Paper proposes angular loss for better face recognition and object classification.
problem Improving intra-class compactness and preventing overfitting in face recognition and object classification.
method Angular loss function to maximize angular gradient, reducing overfitting and requiring only one adjustable constant.
result Our method outperforms other methods in accuracy, discriminative information, and time-efficiency.
Study improves speaker verification accuracy using angular based embedding learning.
problem Improving discriminative power of embeddings for open-set speaker verification.
method Optimizes angular distance and adds margin penalty, applying various angular margin embedding strategies and proposing inter-class regularization.
result Achieved impressive results with 16.5% improvement in EER and 18.2% improvement in minimum detection cost function.
SphereConv improves deep learning by learning angular representations on hyperspheres.
problem Challenges in training deep CNNs due to increased depth and larger parameter space.
method Introduces hyperspherical convolution (SphereConv) and deep hyperspherical convolution networks (SphereNet) to learn angular representations on hyperspheres.
result SphereNet effectively encodes discriminative representation and alleviates training difficulty.
Improved deep neural networks for text-independent speaker recognition.
problem Text-independent speaker recognition using deep neural networks.
method Angular softmax activation, residual frame level connections, cosine similarity, discriminative similarity metric learning.
result Improved speaker recognition accuracy on real-life conditions.
STC systems improved deep learning for ASVspoof2019 challenge.
problem Detecting spoofing attacks in speech recognition.
method Deep learning, Light CNN architecture, angular margin based softmax activation.
result Achieved EER of 1.86% in logical access and 0.54% in physical access scenarios.
Paper classifies curvature measures and confirms a conjecture.
problem Classifying curvature measures and proving the angularity conjecture.
method Investigation of translation-invariant angular curvature measures and use of isometric immersions and Lipschitz-Killing algebra.
result Confirmation of the angularity conjecture.
Formulae for mass and angular momentum transformations under BMS transformations derived from curvature and metric.
problem Deriving transformation formulae for mass and angular momentum under BMS transformations.
method Two approaches: from curvature tensor and metric coefficients.
result Exact expressions for Drey-Streubel angular momentum of a general section.
New method resolves ambiguity in measuring black hole merger angular momentum.
problem Ambiguity in measuring angular momentum during black hole mergers.
method Quasilocal mass and optimal isometric embedding theory.
result New definition of angular momentum free of supertranslation ambiguity.
New method constructs axial vector fields and defines quasi-local spin-angular momentum.
problem Constructing axial vector fields on Riemannian two-spheres.
method Using centre-of-mass unit sphere reference systems and Lie-propagated unit sphere reference systems.
result Constructive definition of quasi-local spin-angular momentum and balance relations.
Study proves inequality linking black hole properties and angular momentum.
problem Establishing a Penrose-type inequality for black holes with 3-sphere horizons.
method Analyzing biaxially symmetric, maximal, asymptotically flat initial data sets for the Einstein equations.
result Equality holds only for stationary Myers-Perry black holes.
Researchers prove CWY angular momentum is supertranslation invariant in double null gauge.
problem Supertranslation invariance of CWY angular momentum in double null gauge.
method Identified and proved supertranslation ambiguity; showed CWY angular momentum is free of this ambiguity.
result CWY angular momentum is supertranslation invariant in double null gauge.
The paper defines cross-section continuity for angular momentum definitions and finds the CWY definition valid.
problem Defining angular momentum at null infinity and ensuring its continuity across different cross-sections.
method Introducing cross-section continuity as a criterion and proving it for specific angular momentum definitions.
result The Chen-Wang-Yau definition of angular momentum satisfies cross-section continuity, while the Compere-Nichols modification does not.
Formulae track evolution of angular momentum and center of mass at null infinity.
problem Tracking the evolution of conserved quantities at null infinity.
method Evolution formulae in Bondi-Sachs coordinates, expressed in terms of shear and news tensors.
result Supertranslation invariance of fluxes, conservation law of angular momentum, duality paradigm.
Proposes sigsoftmax to overcome the softmax bottleneck in language models.
problem Softmax function acts as a bottleneck in neural network representational capacity.
method Identifies the cause of softmax bottleneck and proposes sigsoftmax as a new activation function.
result Sigsoftmax outperforms softmax in language modeling tasks.
New definition of angular momentum avoids supertranslation ambiguity.
problem Supertranslation ambiguity in angular momentum calculations.
method Derived from quasilocal angular momentum and defined at null infinity.
result First supertranslation-invariant definition of angular momentum.
Develops RF-softmax for faster training with softmax cross entropy.
problem High computational cost of training with softmax cross entropy.
method Random Fourier Features for efficient sampling from approximate softmax distribution.
result RF-softmax provides low bias in estimating both softmax distribution and its gradient.
