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.
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.
Efficiently reduces data augmentation size with similar accuracy.
problem Explosive growth in dataset size due to data augmentation.
method Subsampling policies based on model influence and loss.
result Achieves a 90% reduction in augmentation set size while maintaining accuracy.
We describe a correspondence between augmentations and certain representations of the knot group. The correspondence makes the 2-variable augmentation polynomial into a generalization of the classical A-polynomial. It also associates to an augmentation a rank, which is bounded by the bridge number and shares its beha…
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 $[\voct,2\voct)$.
The paper studies arithmeticity and hidden symmetries in fully augmented pretzel link complements.
problem Determining arithmeticity and commensurability of fully augmented pretzel link complements.
method Careful analysis of geometry, including cusp shapes and totally geodesic surfaces.
result Construction of two infinite families of non-arithmetic fully augmented link complements.
The paper analyzes how data augmentation affects the test error in regression models.
problem Understanding the impact of data augmentation on the test error in regression models.
method Characterizes the test error in terms of population quantities and augmentation statistics.
result Provides a tight characterization of the test error in mean squared error.
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.
Data augmentation implicitly regularizes deep networks by penalizing rugosity.
problem Understanding generalization in overparameterized deep networks.
method Data augmentation introduces an implicit regularization penalty based on rugosity.
result Data augmentation penalizes rugosity, leading to better generalization.
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.
Smart Augmentation learns optimal data augmentation for neural networks.
problem Insufficient data for deep neural networks.
method Creates a network that learns to generate augmented data during training.
result Significantly increases accuracy and reduces overfitting.
A connection between holomorphic and generating family invariants of Legendrian knots is established; namely, that the existence of a ruling (or decomposition) of a Legendrian knot is equivalent to the existence of an augmentation of its contact homology. This result was obtained independently and using different metho…
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.
We strengthen the link between holomorphic and generating-function invariants of Legendrian knots by establishing a formula relating the number of augmentations of a knot's contact homology to the complete ruling invariant of Chekanov and Pushkar.
Enhances reinforcement learning from sparse data.
problem Limited data for offline reinforcement learning.
method Trajectory-based data augmentation.
result Improves reinforcement learning performance.
For any Legendrian link, L, in (\R^3, \ker(dz-y\,dx)) we define invariants, Aug_m(L,q), as normalized counts of augmentations from the Legendrian contact homology DGA of L into a finite field of order q where the parameter m is a divisor of twice the rotation number of L. Generalizing a result of Ng and Sabloff for the…
This paper evaluates methods to improve classification on imbalanced datasets.
problem Class imbalance in classification problems.
method Combination of data augmentation and ensemble learning methods.
result Combinations of data augmentation methods with ensemble learning can significantly improve classification performance.
Dropout is typically interpreted as bagging a large number of models sharing parameters. We show that using dropout in a network can also be interpreted as a kind of data augmentation in the input space without domain knowledge. We present an approach to projecting the dropout noise within a network back into the input…
ODVICE augments EHR cohorts using ontology to improve analysis robustness.
problem Limited records in cohorts for rare diseases hamper robust analysis.
method Ontology-driven Monte-Carlo graph spanning algorithm for data augmentation.
result ODVICE augmented cohorts show ~30% improvement in AUC over non-augmented datasets.
For a Legendrian (2,n) torus knot or link with maximal Thurston-Bennequin number, Ekholm, Honda, and Kálmán constructed Cn exact Lagrangian fillings, where Cn is the n-th Catalan number. We show that these exact Lagrangian fillings are pairwise non-isotopic through exact Lagrangian isotopy. To do that, we com…
Stability training improves deep neural networks' robustness without data augmentation.
problem Improving deep neural networks' robustness against input perturbations.
method Stability training as an alternative to data augmentation.
result Stability training outperforms data augmentation in specific transformations and offers improved robustness against a broader range of distortions.
A&R method reduces computational cost for large categorical distributions.
problem High computational cost for large categorical distributions.
method Latent variable augmentation and stochastic variational inference.
result A&R provides a tighter bound on the marginal likelihood and better predictive performance.
Study improves voice conversion model with Mel-spectrogram augmentation.
problem Insufficient speech pairs data for training sequence-to-sequence voice conversion models.
method Experimented with Mel-spectrogram augmentation using SpecAugment policies and proposed new augmentation policies.
result Time axis warping policies showed better performance in training the voice conversion model.
Paper tackles scalable VFL with data augmentation and amortized inference.
problem Collaborative model estimation across multiple clients with distinct covariates.
method Data augmentation, amortized variational approximation, factorized likelihoods.
result Scalable Bayesian VFL framework for various models.
We study the problem of large scale, multi-label visual recognition with a large number of possible classes. We propose a method for augmenting a trained neural network classifier with auxiliary capacity in a manner designed to significantly improve upon an already well-performing model, while minimally impacting its c…
Data augmentation affects estimates' uncertainty and distribution in complex ways.
problem Understanding how data augmentation impacts the variance and limiting distribution of estimates.
method Developed an adaptation of Lindeberg's technique for block dependence.
result Data augmentation can increase rather than decrease uncertainty, and it may shift the double-descent peak of an empirical risk.
