Optimal privacy-preserving algorithm for solving saddle point problems.
problem Solving convex-concave stochastic saddle point problems under differential privacy constraints.
method Recursive regularization technique repurposed for saddle point problems, achieving strong gap rate of O(1/√n + √d/nε).
result Achieves nearly optimal strong gap rate of O(1/√n + √d/nε) with gradient complexity O(min{n^2ε^(1.5)/√d, n^(3/2)}).
Random surfaces have a strong spectral gap with polynomial rate.
problem Understanding spectral gaps in random hyperbolic surfaces.
method Adapting polynomial method for random matrices to Laplacian on surfaces.
result Laplacian spectral gap at least 1/4 - O(1/g^c) for large g.
We present a data-driven framework called generative adversarial privacy (GAP). Inspired by recent advancements in generative adversarial networks (GANs), GAP allows the data holder to learn the privatization mechanism directly from the data. Under GAP, finding the optimal privacy mechanism is formulated as a constrain…
Uniform counting formulas for orthogeodesics in Kleinian groups converge.
problem Counting orthogeodesics in Kleinian groups converging to a limit.
method Spectral gap of the limit manifold and geodesic flow mixing property.
result Asymptotically uniform counting formulas for orthogeodesics.
Epoch gradient descent method (a.k.a. Epoch-GD) proposed by Hazan and Kale (2011) was deemed a breakthrough for stochastic strongly convex minimization, which achieves the optimal convergence rate of O(1/T) with T iterative updates for the {\it objective gap}. However, its extension to solving stochastic min-max pr…
For a second order operator on a compact manifold satisfying the strong Hörmander condition, we give a bound for the spectral gap analogous to the Lichnerowicz estimate for the Laplacian of a Riemannian manifold. We consider a wide class of such operators which includes horizontal lifts of the Laplacian on Riemannian s…
Lasso performs poorly with correlated covariates, but a rescaled approach fixes this.
problem Lasso's performance degrades with correlated covariates, leading to inefficiency.
method Proposes a rescaling method for Lasso to handle correlated covariates effectively.
result Rescaled Lasso provides strong provable guarantees for estimation with quadratic sample complexity.
In this paper we generalize the framework of the feasible descent method (FDM) to a randomized (R-FDM) and a coordinate-wise random feasible descent method (RC-FDM) framework. We show that the famous SDCA algorithm for optimizing the SVM dual problem, or the stochastic coordinate descent method for the LASSO problem, f…
The strong symmetric genus of a finite group is the minimum genus of a compact Riemann surface on which the group acts as a group of automorphisms preserving orientation. A characterization of the infinite number of groups with strong symmetric genus zero and one is well-known and the problem is finite for each strong …
W2S FT often outperforms weak teachers due to low intrinsic dimensionality.
problem Understanding why weak-to-strong finetuning outperforms weak models.
method Analyzing W2S in ridgeless regression setting, focusing on variance reduction.
result Weak teacher's variance is inherited by strong student in shared feature subspace, reduced in discrepancy subspace.
Unified framework for corruption-robust linear bandits with optimal gap-dependent misspecification bounds.
problem Effective learning in linear bandits with corrupted rewards across different corruption models.
method Unified framework for analyzing strong and weak corruption, connection to gap-dependent misspecification, and specialized algorithm.
result Optimal bounds for gap-dependent misspecification in linear bandits.
Develops correlation number for specific potentials and Hitchin representations.
problem Analyzing correlation numbers for potentials with entropy gaps and Hitchin representations.
method Defines a correlation number for pairs of cusped Hitchin representations and explores its connection to the Manhattan curve.
result Establishes a connection between the correlation number and the Manhattan curve, revealing rigidity properties.
The study improves fundamental gap estimates for surfaces with non-constant positive curvature.
problem Estimating the fundamental gap for surfaces with non-constant positive curvature.
method Using a two-point maximum principle, the study establishes log-concavity and fundamental gap estimates.
result Corresponding log-concavity and fundamental gap estimates for surfaces with non-constant positive curvature are derived.
New convergence rates for shuffling gradient methods without strong convexity.
problem Theoretical gap between shuffling gradient methods' empirical success and established convergence rates.
method Proved last-iterate convergence rates for shuffling gradient methods using function value gap.
result First last-iterate convergence rates for shuffling gradient methods without strong convexity.
New research shows label refinement and weak training have limitations for aligning LLMs.
problem Limitations of refinement methods for aligning large language models.
method Analyzed probabilistic assumptions and alternative approaches to label refinement and weak training.
result Label refinement and weak training suffer from irreducible error, leaving a performance gap.
