Language Generation in the Limit

Although current large language models are complex, the most basic specifications of the underlying language generation problem itself are simple to state: given a finite set of training samples from an unknown language, produce valid new strings from the language that don't already appear in the training data. Here we ask what we can conclude about language generation using only this specification, without further assumptions. In particular, suppose that an adversary enumerates the strings of an unknown target language L that is known only to come from one of a possibly infinite list of candidates. A computational agent is trying to learn to generate from this language; we say that the agent generates from L in the limit if after some finite point in the enumeration of L, the agent is able to produce new elements that come exclusively from L and that have not yet been presented by the adversary. Our main result is that there is an agent that is able to generate in the limit for every countable list of candidate languages. This contrasts dramatically with negative results due to Gold and Angluin in a well-studied model of language learning where the goal is to identify an unknown language from samples; the difference between these results suggests that identifying a language is a fundamentally different problem than generating from it.

Microstructures and Accuracy of Graph Recall by Large Language Models

Graphs data is crucial for many applications, and much of it exists in the relations described in textual format. As a result, being able to accurately recall and encode a graph described in earlier text is a basic yet pivotal ability that LLMs need to demonstrate if they are to perform reasoning tasks that involve graph-structured information. Human performance at graph recall has been studied by cognitive scientists for decades, and has been found to often exhibit certain structural patterns of bias that align with human handling of social relationships. To date, however, we know little about how LLMs behave in analogous graph recall tasks: do their recalled graphs also exhibit certain biased patterns, and if so, how do they compare with humans and affect other graph reasoning tasks? In this work, we perform the first systematical study of graph recall by LLMs, investigating the accuracy and biased microstructures (local structural patterns) in their recall. We find that LLMs not only underperform often in graph recall, but also tend to favor more triangles and alternating 2-paths. Moreover, we find that more advanced LLMs have a striking dependence on the domain that a real-world graph comes from -- by yielding the best recall accuracy when the graph is narrated in a language style consistent with its original domain.

From Graphs to Hypergraphs: Hypergraph Projection and its Remediation

We study the implications of the modeling choice to use a graph, instead of a hypergraph, to represent real-world interconnected systems whose constituent relationships are of higher order by nature. Such a modeling choice typically involves an underlying projection process that maps the original hypergraph onto a graph, and is common in graph-based analysis. While hypergraph projection can potentially lead to loss of higher-order relations, there exists very limited studies on the consequences of doing so, as well as its remediation. This work fills this gap by doing two things: (1) we develop analysis based on graph and set theory, showing two ubiquitous patterns of hyperedges that are root to structural information loss in all hypergraph projections; we also quantify the combinatorial impossibility of recovering the lost higher-order structures if no extra help is provided; (2) we still seek to recover the lost higher-order structures in hypergraph projection, and in light of (1)'s findings we propose to relax the problem into a learning-based setting. Under this setting, we develop a learning-based hypergraph reconstruction method based on an important statistic of hyperedge distributions that we find. Our reconstruction method is evaluated on 8 real-world datasets under different settings, and exhibits consistently good performance. We also demonstrate benefits of the reconstructed hypergraphs via use cases of protein rankings and link predictions.

Strategic Evaluation: Subjects, Evaluators, and Society

A broad current application of algorithms is in formal and quantitative measures of murky concepts -- like merit -- to make decisions. When people strategically respond to these sorts of evaluations in order to gain favorable decision outcomes, their behavior can be subjected to moral judgments. They may be described as 'gaming the system' or 'cheating,' or (in other cases) investing 'honest effort' or 'improving.' Machine learning literature on strategic behavior has tried to describe these dynamics by emphasizing the efforts expended by decision subjects hoping to obtain a more favorable assessment -- some works offer ways to preempt or prevent such manipulations, some differentiate 'gaming' from 'improvement' behavior, while others aim to measure the effort burden or disparate effects of classification systems. We begin from a different starting point: that the design of an evaluation itself can be understood as furthering goals held by the evaluator which may be misaligned with broader societal goals. To develop the idea that evaluation represents a strategic interaction in which both the evaluator and the subject of their evaluation are operating out of self-interest, we put forward a model that represents the process of evaluation using three interacting agents: a decision subject, an evaluator, and society, representing a bundle of values and oversight mechanisms. We highlight our model's applicability to a number of social systems where one or two players strategically undermine the others' interests to advance their own. Treating evaluators as themselves strategic allows us to re-cast the scrutiny directed at decision subjects, towards the incentives that underpin institutional designs of evaluations. The moral standing of strategic behaviors often depend on the moral standing of the evaluations and incentives that provoke such behaviors.

