WaveletGAN improves GANs by homogenizing noise through multi-channel wavelet filtering.
problem Current noise generation models in GANs struggle with homogenizing noise, leading to low-fidelity samples.
method Proposes a multi-channel wavelet-based filtering method to homogenize noise in GANs.
result WaveletGAN generates high-fidelity samples with the smallest FIDs on Fashion-MNIST, KMNIST, and SVHN datasets.
Characterizes uncertainty in low-rank matrix completion with noisy data.
problem Uncertainty quantification in low-rank matrix completion with heterogeneous sub-exponential noise.
method Characterizes the distribution of estimated matrix entries under low-rank estimators with heterogeneous sub-exponential noise.
result Explicit formulas for the distribution of estimated matrix entries under Poisson and Binary noise.
This study shows how DDPM can be represented by the OU process.
problem Designing optimal noise schedules for DDPM.
method Formal equivalence between DDPM and OU process, heuristic designs based on Fisher Information.
result Fisher-Information-motivated schedule corresponds to cosine noise schedule.
Polynomial-time tester-learner for general halfspaces with Gaussian adversarial noise.
problem Learning general halfspaces with adversarial label noise.
method Reduction to testable learning of nearly homogeneous halfspaces.
result First polynomial time tester-learner for general halfspaces with dimension-independent misclassification error.
Neural networks can approximate positive homogeneous functions, especially with multiple hidden layers.
problem Approximating positive homogeneous functions with neural networks.
method Using scale-invariant ReLU networks with multiple hidden layers.
result Approximation of positive homogeneous functions is possible with neural networks, especially with two hidden layers.
The paper simplifies quickshift hyperparameter tuning for larger images.
problem Understanding and tuning hyperparameters for quickshift image segmentation.
method Theoretical analysis of a modified quickshift algorithm for homogeneous patches with i.i.d. noise.
result A heuristic to scale quickshift hyperparameters based on image size.
Efficient algorithm for halfspaces with specific noise conditions.
problem Learning halfspaces with Massart and Tsybakov noise.
method PAC active learning algorithm for d-dimensional halfspaces.
result Near-optimal label complexity under Massart noise and lower than passive learning under Tsybakov noise.
Study learning halfspaces with Massart noise under Gaussian distribution, improving previous results.
problem Learning halfspaces with Massart noise under Gaussian distribution, especially when the parameter is 1/2.
method Developed algorithms for general and homogeneous halfspaces with sample and computational complexities.
result Established qualitatively matching lower bounds for the complexities of learning algorithms.
Continuous-time analysis shows SGD with noise prefers flat minima.
problem Optimizing neural networks using SGD with noise.
method Continuous-time model for SGD with noise analysis.
result Optimization prefers flat minima in certain noise regimes.
New algorithm learns halfspaces with adversarial noise efficiently.
problem Learning halfspaces in the presence of adversarial noise.
method Polynomial-time Perceptron-like online active learning algorithm.
result Near-optimal label and sample complexity with isotropic log-concave marginal distribution.
Non-convex SGD learns halfspaces with adversarial label noise efficiently.
problem Agnostically learning halfspaces in adversarial label noise settings.
method Non-convex SGD optimization for halfspace learning.
result Non-convex SGD achieves misclassification error close to optimal with adversarial noise.
A homogeneously saturated equation for the time development of the price of a financial asset is presented and investigated for the pricing of European call options using noise that is distributed as a Student's t-distribution. In the limit that the saturation parameter of the equation equals zero, the standard model o…
Study on deep multi-head self-attention dynamics, proving homogenized limits under specific scalings.
problem Understanding the behavior of deep multi-head self-attention models as depth increases.
method Random model of deep multi-head self-attention, viewing depth as time, and analyzing the residual stream as a particle system.
result Homogenized limit of the dynamics, leading to deterministic or stochastic behavior depending on scaling, with implications for representation collapse.
We present a simple noise-robust margin-based active learning algorithm to find homogeneous (passing the origin) linear separators and analyze its error convergence when labels are corrupted by noise. We show that when the imposed noise satisfies the Tsybakov low noise condition (Mammen, Tsybakov, and others 1999; Tsyb…
New algorithms learn from comparisons to classify data robustly to noise.
problem Learning robust classifiers from noisy data efficiently.
method Introducing comparison queries to active learning, providing noise-tolerant classifiers.
result First time and query efficient algorithms for robust learning under bounded noise.
