phenomena that have posed a challenge for previous accounts: (1) the convergence to more efficient referring expressions across repeated interaction with the same partner, (2) the gradual transfer of partner-specific common ground to strangers, and (3) the influence of communicative context on which conventions eventually form.

cs.CL↗

arXiv2021

Calibrate your listeners! Robust communication-based training for pragmatic speakers

To be good conversational partners, natural language processing (NLP) systems should be trained to produce contextually useful utterances. Prior work has investigated training NLP systems with communication-based objectives, where a neural listener stands in as a communication partner. However, these systems commonly suffer from semantic drift where the learned language diverges radically from natural language. We propose a method that uses a population of neural listeners to regularize speaker training. We first show that language drift originates from the poor uncertainty calibration of a neural listener, which makes high-certainty predictions on novel sentences. We explore ensemble- and dropout-based populations of listeners and find that the former results in better uncertainty quantification. We evaluate both population-based objectives on reference games, and show that the ensemble method with better calibration enables the speaker to generate pragmatic utterances while scaling to a large vocabulary and generalizing to new games and listeners.

cs.CL↗

arXiv2021

Visual resemblance and communicative context constrain the emergence of graphical conventions

From photorealistic sketches to schematic diagrams, drawing provides a versatile medium for communicating about the visual world. How do images spanning such a broad range of appearances reliably convey meaning? Do viewers understand drawings based solely on their ability to resemble the entities they refer to (i.e., as images), or do they understand drawings based on shared but arbitrary associations with these entities (i.e., as symbols)? In this paper, we provide evidence for a cognitive account of pictorial meaning in which both visual and social information is integrated to support effective visual communication. To evaluate this account, we used a communication task where pairs of participants used drawings to repeatedly communicate the identity of a target object among multiple distractor objects. We manipulated social cues across three experiments and a full internal replication, finding pairs of participants develop referent-specific and interaction-specific strategies for communicating more efficiently over time, going beyond what could be explained by either task practice or a pure resemblance-based account alone. Using a combination of model-based image analyses and crowdsourced sketch annotations, we further determined that drawings did not drift toward arbitrariness, as predicted by a pure convention-based account, but systematically preserved those visual features that were most distinctive of the target object. Taken together, these findings advance theories of pictorial meaning and have implications for how successful graphical conventions emerge via complex interactions between visual perception, communicative experience, and social context.

cs.CV↗

arXiv2020

Continual adaptation for efficient machine communication

To communicate with new partners in new contexts, humans rapidly form new linguistic conventions. Recent neural language models are able to comprehend and produce the existing conventions present in their training data, but are not able to flexibly and interactively adapt those conventions on the fly as humans do. We introduce an interactive repeated reference task as a benchmark for models of adaptation in communication and propose a regularized continual learning framework that allows an artificial agent initialized with a generic language model to more accurately and efficiently communicate with a partner over time. We evaluate this framework through simulations on COCO and in real-time reference game experiments with human partners.

cs.CL↗

arXiv2020

Learning to refer informatively by amortizing pragmatic reasoning

A hallmark of human language is the ability to effectively and efficiently convey contextually relevant information. One theory for how humans reason about language is presented in the Rational Speech Acts (RSA) framework, which captures pragmatic phenomena via a process of recursive social reasoning (Goodman & Frank, 2016). However, RSA represents ideal reasoning in an unconstrained setting. We explore the idea that speakers might learn to amortize the cost of RSA computation over time by directly optimizing for successful communication with an internal listener model. In simulations with grounded neural speakers and listeners across two communication game datasets representing synthetic and human-generated data, we find that our amortized model is able to quickly generate language that is effective and concise across a range of contexts, without the need for explicit pragmatic reasoning.

cs.CL↗

arXiv2020

Generalizing meanings from partners to populations: Hierarchical inference supports convention formation on networks

A key property of linguistic conventions is that they hold over an entire community of speakers, allowing us to communicate efficiently even with people we have never met before. At the same time, much of our language use is partner-specific: we know that words may be understood differently by different people based on our shared history. This poses a challenge for accounts of convention formation. Exactly how do agents make the inferential leap to community-wide expectations while maintaining partner-specific knowledge? We propose a hierarchical Bayesian model to explain how speakers and listeners solve this inductive problem. To evaluate our model's predictions, we conducted an experiment where participants played an extended natural-language communication game with different partners in a small community. We examine several measures of generalization and find key signatures of both partner-specificity and community convergence that distinguish our model from alternatives. These results suggest that partner-specificity is not only compatible with the formation of community-wide conventions, but may facilitate it when coupled with a powerful inductive mechanism.

cs.CL↗

arXiv2020

The division of labor in communication: Speakers help listeners account for asymmetries in visual perspective

Recent debates over adults' theory of mind use have been fueled by surprising failures of perspective-taking in communication, suggesting that perspective-taking can be relatively effortful. How, then, should speakers and listeners allocate their resources to achieve successful communication? We begin with the observation that this shared goal induces a natural division of labor: the resources one agent chooses to allocate toward perspective-taking should depend on their expectations about the other's allocation. We formalize this idea in a resource-rational model augmenting recent probabilistic weighting accounts with a mechanism for (costly) control over the degree of perspective-taking. In a series of simulations, we first derive an intermediate degree of perspective weighting as an optimal tradeoff between expected costs and benefits of perspective-taking. We then present two behavioral experiments testing novel predictions of our model. In Experiment 1, we manipulated the presence or absence of occlusions in a director-matcher task and found that speakers spontaneously produced more informative descriptions to account for "known unknowns" in their partner's private view. In Experiment 2, we compared the scripted utterances used by confederates in prior work with those produced in interactions with unscripted directors. We found that confederates were systematically less informative than listeners would initially expect given the presence of occlusions, but listeners used violations to adaptively make fewer errors over time. Taken together, our work suggests that people are not simply "mindblind"; they use contextually appropriate expectations to navigate the division of labor with their partner. We discuss how a resource rational framework may provide a more deeply explanatory foundation for understanding flexible perspective-taking under processing constraints.

cs.CL↗

arXiv2020

Characterizing the dynamics of learning in repeated reference games

The language we use over the course of conversation changes as we establish common ground and learn what our partner finds meaningful. Here we draw upon recent advances in natural language processing to provide a finer-grained characterization of the dynamics of this learning process. We release an open corpus (>15,000 utterances) of extended dyadic interactions in a classic repeated reference game task where pairs of participants had to coordinate on how to refer to initially difficult-to-describe tangram stimuli. We find that different pairs discover a wide variety of idiosyncratic but efficient and stable solutions to the problem of reference. Furthermore, these conventions are shaped by the communicative context: words that are more discriminative in the initial context (i.e. that are used for one target more than others) are more likely to persist through the final repetition. Finally, we find systematic structure in how a speaker's referring expressions become more efficient over time: syntactic units drop out in clusters following positive feedback from the listener, eventually leaving short labels containing open-class parts of speech. These findings provide a higher resolution look at the quantitative dynamics of ad hoc convention formation and support further development of computational models of learning in communication.

cs.CL↗