In this paper we establish a relationship between geodesic nets and critical points of the distance function. We bound the number of balanced points for certain minimizing geodesic nets on manifolds homeomorphic to the -sphere. We also bound the length of certain minimizing geodesic nets.
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48 results for “Critical nets”
On Critical nets in math.DG
Critical nets in k-space have bounded edge lengths and vertices.
problem Understanding the structure and constraints of critical nets in k-dimensional space.
method Analyzing the properties of critical nets under fixed leaf positions and constraints.
result The total length of edges not incident with 1-valent vertices is bounded, and the degree and number of vertices are also bounded.
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.
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.
Catapult phase in neural nets shows exponential loss growth before quick decrease.
problem Understanding phase transitions in neural networks during training.
method Analyzing weight norm and loss behavior for super-critical learning rates.
result Proven existence of catapult phase in quadratic models and two-layer nets.
Improves efficiency and scalability in multi-agent reinforcement learning.
problem Non-stationarity and inefficiency in critic networks due to agent permutations.
method Proposes a permutation invariant critic (PIC) to avoid changes in critic output due to agent permutations.
result Achieves improvements of test episode reward between 15% to 50% on challenging multi-agent particle environment (MPE).
Global convergence of SGD proven for two-layer neural nets with regularization.
problem Proving global convergence of SGD for two-layer neural nets.
method Regularized empirical risk, SGD iterates, Villani functions.
result Global convergence of SGD for a special class of initializations.
MCU-Net combines U-Net and Monte Carlo Dropout for uncertainty in medical image segmentation.
problem Lack of uncertainty representation in deep learning methods for patient-centered healthcare decisions.
method MCU-Net framework using U-Net and Monte Carlo Dropout with four uncertainty metrics.
result MCU-Net maximizes automated performance and refers truly uncertain cases.
Particle filtering is a powerful approach to sequential state estimation and finds application in many domains, including robot localization, object tracking, etc. To apply particle filtering in practice, a critical challenge is to construct probabilistic system models, especially for systems with complex dynamics or r…
A large class of semi-Hamiltonian systems of hydrodynamic type is interpreted as the equations governing families of critical points of functions obeying the classical linear Darboux equations for conjugate nets.The distinguished role of the Euler-Poisson-Darboux equations and associated Lauricella-type functions is em…
MANA-Net improves market predictions by dynamically weighting news sentiments.
problem Aggregated Sentiment Homogenization in financial news data.
method Dynamic market-news attention mechanism to aggregate sentiments.
result MANA-Net outperforms recent market prediction methods by 1.1% Profit & Loss and 0.252 daily Sharpe ratio.
Deep generative models can learn to generate realistic-looking images, but many of the most effective methods are adversarial and involve a saddlepoint optimization, which requires a careful balancing of training between a generator network and a critic network. Maximum mean discrepancy networks (MMD-nets) avoid this i…
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.
A new method for feature fusion in U-Net decoders using difference-based gating.
problem Precise fusion of high-level semantics and low-level details in U-Net decoder reconstruction.
method Proposes two difference-based gating approaches: Feature-difference gating (FDG) and Entropy-difference gating (EDG).
result Both FDG and EDG methods outperform existing attention-based fusion methods, with EDG showing superior performance.
The paper identifies saddlepoints in unsupervised auto-encoding neural nets.
problem The risk landscape of unsupervised least squares in auto-encoding neural nets.
method Established an equivalence between unsupervised least squares and principal manifolds, discussed regularization strategies for auto-encoders.
result All non-trivial critical points in auto-encoding are saddlepoints, which are degenerate in overcomplete auto-encoding.
Paper predicts turbulent flows using physics-informed deep learning.
problem Predicting turbulent flows from fluid simulations.
method Hybrid approach combining RANS and LES with trainable spectral filters and U-net.
result Significant reduction in prediction error for 60 frames ahead.
Extends neural net safety guarantees by proving structural properties.
problem Proving formal guarantees for complex DNN architectures.
method Proves structural properties related to neural net structure to infer safety properties.
result Identifies a larger region of input space for safety properties.
