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Nika Haghtalab

Publications and source records attributed to Nika Haghtalab.

At least 19 recordsLinked to original sources
arXiv2026

Learn Your Own Thoughts: Abstract Token Curriculum

Large Language Models (LLMs) have achieved remarkable reasoning capabilities by utilizing chain-of-thought (CoT) as a scratchpad for intermediate stages of thinking. However, CoT techniques require explicit supervision on thinking tokens, which requires rich, task-specific data. In this work, we propose Abstract Token Curriculum (ATC), a novel curriculum learning framework that elicits effective continuous intermediate representations without direct supervision or manual scratchpad design. ATC gradually increases problem complexity through a sequence of distributions, training the model to develop internal abstract ``thoughts'' in the continuous representation space. This paper provides both theoretical and experimental evidence for the benefits of ATC and its advantages over previous methods for training continuous thoughts. Theoretically, we show that for learning parity functions with single-layer softmax attention using ATC, attention naturally focuses on the CoT tokens in the context that provide the ``easiest path'' to predicting the next token. Experimentally, we show ATC's effectiveness on graph reachability and arithmetic learning tasks.

cs.LG↗
arXiv2026

Distortion of AI Alignment Revisited: RLHF is a Decent Utilitarian Aligner

While Reinforcement Learning from Human Feedback (RLHF) is the standard paradigm for aligning large language models with human preferences, its effectiveness in pluralistic settings has been called into question. Notably, recent work by Gölz et al. (2025) demonstrated that the \textit{distortion} -- defined as the multiplicative gap between the average user utility of the RLHF policy and the optimal average utility -- can scale exponentially with the Bradley-Terry temperature parameter $β$ when users have heterogeneous preferences. In this work, we present a fine-grained analysis of the distortion of RLHF with reward clipping and demonstrate that such exponential degradation is not a fundamental property of the algorithm but rather a consequence of distribution mismatch between the distribution generating preference data ($μ$) and the KL reference policy ($π_{\mathrm{ref}}$). To this end, we establish tight upper and lower bounds on the distortion of RLHF across multiple regimes of the KL regularization strength. We show that in a representative regime, under the Bradley-Terry model, the distortion is $\tildeΘ(βB + β)$, where $B$ is an upper bound on the log density ratio between $μ$ and $π_{\mathrm{ref}}$. In particular, when there is no distribution mismatch (i.e., $μ= π_{\mathrm{ref}}$), RLHF achieves the optimal distortion of $O(β)$ up to a constant. Our results suggest that, to reasonably maximize average utility with RLHF, it is preferable to use on-policy sampled preference data or to fine-tune before RLHF on data from a source close to $μ$.

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arXiv2026

Computationally Efficient Collaborative Communication Via Regularity-Based Coarsening

Our results show that the existence of a short high-utility protocol already suffices for efficient communication. In particular, in a game with $n$ possible observations and $m$ actions: (1) For any achievable target utility $α$, we give an algorithm with $\mathrm{poly}(n, m, 1/ε)$ runtime that designs a protocol achieving utility at least $α-ε$ using only $2^{\mathcal O(CC_α(G))}/ε^2$ bits of communication. Here, $CC_α(G)$ is the minimum number of bits used by any protocol, even a computationally inefficient one, to achieve utility $α$. (2) We prove that this exponential dependence on $CC_α(G)$ is tight up to a constant. That is, unless $\mathrm P=\mathrm{NP}$, no polynomial-time algorithm can in general find optimal protocols using fewer than $2^{CC_α(G) -2}$ bits. We note that our results strictly weaken the assumptions required by prior work in the multi-agent information aggregation literature, filling a gap that had remained elusive even for games with constant $CC_α(G)$. In particular, prior guarantees for agreement-based information aggregation rely on structural assumptions such as informational substitutes or weak learnability. We show that these assumptions already imply $CC_α(G) = O(1)$ and are therefore more restrictive conditions than required by our protocol to succeed. On a technical level, our results involve a novel strengthening of the Frieze-Kannan weak regularity lemma and yield the following powerful polynomial-time transformation tool: for every communication game $G$, it constructs a game $\hat G$ that is a coarsening of the agents' observation spaces into constant-size partitions, such that $G$ and $\hat G$ are indistinguishable with respect to every short communication protocol. This coarsening theorem is the engine behind our algorithm and may be of independent interest.

cs.GT↗
arXiv2026

Post-Training at the Edge of Detectability: A Game-Theoretic Approach to Fine-Tuning

