Study of Legendrian links using Floer theory and cluster varieties.
problem Understanding exact Lagrangian fillings of positive braid Legendrian links.
method Floer-theoretic approach and exact Lagrangian cobordisms.
result Proves that positive braid Legendrian links admit infinitely many exact Lagrangian fillings.
Study of braid varieties and their Legendrian isotopy.
problem Understanding the geometric properties of braid varieties.
method Examined four types of braids and their Legendrian links.
result Each open positroid stratum can be represented as an augmentation variety.
The paper connects Legendrian links to cluster theory and exact Lagrangian fillings.
problem Understanding the relationship between Legendrian links and cluster theory.
method Using exact Lagrangian fillings and cluster theory, the paper establishes connections between Legendrian links and cluster varieties.
result The augmentation variety of certain Legendrian 2-bridge links is isomorphic to a product of cluster varieties.
Study Legendrian graph invariants via augmentation and ruling polynomials.
problem Equivalence of Legendrian isotopy invariants.
method Use augmentation number and ruling polynomial for front projection.
result Show equivalence between augmentation number and ruling polynomial.
Study ablated data augmentation techniques and their mathematical equivalence to penalties.
problem Lack of mathematical understanding of differences between ablated data augmentation techniques.
method Formal model of mean ablated data augmentation and inverted dropout for linear regression; empirical validation for deep networks.
result Ablated data augmentation and inverted dropout are mathematically equivalent to penalties in optimization.
The article introduces a combinatorial differential algebra for cubic planar graphs.
problem Understanding the structure of cubic planar graphs.
method Defining a combinatorial differential graded algebra based on binary sequences and counting.
result The algebra's graded augmentation variety's rational points match (q+1)-colorings of the dual graph.
We study the connection between topological strings and contact homology recently proposed in the context of knot invariants. In particular, we establish the proposed relation between the Gromov-Witten disk amplitudes of a Lagrangian associated to a knot and augmentations of its contact homology algebra. This also impl…
New augmentations of twist knots found that can't be filled.
problem Finding augmentations of twist knots that cannot be filled by orientable Lagrangian fillings.
method Using a Floer-theoretic version of a result from microlocal sheaf theory, showing augmentations cannot be induced by algebraic tori.
result Established new examples of augmentations of Legendrian twist knots that cannot be induced by orientable Lagrangian fillings.
Batch augmentation improves deep learning training by reducing batch size requirements.
problem Training deep neural networks with large batches can lead to overfitting.
method Replicate samples within a batch with different data augmentations.
result Batch augmentation reduces the number of necessary SGD updates for achieving the same accuracy.
Augmentor adds variety to image datasets for machine learning models.
problem Improving model accuracy and generalization in machine learning.
method A high-level API for stochastic, pipeline-based image augmentation.
result Enhanced model performance through diverse image data.
Alexander polynomial derived from knot contact homology and Floer strips.
problem Calculating the Alexander polynomial of a knot.
method Contact homology and Floer theory applied to knot complements.
result Alexander polynomial expressed as an integral of partial derivatives.
This work investigates image augmentations for GAN training, improving image quality.
problem Improving the accuracy and robustness of GAN models for image synthesis.
method Systematic study of various image augmentation techniques for GAN training.
result Vanilla GANs can achieve state-of-the-art generation quality with image augmentations.
The paper connects Chern-Simons invariants to mixed Tate motives in hyperbolic 3-manifolds.
problem Understanding the relationship between Chern-Simons invariants and mixed Tate motives in hyperbolic 3-manifolds.
method Constructing a mixed Tate motive over the invariant trace field whose image equals the Chern-Simons invariant and complex volume.
result The mixed Hodge realization of the motive is a quotient of the path torsor of the augmented character variety.
Generalizes ruling polynomials to Legendrian tangles and proves their composition property.
problem Computing augmentation numbers for Legendrian tangles.
method Generalization of ruling polynomials to Legendrian tangles and proving their composition property.
result Ruling polynomials for Legendrian tangles satisfy the composition axiom.
Study connects knot contact homology to Chern-Simons theory's large N limit.
problem Relate knot contact homology to Chern-Simons theory's large N limit.
method Prove conjecture linking augmentation varieties to Chern-Simons theory's large N limit; characterize HOMFLYPT difference module.
result Classical limit of HOMFLYPT difference module equals degree 0 abelianized knot contact homology.
