In this paper we present the full details of the construction of a Morse-Floer type homology related to the super-quadratic perturbation of the Dirac-geodesic model. This homology is computed explicitly using a Leray-Serre type spectral sequence and this computation leads us to several existence results of Dirac-geodes…
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12 results for “Super-quadratic”
New algorithm extends LMC to more complex potentials.
problem Addressing limitations of existing LMC methods.
method Inexact Proximal Langevin Algorithm (IPLA).
result Improved convergence rates and broader applicability.
In this paper we investigate the properties of a semi-linear problem on a spin manifold involving the Dirac operator, through the construction of Rabinowitz-Floer homology groups. We give several existence results for sub-critical and critical non-linearities as application of the computation of the different homologie…
This paper concerns integral varifolds of arbitrary dimension in an open subset of Euclidean space satisfying integrability conditions on their first variation. Firstly, the study of pointwise power decay rates almost everywhere of the quadratic tilt-excess is completed by establishing the precise decay rate for two-di…
We prove super-quadratic lower bounds for the growth of the filling area function of a certain class of Carnot groups. This class contains groups for which it is known that their Dehn function grows no faster than . We therefore obtain the existence of (finitely generated) nilpotent groups whose Dehn functio…
Compress++ speeds up distribution compression to near-linear time.
problem Accurately summarize a probability distribution using a small number of points efficiently.
method Introduces Compress++, a meta-procedure to speed up any thinning algorithm.
result Achieves points with integration error in time and space.
Precise computations of Dehn functions for subgroups of free group products.
problem Computing precise Dehn functions for subgroups of direct products of free groups.
method Analyzing specific subgroups and using algebraic methods to compute Dehn functions.
result Quartic and quadratic Dehn functions for specific subgroups of free group products.
We give dimension-free regularity conditions for a class of possibly degenerate sub-elliptic equations in the Heisenberg group exhibiting super-quadratic growth in the horizontal gradient; this solves an issue raised by Manfredi & Mingione (Math. Ann. 2007) where only dimension dependent bounds for the growth exponent …
In data summarization we want to choose prototypes in order to summarize a data set. We study a setting where the data set comprises several demographic groups and we are restricted to choose prototypes belonging to group . A common approach to the problem without the fairness constraint is to optimize a c…
Recent research shows that the following two models are equivalent: (a) infinitely wide neural networks (NNs) trained under l2 loss by gradient descent with infinitesimally small learning rate (b) kernel regression with respect to so-called Neural Tangent Kernels (NTKs) (Jacot et al., 2018). An efficient algorithm to c…
New method speeds up neural kernel computations for various activations.
problem Inefficient computation of neural kernels for general activations.
method Fast sketching method using truncated Hermite expansion.
result 106x speedup for approximate CNTK computation on CIFAR-10.
Efficiently estimates Gaussian distributions privately and robustly.
problem Private and robust estimation of Gaussian distributions.
method Efficient algorithms for pure and approximate differential privacy models.
result Optimal sample complexity in both pure and approximate differential privacy settings.