arXiv research

Language models help text classification tasks by predicting next words.

Mathematical approach defines stability conditions for ML models.

Research connects physics and math through ceramic art of Riemann surfaces.

A new optimizer, Grad-Avg, converges faster than SGD and improves classification task performance.

Paper introduces r-DEP classifier for binary classification tasks.

This article offers an introductory look at Khovanov homology and its historical context.

Attribute-aware CF models aims at rating prediction given not only the historical rating from users to items, but also the information associated with users (e.g. age), items (e.g. price), or even ratings (e.g. rating time). This paper surveys works in the past decade developing attribute-aware CF systems, and discover…

We give a mathematical computation of the number of solutions of Apollonius problem, by use of Lie Sphere Geometry. Unlike in higher dimensions, the number of solutions depends only on the topology of the configuration of the 3 objects. It appears that our classification is non redundant, and far simpler than those obt…

We give an alternative to Postnikov's homotopy classification of maps from 3-dimensional CW-complexes to homogeneous spaces G/H of Lie groups. It describes homotopy classes in terms of lifts to the group G and is suitable for extending the notion of homotopy to Sobolev maps. This is required for applications to variati…

Distance metric learning is a branch of machine learning that aims to learn distances from the data, which enhances the performance of similarity-based algorithms. This tutorial provides a theoretical background and foundations on this topic and a comprehensive experimental analysis of the most-known algorithms. We sta…

Math proves deep learning unstable, despite stable neural networks existing.

Paper defines mathematical framework for neural network explainability.

Classifies orientation-reversing homeomorphisms of even periods on surfaces.

We provide a computer-assisted proof of the holomorphy of the quartic and the octic meromorphic differentials arising in the main Theorem 4.11 of our paper 'The Classification of Branched Willmore spheres in the $3$-Sphere and the $4$-Sphere' (arXiv:1706.01405), using the free mathematical software Sage.

New transforms improve signal classification and data analysis.

Motivated by the physical concept of special geometry two mathematical constructions are studied, which relate real hypersurfaces to tube domains and complex Lagrangean cones respectively. Me\-thods are developed for the classification of homogeneous Riemannian hypersurfaces and for the classification of linear transit…

Classifies geodetically convex sets and functions on Heisenberg group.

BCF models estimate causal effects on multiple outcomes in TIMSS data.

This paper introduces collective counterfactual explanations for groups of instances in classification models.

Multilayered artificial neural networks are becoming a pervasive tool in a host of application fields. At the heart of this deep learning revolution are familiar concepts from applied and computational mathematics; notably, in calculus, approximation theory, optimization and linear algebra. This article provides a very…

Estimating the difficulty level of math word problems is an important task for many educational applications. Identification of relevant and irrelevant sentences in math word problems is an important step for calculating the difficulty levels of such problems. This paper addresses a novel application of text categoriza…

Develops a logifold structure for understanding datasets.

Chemical networks outperform spiking neural networks in classification tasks.

Recently, machine learning (ML) has established itself in various worldwide benchmarking competitions in computational biology, including Critical Assessment of Structure Prediction (CASP) and Drug Design Data Resource (D3R) Grand Challenges. However, the intricate structural complexity and high ML dimensionality of bi…

This paper reviews recent advances in the field of optimization under uncertainty via a modern data lens, highlights key research challenges and promise of data-driven optimization that organically integrates machine learning and mathematical programming for decision-making under uncertainty, and identifies potential r…

New type of maps studied with non-vanishing torsion.

Graph classification has recently received a lot of attention from various fields of machine learning e.g. kernel methods, sequential modeling or graph embedding. All these approaches offer promising results with different respective strengths and weaknesses. However, most of them rely on complex mathematics and requir…

Novel approach for creating interpretable classifiers using bilevel optimization of split-rules in NLDTs.

LLMs will inevitably hallucinate due to their mathematical structure.

Classifies smooth isotopy of a specific Lagrangian embedding.

Motion Code models time series dynamics with sparse approximations.

Proposes a robust method for counterfactual classification.

Classifies patterns of symmetry breaking and vacuum degeneracy in scalar and gauge fields.

Enhances graph classification with multiple graphs.

Introduces topological deep learning for neural network classification problems.

Mathematical pipeline identifies structural homology of knotted proteins.

Mathematical conditions and practical computations for adversarial robustness measures are established.

A mixture of shifted asymmetric Laplace distributions is introduced and used for clustering and classification. A variant of the EM algorithm is developed for parameter estimation by exploiting the relationship with the general inverse Gaussian distribution. This approach is mathematically elegant and relatively comput…

First steps towards a mathematical theory of deep convolutional neural networks for feature extraction were made---for the continuous-time case---in Mallat, 2012, and Wiatowski and Bölcskei, 2015. This paper considers the discrete case, introduces new convolutional neural network architectures, and proposes a mathemati…

Data driven classification that relies on neural networks is based on optimization criteria that involve some form of distance between the output of the network and the desired label. Using the same mathematical analysis, for a multitude of such measures, we can show that their optimum solution matches the ideal likeli…

New federated learning algorithms improve model aggregation robustness.

Machine learning classifies braids and discovers new invariants.

Deep convolutional networks provide state of the art classifications and regressions results over many high-dimensional problems. We review their architecture, which scatters data with a cascade of linear filter weights and non-linearities. A mathematical framework is introduced to analyze their properties. Computation…

The paper extends Pearson correlation to multi-variables, useful for noise measurement and feature selection.

In this paper we give the stable classification of ordered, pointed, oriented multi-component curves on surfaces with minimal crossing number less than or equal to 2 such that any equivalent curve has no simply closed curves in its components. To do this, we use the theory of words and phrases which was introduced by V…

GCN and GPCA are mathematically connected, leading to improved node classification performance.

UDENet and ResNet can approximate any function, with ODENet showing UAP for continuous functions.

We describe simply connected compact exceptional simple Lie groups in very elementary way. We first construct all simply connected compact exceptional Lie groups G concretely. Next, we find all involutive automorphisms of G, and determine the group structures of the fixed points subgroup. They correspond to the classif…