We establish continuous maximal regularity results for parabolic differential operators acting on sections of tensor bundles on Riemannian manifolds. As an application, we show that solutions to the Yamabe flow instantaneously regularize and become real analytic in space and time. The regularity result is obtained by i…
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48 results for “maximal regularity”
Maximal regularity for nonuniformly parabolic problems with normal degeneration.
problem Nonuniformly parabolic boundary value problems with degeneration in normal direction.
method Theory of linear parabolic differential equations on noncompact Riemannian manifolds.
result Optimal solution theory for natural degeneration case.
Preventing Value Function Collapse in Ensemble {Q}-Learning by Maximizing Representation Diversitycs.LG
New technique prevents Q-learning collapse by maximizing diversity among ensembles.
problem Value function collapse in ensemble Q-learning.
method Maximizing representation diversity through regularization.
result Regularized approach significantly outperforms existing methods.
Scalable methods for maximizing regularized submodular functions with improved memory and communication complexity.
problem Maximizing submodular functions with negative values and constraints.
method Developed one-pass streaming and distributed algorithms for maximizing regularized submodular functions.
result Improved memory and communication complexity by a factor of O(1/ε) compared to existing work.
Regularity and estimates for -holomorphic discs attached to a maximal totally real submanifoldmath.CV
We prove that pseudo-holomorphic discs attached to a maximal totally real submanifold inherit their regularity from the regularity of the submanifold and of the almost complex structure. The proof is based on the computation of an explicit lower bound for the Kobayashi metric in almost complex manifolds, which also yie…
A fast geometric regularizer improves event camera performance.
problem Event collapse in contrast maximization framework.
method Geometric regularizer to mitigate overfitting.
result State-of-the-art accuracy with reduced computational complexity.
Extends elliptic operator regularity to maximally hypoelliptic operators.
problem Maximally hypoelliptic differential operators and their regularity.
method Define a principal symbol for arbitrary differential operators involving vector fields and their commutators.
result Proves the invertibility of the principal symbol is equivalent to maximally hypoellipticity, answering a conjecture.
This work proposes SDI regularization to improve adversarial robustness.
problem Improving adversarial robustness of deep neural networks.
method SDI regularization term to complement adversarial training.
result Combining SDI with AT variants enhances robustness and generalization.
We prove that any minimal (maximal) strongly regular surface in the three-dimensional Minkowski space locally admits canonical principal parameters. Using this result, we find a canonical representation of minimal strongly regular time-like surfaces, which makes more precise the Weierstrass representation and shows mor…
Optimizes eigenvalues on surfaces with symmetries.
problem Maximizing Laplace and Steklov eigenvalues on Riemann surfaces with symmetries.
method Simplifies existing techniques for conformal class optimization.
result Proves existence and regularity of maximizers for Laplace and Steklov eigenvalues.
The paper defines function spaces on manifolds with bounded or singular geometries.
problem Defining function spaces on manifolds with various geometries.
method Introduces and analyzes Sobolev, Besov, and Bessel potential spaces on uniformly regular and singular Riemannian manifolds.
result Demonstrates maximal regularity for a linear parabolic problem on singular manifolds.
Method introduces topological regularization using information filtering networks.
problem Sparse probabilistic modeling and multicollinear regression.
method Topological regularization via information filtering network.
result Direct application to -norm regularized problems.
Proves properties of maximal hypersurfaces in specific spacetimes.
problem Maximal hypersurfaces in asymptotically AdS spacetimes.
method Uniqueness, existence, and regularity results via mathematical proofs.
result Proves uniqueness, existence, and regularity of maximal hypersurfaces.
The paper proposes effective margin regularization to improve adversarial robustness in deep neural networks.
problem Adversarial vulnerability of deep neural networks (DNNs).
method Regularization of effective weight norm during training to maximize effective margins.
result Effective margin regularization (EMR) boosts adversarial robustness in both standard and adversarial training.
Study finds metrics maximizing one Laplace eigenvalue on 3D and higher manifolds.
problem Maximizing a Laplace eigenvalue on n-dimensional manifolds.
method Existence and regularity results for metrics of same volume in a conformal class.
result Existence and regularity of metrics maximizing the Laplace eigenvalue.
