Searcharxiv⌕ Search

arXiv subjects

Kangning Wang

Publications and source records attributed to Kangning Wang.

At least 19 recordsLinked to original sources
arXiv2026

Dense Language Generation Made Simple: Deterministic, Randomized, and Multi-Order Algorithms

Language generation in the limit is a theoretical framework for studying how a generator can learn to produce new valid strings from a stream of positive examples. In this model, an adversary chooses an unknown language from a countable family and enumerates its elements in an arbitrary order, while the generator must eventually output only elements of the language that have not yet appeared in the enumeration. Reliable generation is thus formalized through two eventual guarantees: validity and novelty relative to the observed data. To further quantify the breadth of the generator's outputs, Kleinberg and Wei (FOCS 2025, STOC 2026) introduced lower density as a measure of output coverage. Given an order representing the importance or relevance of possible outputs, lower density is the asymptotic lower bound, as $n$ grows, on the fraction of the first $n$ elements of the target language that the generator outputs before they appear in the data. Kleinberg and Wei showed that $1/2$ is the optimal lower-density guarantee for deterministic algorithms. We develop a simple and unified framework for obtaining optimal lower-density guarantees. We first give a deterministic algorithm that recovers the optimal guarantee of $1/2$ with a significantly simpler analysis than prior work. We then demonstrate the flexibility of our framework through two extensions. First, against an oblivious adversary, randomization raises the optimal guarantee to $1-1/e$. Second, for any finite collection of orders, the optimal deterministic and randomized guarantees can be achieved simultaneously with respect to every order, so accommodating multiple notions of importance or relevance entails no loss in the optimal guarantee.

cs.DS↗
arXiv2026

Stable Voting Rules on the Edge of Optimal Metric Distortion

We prove the existence of a randomized voting rule with metric distortion at most $2.1248$, within $0.013$ of the lower bound of $2.11264$. Our rule comes from a generalization of \emph{stable $k$-lotteries} developed in the context of committee selection. In contrast to prior work, our rule samples from a single distribution derived from a zero-sum game, without mixing between voting rules. Our result also gives sharp distortion bounds for stable $k$-lotteries. In particular we show that stable $2$-lotteries have distortion $7/3$, despite only relying on aggregate preferences over triples of candidates, and that stable $2$-lotteries are optimal in this class of voting rules.

cs.GT↗
arXiv2026

Spectrum Is Not Enough: A Random-Matrix Account of Data-Free Preconditioning for Differentially Private Learning

At a fixed privacy budget, curvature is exactly the object the budget makes unavailable. A recent answer estimates it from synthetic probes, at neither privacy cost nor distribution shift, and validates a probe by the eigenvalue decay it reproduces. That test reads the spectrum, not the basis, and what a probe reconstructs is unknown. This paper gives a random-matrix account of data-free preconditioning, organized by one dichotomy. Of the two Kronecker factors, the error-signal factor $ G $ and the architecture-determined bulk of the activation factor $ A $ are reconstructible without data up to an explicit error-energy bound; only the data-induced spikes of $ A $ are not. We verify that bound with zero violations along a full training trajectory, though it stays one to nearly three orders of magnitude above the gap it bounds. We locate the failure boundary at a Baik-Ben Arous-Péché threshold: a bulk-only probe suffers an exact damage $s^2/(1-s^2)$ from a spike of strength $s^2$, invisible once its amplitude exceeds the scaled-bulk threshold $( \sqrt {c}/(1+ \sqrt {c}))^{1/2}$, $c = d/n$. The test in use is basis-blind: rotating only the probe eigenbasis at a near-exact matched spectrum inflates the residual by $2.3 \times $ to $89.8 \times $, and a closed-form volume law fixes the within-spectrum ordering of the critical volume while a two-oracle construction proves that no functional of the probe spectrum fixes its magnitude. Over forty seeds on three modalities, per-layer tuning does not transfer to accuracy, no data-free arm beats the flat probe, public-data curvature does on both modalities tested, and the ordering inverts on PathMNIST under real DP noise. The account yields a probe-design protocol and falsifiable predictions for the regimes where data-free curvature can be trusted.

