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Haifeng Xu

Publications and source records attributed to Haifeng Xu.

At least 19 recordsLinked to original sources
arXiv2026

When do prophets profit in prediction markets?

Prediction markets aggregate dispersed beliefs into prices that act as probabilistic forecasts of uncertain events. Classical theory establishes how a better-than-market forecast can yield positive trading profit. However, it hinges crucially on the specific automated market maker (AMM) design, and is not applicable to popular exchanges today which are based on central limit order books. This paper fills that gap. For any prediction market and any proper scoring rule $S$, we exhibit a ``proper'' betting strategy that depends only on the forecaster's prediction $\mathbf{p}$ and the market price $\mathbf{q}$, and earns positive expected profit \emph{whenever} $\mathbf{p}$ outperforms $\mathbf{q}$ under $S$ and the market has sufficient liquidity. Moreover, this proper betting is essentially the only strategy with such robust profitability guarantee. Our proof rests on a decomposition of expected profit that strictly generalizes the classical AMM guarantee and also explains how strategies can profit even without an accuracy edge. Empirically, across thousands of forecasts by AI models, proper betting is the only strategy that reliably converts accuracy into profit, and we further identify systematic forecasting personas and show how the optimal proper strategy varies across them. For feasibility demonstration, we run a monthlong live pilot test on Kalshi; the encouraging preliminary results show that proper betting can survive real-world spreads, fees, discrete fills, and limited liquidity.

cs.AI↗
arXiv2026

Performance Manipulation: Labor Market Implications in AI-assisted Era

Performance manipulation arises when agents exploit easily measurable, routine tasks to inflate observable outcomes without contributing genuine innovation or expert judgment. We formalize this phenomenon in a game-theoretic model in which agents allocate effort along two margins. Creative effort is non-routine cognitive labor whose return is complementary to the agent's private expertise; it is the scarce input that principals seek. Mechanistic effort is the execution of well-defined, rule-based tasks that raise performance independently of expertise, a commoditized input that AI heavily augments. We establish the existence of a symmetric, monotone pure-strategy equilibrium and show that performance-based screening remains viable so long as evaluations retain a sufficient creative component, but collapses into an uninformative pooling equilibrium once AI capability grows large enough to crowd out creative effort. Comparing contest allocations against a single-agent baseline isolates performance manipulation as the competition-induced over-investment in mechanistic effort, which we show is undertaken systematically by low-type agents but not high-type ones. We further prove that more sharply skewed reward structures mitigate this friction by eliciting greater creative effort across the participant pool. Finally, using a novel, language-model-based methodology to measure both effort types from nearly 1,500 Kaggle competition scripts, we provide robust empirical support for the model's predictions.

econ.GN↗
arXiv2026

An Isotonic Mechanism for Overlapping Ownership

Motivated by the problem of improving peer review at large scientific conferences, this paper studies how to elicit self-evaluations to improve review scores in a natural many-to-many owner-item (e.g., author-paper) situation with overlapping ownership. We design a simple, efficient and truthful mechanism to elicit self-evaluations from item owners that can be used to calibrate their noisy review scores in the existing evaluation process (e.g., papers' review scores from peers). Our approach starts by partitioning the owner-item relation structure into disjoint blocks, each sharing a common set of co-owners. We then elicit the ranking of items from each owner and employ isotonic regression to produce adjusted item scores, aligning with both the reported rankings and raw item review scores. We prove that truth-telling by all owners is a payoff dominant Nash equilibrium for any valid partition of the overlapping ownership sets under natural conditions. Moreover, the truthfulness depends on eliciting rankings independently within each block, making block partition optimization crucial for improving statistical efficiency. Despite being computationally intractable in general, we develop a nearly linear-time greedy algorithm that provably finds a performant block partition with appealing robust approximation guarantees. Extensive experiments on both synthetic data and real-world conference review data demonstrate the effectiveness of our mechanism in a pressing real-world problem.

