Automated smoothing does not significantly improve time series classification performance.
problem Improving time series classification algorithms using automated smoothing methods.
method Assessed six smoothing algorithms (moving average, exponential, etc.) on three benchmark classifiers.
result No significant improvement in performance over unsmoothed data.
Unified smoothing for robust classification improves accuracy.
problem Improving robustness of classifiers against adversarial attacks.
method Learned smoothed densities and randomized smoothing.
result Provable robust accuracies higher than state-of-the-art defenses.
Study cyclic group actions on specific high-dimensional manifolds.
problem Classify smooth actions of cyclic groups on certain high-dimensional manifolds.
method Analyzes smooth orientation-preserving actions of Z/m on (n−1)-connected 2n-manifolds. result Classifications up to smooth conjugation for specific cases of n and m. Hierarchical randomized smoothing improves model robustness for complex data.
problem Certifying robustness on complex data (e.g. images, graphs) is challenging.
method Add random noise to a randomly selected subset of entities in a hierarchical manner.
result Hierarchical randomized smoothing yields stronger robustness guarantees with high accuracy.
Proposes sigmoidF1 loss for multilabel classification, improving performance metrics.
problem Lack of smooth, tractable loss functions for multilabel classification.
method Introduces sigmoidF1, a smooth F1 score surrogate loss function.
result sigmoidF1 outperforms other loss functions on various datasets and metrics.
SaR-SVM-STV improves hyperspectral image classification with shape-adaptive reconstruction and denoising.
problem Classifying hyperspectral images with limited labeled data.
method Shape-adaptive Reconstruction (SaR) for pixel preprocessing, SVM for probability estimation, and Smoothed Total Variation (STV) for denoising.
result SaR-SVM-STV outperforms SVM-STV with fewer labeled data.
Graphs can be fooled by small edge changes, but this work protects them.
problem Adversaries can manipulate graph data to mislead graph classification models.
method We introduce a smoothed graph classification model with a robustness guarantee.
result The smoothed model maintains consistent predictions under small adversarial perturbations.
Research aims to explain how ResNets' stability improves image classification performance.
problem Understanding why ResNets enhance image classification performance.
method Examines batch normalization and the dynamical systems view of ResNets to understand stability and smoothness.
result Stability of inter-layer propagation in ResNets contributes to enhanced performance.
Smooth rigid spherical hypersurfaces in C^2 are real analytic.
problem Classifying smooth rigid spherical hypersurfaces in C^2.
method Proving real-analyticity through smoothness.
result Every smooth rigid spherical hypersurface in C^2 is real analytic.
Generic smooth plane-to-plane map germs are topologically equivalent to cones of mappings of the circle. We carry out a complete topological classification of smooth stable mappings of the circle and show how this classification leads, via the result mentioned above, to a topological classification of finitely determin…
We develop a new approach to the classical problem on isotopy classification of embeddings of manifolds into Euclidean spaces. This approach involves studying of a new embedding invariant, of almost-embeddings and of smoothing, as well as explicit constructions of embeddings. Using this approach we obtain complete conc…
The study classifies complex smooth Fano varieties with large pseudoindex.
problem Classifying Fano varieties with specific properties.
method Analyzing Fano varieties with large pseudoindex and Picard number greater than one.
result Classification of Fano varieties with pseudoindex at least n-2 and Picard number greater than one.
The paper classifies smooth structures on product manifolds of 3-connected 8-manifolds with spheres.
problem Classifying smooth structures on product manifolds.
method Computational and classification methods for concordance and diffeomorphism.
result Diffeomorphism classification of MimesS1 for specific M and k. We present a classification theorem for closed smooth spin 2-connected 7-manifolds M. This builds on the almost-smooth classification from the first author's thesis. The main additional ingredient is an extension of the Eells-Kuiper invariant for any closed spin 7-manifold, regardless of whether the spin characteristic…
Analyzes smoothness and classification of maps between manifolds.
problem Analyzing interpolating sesqui-harmonic maps between Riemannian manifolds.
method Derives a conservation law and uses it to show smoothness of weak solutions; obtains classification results.
result Smoothness of weak solutions and classification results for interpolating sesqui-harmonic maps.
Classifies certain high-dimensional manifolds with specific cohomology properties.
problem Classifying smooth manifolds with a specific cohomology structure.
method Analyzes cohomology rings and uses topological equivalences.
result Classifies manifolds up to diffeomorphism, homeomorphism, and homotopy equivalence.
