Edge augmentation connects disconnected graphs by elevating eigenvalues.
problem Connecting disconnected subgraphs in graphs with zero eigenvalues.
method Elevating zero eigenvalues of graph's spectrum to connect subgraphs.
result The algorithm consistently connects graph components, achieving >50% inter-community edges.
We construct the augmentation representation. It is a representation of the fundamental group of the link complement associated to an augmentation of the framed cord algebra. This construction connects representations of two link invariants of different types. We also study properties of the augmentation representation…
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…
We show that one can interweave an unknot into any non-alternating connected projection of a link so that the resulting augmented projection is alternating.
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).
This work analyzes the role of data augmentation in self-supervised learning using RKHS approximation and regression.
problem Limited theoretical understanding of the role of data augmentation in self-supervised learning.
method Geometric characterization of the target function given by augmentation, proving generalization bounds.
result Two generalization bounds are derived, one free of model complexity, the other specific to near-optimal encoders.
New perspective on Heegaard splittings using square complexes and combinatorial measurements.
problem Measuring obstructions to Heegaard splittings in 3-manifolds.
method Square complexes and Guirardel's core, augmented Heegaard diagrams.
result Augmented Heegaard diagrams provide a new way to describe Heegaard splittings with desirable properties.
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…
Data augmentation, a technique in which a training set is expanded with class-preserving transformations, is ubiquitous in modern machine learning pipelines. In this paper, we seek to establish a theoretical framework for understanding data augmentation. We approach this from two directions: First, we provide a general…
The Epstein deformation space parameterizes marked rational maps with prescribed combinatorial and dynamical structure. For the family of quadratic rational maps with a periodic critical cycle of order 4 and an extra critical point not lying in this cycle, S. Koch and I recently showed that the deformation space has in…
New findings on hyperbolicity of augmented links in thickened surfaces.
problem Proving hyperbolicity of links in thickened surfaces.
method Extending hyperbolicity results to generalized augmented cellular alternating links.
result Generalized augmented cellular alternating links in thickened surfaces are hyperbolic.
We give an explicit basis B of the quotient of the Kauffman bracket skein algebra S(Σ) on a surface Σ by the square of an augmentation ideal. As an application, it induces two kinds of finite type invariants of links in a handle body in the sense of Le. Moreover, we construct an embedding of …
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…
Bayesian model selection optimizes data augmentation for improved machine learning robustness.
problem Choosing optimal data augmentation parameters is challenging and often done through trial and error.
method Interprets augmentation parameters as model hyperparameters and uses Bayesian model selection to optimize them.
result Our approach improves calibration and robust performance on various tasks.
Recent empirical results on long-term dependency tasks have shown that neural networks augmented with an external memory can learn the long-term dependency tasks more easily and achieve better generalization than vanilla recurrent neural networks (RNN). We suggest that memory augmented neural networks can reduce the ef…
Proves accuracy guarantees for self-supervised learning with correlated positive pairs.
problem Lack of theoretical guarantees for self-supervised learning with correlated positive pairs.
method Novel augmentation graph concept and spectral decomposition loss.
result Provably accurate features under linear probe evaluation.
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.
The stochastic block model (SBM) is a probabilistic model for community structure in networks. Typically, only the adjacency matrix is used to perform SBM parameter inference. In this paper, we consider circumstances in which nodes have an associated vector of continuous attributes that are also used to learn the node-…
New framework explains data augmentation's role in machine learning.
problem Understanding how data augmentation affects generalization and invariance learning.
method Information-theoretic framework based on mutual information bounds and orbit-averaged loss functions.
result Derives a new generalization bound decomposing the generalization gap into three interpretable terms.
This paper examines how labeling error affects contrastive learning and proposes data dimensionality reduction methods to mitigate its impact.
problem The impact of labeling error on the performance of contrastive learning.
method Data dimensionality reduction methods (e.g., SVD) are applied to reduce false positive samples and improve downstream classification accuracy.
result Data dimensionality reduction methods can mitigate the negative impacts of labeling error on downstream classification performance.
Enhanced EEG classification using augmented covariance matrix.
problem Improving motor imagery classification from EEG signals.
method Proposes a new framework based on the augmented covariance matrix derived from an autoregressive model.
result The augmented covariance matrix outperformed state-of-the-art methods.
Mixes higher-order simplicial complexes for data augmentation.
problem Lack of labeled data for complex systems with multiway interactions.
method Proposes mixup mechanisms for simplicial complexes, including linear and nonlinear mixup, and a convex clustering mixup.
result Synthetic simplicial complexes interpolate between existing data based on homomorphism densities.