On the Actionability of Outcome Prediction

Predicting future outcomes is a prevalent application of machine learning in social impact domains. Examples range from predicting student success in education to predicting disease risk in healthcare. Practitioners recognize that the ultimate goal is not just to predict but to act effectively. Increasing evidence suggests that relying on outcome predictions for downstream interventions may not have desired results. In most domains there exists a multitude of possible interventions for each individual, making the challenge of taking effective action more acute. Even when causal mechanisms connecting the individual's latent states to outcomes is well understood, in any given instance (a specific student or patient), practitioners still need to infer -- from budgeted measurements of latent states -- which of many possible interventions will be most effective for this individual. With this in mind, we ask: when are accurate predictors of outcomes helpful for identifying the most suitable intervention? Through a simple model encompassing actions, latent states, and measurements, we demonstrate that pure outcome prediction rarely results in the most effective policy for taking actions, even when combined with other measurements. We find that except in cases where there is a single decisive action for improving the outcome, outcome prediction never maximizes "action value", the utility of taking actions. Making measurements of actionable latent states, where specific actions lead to desired outcomes, considerably enhances the action value compared to outcome prediction, and the degree of improvement depends on action costs and the outcome model. This analysis emphasizes the need to go beyond generic outcome prediction in interventional settings by incorporating knowledge of plausible actions and latent states.

Fine-Tuning Games: Bargaining and Adaptation for General-Purpose Models

Major advances in Machine Learning (ML) and Artificial Intelligence (AI) increasingly take the form of developing and releasing general-purpose models. These models are designed to be adapted by other businesses and agencies to perform a particular, domain-specific function. This process has become known as adaptation or fine-tuning. This paper offers a model of the fine-tuning process where a Generalist brings the technological product (here an ML model) to a certain level of performance, and one or more Domain-specialist(s) adapts it for use in a particular domain. Both entities are profit-seeking and incur costs when they invest in the technology, and they must reach a bargaining agreement on how to share the revenue for the technology to reach the market. For a relatively general class of cost and revenue functions, we characterize the conditions under which the fine-tuning game yields a profit-sharing solution. We observe that any potential domain-specialization will either contribute, free-ride, or abstain in their uptake of the technology, and we provide conditions yielding these different strategies. We show how methods based on bargaining solutions and sub-game perfect equilibria provide insights into the strategic behavior of firms in these types of interactions, and we find that profit-sharing can still arise even when one firm has significantly higher costs than another. We also provide methods for identifying Pareto-optimal bargaining arrangements for a general set of utility functions.

Reconciling the accuracy-diversity trade-off in recommendations

In recommendation settings, there is an apparent trade-off between the goals of accuracy (to recommend items a user is most likely to want) and diversity (to recommend items representing a range of categories). As such, real-world recommender systems often explicitly incorporate diversity separately from accuracy. This approach, however, leaves a basic question unanswered: Why is there a trade-off in the first place? We show how the trade-off can be explained via a user's consumption constraints -- users typically only consume a few of the items they are recommended. In a stylized model we introduce, objectives that account for this constraint induce diverse recommendations, while objectives that do not account for this constraint induce homogeneous recommendations. This suggests that accuracy and diversity appear misaligned because standard accuracy metrics do not consider consumption constraints. Our model yields precise and interpretable characterizations of diversity in different settings, giving practical insights into the design of diverse recommendations.

Informational Diversity and Affinity Bias in Team Growth Dynamics

Prior work has provided strong evidence that, within organizational settings, teams that bring a diversity of information and perspectives to a task are more effective than teams that do not. If this form of informational diversity confers performance advantages, why do we often see largely homogeneous teams in practice? One canonical argument is that the benefits of informational diversity are in tension with affinity bias. To better understand the impact of this tension on the makeup of teams, we analyze a sequential model of team formation in which individuals care about their team's performance (captured in terms of accurately predicting some future outcome based on a set of features) but experience a cost as a result of interacting with teammates who use different approaches to the prediction task. Our analysis of this simple model reveals a set of subtle behaviors that team-growth dynamics can exhibit: (i) from certain initial team compositions, they can make progress toward better performance but then get stuck partway to optimally diverse teams; while (ii) from other initial compositions, they can also move away from this optimal balance as the majority group tries to crowd out the opinions of the minority. The initial composition of the team can determine whether the dynamics will move toward or away from performance optimality, painting a path-dependent picture of inefficiencies in team compositions. Our results formalize a fundamental limitation of utility-based motivations to drive informational diversity in organizations and hint at interventions that may improve informational diversity and performance simultaneously.

Supervised Hypergraph Reconstruction

We study an issue commonly seen with graph data analysis: many real-world complex systems involving high-order interactions are best encoded by hypergraphs; however, their datasets often end up being published or studied only in the form of their projections (with dyadic edges). To understand this issue, we first establish a theoretical framework to characterize this issue's implications and worst-case scenarios. The analysis motivates our formulation of the new task, supervised hypergraph reconstruction: reconstructing a real-world hypergraph from its projected graph, with the help of some existing knowledge of the application domain. To reconstruct hypergraph data, we start by analyzing hyperedge distributions in the projection, based on which we create a framework containing two modules: (1) to handle the enormous search space of potential hyperedges, we design a sampling strategy with efficacy guarantees that significantly narrows the space to a smaller set of candidates; (2) to identify hyperedges from the candidates, we further design a hyperedge classifier in two well-working variants that capture structural features in the projection. Extensive experiments validate our claims, approach, and extensions. Remarkably, our approach outperforms all baselines by an order of magnitude in accuracy on hard datasets. Our code and data can be downloaded from bit.ly/SHyRe.