New autoencoder framework learns structured latent priors.
problem Learning autoencoders with flexible priors.
method Relational regularization on latent prior, scalable algorithms.
result RAE outperforms existing autoencoders in image generation.
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arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,742 papers · 148 categories
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48 results for “relational regularization”
Study regularization in deep networks, uncovering performance relations and proposing a training schedule.
problem Understanding and optimizing regularization in deep learning models.
method Empirical observations and theoretical analysis of gradient flow dynamics in infinitely wide networks.
result Empirical relations between model performance, coefficient, learning rate, and training steps; optimal regularization parameter prediction; improved training schedule.
Method discovers nonlinear relations from time series data.
problem Identifying directional relations from nonlinear interactions in time series.
method Minimum predictive information regularization method for deep learning.
result Substantially outperforms other methods for learning nonlinear relations.
Sharp bounds on diameter and eigenvalues for amply regular graphs.
problem Finding bounds for amply regular graphs' diameter and eigenvalues.
method New ideas relating discrete Ricci curvature to local matching properties, including a novel construction of a regular bipartite graph.
result Sharp diameter and eigenvalue bounds for amply regular graphs.
The study classifies polynomial relation tubular surfaces in 3-spaces.
problem Classifying tubular surfaces with polynomial curvature relations.
method Analyzing polynomial relations between Gaussian and mean curvatures in Euclidean, hyperbolic, and Lorentzian 3-spaces.
result Determination of sets of polynomial relations for tubular surfaces.
We use normal sections to relate the curvature locus of regular (resp. singular corank 1) 3-manifolds in (resp. ) with regular (resp. singular corank 1) surfaces in (resp. ). For example we show how to generate a Roman surface by a family of ellipses different to S…
New solver SR2 tackles deep neural network training with nonsmooth regularization.
problem Training deep neural networks with nonsmooth regularization to achieve sparsity and efficiency.
method Combines adaptive quadratic regularization with proximal stochastic gradient principles.
result Established worst-case iteration complexity of O(ε^−2) for SR2.
New relation between curvature bounds and spacetime inextendibility.
problem Inextendibility of spacetimes under low regularity conditions.
method Synthetic curvature and causal character analysis.
result Low-regularity spacetimes with unbounded curvature.
New relation between curvature bounds and spacetime inextendibility.
problem Inextendibility of spacetimes under low regularity conditions.
method Synthetic curvature and causal character maximizers.
result Low-regularity inextendibility linked to unbounded curvature.
We study various aspects related to boundary regularity of complete properly embedded Willmore surfaces in H3, particularly those related to assumptions on boundedness or smallness of a certain weighted version of the Willmore energy. We prove, in particular, that small energy controls C1 boundary regularity. We examin…
We obtain polynomial Frobenius manifolds from classical -algebras associated to regular nilpotent elements in simple Lie algebras using the related opposite Cartan subalgebras.
Method estimates multiple related Gaussian distributions using Laplacian regularization.
problem Jointly estimate multiple related zero-mean Gaussian distributions.
method Laplacian regularized stratified model fitting with hyper-parameters to encourage covariance closeness.
result The method performs well, especially in low data regimes, as demonstrated in finance, radar, and weather.
On simple geodesic disks of constant curvature, we derive new functional relations for the geodesic X-ray transform, involving a certain class of elliptic differential operators whose ellipticity degenerates normally at the boundary. We then use these relations to derive sharp mapping properties for the X-ray transform…
Tree-based regularization improves latent variable inference from related datasets.
problem Inferring latent variables from multiple related datasets in causal systems.
method Tree-Based Regularization (TBR) for sparse changes across environments.
result TBR identifies true latent variables up to simple transformations under sparse changes.
Regularization of the classical Laplacian matrices was empirically shown to improve spectral clustering in sparse networks. It was observed that small regularizations are preferable, but this point was left as a heuristic argument. In this paper we formally determine a proper regularization which is intimately related …
Paper proves DN map determination for simple surfaces with low regularity metrics.
problem Determining DN map from scattering relation for surfaces with low regularity metrics.
method Modified technical results and used microlocal analysis for metrics with finite regularity.
result Scattering relation determines DN map for surfaces, and for metrics using Lipschitz distance function.
