Develops a method to compute Morse homology for clean but not necessarily transverse intersections.
problem Computing Morse homology for clean but not necessarily transversely intersecting manifolds.
method Constructs minimal semi-global Kuranishi structures for moduli spaces of Morse trajectories, generalizing obstruction bundle gluing.
result Obtains iterated gluing equals simultaneous gluing, maintaining computability.
Paper computes Atiyah class for DG manifolds of amplitude +1.
problem Computing the Atiyah class for DG manifolds of specific amplitude.
method Computed the Atiyah class by encoding the derived intersection of sections and zero sections of vector bundles.
result Atiyah class vanishes if and only if the intersection is clean.
The study of quotient structures in multi-graded bundles, including double vector bundles.
problem Understanding quotients of multi-graded bundles, especially double vector bundles.
method Analyzing quotients as towers of affine bundles and constructing normal bundles.
result Any quotient of multi-graded bundles fits into a tower of affine bundles.
We prove: If a complete connected smooth surface M in euclidean 3-space has general position, intersects some plane along a clean figure-8 (a loop with total curvature zero) and all compact intersections with planes have central symmetry, then M is a (geometric) cylinder over some central figure-8. On the way, we estab…
This paper uses sheaf theory to constrain knot types in clean intersections.
problem Understanding constraints on knot types in clean intersections.
method Microlocal sheaf theory and 3-manifold theory.
result Existence of a surjective homomorphism preserving longitude and meridian.
We show that the cardinality of the transverse intersection of two compact exact Lagrangian submanifolds in a cotangent bundle is bounded from below by the dimension of the Hom space of sheaf quantizations of the Lagrangians in Tamarkin's category. Our sheaf-theoretic method can also deal with clean and degenerate Lagr…
Clean intersections of Lagrangian knots in 3D are impossible.
problem Prohibiting clean intersections of certain knots in 3D symplectic geometry.
method Symplectic field theory and algebraic constraints on augmentation varieties.
result No Hamiltonian diffeomorphism can cleanly intersect a specific type of knot's conormal bundle.
The paper studies knot types of clean intersections in a 3D space.
problem Identifying knot types in clean intersections.
method Using compactly supported Hamiltonian isotopy and DGA maps.
result Constraints on knot types of intersections.
Study of Poisson homeomorphisms and rigidity of coisotropic submanifolds.
problem Rigidity and non-rigidity phenomena in Poisson geometry.
method Study of Poisson homeomorphisms, use of clean intersection points, and analysis of characteristic partitions.
result Poisson homeomorphisms preserve symplectic foliations and coisotropic submanifolds are flexible.
Floer homotopy theory applies to Lagrangians, overcoming curvature issues.
problem Curvature phenomena in high dimensions for monotone Lagrangians.
method Introduces N-truncated, R-oriented flow categories and module prospectrum. result Well-defined invariants for closed embedded monotone Lagrangians.
A geometric method optimizes over the intersection of two manifolds.
problem Optimizing over the intersection of two manifolds with coupled geometry.
method Geometric method using retraction on one manifold and orthogonal updates.
result Convergence to first-order stationarity under intrinsic transversality.
New concept of coisotropic structures for differentiable stacks defined.
problem Defining coisotropic structures for differentiable stacks.
method Using twisted Dirac structures and Morita equivalences.
result 1-shifted coisotropic structures transfer through Morita equivalences.
Neural networks learn clean data patterns first, then noisy data, leading to improved performance initially but deteriorating later.
problem Improvement in prediction error on clean data during early training of neural networks with noisy labels.
method Theoretical analysis and experiments to explore the dynamics of gradient descent and the impact of clean and noisy data.
result Neural networks prioritize learning clean data patterns first, leading to improved performance initially but deteriorating later due to diminishing gradient dominance of clean samples over noisy ones.
The paper cleans label noise in supervised classification using Bernoulli sampling.
problem Label noise degrades supervised classifier performance.
method Proposes a label noise cleaning method based on Bernoulli random sampling.
result The method separates clean and noisy observations without prior label information.
This is primarily an expository note showing that earlier work of Lai on CR geometry provides a clean interpretation, in terms of a Gauss map, for an adjunction formula for embedded surfaces in an almost complex four manifold. We will see that if F is a surface with genus g in an almost complex four-manifold M, then 2 …
PClean automates Bayesian data cleaning for specific datasets.
problem Bayesian inference for diverse and complex data cleaning.
method Domain-specific probabilistic programming language with custom models and inference.
result PClean programs outperform general-purpose PPLs in accuracy and runtime.
