Study fully augmented links in thickened torus, generalizing S3 results.
problem Classify and describe geometric properties of fully augmented links in thickened torus.
method Geometric analysis and decomposition of link complements into ideal right-angled torihedra.
result Proves Volume Density Conjecture for fully augmented links in thickened torus.
Flat fully augmented links with homeomorphic complements are equivalent.
problem Determining equivalence of flat fully augmented links based on their complements.
method Careful analysis of totally geodesic surfaces and cusps in link complements and their behavior under homeomorphism.
result Complete classification of flat fully augmented link complements with multiple reflection surfaces and symmetries.
Generalizes fully augmented links to doubled 3-manifolds with geometric bounds.
problem Understanding the geometry of fully augmented links in doubled 3-manifolds.
method Constructing fully augmented links on the reflection surface of doubled 3-manifolds and finding bounds on cusp shapes and volumes.
result Bounds on cusp shapes and volumes of hyperbolic links in doubled 3-manifolds.
Fully augmented links have dense volume densities but discrete in certain ranges.
problem Characterizing the volume density spectrum of fully augmented links.
method Analyzing the ratio of volume to the number of augmentations.
result The set of FAL volume densities is dense in $[2\voct, 10\vtet)$ but discrete in $[\voct,2\voct)$.
We study the geometry of fully augmented link complements in S3 by looking at their link diagrams. We extend the method introduced by Thistlethwaite and Tsvietkova to fully augmented links and define a system of algebraic equations in terms of parameters coming from edges and crossings of the link diagrams. Combinin…
This work classifies belted sum decompositions of fully augmented links.
problem Understanding belted sum decompositions of fully augmented links.
method Explicit classifications of thrice punctured spheres in FAL complements, geometric, combinatorial, and diagrammatic characterizations.
result Every FAL complement canonically decomposes into FALs which are either prime or two-fold covers of the Whitehead link.
The paper connects link symmetries to finite subgroups of O(3).
problem Understanding symmetries of flat fully augmented links.
method Developed a dictionary linking graph automorphisms to link symmetries, constructing infinite link classes.
result Symmetry groups of b-prime flat fully augmented links match finite subgroups of O(3).
DAERNN models censored data using neural networks with data augmentation.
problem Handling censored data in expectile regression.
method Data augmentation based Expectile Regression Neural Networks (ERNNs).
result DAERNN outperforms existing censored ERNNs methods and achieves comparable predictive performance to fully observed data.
This paper examines number theoretic and topological properties of fully augmented pretzel link complements. In particular, we determine exactly when these link complements are arithmetic and exactly which are commensurable with one another. We show these link complements realize infinitely many CM-fields as invariant …
For any knot, a 3-sphere triangulation exists with a knotted edge.
problem Finding triangulations of the 3-sphere with specific knot configurations.
method Constructive proof using fully augmented links.
result Constructs one-vertex triangulations of the 3-sphere with knotted edges.
A novel fully asynchronous scheme for distributed reinforcement learning over networks.
problem Policy evaluation in distributed reinforcement learning over networks.
method Design of a stochastic average gradient (SAG) based distributed algorithm and push-pull augmented graph approach.
result The proposed algorithm converges at a linear rate of \(\mathcal{O}(c^k)\) with \(c\in(0,1)\) and \(k\) increasing by one per node update.
Data augmentation has been widely applied as an effective methodology to improve generalization in particular when training deep neural networks. Recently, researchers proposed a few intensive data augmentation techniques, which indeed improved accuracy, yet we notice that these methods augment data have also caused a …
Geometric proof confirms link volume conjecture.
problem Volume conjecture for hyperbolic 3-manifolds.
method Topological and skein theoretic techniques.
result Complements of octahedral fully augmented links are isometric to fundamental shadow links.
Recently, data augmentation in the semi-supervised regime, where unlabeled data vastly outnumbers labeled data, has received a considerable attention. In this paper, we describe an efficient technique for this task, exploiting a recent framework we proposed for missing data imputation called graph imputation neural net…
We present a weakly-supervised data augmentation approach to improve Named Entity Recognition (NER) in a challenging domain: extracting biomedical entities (e.g., proteins) from the scientific literature. First, we train a neural NER (NNER) model over a small seed of fully-labeled examples. Second, we use a reference s…
New examples show no upper bounds on link volumes on incompressible surfaces.
problem Finding upper bounds on volumes of links on incompressible surfaces.
method Examined weakly generalised alternating and fully augmented links on incompressible surfaces.
result Found infinite families of links on incompressible surfaces with no upper bounds on volume.