Improved sample complexity for learning halfspaces with malicious noise.
problem Efficiently learning halfspaces in the presence of malicious noise.
method New analysis of Awasthi et al. algorithm with matrix Chernoff inequality and localization schemes.
result Achieved near-optimal sample complexity of ildeO(d) for isotropic log-concave distributions. We prove a maximum principle for mild solutions to stochastic evolution equations with (locally) Lipschitz coefficients and Wiener noise on weighted L2 spaces. As an application, we provide sufficient conditions for the positivity of forward rates in the Heath-Jarrow-Morton model, considering the associated Musiela …
Efficiently learns halfspaces with malicious noise, near-optimal label complexity.
problem Learning s-sparse halfspaces under malicious label noise. method Active learning algorithm with instance reweighting and empirical risk minimization.
result Near-optimal label complexity of O(slog4d/ε) and noise tolerance Ω(ε). RCLA reduces noise in topological data analysis, preserving essential structure.
problem Noise in large datasets obscures topological features in persistent homology.
method Grid-based RCLA integrates data reduction and denoising with a threshold parameter.
result RCLA provides a theoretical guarantee and automatic parameter selection.
New test for SGD in binary classification reduces computation time.
problem Determining optimal stopping for SGD in binary classification.
method Proposes a new, simple, computationally inexpensive termination criterion for SGD.
result Termination criterion reduces expected misclassification probability.
Study near-optimal bounds for learning Gaussian halfspaces with random noise.
problem Learning general halfspaces with Gaussian distribution and random classification noise.
method Established nearly-matching algorithmic and SQ lower bounds, developed a computationally efficient learning algorithm.
result Sample complexity of learning algorithm is O(d/ε+d/(max{p,ε})2), SQ lower bound is Ω(d1/2/(max{p,ε})2). New analysis shows bias term affects conditions for benign overfitting in linear classifiers.
problem Understanding conditions for good generalization in linear classifiers with bias terms.
method Extending Hashimoto et al.'s results to include bias terms, analyzing covariance structure and label noise.
result Benign overfitting persists in linear classifiers with bias terms, with new constraints on data's covariance structure.
Most existing image denoising approaches assumed the noise to be homogeneous white Gaussian distributed with known intensity. However, in real noisy images, the noise models are usually unknown beforehand and can be much more complex. This paper addresses this problem and proposes a novel blind image denoising algorith…
Paper addresses identifiability and asymptotics of ODE systems from noisy data.
problem Identifying parameters and causal structure of linear ODE systems from discrete observations.
method Developed sufficient conditions for identifiability, proved consistency and asymptotic normality of NLS estimator, constructed confidence sets, and inferred causal structure.
result Consistent and asymptotically normal parameter estimator for linear ODE systems under mild conditions.
Adaptive denoising models adjust the number of steps based on noise level.
problem Generating data with lower intrinsic dimensions.
method Adaptive diffusion models using Doob's h-transform to terminate at a random time.
result Adaptive models simplify termination to a first-hitting rule, enhancing adaptability.
FEDMD-NFDP improves federated learning privacy without sacrificing performance.
problem Privacy leakage in federated learning when sharing predictions.
method Noise-Free Differential Privacy (NFDP) applied to federated model distillation.
result FEDMD-NFDP achieves comparable utility and privacy guarantees.
New estimator robust to adversarial noise and data heterogeneity.
problem Sensitive to adversarial noise and poor performance with heterogeneous data.
method Distributionally robust estimator minimizing worst-case conditional expected loss over adversarial distributions.
result Efficiently finds non-parametric local estimates via convex optimization.
Proposes CDTD, a diffusion model for mixed-type tabular data.
problem Adapting diffusion models to mixed-type tabular data.
method Score matching and score interpolation for continuous features, adaptive noise schedules for categorical features.
result Consistently outperforms state-of-the-art models in mixed-type tabular data.
This paper sets fundamental limits for rank-one matrix estimation with varying noise levels.
problem Estimating a rank-one matrix from Gaussian observations with different noise levels across blocks.
method Novel reduction from heterogeneous noise to homogeneous noise, proving asymptotic error bounds.
result Asymptotically exact formulas for minimum mean-squared error in estimating rank-one matrix and factors.
Exact learning of tree-structured models with side info and noise.
problem Learning tree-structured graphical models with side information and noise.
method Probabilistic tools from strong large deviations theory.
result Exact asymptotics of structure learning from samples.