Reinforcement learning (RL) fine-tuning is widely used in language model training to improve model performance on a target task while limiting drift from a reference policy. A standard way to balance this trade-off is via a KL-regularized RL objective, although this formulation does not by itself provide a principled way to set the regularization coefficient. In practice, the coefficient is typically chosen heuristically or via hyperparameter search, which can lead to unnecessary overhead in training cost or undesirable reward-retention trade-offs. We instead propose a game-theoretic framework that gives this trade-off an explicit statistical interpretation. Specifically, we study a sequential game in which an agent chooses a policy to maximize cumulative reward while a monitor observes policy outputs over time and tests for deviations from the reference policy. Although not originating from the same perspective, we show that the resulting equilibrium policy can nonetheless be expressed as the solution to a KL-regularized RL problem for an optimal regularization parameter that can be viewed as maximizing reward per unit of statistical distinguishability. Drawing on classical results from concave-convex fractional programming, we provide a principled method for learning this equilibrium coefficient via reduction to the KL-regularized RL objective, thus allowing for flexible integration into standard fine-tuning pipelines. In experiments with Qwen3-8B and Llama-3.2-1B, we demonstrate that our methods result in competitive reward-retention trade-offs in a continual learning setting, and illustrate how our framework may be used to audit API providers serving open-source models.

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arXiv2026

Leakage-Robust Bayesian Persuasion

This paper introduces leakage-robust Bayesian persuasion. Situated between public Bayesian persuasion [KG11] (and its multi-receiver variants [CCG23, Xu20]) and private Bayesian persuasion [AB19], it considers settings where one or more signals sent privately by a sender to receivers may be leaked. We design leakage-robust Bayesian persuasion schemes and quantify the price of robustness using two formalisms: - The first notion, $k$-worst-case persuasiveness, requires a signaling scheme to remain persuasive whenever each receiver observes at most $k$ leaked signals from other receivers. Relative to optimal private persuasion, the Price of Robust Persuasiveness ($\mathsf{PoRP}_k$) is $Θ(\min{2^k,n})$ for supermodular sender utilities and $Θ(k)$ for submodular or XOS sender utilities, where $n$ is the number of receivers. In some instances, $Θ(\log k)$ leakages are sufficient for the utility of the optimal leakage-robust persuasion to degenerate to that of public persuasion. - The second notion, expected downstream utility robustness, relaxes the persuasiveness requirement and instead analyzes sender's utility when receivers best respond to their observations. We quantify the Price of Robust Downstream Utility ($\mathsf{PoRU}$) as the gap between the expected sender utility over the randomness in the leakage pattern as compared to private persuasion. For several natural and structured distributions of leakage patterns, we show that $\mathsf{PoRU}$ improves on $\mathsf{PoRP}$, becoming $Θ(k)$ or even $Θ(1)$, where $k$ is the maximum number of leaked signals observable to each receiver across leakage patterns in the distribution. En route to these results, we show that subsampling and masking serve as general-purpose algorithmic paradigms for transforming private persuasion schemes into leakage-robust schemes, with minmax-optimal loss in sender utility.

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arXiv2026

Calibrated Stackelberg Games: Learning Optimal Commitments Against Calibrated Agents

We introduce \emph{Calibrated Stackelberg Games (CSGs)}, a generalization of the standard Stackelberg Games (SGs) framework. In CSGs, a principal repeatedly interacts with an agent who (contrary to standard SGs) does not have direct access to the principal's action but instead best-responds to calibrated forecasts about it. This framework provides a powerful and realistic modeling tool that goes beyond assuming that agents use ad hoc and highly specified algorithms for interacting in strategic settings and instead builds on statistical foundations of forecasts and calibration. We show that in CSGs, despite both the principal and the agent having less information than in standard SGs, the principal's optimal utility remains upper and lower bounded by the Stackelberg value of the one-shot game, in both finite and continuous settings. Alongside CSGs, we develop stronger notions of calibration and corresponding algorithms that address two central challenges for calibration in game-theoretic environments. First, achieving point-wise calibration typically incurs an error that scales exponentially with the dimension of the strategy space. Second, the principal's convergence rate in CSGs depends critically on the adaptivity of the agent's calibration algorithm. To address these challenges, we establish a meaningful, efficiently achievable relaxation of calibration based on conditioning on best-response regions. This yields the first notion of calibration in games with a statistical rate that only depends on the number of agents' actions rather than the dimension of the principal's strategy space and that leads to no-swap regret for the agent. We further develop adaptive calibration algorithms for the agents that provide fine-grained, any-time calibration guarantees against adversarial sequences, enabling the principal to achieve faster convergence in CSGs.