New study on neural network calibration, linking it to generalization gap.
problem Neural networks lack strong guarantees on calibration.
method Decomposed calibration error into train set and generalization gap.
result Models with small generalization gap are well-calibrated.
Uniformly random permutations converge to regular representation on surface groups.
problem Understanding the behavior of random homomorphisms to symmetric groups.
method Polynomial approximation and random walk analysis.
result Strong convergence of random representations to regular representation.
KZImputer improves time series data quality with adaptive imputation for short to medium-sized gaps.
problem Missing data in time series analysis.
method Adaptive imputation method for univariate time series with tailored strategies for different gap positions.
result KZImputer achieves strong performance, especially for high missingness rates and high-sparsity regimes.
New method explains ML performance gaps without causal knowledge.
problem Understanding why ML algorithms perform differently across domains.
method Nonparametric hierarchical decomposition framework.
result Detailed variable-level explanations for performance gaps.
We obtain option pricing formulas for stock price models in which the drift and volatility terms are functionals of a continuous history of the stock prices. That is, the stock dynamics follows a nonlinear stochastic functional differential equation. A model with full memory is obtained via approximation through a stoc…
The study uses Random Matrix Theory to identify structural changes in stock markets during shocks.
problem Understanding structural changes in stock markets during exogenous shocks.
method Random Matrix Theory and complexity gap analysis.
result The complexity gap collapses during shocks, indicating strong synchronization, and widens before shocks, signaling a rich structure.
Sharp Hardy and spectral gap inequalities found on special irreversible Finsler manifolds.
problem Understanding Hardy and spectral gap inequalities on irreversible Finsler manifolds.
method Finslerian extension of the method of Riccati pairs.
result Sharpness of Hardy and spectral gap inequalities on specific Finsler manifolds.
Several recently proposed architectures of neural networks such as ResNeXt, Inception, Xception, SqueezeNet and Wide ResNet are based on the designing idea of having multiple branches and have demonstrated improved performance in many applications. We show that one cause for such success is due to the fact that the mul…
Study on private algorithms for saddle point and variational inequalities, improving efficiency and applicability.
problem Private algorithms for solving saddle point and variational inequalities under differential privacy constraints.
method Developed a recursive regularization algorithm for both Euclidean and non-Euclidean setups, providing bounds on strong SP-gap and VI-gap.
result Achieved nearly optimal rates for strong SP-gap and VI-gap under (ε,δ)-differential privacy, applicable to various p,q setups. This study bridges the gap between spatial and spectral GNNs.
problem Lack of direct comparison and cross-reference of existing GNNs.
method Systematically categorizes and examines GNNs into spatial and spectral domains.
result Establishes a strong relationship between spatial and spectral GNNs.
Paper explores generalization of minimax learners, proposing a new metric.
problem Understanding how minimax learners perform on unseen data.
method Proposes a new metric, the primal gap, to study generalization of minimax learners.
result Derives generalization error bounds for the primal gap in nonconvex-concave settings.
New method closes certification gap for adversarially trained models.
problem Certifying robustness of adversarially trained neural networks.
method Nonconvex low-rank SDP relaxation with polynomial-time optimization.
result Strong certifications comparable to SDP methods, but with fewer variables.
We consider a new family of operators for reinforcement learning with the goal of alleviating the negative effects and becoming more robust to approximation or estimation errors. Various theoretical results are established, which include showing on a sample path basis that our family of operators preserve optimality an…
New algorithm solves saddle point problems in Banach spaces.
problem Solving saddle point problems in real reflexive Banach spaces.
method Stochastic Bregman Primal-Dual Splitting Algorithm with relative smoothness and strong convexity assumptions.
result Almost sure convergence to saddle points under various conditions.
Hybrid framework injects TSLM insights into GRLM for robust time-series reasoning.
problem Lack of domain-specific knowledge in large language models for time-series reasoning.
method Hybrid knowledge-injection framework combining RLVR for efficient knowledge transfer.
result Consistently outperforms existing models by 7.9%-26.1% on multivariate time-series benchmarks.
FraudTransformer detects payment fraud by preserving event order and time gaps.
problem Detecting payment fraud in real-world banking streams with irregular time gaps.
method Augments a GPT-style architecture with a dedicated time encoder and a learned positional encoder.
result FraudTransformer outperforms classical and transformer baselines, achieving highest AUROC and PRAUC on held-out test set.
Proves pinched Ricci curvature conjecture in all dimensions.
problem Pinched Ricci curvature conjecture in complete non-compact manifolds.
method Develops a lifting technique to handle collapsed manifolds and proves a Ricci flow curvature estimate.
result Direct analogue of Hamilton's result in all dimensions.