cs.LG↗
arXiv2026

Persuasion by Parts

Classical Bayesian persuasion assumes that an information designer can condition signals on the entire state. We propose persuasion by parts. In this model, the receiver's payoff from acting is $X = \sum_{i=1}^n X_i$ for independent coordinates $X_1,\ldots,X_n$ observed by separate sources. The designer commits in advance to a product experiment, in which each source $i$ can condition its signal only on $X_i$. Given the signals, the receiver computes her posterior mean $y$ of $X$ and acts with probability $g(y)$, where $g\colon \mathbb{R} \to [0,1]$ is a nondecreasing function. The designer aims to maximize the probability of action. Let $V_{\mathrm{prod}}(g)$ and $V_{\mathrm{joint}}(g)$ be the supremum probabilities of action under persuasion by parts and under joint persuasion, respectively. When the designer knows $g$, we show $$ V_{\mathrm{prod}}(g) \;\ge\; c\,V_{\mathrm{joint}}(g)^2 \qquad\text{for every nondecreasing } g\colon \mathbb{R} \to [0,1], $$ where $c > 0$ is an absolute constant independent of $n$ and the prior; the exponent $2$ is tight. When $g$ is unknown, we construct a product experiment $Π$ from the prior alone, whose probability of action $V_Π(g)$ satisfies $$ V_Π(g) \;\ge\; c_\varepsilon\,V_{\mathrm{joint}}(g)^{2 + \varepsilon} \qquad\text{for every } \varepsilon > 0 \text{ and every nondecreasing } g\colon \mathbb{R} \to [0,1], $$ where $c_\varepsilon > 0$ depends only on $\varepsilon$.

cs.GT↗
arXiv2026

A Geometric Analysis of Gains from Trade

We provide a geometric proof that the random proposer mechanism is a $4$-approximation to the first-best gains from trade in bilateral exchange. We then refine this geometric analysis to recover the $3.147$-approximation guarantee previously established by Fei (2022).

cs.GT↗
arXiv2026

NeuroDETR: Multiscale Discrete Spatiotemporal Tokenization for Asynchronous EEG Event Detection

Asynchronous EEG event detection supports practical brain-computer interfaces by identifying event classes and temporal boundaries directly from continuous recordings without predefined event boundaries at inference time. The primary challenge lies in extracting event-related patterns embedded in ongoing background activity. To address this, we propose \textbf{NeuroDETR}, a discrete spatiotemporal multiscale framework that combines structured tokenization with event-aware feature refinement. Multiscale temporal codebooks capture brief responses and sustained dynamics, while Spatial-Pyramid VQ hierarchically encodes spatial structure across EEG channels. These complementary representations form a compact event memory for jointly classifying events and estimating their onsets and offsets. Before tokenization, we apply FOCAL, an event-aware sparse attention module that uses predicted event presence to guide temporal feature refinement and spatial aggregation, emphasizing likely event periods while preserving context across the recording. Experiments on eight EEG datasets that span diverse paradigms demonstrate state-of-the-art performance. These findings provide a basis for the development of BCI systems that recognize meaningful neural activity during continuous interaction and monitoring.