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arXiv2026

Provably Optimal Learning Algorithms for Assistance Games

This paper studies an online variant of the assistance games framework, where an informed agent and an uninformed agent repeatedly interact over $T$ timesteps to optimize a common reward function. While the informed agent (the human) observes a latent state of the world, the uninformed agent (the assistant) observes only the human's actions. We provide the first provably efficient learning algorithms for repeated assistance games. We introduce the notion of assistance regret: the gap between the cumulative utility of interactions and that of the optimal joint policies in hindsight, which map latent states to action pairs. We present decentralized algorithms for both the human and the assistant that achieve a $(1-1/e)$-approximate assistance regret rate of $\widetilde{O}(T^{3/4})$, with runtime polynomial in the size of the action and state spaces. These algorithms are general; in particular, they accommodate any no-regret algorithm for the assistant. We prove that achieving a regret approximation factor better than $(1-1/e)$ is computationally intractable. Furthermore, we demonstrate how these generic no-regret algorithms can be tailored to a pseudo-decentralized setting -- using a shared random string -- to achieve a rate of $\widetilde{O}(T^{1/2})$, optimal up to logarithmic factors.

cs.LG↗
arXiv2026

Blackwell Approachability and Gradient Equilibrium are Equivalent

Gradient equilibrium (GEQ) is a recently introduced online optimization framework that generalizes first-order stationarity from offline optimization and abstracts problems like online conformal prediction. While GEQ has curious similarities with known online learning frameworks, namely regret minimization, prior work has shown that GEQ error and regret are incomparable objectives, leaving open a precise understanding of how GEQ fits into the broader online learning landscape. In this work, we show that GEQ is equivalent to Blackwell approachability in the algorithmic sense. That is, a Blackwell approachability problem can always be solved using queries to a black-box GEQ oracle, with no asymptotic loss in the oracle's error rate, and vice versa. Taken together with known equivalences between approachability, regret minimization, and calibration, these results imply that GEQ is equivalent to these frameworks, as well. Our reductions are efficient and can be used to transfer refined guarantees, such as optimism and strong adaptivity, from regret minimization to GEQ. Along the way, we also identify necessary and sufficient conditions for GEQ, and establish reductions between different notions of GEQ with unconstrained and constrained decision sets.

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arXiv2026

DiPOD: Diffusion Policy Optimization without Drifting Apart

RL post-training has become increasingly pivotal for improving diffusion policies, but existing diffusion policy-gradient methods are often unstable and cannot achieve reliable policy improvement. We identify the cause as the double-drift phenomenon: optimizing a variational surrogate can let the ELBO separate from the true log-likelihood, which then makes the resulting proxy policy gradient misaligned with the true policy gradient of expected return. We propose \textbf{DiPOD}, a diffusion policy optimization framework that maintains tight-bound behavior throughout training by interleaving self-distillation with policy-improving gradient updates. This leads to a simple and practical algorithm: augmenting each diffusion policy-gradient update with an on-policy ELBO regularizer. Across diffusion language model post-training and continuous-control diffusion policies, DiPOD substantially stabilizes training and reaches higher rewards than previous methods.

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arXiv2026

Strategic Feature Selection

When algorithmic predictors inform resource allocation in high-stakes domains such as healthcare, these predictors must account for strategic manipulation of input features. The typical solution is to redesign the predictor itself to explicitly account for strategic interactions. In practice, however, decision makers are often constrained to adjusting coarser levers within existing prediction pipelines. For example, healthcare organizations often select which features to exclude based on perceived manipulability, while using standard regularization procedures to shrink the coefficients of retained features. In this work, we initiate a formal study of strategic classification through feature selection and its interaction with ridge regularization. Our main finding is that excluding individual features based on their manipulability alone is generally suboptimal. We provide a fine-grained characterization of the performance of a feature subset under optimal regularization, yielding new insights for policy design. Motivated by this characterization, we develop a practical algorithm for jointly choosing the feature set and the level of ridge regularization. Through a real-world case study on a healthcare payments benchmark, we illustrate how our algorithm can guide the design of coarse policy levers in practice. Our results provide a principled, practical framework for mitigating the effects of strategic behavior in algorithmic decision-making systems.

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arXiv2026

On Surjectivity of Neural Networks: Can you elicit any behavior from your model?