Contrastive learning properties studied, including feature suppression and hierarchical learning.
problem Feature suppression and hierarchical learning in contrastive learning.
method Generalized contrastive loss, instance-based contrastive learning, explicit and controllable competing features.
result Contrastive learning can suppress and prevent the learning of competing features.
In this paper we analyze symmetries, hidden symmetries, and commensurability classes of (ε,dL)-twisted knot complements, which are the complements of knots that have a sufficiently large number of twists in each of their twist regions. These knot complements can be constructed via long Dehn fillings on fully augmen…
LcGAN generates synthetic CT images for hemorrhagic lesion segmentation.
problem Scarce training data for hemorrhagic lesion segmentation.
method Lesion conditional Generative Adversarial Network (LcGAN) for synthetic image generation.
result Segmentation improved by 12.8% with synthetic data augmentation.
AugMask trains diffusion models on incomplete tabular data by augmenting missing values and applying denoising supervision.
problem Training diffusion models on incomplete tabular data with missing values.
method AugMask uses stochastic augmentation and denoising supervision to adapt diffusion models to incomplete data.
result AugMask enables diffusion-based tabular generators to outperform specialized missing-aware baselines across various datasets and missingness regimes.
Fully convolutional neural networks (FCN) have been shown to achieve state-of-the-art performance on the task of classifying time series sequences. We propose the augmentation of fully convolutional networks with long short term memory recurrent neural network (LSTM RNN) sub-modules for time series classification. Our …
Augmented KRnet improves flow-based generative modeling by maintaining exact invertibility.
problem Maintaining exact invertibility in flow-based generative models.
method Integrates augmented dimensions into KRnet to achieve full nonlinear updates in two iterations, keeping exact invertibility.
result Augmented KRnet achieves full nonlinear updates in two iterations, maintaining exact invertibility.
A new method solves distributed optimization problems over networks.
problem Solving optimization problems over networks with local cost functions and limited communication.
method Distributed semismooth Newton based augmented Lagrangian method.
result The method efficiently solves distributed optimization problems over networks.
Data augmentation (DA) is commonly used during model training, as it significantly improves test error and model robustness. DA artificially expands the training set by applying random noise, rotations, crops, or even adversarial perturbations to the input data. Although DA is widely used, its capacity to provably impr…
Self-supervised learning, which learns by constructing artificial labels given only the input signals, has recently gained considerable attention for learning representations with unlabeled datasets, i.e., learning without any human-annotated supervision. In this paper, we show that such a technique can be used to sign…
New method fractures hyperbolic manifolds using cone singularities.
problem Deforming hyperbolic manifolds with cone singularities.
method Direct manipulation of a fundamental polyhedron to change cone angles.
result Upper unknotting tunnels of highly twisted links can be drilled out.
Synthetic augmentation helps but not always in imbalanced learning.
problem Imbalanced learning causes poor performance on rare classes.
method Developed a statistical framework for synthetic augmentation in imbalanced learning.
result Synthetic augmentation is not always beneficial and depends on the imbalance regime.
We propose a new data-augmentation strategy for fully Bayesian inference in models with binomial likelihoods. The approach appeals to a new class of Polya-Gamma distributions, which are constructed in detail. A variety of examples are presented to show the versatility of the method, including logistic regression, negat…
Variable selection is one of the most important tasks in statistics and machine learning. To incorporate more prior information about the regression coefficients, the constrained Lasso model has been proposed in the literature. In this paper, we present an inexact augmented Lagrangian method to solve the Lasso problem …
Study shows surgeries on specific links result in L-spaces.
problem Understanding surgeries on specific links and their outcomes.
method Proving surgeries on chainmail links yield L-spaces using alternating surgeries.
result Alternating surgeries on chainmail links result in total L-spaces.
Over the past decade, multivariate time series classification has received great attention. We propose transforming the existing univariate time series classification models, the Long Short Term Memory Fully Convolutional Network (LSTM-FCN) and Attention LSTM-FCN (ALSTM-FCN), into a multivariate time series classificat…
Role-wise data augmentation improves knowledge distillation effectiveness.
problem Existing knowledge distillation methods fail to utilize the full potential of teacher-student data interaction.
method Design and implement data augmentation agents with distinct roles for teacher and student.
result Specially tailored data points enhance the demonstration of teacher's knowledge to the student.
