arXiv subjects

Zhengyang Liu

Publications and source records attributed to Zhengyang Liu.

At least 19 recordsLinked to original sources

arXiv2026

Settling the Complexity of Hylland--Zeckhauser Equilibria

The Hylland--Zeckhauser (HZ) mechanism is a foundational framework for allocating indivisible goods in one-sided matching markets via lotteries supported by competitive prices and equal artificial budgets. We resolve the exact computational complexity of the HZ scheme by proving that computing an exact HZ equilibrium is FIXP-complete, thereby settling a conjecture of Vazirani and Yannakakis. Notably, this hardness persists even when computing the equilibrium allocation alone. We establish our hardness result via a reduction that encodes quadratic fixed-point equations into a reciprocal variational inequality. On the algorithmic side, we present a deterministic polynomial-time approximation algorithm that achieves an additive error of $0.0755211 + δ$ for any $δ> 0$, significantly improving upon the previous $1/e$ guarantee.

cs.GT↗

arXiv2026

On the Complexity of Exact Autobidding Equilibria

Autobidding equilibria link advertisers' value multipliers or participation probabilities through aggregate budget and return-on-investment (ROI) constraints. We establish the exact computational complexity of finding these equilibria across several canonical settings: exact equilibrium computation is $\mathsf{FIXP}$-complete for second-price ROI pacing, budget- or ROI-constrained generalized second-price (GSP) sponsored shopping, and second-price throttling. Furthermore, approximating the equilibrium control vector in distance to a true equilibrium is $\mathsf{FIXP}_{a}$-complete when the target accuracy is provided as input.

cs.GT↗

arXiv2026

Physics-Informed Functional Tucker Method with RKHS Factors for Sparse Spatiotemporal Reconstruction

Reconstructing physical dynamics from fixed sparse sensors and missing frames is a fundamental challenge in scientific research. Sparsity leaves large regions of the field unconstrained, making the inverse problem ill-posed: a model may fit the observed sensors while producing inaccurate off-sensor structures or unreliable predictions between support frames. To this end, we propose PhysFTM---a physics-informed functional Tucker model that parameterizes the Tucker mode factors in reproducing kernel Hilbert spaces (RKHSs) and incorporates PDE constraints through finite-difference residuals evaluated at off-sensor collocation points. These residuals provide additional physical information in regions without direct observational supervision. PhysFTM first reconstructs continuous spatial fields at support frames via an alternating minimization scheme, optimizing the Tucker core tensor and the RKHS-based factors separately. To enable missing-frame reconstruction, PhysFTM constructs a continuous trajectory in Tucker-core space, which is decoded by the learned spatial RKHS-FTM representation to recover the full spatiotemporal field. Experiments on Allen--Cahn, Navier--Stokes, three-dimensional Heat equations, and a three-dimensional gridded Copernicus ocean reanalysis demonstrate accurate 2D/3D reconstruction under two missing-frame protocols. Code is available at https://github.com/liusirzzz/PhysFTM.

cs.CV↗

arXiv2026

GSP Autobidding Equilibria with Few Advertisers or Slots

In sponsored-shopping auctions, one advertiser may win several positions, and a product that is never displayed may determine the prices of several winners. Under generalized second-price (GSP) pricing without self-pricing, these interactions couple allocation and payment through a single global ranking. We prove that exact autobidding equilibria under budget and return-on-investment (ROI) constraints can be computed in polynomial time whenever either the number $n$ of advertisers or the number $K$ of display slots is fixed. Our algorithms rely on two structural reductions. With few advertisers, the payment polytopes of tied bid layers combine by a Minkowski sum, giving a fixed-dimensional representation of exponentially many rankings. With few slots, budget equilibria admit threshold recovery and an exact submodular description of attainable payments at the display boundary. For ROI, we prove that every group-consecutive equilibrium has a representative with at most $K+2$ nonunit multipliers, preserving the item and price in every displayed slot. In each case, the reduction leads to polynomially many systems of polynomial equations and inequalities in bounded dimension. The algorithms compute exact multipliers and explicit distributions over valid group-consecutive rankings, with support at most $n+1$; for ROI with few slots, this improves to $\min\{n+1,K+3\}$.

