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.
Online isotonic regression achieves optimal regret with a covering net approach.
problem Online isotonic regression with adversarial label placement.
method Exponential Weights algorithm over a covering net of isotonic functions.
result Exponential Weights achieves O(T1/3log2/3(T)) regret, matching a lower bound. New training method for neural nets using multilevel entropic regularization.
problem Training efficiency and generalization bounds for neural nets.
method Multilevel relative entropy, chaining mutual information, Gibbs posterior distribution.
result Proves the Gibbs posterior achieves the unique minimum of the empirical risk minimization problem.
A new method for semi-supervised learning of sparse features using elastic-net.
problem Semi-supervised learning of sparse features in generalized linear models.
method Generalized Semi-Supervised Elastic-Net (s2net) framework.
result The s2net framework improves upon supervised elastic-net methods for semi-supervised learning.
Butterfly-Net improves CNN performance with structured connections and initialization.
problem Improving the performance of convolutional neural networks (CNNs).
method Butterfly-Net introduces structured and sparse cross-channel connections, and Butterfly initialization strategy.
result Butterfly-Net approximates Fourier representations with exponentially decaying error as depth increases.
Deep learning system diagnoses AVNFH from plain radiographs.
problem Challenging AVNFH diagnosis from plain radiographs.
method Deep convolutional neural networks for end-to-end diagnosis.
result AVN-net achieves state-of-the-art AUC of 0.97 in AVNFH detection.
Sharp bounds on scalar curvature spectrum and rigidity theorems.
problem Understanding scalar curvature bounds and rigidity on manifolds.
method Sharp upper bounds for the bottom spectrum of the Beltrami Laplacian, scalar curvature rigidity theorem.
result Sharp upper bound for the bottom spectrum of the Beltrami Laplacian and scalar curvature rigidity theorem.
Improved music source separation using spectrogram feature loss.
problem Music source separation quality improvement.
method Added a high-level feature loss term from spectrograms using a VGG net to a deep learning model.
result Improvement in separation quality of drums and vocals from songs.
New approach explains machine learning models better.
problem Understanding how machine learning models make decisions.
method Augmented Bayesian regression mixture model with elastic nets.
result Proposed approach outperforms state-of-the-art in explaining models.
The net-premium principle is considered to be the most genuine and fair premium principle in actuarial applications. However, an insurance company, applying the net-premium principle, goes bankrupt with probability one in the long run, even if the company covers its entire costs by collecting the respective fees from i…
We define a new notion of total curvature, called net total curvature, for finite graphs embedded in Rn, and investigate its properties. Two guiding principles are given by Milnor's way of measuring the local crookedness of a Jordan curve via a Crofton-type formula, and by considering the double cover of a given graph …
This paper consider penalized empirical loss minimization of convex loss functions with unknown non-linear target functions. Using the elastic net penalty we establish a finite sample oracle inequality which bounds the loss of our estimator from above with high probability. If the unknown target is linear this inequali…
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.
Paper transforms deep rectifier networks into shallow ones for analysis.
problem Understanding the complexity of deep neural networks.
method Transformation of deep rectifier networks into shallow ones.
result Shallow networks can represent deep networks with fewer functions.
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.
A new method tracks index using topological data analysis for sparse portfolios.
problem Sparse index tracking with robust risk management.
method Topological learning via Vietoris-Rips filtration for sparse regularization.
result The method outperforms state-of-the-art techniques in various market conditions.
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.
Study uses neural networks to filter financial spillovers from noise.
problem Accurately measuring spillovers in financial markets from noise.
method Neural network-based denoising of covariance matrices.
result Developed markets are net transmitters of volatility spillovers, but can become receivers during stress.
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 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.
Lung segmentation accuracy varies little across diverse datasets.
problem Limited clinical applicability of automated lung segmentation methods.
method Comparison of four deep learning approaches and two standard algorithms on diverse datasets.
result Standard U-net approach yields higher accuracy on routine imaging data.
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.
New proof shows deep neural nets can have sub-optimal local minima.
problem Can over-parameterization eliminate sub-optimal local minima in deep neural networks?
method Counter-example with generic input data and non-linear activation functions.
result Sub-optimal local minima exist in deep neural networks regardless of width.
IC-nets on confocal conics found in grid-like straight lines.
problem Understanding the geometric properties of grid-like straight lines with incircle quadrilaterals.
method Investigation of checkerboard IC-nets in plane and higher dimensions, using Laguerre geometry and 9 inspheres incidence theorem.
result Vertices of checkerboard IC-nets lie on confocal conics.
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.