cs.GT↗
arXiv2026

T-TAMER: Provably Taming Trade-offs in ML Serving

As machine learning models continue to grow in size and complexity, efficient serving faces increasingly broad trade-offs spanning accuracy, latency, resource usage, and other objectives. Multi-model serving further complicates these trade-offs; for example, in cascaded models, each early-exit decision balances latency reduction against potential accuracy loss. Despite the pervasiveness and importance of such trade-offs, current strategies remain largely heuristic and case-specific, limiting both their theoretical guarantees and general applicability. We present a general framework, T-Tamer, which formalizes this setting as a multi-stage decision process, where the objective is to determine both when to exit and which model to consult. Our main result shows that recall (i.e., the ability to revisit earlier models) is both necessary and sufficient for achieving provable performance guarantees. In particular, we prove that strategies without recall cannot obtain any constant-factor approximation to the optimal trade-off, whereas recall-based strategies provably attain the optimal trade-off in polynomial time. We validate our analysis through experiments on synthetic datasets and early-exit workloads for vision and NLP benchmarks. The results show that recall-based strategies consistently yield efficient accuracy-latency trade-offs. We hope this work provides a principled foundation for bridging heuristic practice with theoretical guarantees in the design of early-exit and cascaded models.

cs.LG↗
arXiv2026

Escaping Model Collapse via Synthetic Data Verification: Near-term Improvements and Long-term Convergence

Synthetic data has been increasingly used to train frontier generative models. However, recent studies raise key concerns that iteratively retraining a generative model on its self-generated synthetic data may keep deteriorating model performance, a phenomenon often coined model collapse. In this paper, we investigate ways to modify the synthetic retraining process to avoid model collapse, and even possibly help reverse the trend from collapse to improvement. Our key finding is that by injecting information through an external synthetic data verifier, whether a human or a better model, synthetic retraining will not cause model collapse. Specifically, we situate our theoretical analysis in the fundamental linear regression setting, showing that verifier-guided retraining can yield near-term improvements, but ultimately drives the parameter estimate to the verifier's "knowledge center" in the long run. Our theory further predicts that, unless the verifier is perfectly reliable, these early gains will plateau and may even reverse. Indeed, our experiments across linear regression, Variational Autoencoders (VAEs) trained on MNIST, and fining-tuning SmolLM2-135M on the XSUM task confirm these theoretical insights.

stat.ML↗
arXiv2026

How to sell a service with uncertain outcomes

Motivated by the recent popularity of machine learning training services, we introduce a contract design problem in which a provider sells a service that results in an outcome of uncertain quality for the buyer. The seller has a set of actions that lead to different distributions over outcomes. We focus on a setting in which the seller has the ability to commit to an action and the buyer is free to accept or reject the outcome after seeing its realized quality. We propose a two-stage payment scheme where the seller designs a menu of contracts, each of which specifies an action, an upfront price and a vector of outcome-dependent usage prices. Upon selecting a contract, the buyer pays the upfront price, and after observing the realized outcome, the buyer either accepts and pays the corresponding usage price, or rejects and is exempt from further payment. We show that this two-stage payment structure is necessary to maximize profit: only upfront price or only usage prices is insufficient. We then study the computational complexity of computing a profit-maximizing menu. While computing the optimal profit is NP-hard even for two buyer types, we derive a fully-polynomial time approximation scheme (FPTAS) for the optimal profit for a constant number of buyer types. Finally, we prove that in the single-parameter setting in which buyers' valuations are parametrized by a single real number, there exists a revenue-optimal menu consisting of a single contract.

cs.GT↗
arXiv2026

Fine-Tuning Improves Information Conveyance in Language Models

Fine-tuning is often believed to reduce uncertainty and diversity in large language models, but existing analyses overlook output length, a key confounder, and therefore fail to capture how uncertainty is distributed across an entire generation rollout. To address this, we propose Canopy Entropy ($\mathrm{CE}^\star$), a measure that views language generation from a tree perspective, where ``canopy'' represents the space of all possible rollouts, making $\mathrm{CE}^\star$ naturally quantify the effective size of the generation space. $\mathrm{CE}^\star$ jointly captures uncertainty in both the output length $N$ and the generated sequence $Y_{1:N}$ -- indeed, we show that it equals to total Shannon entropy $H(N, Y_{1:N}\mid X)$, where $X$ denotes the prompt. This formulation yields interpretable metrics, including a length-entropy correlation term $ρ(N, r_N)$, where $r_N$ is the entropy rate, quantifying information conveyance efficiency by indicating whether longer outputs are more or less informative per token. Empirically, across tasks and model families, we find that fine-tuned models consistently exhibit stronger positive correlation $ρ(N, r_N)$, even when total entropy decreases. Furthermore, after controlling for model family, task, prompt, and output-length effects, we find that fine-tuning nearly triples the correlation strength between entropy rate and semantic diversity, suggesting that aligned models convert token uncertainty into semantic diversity more efficiently. Overall, these results demonstrate that fine-tuning does not simply reduce uncertainty, but fundamentally reorganizes it into more informative and semantically meaningful generations. Our code is available at https://github.com/WeiyiTian/canopy-entropy.