CDC-FM improves generative model quality-generalization tradeoff by regularizing with geometry-aware noise.
problem Tradeoff between high sample quality and memorization in deep generative models.
method Introduces Carré du champ flow matching (CDC-FM) that replaces homogeneous noise with anisotropic Gaussian noise capturing latent data manifold geometry.
result CDC-FM consistently offers better quality-generalization tradeoff across diverse datasets and architectures.
It has been a long-standing problem to efficiently learn a halfspace using as few labels as possible in the presence of noise. In this work, we propose an efficient Perceptron-based algorithm for actively learning homogeneous halfspaces under the uniform distribution over the unit sphere. Under the bounded noise condit…
Bayesian optimisation tackles stochastic MPC hyper-parameter tuning.
problem Fine-tuning hyper-parameters in stochastic MPC models.
method Heteroscedastic Bayesian optimisation framework.
result Framework effectively tunes hyper-parameters in control problems.
Study on sparse recovery with mixed-quality data, establishing sample-size conditions.
problem Sparse recovery with heterogeneous noise from high- and low-quality sources.
method Establishes linear trade-off for sufficient conditions, analyzes LASSO algorithm.
result Linear trade-off for sufficient conditions, robustness of LASSO to data heterogeneity.
In rank aggregation (RA), a collection of preferences from different users are summarized into a total order under the assumption of homogeneity of users. Model misspecification in RA arises since the homogeneity assumption fails to be satisfied in the complex real-world situation. Existing robust RAs usually resort to…
Algorithm learns halfspaces with Tsybakov noise in polynomial time.
problem PAC learning halfspaces with adversarial noise.
method Reduction to certifying non-optimality, iterative process, warm-start algorithm.
result First polynomial-time algorithm for learning halfspaces with Tsybakov noise.
Efficiently learns sparse halfspaces with noisy labels.
problem Learning sparse halfspaces with arbitrary bounded noise.
method Polynomial time algorithm for active learning with improved label complexity.
result First efficient algorithm with label complexity polynomial in 1−2η1. Introduces new types of homogeneous spaces and their properties.
problem Defining and understanding new types of homogeneous spaces.
method Introducing and analyzing (strongly) (Θ-)discrete homogeneous spaces. result Discovers relationships between new and existing homogeneous space types.
We address the problem of estimating the parameters of a time-homogeneous Markov chain given only noisy, aggregate data. This arises when a population of individuals behave independently according to a Markov chain, but individual sample paths cannot be observed due to limitations of the observation process or the need…
The paper connects flatness to generalization in learning multi-index models with neural networks.
problem Understanding the generalization of non-convex neural networks using flatness measures.
method Analyzes 2-layer non-convex homogeneous neural networks and their connection to multi-index models.
result Flattest interpolators achieve small population loss and generalize well, establishing a direct link between flatness and generalization.
Introduces homogeneity supermanifolds for studying graded structures.
problem Graded structures on supermanifolds.
method Homogeneity degrees and weight vector field.
result Proofs of homogeneous Poincaré Lemma, Frobenius Theorem, and Darboux Theorem.
Recently, it is shown that each regular homogeneous Finsler space M admits at least one homogeneous geodesic through any point o∈M. The purpose of this article is to study the existence of homogeneous geodesics on singular homogeneous (α,β)-spaces, specially, homogeneous Kropina spaces. We show that any homoge…
In this paper, we study homogeneous geodesics in homogeneous Finsler spaces. We first give a simple criterion that characterizes geodesic vectors. We show that the geodesics on a Lie group, relative to a bi-invariant Finsler metric, are the cosets of the one-parameter subgroups. The existence of infinitely many homogen…
We prove that the Penrose limit of a spacetime along a homogeneous geodesic is a homogeneous plane wave spacetime and that the Penrose limit of a reductive homogeneous spacetime along a homogeneous geodesic is a Cahen--Wallach space. We then consider several homogenous examples to show that these results are indeed sha…
We prove that under some purely algebraic conditions every locally homogeneous structure modelled on some homogeneous space is induced by a locally homogeneous structure modelled on a different homogeneous space.
New algorithm learns PTFs with noisy data efficiently.
problem Learning low-degree PTFs with noisy data efficiently.
method Structural result and novel robust Chow vector estimation.
result PAC learns PTFs with nasty noise using efficient samples.
Our purpose is to use a Darboux homogenous derivative to understand the harmonic maps with values in homogeneous space. We present a characterization of these harmonic maps from the geometry of homogeneous space. Furthermore, our work covers all type of invariant geometry in homogeneous space.
We show that a Lorentzian homogeneous space admitting a homogeneous structure of type T1 + T3 is either a (locally) symmetric space or a singular homogeneous plane wave.