Learn invariances in neural networks by optimizing over augmentation parameters.
problem Lack of knowledge about present invariances and their extent in data.
method Parameterize a distribution over augmentations and optimize network parameters and augmentation parameters simultaneously.
result Recover correct set and extent of invariances on various tasks from training data alone.
Regularising for invariance to data augmentation improves machine learning models.
problem Improving generalization in machine learning models through data augmentation.
method Explicit regularisation to encourage invariance at the level of individual model predictions.
result Explicit regularisation improves generalization and equalizes performance differences between objectives.
Bayesian network learns data invariances without augmentation.
problem Learning invariances in neural networks without manual design.
method Bayesian approach infers weight-sharing schemes from data.
result Model outperforms non-invariant networks on specific tasks.
GALA framework learns invariant graph representations via environment augmentation with minimal assumptions.
problem Learning invariant graph representations from different environments without additional assumptions.
method Developed GALA framework with minimal assumptions of variation sufficiency and consistency. Uses an assistant model to differentiate graph environment changes.
result Extracting maximally invariant subgraphs to proxy predictions identifies underlying invariant subgraphs for successful out-of-distribution generalization.
Framework adds invariance to pretrained networks without fine-tuning.
problem Adding invariance to pretrained networks without altering original behavior.
method Post-training augmentation invariance framework with Markov-Wasserstein minimization and Wasserstein correlation maximization losses.
result Adapter networks improve classification accuracy on rotated and noisy images.
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.
Counterfactual data augmentations may not ensure OOD robustness if performed by a context-guessing machine.
problem Deep learning models lack out-of-distribution robustness due to reliance on spurious features.
method Theoretical analysis and demonstration of counterfactual data augmentations performed by a context-guessing machine.
result Counterfactual data augmentations by a context-guessing machine do not lead to robust OOD classifiers.
GCNNs gain rotation invariance with more training augmentation, making SVD-Universal more effective.
problem Improving robustness of GCNNs to adversarial attacks.
method SVD-Universal technique applied to GCNNs trained with larger rotations.
result SVD-Universal becomes more effective as GCNNs gain rotation invariance.
This paper characterizes extensions of augmented racks and constructs invariants for surfaces.
problem Characterizing extensions of augmented racks and constructing invariants for surfaces.
method Characterization of rack extensions through fibrant and additive cohomology, construction of invariants using cocycles.
result Characterization of extensions of augmented racks and construction of surface invariants.
Develops a statistical framework for self-supervised representation learning using data augmentation.
problem Lack of theoretical understanding of data augmentation in nonlinear settings.
method Augmentation invariant manifold learning framework and stochastic optimization algorithm.
result Improves downstream analysis by exploiting manifold's geometric structure and invariant property of augmented data.
Theoretical comparison of three invariance approaches in deep linear networks.
problem Understanding invariance in deep linear networks.
method Data augmentation, regularization, and hard-wiring approaches.
result Regularization introduces additional critical points, but they remain saddles except for the global optimum.
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…
Data augmentation can achieve the same statistical benefits as full augmentation up to an approximation error.
problem Data augmentation in learning problems
method Using Fourier analysis and representation theory of finite groups
result Partial data augmentation achieves the same minimax rates as full augmentation
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.
Method learns invariances in deep nets without human validation.
problem Manual selection of data augmentation parameters is cumbersome.
method Differentiable Laplace approximation for Bayesian model selection.
result Method successfully recovers invariances and improves generalization.
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.
Invariances to translation, rotation and other spatial transformations are a hallmark of the laws of motion, and have widespread use in the natural sciences to reduce the dimensionality of systems of equations. In supervised learning, such as in image classification tasks, rotation, translation and scale invariances ar…
Data augmentation is commonly used to encode invariances in learning methods. However, this process is often performed in an inefficient manner, as artificial examples are created by applying a number of transformations to all points in the training set. The resulting explosion of the dataset size can be an issue in te…
Data augmented bootstrap unifies various confidence interval construction methods.
problem Constructing confidence intervals from data transformations.
method Data augmented bootstrap (DAB) framework.
result Establishes theoretical coverage results for DAB methods.
We introduce augmented biracks and define a (co)homology theory associated to augmented biracks. The new homology theory extends the previously studied Yang-Baxter homology with a combinatorial formulation for the boundary map and specializes to N-reduced rack homology when the birack is a rack. We introduce augmente…
This paper tackles confounding biases in data augmentation.
problem Mitigating spurious correlations and confounding variables in training data.
method Formal analysis and counterfactual data augmentation.
result Removing confounding biases leads to invariant features and better generalization.
Homotopy cardinality counts augmentations of Legendrian knots.
problem Counting augmentations of Legendrian knots.
method Assigning ruling polynomials and proving homotopy cardinality results.
result Homotopy cardinality of representation categories is a multiple of ruling polynomials.
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 describe a presentation for the augmented fundamental rack of a link in the lens space L(p,1). Using this presentation, the (enhanced) counting rack invariants that have been defined for the classical links are applied to the links in L(p,1). In this case, the counting rack invariants also include the informatio…
New method disentangles style features from data augmentations.
problem Difficulty in deducing which data attributes are 'style' and should be discarded.
method Structured data augmentation with multiple style embedding spaces, maximizing joint entropy.
result Empirically demonstrates benefits on synthetic and real-world data.