Proposes AE for robust PCA, improving robustness to outliers.
problem PCA's sensitivity to outliers.
method Angular Embedding (AE) and Truncated Angular Embedding (TAE).
result AE/TAE outperforms state-of-the-art RPCA methods.
Establishes a Penrose-type inequality for axisymmetric initial data with angular momentum and charge.
problem Establishing a Penrose-type inequality for axisymmetric initial data with angular momentum and charge.
method Maximal, axisymmetric initial data for the Einstein-Maxwell equations satisfying the weak energy condition. Rigidity statement proven.
result Reduces to the conjectured Penrose inequality with angular momentum and charge under certain conditions.
The paper provides bounds for the empirical angular measure and applies them to improve statistical learning in extreme regions.
problem Estimating the angular measure in high-dimensional data with different distributions.
method Established bounds for the maximal deviations of the empirical angular measure from the true measure, using rank transformation and analyzing the most extreme observations.
result The bounds provide performance guarantees for statistical learning procedures in extreme regions, such as binary classification and anomaly detection.
Hierarchical Softmax approximates class probabilities for large datasets efficiently.
problem Computational inefficiency of Softmax for large-scale classification tasks.
method Used Hierarchical Softmax to approximate class probabilities efficiently.
result Hierarchical Softmax performance degrades as the number of classes increases.
Study limits of quasi-local angular momentum at infinity of gravitating systems.
problem Understanding limits of quasi-local angular momentum at infinity of gravitating systems.
method Based on optimal isometric embedding and quasilocal mass theory, the study defines and analyzes the limits of quasi-local angular momentum at spatial and null infinity.
result Limits of quasi-local angular momentum are discussed at spatial and null infinity of an isolated gravitating system.
New memory effect discovered in gravitational wave behavior.
problem Understanding gravitational wave behavior in spacetimes with angular momentum.
method Mathematical analysis of Minkowski spacetime and Kerr black holes.
result Angular momentum memory effect observed at future null infinity.
Study finds mass bound for 3-manifolds with boundary, angular momentum, and charge.
problem Establishing precise mass lower bound for asymptotically flat 3-manifolds.
method Analyzes nonnegative scalar curvature and minimal surface boundary conditions, without simple connectivity and completeness.
result Proves mass lower bound in terms of angular momentum and charge, without restrictive assumptions.
Revises logistic-softmax likelihood for Bayesian meta-learning in few-shot classification.
problem Inherent uncertainty in logistic-softmax leads to suboptimal performance in meta-learning.
method Redesigns logistic-softmax likelihood with a temperature parameter for better control of prior confidence.
result Achieves well-calibrated uncertainty estimates and comparable/superior performance on benchmark datasets.
We exam the validity of the definition of the ADM angular momentum without the parity assumption. Explicit examples of asymptotically flat hypersurfaces in the Minkowski spacetime with zero ADM energy-momentum vector and finite non-zero angular momentum vector are presented. We also discuss the Beig-Ó Murchadha-Regge-T…
Paper introduces Balanced Meta-Softmax for better long-tailed visual recognition.
problem Long-tailed distribution mismatch between training and testing data.
method Balanced Meta-Softmax, an unbiased extension of Softmax, using a Meta Sampler.
result Balanced Meta-Softmax outperforms state-of-the-art solutions on visual recognition and instance segmentation.
Paper introduces hierarchical softmax for global hierarchical classification tasks.
problem Improving classification accuracy in tasks with class hierarchies.
method Global hierarchical neural networks using hierarchical softmax.
result Hierarchical softmax outperforms regular softmax in multiple datasets.
DS-Softmax speeds up softmax inference by learning sparse experts.
problem Expensive softmax computations for large output classes.
method Sparse mixture of sparse experts for efficient top-k class retrieval.
result Significant computation reductions achieved at no performance loss.
Softmax emerges naturally in neural networks as a measure of conditional mutual information.
problem The artificial nature of softmax in neural networks.
method Information-theoretic perspective to derive log-softmax and evaluate conditional mutual information.
result Training deterministic neural networks through log-softmax maximises conditional mutual information.
Generative models improve angular variable simulation in high dimensions.
problem Lack of flexibility and scalability in simulating multivariate angular variables.
method Introducing generative adversarial networks, normalizing flows, and flow matching.
result Deep learning methods outperform classical parametric models in complex data structures.
We show how to reduce the general formulation of the mass-angular momentum-charge inequality, for axisymmetric initial data of the Einstein-Maxwell equations, to the known maximal case whenever a geometrically motivated system of equations admits a solution. It is also shown that the same reduction argument applies to …
New method uses neural networks for accurate angle estimation in noisy conditions.
problem Accurately estimate angles from noisy measurements in various applications.
method Directed Graph Neural Networks (GNNSync) for end-to-end trainable framework.
result GNNSync achieves competitive performance, even at high noise levels.