Aug-Gen improves music generation by augmenting training data with model-produced examples.
problem Lack of high-quality training data for specific musical styles.
method Dataset augmentation using generated examples during training.
result Aug-Gen improves both training duration and quality of generated music.
Clean intersections of Lagrangian knots in 3D are impossible.
problem Prohibiting clean intersections of certain knots in 3D symplectic geometry.
method Symplectic field theory and algebraic constraints on augmentation varieties.
result No Hamiltonian diffeomorphism can cleanly intersect a specific type of knot's conormal bundle.
We study the relationship between Ng's abelian cord ring and SL(2,C) characters of the two-fold branched cover Σ(K). Augmentations, and their corresponding rank, play a central role in the relationship. Our study also leads to a correspondence between trace-free SL(2,C) characters of a knot complement and augmentatio…
Task-agnostic data augmentation shows little benefit for pretrained transformers.
problem Evaluating the effectiveness of task-agnostic data augmentation on pretrained transformers.
method Conducted a systematic examination of two data augmentation techniques (Easy Data Augmentation and Back-Translation) across 5 tasks, 6 datasets, and 3 pretrained transformer models.
result Data augmentation techniques previously effective for non-pretrained models fail to consistently improve performance for pretrained transformers, even with limited training data.
SapAugment learns adaptive augmentation policies for better model training.
problem Fixed data augmentation methods often apply the same augmentation to all samples, ignoring sample difficulty.
method SapAugment adapts augmentation parameters based on training loss, learning a sample-adaptive policy.
result SapAugment achieves up to 21% relative reduction in word error rate on LibriSpeech dataset.
Paper improves music transcription models with invariance and data augmentation.
problem Improving accuracy of frame-based music transcription models.
method Translation-invariant network combining filterbank and CNN, trained with pitch-shift augmented data.
result Top-performing model in MIREX evaluation, reducing model complexity and avoiding overfitting.
This work analyzes benefits and limitations of data augmentation and feature averaging in deep learning models.
problem Theoretical understanding of incorporating invariance into deep learning models is lacking.
method Data augmentation and feature averaging are analyzed in the context of invariance in deep learning.
result Training with data augmentation leads to better estimates of risk and gradients, and feature averaging reduces generalization error with convex losses.
New framework explains diverse impacts of data augmentation.
problem Understanding the varied effects of data augmentation on model performance.
method Developed a theoretical framework to characterize DA's impact on linear models.
result Data augmentation induces implicit spectral regularization through two effects.
Data augmentation improves deep learning efficiency.
problem Uncertainty quantification in deep learning models.
method Data augmentation techniques combined with Monte Carlo methods.
result Data augmentation leads to efficiency gains in deep learning.
By developing data augmentation methods unique to the negative binomial (NB) distribution, we unite seemingly disjoint count and mixture models under the NB process framework. We develop fundamental properties of the models and derive efficient Gibbs sampling inference. We show that the gamma-NB process can be reduced …
ISDA augments deep networks by adding semantic transformations.
problem Improving deep network generalization through semantic data augmentation.
method ISDA augments deep feature space by estimating covariance and drawing random vectors.
result ISDA consistently improves deep model performance on various datasets.
New algorithms tackle data challenges in physics model selection.
problem Lack of labeled data, high dimensionality, and inapplicability of data augmentation techniques to physics data.
method Two algorithms: feature selection and data augmentation combined with classifiers and stacking ensemble.
result Achieved 90% accuracy on nonlinear structural mechanics classification problem.
This paper proposes a method for instrument classification in polyphonic music using monophonic data.
problem Instrument classification in polyphonic music from monophonic data.
method Data augmentation techniques including overlaying audio segments of the same genre, pitch, and tempo synchronization. Convolutional Neural Networks used for classification.
result An ensemble of VGG-like classifiers trained on non-augmented, pitch-synchronized, tempo-synchronized and genre-similar excerpts achieved above 80% LRAP.
Study shows how to separate jets on complex varieties using coverings.
problem Separating jets on complex varieties of maximal Albanese dimension.
method Using finite abelian étale covers and moving Seshadri constants.
result Existence of abelian covers that separate jets.
AAL method generates few-shot tasks from unlabeled data for unsupervised few-shot learning.
problem Lack of unsupervised few-shot learning methods.
method Randomly label a subset of images, apply data augmentation, and use generated labels for target sets.
result Learned models achieve good generalization on Omniglot and Mini-Imagenet.
