This paper presents a set of formulas and equations to compute the longest counting sequence of convex polyominoes of degree of convexity at most 2.

The paper analyzes low-degree estimation thresholds for recovering hidden signals in planted hypergraphs and tensor PCA, establishing sharp phase transitions and providing polynomial-time recovery alg…

The paper improves Banaszczyk's inequality, providing a significantly better tail estimate for the discrete Gaussian measure on a lattice, which has applications in analyzing dual attacks against the…

The paper analyzes preference-shaped expected improvement criteria for Bayesian multiobjective optimization, precisely characterizing when transformations preserve key properties like exact computatio…

This paper settles the complexity of three sketching problems in graphs and distributions.

The paper develops a unified theoretical framework to systematically characterize the optimal privacy-utility trade-off (PUT) and optimal Local Differential Privacy (LDP) channels for general statisti…

This paper derives multivariate generating functions to refine the enumeration of Fibonacci polyominoes.

The paper characterizes the minimax optimal excess-risk rate for pure $\varepsilon$-DP stochastic convex optimization with heavy-tailed gradients, providing an algorithm that achieves this rate.

The paper analyzes the structured CVP distance on the log-unit lattice of cyclotomic fields, significantly reducing the conjectured CDPR factor for the ML-KEM cryptosystem from exponential to sub-poly…

This paper introduces a novel framework for differentially private sampling by using the Wasserstein distance as the utility measure, proposing the Wasserstein Projection Mechanism (WPM) to address li…

The paper introduces the $\alpha$-Wasserstein mechanism to achieve Rényi Pufferfish Privacy using Laplace and Gaussian noise, demonstrating that it generalizes existing privacy frameworks and reduces…

The paper establishes new hardness amplification results for Learning Parity with Noise (LPN) and its sparse variants, showing that solving the problem on a small fraction of instances implies solving…

The paper refutes Steurer's conjecture regarding the existence of large constant-separated sets within families of unit-norm vectors with low average correlation, using high-dimensional expanders to s…

This paper improves the theoretical bounds for estimating discrete probability distributions using the $\ell_\infty$ norm, resolving several open questions in the field.

The paper systematically studies the trade-offs between the number of slopes, bends per edge, and required area for planar drawings of bounded-degree graphs, providing new constructions for high-degre…

This paper develops a perturbation theory for spherical Hellinger-Kantorovich (SHK) gradient flows, providing explicit, time-dependent bounds on divergence metrics to guarantee differential privacy fo…

The paper establishes tight upper and lower bounds on the statistical cost of approximate machine unlearning for smooth strongly convex losses, showing that the optimal unlearning rate depends critica…

The paper introduces a unified theoretical framework for gradient aggregation in multi-objective optimization, establishing convergence rates and sufficient conditions for achieving Pareto stationarit…

The paper investigates the relationship between optimal proof systems and recursive jump operators, showing that while the existence of a jump operator rules out optimality, the converse is provably h…

The paper introduces an optimal black-box auditing framework using Donsker-Varadhan estimators to estimate Rényi differential privacy (RDP) guarantees for machine learning algorithms.