DG algorithms often fail to generalize well in limited domains, highlighting necessary vs. sufficient conditions.
problem DG algorithms fail to consistently outperform ERM in limited domains.
method Examined necessary and sufficient conditions for DG, proposing a subspace alignment method.
result DG methods focus on sufficient conditions, often neglecting necessary conditions, leading to generalization failures.
New conditions prevent gaps in optimal control problems.
problem Preventing gaps in optimal control problems with state constraints.
method Developed new sufficient conditions not relying on convexity.
result Derived bounds for the size of the relaxation gap.
Establishes a condition for multiclass classification-calibration of Gamma-Phi losses.
problem Ensuring classification-calibration of multiclass Gamma-Phi losses.
method Develops a general sufficient condition for classification-calibration of Gamma-Phi losses.
result Proves the first family of nonconvex multiclass surrogate losses for which classification-calibration has been fully justified.
Study abelianization of Lie algebroids and groupoids, providing conditions for existence.
problem Existence conditions for abelianization of Lie algebroids and groupoids.
method Investigation of abelianization for Lie algebroids and groupoids, providing necessary and sufficient conditions.
result Necessary and sufficient conditions for the existence of abelianization in both Lie algebroids and groupoids.
Proves sufficient condition for 2D orbifolds to be good.
problem Characterizing 2D orbifolds as good.
method Analyzes orbifold fundamental groups for goodness.
result Connected 2D orbifolds with infinite orbifold fundamental group are good.
New findings on flatness for specific driftless systems.
problem Determining flatness for driftless systems with m inputs and 2m or 2m-1 states.
method Using pure prolongation, the paper presents new sufficient conditions for flatness.
result The conditions proposed broaden the class of recognized flat systems.
Paper proves min-vol NMF robust to noise under expanded condition.
problem Robustness of min-vol NMF to noise.
method Proved robustness under expanded sufficiently scattered condition.
result Proves min-vol NMF identifies groundtruth factors in noise.
Condition found for spinc structures on a specific type of manifold.
problem Existence of spinc structures on real Bott manifolds.
method Provided a necessary and sufficient condition.
result Condition for spinc structures on real Bott manifolds established.
New condition for reconstructing Morse functions on 3D manifolds.
problem Reconstructing Morse functions with specific level sets.
method Studied a necessary and sufficient condition for reconstruction.
result New condition strengthens previous sufficient conditions.
We study the necessary and sufficient conditions for a Finsler surface with (α,β)-metrics to be with reversible geodesics.
A new sufficient condition ensures convergence of Adam and RMSProp in non-convex settings.
problem Adam and RMSProp diverge in convex settings, despite being influential for deep learning.
method Introduces a sufficient condition based on base learning rate and historical second-order moments.
result Guarantees global convergence of generic Adam/RMSProp in non-convex optimization.
The Hilbert map's image is discussed, showing when it's surjective.
problem Understanding when the Hilbert map is surjective.
method Analyzing the Hilbert map's properties to determine surjectivity.
result Necessary and sufficient conditions for the Hilbert map to be surjective.
The paper simplifies conditions for optimal paths on manifolds avoiding obstacles.
problem Finding optimal paths on manifolds avoiding obstacles.
method Study of sufficient conditions for optimality on Riemannian manifolds and Lie groups.
result New conditions for optimality are provided in terms of matrix invertibility.
Develops a nonparametric graphical model for conditional independence.
problem Evaluation of conditional independence without distributional assumptions.
method Nonlinear sufficient dimension reduction techniques applied to a nonparametric graphical model.
result Method outperforms existing methods in non-Gaussian settings and high-dimensional data.
The paper modifies a warped product space to find conditions for constant height functions.
problem Finding sufficient conditions for the height function to be constant in a modified warped product space.
method The paper modifies the warped product space by adding a warping function and discusses the sufficient condition for the height of immersed surfaces.
result The paper establishes a sufficient condition for the height function to be constant in the modified warped product space.
Easy conditions found for simplifying complex systems.
problem Linearizing complex two-input systems.
method Endogenous dynamic feedback with a dimension of at most two.
result Necessary and sufficient conditions for linearizability.
