New methods protect malware classification networks from adversarial attacks.
problem Adversarial perturbations compromise malware classification networks.
method Training restricted networks with non-negative weight restrictions and relaxing constraints.
result Improved classifier accuracy while maintaining resistance to adversarial attacks.
A new SBM for non-negative zero-inflated edge weights in networks.
problem Modeling international trading networks with non-negative zero-inflated edge weights.
method Restricted Tweedie distribution and nodal information accounting.
result Efficient two-step algorithm for estimating covariate effects.
VAE enhances NMF for probabilistic non-negative matrix factorisation.
problem Non-negative matrix factorisation with probabilistic coefficients.
method Design a VAE network with non-negative weights and non-negative Weibull distribution.
result Effective probabilistic NMF for generating new data and linking latent and input variables.
We study stability properties of f-minimal hypersurfaces isometrically immersed in weighted manifolds with non-negative Bakry-Emery Ricci curvature under volume growth conditions. Moreover, exploiting a weighted version of a finiteness result and the adaptation to this setting of Li-Tam theory, we investigate the top…
The study proves a new inequality and formula for manifolds with non-negative Ricci curvature.
problem Proving a sharp mean value inequality for non-negative superharmonic functions.
method Develops a new sharp mean value inequality and an explicit formula for weighted scalar curvature.
result The new inequality removes the radius restriction of Schoen-Yau's result and provides an explicit formula for integral of weighted scalar curvature.
Convex neural networks enforce convex constraints on weights and activations, improving generalization.
problem Improving generalization and reducing overfitting in neural networks.
method Enforce convex constraints on weights and activations, using non-negative weights and non-decreasing convex activation functions.
result Convex neural networks self-regularize, outperforming base architectures and achieving similar performance to convolutional architectures.
Sharp isoperimetric inequality on Finsler manifolds with non-negative Ricci curvature.
problem Proving an isoperimetric inequality on Finsler metric measure manifolds.
method Defining volume entropy and second Cheeger constant, proving sharp inequality.
result Sharp isoperimetric inequality involving volume entropy and weighted Ricci curvature.
Non-negative matrix factorization is a popular tool for decomposing data into feature and weight matrices under non-negativity constraints. It enjoys practical success but is poorly understood theoretically. This paper proposes an algorithm that alternates between decoding the weights and updating the features, and sho…
Study on stable minimal hypersurfaces under Ricci curvature constraints.
problem Stability of weighted minimal hypersurfaces under Ricci curvature bounds.
method Derive geometric consequences and prove a Schoen-Yau type criterion.
result Structure theorem for three-dimensional weighted manifolds of non-negative Ricci curvature.
This work shows MLPs can approximate monotonic functions without bounded activations.
problem Optimizing MLPs with monotonic constraints and bounded activations.
method Generalized theoretical results showing MLPs with non-negative weights and saturating activations are universal approximators.
result MLPs with non-negative weights and saturating activations are universal approximators for monotonic functions.
Proposes a new method to improve regression models with reweighted samples.
problem Improves regression models' performance under low sample sizes and covariate perturbations.
method Reparametrizes sample weights using a doubly non-negative matrix and solves the reweighted estimate efficiently.
result Adversarial reweighting strategy delivers promising results on various datasets.
In this paper we prove that on a complete smooth metric measure space with non-negative Bakry-Émery-Ricci curvature if the space of weighted L^2 harmonic one-forms is non-trivial then the weighted volume of the manifold is finite and universal cover of the manifold splits isometrically as the product of the real line w…
Study semilinear equations on weighted manifolds to prove rigidity.
problem Prove rigidity of weighted manifolds via classification of semilinear equations.
method Classify positive solutions at the Sobolev-critical exponent, proving rigidity and weight triviality.
result Existence of positive solutions implies rigidity and weight triviality under certain curvature conditions.
In this letter, we propose enhanced factored three way restricted Boltzmann machines (EFTW-RBMs) for speech detection. The proposed model incorporates conditional feature learning by multiplying the dynamical state of the third unit, which allows a modulation over the visible-hidden node pairs. Instead of stacking prev…
Non-negative constraints improve neural network defenses.
problem Effective defenses against adversarial attacks in neural networks.
method Non-negative weight constraints applied to binary and non-binary classification problems.
result Non-negative constraints can improve resistance to adversarial attacks, especially in binary classification with asymmetric costs.
