arXiv subjects

Jon Kleinberg

Publications and source records attributed to Jon Kleinberg.

At least 19 recordsLinked to original sources

arXiv2026

Learning Distributions from Multiple Data Providers

Motivated by learning from heterogeneous and overlapping data providers, we study a stylized model of distribution learning from restricted conditional samples. The goal is to learn an unknown distribution $p$ on a finite domain $[n]$. The learner is given a fixed family of queryable sets $\mathscr{S} \subseteq 2^{[n]}$, and each query to $S \in \mathscr{S}$ returns an independent sample from the conditional distribution $p(\cdot \mid S)$. Learnability is governed by the co-occurrence graph associated with $\mathscr{S}$: two domain elements are adjacent if they appear together in some queryable set. Pointwise consistency is achievable when this graph is connected on the target support. PAC learning requires more: it is possible when the co-occurrence graph is complete. The optimal sample complexity of PAC learning ranges from nearly linear to quadratic. Every query family with complete co-occurrence graph admits sample complexity $\widetilde O(n^2/ε^2)$, and this bound is tight in the worst case. On the other hand, if $[n]$ is queryable then ordinary sampling improves the bound to $Θ(n/ε^2)$, and this cannot be improved further even if every set is queryable. More generally, we identify hierarchical comparabilityas a sufficient structural condition on $\mathscr S$ under which the optimal complexity is nearly linear, $\widetilde Θ(n/ε^2)$, with pairwise query families as a canonical example. Finally, the full range of polynomial rates between linear and quadratic is attainable: for every $α\in (1,2)$, there exists a query family with optimal PAC rate $\widetilde Θ(n^α/ε^2)$.

cs.DS↗

arXiv2026

LLM Detection as an Intervention: Downstream Impact under Strategic User Behavior

As LLM adoption becomes more widespread, there is a growing interest in detecting LLM-generated content, for example through LLM detection tools and through heuristics based on language patterns. Detectors operate as an intervention that steers not only the detected attribute itself, but also downstream metrics such as LLM usage and output quality. In this work, we demonstrate how imperfect LLM detectors lead to counterintuitive impacts on these downstream metrics, by distorting how users are incentivized to use LLMs in their workflow. We develop a stylized model which captures how users strategically choose how much to use the LLM and how to post-process content to reduce the detected attribute. Using this model, we show that LLM detection can counterintuitively lead humans to increase their LLM usage. Moreover, even when reducing the detected attribute improves output quality, we find that introducing an LLM detector can lead users to produce lower quality outputs. In contrast, we show that detectors result in a clean "rise-then-fall" pattern for the detected attribute, which we empirically reproduce for word frequencies on arXiv abstracts. Altogether, our work illustrates how LLM detection can distort LLM usage and output quality, uncovering failure modes when LLM detectors operate as an intervention on these downstream metrics.

cs.AI↗

arXiv2026

Validity, Sparse Holes, and Breadth in Language Generation: Banach Density, Topology, and Geometry

Language generation in the limit, rooted in work of Gold and Angluin and revived by Kleinberg and Mullainathan, studies generation under minimal assumptions: an adversary enumerates strings from an unknown target language $K$, and an algorithm must eventually generate unseen strings from $K$. A central question is the tension between validity and breadth: can a generator avoid hallucination while covering the hidden language broadly? In our previous work, we proved that every countable language class admits the optimal 1/2 lower-asymptotic-density guarantee. This prefix-based measure makes validity and breadth universally compatible. Here we replace prefix averaging by the local requirement of lower Banach density, which examines every long interval or box. We prove that for some countable language collections, every eventually valid generator must leave arbitrarily large sparse holes. Thus a worst-case local form of mode collapse is unavoidable: sparse holes are forced by the requirement of valid generation itself. This local notion reveals structure hidden by prefix averaging. In one dimension, the problem is intrinsically topological and combinatorial: finite Cantor--Bendixson rank guarantees the optimal lower Banach density 1/2, whereas infinite-rank classes can force density zero. In dimensions $d \geq 2$, Ramsey/discrepancy geometry adds in to force ordinary Banach density zero even for a singleton language class. We introduce filtered lower Banach density to remove this geometric obstruction and prove a $1/2-ε$ guarantee for finite-rank classes. We also establish a dichotomy for $f$-window densities, interpolating between lower asymptotic and lower Banach density.