Greg McShane introduced a remarkable identity for lengths of simple closed geodesics on the once punctured torus with a complete, finite volume hyperbolic structure. Bowditch later generalized this and gave sufficient conditions for the identity to hold for general type-preserving representations of a free group on two…
The study finds necessary and sufficient conditions for C1-hypersurfaces to have nowhere C1-regular parallel sets.
problem Conditions for C1-hypersurfaces to have nowhere C1-regular parallel sets. method Proves a necessary and sufficient condition for C1-hypersurfaces to have nowhere C1-regular parallel sets. result A necessary and sufficient condition for C1-hypersurfaces to have nowhere C1-regular parallel sets. Unified neural network for linear and nonlinear dimension reduction.
problem Efficiently perform linear and nonlinear sufficient dimension reduction.
method Belted and Ensembled Neural Network (BENN) framework.
result Unified framework for both linear and nonlinear dimension reduction.
We give a sufficient condition for a branched surface in a 3 dimensional manifold to fully carry a lamination, giving a piece of answer to a classical question of D. Gabai.
We give topological conditions to ensure that a noncollapsed almost Ricci-flat 4-manifold admits a Ricci-flat metric. One sufficient condition is that the manifold is spin and has a nonzero A-hat genus. Another condition is that the fundamental group is infinite or, more generally, of sufficiently large cardinality.
Necessary and sufficient condition is given for a set A⊂R1 to be a subset of the critical values set for a Ck function f:Rm→R1.
We address some theoretical guarantees for Schatten-p quasi-norm minimization (p∈(0,1]) in recovering low-rank matrices from compressed linear measurements. Firstly, using null space properties of the measurement operator, we provide a sufficient condition for exact recovery of low-rank matrices. This condition…
Guilbault and author prove sufficient conditions for Z-compactifiability of certain manifolds.
problem Establishing sufficient conditions for Z-compactifiability of manifolds. method Introducing additional conditions to prove Z-compactifiability of Mnimes[−2,2] implies Z-compactifiability of Mn. result There exist infinitely many non-pseudo-collarable 4-manifolds which are Z-compactifiable. In this short note, we give a sufficient condition for almost smooth compact metric measure spaces to satisfy the Bakry-Émery condition BE(K,N). The sufficient condition is satisfied for the glued space of any two (not necessary same dimensional) closed pointed Riemannian manifolds at their base points. This tells …
Defines and studies Clairaut Riemannian maps between manifolds and Ricci solitons.
problem Characterizing and analyzing Clairaut Riemannian maps.
method Using geodesic curves, necessary and sufficient conditions for harmonicity and Clairaut maps are derived.
result Necessary conditions for various properties of Clairaut Riemannian maps are established.
New Milnor's invariant condition for topologically slice links.
problem Conditions for topologically slice links involving Milnor's invariant.
method Different Milnor's invariant condition to handle cases not covered by previous theorem.
result New sufficient conditions for topologically slice links.
We find a necessary and sufficient condition for a compact 7-manifold to admit a G~2-structure. As a result we find a sufficient condition for an open 7-manifold to admit a closed 3-form of G~2-type.
I.A.B. Strachan introduced the notion of a natural Frobenius submanifold of a Frobenius manifold and gave a sufficient but not necessary condition for a submanifold to be a natural Frobenius submanifold. This paper will give a necessary and sufficient condition and classify the natural Frobenius hypersurfaces.
New conditions ensure geodesic connectedness of affine manifolds.
problem Ensuring geodesic connectedness in affine manifolds.
method New sufficient conditions for geodesic connectedness, weaker than previous work.
result Elementary proof of geodesic connectedness.
We formulate a sufficient condition for the existence of a consistent price system (CPS), which is weaker than the conditional full support condition (CFS) introduced by Guasoni, Rasonyi, and Schachermayer [Ann. Appl. Probab., 18(2008), pp. 491-520] . We use the new condition to show the existence of CPSs for certain p…
In this paper, we give sufficient conditions for a Perron number, given as the leading eigenvalue of an aperiodic matrix, to be a pseudo-Anosov dilatation of a compact surface. We give an explicit construction of the surface and the map when the sufficient condition is met.
Low-rank matrix recovery has found many applications in science and engineering such as machine learning, signal processing, collaborative filtering, system identification, and Euclidean embedding. But the low-rank matrix recovery problem is an NP hard problem and thus challenging. A commonly used heuristic approach is…
New method uses sufficient statistics to infer causal relationships from observational data.
problem Inferring causal relationships from observational data with hidden variables.
method Information Bottleneck method applied to find functional sufficient statistics.
result New causal rules not obtainable from standard methods, validated on simulated and real data.