Given a trained neural network, can any specified output be generated by some input? Equivalently, does the network correspond to a function that is surjective? In generative models, surjectivity implies that any output, including harmful or undesirable content, can in principle be generated by the networks, raising concerns about model safety and jailbreak vulnerabilities. In this paper, we prove that many fundamental building blocks of modern neural architectures, such as networks with pre-layer normalization and linear-attention modules, are almost always surjective. As corollaries, widely used generative frameworks, including GPT-style transformers and diffusion models with deterministic ODE solvers, admit inverse mappings for arbitrary outputs. By studying surjectivity of these modern and commonly used neural architectures, we contribute a formalism that sheds light on their unavoidable vulnerability to a broad class of adversarial attacks.

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arXiv2026

Three Years of r/ChatGPT: Societal Impact Evaluations from Social Media Data

ChatGPT was launched on November 30, 2022; the r/ChatGPT subreddit was created just one day later. Since then, chatbot-based AI products have gone from niche proofs-of-concept to widely-used household names. However, the ways in which adoption has developed among the public remains poorly understood. In this paper, we develop a framework for using social media as a data source for understanding the societal impact of widely-adopted consumer AI products, and propose PuLSE (Public and Longitudinal Signals for Evaluation), a general approach to monitoring for societally-impactful trends in real time. We apply our framework to conduct what is, to the best of our knowledge, the first longitudinal study of r/ChatGPT. We find that, overall, r/ChatGPT posts over time illustrate the normalization of ChatGPT as an everyday consumer product rather than an exceptional, novel technology. However, our retrospective analysis also finds that posts about using ChatGPT for mental health support, and posts about developing emotional attachments to ChatGPT, both rise steadily in frequency almost immediately after the launch of GPT-4o in May 2024. We show that PuLSE can detect the increase in emotional engagement as early as October 2024 -- months before OpenAI made any (public) acknowledgment of this impact. An interactive site to explore our results and methods, updated daily with live data, is available at rchatgpt-pulse.github.io.

cs.CY↗
arXiv2026

Pluralistic Leaderboards

Recent leaderboard-based evaluations of large language models aggregate user feedback by fitting a Bradley--Terry model to pairwise comparisons, producing a single global ranking based on a latent quality score. While appealing for its simplicity, this approach is incompatible with heterogeneous preferences: when LLMs are used across diverse tasks and use cases, users who favor fundamentally different model behaviors can be systematically misrepresented when collapsed into a single quality score. To address this issue, we study \emph{pluralistic leaderboards} that aim to remain \emph{stable} with respect to heterogeneous user populations. Drawing on ideas from social choice theory, we adapt the notion of \emph{local stability}, which requires that no model outside the top-$k$ positions is collectively preferred to the top-$k$ set by more than $O(1/k)$ fraction of users. Building on techniques from the social choice literature, we design an alternative leaderboard mechanism that satisfies local stability while eliciting only $\widetilde{O}(k)$ pairwise comparisons per user, where $k$ is the size of the prefix for which stability is guaranteed. Using data from LMArena, we show that standard Bradley--Terry aggregation can violate local stability in practice, whereas our method provides substantially stronger stability guarantees.

cs.GT↗
arXiv2026

Subliminal Effects in Your Data: A General Mechanism via Log-Linearity

Training modern large language models (LLMs) has become a veritable smorgasbord of algorithms and datasets designed to elicit particular behaviors, making it critical to develop techniques to understand the effects of datasets on the model's properties. This is exacerbated by recent experiments that show datasets can transmit signals that are not directly observable from individual datapoints, posing a conceptual challenge for dataset-centric understandings of LLM training and suggesting a missing fundamental account of such phenomena. Towards understanding such effects, inspired by recent work on the linear structure of LLMs, we uncover a general mechanism through which hidden subtexts can arise in generic datasets. We introduce Logit-Linear-Selection (LLS), a method that prescribes how to select subsets of a generic preference dataset to elicit a wide range of hidden effects. We apply LLS to discover subsets of real-world datasets so that models trained on them exhibit behaviors ranging from having specific preferences, to responding to prompts in a different language not present in the dataset, to taking on a different persona. Crucially, the effect persists for the selected subset, across models with varying architectures, supporting its generality and universality.