Linear-Core Surrogates combine fast optimization and statistical efficiency in classification and structured prediction.
problem The trade-off between smoothness and margin-based losses in classification and structured prediction.
method Linear-Core (LC) Surrogates, a family of convex loss functions that stitch a linear core to a smooth tail.
result LC Surrogates achieve fast linear consistency rates while maintaining differentiability and strict H-consistency bounds. Denoised smoothing defends pretrained classifiers against adversarial attacks.
problem Adversarial attacks on pretrained classifiers.
method Prepending a denoiser to any off-the-shelf classifier using randomized smoothing.
result Guaranteed ℓp-robustness to adversarial examples without modifying the pretrained classifier. The study develops a theory for structured prediction using smooth convex surrogates.
problem Developing a theoretical framework for structured prediction.
method Characterizing smooth convex surrogates compatible with task losses and deriving statistical guarantees.
result Derives tight bounds for the calibration function and novel results for existing surrogate frameworks.
DropEdge improves deep GCNs for node classification by reducing over-fitting and over-smoothing.
problem Over-fitting and over-smoothing in deep GCNs for node classification.
method Randomly removes edges from the input graph at each training epoch to reduce over-fitting and over-smoothing.
result DropEdge improves performance on various GCN models and prevents over-smoothing.
Paper analyzes and improves graph convolutional networks for node classification.
problem Over-smoothing in GCNs causes poor performance in node classification tasks.
method Interpreted GCNs from an optimization perspective, introduced metrics to measure over-smoothing, derived a new kernel GCN+.
result GCN+ reduces over-smoothing and improves node classification performance.
Certified robustness for ImageNet models with randomized smoothing.
problem Creating robust models against adversarial attacks.
method Randomized smoothing with Gaussian noise.
result Certified top-1 accuracy of 49% on ImageNet under small ℓ2 perturbations. The paper computes smooth structures on a specific product manifold.
problem Computing the number of smooth structures on a product manifold.
method Using known low-dimensional computations of stable homotopy groups of spheres, the paper determines the inertia group of the product manifold.
result The paper establishes a diffeomorphism classification of all smooth manifolds homeomorphic to CP3imesSk for 1≤k≤7. Paper establishes a universal growth rate for smooth surrogate losses in classification.
problem Analyzing growth rates of consistency bounds for various surrogate losses.
method Proves square-root growth rate for smooth margin-based losses; extends to multi-class classification.
result Demonstrates a universal square-root growth rate for smooth comp-sum and constrained losses.
Improved OOD detection using label smoothing and k-NN density estimates.
problem Detecting out-of-distribution examples in classification models.
method Label smoothing and k-NN density estimate on intermediate activations.
result Label smoothing improves OOD detection performance, both theoretically and empirically.
Study on rational projective planes with small index singularities.
problem Existence and classification of rational homology projective planes with small index quotient singularities.
method Topological and smooth obstructions analysis, classification of singularities.
result Classification of quotient singularities for rational homology projective planes with indices up to three.
Automorphisms of finite order and real forms of "smooth" affine Kac-Moody algebras are studied, i.e. of 2-dimensional extensions of the algebra of smooth loops in a simple Lie algebra. It is shown that they can be parametrized by certain invariants and that in particular the classification of involutions essentially fo…
Label smoothing improves model robustness against misspecification.
problem Improving model robustness against model misspecification.
method Introducing modified label smoothing (MLSLR) that maintains consistent probability estimation while modifying the loss function.
result MLSLR exhibits higher robustness against model misspecification than conventional label smoothing.
New algorithms achieve better regret bounds for online classification with relaxed benchmarks.
problem Competing with worst-case optimal binary loss in online classification.
method Comparing against predictors robust to small input perturbations, performing well under Gaussian smoothing, or maintaining a prescribed output margin.
result Regret guarantees depend only on VC dimension and instance space complexity, with an O(log(1/γ)) dependence on the generalized margin. Classifies singularities of smooth vector fields on the line.
problem Classifying singularities of smooth vector fields on the line.
method Local classification with respect to C1-conjugacy, including normal forms and unfoldings. result Complete description of the 1-d case achieved.
A new framework SIMBA improves graph classification performance on size-imbalanced datasets.
problem Size imbalance in graph classification leads to poor model performance.
method Energy-guided structural smoothing between head and tail graphs, re-weighting based on energy propagation.
result SIMBA outperforms existing methods in size-imbalanced graph classification tasks.