cs.DM↗

arXiv2026

Language Identification with Succinct Machine-Independent Traces

Motivated by the power of large language models, there has been renewed interest in the Gold-Angluin model of language identification in the limit, with an eye toward variants of the model that might overcome the negative results for its original formulation. Recent papers on this question have proposed looking at computational traces and annotations of training strings as a source of additional power for a learner, reflecting empirical regularities such as the way that commented source code is easier to learn from than arbitrary source code, and text annotated with algorithmically generated chain-of-thought tokens can be easier to learn from than the raw text itself. This recent work has shown positive results for language identification in the presence of such computational traces, but the traces in these positive results come from explicit automata-theoretic machine models that generate the language, where the underlying vocabulary of tokens for the traces is very large. In this paper, we address two fundamental issues left open by this line of work: can we achieve positive results with traces that use only a small alphabet, and can we define traces directly from the language itself, without requiring an underlying machine model that generates it? We establish positive results for both of these questions: for an arbitrary collection of languages, we show how to define computational traces that enable identification in the limit, using an alphabet of tokens that is linear in the size of the alphabet that the languages are defined over, and independent of any other properties of the languages.

cs.CL↗

arXiv2026

Globally Consistent Coloring Schemes for Language Identification

We study how little extra information is needed to make adversarial language learning possible. In Gold's model of language identification in the limit, a learner is given an enumeration of the strings from an unknown language chosen from a countable language collection. The learner guesses the identity of the language over the course of the enumeration, and it succeeds if, eventually, all of its guesses are the correct language. Classical results of Gold and Angluin show that many natural collections cannot be learned in this way. Recent work on trace colorings, motivated by the success of thinking-trace strategies in language learning, overcomes this obstruction by annotating every symbol of every string with a color. We ask whether the learner really needs this whole sequence of colors, or whether one color at the end of each string (a terminal coloring) is enough for language identification. We show that just one terminal bit per string is enough for every countable collection of infinite languages. In fact, the colorings can be chosen collection-independently: there is a single assignment of a two-color terminal coloring to every infinite language such that the same preassigned colorings identify every countable subcollection. Thus, in this model, an entire color trace can be compressed to one bit attached to the end of each example. Our global construction uses transfinite recursion, and we prove that this kind of nonconstructivity is unavoidable for any bounded number of colors. As a notion of constructivity, we use the formalism of Borel maps (a regularity condition satisfied by natural explicit constructions); we show that no global terminal coloring with a finite number of colors defined by a Borel map can identify all countable subcollections. By contrast, known trace-coloring constructions are Borel when encoded as terminal colorings, but require infinitely many colors.

cs.CL↗

arXiv2026

Position: Use Sparse Autoencoders to Discover Unknowns

While sparse autoencoders (SAEs) have generated significant excitement, a series of negative results have added to skepticism about their usefulness. Here, we establish a conceptual distinction that reconciles competing narratives surrounding SAEs. We argue that even if SAEs may be less effective for \textit{acting on known concepts}, SAEs are especially powerful tools for \textit{discovering unknown concepts}. This distinction separates existing negative results from positive results, and suggests several classes of SAE applications. Specifically, we outline use cases for SAEs in (i) ML interpretability, explainability, fairness, auditing, and safety, and (ii) social and health sciences.

cs.LG↗

arXiv2026

Quantifying and Mitigating Consensus Disparity in Social and Information Networks

We introduce a computational framework to measure and optimize disparity, which corresponds to the difference in consensus outcomes attributable to distinct social groups, under classical models of opinion dynamics. We study this problem in the Friedkin-Johnsen setting under uncertainty about group structure and characterize its algorithmic complexity. For the structural analysis, we demonstrate that disparity can be arbitrarily larger than polarization in well-connected networks that nonetheless carry an identifiable group structure. For the mitigation problem, we derive robust formulations and active set optimization procedures to minimize worst-case disparity via recommendation reweighing and opinion seeding. Our methods provide provable guarantees and are validated on multiple real-world social networks. The results bridge opinion dynamics and network optimization, offering computational tools for analyzing and reducing polarization in social networks.

cs.SI↗

arXiv2026

AI Behavioral Science

We outline a foundation for a new field of ``AI Behavioral Science,'' covering three perspectives. First, as AI becomes ubiquitous and is increasingly proprietary and opaque, it becomes vital to develop techniques for assessing AI behavior. We outline how tools developed to assess people's behaviors by social scientists can be used to assess and infer AI's behaviors biases, tendencies, and heuristics. Second, we also discuss how AI can change the ways in which we learn about human behavior. Beyond its computational power, AI offers new techniques for simulating, inferring, and predicting human behaviors that we outline and discuss. Third, as humans and AI are interacting in increasingly complex and intertwined systems, we need to understand the implications for the resulting economic and political outcomes. We outline issues that are increasingly pressing concerning the future of human-AI interactions and potential changes and disruptions that can ensue.