CPR adds entropy maximization to improve continual learning methods.
problem Catastrophic forgetting in continual learning.
method Classifier-Projection Regularization (CPR) adds an entropy maximization term to existing regularization methods.
result CPR improves accuracy and plasticity in continual learning methods.
Maximal correlation framework improves fairness in machine learning algorithms.
problem Ensuring fairness in machine learning algorithms.
method Introducing maximal correlation framework for fairness constraints and deriving regularizers.
result The approach provides smooth performance-fairness tradeoff curves and competitive performance.
We construct low regularity solutions of the vacuum Einstein constraint equations. In particular, on 3-manifolds we obtain solutions with metrics in $H^s\loc$ with . The theory of maximal asymptotically Euclidean solutions of the constraint equations descends completely the low regularity setting. Moreove…
Entropy regularization is used to get improved optimization performance in reinforcement learning tasks. A common form of regularization is to maximize policy entropy to avoid premature convergence and lead to more stochastic policies for exploration through action space. However, this does not ensure exploration in th…
By a theorem of Banyaga the group of diffeomorphisms of a manifold preserving a regular contact form is a central extension of the commutator of the group of symplectomorphisms of the base . We show that if is a Hamiltonian maximal torus in the group of symplectomorphism of , then its pr…
Algorithme EM régulariséstat.ML
Regularized EM algorithm improves clustering performance with small sample sizes.
problem Performance reduction in EM algorithm due to small sample size and poorly conditioned covariance matrices.
method Regularized EM algorithm that uses prior knowledge to ensure positive definiteness of covariance matrices.
result The regularized EM algorithm outperforms standard EM in clustering tasks with small sample sizes.
In this paper we study the spacelike-characteristic Cauchy problem for the Einstein vacuum equations. We prove that given initial data on a maximal compact spacelike hypersurface and the outgoing null hypersurface emanating from , the time of ex…
The ratio of volume to crossing number of a hyperbolic knot is known to be bounded above by the volume of a regular ideal octahedron, and a similar bound is conjectured for the knot determinant per crossing. We investigate a natural question motivated by these bounds: For which knots are these ratios nearly maximal? We…
Proposes a framework to maximize mutual information in VAE models for better latent code representation.
problem Lack of explicit measurement of the quality of learned representations in VAE models.
method Variational Mutual Information Maximization Framework for VAE.
result Maximizes mutual information between latent codes and observations, improving latent code representation.
We find maximal representatives within equivalence classes of metric spheres. For Ahlfors regular spheres these are uniquely characterized by satisfying the seemingly unrelated notions of Sobolev-to-Lipschitz property, or volume rigidity. We also apply our construction to solutions of the Plateau problem in metric spac…
This paper optimizes revenue and resource balance in network revenue management.
problem Maximizing revenue while ensuring fair resource consumption across different suppliers.
method Introduces a regularized revenue objective and a primal-dual UCB algorithm for continuous prices and balancing.
result Achieves a worst-case regret of for revenue maximization and balancing.
In this paper we consider the problem of maximizing the Area under the ROC curve (AUC) which is a widely used performance metric in imbalanced classification and anomaly detection. Due to the pairwise nonlinearity of the objective function, classical SGD algorithms do not apply to the task of AUC maximization. We propo…
Proposes a novel graph self-training method with EM regularization for semi-supervised node classification.
problem Handles noisy graph structures and feature spaces in semi-supervised node classification.
method Introduces an Expectation-Maximization (EM) regularization scheme for uncertainty-aware pseudo-label generation and model retraining.
result Significantly outperforms strong baselines by up to 2.5% in accuracy.
We discuss a recurrent geometrical method, due to Élie Cartan and von Weber ([1],[11]) enabling us to determine, step by step, the maximal integral manifolds of a not necessarily integrable nor regular Pfaffian system. The dimensions of such integral manifolds can, of course, vary from point to point but more so can va…
We consider a stochastic optimal control problem in a market model with temporary and permanent price impact, which is related to an expected utility maximization problem under finite fuel constraint. We establish the initial condition fulfilled by the corresponding value function and show its first regularity property…
GPMD solves regularized RL with linear convergence, promoting structural policies.
problem Regularized reinforcement learning to encourage exploration and structural policies.
method Policy mirror descent with generalized convex regularizers and Bregman divergence.
result GPMD converges linearly to the global solution over a wide range of learning rates.
