A new model embeds word and label hierarchies in hyperbolic space for HMLC.
problem Learning mappings from word hierarchies to label hierarchies in hierarchical multi-label classification.
method Proposes a Hyperbolic Interaction Model (HyperIM) to learn label-aware document representations in hyperbolic space.
result Demonstrates improved performance for HMLC compared to state-of-the-art methods.
C-HMCNN(h) improves HMC classification by leveraging class hierarchy.
problem Hierarchical multi-label classification with class hierarchy constraints.
method Exploits class hierarchy to produce coherent predictions for multi-label classification.
result C-HMCNN(h) outperforms state-of-the-art models in HMC classification.
Paper investigates methods to improve classification by inducing a hierarchy from flat labels.
problem Improving classification performance on datasets lacking a natural hierarchy.
method The approach involves clustering conditional distributions and using a hierarchical classifier with the induced hierarchy.
result The methods can discover latent hierarchies and improve accuracy in various applications.
An important problem in multi-label classification is to capture label patterns or underlying structures that have an impact on such patterns. This paper addresses one such problem, namely how to exploit hierarchical structures over labels. We present a novel method to learn vector representations of a label space give…
Enhances image classification by integrating semantic hierarchy into CNN models.
problem Limited use of external guidance in image classification.
method Integrates label-hierarchy knowledge into CNN-based classifiers and uses order-preserving embeddings.
result Boosts image classification performance through semantic hierarchy integration.
The thesis introduces methods to use semantic hierarchy in image classification.
problem Limited work in training image classifiers with non-conventional external guidance.
method Injects label hierarchy knowledge into arbitrary classifiers and uses order-preserving embeddings for image classification.
result Both embedding-based models and CNN-classifiers with hierarchical information outperform a hierarchy-agnostic model.
Hierarchy Of Multi-label classifiers (HOMER) is a multi-label learning algorithm that breaks the initial learning task to several, easier sub-tasks by first constructing a hierarchy of labels from a given label set and secondly employing a given base multi-label classifier (MLC) to the resulting sub-problems. The prima…
Proposes a hierarchical curriculum loss to improve model accuracy and interpretability.
problem Flat label spaces in classification algorithms fail to capture dependencies in real-world data.
method Introduces hierarchical curriculum loss with two properties: satisfying hierarchical constraints and providing non-uniform label weights.
result The proposed loss function significantly outperforms multiple baselines on real-world image datasets.
This paper tackles multilabel classification by exploiting label sparsity and hierarchy.
problem Sparse label vectors and unknown label hierarchy in large-scale multilabel classification problems.
method Data-dependent grouping and hierarchical partitioning to solve multilabel classification problems in a lower-dimensional space.
result Our methods achieve competitive accuracy with significantly lower computational costs compared to other methods.
The problem of multilabel classification when the labels are related through a hierarchical categorization scheme occurs in many application domains such as computational biology. For example, this problem arises naturally when trying to automatically assign gene function using a controlled vocabularies like Gene Ontol…
New method optimizes hierarchical multi-label classification results.
problem Optimizing classification results respecting class hierarchy and classifier scores.
method Introducing CATCH objective function and mLPR metric to rank multi-label classification results.
result HierRank algorithm optimizes CATCH, improving decision accuracy.
HCC extends conformal prediction to handle class hierarchies, improving prediction reliability.
problem Uncertainty quantification in classification models with class hierarchy considerations.
method Formulates HCC as a constrained optimization problem, ensuring coverage guarantees with a smaller subset of candidate solutions.
result HCC produces more reliable prediction sets by leveraging class hierarchy information.
A framework uses POMDPs to assess hierarchical clustering quality.
problem No agreed methodology for evaluating hierarchical clustering without ground-truth labels.
method Modelled as a POMDP, assessing search support for hierarchical structures.
result Proposes a novel measure for assessing hierarchical clustering quality.
This work improves graph inference using the degree-4 sum-of-squares hierarchy.
problem Recovering ground-truth binary labelings from corrupted edge observations.
method Apply the degree-4 sum-of-squares hierarchy to a quadratic combinatorial optimization problem.
result The solution of the dual problem is related to edge weights of Johnson and Kneser graphs.
Hierarchical text classification has many real-world applications. However, labeling a large number of documents is costly. In practice, we can use semi-supervised learning or weakly supervised learning (e.g., dataless classification) to reduce the labeling cost. In this paper, we propose a path cost-sensitive learning…
Proves deep networks can learn hierarchical structures efficiently.
problem Understanding how deep networks learn hierarchical structures in data.
method Random Hierarchy Models, gradient-based methods, layerwise training.
result Proves deep networks can efficiently learn hierarchical structures.