cs.GT↗

arXiv2026

The Complexity of Exact and Approximate Nash Equilibria in Anonymous Games

We prove that, for every fixed rational $c>0$, computing a $2^{-n^c}$-approximate Nash equilibrium in an $n$-player two-strategy anonymous game is $\mathsf{PPAD}$-complete. This holds even when one strategy always pays $1/2$ and, for all but two players, the other is constant outside at most five opponent counts. The reduction uses coefficient estimates to simulate circuit constraints approximately. Exact computation requires eliminating the simulation error: with three strategies, a separate construction uses polynomial roots to implement circuit gates exactly. This yields $\mathsf{FIXP}$-completeness of exact equilibrium computation under separable-linear reductions and $\mathsf{FIXP}_a$-completeness of approximation in distance to an exact equilibrium.

cs.GT↗

arXiv2026

Optimal Multi-Item Auctions with I.I.D. Values

We study revenue-maximizing multi-item auctions under dominant-strategy incentive compatibility (DSIC) and ex-post individual rationality. Buyers have additive valuations, and all item values are independent draws from a common finite distribution. For every two-point distribution and arbitrary numbers of buyers and items, we give an explicit deterministic mechanism that is optimal among all randomized mechanisms satisfying these requirements, together with a polynomial-time algorithm for computing the optimal expected revenue. For general finite-support distributions, computing the exact optimal revenue is $\#\mathrm P$-hard, both for a single buyer with an arbitrary number of items and for two items with an arbitrary number of buyers. For a single buyer, we also establish hardness of computing an optimal mechanism. Building on prior work, we also obtain exact and approximate algorithms under different parameter restrictions. Exact polynomial-time optimization is possible whenever any two of the buyer count, item count, and support size are fixed. When only the item count is fixed, a polynomial-time approximation scheme constructs a mechanism with expected revenue at least a $1-\varepsilon$ fraction of the optimum for every fixed $0<\varepsilon<1$. All these algorithms satisfy DSIC and ex-post individual rationality.

cs.GT↗

arXiv2026

Sharp Second-Best Welfare in Bilateral and Matching Markets

How much social welfare must a market lose because values are private? We determine the sharp ratio of second-best to first-best welfare under independent nonnegative types, Bayesian incentive compatibility, interim individual rationality, and no expected budget deficit. The ratio is approximately $0.8882516903$ for arbitrary priors and $0.9113893681$ when buyers have monotone hazard rates and sellers are unrestricted. The arbitrary-prior guarantee holds for every downward-closed family of feasible matchings; the MHR guarantee holds when every matching of a compatibility graph is feasible. Both constants are \revise{attained}{sharp} already in bilateral trade. The proof keeps the sellers' initial endowment inside the budget Lagrangian. For arbitrary priors, a common threshold decomposition reduces the problem to three-parameter power-law distributions. For monotone hazards, common transformations of buyer and seller scores reduce it to shifted capped exponential buyers; a typewise allocation certificate and an explicit worst-case seller satisfy the same boundary equation. The bilateral-to-matching framework, with a welfare endowment charge and an MHR-preserving packing argument, transfers these affine inequalities without loss. We give exact variational characterizations of both constants and reproducible interval certificates for their numerical evaluation. Unrestricted signed transfers also permit pointwise strong budget balance.

cs.GT↗

arXiv2026

From Bilateral Trade to Matching Markets: Sharp Gains from Trade

We study gains from trade in matching markets with independent private values and costs, Bayesian incentive compatibility, interim individual rationality, and no expected budget deficit. A second-best guarantee for finite bilateral trade extends without loss to matching markets with independent Borel priors, arbitrary downward-closed feasibility, and finite expected first-best gains. For bounded buyers with monotone hazard rates and arbitrary bounded sellers, we determine the exact worst-case ratio of second-best to first-best gains, approximately $0.72490721$. For binary buyers and sellers with at most $m$ types, we determine the exact ratio for every $m$, including $8/9$ when $m=2$ and a limit of $4/5$ as $m$ grows. Both families of bounds are tight already in bilateral trade.

cs.GT↗

arXiv2026

Tight Inapproximability of Pacing and Throttling Equilibria in Second-Price Auctions

Budget-constrained advertisers commonly rely on two control mechanisms: pacing scales bids, whereas throttling randomizes participation. We prove that, in second-price auctions, these two different mechanisms share the same sharp approximation-hardness threshold. For pacing, computing a $γ$-approximate equilibrium is $\mathsf{PPAD}$-hard for every constant $γ\in[0,1)$. For throttling, computing a $δ$-approximate equilibrium is $\mathsf{PPAD}$-hard for every constant $δ\in(0,1)$. At parameter $1$, the complementarity requirement becomes vacuous and the all-zero solution is feasible. That is, approximation does not eliminate the fixed-point barrier at any nontrivial parameter value.