Binary testing for softmax models requires many samples, similar to leverage score models.
problem Binary hypothesis testing for softmax models and leverage score models.
method Analyzing sample complexity and drawing analogies between models.
result Sample complexity is asymptotically \(O(ε^{-2})\), where \(ε\) is the distance between model parameters.
A new index ASI quantifies angular separation of network communities in hyperbolic space.
problem Quantifying angular separation of network communities in high-dimensional data.
method Introducing Angular Separability Index (ASI) and a statistical test.
result ASI reveals significant phenomena in network geometry, including dimensionality jumps and intrinsic dimensionality detection.
New algorithms make softmax optimization unbiased and scalable.
problem Efficiently computing softmax distributions with large categories.
method Proposed unbiased algorithms for maximizing softmax likelihood.
result Comprehensive outperformance on seven real-world datasets.
We present a general sufficient condition for the formation of black holes due to concentration of angular momentum. This is expressed in the form of a universal inequality, relating the size and angular momentum of bodies, and is proven in the context of axisymmetric initial data sets for the Einstein equations which …
AngularGrad optimizes CNNs by considering gradient direction, improving convergence.
problem Dying gradient problem and inefficiency in exploiting gradient curvature.
method AngularGrad considers gradient direction/angle, generating a score for step size control.
result AngularGrad outperforms state-of-the-art optimizers in benchmark tests.
Study reformulates Finsler metrizability problems using geodesic invariance.
problem Finsler metrizability problems for sprays.
method Reformulate problems in terms of geodesic invariance of tensors (metric and angular).
result Gyroscopic sprays have geodesically invariant angular metric.
The paper investigates polynomial alternatives to softmax in transformer models.
problem The effectiveness of softmax attention in transformers is questioned.
method The authors explore polynomial activations as alternatives to softmax, focusing on their ability to regularize the attention matrix.
result Certain polynomials can serve as effective substitutes for softmax in transformer applications, achieving strong performance.
Softmax temperature influences model representation rank and performance.
problem Understanding and optimizing softmax function's impact on model representations.
method Investigated softmax function's role in deep neural networks, introduced rank deficit bias.
result Softmax temperature affects model representation rank and can improve performance.
In the present work we establish a quantization result for the angular part of the energy of solu- tions to elliptic linear systems of Schrödinger type with antisymmetric potentials in two dimension. This quantization is a consequence of uniform Lorentz-Wente type estimates in degenerating annuli. We derive from this a…
We prove that extreme Kerr initial data set is a unique absolute minimum of the total mass in a (physically relevant) class of vacuum, maximal, asymptotically flat, axisymmetric data for Einstein equations with fixed angular momentum. These data represent non-stationary, axially symmetric, black holes. As a consequence…
Improved classifier accuracy by using more of the class-specific structure in trained models.
problem Softmax ignores valuable information encoded in the full array of class response distributions.
method Developed a hybrid classifier (Softmax-Pooling Hybrid, SPH) that uses Softmax on high-scoring samples and a log-likelihood method on low-scoring samples. result Reduces test set error by 6% to 23% using the exact same trained model.
Cross-entropy loss together with softmax is arguably one of the most common used supervision components in convolutional neural networks (CNNs). Despite its simplicity, popularity and excellent performance, the component does not explicitly encourage discriminative learning of features. In this paper, we propose a gene…
AGCA approximates angular variation on the unit sphere, reducing extremal dependence problems to eigenanalysis.
problem Approximating angular variation in multivariate extremes.
method Anchored geodesic component analysis (AGCA) approximates angular variation by great subspheres constrained to pass through a chosen reference direction.
result AGCA finds concentrated tail directions in daily equity-portfolio losses, explaining about 91% of anchored variation.
Paper proposes a new softmax loss for better performance in Positive and Unlabeled data tasks.
problem Current softmax losses and sampling schemes have drawbacks in Positive and Unlabeled learning.
method Proposes Relaxed Softmax (RS) loss and a new negative sampling scheme.
result New training objective drives uplifts in performance on textual and recommendation datasets.
Investigates physical properties on surfaces of rotation using Clairaut's theorem.
problem Understanding specific energy and angular momentum on surfaces of rotation.
method Used Clairaut's theorem with geodesic conditions to derive specific energy and angular momentum.
result Physical expressions for specific energy and angular momentum on surfaces of rotation were derived.
We show that extreme Myers-Perry initial data realize the unique absolute minimum of the total mass in a physically relevant (Brill) class of maximal, asymptotically flat, bi-axisymmetric initial data for the Einstein equations with fixed angular momenta. As a consequence, we prove the relevant mass-angular momentum in…