Adversarially robust generalization theory via Jacobian regularization for deep neural networksstat.ML
This study connects Jacobian regularization to adversarial robustness and improves generalization.
problem Adversarial attacks make deep neural networks vulnerable.
method Developed a connection between Jacobian regularization and adversarial training, and established robust generalization gaps.
result Jacobian norms are related to both standard and robust generalization.
Transformers model contextual relations using probabilistic measures, revealing their expressive power.
problem Lack of clear understanding of Transformer's ability to model contextual relations.
method Introduced a measure-theoretic framework connecting softmax attention and entropy-regularized optimal transport.
result Transformer architectures can approximate arbitrary contextual relations, and the choice of normalization affects how these relations are represented.
Study MinMax methods for optimization problems, including optimal transport.
problem Optimization problems, especially optimal transport.
method MinMax framework, regularization, neural networks, approximation theorems.
result Justification of neural networks for solving optimization problems.
Embedding-based methods for knowledge base completion (KBC) learn representations of entities and relations in a vector space, along with the scoring function to estimate the likelihood of relations between entities. The learnable class of scoring functions is designed to be expressive enough to cover a variety of real…
Via Gauge theory, we give a new proof of partial regularity for harmonic maps in dimension m>2 into arbitrary targets. This proof avoids the use of adapted frames and permits to consider targets of "minimal" C^2 regularity. The proof we present moreover extends to a large class of elliptic systems of quadratic growth.
Regularization is essential when training large neural networks. As deep neural networks can be mathematically interpreted as universal function approximators, they are effective at memorizing sampling noise in the training data. This results in poor generalization to unseen data. Therefore, it is no surprise that a ne…
The paper introduces sections in metric spaces with properties related to Ahlfors-David regularity and convexity.
problem Understanding properties of sections in metric spaces.
method Definition and investigation of intrinsically quasi-isometric sections in metric spaces.
result Properties of sections, including Ahlfors-David regularity and convexity, are defined and investigated.
This paper uses the relationship between graph conductance and spectral clustering to study (i) the failures of spectral clustering and (ii) the benefits of regularization. The explanation is simple. Sparse and stochastic graphs create a lot of small trees that are connected to the core of the graph by only one edge. G…
We introduce -regular maps, which generalize two previously studied classes of maps: affinely -regular maps and totally skew embeddings. We exhibit some explicit examples and obtain bounds on the least dimension of a Euclidean space into which a manifold can be embedded by a -regular map. The problem c…
Inspired by the concept of evolutoids of planar curves, we present the concept of evolutoids for regular surfaces as an envelope of a two-parameter family of lines in Euclidean 3-space. We give an explicit parametrization for such evolutoids. Besides, we used the theory of singularities to study the local behavior of r…
A new ICA method adds L1-regularization for better interpretability of fMRI data.
problem Improving interpretability of ICA features in high-dimensional fMRI data.
method L1-regularization added to ICA cost function, solved by DCA.
result Validated on synthetic and real fMRI data, improving feature interpretability.
New autoencoder improves latent space learning by optimizing sliced Gromov-Wasserstein discrepancies.
problem Improving inner discrepancy between prior and posterior distributions in autoencoders.
method Proposed spherical sliced fused Gromov Wasserstein (SSFG) and variants (MSSFG, PSSFG) to find important directions.
result New autoencoders achieve favorable performance in latent manifold learning, image generation, and reconstruction.
A Dehn surgery description of regular finite cyclic covering spaces of rational homology spheresmath.GT
We provide related Dehn surgery descriptions for rational homology spheres and a class of their regular finite cyclic covering spaces. As an application, we use the surgery descriptions to relate the Casson invariants of the covering spaces to that of the base space. Finally, we show that this places restrictions on th…
New knot quandle structure for twist-spun trefoils discovered.
problem Understanding symmetries of knot-spun structures.
method Defined Schläfli quandles and studied their relationship with knot quandles.
result The knot quandle of the twist-spun trefoil is a central extension of a Schläfli quandle.
Eta invariants and regularized determinants for odd dimensional hyperbolic manifolds with cuspsmath.DG
We study the eta invariants of Dirac operators and the regularized determinants of Dirac Laplacians over hyperbolic manifolds with cusps. We follow Werner M"uller and use relative traces to define these spectral invariants. We show the regularity of eta and zeta functions at s=0. The Selberg trace formula and the detai…
Monotonic relationship found between in-distribution and out-of-distribution performance.
problem Understanding performance of machine learning models under distribution shifts.
method Analyzing ridge-regularized models and linear inverse problems under covariate shift.
result Monotonic relationship between in-distribution and out-of-distribution performance for certain models.
