arXiv subjects

Pinyan Lu

Publications and source records attributed to Pinyan Lu.

At least 19 recordsLinked to original sources

arXiv2026

Auctions with Contract Design

We consider a new auction model where the bidders' utilities and the auctioneer's revenue depend on a quality factor of the transaction determined by costly and strategic investments of the bidders. Applications of our model include ad auctions, government concessions and crowdsourcing contests. Crucially, these quality-enhancing efforts made by the bidders are often sunk costs incurred prior to the allocation, creating a fundamental moral hazard problem where the risk of losing the auction discourages investments. In this paper, we study the design of revenue-maximizing contracts integrated into auctions: the auctioneer commits to a transfer rule that rewards the winner for the ex-post realized quality of the transaction to incentivize higher effort. Our new framework is a natural generalization of both the auction theory and the principal-agent model. We consider both the second-price and the first-price auctions. We show that natural symmetric Bayes Nash equilibria exist in both auctions. Assuming these natural equilibria are played by the bidders and the number of bidders is large, we study linear contracts and derive the optimal reward factor of the transfer rule that maximizes the auctioneer's revenue. As the main result, we show that the optimal reward factor converges to the auctioneer's marginal benefit from the quality, as the number of bidders grows. That is, it is optimal for the auctioneer to fully pass through the quality value to the winner. This observation is largely independent of the auction rule used: we derive a revenue equivalence theorem showing that the revenue remains the same as long as symmetric Bayes Nash equilibria exist. Lastly, by quantitatively comparing with the standard auctions where no quality reward is used, we show that the use of contracts effectively improves the revenue by incentivizing high investments from the bidders.

cs.GT↗

arXiv2026

Fair Division by Contribution: A Shapley Value Perspective

In many resource allocation problems, agents' valuations are best interpreted not as subjective preferences, but as the value they generate from receiving resources. Such valuations capture productivity, effectiveness, or technology, and may differ significantly across agents. In these settings, classical fairness notions such as proportionality or envy-freeness fail to reflect agents' heterogeneous contributions to the collective outcome. Motivated by this perspective, we introduce \emph{Shapley Value Fairness (SVF)} for the allocation of divisible goods without monetary transfers. SVF interprets an agent's entitlement as her expected marginal contribution to optimal social welfare, and uses the Shapley value of the associated welfare maximization game as a normative fairness benchmark. We position SVF relative to existing fairness notions and show that it provides a natural bridge between fairness and efficiency in contribution-based environments. Since exact implementation of the Shapley value is generally infeasible without transfers, SVF naturally leads to the problem of finding allocations that approximate this benchmark as well as possible. We provide a systematic worst-case analysis of the achievable Shapley approximation ratio. For general concave valuations, we establish a tight $\Theta(\ln n)$ bound. For capped concave valuations with bounded demands, this bound improves to $\Theta(\ln D)$, where $D$ is the maximum aggregate demand for any item. For linear valuations, we further refine the bound to $\Theta(\min\{k, \ln \gamma, \ln n\})$ in terms of the number of agent types $k$ and the value fluctuation ratio $\gamma$, and show that all bounds are asymptotically tight. Regarding per-instance guarantees, we show that a near-optimal approximation allocation can be computed efficiently (with high probability) via sampling for general concave valuations.

cs.GT↗

arXiv2026

Benchmark-Tight Approximation Ratio of Simple Mechanism for a Unit-Demand Buyer

We study revenue maximization in the unit-demand single-buyer setting. Our main result is that \textsf{Uniform-Ironed-Virtual-Value Item Pricing} guarantees a {\em tight} $3$-approximation to the \textsf{Duality Relaxation Benchmark} [Chawla-Malec-Sivan, EC'10/GEB'15; Cai-Devanur-Weinberg, STOC'16/ SICOMP'21], breaking the barrier of $4$ since [Chawla-Hartline-Malec-Sivan, STOC'10; Chawla-Malec-Sivan, EC'10/GEB'15]. To our knowledge, this is the first {\em benchmark-tight} revenue guarantee of any simple multi-item mechanism. Technically, all previous works employ \textsf{Myerson Auction} as an intermediary. The barrier of $4$ follows as \textsf{Uniform-Ironed-Virtual-Value Item Pricing} achieves a {\em tight} $2$-approximation to \textsf{Myerson Auction}, which then achieves a {\em tight} $2$-approximation to \textsf{Duality Relaxation Benchmark}. Instead, our new approach avoids \textsf{Myerson Auction}, thus enabling the improvement. Central to our work are a {\em benchmark-based} $3$-competitive prophet inequality and its {\em fully constructive} proof. Such variant prophet inequalities shall find future applications, e.g., to Multi-Item Mechanism Design where optimal revenues are relaxed to various more accessible benchmarks. We complement our benchmark-tight ratio with an impossibility result. All previous works and ours follow the {\em single-dimensional representative} approach introduced by [Chawla-Hartline-Kleinberg, EC'07]. Against \textsf{Duality Relaxation Benchmark}, it turns out that this approach cannot beat our bound of $3$ for a large class of \textsf{Item Pricing}'s.

