A new method for domain generalization using source-specific classifiers.
problem Generalizing across multiple sources for any target domain.
method Multiple domain-specific classifiers and a domain agnostic component.
result Improved performance on public benchmarks.
Hierarchical models are versatile tools for joint modeling of data sets arising from different, but related, sources. Fully Bayesian inference may, however, become computationally prohibitive if the source-specific data models are complex, or if the number of sources is very large. To facilitate computation, we propose…
PDGMM-VAE uses adaptive priors for better ICA recovery.
problem Nonlinear ICA recovery of latent source signals.
method Adaptive per-dimension Gaussian mixture model priors in a variational autoencoder.
result PDGMM-VAE effectively recovers source-specific non-Gaussian marginals.
Interventional domain adaptation improves feature transferability by removing spurious correlations.
problem Improper feature transferability due to spurious correlations in domain adaptation.
method Intervention strategy using unlabeled target data to generate counterfactual features and train discriminability invariance.
result Consistent performance improvements over state-of-the-art approaches in various domain adaptation tasks.
The task of clustering a set of objects based on multiple sources of data arises in several modern applications. We propose an integrative statistical model that permits a separate clustering of the objects for each data source. These separate clusterings adhere loosely to an overall consensus clustering, and hence the…
Characterizes discrete nets with characteristic properties on larger parameter rectangles.
problem Classify discrete and smooth surfaces with specific properties.
method Imposes characteristic properties on larger parameter rectangles for nets.
result Characterizes discrete multi-nets leading to classical smooth surfaces.
The paper explores discrete isothermic nets using checkerboard patterns in quadrilateral nets.
problem Defining and understanding discrete isothermic nets in quadrilateral nets.
method Using checkerboard patterns and discrete differential geometry to define and analyze isothermic nets.
result The class of isothermic nets is invariant under dualization and Moebius transformations.
Deep nets outperform shallow nets in complex feature realization.
problem Realizing complex data features with deep nets.
method Refined covering number estimates and analysis of approximation rates.
result Deep nets can improve performance without additional capacity costs for complex features.
In this paper, we introduce transformations of deep rectifier networks, enabling the conversion of deep rectifier networks into shallow rectifier networks. We subsequently prove that any rectifier net of any depth can be represented by a maximum of a number of functions that can be realized by a shallow network with a …
Discretizes special surfaces using Koenigs nets.
problem Integrable structure of special surfaces.
method Discretisation via Koenigs nets.
result Preserves integrable structure in discretization.
We discuss discretization of Koenigs nets (conjugate nets with equal Laplace invariants) and of isothermic surfaces. Our discretization is based on the notion of dual quadrilaterals: two planar quadrilaterals are called dual, if their corresponding sides are parallel, and their non-corresponding diagonals are parallel.…
Classifies nets with area-preserving transformations into two types.
problem Classifying nets with area-preserving transformations.
method Classification using Combescure transformations and isotropic metric duality.
result Found two classes of nets: cone nets and Koenigs nets.
The paper tackles uncertainty quantification in multi-source settings.
problem Uncertainty quantification under covariate shift is challenging in multi-source settings.
method The paper addresses this by proposing two extensions of weighted conformal prediction: merge-based aggregation and data-pooling.
result Theoretical guarantees are provided for the proposed approaches, and experiments validate their effectiveness.
Defines CAMC discrete nets and their properties.
problem Understanding CAMC discrete nets and their properties.
method Defining CAMC discrete nets and proving properties.
result Properties of CAMC discrete nets are equivalent to properties of compatible interpolating quadrics.
The paper connects geodesic nets to distance function critical points.
problem Understanding the relationship between geodesic nets and distance function critical points.
method Established a relationship between geodesic nets and critical points of the distance function.
result Bounded the number of balanced points and the length of certain minimizing geodesic nets.
We study local and global approximations of smooth nets of curvature lines and smooth conjugate nets by respective discrete nets (circular nets and planar quadrilateral nets) with infinitesimal quads. It is shown that choosing the points of discrete nets on the smooth surface one can obtain second-order approximation g…
Circular nets with spherical parameter lines have geometric properties related to Darboux cyclides and terminating Laplace sequences.
problem Discretizing surfaces with spherical curvature lines.
method Lie-geometric discretisation in terms of principal contact element nets.
result Circular nets with two families of spherical parameter lines are related to Darboux cyclides.