Classifies smooth isotopy of a specific Lagrangian embedding.
problem Classifying Lagrangian embeddings of a specific form.
method Smooth isotopy classification for all dimensions n≥3. result Lagrangian embeddings are fully classified up to isotopy.
The paper proposes a method to model non-smooth functions using clustering, classification, and Gaussian process modeling.
problem Modeling discontinuities and non-smoothness in expensive computational models.
method Three-stage approach combining clustering, classification, and Gaussian process modeling.
result The approach successfully models discontinuities and non-smoothness in various functions.
Classifies equivariant vector bundles over toric manifolds.
problem Classifying vector bundles over toric manifolds.
method Klyachko-type classification over invariant affine charts.
result Generalizes Klyachko's classification of toric vector bundles.
We present a local classification of smooth projective surfaces in 3-space via projective transformations in accordance with singularity types of central projections up to codimension 4. We also discuss relations between our classification of Monge forms and bifurcations of parabolic curves and flecnodal curves.
New defense method against physical attacks on image classification models.
problem Defending against physically realizable attacks on image classification models.
method Proposed a new abstract adversarial model, rectangular occlusion attacks, and developed two approaches for efficiently computing adversarial examples.
result Adversarial training using the new attack yields robust image classification models against physical attacks.
We characterize those closed 2k-manifolds admitting smooth maps into (k+1)-manifolds with only finitely many critical points, for k∈{2,4}. We compute then the minimal number of critical points of such smooth maps for k=2 and, under some fundamental group restrictions, also for k=4. The main ingredients ar…
Improved online classification with accurate predictions.
problem Online classification challenges with limited data.
method Designing an online learner that uses predictions to reduce regret.
result Expected regret is better than worst-case analysis, especially with accurate predictions.
Classifies Real line bundles with Real connections on manifolds with involution.
problem Classifying Real line bundles with Real connections on manifolds with involution.
method Defines Real smooth Deligne cohomology to interpolate between equivariant sheaf cohomology and smooth imaginary-valued forms.
result Classifies Real line bundles with Real connections on manifolds with involution.
Improved signal classification using multiple wavelets and their smooth coefficients.
problem Signal classification accuracy declines with reduced attributes.
method Transform data with multiple wavelets, combine outputs, apply ensemble classifiers.
result Proposed technique outperforms raw data and single wavelet approaches.
Paper tackles over-smoothing in deep GCNs, proposing DropEdge to improve performance.
problem Over-smoothing reduces expressivity in deep GCNs, especially affecting node classification.
method Theoretical analysis of GCN behavior with depth, proposing DropEdge to alleviate over-smoothing.
result DropEdge improves performance on various GCNs, shallow and deep.
In this paper we prove that no complex surface of general type is diffeomorphic to a rational surface, thereby completing the smooth classification of rational surfaces and the proof of the Van de Ven conjecture on the smooth invariance of Kodaira dimension.
A Fourier-based learning algorithm for multiclass classification.
problem Highly nonlinear multiclass classification problems.
method Smoothing technique with low-pass filters to calculate probability distributions.
result Probabilistic explanation for classification without kernel functions.
Study on 3D foliated dynamical systems with Hilbert reciprocity law.
problem Understanding and classifying 3D foliated dynamical systems.
method Decomposition theorem, concrete examples construction, integration theory for smooth Deligne cohomology.
result Introduction of geometric Hilbert reciprocity law for 3D FDS.
In this paper, we classify smooth 5-manifolds with fundamental group isomorphic to $\z/2$ and universal cover diffeomorphic to S2×S3. This gives a classification of smooth free involutions on S2×S3 up to conjugation.
A new loss function improves deep learning performance without class separation constraints.
problem Training deep learning architectures for classification.
method Minimizing smoothness of label signals on similarity graphs.
result The proposed loss function leads to similar classification performance as cross-entropy, with added robustness.
New optimization method combines gradient clipping and non-Euclidean smoothness.
problem Improving optimization in non-Euclidean spaces for machine learning.
method Hybrid of steepest descent and conditional gradient, incorporating weight decay.
result Achieves optimal convergence rate and demonstrates effectiveness in deep learning.
Deep neural networks with various activation functions can approximate Hölder smooth functions.
problem Expressivity of deep neural networks with general activation functions.
method Investigates approximation ability of deep neural networks with a broad class of activation functions, including Hölder smooth functions.
result Derives the required depth, width, and sparsity of deep neural networks to approximate Hölder smooth functions.