Paper explores limits of distributed dislocations in geometric and constitutive paradigms.
problem Understanding limits of distributed dislocations in geometric and constitutive paradigms.
method Review and comparison of geometric and constitutive paradigms, analysis of edge dislocations in both paradigms.
result Homogenization theories in geometric and constitutive paradigms are consistent and identical in the case of constitutive relations having discrete symmetries.
Deep learning approximates geometric measures of planar curves.
problem Approximating differential invariants of planar curves.
method Utilizing deep neural networks to estimate geometric measures of planar curves.
result Deep neural networks can learn to overcome instabilities and sampling artifacts.
FiberNet integrates geometry into machine learning for clearer classification.
problem Lack of interpretability in traditional deep learning.
method Reformulates classification as geometric optimization on fiber bundles, introducing learnable Riemannian metrics and variational prototype optimization.
result Clear geometric interpretability and efficiency in classification.
Survey on automating geometry problem solving with large models.
problem Automating geometric problem solving with spatial understanding and logical reasoning.
method Synthesizes GPS advancements through benchmark construction, parsing, and reasoning paradigms.
result Unified analytical paradigm and emerging opportunities identified.
The paper proposes new interpretability paradigms to improve model faithfulness.
problem Improving the accuracy of explanations for complex models.
method Examining and evolving existing paradigms, proposing new models.
result Three new paradigms for interpretability are presented.
Extends diffusion models to non-Euclidean spaces with geometric priors.
problem Difficulties in natural sciences with symmetries and non-Euclidean data.
method Constructs a noising process and neural network equivariant to symmetry group, approximates score function.
result Model can generate complex scalar and vector fields on synthetic and real-world data.
New scalable geometric framework for SPD matrices.
problem Costly spectral computations in SPD matrix analysis.
method Efficient computation of extreme generalized eigenvalues through Hilbert and Thompson geometries of the semidefinite cone.
result Existence and uniqueness of a novel iterative mean of SPD matrices.
This paper analyzes Barlow Twins' representation efficiency using information-geometric methods.
problem Understanding and comparing the efficiency of self-supervised learning methods.
method Introduces an information-geometric framework to quantify representation efficiency and applies it to Barlow Twins.
result Proves that Barlow Twins achieves optimal representation efficiency (η=1).
In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man ifold geometry using either local or global features of the data. Building on t…
This review explores resampling techniques for imbalanced binary classification.
problem Imbalanced classes lead to poor prediction results in classification.
method Classical, cost-sensitive, and Neyman-Pearson paradigms with resampling techniques and classification methods.
result Complex dynamics among resampling techniques, base methods, metrics, and imbalance ratios.
Combines cost-sensitive and Neyman-Pearson paradigms for better binary classification.
problem Asymmetric binary classification problems with unequal error severities.
method Develops TUBE-CS algorithm to bridge cost-sensitive and Neyman-Pearson paradigms.
result High-probability control of population type I error.
New method uses geometric properties for better density estimation.
problem Uncertainty quantification in ambiguous tasks.
method Winner-takes-all training with centroidal Voronoi tessellations.
result Improved quantization and density estimation.
New method for high-fidelity shape representations from raw data.
problem Creating accurate shape representations from raw data.
method A simple loss function encouraging neural network to vanish on input point cloud and have unit norm gradient.
result Our method produces high-fidelity, smooth, and natural zero level set surfaces.
We present two paradigms relating algebraic, topological and quantum computational statistics for the topological model for quantum computation. In particular we suggest correspondences between the computational power of topological quantum computers, computational complexity of link invariants and images of braid grou…
MCBP detects boundaries in high-dimensional data using curvature.
problem Boundary detection in high-dimensional data.
method MCBP uses mean curvature to model data manifold curvature.
result MCBP improves clustering performance in complex scenarios.
Unified mathematical theory for analyzing biomolecular geometry and flexibility.
problem Lack of a unified mathematical theory for analyzing biomolecular geometry and flexibility.
method Introducing de Rham-Hodge theory, Helmholtz-Hodge decomposition, and discrete exterior calculus.
result Unified framework for predicting macromolecular flexibility and natural modes.
New equations reveal moduli space rigidity in geometric deformations.
problem Understanding moduli space rigidity in geometric deformations.
method Coupled Hitchin-He equations, Lax pair, nonlinear embedding.
result Moduli space is analytically isomorphic to the classical case for small deformations.