cs.LG↗
arXiv2025

Diffusion Language Models are Provably Optimal Parallel Samplers

Diffusion language models (DLMs) have emerged as a promising alternative to autoregressive models for faster inference via parallel token generation. We provide a rigorous foundation for this advantage by formalizing a model of parallel sampling and showing that DLMs augmented with polynomial-length chain-of-thought (CoT) can simulate any parallel sampling algorithm using an optimal number of sequential steps. Consequently, whenever a target distribution can be generated using a small number of sequential steps, a DLM can be used to generate the distribution using the same number of optimal sequential steps. However, without the ability to modify previously revealed tokens, DLMs with CoT can still incur large intermediate footprints. We prove that enabling remasking (converting unmasked tokens to masks) or revision (converting unmasked tokens to other unmasked tokens) together with CoT further allows DLMs to simulate any parallel sampling algorithm with optimal space complexity. We further justify the advantage of revision by establishing a strict expressivity gap: DLMs with revision or remasking are strictly more expressive than those without. Our results not only provide a theoretical justification for the promise of DLMs as the most efficient parallel sampler, but also advocate for enabling revision in DLMs.

cs.LG↗
arXiv2025

Sample-Adaptivity Tradeoff in On-Demand Sampling

We study the tradeoff between sample complexity and round complexity in on-demand sampling, where the learning algorithm adaptively samples from $k$ distributions over a limited number of rounds. In the realizable setting of Multi-Distribution Learning (MDL), we show that the optimal sample complexity of an $r$-round algorithm scales approximately as $dk^{Θ(1/r)} / ε$. For the general agnostic case, we present an algorithm that achieves near-optimal sample complexity of $\widetilde O((d + k) / ε^2)$ within $\widetilde O(\sqrt{k})$ rounds. Of independent interest, we introduce a new framework, Optimization via On-Demand Sampling (OODS), which abstracts the sample-adaptivity tradeoff and captures most existing MDL algorithms. We establish nearly tight bounds on the round complexity in the OODS setting. The upper bounds directly yield the $\widetilde O(\sqrt{k})$-round algorithm for agnostic MDL, while the lower bounds imply that achieving sub-polynomial round complexity would require fundamentally new techniques that bypass the inherent hardness of OODS.

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arXiv2025

Panprediction: Optimal Predictions for Any Downstream Task and Loss

Supervised learning is classically formulated as training a model to minimize a fixed loss function over a fixed distribution, or task. However, an emerging paradigm instead views model training as extracting enough information from data so that the model can be used to minimize many losses on many downstream tasks. We formalize a mathematical framework for this paradigm, which we call panprediction, and study its statistical complexity. Formally, panprediction generalizes omniprediction and sits upstream from multi-group learning, which respectively focus on predictions that generalize to many downstream losses or many downstream tasks, but not both. Concretely, we design algorithms that learn deterministic and randomized panpredictors with $\tilde{O}(1/\varepsilon^3)$ and $\tilde{O}(1/\varepsilon^2)$ samples, respectively. Our results demonstrate that under mild assumptions, simultaneously minimizing infinitely many losses on infinitely many tasks can be as statistically easy as minimizing one loss on one task. Along the way, we improve the best known sample complexity guarantee of deterministic omniprediction by a factor of $1/\varepsilon$, and match all other known sample complexity guarantees of omniprediction and multi-group learning. Our key technical ingredient is a nearly lossless reduction from panprediction to a statistically efficient notion of calibration, called step calibration.

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arXiv2025

Distortion of AI Alignment: Does Preference Optimization Optimize for Preferences?

After pre-training, large language models are aligned with human preferences based on pairwise comparisons. State-of-the-art alignment methods (such as PPO-based RLHF and DPO) are built on the assumption of aligning with a single preference model, despite being deployed in settings where users have diverse preferences. As a result, it is not even clear that these alignment methods produce models that satisfy users on average -- a minimal requirement for pluralistic alignment. Drawing on social choice theory and modeling users' comparisons through individual Bradley-Terry (BT) models, we introduce an alignment method's distortion: the worst-case ratio between the optimal achievable average utility, and the average utility of the learned policy. The notion of distortion helps draw sharp distinctions between alignment methods: Nash Learning from Human Feedback achieves the minimax optimal distortion of $(\frac{1}{2} + o(1)) \cdot β$ (for the BT temperature $β$), robustly across utility distributions, distributions of comparison pairs, and permissible KL divergences from the reference policy. RLHF and DPO, by contrast, suffer $\geq (1 - o(1)) \cdot β$ distortion already without a KL constraint, and $e^{Ω(β)}$ or even unbounded distortion in the full setting, depending on how comparison pairs are sampled.

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