Enhances particle filters with neural augmentation for multi-sub-state tracking.
problem Particle filters struggle with complex or approximated models and low latency requirements.
method Learning Flock (LF) uses a neural network to correct particle weights based on sub-particle relationships.
result LF improves performance, robustness, and latency in radar multi-target tracking.
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.
The paper explains how data augmentation improves semi-supervised learning efficiency.
problem Improving accuracy from a small fraction of labeled data.
method Data augmentation induces a similarity graph, which is graph-Laplacian-regularized for downstream learning.
result A fast transductive rate of O(1/nL) is achieved, reducing the number of labels needed. Expert-augmented algorithm boosts scores in Montezuma's Revenge.
problem Sparse rewards in Montezuma's Revenge.
method Expert-augmented actor-critic algorithm.
result Achieves above 27,000 points consistently, surpassing expert performance.
Online data augmentation improves forecasting performance in deep learning.
problem Insufficient training data for forecasting tasks.
method An online data augmentation framework that generates synthetic samples during training.
result Online data augmentation leads to better forecasting performance.
In this article we study the differential graded algebra (DGA) invariant associated to Legendrian knots in tight lens spaces. Given a grid number one diagram for a knot in L(p, q), we show how to construct a special Lagrangian diagram suitable for computing the DGA invariant for the Legendrian knot specified by the dia…
We propose an efficient algorithm for sparse signal reconstruction problems. The proposed algorithm is an augmented Lagrangian method based on the dual sparse reconstruction problem. It is efficient when the number of unknown variables is much larger than the number of observations because of the dual formulation. More…
Data augmentation improves model robustness by enforcing a margin.
problem Understanding how data augmentation provably improves model robustness.
method Analyzed linear and nonlinear models, quantifying the margin introduced by data augmentation.
result Commonly used data augmentation techniques may only introduce significant margin after adding exponentially many points.
Survey of data augmentation methods for improving deep learning on time series data.
problem Limited labeled data in real-world time series applications.
method Review and comparison of data augmentation methods for time series.
result Empirical comparison of data augmentation methods for various time series tasks.
ARM estimator improves gradient backpropagation in binary networks.
problem Improving gradient backpropagation through stochastic binary layers.
method ARM estimator using augment-REINFORCE-merge approach.
result ARM estimator achieves state-of-the-art performance in binary models.
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.
Given a knot K in S3, a question raised by Cappell and Shaneson asks if the meridional rank of K equals the bridge number of K. Using augmentations in knot contact homology we consider the persistence of equality between these two invariants under satellite operations on K with a braid pattern. In particular…
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.
The study analyzes how data augmentation helps isolate content from style in self-supervised learning.
problem Understanding how data augmentation affects the separation of content and style in self-supervised learning.
method Formulated a latent variable model with content and style components, studied identifiability of latent representation, and introduced a dataset to test the theory.
result Sufficient conditions for identifying the invariant content partition in self-supervised learning.
We study certain linear representations of the knot group that induce augmentations of knot contact homology. This perspective on augmentations enhances our understanding of the relationship between the augmentation polynomial and the A-polynomial of the knot. For example, we show that for 2-bridge knots the polynomial…
We study the geometry of oriented right-angled hexagons in H^4, the hyperbolic 4-space, via Clifford numbers or quaternions. We show how to augment alternate sides of such a hexagon so that for the non-augmented sides, we can define quaternion half side-lengths whose angular parts are obtained from half the Euler angle…
ARSM estimator improves gradient backpropagation for categorical variables.
problem Improving gradient backpropagation through categorical variables.
method ARSM combines variable augmentation, REINFORCE, Rao-Blackwellization, and variable swapping.
result ARSM outperforms existing estimators and provides variance reduction methods.
Proposes a data augmentation method to improve multi-label learning performance.
problem Improving multi-label learning by exploiting label correlations and data augmentation.
method Proposes a novel data augmentation approach that performs clustering on real examples and treats cluster centers as virtual examples, promoting local smoothness through a regularization term.
result Extensive experiments show that the proposed method outperforms state-of-the-art multi-label learning approaches.
Generative model boosts bone lesion classification with augmented data.
problem Class imbalance and limited training data for bone lesion classification.
method Cycle-consistent GAN for image patch translation across bones.
result Generative augmentation improves classifier performance on held-out test set.
Greedy AutoAugment improves accuracy with less computation.
problem Finding effective data augmentation policies to cover the search space.
method Greedy approach to reduce the number of trials from exponential to linear growth.
result Greedy AutoAugment increases accuracy by 360 times with fewer resources.
Develops a data augmentation method for models with gamma functions.
problem Models with gamma functions lack natural conjugate priors, complicating inference and prediction.
method Derives Pólya Inverse Gamma distributions and applies them to scalable EM and MCMC algorithms.
result Provides scalable algorithms for inference and prediction in models with gamma functions.
New method augments data for segmentation tasks using generative models.
problem Limited annotated data for deep learning segmentation.
method Task-driven data augmentation with generative models modeling deformation fields and intensity.
result Significantly outperforms conventional augmentation techniques in segmentation tasks.