New method improves blackbox attack transferability by perturbing feature hierarchy.
problem Improving transferability of blackbox attacks across different models and datasets.
method Perturbs representations throughout feature hierarchy to mimic other classes.
result Achieves 10x increase in targeted success rate compared to other methods.
The time complexity of support vector machines (SVMs) prohibits training on huge data sets with millions of data points. Recently, multilevel approaches to train SVMs have been developed to allow for time-efficient training on huge data sets. While regular SVMs perform the entire training in one -- time consuming -- op…
Paper tackles interpretability in deep learning for multi-label learning.
problem Machine learning models are often hard to interpret.
method Combines deep autoencoder and multi-label classifiers.
result Proposes interpretable label hierarchies and dependencies.
This paper improves neural tangent kernels for better generalization and local elasticity.
problem Performance gap between neural tangent kernels and real-world neural networks.
method Introduces label-aware kernels using Hoeffding decomposition.
result Models trained with proposed kernels simulate NNs better in terms of generalization and local elasticity.
Proposes a method to improve hierarchical clustering using set-level structural priors.
problem Lack of supervision for non-leaf structure in hierarchical clustering.
method Introduces set-level structural priors for semi-supervised hyperbolic hierarchical clustering.
result Improves label consistency and similarity-based tree quality over baselines.
Loss assigns examples to classes and superclasses in hierarchical data.
problem Learning from hierarchical classification problems with known class hierarchy.
method Introduces a loss function that considers the hierarchy of classes, aiming for consistent classification across different granularities.
result Improves accuracy and reduces coarse errors in classification compared to cross-entropy loss.
New deep architecture models uncertainty by sharing neural connectivity patterns.
problem Uncertainty modeling in deep neural networks remains challenging.
method Proposes a new deep architecture that shares neural connectivity patterns between generative and discriminative networks to model a confounder.
result Demonstrates significant improvement in uncertainty estimation compared to state-of-the-art methods.
The paper addresses calibration in label ranking, a structured prediction task.
problem Calibration in label ranking is not well understood and often poorly calibrated.
method Formalized calibration for label ranking, developed a hierarchy of notions, and empirically evaluated models.
result Popular label ranking models are often poorly calibrated, with differences between sub-ranking and top-k metrics.
Constructs integrable hierarchies for generalized Frobenius manifolds with non-flat unity.
problem Integrable hierarchies for generalized Frobenius manifolds with non-flat unity.
method Constructs a bihamiltonian integrable hierarchy of hydrodynamic type.
result Integrable hierarchy possesses Virasoro symmetries and a tau structure.
Study improves product categorization on Amazon using multi-modal fusion.
problem Multi-label product categorization in e-commerce.
method Late fusion of image, description, and title modalities using modified CNN and ResNet-50 models.
result Tri-modal late fusion model achieved an F1 score of 88.2%, significantly better than single modal models. Study identifies pitfalls in assessing hierarchies for multi-class classification.
problem Lack of understanding in selecting hierarchies for multi-class classification.
method Analyzed and compared popular approaches to extracting hierarchies.
result Hierarchy quality becomes irrelevant when using powerful classifiers.
Super tau-covers extend bihamiltonian hierarchies' symmetries.
problem Extending symmetries of bihamiltonian hierarchies.
method Constructing super tau-covers for bihamiltonian integrable hierarchies.
result Symmetries of bihamiltonian hierarchies extended to super tau-covers.
Hydrodynamic hierarchy deformed using conservation laws.
problem Deforming a hydrodynamic hierarchy with non-vanishing Nijenhuis torsion.
method Using a chain of conservation laws to deform the hierarchy.
result The resulting hierarchy has non-vanishing Nijenhuis torsion but vanishing Haantjes tensor.
New method improves LLM judge accuracy by accounting for dependencies in aggregated binary labels.
problem Classical label aggregation methods fail to account for dependencies among LLM judges, leading to miscalibrated predictions.
method Dependence-aware models based on Ising graphical models and latent factors.
result The proposed method outperforms classical methods on real-world datasets, reducing excess risk.
Legendre transformations link related integrable hierarchies.
problem Understanding relationships between integrable hierarchies.
method Legendre-type transformations of generalized Frobenius manifolds.
result Linear reciprocal transformations link related hierarchies.
