Robustness via curvature regularization, and vice versa

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As one of the major threats to women's health worldwide, breast cancer requires early diagnosis and accurate classification, since they are key to optimizing therapeutic interventions and ensuring precise prognosis. Recently, deep learning has demonstrated ...

Many empirical studies have provided evidence for the emergence of algorithmic mechanisms (abilities) in the learning of language models, that lead to qualitative improvements in the model capabilities. Yet, a theoretical characterization of how such mecha ...

In this paper, we consider a compact connected manifold (X, g) of negative curvature, and a family of semi-classical Lagrangian states f(h)(x) = a(x)e(i phi(x)/h) on X. For a wide family of phases phi, we show that f(h), when evolved by the semi-classical ...

We describe the first gradient methods on Riemannian manifolds to achieve accelerated rates in the non-convex case. Under Lipschitz assumptions on the Riemannian gradient and Hessian of the cost function, these methods find approximate first-order critical ...

Quantum Field Theory(QFT) as one of the most promising frameworks to study high energy and condensed matter physics, has been mostly developed by perturbative methods. However, perturbative methods can only capture a small island of the space of QFTs. QFT ...

Hyperbolic lattices are a new type of synthetic materials based on regular tessellations in non-Euclidean spaces with constant negative curvature. While so far, there has been several theoretical investigations of hyperbolic topological media, experimental ...

The work presented in this thesis lies at the intersection of Machine Learning (ML) and control theory. The first part is dedicated to the design of Deep Neural Network (DNN) architectures with specific numerical properties, inspired by dynamical systems m ...

In this paper we study Weingarten surfaces and explore their potential for fabrication-aware design in freeform architecture. Weingarten surfaces are characterized by a functional relation between their principal curvatures that implicitly defines approxim ...

In this PhD manuscript, we explore optimisation phenomena which occur in complex neural networks through the lens of

2

-layer diagonal linear networks. This rudimentary architecture, which consists of a two layer feedforward linear network with a diagonal ...

We present the cosmological implications from final measurements of clustering using galaxies, quasars, and Ly alpha forests from the completed Sloan Digital Sky Survey (SDSS) lineage of experiments in large-scale structure. These experiments, composed of ...

Today, machine learning algorithms are often distributed across multiple machines to leverage more computing power and more data. However, the use of a distributed framework entails a variety of security threats. In particular, some of the machines may mis ...

In this paper, we tackle the problem of static 3D cloth draping on virtual human bodies. We introduce a two-stream deep network model that produces a visually plausible draping of a template cloth on virtual 3D bodies by extracting features from both the b ...

Proteins are foundational biomolecules of life playing a crucial role in a myriad of biological processes. Their function often requires interplay with other biomolecules, including proteins themselves. Protein-protein interactions (PPIs) are essential for ...

In this work, we consider the stability of a spherical shell under combined loading from a uniform external pressure and a homogenous natural curvature. Nonmechanical stimuli, such as one that tends to modify the rest curvature of an elastic body, are prev ...

The flow of a thin film coating the underside of an inclined substrate is studied. We measure experimentally spatial growth rates and compare them to the linear stability analysis of a flat film modelled by the lubrication equation. When forced by a statio ...

Mechanical watches are complex and sensitive systems that have to maintain a faultless precision over their lifetime. However, this precision can be altered by disturbances occurring during the functioning time, such as friction, lubricant drying, or wear, ...

This paper deals with the theory of primary aberrations for perturbed double-plane symmetric optical systems consisting of a combination of tilted and decentered surfaces and a circular pupil. First, the analytical expressions describing the full field beh ...

Let M be a C-2-smooth Riemannian manifold with boundary and N a complete C-2-smooth Riemannian manifold. We show that each stationary p-harmonic mapping u: M -> N, whose image lies in a compact subset of N, is locally C-1,C-alpha for some alpha is an eleme ...

Some preliminary results and experimental details of Near-field Scanning Optical Microscopy (NSOM) operation in liquids have been reported by us earlier(1-4). Here we present the first use of custom made polystyrene/poly (methyl methacrylate) (PMMA) optica ...

For sequences of warped product metrics on a 3-torus satisfying the scalar curvature bound Rj = -1j, uniform upper volume and diameter bounds, and a uniform lower area bound on the smallest minimal surface, we find a subsequence which converges in both the ...

Robustness via curvature regularization, and vice versa

Chattez avec Graph Search

Mspo: a Machine Learning Hyperparameter Optimization Method for Enhanced Breast Cancer Image Classification

A phase transition between positional and semantic learning in a solvable model of dot-product attention

How Lagrangian States Evolve Into Random Waves

An Accelerated First-Order Method for Non-convex Optimization on Manifolds

Nonperturbative Quantum Field Theory in Curved Spacetime

Anomalous and Chern topological waves in hyperbolic networks

Navigating the Loop: From Control Systems to Neural Networks and Back

Computational Design of Weingarten Surfaces

Deep Learning Theory Through the Lens of Diagonal Linear Networks

Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: Cosmological implications from two decades of spectroscopic surveys at the Apache Point Observatory

Robust Machine Learning - Distributed Methods for Safe AI

GarNet++: Improving Fast and Accurate Static 3D Cloth Draping by Curvature Loss

Engineering novel protein interactions with therapeutic potential using deep learning-guided surface design

Nonlinear buckling behavior of a complete spherical shell under uniform external pressure and homogenous natural curvature

Instability of a thin viscous film flowing under an inclined substrate: steady patterns

Tribological Approach to the Watch Movements

Full field dependence of primary aberrations in perturbed double-plane symmetric systems with a circular pupil

Some regularity results for p-harmonic mappings between Riemannian manifolds

Chemically etched plastic optical fiber probe for near-field scanning optical microscopy in liquids

Warped tori with almost non-negative scalar curvature