Knowledge graph reasoning is a critical task in natural language processing. The task becomes more challenging on temporal knowledge graphs, where each fact is associated with a timestamp. Most existing methods focus on reasoning at past timestamps and they are not able to predict facts happening in the future. This pa…
SSH-Net: A Deep Neural Network for Predicting Failure Time Distribution Functions under Competing Risks with GPU Data
problem Predicting failure time distribution functions under competing risks
method Structured Segmented Hazard Deep Neural Network (SSH-Net)
result Prediction accuracy validated through simulation studies and GPU data
Study tackles balancing policy switching costs in offline RL.
problem Balancing the cost of policy switching in offline RL.
method Optimal transport ideas and Net Actor-Critic algorithm.
result Demonstrated efficiency on multiple RL benchmarks.
Machine learning predicts greenhouse gas emissions for undisclosed companies.
problem Lack of GHG emissions data for most companies.
method Trained machine learning model on disclosed data to estimate emissions.
result Model accurately predicts emissions for undisclosed companies.
Study shows critical initialisation not crucial for ReLU networks under dropout limits.
problem Effect of initialisation on training speed and generalisation in ReLU networks.
method Large-scale statistical analysis of over 12,000 trained networks.
result Non-critical initialisations perform similarly to critical initialisations in terms of performance.
This paper provides theoretical guarantees for SPCA using the Elastic Net.
problem Lack of theoretical guarantees for the SPCA algorithm.
method Revisited and improved the SPCA algorithm of Zou et al. (2006) using the Elastic Net.
result Both algorithms can recover the principal subspace consistently under mild conditions.
Modern audio source separation techniques rely on optimizing sequence model architectures such as, 1D-CNNs, on mixture recordings to generalize well to unseen mixtures. Specifically, recent focus is on time-domain based architectures such as Wave-U-Net which exploit temporal context by extracting multi-scale features. …
Accurate prediction of disease trajectories is critical for early identification and timely treatment of patients at risk. Conventional methods in survival analysis are often constrained by strong parametric assumptions and limited in their ability to learn from high-dimensional data, while existing neural network mode…
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.
We investigate the common underlying discrete structures for various smooth and discrete nets. The main idea is to impose the characteristic properties of the nets not only on elementary quadrilaterals but also on larger parameter rectangles. For discrete planar quadrilateral nets, circular nets, -nets and conical…
Optimal feature learning strength improves generalization in deep networks.
problem Understanding how feature learning strength affects generalization in practical settings.
method Empirical studies and theoretical analysis of gradient flow dynamics in two-layer ReLU nets.
result Optimal feature learning strength yields substantial generalization gains, contrary to the prevailing intuition.
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 implementation of the Own Risk and Solvency Assessment is a critical issue raised by Pillar II of Solvency II framework. In particular the Overall Solvency Needs calculation left the Insurance companies to define an optimal entity-specific solvency constraint on a multi-year time horizon. In a life insurance societ…
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.
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 Nettingq-fin.RM
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.
This paper considers the power of deep neural networks (deep nets for short) in realizing data features. Based on refined covering number estimates, we find that, to realize some complex data features, deep nets can improve the performances of shallow neural networks (shallow nets for short) without requiring additiona…
Supercyclidic netsmath.DG
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.
Local Lipschitz property of the map which puts in correspondence to N--net its Chebyshev centermath.MG
We prove local Lipschitz property of the map which puts in correspondence to each --net different from --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.
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…
WindDragon forecasts wind power with deep learning.
problem Accurate short-term wind power forecasting is crucial for grid operation.
method Automated Deep Learning combined with Numerical Weather Predictions.
result Automated Deep Learning improves wind power forecasting accuracy.
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.
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.
Obtaining accurate and reliable images from low-dose computed tomography (CT) is challenging. Regression convolutional neural network (CNN) models that are learned from training data are increasingly gaining attention in low-dose CT reconstruction. This paper modifies the architecture of an iterative regression CNN, BC…