It is known that evaluating a certain approximation to the Jones polynomial for the plat closure of a braid is a BQP-complete problem. That is, this problem exactly captures the power of the quantum circuit model. The one clean qubit model is a model of quantum computation in which all but one qubit starts in the maxim…
This paper presents a statistical method of single-channel speech enhancement that uses a variational autoencoder (VAE) as a prior distribution on clean speech. A standard approach to speech enhancement is to train a deep neural network (DNN) to take noisy speech as input and output clean speech. Although this supervis…
INN method refines clean labeled data from noisy labels.
problem Handling noisy labels in deep neural networks.
method INN method based on memorization effect at neighbor regions.
result INN method resolves memorization effect shortcomings.
Study improves resilience against adversarial clean-label attacks in real and noisy settings.
problem Ensuring accurate predictions in the presence of adversarial clean-label samples.
method Sequential learning from a stream of i.i.d. data, allowing abstention for uncertain predictions.
result Theoretical analysis and adaptations for the agnostic setting with a clean-label adversary and noise.
The graph-based semi-supervised label propagation algorithm has delivered impressive classification results. However, the estimated soft labels typically contain mixed signs and noise, which cause inaccurate predictions due to the lack of suitable constraints. Moreover, available methods typically calculate the weights…
Trimming helps in conformal prediction when it separates anomaly scores.
problem Effectiveness of trimming in conformal prediction under contamination.
method Analyse fixed-threshold trimming as a replacement of the contaminated calibration law with a retained law.
result Trimming helps when it separates anomaly scores, reducing clean-target coverage to a one-dimensional score-CDF transfer problem.
We construct a pair of compact, eight-dimensional, two-step Riemannian nilmanifolds M and M′ which are isospectral for the Laplace operator on functions and such that M has completely integrable geodesic flow in the sense of Liouville, while M′ has not. Moreover, for both manifolds we analyze the structure of t…
New method improves false-/true-positive-rate estimation in fraud detection with noisy labels.
problem Estimating FPR/TPR in fraud detection with class-conditional label noise.
method Directly cleaning model's validation data to de-correlate cleaning error with model scores.
result Improves accuracy of FPR/TPR estimates, especially in asymmetric label noise scenarios.
Bullseye Polytope improves clean-label poisoning attacks in transfer learning.
problem Poisoning neural networks with correctly labeled data.
method Creates poison images with centers close to target images in feature space.
result Improves attack success rate by 26.75% in end-to-end transfer learning.
Improved portfolio optimization method yields better risk-adjusted returns.
problem Optimizing global minimum variance portfolios with reduced risk.
method k-fold boosted k−BAHC covariance cleaning procedure for correlation matrices. result Our method outperforms other filtering methods in Sharpe ratios, despite higher turnover.
We apply basic statistical reasoning to signal reconstruction by machine learning -- learning to map corrupted observations to clean signals -- with a simple and powerful conclusion: it is possible to learn to restore images by only looking at corrupted examples, at performance at and sometimes exceeding training using…
SSMs can be poisoned with clean labels, leading to generalization failure.
problem The implicit bias of SSMs can be manipulated by including special training examples with clean labels.
method Formal proof and empirical demonstration of the phenomenon.
result SSMs can fail to generalize even with clean labels, due to the inclusion of special training examples.
Cincer cleans both new and past data by identifying and relabeling suspicious and counter-examples.
problem Sequential learning under label noise, especially in applications with human supervision.
method Cincer uses example-based explanations to identify and relabel suspicious and counter-examples, leveraging Fisher information matrix approximation.
result Cincer achieves better data and models by clarifying the model's suspicions, especially with FIM approximation.
In this paper, we present a reverberation removal approach for speaker verification, utilizing dual-label deep neural networks (DNNs). The networks perform feature mapping between the spectral features of reverberant and clean speech. Long short term memory recurrent neural networks (LSTMs) are trained to map corrupted…
Adversarial training leads to clean data generalization with significant robust overfitting gap.
problem Significant robust generalization gap in adversarial training.
method Two theoretical views: representation complexity and training dynamics.
result ReLU nets with O(ND) extra parameters can achieve CGRO. Self-supervised method predicts clean signal and noise distribution from noisy images.
problem Blind denoising and noise estimation in biomedical images with limited clean data.
method Two neural networks jointly predict clean signal and noise distribution from noisy observations.
result Significantly outperforms state-of-the-art algorithms on six biomedical image datasets.