New proof for convex solutions of Monge-Ampère equation.
problem Interior regularity of strictly convex solutions
method Doubling inequality for Hessian in extrinsic distance function
result Interior regularity established
We demonstrate that almost all non-parametric dimensionality reduction methods can be expressed by a simple procedure: regularized loss minimization plus singular value truncation. By distinguishing the role of the loss and regularizer in such a process, we recover a factored perspective that reveals some gaps in the c…
Maximizing energy on flexible curves yields regular or convex polygons.
problem Finding the shape of a flexible curve that maximizes a given energy function.
method Analyzing the energy function and properties of flexible curves.
result Maximizers are regular or convex n-gons, with each edge of length 1.
New method learns adaptive exploration strategies for dynamic tasks.
problem Learning effective exploration strategies in changing environments.
method Informed policy regularization to reduce sample complexity of RNN-based policies.
result Method learns efficient exploration strategies balancing information gathering and reward maximization.
Solves Deligne-Simpson problem for special connections on Gm.
problem Existence of Fuchsian connections with specific singularities.
method Theory of fundamental and regular strata, lattice chain filtration, quiver varieties.
result Characterization of rigid connections with unipotent monodromy at infinity.
We consider a geometrically finite discrete group of conformal transformations of the sphere. Further we consider distributions which are supported on the limit set and are invariant with conformal weight. We estimate their regularity in terms of the conformal weight, the Hausdorff dimension of the limit set, and the m…
This paper addresses the problem of sparsity penalized least squares for applications in sparse signal processing, e.g. sparse deconvolution. This paper aims to induce sparsity more strongly than L1 norm regularization, while avoiding non-convex optimization. For this purpose, this paper describes the design and use of…
Choquet regularization improves exploration in RL.
problem Improving exploration in reinforcement learning.
method Introducing Choquet regularizers to measure and manage exploration, reformulating RL problems and deriving explicit solutions.
result Explicit optimal distributions and Choquet regularizers for various exploratory samplers.
Standard accuracy metrics indicate that modern reading comprehension systems have achieved strong performance in many question answering datasets. However, the extent these systems truly understand language remains unknown, and existing systems are not good at distinguishing distractor sentences, which look related but…
Proves Gannon-Lee theorem for spacetimes.
problem Classical singularity theorems for spacetimes.
method Proves theorem for spacetimes, shows geodesic properties.
result Gannon-Lee theorem holds for spacetimes.
Maximality of the futures of points in globally hyperbolic maximal conformally flat spacetimesmath.DG
Maximal spacetimes have unique past/future sets.
problem Characterizing maximal spacetimes.
method Developing map analysis and diamond properties.
result Maximal spacetimes have unique past/future sets.
DAC enhances exploration in reinforcement learning with entropy regularization.
problem Improving exploration efficiency in reinforcement learning.
method Sample-aware entropy regularization using replay buffer action distributions.
result DAC significantly outperforms existing algorithms in reinforcement learning tasks.
Anisotropic curvature flow of networks shows unique solutions and behavior under finite time.
problem Existence and behavior of networks under anisotropic curvature flow.
method Existence, uniqueness, and regularity of maximal geometric solutions proven.
result Existence of maximal geometric solutions and behavior under finite time.
Study on a metric for disk automorphisms with maximal modulus.
problem Characterizing the metric on disk automorphisms.
method Explicit formula for the metric induced by maximal modulus.
result Characterized almost regular Finsler structure.
In this paper we combine our recent work on regular globally hyperbolic maximal anti-de Sitter structures with the classical theory of globally hyperbolic maximal Cauchy-compact anti-de Sitter manifolds in order to define an augmented moduli space. Moreover, we introduce a coordinate system in this space that resembles…
Design of reliable systems must guarantee stability against input perturbations. In machine learning, such guarantee entails preventing overfitting and ensuring robustness of models against corruption of input data. In order to maximize stability, we analyze and develop a computationally efficient implementation of Jac…
In this paper, we prove global second derivative estimates for solutions of the Dirichlet problem for the Monge-Ampere equation when the inhomogeneous term is only assumed to be Holder continuous. As a consequence of our approach, we also establish the existence and uniqueness of globally smooth solutions to the second…