arXiv research

Classifies stability of flat-core $p$-elasticae pinned at boundaries.

This paper analyzes HTL using stability theory for binary classification.

Mathematical approach defines stability conditions for ML models.

Fair classification has been a topic of intense study in machine learning, and several algorithms have been proposed towards this important task. However, in a recent study, Friedler et al. observed that fair classification algorithms may not be stable with respect to variations in the training dataset -- a crucial con…

Recent work has studied the reasons for the remarkable performance of deep neural networks in image classification. We examine batch normalization on the one hand and the dynamical systems view of residual networks on the other hand. Our goal is in understanding the notions of stability and smoothness of the inter-laye…

The paper classifies and analyzes the stability of elastic curves with fixed endpoints.

New invariant for classifying 4-manifolds up to cobordism.

A novel weighted feature selection method using fuzzy sets improves classification accuracy and stability.

Proposes a stable classifier using inflated argmax for multiclass classification.

Study finds significant instability in node embeddings due to randomness.

Stability results for geometric equations in warped product spaces.

The stability of statistical analysis is an important indicator for reproducibility, which is one main principle of scientific method. It entails that similar statistical conclusions can be reached based on independent samples from the same underlying population. In this paper, we introduce a general measure of classif…

Interpretable classification models are built with the purpose of providing a comprehensible description of the decision logic to an external oversight agent. When considered in isolation, a decision tree, a set of classification rules, or a linear model, are widely recognized as human-interpretable. However, such mode…

The study examines stability and classification of special minimal hypersurfaces in high dimensions.

Noise in RNNs promotes flatter minima and more stable dynamics.

The paper compactifies stability conditions on curves, akin to Teichmüller theory.

Many of our core assumptions about how neural networks operate remain empirically untested. One common assumption is that convolutional neural networks need to be stable to small translations and deformations to solve image recognition tasks. For many years, this stability was baked into CNN architectures by incorporat…

Following Cao-Hamilton-Ilmanen, in this paper we study the linear stability of Perelman's $ν$-entropy on Einstein manifolds with positive Ricci curvature. We observe the equivalence between the linear stability restricted to the transversal traceless symmetric 2-tensors and the stability of Einstein manifolds with resp…

Design of reliable systems must guarantee stability against input perturbations. In machine learning, such guarantee entails preventing overfitting and ensuring robustness of models against corruption of input data. In order to maximize stability, we analyze and develop a computationally efficient implementation of Jac…

Flashback Learning balances model stability and plasticity in continual learning.

We introduce the notion of reticular Legendrian unfoldings in order to investigate stabilities of bifurcations of wavefronts generated by a hypersurface germ with a boundary, a corner, or an r-corner in a smooth n dimensional manifold. We define several stabilities of reticular Legendrian unfoldings and prove that they…

In this paper, we formulate the notion of the $\mathcal{F}$-stability of self-shrinking solutions to mean curvature flow in arbitrary codimension. Then we give some classifications of the $\mathcal{F}$-stable self-shrinkers in arbitrary codimension, in codimension one case, our results reduce to Colding-Minicozzi's res…

New approach uses hinge loss for iterative regularization in classification.

Supervised classification is the most active and emerging research trends in today's scenario. In this view, Artificial Neural Network (ANN) techniques have been widely employed and growing interest to the researchers day by day. ANN training aims to find the proper setting of parameters such as weights ($\textbf{W}$) …

Sparse representation based classification (SRC) methods have achieved remarkable results. SRC, however, still suffer from requiring enough training samples, insufficient use of test samples and instability of representation. In this paper, a stable inverse projection representation based classification (IPRC) is prese…

Predictive process monitoring is concerned with the analysis of events produced during the execution of a business process in order to predict as early as possible the final outcome of an ongoing case. Traditionally, predictive process monitoring methods are optimized with respect to accuracy. However, in environments …

Classifies and analyzes the stability of black hole event horizon birth points using contact geometry.

Node2vec embeddings are unstable and unstable with parameter choices.

New method turns optimization algorithms into uniformly stable learning algorithms for non-Euclidean norms.

Proposes BN layers for neural networks on complex domains, improving training stability and accuracy.

Classifies very stable Higgs bundles for complex groups.

We introduce a new braid-theoretic framework with which to understand the Legendrian and transversal classification of knots, namely a Legendrian Markov Theorem without Stabilization which induces an associated transversal Markov Theorem without Stabilization. We establish the existence of a nontrivial knot-type specif…

This paper defines a positive and unlabeled classification problem for standard GANs, which then leads to a novel technique to stabilize the training of the discriminator in GANs. Traditionally, real data are taken as positive while generated data are negative. This positive-negative classification criterion was kept f…

AUASE embeds dynamic networks with stability guarantees for node comparison.

Despite their impressive performance, deep convolutional neural networks (CNNs) have been shown to be sensitive to small adversarial perturbations. These nuisances, which one can barely notice, are powerful enough to fool sophisticated and well performing classifiers, leading to ridiculous misclassification results. In…

Debt-financed collateral in DeFi increases stability risks.

Deep SMOTE improves SMOTE's stability and accuracy in imbalanced classification.

Paper introduces a differentiable regularizer for condition number to improve neural network stability.

New risk control method for non-monotonic losses in complex parameters.

This paper gives a description of the full space of Bridgeland stability conditions on the bounded derived category of a contraction algebra associated to a 3-fold flop. The main result is that the stability manifold is the universal cover of a naturally associated hyperplane arrangement, which is known to be simplicia…

We study the recently introduced stability training as a general-purpose method to increase the robustness of deep neural networks against input perturbations. In particular, we explore its use as an alternative to data augmentation and validate its performance against a number of distortion types and transformations i…

RENT selects stable features for robust model interpretation.

Constraints improve deep neural network training by stabilizing and enhancing robustness.

Bayesian explanations are more resilient to adversarial attacks than deterministic ones.

Study on stability of non-diagonal Einstein metrics on specific homogeneous spaces.

New algorithms improve federated learning accuracy and stability with real-world data.

We prove the K-moduli space of cubic threefolds is identical to their GIT moduli. More precisely, the K-(semi,poly)-stability of cubic threefolds coincide to the corresponding GIT stabilities, which could be explicitly calculated. In particular, this implies that all smooth cubic threefolds admit Kähler-Einstein metric…

In this paper, we study stability and instability problem for type-II partitioning problem. First, we make a complete classification of stable type-II stationary hypersurfaces in a ball in a space form as totally geodesic $n$-balls. Second, for general ambient spaces and convex domains, we give some topological restric…