cs.HC↗

arXiv2026

On Language Generation in the Limit with Bounded Memory

We study language generation in the limit under bounded memory. In this task, a learner observes examples from an unknown target language one at a time and must eventually output only new valid examples. Prior work assumes access to the entire history, a strong assumption since realistic algorithms retain limited past information. Classical work in learning theory shows memory constraints dramatically alter learnability; we extend this to language generation. First, we study memoryless generators. Under a mild enumeration restriction, every countable collection of infinite languages remains generable without memory. Without this restriction, we exactly characterize when memoryless generation is possible. For finite collections, we characterize the optimal minimax density achievable by memoryless generators -- the best density guaranteed against any collection of a given size. This combinatorial bound relies on Sperner's theorem and symmetric chain decompositions. We further show that a sliding window of the last $W$ examples does not improve this worst-case density, whereas allowing it to store $b$ adaptively chosen past examples improves the achievable density for every $b \geq 1$. Finally, we revisit identification in the limit, where the learner must converge to a single correct hypothesis for the target language. We focus on its incremental variant, where the learner remembers only its previous guess. Here, although exact identification fails on a collection of just three languages, a mild relaxation requiring convergence to an ``approximate'' version of the target is achievable for every finite collection. These results show bounded memory affects these tasks differently: generation remains achievable for every countable collection, while density and identification are confined to finite collections, with guarantees weakening as the collection grows.

cs.DS↗

arXiv2026

Mistake-Bounded Language Generation

We investigate the learning task of language generation in the limit, but shift focus from the traditional time-of-last-mistake metric of a generator's success to a new notion of "mistake-bounded generation." While existing results for language generation in the limit focus on guaranteeing eventual consistency, they are blind to the cumulative error incurred during the learning process. We address this by shifting the goal to minimizing the total number of invalid elements output by a generation algorithm. We establish a formal reduction to the Learning from Correct Demonstrations framework of Joshi et al. (2025), enabling a general recipe for deriving mistake bounds via weighted update rules. For finite classes, we provide an algorithm that simultaneously achieves an optimal last-mistake time of $\mathsf{Cdim}(L)$ and a mistake bound of $\lfloor \log_2 |L| \rfloor$, whereas for the non-uniform setting of countably infinite streams of languages, we prove a fundamental trade-off: achieving logarithmic mistakes $O(\log i)$ necessarily precludes convergence guarantees established in prior work. Finally, we show that our framework can be extended to accommodate noisy adversaries and guarantee mistake bounds that scale with the adversary's suboptimality.

cs.LG↗

arXiv2026

AI-Assisted Decision Making with Human Learning

AI systems increasingly support human decision-making. In many cases, despite the algorithm's superior performance, the final decision remains in human hands. For example, an AI may assist doctors in determining which diagnostic tests to run, but the doctor ultimately makes the diagnosis. This paper studies such AI-assisted decision-making settings, where the human learns through repeated interactions with the algorithm. In our framework, the algorithm -- designed to maximize decision accuracy according to its own model -- determines which features the human can consider. The human then makes a prediction based on their own less accurate model. We observe that the discrepancy between the algorithm's model and the human's model creates a fundamental tradeoff: Should the algorithm prioritize recommending more informative features, encouraging the human to learn their importance, even if it results in less accurate predictions in the short term until learning occurs? Or is it preferable to forgo educating the human and instead select features that align more closely with their existing understanding, minimizing the immediate cost of learning? Our analysis reveals how this trade-off is shaped by both the algorithm's patience (the time-discount rate of its objective over multiple periods) and the human's willingness and ability to learn. We show that optimal feature selection has a surprisingly clean combinatorial characterization, reducible to a stationary sequence of feature subsets that is tractable to compute. As the algorithm becomes more "patient" or the human's learning improves, the algorithm increasingly selects more informative features, enhancing both prediction accuracy and the human's understanding.

cs.AI↗

arXiv2026

How Many Features Can a Language Model Store Under the Linear Representation Hypothesis?

