New proof for higher rank subvarieties in genus three.
problem Classifying higher rank invariant subvarieties in genus three.
method Uses recent techniques developed by Apisa and Wright.
result Short and simplified proof of classification.
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48 results for “rank classification”
We complete the classification of rank two affine manifolds in the moduli space of translation surfaces in genus three. Combined with a recent result of Mirzakhani and Wright, this completes the classification of higher rank affine manifolds in genus three.
Classifies links with small Khovanov homology ranks.
problem Classifying links with specific ranks in Khovanov homology.
method Previous results combined with new classifications.
result All links with ranks ≤ 8 and three-component links with ranks ≤ 12 are classified.
Smooth classification of Cartan actions of higher rank semisimple Lie groups and their latticesmath.DG
Let G be a connected semisimple Lie group without compact factors whose real rank is at least 2, and let Γ\subset G be an irreducible lattice. We provide a C^\infty classification for volume-preserving Cartan actions of Γand G. Also, if G has real rank at least 3, we provide a C^\infty classification for volume-preserv…
This article announces the completion of the classification of rank 4 locally projective polytopes and their quotients. There are seventeen universal locally projective polytopes (nine nondegenerate). Amongst their 441 quotients are a further four (nonuniversal) regular polytopes, and 152 nonregular but section regular…
This work transfers fairness notions from binary classification to learning to rank.
problem Fairness concerns in automated ranking systems.
method Formalism to incorporate fairness objectives in learning to rank with provable guarantees.
result Improves ranking fairness substantially with minimal loss in model quality.
Joint Ranking SVM and Binary Relevance with Robust Low-Rank Learning for Multi-Label Classificationcs.LG
Multi-label classification studies the task where each example belongs to multiple labels simultaneously. As a representative method, Ranking Support Vector Machine (Rank-SVM) aims to minimize the Ranking Loss and can also mitigate the negative influence of the class-imbalance issue. However, due to its stacking-style …
Paper classifies structures on 5D manifolds with specific rank and conditions.
problem Classifying tangent distributions on 5D manifolds.
method Established necessary and sufficient topological condition for existence.
result Classification of structures up to homotopy as formal Cartan distributions.
The paper classifies links with low rank knot Floer and Khovanov homologies.
problem Detecting and classifying links with low rank knot Floer and Khovanov homologies.
method Generalized link Floer homology, used to obtain rank bounds and classify links.
result Knot Floer homology detects and .
In this paper, we study real hypersurfaces in complex Grassmannians of rank two. First, the nonexistence of mixed foliate real hypersurfaces is proven. With this result, we show that for Hopf hypersurfaces in complex Grassmannians of rank two, the Reeb principal curvature is constant along integral curves of the Reeb v…
A new method classifies color images using quaternion algebra.
problem Classifying color images with preserved intrinsic relationships.
method LSQMM model with quaternion nuclear norm regularization and ADMM algorithm.
result LSQMM outperforms state-of-the-art methods in classification accuracy and efficiency.
DRSVM uses deep learning to rank relative attributes between image pairs.
problem Classifying relative attributes between image pairs.
method Deep Siamese network with rank SVM loss function.
result DRSVM outperforms state-of-the-art methods on multiple datasets.
New structural result classifies actions on symmetric spaces.
problem Classify cohomogeneity one actions on symmetric spaces.
method Developed new structural result and applied to specific cases.
result Classified cohomogeneity one actions on SL(n,R)/SO(n), n>1.
This paper ranks pre-trained DNNs using a novel SI measure.
problem Optimizing pre-trained DNN selection for transfer learning.
method Automated ranking via Separation Index (SI) on target datasets.
result Ranked pre-trained DNNs improve classification performance.
We classify up to coarse equivalence all countable abelian groups of finite torsion free rank. The Q-cohomological dimension and the torsion free rank are the two invariants that give us such classification. We also prove that any countable abelian group of finite torsion free rank is coarsely equivalent to Z^n + H whe…
Discriminative calibration: Check Bayesian computation from simulations and flexible classifierstat.ML
Proposes a new method to improve Bayesian computation accuracy using flexible classification.
problem Bayesian computations accuracy check using rank-based simulation-based calibration has limitations.
method Replaces marginal rank test with a flexible classification approach that learns from data.
result Improves statistical power and provides an interpretable divergence measure of miscalibration.