cs.GT↗

arXiv2026

Support Contraction for Well-Supported Nash Equilibria

We introduce the support contraction, a structural procedure for computing well-supported Nash equilibria (WSNE) in bimatrix games. On a common action rectangle, the procedure alternately retains the support of a row maximin strategy for the row-payoff matrix and the support of a column maximin strategy for the column-payoff matrix. Each restriction preserves the value of the matrix game that selected it and can only increase the other value. At a stable rectangle, full support of the two maximizing strategies and complementary slackness make every surviving action tight. Crossing the two minimax strategies then gives an exact Nash equilibrium of the retained subgame, while the two zero-sum values bound deviations to deleted actions. Support contraction gives a deterministic polynomial-time algorithm that computes a $1/2$-WSNE of every rational bimatrix game with payoffs in $[0,1]$, with no additive slack, and a deterministic $O(ε^{-2}\log^2 n)$-bit two-party protocol for a $(1/2+ε)$-WSNE. The same support-contraction certificate, preceded by randomized one-sided localization, gives an $O(ε^{-2}n\log n)$ payoff-query algorithm for the same guarantee, improving the $ε^{-4}$ dependence to $ε^{-2}$.

cs.GT↗

arXiv2026

Second-Best Bilateral Trade is $1/2$ Efficient

The landmark Myerson-Satterthwaite Theorem establishes a fundamental impossibility in bilateral trade: no Bayesian incentive-compatible mechanism can simultaneously achieve ex-post efficiency, individual rationality, and strong budget balance. We resolve a long-standing open question regarding the efficiency loss imposed by these constraints. Specifically, we prove that the Bayesian-optimal (second-best) mechanism always captures at least half of the first-best gains from trade ($\mathrm{SB}\ge\frac{1}{2}\mathrm{FB}$). This result is tight, definitively closing the gap between the previously best-known bounds of $0.317$ and $0.736$.

cs.GT↗

arXiv2026

HandCept: A Visual-Inertial Fusion Framework for Accurate Proprioception in Dexterous Hands

As robotics progresses toward general manipulation, dexterous hands are becoming increasingly critical. However, proprioception in dexterous hands remains a bottleneck due to limitations in volume and generality. In this work, we present HandCept, the first visual-inertial proprioception framework designed to overcome the challenges of traditional joint angle estimation methods for dexterous hands. HandCept addresses the difficulty of achieving accurate and robust joint angle estimation in dynamic environments where both visual and inertial measurements are prone to noise and drift. It leverages a zero-shot learning approach using a wrist-mounted RGB-D camera and 9-axis IMUs, fused in real time via a latency-free Extended Kalman Filter (EKF). Our results show that HandCept achieves joint angle estimation errors generally between $2^{\circ}$ and $4^{\circ}$ without observable drift, outperforming visual-only and inertial-only methods. Furthermore, we validate the stability and uniformity of the IMU system, demonstrating that a common base frame across IMUs simplifies system calibration. To support sim-to-real transfer, we also open-source our high-fidelity rendering pipeline, which is essential for training without real-world ground truth. This work offers a robust, generalizable solution for proprioception in dexterous hands, with significant implications for robotic manipulation and human-robot interaction. https://github.com/huangjund/blenderYCB

cs.RO↗

arXiv2026

Pacing Equilibria in Second-Price Auctions with Few Goods

In this paper, we investigate the computation of second-price pacing equilibria (SPPEs), a foundational model in online advertising auctions. We present a polynomial-time algorithm for computing exact SPPEs in instances with a constant number of goods. Our core technique maps buyers' pacing multipliers to the highest bids on each good, effectively partitioning the parameter space into a set of distinct geometric cells. By enumerating these cells, we fix the relative ordering of the bids and reduce the problem of equilibrium computation to a linear feasibility program. Finally, we demonstrate that this tractability extends to large-scale markets with an arbitrary number of goods, provided the goods can be aggregated into a constant number of valuation types.

cs.GT↗

arXiv2026

EpiBench: Benchmarking Multi-turn Research Workflows for Multimodal Agents

Scientific research follows multi-turn, multi-step workflows that require proactively searching the literature, consulting figures and tables, and integrating evidence across papers to align experimental settings and support reproducible conclusions. This joint capability is not systematically assessed in existing benchmarks, which largely under-evaluate proactive search, multi-evidence integration and sustained evidence use over time. In this work, we introduce EpiBench, an episodic multi-turn multimodal benchmark that instantiates short research workflows. Given a research task, agents must navigate across papers over multiple turns, align evidence from figures and tables, and use the accumulated evidence in the memory to answer objective questions that require cross paper comparisons and multi-figure integration. EpiBench introduces a process-level evaluation framework for fine-grained testing and diagnosis of research agents. Our experiments show that even the leading model achieves an accuracy of only 29.23% on the hard split, indicating substantial room for improvement in multi-turn, multi-evidence research workflows, providing an evaluation platform for verifiable and reproducible research agents.