cs.GT↗

arXiv2026

Unveiling Memorization-Generalization Coexistence: A Case Study on Arithmetic Tasks with Label Noise

Highly over-parameterized models can simultaneously memorize noisy labels and generalize well, yet how these behaviors coexist remains poorly understood. In this work, we investigate the underlying mechanisms of this coexistence using modular arithmetic tasks under heavy label noise. Through extensive experiments on two-layer neural networks, we find that larger models tend to generalize better under appropriate optimization and model configurations, while noisy labels are memorized faster than clean data. Over-parameterized models internally form a generalization structure, but its expression in the output is suppressed by the need to fit noisy labels. Remarkably, even with 80\% label noise, near-perfect test accuracy can be achieved by extracting this internal structure using frequency-based methods. We further propose a task-agnostic method to partition networks into generalization and memorization components. Although this subnetwork improves generalization, it is limited compared with frequency-based extraction, indicating that the generalization structure is distributed across neurons and motivating the development of new tools to retrieve generalizable knowledge from over-parameterized networks.

cs.LG↗

arXiv2026

SHAPE: Stage-aware Hierarchical Advantage via Potential Estimation for LLM Reasoning

Process supervision has emerged as a promising approach for enhancing LLM reasoning, yet existing methods fail to distinguish meaningful progress from mere verbosity, leading to limited reasoning capabilities and unresolved token inefficiency. To address this, we propose Stage-aware Hierarchical Advantage via Potential Estimation (SHAPE), a framework that formalizes reasoning as a trajectory through a state space of empirical solvability. SHAPE introduces a hierarchical credit assignment mechanism: at the segment level, it employs a stage-aware advantage function to prioritize efficient breakthroughs in low-potential states; at the token level, it utilizes entropy-driven redistribution to sharpen execution signals. Extensive experiments in math reasoning across three base models and five benchmarks demonstrate that SHAPE achieves an average accuracy gain of 3% with 30% reduced token consumption.

cs.LG↗

arXiv2026

Budget-Constrained Agentic Large Language Models: Intention-Based Planning for Costly Tool Use

We study budget-constrained tool-augmented agents, where a large language model must solve multi-step tasks by invoking external tools under a strict monetary budget. We formalize this setting as sequential decision making in context space with priced and stochastic tool executions, making direct planning intractable due to massive state-action spaces, high variance of outcomes and prohibitive exploration cost. To address these challenges, we propose INTENT, an inference-time planning framework that leverages an intention-aware hierarchical world model to anticipate future tool usage, risk-calibrated cost, and guide decisions online. Across cost-augmented StableToolBench, INTENT strictly enforces hard budget feasibility while substantially improving task success over baselines, and remains robust under dynamic market shifts such as tool price changes and varying budgets.

cs.AI↗

arXiv2026

Muon in Associative Memory Learning: Training Dynamics and Scaling Laws

Muon updates matrix parameters via the matrix sign of the gradient and has shown strong empirical gains, yet its dynamics and scaling behavior remain unclear in theory. We study Muon in a linear associative memory model with softmax retrieval and a hierarchical frequency spectrum over query-answer pairs, with and without label noise. In this setting, we show that Gradient Descent (GD) learns frequency components at highly imbalanced rates, leading to slow convergence bottlenecked by low-frequency components. In contrast, the Muon optimizer mitigates this imbalance, leading to faster and more uniform progress. Specifically, in the noiseless case, Muon achieves an exponential speedup over GD; in the noisy case with a power-law frequency spectrum, we derive Muon's scaling law and demonstrate its superior scaling efficiency over GD. Furthermore, we show that Muon can be interpreted as an implicit matrix preconditioner arising from adaptive task alignment and block-symmetric gradient structure. In contrast, the preconditioner with coordinate-wise sign operator could match Muon under oracle access to unknown task representations, which is infeasible for SignGD in practice. Experiments on synthetic long-tail classification and LLaMA-style pre-training corroborate the theory.