cs.LG↗
arXiv2026

Online Matching in Convex Bipartite Graphs

Online resource-allocation systems, like outpatient scheduling and spectrum allocation, often assign sequentially arriving requests to an ordered pool of scarce resources, where each request accepts a contiguous interval of feasible options. We study the resulting online matching problem on convex bipartite graphs under irrevocable decisions and adversarial arrivals. We first show that convexity alone does not improve the classic worst-case guarantee of 1-1/e, achieved by Ranking. We then consider the uniform-length model, in which every online request has exactly d consecutive offline neighbors. We propose Flip, which uses one random bit to commit ex-ante to either earliest-feasible assignment or latest-feasible assignment. Although either natural deterministic policy can waste capacity and be asymptotically only 1/2-competitive, we show that their randomized mixture is 2/3-competitive. This guarantee is tight for Flip and remains valid against a semi-adaptive adversary that observes the selected policy before choosing the arrival order. We also prove that no randomized online algorithm can achieve a competitive ratio strictly larger than 3/4 in the uniform-length model.

cs.DS↗
arXiv2026

CRISP: Calibration-Aware Visual State Space Duality for Remote Sensing Semantic Segmentation

State space models, especially Visual State Space Duality (VSSD), have emerged as efficient linear-time alternatives to Transformers for dense visual tasks. However, we observe that VSSD compresses spatial context into a global aggregation that suppresses high-frequency responses, causing excessive boundary smoothing in remote sensing semantic segmentation. To address this, we propose CRISP, a calibration framework with two components. Its core, the Duality Calibration Operator (DCO), restores local contrast and boundary responses through residual injection and frequency calibration within the VSSD backbone, without altering its linear complexity. To retain the recovered detail, an Orthogonal Multi-Prototype (OMP) head assigns multiple orthogonally constrained prototypes per class to model large intra-class variance. Extensive experiments on Potsdam, Vaihingen, and LoveDA show that, with approximately 30M parameters, CRISP achieves consistent gains in mean F1 (mF) and mIoU while remaining competitive with state-of-the-art methods. Code is available at https://github.com/crazylifeha/CRISP.

cs.CV↗
arXiv2026

Pessimal Elections for Approximately Dominating Sets

Condorcet's paradox is a foundational result in social choice theory, showing that no matter which candidate wins an election, a majority of voters may prefer some losing candidate. Worse still, even if the election can choose a committee of $k$ winners, some loser may beat every winner in a majority vote. Recent work showed that this obstruction can be sidestepped by relaxing the majority threshold. For all $\varepsilon > 0$, any election can select a committee of $O(1/\varepsilon^2)$ winners such that no loser is preferred to every winner by $\frac12 + \varepsilon$ fraction of voters. We present a simple construction, found by GPT-5.6 Sol Ultra, which proves that this result is tight up to a constant factor.

cs.GT↗
arXiv2026

Distortion of Metric Voting with Bounded Randomness

We study the design of voting rules in the metric distortion framework. It is known that any deterministic rule suffers distortion of at least $3$, and that randomized rules can achieve distortion strictly less than $3$, often at the cost of reduced transparency and interpretability. In this work, we explore the trade-off between these paradigms by asking whether it is possible to break the distortion barrier of $3$ using only "bounded" randomness. We answer in the affirmative by presenting a voting rule that (1) achieves distortion of at most $3 - \varepsilon$ for some absolute constant $\varepsilon > 0$, and (2) selects a winner uniformly at random from a deterministically identified list of constant size. Our analysis builds on new structural results for the distortion and approximation of Maximal Lotteries and Stable Lotteries.

cs.GT↗
arXiv2026

The Price of Competitive Information Disclosure

In many decision-making scenarios, individuals strategically choose what information to disclose to optimize their own outcomes. It is unclear whether such strategic information disclosure can lead to good societal outcomes. To address this question, we consider a competitive Bayesian persuasion model in which multiple agents selectively disclose information about their qualities to a principal, who aims to choose the candidates with the highest qualities. Using the price-of-anarchy framework, we quantify the inefficiency of such strategic disclosure. We show that the price of anarchy is at most a constant when the agents have independent quality distributions, even if their utility functions are heterogeneous. This result provides the first theoretical guarantee on the limits of inefficiency in Bayesian persuasion with competitive information disclosure.