Mathematical formulas for elliptic curve integrals solve anomaly equations.
problem Mathematical formulation of contact term singularities on elliptic curves.
method Residue formulas and holomorphic anomaly equations.
result Regularized integrals on elliptic curves satisfy holomorphic anomaly equations.
We consider the two problems of predicting links in a dynamic graph sequence and predicting functions defined at each node of the graph. In many applications, the solution of one problem is useful for solving the other. Indeed, if these functions reflect node features, then they are related through the graph structure.…
New test determines appropriate number of biclusters in relational data.
problem Determining the correct number of biclusters in relational data matrices.
method Proposes a new statistical test that does not require regular-grid assumptions.
result Derives asymptotic behavior of the test statistic for both null and alternative cases.
We study regularity properties of the dynamic value functions of primal and dual problems of optimal investing for utility functions defined on the whole real line. Relations between decomposition terms of value processes of primal and dual problems and between optimal solutions of basic and conditional utility maximiz…
New algorithm adds Hessian regularization to improve neural network robustness.
problem Improving neural network robustness against adversarial attacks.
method Proposes an efficient algorithm to train neural networks with Hessian operator-norm regularization.
result Hessian operator-norm regularization increases neural network robustness over input gradient regularization.
We investigate the learning rate of multiple kernel learning (MKL) with and elastic-net regularizations. The elastic-net regularization is a composition of an -regularizer for inducing the sparsity and an -regularizer for controlling the smoothness. We focus on a sparse setting where the total …
A deep neural network model is a powerful framework for learning representations. Usually, it is used to learn the relation by exploiting the regularities in the input . In structured output prediction problems, is multi-dimensional and structural relations often exist between the dimensions. The motiv…
This paper has been withdrawn by the author due to a crucial error related with the consideration of regular points
Characterizes regular parallelisms in 3D space with 2-torus action.
problem Characterizing regular parallelisms in 3D space with 2-torus action.
method Characterization using compactness, equivalence relations, and properties of complex vector spaces.
result There is a 1-dimensional subtorus fixing every parallel class, leading to 2- or 3-dimensional regular parallelisms.
Diagonal linear networks converge to lasso regularization path during training.
problem Understanding the regularization behavior of diagonal linear networks.
method Analyzing the training trajectory of diagonal linear networks and comparing it to the lasso regularization path.
result The training trajectory of diagonal linear networks is closely related to the lasso regularization path.
Deep Matrix Factorization (DMF) is an emerging approach to the problem of matrix completion. Recent works have established that gradient descent applied to a DMF model induces an implicit regularization on the rank of the recovered matrix. In this work we interpret the DMF model through the lens of spectral geometry. T…
Extends Tanaka theory to supergeometry for upper bounds on supersymmetry.
problem Bounding supersymmetry dimensions of supergeometries.
method Extends Tanaka theory to supergeometry.
result Obtains an upper bound on supersymmetry dimensions.
Symmetry-regularized Neural ODEs improve model stability and interpretability.
problem Improving the stability and physical interpretability of Neural ODEs.
method Integrating Lie symmetries and conservation laws into the loss function.
result Symmetry-regularized Neural ODEs enhance model stability and interpretability.
LLE produces unwanted results without regularization, which can be prevented with regularization.
problem LLE's inherent unwanted results without regularization.
method Mathematical proof and numerical examples of regularization effectiveness.
result Regularization prevents unwanted results in LLE.
Study improves regularity estimates for harmonic maps into ellipsoids.
problem Independence of regularity estimates on harmonic maps with varying target dimensions.
method Analyzes harmonic maps into ellipsoids, uses Palais-Smale sequences, and critical metrics.
result Enhanced regularity estimates for Laplace harmonic eigenmaps.
Many classification problems involve data instances that are interlinked with each other, such as webpages connected by hyperlinks. Techniques for "collective classification" (CC) often increase accuracy for such data graphs, but usually require a fully-labeled training graph. In contrast, we examine how to improve the…