Proposes robust model through Wasserstein geodesic interpolation of training data.
problem Improving model robustness through data augmentation.
method Augment data by finding worst-case Wasserstein barycenter on geodesic path.
result Improves robustness on CIFAR-10 up to 7.7% and on CIFAR-100 up to 16.8%.
SBA improves neural network generalization by dynamically augmenting data.
problem Lack of direct supervision in data augmentation for generalization.
method Stochastic Batch Augmentation with dynamic soft label regularization.
result SBA improves generalization and speeds up training.
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…
We define an algebraic/combinatorial object on the front projection Σ of a Legendrian knot called a Morse complex sequence, abbreviated MCS. This object is motivated by the theory of generating families and provides new connections between generating families, normal rulings, and augmentations of the Chekanov-Eliashb…
The variational autoencoder (VAE) framework remains a popular option for training unsupervised generative models, especially for discrete data where generative adversarial networks (GANs) require workaround to create gradient for the generator. In our work modeling US postal addresses, we show that our discrete VAE wit…
GraphACL learns graph representations without augmentation or homophily assumptions.
problem Learning graph representations on heterophilic graphs (nodes with different labels and features).
method Asymmetric Contrastive Learning for Graphs (GraphACL) considers an asymmetric view of neighboring nodes.
result GraphACL significantly outperforms state-of-the-art methods on both homophilic and heterophilic graphs.
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.
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 …
Manipulating data, such as weighting data examples or augmenting with new instances, has been increasingly used to improve model training. Previous work has studied various rule- or learning-based approaches designed for specific types of data manipulation. In this work, we propose a new method that supports learning d…
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.
Enhances financial time-series prediction by adapting pre-trained models to new data.
problem Adapting pre-trained financial models to new data sets efficiently.
method Augmented Bilinear Network that retains and adjusts pre-trained neural network knowledge.
result Improves prediction performance and reduces model complexity.
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.
Aims to create a world model without baggage, achieving good performance.
problem Creating world models without baggage and limitations.
method Self-supervised representation learning, frame and action stacking, data augmentation.
result Good performance on the Atari 100k benchmark.
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.
Diffusion models optimize objectives similar to ELBO with Gaussian noise augmentation.
problem Optimizing diffusion models for high perceptual quality.
method Showed diffusion objectives are weighted ELBOs over noise levels, with Gaussian noise augmentation.
result Diffusion objectives equate to ELBO with Gaussian noise augmentation under monotonic weighting.
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.
We present the Video Ladder Network (VLN) for efficiently generating future video frames. VLN is a neural encoder-decoder model augmented at all layers by both recurrent and feedforward lateral connections. At each layer, these connections form a lateral recurrent residual block, where the feedforward connection repres…
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.
Deep learning has significant potential for medical imaging. However, since the incident rate of each disease varies widely, the frequency of classes in a medical image dataset is imbalanced, leading to poor accuracy for such infrequent classes. One possible solution is data augmentation of infrequent classes using syn…
Study examines how data augmentation impacts optimization in linear regression.
problem Understanding how data augmentation schedules affect optimization in linear regression.
method Analyzed the effect of augmentation on optimization in linear regression with MSE loss, using classical convex optimization and recent work on implicit bias.
result Proved that under certain joint schedules for learning rate and augmentation scheme, augmented gradient descent converges and characterized the resulting minimum.
Data augmentation doesn't improve robustness, contrary to belief.
problem The effectiveness of data augmentation in improving model robustness is questioned.
method Taking a Domain Generalization viewpoint, the study examines the robustness of augmented representations.
result Augmented representations are not robust to distortions used during training.
This paper improves auto-augment efficiency by sharing augmentation weights.
problem Efficient evaluation of augmentation policies for model training.
method Augmentation-Wise Weight Sharing (AWS) to create a fast yet accurate proxy task.
result Augmentation policies found achieve superior accuracies compared to existing methods.
Simple policy search outperforms advanced learnable test-time augmentation techniques.
problem Improving predictive performance through test-time data augmentation.
method Greedy policy search (GPS) for learning test-time augmentation policies.
result Augmentation policies learned with GPS achieve superior predictive performance and robustness.
New measures quantify how data augmentation improves model performance.
problem Understanding the effectiveness of data augmentation in deep learning.
method Introduced Affinity and Diversity measures to quantify augmentation performance.
result Augmentation performance is best achieved by optimizing both Affinity and Diversity.
CNNs encode data augmentation transformations, especially in early layers.
problem Whether neural network features encode data augmentation transformations.
method Systematic approach using pre-trained vision models to predict augmentation transformations.
result Neural network features encode data augmentation transformations, especially in early layers.
WeMix improves data augmentation by correcting bias in deep learning.
problem Data augmentation's effectiveness is limited by data bias.
method Developed AugDrop and MixLoss algorithms to correct data bias.
result WeMix improves data augmentation performance through bias correction.