cs.CL↗

arXiv2026

LLMs Judge Themselves: A Game-Theoretic Framework for Human-Aligned Evaluation

Ideal or real - that is the question.In this work, we explore whether principles from game theory can be effectively applied to the evaluation of large language models (LLMs). This inquiry is motivated by the growing inadequacy of conventional evaluation practices, which often rely on fixed-format tasks with reference answers and struggle to capture the nuanced, subjective, and open-ended nature of modern LLM behavior. To address these challenges, we propose a novel alternative: automatic mutual evaluation, where LLMs assess each other's output through self-play and peer review. These peer assessments are then systematically compared with human voting behavior to evaluate their alignment with human judgment. Our framework incorporates game-theoretic voting algorithms to aggregate peer reviews, enabling a principled investigation into whether model-generated rankings reflect human preferences. Empirical results reveal both convergences and divergences between theoretical predictions and human evaluations, offering valuable insights into the promises and limitations of mutual evaluation. To the best of our knowledge, this is the first work to jointly integrate mutual evaluation, game-theoretic aggregation, and human-grounded validation for evaluating the capabilities of LLMs.

cs.CL↗

arXiv2025

PRIM: Towards Practical In-Image Multilingual Machine Translation

In-Image Machine Translation (IIMT) aims to translate images containing texts from one language to another. Current research of end-to-end IIMT mainly conducts on synthetic data, with simple background, single font, fixed text position, and bilingual translation, which can not fully reflect real world, causing a significant gap between the research and practical conditions. To facilitate research of IIMT in real-world scenarios, we explore Practical In-Image Multilingual Machine Translation (IIMMT). In order to convince the lack of publicly available data, we annotate the PRIM dataset, which contains real-world captured one-line text images with complex background, various fonts, diverse text positions, and supports multilingual translation directions. We propose an end-to-end model VisTrans to handle the challenge of practical conditions in PRIM, which processes visual text and background information in the image separately, ensuring the capability of multilingual translation while improving the visual quality. Experimental results indicate the VisTrans achieves a better translation quality and visual effect compared to other models. The code and dataset are available at: https://github.com/BITHLP/PRIM.

cs.CL↗

arXiv2025

A Performance Model for Warp Specialization Kernels

This paper presents a performance model tailored for warp specialization kernels, focusing on factors such as warp size, tilling size, input matrix size, memory bandwidth, and thread divergence. Our model offers accurate predictions of execution time by leveraging differential equations validated through simulations and experiments. The insights gained from this model not only enhance our understanding of warp specialization techniques but also have practical implications for optimizing GPU-accelerated applications through compiler optimizations, kernel parameter tuning, and algorithm design.

cs.PL↗

arXiv2025

Acoustic-Driven Surface Cleaning with Millimeter-Sized Bubbles at Translational Resonance

Traditional surface cleaning methods often suffer from drawbacks such as chemical harshness, potential for surface damage, and high energy consumption. This study investigates an alternative approach: acoustic-driven surface cleaning using millimeter-sized bubbles excited at low, sub-cavitation frequencies. We identify and characterize a distinct translational resonance of these bubbles, occurring at significantly lower frequencies (e.g., 50 Hz for 1.3 mm diameter bubbles) than the Minnaert resonance for a bubble of the same size. Experiments reveal that at this translational resonance, stationary bubbles exhibit amplified lateral swaying, while bubbles sliding on an inclined surface display pronounced "stop-and-go" dynamics. The theoretical model treats the bubble as a forced, damped harmonic oscillator, where surface tension provides the restoring force and the inertia is dominated by the hydrodynamic added mass of the surrounding fluid. It accurately predicts the observed resonant frequency scaling with bubble size ($\propto R_0^{-3/2}$). Cleaning efficacy, assessed using protein-based artificial soil on glass slides, was improved by approximately 90\% when bubbles were driven at their translational resonant frequency compared to off-resonant frequencies or non-acoustic conditions. These findings demonstrate that leveraging translational resonance enhances bubble-induced shear and agitation, offering an effective and sustainable mechanism for surface cleaning.

cond-mat.soft↗