cs.LG↗

arXiv2026

A Provable Expressiveness Hierarchy in Hybrid Linear-Full Attention

Transformers serve as the foundation of most modern large language models. To mitigate the quadratic complexity of standard full attention, various efficient attention mechanisms, such as linear and hybrid attention, have been developed. A fundamental gap remains: their expressive power relative to full attention lacks a rigorous theoretical characterization. In this work, we theoretically characterize the performance differences among these attention mechanisms. Our theory applies to all linear attention variants that can be formulated as a recurrence, including Mamba, DeltaNet, etc. Specifically, we establish an expressiveness hierarchy: for the sequential function composition-a multi-step reasoning task that must occur within a model's forward pass, an ($L+1$)-layer full attention network is sufficient, whereas any hybrid network interleaving $L-1$ layers of full attention with a substantially larger number ($2^{3L^2}$) of linear attention layers cannot solve it. This result demonstrates a clear separation in expressive power between the two types of attention. Our work provides the first provable separation between hybrid attention and standard full attention, offering a theoretical perspective for understanding the fundamental capabilities and limitations of different attention mechanisms.

cs.LG↗

arXiv2026

BAPS: A Fine-Grained Low-Precision Scheme for Softmax in Attention via Block-Aware Precision reScaling

As the performance gains from accelerating quantized matrix multiplication plateau, the softmax operation becomes the critical bottleneck in Transformer inference. This bottleneck stems from two hardware limitations: (1) limited data bandwidth between matrix and vector compute cores, and (2) the significant area cost of high-precision (FP32/16) exponentiation units (EXP2). To address these issues, we introduce a novel low-precision workflow that employs a specific 8-bit floating-point format (HiF8) and block-aware precision rescaling for softmax. Crucially, our algorithmic innovations make low-precision softmax feasible without the significant model accuracy loss that hampers direct low-precision approaches. Specifically, our design (i) halves the required data movement bandwidth by enabling matrix multiplication outputs constrained to 8-bit, and (ii) substantially reduces the EXP2 unit area by computing exponentiations in low (8-bit) precision. Extensive evaluation on language models and multi-modal models confirms the validity of our method. By alleviating the vector computation bottleneck, our work paves the way for doubling end-to-end inference throughput without increasing chip area, and offers a concrete co-design path for future low-precision hardware and software.

cs.LG↗

arXiv2025

Understanding the Ability of LLMs to Handle Character-Level Perturbation

This work investigates the resilience of contemporary large language models (LLMs) against frequent character-level perturbations. We examine three types of character-level perturbations including introducing numerous typos within words, shuffling the characters in each word, and inserting a large number of invisible characters into the text. Surprisingly, even under severe perturbation, such as shuffling nearly all words character-wise to produce text that is almost unreadable to humans, or inserting invisible characters which are several times more than the visible ones as noise, many LLMs still maintain notable performance. We explore the underlying causes of this robustness and find that LLMs exhibit remarkable resilience to chaotic segmentation and fragmented tokenization. Furthermore, we examine the mechanisms by which LLMs remove perturbations to correctly comprehend text, including both implicit and explicit mechanisms for character-level perturbation. We hope that our findings on the low-level robustness of LLMs will unveil their inherent architectural strengths, reveal the potential risks of their misuse, and inform the reliable deployment of LLMs across diverse application scenarios.

cs.CL↗

arXiv2025

The Query Complexity of Uniform Pricing

Real-world pricing mechanisms are typically optimized using training data, a setting corresponding to the \textit{pricing query complexity} problem in Mechanism Design. The previous work [LSTW23] studies the \textit{single-distribution} case, with tight bounds of $\widetilde{\Theta}(\varepsilon^{-3})$ for a \textit{general} distribution and $\widetilde{\Theta}(\varepsilon^{-2})$ for either a \textit{regular} or \textit{monotone-hazard-rate (MHR)} distribution, where $\varepsilon \in (0, 1)$ denotes the (additive) revenue loss of a learned uniform price relative to the Bayesian-optimal uniform price. This can be directly interpreted as ``the query complexity of the {\em \textsf{Uniform Pricing}} mechanism, in the \textit{single-distribution} case''. Yet in the \textit{multi-distribution} case, can the regularity and MHR conditions still lead to improvements over the tight bound $\widetilde{\Theta}(\varepsilon^{-3})$ for general distributions? We answer this question in the negative, by establishing a (near-)matching lower bound $\Omega(\varepsilon^{-3})$ for either \textit{two regular distributions} or \textit{three MHR distributions}. We also address the \textit{regret minimization} problem and, in comparison with the folklore upper bound $\widetilde{O}(T^{2 / 3})$ for general distributions (see, e.g., [SW24]), establish a (near-)matching lower bound $\Omega(T^{2 / 3})$ for either \textit{two regular distributions} or \textit{three MHR distributions}, via a black-box reduction. Again, this is in stark contrast to the tight bound $\widetilde{\Theta}(T^{1 / 2})$ for a single regular or MHR distribution.