SketchGraphs dataset aids in modeling CAD designs.
problem Training models to reason about CAD designs efficiently.
method Collection of 15 million sketches with geometric constraint graphs.
result Demonstrated use cases for generative modeling and conditional generation.
Generalizes Sobolev IPM for graph-based measures using Orlicz geometric structure.
problem Limitation of Le et al. (2025) framework to Lp geometry. method Generalizes Sobolev IPM through Orlicz geometric structure, employing convex functions to capture nuanced geometric relationships.
result GSI-M reduces to a simple univariate optimization problem, achieving remarkable computational efficiency.
Paper proposes SPO paradigm for better portfolio optimization in real markets.
problem Real-world trading frictions and constraints affect portfolio optimization quality.
method SPO paradigm with decision-focused training using surrogate loss and linear predictors.
result Decision-focused training improves risk-adjusted performance and robustness.
The paper improves Monte Carlo methods for optimization problems.
problem Efficiently solving optimization problems with biased Monte Carlo estimators.
method Introduces Multilevel Monte Carlo (MLMC) within Sample Average Approximation (SAA).
result Establishes uniform convergence and sample complexity for MLMC in SAA.
Graphs from features improve classification accuracy in tasks.
problem Traditional classification tasks can be improved by incorporating relational information.
method Construct geometric graphs from features and use them in Graph Convolutional Networks.
result Graphs derived from features increase classification accuracy and improve class separation.
This paper extends geometric study of neural networks to non-differentiable layers and random walks.
problem Understanding the geometric properties of neural networks, especially those with non-differentiable activation functions.
method Singular Riemannian geometry approach to convolutional, residual, and recursive neural networks.
result Illustrated geometric findings with numerical experiments on image classification and thermodynamic problems.
This work tackles missing annotations in large sensor datasets.
problem Missing annotations in large sensor datasets negatively affect supervised learning system performance.
method Proposes and evaluates three paradigms to handle gaps: dropping, single label, and unique label, along with a hybrid combination.
result Evaluation of proposed paradigms and hybrid combination shows significant performance improvement.
Unified method for analyzing evolving manifolds using de Rham-Hodge theory.
problem Analysis of evolving geometric and topological properties of manifolds.
method Evolutionary de Rham-Hodge method applied to filtration-induced families of de Rham complexes.
result Three sets of topology-preserving singular spectra reveal topological persistence and geometric progression.
In school, a teacher plays an important role in various classroom teaching patterns. Likewise to this human learning activity, the learning using privileged information (LUPI) paradigm provides additional information generated by the teacher to 'teach' learning models during the training stage. Therefore, this novel le…
In this paper, simple mathematical models from Control Theory are applied to three very important economic paradigms, namely (a) minimum wages in self-regulating markets, (b) market-versus-true values and currency rates, and (c) government spending and taxation levels. Analytical solutions are provided in all three par…
This paper proposes a new geometric model optimization method.
problem Building adaptive manifold models with dynamic geometry.
method Optimizing metric tensor field on a manifold with variational framework.
result Metric optimization yields models with greater expressive power than fixed geometry models.
This research compares masked diffusion models to autoregressive language models, focusing on architectural differences.
problem Comparing masked diffusion models to autoregressive language models due to architectural differences.
method Equitably compare MDMs within a decoder-only framework, investigating architectural influences.
result Decoder-only MDMs can achieve significant speedups and comparable perplexity with temperature annealing.
Kernel VICReg improves SSL in RKHS, capturing nonlinear structures.
problem Limited ability of existing SSL methods to handle nonlinear dependencies.
method Kernel VICReg framework in RKHS, kernelizing VICReg objectives.
result Kernel VICReg mitigates representational collapse and improves performance.
Unified framework for DRO using OT with constraints.
problem Handling ambiguity in likelihood ratios and outcomes.
method Unified framework leveraging optimal transport with conditional moment constraints.
result Unified approach enables adversarial perturbation of likelihood ratios and outcomes.
Paper classifies institutions based on credit, debit, and funding adjustment paradigms.
problem Classifying institutions based on credit, debit, and funding adjustment paradigms.
method Mathematical framework based on the principle of invariance.
result Improved solution of principle of invariance equations for accurate metrics calculation.