This paper considers a restriction to non-negative matrix factorization in which at least one matrix factor is stochastic. That is, the elements of the matrix factors are non-negative and the columns of one matrix factor sum to 1. This restriction includes topic models, a popular method for analyzing unstructured data.…
Sharp isoperimetric inequality for Finsler manifolds with non-negative Ricci curvature.
problem Proving an isoperimetric inequality for Finsler manifolds with specific curvature properties.
method Analyzing measured Finsler manifolds with non-negative Ricci curvature and Euclidean volume growth.
result Sharp isoperimetric inequality and rigidity results for the inequality.
Streaming method improves weakly submodular function approximation.
problem Optimizing weakly submodular functions with streaming algorithms.
method Streaming algorithm for RSC and RSM functions.
result Constant factor approximation for weakly submodular functions.
The paper proves conditions for compact Kähler manifolds to be projective or rationally connected.
problem Conditions for compact Kähler manifolds to be projective or rationally connected.
method Proves conditions using quasi-positive and non-negative curvature.
result Compact Kähler manifolds satisfying certain curvature conditions are projective or rationally connected.
The paper generalizes a Steklov eigenvalue inequality for substatic triples under non-negative Ricci curvature.
problem Estimating Steklov eigenvalues for substatic triples under non-negative Ricci curvature.
method Generalization of Fraser-Li type inequality for substatic triples under non-negative Ricci curvature associated with an affine connection.
result The paper provides a new inequality for Steklov eigenvalues of substatic triples.
Study improves understanding of Ricci curvature in manifolds.
problem Understanding Ricci curvature in manifolds with specific assumptions.
method Exploring m-intermediate Ricci curvature and proving comparison theorems.
result Stable weighted slicing in manifolds with non-negative m-intermediate Ricci curvature has almost non-negative Ricci curvature.
Non-negative matrix factorization is a basic tool for decomposing data into the feature and weight matrices under non-negativity constraints, and in practice is often solved in the alternating minimization framework. However, it is unclear whether such algorithms can recover the ground-truth feature matrix when the wei…
New findings on neural networks with non-negative weights and low training error.
problem Does a low training error imply a small outer norm for two-layer neural networks?
method Covering number argument and fat-shattering dimension analysis.
result For non-negative output weights, low training error guarantees a well-controlled outer norm.
New algorithm provably converges to second-order stationary points in NMF.
problem Understanding convergence to local minima in NMF.
method Multiplicative weight update dynamics, concurrent updates, and simplex reduction.
result Provable convergence to second-order stationary points.
We tackle causal inference under conditional moment restrictions using importance weighting.
problem Challenges in causal inference under conditional moment restrictions, especially in high-dimensional settings.
method Transform conditional moment restrictions to unconditional moment restrictions through importance weighting.
result Successfully estimate nonparametric functions defined under conditional moment restrictions.
New weight initialisation for ICNNs accelerates learning and improves generalization.
problem Lack of effective initialisation strategies for ICNNs due to their unique weight and activation properties.
method Derived a principled weight initialisation by generalizing signal propagation theory for ICNNs with non-negative weights.
result Principled initialisation effectively accelerates learning and leads to better generalization in ICNNs.
A collaborative convex framework for factoring a data matrix X into a non-negative product AS, with a sparse coefficient matrix S, is proposed. We restrict the columns of the dictionary matrix A to coincide with certain columns of the data matrix X, thereby guaranteeing a physically meaningful dictionary and …
Enhances sparse coding for motion data classification.
problem Efficiently decompose motion data into sparse combinations.
method Combines DTW and kernelized sparse coding with non-negative constraints.
result Effective in motion capture data interpretation and discrimination.
Paper reformulates UOT as non-negative penalized linear regression for efficient algorithms.
problem Optimal transport with relaxed marginal conditions.
method Reformulate UOT as non-negative penalized linear regression, propose multiplicative updates.
result Efficient algorithms for UOT with quadratic penalties, continuity of solutions.
Bound on integral of scalar curvature on non-parabolic manifolds.
problem Bounding integral of scalar curvature on non-parabolic manifolds.
method Using monotonicity formulas of Colding and Minicozzi.
result Explicit bound on asymptotic weighted scaling invariant integral of scalar curvature.
We treat a discrete-time asset allocation problem in an arbitrage-free, generically incomplete financial market, where the investor has a possibly non-concave utility function and wealth is restricted to remain non-negative. Under easily verifiable conditions, we establish the existence of optimal portfolios.
We prove that n-dimensional (n⩾3) complete and non-compact metric measure spaces with non-negative weighted Ricci curvature in which some Caffarelli-Kohn-Nirenberg type inequality holds are close to the model metric measure n-space (i.e., the Euclidean metric n-space).