cs.GT↗
arXiv2026

Approximating Gains-from-Trade in Matching Markets

A central challenge in mechanism design is to develop truthful trade mechanisms that maximize the expected gains-from-trade (GFT) in two-sided markets with strategic agents. As achieving the full GFT is generally impossible, much of the literature has focused on constant-factor approximations. Existing results, however, are limited to the highly structured settings of bilateral trade and double auctions, in which every buyer can trade with every seller. We consider the significantly more general setting of two-sided matching markets with arbitrary downward-closed constraints on the family of allowed matchings. For this setting, we present a simple randomized truthful mechanism that guarantees a constant-factor approximation to the optimal expected GFT. This result also resolves an open problem posed by Cai, Goldner, Ma, and Zhao (2021).

cs.GT↗
arXiv2026

Additively Competitive Secretaries

In the secretary problem, a set of secretary candidates arrive in a uniformly random order and reveal their values one by one. A company, who can only hire one candidate and hopes to maximize the expected value of its hire, needs to make irrevocable online decisions about whether to hire the current candidate. The classical framework of evaluating a policy is to compute its worst-case competitive ratio against the optimal solution in hindsight, and there the best policy -- the ``$1/e$ law'' -- has a competitive ratio of $1/e$. We propose an alternative evaluation framework through the lens of regret -- the worst-case additive difference between the optimal hindsight solution and the expected performance of the policy, assuming that each value is normalized between $0$ and $1$. The $1/e$ law for the classical framework has a regret of $1 - 1/e \approx 0.632$; by contrast, we show that the class of ``pricing curves'' algorithms can guarantee a regret of at most $1/4 = 0.25$ (which is tight within the class), and the class of ``best-only pricing curves'' algorithms can guarantee a regret of at most $0.190$ (with a lower bound of $0.171$). In addition, we show that in general, no policy can give a regret guarantee better than $0.152$. Finally, we discuss other objectives in our regret-minimization framework, such as selecting the top-$k$ candidates for $k > 1$, or maximizing revenue during the selection process.

cs.DS↗
arXiv2026

Winning in the Limit: Average-Case Committee Selection with Many Candidates

We study the committee selection problem in the canonical impartial culture model with a large number of voters and an even larger candidate set. Here, each voter independently reports a uniformly random preference order over the candidates. For a fixed committee size $k$, we ask when a committee can collectively beat every candidate outside the committee by a prescribed majority level $α$. We focus on two natural notions of collective dominance, $α$-winning and $α$-dominating sets, and we identify sharp threshold phenomena for both of them using probabilistic methods, duality arguments, and rounding techniques. We first consider $α$-winning sets. A set $S$ of $k$ candidates is $α$-winning if, for every outside candidate $a \notin S$, at least an $α$-fraction of voters rank some member of $S$ above $a$. We show a sharp threshold at \[ α_{\mathrm{win}}^\star = 1 - \frac{1}{k}. \] Specifically, an $α$-winning set of size $k$ exists with high probability when $α< α_{\mathrm{win}}^\star$, and is unlikely to exist when $α> α_{\mathrm{win}}^\star$. We then study the stronger notion of $α$-dominating sets. A set $S$ of $k$ candidates is $α$-dominating if, for every outside candidate $a \notin S$, there exists a single committee member $b \in S$ such that at least an $α$-fraction of voters prefer $b$ to $a$. Here we establish an analogous sharp threshold at \[ α_{\mathrm{dom}}^\star = \frac{1}{2} - \frac{1}{2k}. \] As a corollary, our analysis yields an impossibility result for $α$-dominating sets: for every $k$ and every $α> α_{\mathrm{dom}}^\star = 1 / 2 - 1 / (2k)$, there exist preference profiles that admit no $α$-dominating set of size $k$. This corollary improves the best previously known bounds for all $k \geq 2$.