The paper analyzes the convergence of CART under a SID condition, improving previous results.
problem Investigating the convergence rate of CART under a sufficient impurity decrease condition.
method Established an upper bound on prediction error under SID condition, introduced easily verifiable conditions.
result Improved convergence rate of CART under SID condition, demonstrated examples of error bound limitations.
Listing has recently extended results of Kozameh, Newman and Tod for four-dimensional spacetimes and presented a set of necessary and sufficient conditions for a metric to be locally conformally equivalent to an Einstein metric in all semi-Riemannian spaces of dimension n>3 -- subject to a non-degeneracy restriction on…
Quantized neural networks can represent all fixed-point functions under certain conditions.
problem Expressive power of quantized neural networks under fixed-point arithmetic.
method Analyzing necessary and sufficient conditions for quantized networks to represent all fixed-point functions.
result Various popular activation functions satisfy the sufficient condition for representing all fixed-point functions.
New approach proves convergence of SA and SGD with weaker conditions.
problem Proving convergence of SA and SGD with relaxed noise conditions.
method Introduces GSLLN to decouple function and noise properties.
result Derives sufficient conditions for convergence of SA and SGD.
Paper extends Green-Osher inequality for convex bodies at dilation position.
problem Extending Green-Osher inequality for specific geometric configurations.
method Analyzes strictly convex bodies at dilation position and derives necessary and sufficient conditions.
result Establishes extended Green-Osher inequality with conditions for equality.
The object of this paper is to obtain the concircular curvature tensor of the semi symmetric non-metric connection on the Weyl manifold and to give a necessary and sufficient condition for a semi symmetric non-metric connection to be S-concircular.
In this paper, we propose new conditions guaranteeing that the trajectories of a mechanical control system can track any curve on the configuration manifold. We focus on systems that can be represented as forced affine connection control systems and we generalize the sufficient conditions for tracking known in the lite…
The paper establishes conditions for strict power concavity in convolutions.
problem Conditions for strict power concavity in convolutions.
method Analyzes sufficient conditions for strict parabolic power concavity of convolutions.
result Establishes sufficient conditions for strict power concavity of convolutions.
Paper finds conditions for non-Einstein relative Yamabe metrics.
problem Finding relative Yamabe metrics with positive scalar curvature.
method Sufficient condition for positive constant scalar curvature metrics on manifolds with boundary.
result Examples of non-Einstein relative Yamabe metrics with positive scalar curvature.
The paper defines conditions for para-Kaehler immersions and classifies them between forms.
problem Existence and classification of para-Kaehler immersions.
method Necessary and sufficient conditions for para-Kaehler immersions in para-Kaehler space forms.
result Local para-Kaehler immersions cannot be globally extended on simply connected para-Kaehler manifolds.
Let Pi: M -> B be an onto maximal rank map or a Riemannian submersion between Riemannian manifolds M and B. Initially, we prove necessary and sufficient conditions for any fiber F to be roughly isometric to M. Then, we prove necessary and sufficient conditions for Pi to be a rough isometry. As a corollary M is roughly …
The paper studies maps between Riemannian and Kähler manifolds, focusing on Clairaut semi-invariant Riemannian maps.
problem Analyzing maps between Riemannian and Kähler manifolds, particularly Clairaut semi-invariant Riemannian maps.
method Recalled and defined Clairaut semi-invariant Riemannian maps, derived necessary and sufficient conditions for geodesic curves and maps, and explored foliations and product manifolds.
result Necessary and sufficient conditions for various properties of Clairaut semi-invariant Riemannian maps were derived.
We consider a problem of optimal investment with intermediate consumption in the framework of an incomplete semimartingale model of a financial market. We show that a necessary and sufficient condition for the validity of key assertions of the theory is that the value functions of the primal and dual problems are finit…
The paper finds conditions for Yamabe solitons' metrics to be constant scalar curvature.
problem Finding conditions for Yamabe solitons' metrics to be constant scalar curvature.
method Using properties of conformal vector fields to find sufficient conditions.
result Sufficient conditions on soliton vector fields under which their metrics are of Yamabe metrics.