Smart Close-out Netting aims to automate close-out netting processes.
problem Inefficiencies in close-out netting processes for financial institutions.
method Standardisation and automation of legal and regulatory processes using a data-driven framework and controlled natural language.
result Standardisation and automation can improve close-out netting processes for prudentially regulated financial institutions.
Supercyclides are surfaces with a characteristic conjugate parametrization consisting of two families of conics. Patches of supercyclides can be adapted to a Q-net (a discrete quadrilateral net with planar faces) such that neighboring surface patches share tangent planes along common boundary curves. We call the result…
Integrable nets described with curvature relations to pseudospherical surfaces.
problem Describing integrable curve nets and their geometric properties.
method Overview of second-order invariants, specific example of concordant nets, and construction of pseudospherical surfaces.
result Concordant Chebyshev nets correspond to pairs of pseudospherical surfaces.
Paper uses replica analysis to optimize net present value in investment portfolios.
problem Maximizing net present value in portfolios of multiple development projects.
method Replica analysis applied to optimization problem with budget and investment constraints.
result Replica analysis yields higher net present value than conventional methods.
We prove local Lipschitz property of the map which puts in correspondence to each N--net different from (N−1)--net its Chebyshev center. If dimension of Eucledean or Lobachevskii space is greater than 1 and net consists of more than 2 points we show that this map is not Lipschits in a neighbourhood of the space of …
Unified framework for U-Net design and analysis.
problem Understudied design and architecture of U-Nets.
method Theoretical results, Multi-ResNets, function constraints encoding.
result Competitive and superior performance in various tasks.
BCD-Net improves low-dose CT image reconstruction.
problem Challenges in obtaining accurate low-dose CT images.
method Modified iterative regression CNN, BCD-Net, with faster numerical solvers.
result BCD-Net achieves better image quality and generalization than state-of-the-art methods.
Two-dimensional affine A-nets in 3-space are quadrilateral meshes that discretize surfaces parametrized along asymptotic lines. The characterizing property of A-nets is planarity of vertex stars, so for generic A-nets the elementary quadrilaterals are skew. We classify the simply connected affine A-nets that can be ext…
New PCA method handles multiple datasets and detects sparse patterns robustly.
problem Handling multi-source data with sparse and outlier-robust PCA.
method Developed a regularization problem with a penalty for structured sparsity and outlier resistance.
result The method detects global and local patterns across multiple data sources robustly.
New algorithm selects genes for cancer classification using adaptive elastic net and conditional mutual information.
problem Selecting informative genes for microarray cancer classification.
method Adaptive Elastic Net with Conditional Mutual Information (AEN-CMI).
result AEN-CMI achieves the best classification performance with fewer genes.
The paper examines special Q-nets that terminate after a finite number of Laplace steps.
problem Understanding the termination of Laplace sequences in Q-nets.
method Analyzing discrete Koenigs nets and their Laplace sequences.
result For certain Koenigs nets, Laplace sequences terminate after a finite number of steps.
Stable nets on convex hypersurfaces maintain their shape under small perturbations.
problem Maintaining the shape of nets on convex surfaces under slight changes.
method Constructing stable geodesic nets on convex hypersurfaces.
result Stable geodesic nets on convex hypersurfaces do not change shape under small perturbations.
We consider n-dimensional discrete motions such that any two neighbouring positions correspond in a pure rotation ("rotating motions"). In the Study quadric model of Euclidean displacements these motions correspond to quadrilateral nets with edges contained in the Study quadric ("rotation nets"). The main focus of ou…
Generic metrics make geodesic nets dense.
problem Density of geodesic nets under generic metrics.
method Proving density for Baire-generic metrics.
result Union of geodesic nets images is dense.
Paper finds the best way to estimate neural net distance from samples.
problem Estimating the neural net distance from samples.
method Developed minimax lower and upper bounds for the neural net distance.
result Lower and upper bounds match, validating the empirical neural net distance.
The paper explores Guichard nets and their dual properties.
problem Understanding Guichard nets and their dual systems.
method Introduced Combescure transformations and Bäcklund-type transformations.
result Permutability theorem for dual systems of Guichard nets.