The Chekanov-Eliashberg differential graded algebra of a Legendrian knot L is a rich source of Legendrian knot invariants, as is the theory of generating families. The set P(L) of homology groups of augmentations of the Chekanov-Eliashberg algebra is an invariant, as is a count of objects from the theory of generating …
We introduce a notion of cardinality for the augmentation category associated to a Legendrian knot or link in standard contact R^3. This `homotopy cardinality' is an invariant of the category and allows for a weighted count of augmentations, which we prove to be determined by the ruling polynomial of the link. We prese…
In this article, associated to a (bordered) Legendrian graph, we study and show the equivalence between two Legendrian isotopy invariants: augmentation number via point-counting over a finite field, for the augmentation variety of the associated Chekanov-Eliashberg differential graded algebra, and ruling polynomial via…
In this article, associated to a (bordered) Legendrian graph, we study and show the equivalence between two categorical Legendrian isotopy invariants: the augmentation category, a unital A∞-category, which lifts the set of augmentations of the associated Chekanov-Eliashberg DGA, and a DG category of construct…
This work explains how tempering improves Bayesian neural networks by reducing the impact of data augmentation.
problem Improper sharpening of Bayesian neural networks leads to suboptimal performance.
method Theoretical analysis and empirical evaluations of simplified settings and group convolutions.
result Tempering reduces the misspecification due to modeling augmentations as independent and identically distributed (i.i.d.) data.
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…
Paper presents a world model that learns invariant causal features using contrastive unsupervised learning.
problem Learning invariant causal features in unsupervised settings.
method Contrastive unsupervised learning with intervention invariant auxiliary task.
result Significantly outperforms state-of-the-art methods on out-of-distribution point navigation tasks.
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.
Paper analyzes self-supervised learning using causal methods and proposes a new objective.
problem Lack of theoretical understanding of self-supervised learning success.
method Uses a causal framework to enforce invariance constraints on proxy classifiers.
result ReLIC objective improves generalization guarantees and outperforms existing methods.
This work characterizes how data augmentation shapes neural representations.
problem Understanding the impact of data augmentation on neural network representations.
method Embedding neural network hidden representations into a metric space invariant to transformations, analyzing shape-space trajectories.
result Increasing data augmentation strength leads to well-behaved trajectories in the embedded space, and different augmentation types steer representations in distinct directions.
Metric evaluates symmetry-breaking in datasets, revealing severe biases.
problem Symmetry-breaking in datasets can hinder the performance of symmetry-aware methods.
method Developed a metric to quantify symmetry-breaking using a two-sample classifier test.
result Symmetry-breaking can prevent optimal performance of invariant methods, even when labels are invariant.
Data augmentation affects feature importance, enhancing learning for neural networks.
problem Understanding the effect of data augmentation on feature importance and learning dynamics.
method Analyzing a two-layer convolutional neural network in a multi-view data model.
result Data augmentation alters feature importance, making certain features more likely to be learned.
Associated to Legendrian links in the standard contact three-space, Ruling polynomials are Legendrian isotopy invariants, which also compute augmentation numbers, that is, the points-counting of augmentation varieties for Legendrian links (up to a normalized factor) \cite{HR15}. In this article, we generalize this pict…
New attacks show data augmentation may not improve privacy.
problem Measuring privacy risk in models trained with data augmentation.
method Formulated membership inference as a set classification problem, designed input permutation invariant features.
result Proposed approach universally outperforms original methods on models trained with data augmentation.
While recent progress has spawned very powerful machine learning systems, those agents remain extremely specialized and fail to transfer the knowledge they gain to similar yet unseen tasks. In this paper, we study a simple reinforcement learning problem and focus on learning policies that encode the proper invariances …
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…
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…
This paper explores a variety of models for frame-based music transcription, with an emphasis on the methods needed to reach state-of-the-art on human recordings. The translation-invariant network discussed in this paper, which combines a traditional filterbank with a convolutional neural network, was the top-performin…
RIA method improves OoD generalization for covariate shift.
problem Improving out-of-distribution generalization under covariate shift.
method Adversarial label invariant graph data augmentations for OoD generalization.
result RIA method achieves high accuracy compared to OoD baselines.
Compute group cohomology for mapping class group with non-symplectic coefficients.
problem Compute group cohomology for mapping class group with non-symplectic coefficients.
method Compute the invariant subspace of the rational group ring of a surface, truncated by powers of the augmentation ideal, under the action of the mapping class group.
result First group cohomology computation for the mapping class group with non-symplectic coefficients.
Learning discrete representations of data is a central machine learning task because of the compactness of the representations and ease of interpretation. The task includes clustering and hash learning as special cases. Deep neural networks are promising to be used because they can model the non-linearity of data and s…
Knot invariants and quiver stability linked through full twists.
problem Relating knot invariants to quiver stability under twists.
method Using HOMFLY-PT skein relations and linking/unlinking operations on symmetric quivers.
result Full twists on knots correspond to unlinking or linking of augmented symmetric quivers, confirming stable growth in both.
Data augmentation is a widely used trick when training deep neural networks: in addition to the original data, properly transformed data are also added to the training set. However, to the best of our knowledge, a clear mathematical framework to explain the performance benefits of data augmentation is not available. In…