cs.GT↗

arXiv2025

Tight Regret Bounds for Fixed-Price Bilateral Trade

We examine fixed-price mechanisms in bilateral trade through the lens of regret minimization. Our main results are twofold. (i) For independent values, a near-optimal $\widetilde{\Theta}(T^{2/3})$ tight bound for $\textsf{Global Budget Balance}$ fixed-price mechanisms with two-bit/one-bit feedback. (ii) For correlated/adversarial values, a near-optimal $\Omega(T^{3/4})$ lower bound for $\textsf{Global Budget Balance}$ fixed-price mechanisms with two-bit/one-bit feedback, which improves the best known $\Omega(T^{5/7})$ lower bound obtained in the work [BCCF24] and, up to polylogarithmic factors, matches the $\widetilde{\mathcal{O}}(T^{3 / 4})$ upper bound obtained in the same work. Our work in combination with the previous works [CCCFL24mor, CCCFL24jmlr, AFF24, BCCF24] (essentially) gives a thorough understanding of regret minimization for fixed-price bilateral trade. En route, we have developed two technical ingredients that might be of independent interest: (i) A novel algorithmic paradigm, called $\textit{{fractal elimination}}$, to address one-bit feedback and independent values. (ii) A new $\textit{lower-bound construction}$ with novel proof techniques, to address the $\textsf{Global Budget Balance}$ constraint and correlated values.

cs.GT↗

arXiv2025

Local Search for Clustering in Almost-linear Time

We propose the first \emph{local search} algorithm for Euclidean clustering that attains an $O(1)$-approximation in almost-linear time. Specifically, for Euclidean $k$-Means, our algorithm achieves an $O(c)$-approximation in $\tilde{O}(n^{1 + 1 / c})$ time, for any constant $c \ge 1$, maintaining the same running time as the previous (non-local-search-based) approach [la Tour and Saulpic, arXiv'2407.11217] while improving the approximation factor from $O(c^{6})$ to $O(c)$. The algorithm generalizes to any metric space with sparse spanners, delivering efficient constant approximation in $\ell_p$ metrics, doubling metrics, Jaccard metrics, etc. This generality derives from our main technical contribution: a local search algorithm on general graphs that obtains an $O(1)$-approximation in almost-linear time. We establish this through a new $1$-swap local search framework featuring a novel swap selection rule. At a high level, this rule ``scores'' every possible swap, based on both its modification to the clustering and its improvement to the clustering objective, and then selects those high-scoring swaps. To implement this, we design a new data structure for maintaining approximate nearest neighbors with amortized guarantees tailored to our framework.

cs.DS↗

arXiv2024

Incentives for Early Arrival in Cost Sharing

In cooperative games, we study how values created or costs incurred by a coalition are shared among the members within it, and the players may join the coalition in a online manner such as investors invest a startup. Recently, Ge et al. [10] proposed a new property called incentives for early arrival (I4EA) in such games, which says that the online allocation of values or costs should incentivize agents to join early in order to prevent mutual strategic waiting. Ideally, the allocation should also be fair, so that agents arriving in an order uniformly at random should expect to get/pay their Shapley values. Ge et al. [10] showed that not all monotone value functions admit such mechanisms in online value sharing games. In this work, we show a sharp contrast in online cost sharing games. We construct a mechanism with all the properties mentioned above, for every monotone cost function. To achieve this, we first solve 0-1 valued cost sharing games with a novel mechanism called Shapley-fair shuffle cost sharing mechanism (SFS-CS), and then extend SFS-CS to a family called generalized Shapley-fair shuffle cost sharing mechanisms (GSFS-CS). The critical technique we invented here is a mapping from one arrival order to another order so that we can directly apply marginal cost allocation on the shuffled orders to satisfy the properties. Finally, we solve general valued cost functions, by decomposing them into 0-1 valued functions in an online fashion.