We analyze the convergence behaviour of a recently proposed algorithm for regularized estimation called Dual Augmented Lagrangian (DAL). Our analysis is based on a new interpretation of DAL as a proximal minimization algorithm. We theoretically show under some conditions that DAL converges super-linearly in a non-asymp…
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…
We connect knot contact homology to colored HOMFLY-PT polynomials using SFT and recursion.
problem Understanding colored HOMFLY-PT polynomials for knots and links.
method Legendrian Symplectic Field Theory, large N duality, Witten's connection, induction, elimination theory. result Established a recursion relation for colored HOMFLY-PT polynomials using SFT and elimination theory.
The paper studies knot types of clean intersections in a 3D space.
problem Identifying knot types in clean intersections.
method Using compactly supported Hamiltonian isotopy and DGA maps.
result Constraints on knot types of intersections.
New approach uses text generation to boost AI agent development.
problem Lack of training data hinders AI agent development.
method Used encoder-decoder generative models, focusing on conditional variational auto-encoders.
result Significantly improved AI agent performance in low-resource cases.
Worldsheet skein D-module for Hopf link conormal uniquely determines partition functions.
problem Understanding HOMFLYPT polynomials and their geometric origins.
method Defining worldsheet skein module and D-module, considering skein valued open curve counts.
result Worldsheet skein D-module for Hopf link conormal is generated by three operator polynomials.
Study shows low-complexity models can perform as well as state-of-the-art on small datasets.
problem Performance of deep learning models on small datasets.
method Wide variety of experiments with different deep learning architectures on small datasets.
result Low-complexity models can perform comparably well or better than state-of-the-art models on small datasets.
Domain Fusion uses GANs to augment data for low-volume target datasets.
problem High costs in data development for deep learning applications.
method Multi-domain learning GANs to generate new samples.
result Domain Fusion achieves better classification accuracy with less data.
Metalearned neural memory improves learning across various tasks.
problem Improving neural network adaptability and memory function.
method Augmenting neural networks with a metalearned external memory mechanism.
result The model achieves strong performance on diverse learning problems.
Using the duality between Wilson loop expectation values of SU(N) Chern-Simons theory on S3 and topological open-string amplitudes on the local mirror of the resolved conifold, we study knots on S3 and their invariants encoded in colored HOMFLY polynomials by means of topological recursion. In the context of the …
New method solves constrained optimization problems efficiently.
problem Equality-constrained nonlinear, nonconvex optimization problems.
method Adaptive inexact Newton method with randomized iterative sketching.
result Global almost sure convergence and local linear/superlinear convergence.
A new decentralized algorithm DESTINY solves optimization over Stiefel manifold with single communication round.
problem Decentralized optimization over the Stiefel manifold with private data.
method Gradient tracking with approximate augmented Lagrangian function.
result DESTINY achieves global convergence with a single communication round.
Efficiently solves large-scale SVMs with sparse semismooth Newton method.
problem Numerical difficulties in solving large-scale SVMs.
method Sparse semismooth Newton based augmented Lagrangian method.
result Outperforms state-of-the-art solvers for large-scale SVMs.
Researchers found that avoiding synthetic data generation prevents model collapse in machine learning.
problem Model collapse in machine learning where models degenerate over generations.
method Comparing discard and augment workflows, focusing on Linear Regression.
result Theoretical evidence shows that for Linear Regression, test risk is bounded by π²/6 of original data alone.
Improved skin lesion classification with neural networks and data augmentation.
problem Skin lesion classification accuracy improvement.
method Multi-scale convolutional neural networks and domain-specific image augmentation.
result Proposed method outperforms state-of-the-art approaches on ISIC2016 and ISIC2017 tasks.
A fundamental task in machine learning and related fields is to perform inference on Bayesian networks. Since exact inference takes exponential time in general, a variety of approximate methods are used. Gibbs sampling is one of the most accurate approaches and provides unbiased samples from the posterior but it has hi…
DPGDS models sequential count data with deep hierarchical structure and temporal dependencies.
problem Modeling sequentially observed multivariate count data with hierarchical and temporal dependencies.
method Developed deep Poisson-gamma dynamical systems with data augmentation and MCMC inference.
result Demonstrated excellent predictive performance and interpretable latent structure.
Improved reinforcement learning for 3D games using SLAM and object detection.
problem Challenges in 3D game environments, especially partial observability and combinatorial spaces.
method Augmented Deep Q-Learning Network with SLAM and object detection for better policy learning.
result Our approach consistently learns better policies in 3D games like Doom.