Improved robust regression with clean covariates achieves better rates than Huber's model.
problem Robust regression under adaptive contamination of responses with clean covariates.
method Exploiting clean covariates to construct an estimator achieving better rates than Huber's model.
result Improved estimation rate even with constant contamination, achieving consistency.
For a real valued periodic smooth function u on R, n≥0, one defines the osculating polynomial φs (of order 2n+1) at a point s∈R to be the unique trigonometric polynomial of degree n, whose value and first 2n derivatives at s coincide with those of u at s. We will say that a point s is a clean maximal flex …
R package tsrobprep cleans and prepares time series data robustly.
problem Inefficient methods for handling missing values and outliers in time series data.
method Model-based methods for imputation and outlier detection considering time series properties.
result Robust and tunable methods for data preprocessing in time series analysis.
Enhances deep learning robustness to noise without sacrificing clean data accuracy.
problem Robustness of deep neural networks to input noise.
method Discriminative loss at penultimate layer and class-wise feature alignment with Gaussian noise.
result Improves robustness to various perturbations without degrading clean data accuracy.
Image classification problems are typically addressed by first collecting examples with candidate labels, second cleaning the candidate labels manually, and third training a deep neural network on the clean examples. The manual labeling step is often the most expensive one as it requires workers to label millions of im…
We consider the problem of prediction by a machine learning algorithm, called learner, within an adversarial learning setting. The learner's task is to correctly predict the class of data passed to it as a query. However, along with queries containing clean data, the learner could also receive malicious or adversarial …
New method generates clean data from corrupted observations.
problem Generating clean data from corrupted observations.
method Iterative update of a transport map using black-box corruption channel access.
result Converges to a self-consistent transport map that effectively inverts the corruption channel.
Study proposes a clustering and logistic regression algorithm for PU classification under Non-SCAR.
problem PU classification under Non-SCAR condition when SCAR condition is unsatisfied.
method 2-means clustering followed by logistic regression.
result Efficacy of the proposed algorithm demonstrated on 11 real data sets and a synthetic set.
Label noise may affect the generalization of classifiers, and the effective learning of main patterns from samples with noisy labels is an important challenge. Recent studies have shown that deep neural networks tend to prioritize the learning of simple patterns over the memorization of noise patterns. This suggests a …
The US Census Bureau corrupts data to protect privacy, but we show how to clean and analyze it effectively.
problem Analyzing Census data with intentional corruption to maintain privacy.
method Formulated a semiparametric model, proposed data cleaning, estimation, and inference procedures.
result Demonstrated that data cleaning can maintain precision and provided theoretical and empirical support.
A graph helps understand Artin groups better.
problem Understanding the structure of Artin groups.
method Constructing a marking graph with transverse parabolic subgroups and defining natural moves.
result The marking graph is quasi-isometric to the group modulo its center.
Study connects covariance cleaning theory to information theory for heavy-tailed distributions.
problem Optimizing covariance matrices for heavy-tailed distributions using information theory.
method Minimizing Frobenius norm and information loss between true and estimated covariance matrices.
result Asymptotic regime of large matrices minimizes information loss for Student's t distributions.
TS-Fault benchmarks TSF models against structural faults.
problem Evaluating the robustness of time series forecasting models against structured events.
method TS-Fault uses parameterized fault scenarios with controllable difficulty.
result Three findings contradict common leaderboard intuition.
Paper cleans option price datasets by removing outliers.
problem Unusual option prices in datasets.
method Statistical techniques to identify and remove outliers.
result Removes option prices violating no arbitrage assumption.
Graph neural networks (GNNs) are widely used in many applications. However, their robustness against adversarial attacks is criticized. Prior studies show that using unnoticeable modifications on graph topology or nodal features can significantly reduce the performances of GNNs. It is very challenging to design robust …
The purpose of the paper is to present a new pricing method for clean spread options, and to illustrate its main features on a set of numerical examples produced by a dedicated computer code. The novelty of the approach is embedded in the use of structural models as opposed to reduced-form models which fail to capture …