Classifies rank-one submanifolds in Euclidean space.
problem Classifying submanifolds with singularities.
method Associate degree to ruled submanifolds and analyze singularities.
result An open and dense subset of rank-one submanifolds is the union of cylindrical, conical, and tangent regions.
The main result of this paper is the classification of the real irreducible representations of compact Lie groups with vanishing homogeneity rank.
We consider cohomogeneity one homogeneous disk bundles and adress the question when these admit a nonnegatively curved invariant metric with normal collar, i.e., such that near the boundary the metric is the product of an interval and a normal homogeneous space. If such a bundle is not (the quotient of) a trivial bundl…
Network node embedding is an active research subfield of complex network analysis. This paper contributes a novel approach to learning network node embeddings and direct node classification using a node ranking scheme coupled with an autoencoder-based neural network architecture. The main advantages of the proposed Dee…
New findings show DNC is not optimal for deep models, revealing a low-rank bias.
problem Theoretical limitations of DNC in non-linear models and multi-class classification.
method Analysis of non-linear models of arbitrary depth in multi-class classification.
result DNC stops being optimal for DUFM when going beyond two layers or two classes, due to a low-rank bias.
In multiclass classification, the goal is to learn how to predict a random label , valued in with , based upon observing a r.v. , taking its values in with say, by means of a classification rule with minimum prob…
GCL-LRR improves node classification in noisy graphs.
problem Noise in real-world graph data impairs GNNs' effectiveness.
method Two-stage transductive learning with low-rank regularization and attention.
result Improved node classification performance in noisy graphs.
Classifies vector field algebras in complex space.
problem Classifying vector field algebras in complex space.
method Classical results and proofs for vector fields in 2 and 3 variables, extended to arbitrary N.
result Lie's classification for vector fields in .
Proposes semi-supervised feature ranking for handling high-dimensional, unlabeled data.
problem Handling high-dimensional, unlabeled data in machine learning.
method Tree ensembles and Relief family algorithms for semi-supervised feature ranking.
result Semi-supervised feature ranking outperforms supervised methods across most datasets.
In classification problems, sampling bias between training data and testing data is critical to the ranking performance of classification scores. Such bias can be both unintentionally introduced by data collection and intentionally introduced by the algorithm, such as under-sampling or weighting techniques applied to i…
Iterative subtraction method for Feature Rankingphysics.data-an
Training features used to analyse physical processes are often highly correlated and determining which ones are most important for the classification is a non-trivial tasks. For the use case of a search for a top-quark pair produced in association with a Higgs boson decaying to bottom-quarks at the LHC, we compare feat…
Study ranks of elliptic curves via prime averages.
problem Classifying elliptic curves by rank.
method Average Frobenius trace over primes, data science experiments.
result Oscillating pattern in average trace values, correlates with rank.
Classifies measures for Anosov subgroups in higher ranks.
problem Classifying horospherical invariant measures for Anosov subgroups.
method Geometric approach, not relying on flows or ergodic theorems.
result Extends results from rank one to higher ranks, solving open problems.
Ranking via Robust Binary Classification and Parallel Parameter Estimation in Large-Scale Datastat.ML
We propose RoBiRank, a ranking algorithm that is motivated by observing a close connection between evaluation metrics for learning to rank and loss functions for robust classification. The algorithm shows a very competitive performance on standard benchmark datasets against other representative algorithms in the litera…
The problem of bipartite ranking, where instances are labeled positive or negative and the goal is to learn a scoring function that minimizes the probability of mis-ranking a pair of positive and negative instances (or equivalently, that maximizes the area under the ROC curve), has been widely studied in recent years. …
Study classifies Calabi-Yau threefolds with non-Gorenstein involutions.
problem Understanding non-Gorenstein involutions on Calabi-Yau threefolds.
method Classification of Calabi-Yau threefolds with specific properties.
result Classification of Calabi-Yau threefolds with Picard rank one and non-Gorenstein involutions.