cs.GT↗

arXiv2024

Sample-Based Matroid Prophet Inequalities

We study matroid prophet inequalities when distributions are unknown and accessible only through samples. While single-sample prophet inequalities for special matroids are known, no constant-factor competitive algorithm with even a sublinear number of samples was known for general matroids. Adding more to the stake, the single-sample version of the question for general matroids has close (two-way) connections with the long-standing matroid secretary conjecture. In this work, we give a $(\frac14 - \varepsilon)$-competitive matroid prophet inequality with only $O_\varepsilon(\mathrm{poly} \log n)$ samples. Our algorithm consists of two parts: (i) a novel quantile-based reduction from matroid prophet inequalities to online contention resolution schemes (OCRSs) with $O_\varepsilon(\log n)$ samples, and (ii) a $(\frac14 - \varepsilon)$-selectable matroid OCRS with $O_\varepsilon(\mathrm{poly} \log n)$ samples which carefully addresses an adaptivity challenge.

cs.DS↗

arXiv2024

Design and Characterization of Strategy-Proof Mechanisms for Two-Facility Game on a Line

We focus on the problem of placing two facilities along a linear space to serve a group of agents. Each agent is committed to minimizing the distance between her location and the closest facility. A mechanism is an algorithm that maps the reported agent locations to the facility locations. We are interested in mechanisms without money that are deterministic, strategy-proof, and provide a bounded approximation ratio for social cost. It is a fundamental problem to characterize the family of strategy-proof mechanisms with a bounded approximation ratio. Fotakis and Tzamos already demonstrated that the deterministic strategy-proof mechanisms for the 2-facility game problem are mechanisms with a unique dictator and the leftmost-rightmost mechanism. In this paper, we first present a more refined characterization of the first family. We then reveal three new classes of strategy-proof mechanisms that show the intricacy of structure within this family. This helps us get a more complete picture of the characterization of the 2-facility game problem, and may also have value in understanding and solving more general facility allocation game problems. Besides, based on our refined characterization, we surprisingly find that prediction cannot effectively improve the performance of the mechanism in the two-facility game problem, while this methodology to overcome bad approximation ratio works in many other mechanism design problems. We show that if we require that the mechanism admits a bounded approximation ratio when the prediction is arbitrarily bad, then at the same time, the mechanism can never achieve sublinear approximation ratios even with perfect prediction.

cs.GT↗

arXiv2023

Competitive Auctions with Imperfect Predictions

The competitive auction was first proposed by Goldberg, Hartline, and Wright. In their paper, they introduce the competitive analysis framework of online algorithm designing into the traditional revenue-maximizing auction design problem. While the competitive analysis framework only cares about the worst-case bound, a growing body of work in the online algorithm community studies the learning-augmented framework. In this framework, designers are allowed to leverage imperfect machine-learned predictions of unknown information and pursue better theoretical guarantees when the prediction is accurate(consistency). Meanwhile, designers also need to maintain a nearly-optimal worst-case ratio(robustness). In this work, we revisit the competitive auctions in the learning-augmented setting. We leverage the imperfect predictions of the private value of the bidders and design the learning-augmented mechanisms for several competitive auctions with different constraints, including digital good auctions, limited-supply auctions, and general downward-closed permutation environments. For all these auction environments, our mechanisms enjoy $1$-consistency against the strongest benchmark $OPT$, which is impossible to achieve $O(1)$-competitive without predictions. At the same time, our mechanisms also maintain the $O(1)$-robustness against all benchmarks considered in the traditional competitive analysis. Considering the possible inaccuracy of the predictions, we provide a reduction that transforms our learning-augmented mechanisms into an error-tolerant version, which enables the learning-augmented mechanism to ensure satisfactory revenue in scenarios where the prediction error is moderate.

cs.GT↗

arXiv2023

Two-State Spin Systems with Negative Interactions

We study the approximability of computing the partition functions of two-state spin systems. The problem is parameterized by a $2\times 2$ symmetric matrix. Previous results on this problem were restricted either to the case where the matrix has non-negative entries, or to the case where the diagonal entries are equal, i.e. Ising models. In this paper, we study the generalization to arbitrary $2\times 2$ interaction matrices with real entries. We show that in some regions of the parameter space, it's \#P-hard to even determine the sign of the partition function, while in other regions there are fully polynomial approximation schemes for the partition function. Our results reveal several new computational phase transitions.

cs.CC↗