Brain computer interfaces (BCI) enable direct communication with a computer, using neural activity as the control signal. This neural signal is generally chosen from a variety of well-studied electroencephalogram (EEG) signals. For a given BCI paradigm, feature extractors and classifiers are tailored to the distinct ch…
MapLUR uses deep learning on map images to estimate NO2 pollution, outperforming traditional methods.
problem Limited availability of data for traditional LUR models makes them hard to adapt to new areas.
method Data-driven, open-source approach using convolutional neural networks trained on map data.
result MapLUR significantly outperforms traditional LUR models, including those with manually engineered features.
MARGINATTACK improves zero-confidence adversarial attacks' accuracy and efficiency.
problem Improving zero-confidence adversarial attacks' accuracy and efficiency.
method Proposes MARGINATTACK, a zero-confidence attack framework that computes margin with improved accuracy and efficiency.
result MARGINATTACK computes a smaller margin than state-of-the-art zero-confidence attacks and matches state-of-the-art fix-perturbation attacks.
New algorithm improves feature selection for streaming data.
problem Traditional OSFS methods assume all data available at runtime, but features and samples stream concurrently.
method Introduces Geometric Online Adaption (GOA) for concurrent streaming of features and samples.
result GOA outperforms SAOLA on various datasets and in the OSFS-SS setting.
CATNet predicts CAT bond spreads using graph-based deep learning.
problem Complex, relational data in CAT bonds not well captured by traditional models.
method CATNet applies R-GCN to CAT bond primary market as a graph.
result CATNet outperforms Random Forest and XGBoost benchmarks.
This work uncovers the tropical analogue for measured laminations of the convex hull construction of decorated Teichmueller theory, namely, it is a study in coordinates of geometric degeneration to a point of Thurston's boundary for Teichmueller space. This may offer a paradigm for the extension of the basic cell decom…
Thanks to the advances in machine learning, data-driven analysis tools have become valuable solutions for various applications. However, there still remain essential challenges to develop effective data-driven methods because of the need to acquire a large amount of data and to have sufficient computing power to handle…
Data science models, although successful in a number of commercial domains, have had limited applicability in scientific problems involving complex physical phenomena. Theory-guided data science (TGDS) is an emerging paradigm that aims to leverage the wealth of scientific knowledge for improving the effectiveness of da…
The latest techniques from Neural Networks and Support Vector Machines (SVM) are used to investigate geometric properties of Complete Intersection Calabi-Yau (CICY) threefolds, a class of manifolds that facilitate string model building. An advanced neural network classifier and SVM are employed to (1) learn Hodge numbe…
Locally adaptive federated learning improves convergence in distributed machine learning.
problem Balancing local updates in federated learning leads to slow convergence.
method Locally adaptive federated learning algorithms that use uncoordinated stepsizes based on local geometric information.
result Locally adaptive methods can be particularly efficient in overparameterized settings and outperform standard federated algorithms.
In recent studies the truncated Levy process (TLP) has been shown to be very promising for the modeling of financial dynamics. In contrast to the Levy process, the TLP has finite moments and can account for both the previously observed excess kurtosis at short timescales, along with the slow convergence to Gaussian at …
Adjoined Networks trains both base and compressed networks together for efficient model compression.
problem Efficiently compressing deep neural networks while maintaining accuracy.
method Adjoined Networks (AN) trains both a base network and a smaller compressed network simultaneously, sharing parameters.
result AN achieves 71.8% top-1 accuracy with 1.8M parameters and 1.6 GFLOPs on ImageNet.
Enhances data programming with continuous labeling functions for better model performance.
problem Scarcity of labeled data hampers supervised learning models.
method Integrates continuous scoring functions and quality guides into a generative model to improve data programming reliability.
result Continuous labeling functions lead to improved recall and more stable model performance.
New approach to counterfactual reasoning avoids demographic interventions.
problem Limitations of traditional counterfactual reasoning in AI systems.
method Backtracking counterfactual approach instead of interventional.
result Allows addressing social concerns without demographic interventions.
This paper is concerned with a recently developed paradigm for population-based optimization, termed particle filter optimization (PFO). This paradigm is attractive in terms of coherence in theory and easiness in mathematical analysis and interpretation. Current PFO algorithms only work for single-objective optimizatio…
Graph Polish optimizes molecular structures by minimizing changes and maximizing preservation.
problem Error-prone traditional molecular optimization methods.
method Graph Polish transforms optimization into a polishing task, focusing on optimization centers and minimizing changes.
result Significant advantage over state-of-the-art methods on multiple optimization tasks.