We introduce a mathematical framework for the linear representation hypothesis (LRH), which asserts that intermediate layers of language models store features linearly. We separate the hypothesis into two claims: linear representation (features are linearly embedded in neuron activations) and linear accessibility (features can be linearly decoded). We then ask: How many neurons $d$ suffice to both linearly represent and linearly access $m$ features? Classical results in compressed sensing imply that for $k$-sparse inputs, $d = O(k\log (m/k))$ suffices if we allow non-linear decoding algorithms (Candes and Tao, 2006; Candes et al., 2006; Donoho, 2006). However, the additional requirement of linear decoding takes the problem out of the classical compressed sensing, into linear compressed sensing. Our main theoretical result establishes nearly-matching upper and lower bounds for linear compressed sensing. We prove that $d = Ω_ε(\frac{k^2}{\log k}\log (m/k))$ is required while $d = O_ε(k^2\log m)$ suffices. The lower bound establishes a quantitative gap between classical and linear compressed setting, illustrating how linear accessibility is a meaningfully stronger hypothesis than linear representation alone. The upper bound confirms that neurons can store an exponential number of features under the LRH, giving theoretical evidence for the "superposition hypothesis" (Elhage et al., 2022). The upper bound proof uses standard random constructions of matrices with approximately orthogonal columns. The lower bound proof uses rank bounds for near-identity matrices (Alon, 2003) together with Turán's theorem (bounding the number of edges in clique-free graphs). We also show how our results do and do not constrain the geometry of feature representations and extend our results to allow decoders with an activation function and bias.

cs.LG↗

arXiv2025

What's Producible May Not Be Reachable: Measuring the Steerability of Generative Models

How should we evaluate the quality of generative models? Many existing metrics focus on a model's producibility, i.e. the quality and breadth of outputs it can generate. However, the actual value from using a generative model stems not just from what it can produce but whether a user with a specific goal can produce an output that satisfies that goal. We refer to this property as steerability. In this paper, we first introduce a mathematical decomposition for quantifying steerability independently from producibility. Steerability is more challenging to evaluate than producibility because it requires knowing a user's goals. We address this issue by creating a benchmark task that relies on one key idea: sample an output from a generative model and ask users to reproduce it. We implement this benchmark in user studies of text-to-image and large language models. Despite the ability of these models to produce high-quality outputs, they all perform poorly on steerability. These results suggest that we need to focus on improving the steerability of generative models. We show such improvements are indeed possible: simple image-based steering mechanisms achieve more than 2x improvement on this benchmark.

cs.LG↗

arXiv2025

Language Generation and Identification From Partial Enumeration: Tight Density Bounds and Topological Characterizations

The success of large language models (LLMs) has motivated formal theories of language generation and learning. We study the framework of \emph{language generation in the limit}, where an adversary enumerates strings from an unknown language $K$ drawn from a countable class, and an algorithm must generate unseen strings from $K$. Prior work showed that generation is always possible, and that some algorithms achieve positive lower density, revealing a \emph{validity--breadth} trade-off between correctness and coverage. We resolve a main open question in this line, proving a tight bound of $1/2$ on the best achievable lower density. We then strengthen the model to allow \emph{partial enumeration}, where the adversary reveals only an infinite subset $C \subseteq K$. We show that generation in the limit remains achievable, and if $C$ has lower density $α$ in $K$, the algorithm's output achieves density at least $α/2$, matching the upper bound. This generalizes the $1/2$ bound to the partial-information setting, where the generator must recover within a factor $1/2$ of the revealed subset's density. We further revisit the classical Gold--Angluin model of \emph{language identification} under partial enumeration. We characterize when identification in the limit is possible -- when hypotheses $M_t$ eventually satisfy $C \subseteq M \subseteq K$ -- and in the process give a new topological formulation of Angluin's characterization, showing that her condition is precisely equivalent to an appropriate topological space having the $T_D$ separation property.

cs.DS↗

arXiv2025

Modeling the Economic Impacts of AI Openness Regulation

Regulatory frameworks, such as the EU AI Act, encourage openness of general-purpose AI models by offering legal exemptions for "open-source" models. Despite this legislative attention on openness, the definition of open-source foundation models remains ambiguous. This paper models the strategic interactions among the creator of a general-purpose model (the generalist) and the entity that fine-tunes the general-purpose model to a specialized domain or task (the specialist), in response to regulatory requirements on model openness. We present a stylized model of the regulator's choice of an open-source definition to evaluate which AI openness standards will establish appropriate economic incentives for developers. Our results characterize market equilibria -- specifically, upstream model release decisions and downstream fine-tuning efforts -- under various openness regulations and present a range of effective regulatory penalties and open-source thresholds. Overall, we find the model's baseline performance determines when increasing the regulatory penalty vs. the open-source threshold will significantly alter the generalist's release strategy. Our model provides a theoretical foundation for AI governance decisions around openness and enables evaluation and refinement of practical open-source policies.