We study the variety of actions of a fixed (Chevalley) group on arbitrary geodesic, Gromov hyperbolic spaces. In high rank we obtain a complete classification. In rank one, we obtain some partial results and give a conjectural picture.
We classify all rank two affine manifolds in strata in genus three with two zeros. This confirms a conjecture of Maryam Mirzakhani in these cases. Several technical results are proven for all strata in genus three, with the hope that they may shed light on a complete classification of rank two manifolds in genus three.
A new method for forming learning objectives using the sum of ranked range.
problem Forming learning objectives from aggregated values.
method Sum of ranked range (SoRR) minimization with DCA.
result The proposed method effectively forms learning objectives and is applicable to binary and multi-label/multi-class classification.
Study classifies special Hessian rank 2 hypersurfaces in 4D space.
problem Classifying hypersurfaces with constant Hessian rank 2.
method Power series method of equivalence, Lie's classification spirit.
result 34 inequivalent terminal branches, each with a nonempty moduli space.
Qwen3-8B outperforms classical models in financial text classification.
problem Financial text classification for trading systems and sentiment analysis.
method Noisy Embedding Instruction Finetuning and Rank-stabilized Low-Rank Adaptation.
result Qwen3-8B achieves better classification accuracy and fewer training epochs.
A low-rank transformation learning framework for subspace clustering and classification is here proposed. Many high-dimensional data, such as face images and motion sequences, approximately lie in a union of low-dimensional subspaces. The corresponding subspace clustering problem has been extensively studied in the lit…
A hyperbolic lattice is called \textit{-reflective} if its automorphism group is generated by - and -reflections up to finite index. In this paper we prove that the fundamental polyhedron of a -arithmetic cocompact reflection group in the three-dimensional Lobachevsky space contains an edge s…
Towards Model-Agnostic Post-Hoc Adjustment for Balancing Ranking Fairness and Algorithm Utilitycs.LG
Proposes a method to balance fairness and utility in ranking models.
problem Systematic disparity across protected groups in ranking models.
method Model-agnostic post-processing framework using dynamic programming.
result Achieves a balance between fairness and utility across various metrics and datasets.
A hyperbolic lattice is called \textit{-reflective} if the subgroup of its automorphism group generated by all - and -reflections is of finite index. The main result of this article is a complete classification of -reflective maximal anisotropic lattices of rank .
Study shows rank of knot Floer homology detects Hopf links and classifies second smallest links.
problem Detecting and classifying links based on knot Floer homology ranks.
method Analyzes knot Floer homology ranks to identify and classify links.
result Classifies links of the second smallest knot Floer homology.
Reduced-rank method improves least-squares regression under output regularity.
problem Least-squares regression with infinite dimensional outputs.
method Reduced-rank method for solving least-squares problems with output regularity assumptions.
result Learning bounds and improved statistical performance compared to full-rank method.
Many classification problems focus on maximizing the performance only on the samples with the highest relevance instead of all samples. As an example, we can mention ranking problems, accuracy at the top or search engines where only the top few queries matter. In our previous work, we derived a general framework includ…
Hutter (2007) recently introduced the loss rank principle (LoRP) as a generalpurpose principle for model selection. The LoRP enjoys many attractive properties and deserves further investigations. The LoRP has been well-studied for regression framework in Hutter and Tran (2010). In this paper, we study the LoRP for clas…
New algorithm improves asset ranking for better cross-sectional portfolios.
problem Sub-optimal ranking of assets in cross-sectional systematic strategies.
method Learning-to-rank algorithms to enhance portfolio construction.
result Modern machine learning ranking algorithms boost Sharpe Ratios by approximately threefold.
Exponentially fast SMF algorithm for multi-class classification.
problem Learning interpretable features from high-dimensional data.
method Novel framework that 'lifts' SMF as a low-rank matrix estimation problem.
result Provable exponential convergence to global minimizer under mild assumptions.
Framework ranks sectors influenced by Indian Union Budgets.
problem Real-time analysis of budgetary impacts on sector-specific equity performance.
method Fine-tuned embeddings and language models for sector identification and performance ranking.
result 0.997 NDCG score in predicting sector ranks based on post-budget performances.