Two new algorithms solve privacy-constrained SVI and SSP problems.
problem Privacy-constrained stochastic variational inequality and saddle-point problems.
method Proposed Noisy Stochastic Extragradient (NSEG) and Noisy Inexact Stochastic Proximal Point (NISPP) algorithms.
result Optimal risk bounds for weak gap function with sampling with replacement.
Random Forests (RFs) are strong machine learning tools for classification and regression. However, they remain supervised algorithms, and no extension of RFs to the one-class setting has been proposed, except for techniques based on second-class sampling. This work fills this gap by proposing a natural methodology to e…
Mantis improves time series classification using a transformer model trained on synthetic data.
problem Insufficient application of foundation models to time series classification.
method Pre-trained transformer model on synthetic data, enhanced test-time methodology.
result Mantis achieves state-of-the-art performance across diverse datasets.
We address the problem of estimating the mixing time of a Markov chain from a single trajectory of observations. Unlike most previous works which employed Hilbert space methods to estimate spectral gaps, we opt for an approach based on contraction with respect to total variation. Specifically, we estimate the contracti…
We demonstrate, theoretically and empirically, that adversarial robustness can significantly benefit from semisupervised learning. Theoretically, we revisit the simple Gaussian model of Schmidt et al. that shows a sample complexity gap between standard and robust classification. We prove that unlabeled data bridges thi…
New Holder bounds improve variational inference by flattening thermodynamic curves.
problem Improving variational inference by addressing performance gaps between theory and practice.
method Generalizing thermodynamic integration to weighted Holder mean, introducing Holder bounds.
result Holder bounds promise a one-step approximation of exact marginal log-likelihood.
Study reveals bias in machine learning conference reviews.
problem Bias in machine learning conference review process.
method Comprehensive analysis of ICLR papers from 2017-2020.
result Strong institutional bias in accept/reject decisions.
New bounds on trajectory safety in training models with Langevin Dynamics.
problem Bounding the probability of a model's trajectory staying away from a designated failure region.
method Analyzes Langevin dynamics on smooth, strongly convex loss landscapes, introducing shape-free and local relaxation bounds.
result The in-set probability relaxes to the static value after a burn-in time of order d, using only the global spectral gap of the loss.
Study risk bounds for distributed ERM with general loss functions and hypothesis spaces.
problem Limited theoretical analysis for distributed ERM with general loss functions and hypothesis spaces.
method Derive tight risk bounds under assumptions on hypothesis space and loss function.
result Developed more general risk bound for distributed ERM without strong convexity restriction.
Sine activation functions enable two-layer neural networks to learn modular addition more efficiently.
problem Learning modular addition with two-layer neural networks.
method Introduced and analyzed sine activation functions, providing theoretical and empirical evidence.
result Sine activation functions allow for constant-width network realizations of modular addition, whereas ReLU networks require linear width scaling.
Survey of rigidity and gap phenomena in sphere-ball submanifolds.
problem Rigidity and gap phenomena in submanifolds of sphere and ball.
method Comparison of techniques, pinching and gap theorems, Morse index and topology.
result Free boundary condition in ball forces stronger rigidity than in sphere.
New graph feedback model for bandits with improved regret bounds.
problem Understanding how graph structure affects regret in bandit problems.
method Introduced fractional weak domination number and k-packing independence number to capture upper and lower bounds on regret. Used strong duality theorem to derive upper and lower bounds. result Proved general upper and lower bounds on regret for various graph structures, showing tightness up to a logarithmic factor.
The study finds that firm membership in flagship indices and TCFD endorsement are strong predictors of a wider Disclosure-Performance Gap.
problem The Aggregate Confusion hypothesis and the measurement of greenwashing in environmental disclosures.
method The study uses a Disclosure-Performance Gap (DPG) model to measure the divergence between voluntary environmental disclosures and realised emissions performance for 200 large European firms. The model selection process involved multiple stages and robust standard errors.
result Firm membership in flagship indices and TCFD endorsement are strong predictors of a wider gap, while renewable energy use and environmental capital expenditure significantly narrow the gap.
We decompose the evidence lower bound to show the existence of a term measuring the total correlation between latent variables. We use this to motivate our β-TCVAE (Total Correlation Variational Autoencoder), a refinement of the state-of-the-art β-VAE objective for learning disentangled representations, requiring n…
We present atomistic molecular dynamics simulations of two Polyethylene systems where all entanglements are trapped: a perfect network, and a melt with grafted chain ends. We examine microscopically at what level topological constraints can be considered as a collective entanglement effect, as in tube model theories, o…
Unified framework for causal inference under sample selection.
problem Causal inference under sample selection with treatment and outcome non-randomness.
method ForestRiesz estimator, Riesz representation framework.
result ForestRiesz estimator yields more stable treatment effect estimates than conventional double machine learning approaches.