cs.CL↗
arXiv2026

Beyond Majority Voting: LLM Aggregation by Leveraging Higher-Order Information

With the rapid progress of multi-agent large language model (LLM) reasoning, how to effectively aggregate answers from multiple LLMs has emerged as a fundamental challenge. Standard majority voting treats all answers equally, failing to consider latent heterogeneity and correlation across models. In this work, we design two new aggregation algorithms called Optimal Weight (OW) and Inverse Surprising Popularity (ISP), leveraging both first-order and second-order information. Our theoretical analysis shows these methods provably mitigate inherent limitations of majority voting under mild assumptions, leading to more reliable collective decisions. We empirically validate our algorithms on synthetic datasets, popular LLM fine-tuning benchmarks such as UltraFeedback and MMLU, and a real-world healthcare setting ARMMAN. Our algorithms consistently outperform standard baselines, establishing a robust, training-free framework for effective multi-agent LLM aggregation.

cs.LG↗
arXiv2026

Welfare as a Guiding Principle for Machine Learning -- From Compass, to Lens, to Roadmap

Decades of research in machine learning have given us powerful tools for making accurate predictions. But when used in social settings and on human inputs, better accuracy does not immediately translate to better social outcomes. To effectively promote social well-being through machine learning, this position article advocates for the wide adoption of \emph{social welfare} as a guiding principle. The field of welfare economics asks: how should we allocate limited resources to self-interested agents in a way that maximizes social benefit? We argue that this perspective applies to many modern applications of machine learning in social contexts. As such, we propose that welfare serves as an additional core criterion in the design, study, and use of learning algorithms, complementing the conventional pillars of optimization, generalization, and expressivity, and as a compass guiding both theory and practice.

cs.LG↗
arXiv2026

AI Realtor: Towards Grounded Persuasive Language Generation for Automated Copywriting

This paper develops an agentic framework that employs large language models (LLMs) for grounded persuasive language generation in automated copywriting, with real estate marketing as a focal application. Our method is designed to align the generated content with user preferences while highlighting useful factual attributes. This agent consists of three key modules: (1) Grounding Module, mimicking expert human behavior to predict marketable features; (2) Personalization Module, aligning content with user preferences; (3) Marketing Module, ensuring factual accuracy and the inclusion of localized features. We conduct systematic human-subject experiments in the domain of real estate marketing, with a focus group of potential house buyers. The results demonstrate that marketing descriptions generated by our approach are preferred over those written by human experts by a clear margin while maintaining the same level of factual accuracy. Our findings suggest a promising agentic approach to automate large-scale targeted copywriting while ensuring factuality of content generation.

cs.AI↗
arXiv2026

No-Regret Bayesian Recommendation to Homogeneous Users

We introduce and study the online Bayesian recommendation problem for a recommender system platform. The platform has the privilege to privately observe a utility-relevant \emph{state} of a product at each round and uses this information to make online recommendations to a stream of myopic users. This paradigm is common in a wide range of scenarios in the current Internet economy. The platform commits to an online recommendation policy that utilizes her information advantage on the product state to persuade self-interested users to follow the recommendation. Since the platform does not know users' preferences or beliefs in advance, we study the platform's online learning problem of designing an adaptive recommendation policy to persuade users while gradually learning users' preferences and beliefs en route. Specifically, we aim to design online learning policies with no \emph{Stackelberg regret} for the platform, i.e., against the optimal benchmark policy in hindsight under the assumption that users will correspondingly adapt their responses to the benchmark policy. Our first result is an online policy that achieves double logarithmic regret dependence on the number of rounds. We also present an information-theoretic lower bound showing that no adaptive online policy can achieve regret with better dependency on the number of rounds. Finally, by formulating the platform's problem as optimizing a linear program with membership oracle access, we present our second online recommendation policy that achieves regret with polynomial dependence on the number of states but logarithmic dependence on the number of rounds.