Twisted U- and twisted U/K-hierarchies are soliton hierarchies introduced by Terng to find higher flows of the generalized sine-Gordon equation. Twisted O(J)×O(J)O(J,J)-hierarchies are among the most important classes of twisted hierarchies. In this paper, interesting first and higher flows of twi…
Tail-GNNs improve protein function prediction using relational reinforcement.
problem Predicting hierarchical protein functions from sequence data.
method Combining Tail-GNNs with dilated convolutional networks for multi-task learning.
result Significant improvement in F_1 score for protein function prediction.
In this article we propose a novel ranking algorithm, referred to as HierLPR, for the multi-label classification problem when the candidate labels follow a known hierarchical structure. HierLPR is motivated by a new metric called eAUC that we design to assess the ranking of classification decisions. This metric, associ…
Derive bihamiltonian structure for rational reduction of 2D-Toda hierarchy
problem Derive bihamiltonian structure for rational reduction of 2D-Toda hierarchy
method Direct computations
result Derive local bihamiltonian structure
We propose a formally completely integrable extension of heat hierarchy based on the space of symmetries isomorphic to the Weyl algebra A1. The extended heat hierarchy will be the basic model for the analysis of the extension of KP hierarchy, and other integrable equations.
Wise's Quasiconvex Hierarchy Theorem classifying hyperbolic virtually compact special groups in terms of quasiconvex hierarchies played an essential role in Agol's proof of the Virtual Haken Conjecture. Answering a question of Wise, we construct a new virtual quasiconvex hierarchy for relatively hyperbolic virtually co…
New hierarchies derived from KP hierarchy using non-formal operators and Yang-Mills action.
problem Formal solutions of KP hierarchy and their non-formal counterparts.
method Developed new hierarchies of non-linear equations on non-formal pseudo-differential operators.
result Expressed one hierarchy as Yang-Mills action minimization.
Symmetry reduction of Painlevé IV to Flaschka-Newell Painlevé II
problem Isomonodromic deformation problem associated with rank-two meromorphic connections
method Symmetry Ψ(−λ)=σ1Ψ(λ)σ1 result Induced isomonodromic dynamics coincides with Flaschka-Newell Painlevé II hierarchy
Scroll structures on solutions of 4D integrable equations are involutive and governed by a dispersionless hierarchy.
problem Characterizing the geometry of solutions to 4D integrable equations.
method Defining rational normal scrolls and showing their involutivity.
result Involutive scroll structures are governed by a dispersionless integrable hierarchy.
Constructs tri-Hamiltonian structure and Frobenius manifold for asymmetric gAL hierarchy
problem Tri-Hamiltonian structure and Frobenius manifold for asymmetric gAL hierarchy
method Local tri-Hamiltonian structure construction and Frobenius manifold construction
result Dispersionless limits of flows belong to Principal Hierarchy
A relation between the Goldstein-Petrich hierarchy for plane curves and the Toda lattice hierarchy is investigated. A representation formula for plane curves is given in terms of a special class of τ-functions of the Toda lattice hierarchy. A representation formula for discretized plane curves is also discussed.
HAKE embeds entities in polar coordinates to model semantic hierarchies in knowledge graphs.
problem Lack of modeling semantic hierarchies in knowledge graph embeddings.
method HAKE embeds entities in a polar coordinate system, where the radial coordinate represents hierarchy levels and the angular coordinate distinguishes entities at the same level.
result HAKE significantly outperforms existing methods on link prediction tasks in knowledge graphs.
New integrable deformations for topological hierarchies from Frobenius manifolds.
problem Integrable deformations of topological hierarchies from Frobenius manifolds.
method Construction of integrable deformations with polynomial tau-structures.
result Conjecture of universal object for Riemann--Hopf hierarchy.
We introduce two families of soliton hierarchies: the twisted hierarchies associated to symmetric spaces. The Lax pairs of these two hierarchies are Laurent polynomials in the spectral variable. Our constructions gives a hierarchy of commuting flows for the generalized sine-Gordon equation (GSGE), which is the Gauss-Co…
A new method compares image classifiers using adaptive sampling of natural images.
problem Evaluation of image classifiers on small, fixed test sets may not generalize to real-world images.
method Adaptive sampling from a large corpus of unlabeled images to maximize classifier discrepancies measured by WordNet hierarchy.
result Human labeling of model-dependent image sets reveals relative classifier performance.
We compute the central invariants of the bihamiltonian structures of the constrained KP hierarchies, and show that these integrable hierarchies are topological deformations of their hydrodynamic limits.
We prove that the extended Toda hierarchy of \cite{CDZ} admits nonabelian Lie algebra of infinitesimal symmetries isomorphic to the half of the Virasoro algebra. The generators Lm, m≥−1 of the Lie algebra act by linear differential operators onto the tau function of the hierarchy. We also prove that the tau fu…