cs.GT↗

arXiv2025

Tracking Patterns in Toxicity and Antisocial Behavior Over User Lifetimes on Large Social Media Platforms

An increasing amount of attention has been devoted to the problem of "toxic" or antisocial behavior on social media. In this paper we analyze such behavior at very large scales: we analyze toxicity over a 14-year time span on nearly 500 million comments from Reddit and Wikipedia, grounded in two different proxies for toxicity. At the individual level, we analyze users' toxicity levels over the course of their time on the site, and find a striking reversal in trends: both Reddit and Wikipedia users tended to become less toxic over their life cycles on the site in the early (pre-2013) history of the site, but more toxic over their life cycles in the later (post-2013) history of the site. We also find that toxicity on Reddit and Wikipedia differ in a key way, with the most toxic behavior on Reddit exhibited in aggregate by the most active users, and the most toxic behavior on Wikipedia exhibited in aggregate by the least active users. Finally, we consider the toxicity of discussion around widely-shared pieces of content, and find that the trends for toxicity in discussion about content bear interesting similarities with the trends for toxicity in discussion by users.

cs.SI↗

arXiv2025

Anatomy of a Machine Learning Ecosystem: 2 Million Models on Hugging Face

Many have observed that the development and deployment of generative machine learning (ML) and artificial intelligence (AI) models follow a distinctive pattern in which pre-trained models are adapted and fine-tuned for specific downstream tasks. However, there is limited empirical work that examines the structure of these interactions. This paper analyzes 1.86 million models on Hugging Face, a leading peer production platform for model development. Our study of model family trees -- networks that connect fine-tuned models to their base or parent -- reveals sprawling fine-tuning lineages that vary widely in size and structure. Using an evolutionary biology lens to study ML models, we use model metadata and model cards to measure the genetic similarity and mutation of traits over model families. We find that models tend to exhibit a family resemblance, meaning their genetic markers and traits exhibit more overlap when they belong to the same model family. However, these similarities depart in certain ways from standard models of asexual reproduction, because mutations are fast and directed, such that two `sibling' models tend to exhibit more similarity than parent/child pairs. Further analysis of the directional drifts of these mutations reveals qualitative insights about the open machine learning ecosystem: Licenses counter-intuitively drift from restrictive, commercial licenses towards permissive or copyleft licenses, often in violation of upstream license's terms; models evolve from multi-lingual compatibility towards english-only compatibility; and model cards reduce in length and standardize by turning, more often, to templates and automatically generated text. Overall, this work takes a step toward an empirically grounded understanding of model fine-tuning and suggests that ecological models and methods can yield novel scientific insights.

cs.SI↗

arXiv2025

Learning to Imitate with Less: Efficient Individual Behavior Modeling in Chess

As humans seek to collaborate with, learn from, and better understand artificial intelligence systems, developing AIs that can accurately emulate individual decision-making becomes increasingly important. Chess, a long-standing AI benchmark with precise skill measurement, offers an ideal testbed for human-AI alignment. However, existing approaches to modeling human behavior require prohibitively large amounts of data from each individual, making them impractical for new or sparsely represented users. In this work, we introduce Maia4All, a framework designed to learn and adapt to individual decision-making styles efficiently, even with limited data. Maia4All achieves this through a two-stage optimization process: (1) an enrichment step, which bridges population and individual-level human behavior modeling with a prototype-enriched model, and (2) a democratization step, which leverages ability levels or user prototypes to initialize and refine individual embeddings with minimal data. Our experimental results show that Maia4All can accurately predict individual moves and profile behavioral patterns with high fidelity, establishing a new standard for personalized human-like AI behavior modeling in chess. Maia4All achieves individual human behavior modeling in chess with only 20 games, compared to the 5,000 games required previously, representing a significant improvement in data efficiency. Our work provides an example of how population AI systems can flexibly adapt to individual users using a prototype-enriched model as a bridge. This approach extends beyond chess, as shown in our case study on idiosyncratic LLMs, highlighting its potential for broader applications in personalized AI adaptation.

cs.AI↗