cs.GT↗
arXiv2026

Optimal Path Planning in Hostile Environments

Coordinating agents through hazardous environments, such as aid-delivering drones navigating conflict zones or field robots traversing deployment areas filled with obstacles, poses fundamental planning challenges. We introduce and analyze the computational complexity of a new multi-agent path planning problem that captures this setting. A group of identical agents begins at a common start location and must navigate a graph-based environment to reach a common target. The graph contains hazards that eliminate agents upon contact but then enter a known cooldown period before reactivating. In this discrete-time, fully-observable, deterministic setting, the planning task is to compute a movement schedule that maximizes the number of agents reaching the target. We first prove that, despite the exponentially large space of feasible plans, optimal plans require only polynomially-many steps, establishing membership in NP. We then show that the problem is NP-hard even when the environment graph is a tree. On the positive side, we present a polynomial-time algorithm for graphs consisting of vertex-disjoint paths from start to target. Our results establish a rich computational landscape for this problem, identifying both intractable and tractable fragments.

cs.GT↗
arXiv2026

The Complexity of Tullock Contests

Despite the extensive literature on Tullock contests, computational results for the general model with heterogeneous contestants remain scarce. This paper studies the algorithmic complexity of computing a pure Nash Equilibrium (PNE) in such general Tullock contests. We find that the elasticity parameters {r_i}, which govern the returns to scale of contestants' production functions, play a decisive role in the problem's complexity. Our core conceptual insight is that the computational hardness is determined specifically by the number of contestants with medium elasticity (r_i \in (1, 2]). This is illustrated by a complete set of algorithmic results under two parameter regimes: -Efficient Regime: When the number of contestants with medium elasticity is logarithmically bounded by the total number of contestants (O(log n)), we provide an algorithm that determines the existence of a PNE and computes an epsilon-PNE in polynomial time in both n and log(1/epsilon) (i.e., Poly(n,log(1/epsilon))) whenever it exists. This result generalizes classical findings for concave (r_i <= 1) and convex (r_i > 2) cases, establishing computational tractability for a broader class of mixed-elasticity contests. -Hard Regime: In contrast, we show when the number of medium elasticity contestants exceed Omega(log n), determining the existence of PNEs is NP-complete and it is impossible for any algorithm to compute an epsilon-PNE within running time Poly(n,log(1/epsilon)). We then design a Fully Polynomial-Time Approximation Scheme (FPTAS) that computes an epsilon-PNE in Poly(n,1/epsilon), guaranteeing efficient approximations for hard instances.

cs.GT↗
arXiv2026

Information Design With Large Language Models

Information design is typically studied through the lens of Bayesian signaling, where signals shape beliefs purely based on their correlation with the true state of the world. However, behavioral economics and psychology emphasize that human decision-making is more complex and can depend on how information is framed. This paper formalizes a language-based notion of framing and bridges this to the popular Bayesian-persuasion model. We model framing as a possibly non-Bayesian, linguistic way to influence a receiver's prior belief, while a signaling/recommendation scheme can further refine this belief in the classic Bayesian way. A key challenge in systematically optimizing in this framework is the vast space of possible framings and the difficulty of predicting their effects on receivers. Based on growing evidence that Large Language Models (LLMs) can effectively serve as proxies for human behavior, we formulate a theoretical model based on access to a framing-to-belief mapping. This model then enables us to precisely characterize when solely optimizing framing or jointly optimizing framing and signaling is tractable. We substantiate our theoretical analysis with an empirical study that leverages LLMs to optimize over the natural-language framing space using an iterative prompt optimization method combined with analytical solvers for optimal signaling schemes.

cs.GT↗
arXiv2026

GenAI vs. Human Creators: Procurement Mechanism Design in Two-/Three-Layer Markets