In this note it is shown that Berwald spaces admitting the same norm-preserving torsion-free affine connection have the same (weighted) Ricci curvatures. Combing this with Szabó's Berwald metrization theorem one can apply the Cheeger-Gromoll splitting theorem in order to get a full structure theorem for Berwald spaces …
Sharp Hardy inequalities on Riemannian submanifolds with non-negative curvature.
problem Establishing Hardy inequalities for submanifolds in Riemannian geometry.
method Analyzing distance functions and using Riemannian submanifolds with non-negative curvature.
result Sharp weighted Hardy inequalities valid for compact and non-compact submanifolds, even in compact ambient manifolds.
Every connected, weighted graph with non-negative curvature has exactly two ends.
problem Characterizing the structure of connected, weighted graphs with non-negative curvature.
method Extremal Lipschitz extensions, variational principle, study of harmonic functions.
result Every salami has exactly two ends and no vertices with positive curvature.
We study minimal graphic functions on complete Riemannian manifolds $\Si$ with non-negative Ricci curvature, Euclidean volume growth and quadratic curvature decay. We derive global bounds for the gradients for minimal graphic functions of linear growth only on one side. Then we can obtain a Liouville type theorem with …
We generalize most of the known Ricci flow invariant non-negative curvature conditions to less restrictive negative bounds that remain sufficiently controlled for a short time. As an illustration of the contents of the paper, we prove that metrics whose curvature operator has eigenvalues greater than −1 can be evolve…
Proves positive mass theorem for non-spin manifolds with distributional curvature.
problem Proving the positive mass theorem for non-spin manifolds with distributional curvature.
method Using manifolds with asymptotically flat metrics and distributional curvature, the authors show non-negative ADM mass under specific conditions.
result The generalized ADM mass is non-negative for the specified conditions.
Monotonicity and rigidity of W-entropy proved in singular spaces.
problem Entropy behavior in singular metric measure spaces.
method Space-time Wasserstein control to show monotonicity and rigidity.
result Entropy dissipation rate and rigidity models in singular spaces.
We derive a weighted L2-estimate of the Witten spinor in a complete Riemannian spin manifold (Mn,g) of non-negative scalar curvature which is asymptotically Schwarzschild. The interior geometry of M enters this estimate only via the lowest eigenvalue of the square of the Dirac operator on a conformal compactifi…
Given a collection of data points, non-negative matrix factorization (NMF) suggests to express them as convex combinations of a small set of `archetypes' with non-negative entries. This decomposition is unique only if the true archetypes are non-negative and sufficiently sparse (or the weights are sufficiently sparse),…
A new method lifts training of input-convex neural networks to avoid dead weights and plateaued loss.
problem Training input-convex neural networks with non-negative weights.
method Introduces a hypernetwork that emits non-negative weights from a summary of the input batch, adding stochasticity to soften the loss landscape.
result The lift method achieves lower test loss than projected gradient descent and direct softplus reparametrization.
The study proves triviality and rigidity results for Ricci solitons and estimates their conjugate radius.
problem Understanding the properties and behavior of Ricci solitons.
method Analytical proofs and estimates for various types of Ricci solitons.
result Upper bounds and estimates for conjugate radius of Ricci solitons.
A new algorithm resamples Bernoulli race particle filters using true weights.
problem Handling intractable weights in particle filters.
method Proposes a novel resampling method using true weights with an unbiased estimator.
result Demonstrates lower variance in filtering estimates compared to standard methods.
Weighted Lie algebroids were recently introduced as Lie algebroids equipped with an additional compatible non-negative grading, and represent a wide generalisation of the notion of a VB -algebroid. There is a close relation between two term representations up to homotopy of Lie algebroids and VB - algebroids. In this p…
For asymptotically flat initial data of Einstein's equations satisfying an energy condition, we show that the Penrose inequality holds between the ADM mass and the area of an outermost apparent horizon, if the data are restricted suitably. We prove this by generalizing Geroch's proof of monotonicity of the Hawking mass…
Monotone neural networks can approximate and interpolate functions efficiently.
problem Understanding the efficiency and expressiveness of monotone neural networks.
method Solving the monotone interpolation problem using depth-4 networks and comparing size bounds with arbitrary networks.
result Monotone neural networks can approximate and interpolate functions efficiently, but may require exponential size in high dimensions.
This work creates a CS for non-negative heavy-tailed data with bounded mean.
problem Constructing a confidence sequence for non-negative heavy-tailed data with bounded mean.
method Non-parametric, non-asymptotic lower confidence sequence construction.
result The constructed CS is efficient and can be converted into a closed-interval CS.