Improved generalization with semantic perturbations using normalizing flows.
problem Overfitting in deep neural networks training.
method Use normalizing flows for generating semantically meaningful perturbations in latent space.
result Achieved 96.6% test accuracy on CIFAR-10 with ResNet-18, outperforming existing methods.
The study analyzes consistency-based SSL methods and proposes a new framework.
problem Improving performance in semi-supervised learning with minimal labeled data.
method Analysis of consistency-based SSL methods, including the Π-model, and proposing a new framework. result A simple extension of the Hidden Manifold Model that incorporates data-augmentation schemes.
Generalizes Thistlethwaite-Tsvietkova method to 3-manifolds.
problem Determining the hyperbolic structure of 3-manifolds.
method Polyhedral decomposition, PSL(2,ℂ) representations, Thurston equations.
result Solutions to equations correspond to complete hyperbolic structures.
We present a discriminative clustering approach in which the feature representation can be learned from data and moreover leverage labeled data. Representation learning can give a similarity-based clustering method the ability to automatically adapt to an underlying, yet hidden, geometric structure of the data. The pro…
Neurally Augmented ALISTA improves sparse reconstruction performance.
problem Improving sparse reconstruction performance with theoretical guarantees and empirical improvements.
method Integrates an LSTM network to compute adaptive step sizes and thresholds for each target vector during reconstruction.
result Empirical performance is further improved, especially as compression ratios become more challenging.
DRL optimizes asset managers' hedging timing based on market conditions.
problem Optimal timing for hedging strategies given market conditions.
method Deep Reinforcement Learning framework with contextual information, lagged observations, and robust testing.
result Our approach achieves superior returns and lower risk compared to standard methods.
This paper tackles overfitting in CTR models by introducing Multi-Epoch learning with Data Augmentation.
problem Overfitting of the embedding layer in CTR models during multi-epoch training.
method Introduces Multi-Epoch learning with Data Augmentation (MEDA) framework to reduce overfitting and enhance performance.
result MEDA minimizes overfitting and achieves data augmentation through varied embedding spaces, improving performance without overfitting.
Proposes neural delay differential equations for stable system identification with partially observed states.
problem Learning stable models for systems with partial or delayed observations.
method Augments states with history, uses neural delay differential equations, and ensures stability through time delay analysis.
result The approach ensures stability of learned models for partially observed systems.
CCLF improves sample efficiency in RL by prioritizing informative samples.
problem Learning from high-dimensional observations is challenging and unstable.
method Contrastive-Curiosity-Driven Learning Framework (CCLF) that prioritizes informative samples.
result CCLF improves sample efficiency and learning performance in RL.
We show that the multi-class support vector machine (MSVM) proposed by Lee et. al. (2004), can be viewed as a MAP estimation procedure under an appropriate probabilistic interpretation of the classifier. We also show that this interpretation can be extended to a hierarchical Bayesian architecture and to a fully-Bayesia…
The variational autoencoder (VAE) framework is a popular option for training unsupervised generative models, featuring ease of training and latent representation of data. The objective function of VAE does not guarantee to achieve the latter, however, and failure to do so leads to a frequent failure mode called posteri…
A new method solves large-scale sparse group square-root Lasso problems efficiently.
problem Large-scale linearly constrained sparse group square-root Lasso problems.
method Dual semismooth Newton based augmented Lagrangian method (ALM).
result The proposed method efficiently solves the problem with numerical experiments demonstrating its effectiveness.
A novel approach of training data augmentation and domain adaptation is presented to support machine learning applications for cognitive radio. Machine learning provides effective tools to automate cognitive radio functionalities by reliably extracting and learning intrinsic spectrum dynamics. However, there are two im…
This paper proposes CSADA to make DNNs cost-sensitive.
problem Over-parameterization challenges cost-sensitive classification in DNNs.
method CSADA framework using adversarial data augmentation.
result CSADA effectively minimizes overall cost and reduces critical errors.
AI enhances pollen recognition in veterinary imaging using holographic microscopy.
problem Challenges in recognizing pollen in holographic images due to speckle noise and artifacts.
method Training YOLOv8s and MobileNetV3L on dual-modality dataset, employing WGAN-SN for synthetic data augmentation.
result GAN-based augmentation improves object detection and classification in holographic images, closing the performance gap.
Mixup improves feature learning by mixing common and rare features.
problem Improving generalization in deep learning models.
method Mixup, a data augmentation technique, is applied to feature learning. Theoretical and experimental studies are conducted to understand its benefits.
result Mixup effectively learns rare features from common ones, leading to better generalization.