arXiv research

Edge augmentation connects disconnected graphs by elevating eigenvalues.

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).

This work analyzes the role of data augmentation in self-supervised learning using RKHS approximation and regression.

New perspective on Heegaard splittings using square complexes and combinatorial measurements.

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.

We give an explicit basis $\mathcal{B}$ of the quotient of the Kauffman bracket skein algebra $\mathcal{S} (Σ)$ 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.

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.

AugMask trains diffusion models on incomplete tabular data by augmenting missing values and applying denoising supervision.

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.

This paper examines how labeling error affects contrastive learning and proposes data dimensionality reduction methods to mitigate its impact.

Enhanced EEG classification using augmented covariance matrix.

Mixes higher-order simplicial complexes for data augmentation.

Proposes robust model through Wasserstein geodesic interpolation of training data.

SBA improves neural network generalization by dynamically augmenting data.

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.

The paper connects Legendrian links to cluster theory and exact Lagrangian fillings.

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.

Enhances financial time-series prediction by adapting pre-trained models to new data.

Geometric proof confirms link volume conjecture.

Aims to create a world model without baggage, achieving good performance.

Clean intersections of Lagrangian knots in 3D are impossible.

Diffusion models optimize objectives similar to ELBO with Gaussian noise augmentation.

Study shows surgeries on specific links result in 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.

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.

Data augmentation doesn't improve robustness, contrary to belief.

This paper improves auto-augment efficiency by sharing augmentation weights.

WeMix improves data augmentation by correcting bias in deep learning.

The paper connects Chern-Simons invariants to mixed Tate motives in hyperbolic 3-manifolds.

A new method reduces memory requirements for Graph Transformers by sparsely training a network.

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…