With the rapid advancement of generative AI (GenAI), mechanism design adapted to its unique characteristics poses new theoretical and practical challenges. Unlike traditional goods, content from one domain can enhance the training and performance of GenAI models in other domains. For example, OpenAI's video generation model Sora (Liu et al., 2024b) relies heavily on image data to improve video generation quality. In this work, we study nonlinear procurement mechanism design under data transferability, where online platforms employ both human creators and GenAI to satisfy cross-domain content demand. We propose optimal mechanisms that maximize either platform revenue or social welfare and identify the specific properties of GenAI that make such high-dimensional design problems tractable. Our analysis further reveals which domains face stronger competitive pressure and which tend to experience overproduction. Moreover, the growing role of data intermediaries, including labeling companies such as Scale AI and creator organizations such as The Wall Street Journal, introduces a third layer into the traditional platform-creator structure. We show that this three-layer market can result in a lose-lose outcome, reducing both platform revenue and social welfare, as large pre-signed contracts distort creators' incentives and lead to inefficiencies in the data market. These findings suggest a need for government regulation of the GenAI data ecosystem, and our theoretical insights are further supported by numerical simulations.

cs.GT↗
arXiv2026

The Keychain Problem: On Minimizing the Opportunity Cost of Uncertainty

In this paper, we introduce a family of sequential decision-making problems, collectively termed the Keychain Problem, that involve exploring a set of actions to maximize expected payoff when only a subset of actions are available in each stage. In an instance of the Keychain Problem, a locksmith faces a sequence of decisions, each of which involves selecting one key from a keychain (a subset of keys) to attempt to open a lock. Given a Bayesian prior on the effectiveness of keys, the locksmith's goal is to minimize the opportunity cost, which is the expected number of rounds in which the chain has a correct key but our selected key is incorrect. We study the computation of the Bayes optimal solution for Keychain Problems. Employing polynomial-time reductions, we establish formal connections between natural variants of the Keychain Problem and well-studied algorithmic economics problems on bipartite graphs. When the keychain order is known to the locksmith, we show that it reduces to Maximum Weight Bipartite Matching (MWBM). More general is the situation when the keychain order is sampled from a prior distribution (possibly correlated with the correct key). Here the Keychain Problem reduces to a novel generalization of MWBM which we coin the Maximum Weight Laminar Matching, which then further reduces to combinatorial auctions under XOS valuation functions. Finally, we show that when the locksmith can choose the keychain order, the Keychain problem reduces from a classic NP-hard combinatorial problem, again, on bipartite graphs. Besides implying algorithmic results and deepening our structural understanding about the Keychain Problem, our established reductions also find applications beyond -- for example, to the Philosopher Inequality for online bipartite matching.

cs.GT↗
arXiv2026

Do AI Overviews Benefit Search Engines? An Ecosystem Perspective

The integration of AI Overviews into search engines enhances user experience but diverts traffic from content creators, potentially discouraging high-quality content creation and causing user attrition that undermines long-term search engine profit. To address this issue, we propose a game-theoretic model of creator competition with costly effort, characterize equilibrium behavior, and design two incentive mechanisms: a citation mechanism that references sources within an AI Overview, and a compensation mechanism that offers monetary rewards to creators. For both cases, we provide structural insights and near-optimal profit-maximizing mechanisms. Evaluations on real click data show that although AI Overviews harm long-term search engine profit, interventions based on our proposed mechanisms can increase long-term profit across a range of realistic scenarios, pointing toward a more sustainable trajectory for AI-enhanced search ecosystems.

cs.GT↗
arXiv2026

Partitionable Diffractive Neural Networks for Multifunctional Optical Operations

Diffractive neural network (DNN), which can perform machine learning tasks based on the light propagation and diffraction, has recently emerged as a promising optical computing paradigm due to its high parallel processing speed and low power consumption nature. However, existing diffractive network architectures face challenges in implementing functional reconfiguration. Once a diffractive neural network is fabricated, its functionality is fixed. Deploying such systems for different tasks typically requires reconstructing the entire physical setup, which significantly compromises hardware efficiency in practical applications. In this work, we propose the multifunctional partitionable diffractive neural networks (PDNNs) that can generate networks with additional capabilities by stacking multiple sub-modules with independent functions in the horizontal direction. Each submodule functions as an independent diffractive network capable of performing specific imaging or classification tasks. When these submodules are combined, they can form a new network with additional functionalities. Moreover, assembling these submodules in different configurations enables structures with diverse functions. This powerful PDNN framework demonstrates remarkable advantages in flexibility and reconfigurability for multitask operations, opening a new pathway for realizing multifunctional and integrated optical artificial intelligence systems.

physics.optics↗