Compress U-net by over 1000x with knowledge distillation.
problem Compressing U-net architecture while maintaining performance.
method Knowledge distillation with regularization methods.
result Compressed U-net by 1000x with negligible performance drop.
A geodesic net with 4 boundary vertices and 25 balanced vertices is constructed.
problem Constructing geodesic nets with specific vertex types and properties.
method Novel approach to increase the number of balanced vertices from 16 to 25.
result First net with four boundary vertices and 25 balanced vertices, including non-symmetric balanced vertices.
Researchers prove NP-hardness of learning parameter-bounded Bayes nets.
problem Learning parameter-bounded Bayes nets is computationally hard.
method Proved NP-hardness of learning parameter-bounded Bayes nets and a promise search variant.
result Proved NP-hardness of a promise search variant of LEARN.
Optimizing quantum graphs yields geodesic nets on surfaces.
problem Finding optimal quantum graphs for geodesic nets.
method Optimizing functionals from spectral theory to find geodesic nets.
result Critical metrics for eigenvalues give rise to geodesic nets.
Dual U-net models improve multi-channel MRI image reconstruction.
problem Improving MRI image reconstruction from multi-channel data.
method Two-element U-nets (W-nets) in k-space and image domains, evaluated for four configurations.
result Dual domain methods are more advantageous for simultaneous reconstruction of all channels.
First example of geodesic net with 4 boundary vertices, not a tree.
problem Constructing geodesic nets with specific properties.
method Constructing a geodesic net with 4 unbalanced vertices and 16 balanced vertices.
result First example of irreducible geodesic net with 4 boundary vertices, not a tree.
Geodesic nets on flat spheres are studied using Gauss-Bonnet theorem.
problem Existence and non-existence of specific geodesic nets on flat spheres.
method The theorem of Gauss-Bonnet is applied to demonstrate results.
result Existence and non-existence of geodesic nets on regular doubled polygons.
Geometric approach uses Bäcklund transformations to create integrable discrete analogs of surface nets.
problem Creating integrable discrete analogs of surface nets and conjugate nets.
method Interpreting classical differential geometry results through Bäcklund transformations and applying permutability properties.
result Integrable discrete analogs of asymptotic and conjugate nets are constructed.
This research explores the dynamics of linearised neural nets, revealing distinct learning phases and layer growth rates.
problem Understanding the fundamental mechanics of neural nets and their learning dynamics.
method Derivation of properties of learning dynamics in general multi-layer linear neural nets, including orthogonal networks.
result Linear multi-layer neural nets exhibit distinct phases of learning with different layer growth rates, and nonlinearity affects these dynamics.
Deep nets' optima are surprisingly connected by simple paths.
problem Understanding the loss landscape of deep nets.
method Mathematical explanations based on generic properties of well-trained nets.
result Optima in deep nets are connected by piece-wise linear paths.
Semi-supervised anomaly detection with domain adaptation.
problem Anomaly detection with limited labeled data across domains.
method IRAD method: learns domain-invariant representations using adversarial learning and anomaly detector trained on these representations.
result IRAD outperforms baseline models across various datasets.
We consider discrete nets in Grassmannians Grd which generalize Q-nets (maps ZN→Pd with planar elementary quadrilaterals) and Darboux nets (Pd-valued maps defined on the edges of ZN such that quadruples of points corresponding to elementary squares are all co…
U-Net trained to recover acoustic interference striations from distorted data.
problem Recovering acoustic interference striations from distorted signals.
method Training a U-Net using a random mode-coupling matrix model to generate training data.
result U-Net successfully recovers AISs under various conditions.
Deep ReLU nets with width d+1 can approximate any convex function on [0,1]^d.
problem Approximating continuous functions on the unit cube with ReLU nets.
method Observing the convexity of ReLU activations and proving approximation by nets of width d+1.
result ReLU nets with width d+1 can approximate any continuous convex function on [0,1]^d arbitrarily well.
The paper creates symmetrical discrete minimal nets using Schwarz reflection.
problem Creating symmetrical discrete minimal nets.
method Extending Schwarz reflection principle to discrete minimal surfaces.
result Global examples of discrete minimal nets with high symmetry.