cs.GT↗
arXiv2026

Auditing for Core Stability in Participatory Budgeting

We consider the participatory budgeting problem where each of $n$ voters specifies additive utilities over $m$ candidate projects with given sizes, and the goal is to choose a subset of projects (i.e., a committee) with total size at most $k$. Participatory budgeting mathematically generalizes multiwinner elections, and both have received great attention in computational social choice recently. A well-studied notion of group fairness in this setting is core stability: Each voter is assigned an "entitlement" of $\frac{k}{n}$, so that a subset $S$ of voters can pay for a committee of size at most $|S| \cdot \frac{k}{n}$. A given committee is in the core if no subset of voters can pay for another committee that provides each of them strictly larger utility. This provides proportional representation to all voters in a strong sense. In this paper, we study the following auditing question: Given a committee computed by some preference aggregation method, how close is it to the core? Concretely, how much does the entitlement of each voter need to be scaled down by, so that the core property subsequently holds? As our main contribution, we present computational hardness results for this problem, as well as a logarithmic approximation algorithm via linear program rounding. We show that our analysis is tight against the linear programming bound. Additionally, we consider two related notions of group fairness that have similar audit properties. The first is Lindahl priceability, which audits the closeness of a committee to a market clearing solution. We show that this is related to the linear programming relaxation of auditing the core, leading to efficient exact and approximation algorithms for auditing. The second is a novel weakening of the core that we term the sub-core, and we present computational results for auditing this notion as well.

cs.GT↗
arXiv2025

Strategyproof Tournament Rules for Teams with a Constant Degree of Selfishness

We revisit the well-studied problem of designing fair and manipulation-resistant tournament rules. In this problem, we seek a mechanism that (probabilistically) identifies the winner of a tournament after observing round-robin play among $n$ teams in a league. Such a mechanism should satisfy the natural properties of monotonicity and Condorcet consistency. Moreover, from the league's perspective, the winner-determination tournament rule should be strategyproof, meaning that no team can do better by losing a game on purpose. Past work considered settings in which each team is fully selfish, caring only about its own probability of winning, and settings in which each team is fully selfless, caring only about the total winning probability of itself and the team to which it deliberately loses. More recently, researchers considered a mixture of these two settings with a parameter $λ$. Intermediate selfishness $λ$ means that a team will not lose on purpose unless its pair gains at least $λs$ winning probability, where $s$ is the individual team's sacrifice from its own winning probability. All of the dozens of previously known tournament rules require $λ= Ω(n)$ to be strategyproof, and it has been an open problem to find such a rule with the smallest $λ$. In this work, we make significant progress by designing a tournament rule that is strategyproof with $λ= 11$. Along the way, we propose a new notion of multiplicative pairwise non-manipulability that ensures that two teams cannot manipulate the outcome of a game to increase the sum of their winning probabilities by more than a multiplicative factor $δ$ and provide a rule which is multiplicatively pairwise non-manipulable for $δ= 3.5$.

cs.GT↗
arXiv2025

Approximately Dominating Sets in Elections

Condorcet's paradox is a fundamental result in social choice theory which states that there exist elections in which, no matter which candidate wins, a majority of voters prefer a different candidate. In fact, even if we can select any $k$ winners, there still may exist another candidate that would beat each of the winners in a majority vote. That is, elections may require arbitrarily large dominating sets. We show that approximately dominating sets of constant size always exist. In particular, for every $\varepsilon > 0$, every election (irrespective of the number of voters or candidates) can select $O(\frac{1}{\varepsilon ^2})$ winners such that no other candidate beats each of the winners by a margin of more than $\varepsilon$ fraction of voters. Our proof uses a simple probabilistic construction using samples from a maximal lottery, a well-studied distribution over candidates derived from the Nash equilibrium of a two-player game. In stark contrast to general approximate equilibria, which may require support logarithmic in the number of pure strategies, we show that maximal lotteries can be approximated with constant support size. These approximate maximal lotteries may be of independent interest.

cs.GT↗