The aim of this paper is to study the local components of the relativistic time dependent d-linear connections, d-torsions, d-curvatures and deflection d-tensors with respect to an adapted basis on the 1-jet space . The Ricci identities, together with their corresponding identities of deflection d-tensors, …
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17 results for “deflection”
New approach deflects adversarial attacks by causing them to resemble target classes.
problem Ongoing cycle of stronger defenses being broken by more advanced attacks.
method Combines three detection mechanisms in Capsule Networks to achieve state-of-the-art performance on both standard and defense-aware attacks. Uses human study to show attacks can no longer be called adversarial.
result Attack images can no longer be called adversarial because they are classified the same way as humans do.
The number of Italian firms in function of the number of workers is well approximated by an inverse power law up to 15 workers but shows a clear downward deflection beyond this point, both when using old pre-1999 data and when using recent (2014) data. This phenomenon could be associated with employent protection legis…
The aim of this paper is to present the main geometrical objects on the dual 1-jet bundle (this is the polymomentum phase space of the De Donder-Weyl covariant Hamiltonian formulation of field theory) that characterize our approach of multi-time Hamilton geometry. In this direction, we firstly intro…
Shells resist three out of six possible loads if simply connected.
problem Understanding the load resistance of shells.
method Formal mathematical analysis of shell strains and deflections.
result The space of strains is three-dimensional for simply-connected shells.
The paper introduces the notion of h-normal Γ-linear connection \nabla on 1-jet fibre bundle J^1(T,M), and studies its local d-torsions and d-curvatures togheter with theirs Bianchi identities. Also, it presents the important deflection d-tensors identities attached to \nabla.
We pursue a geometrical approach to gravitational lensing theory. We present a survey of the background theory of General Relativity, including particular properties of the Schwarzschild and Kerr solutions. Next we outline a proof of the Gauss Bonnet theorem and its applications to surfaces in optical geometry, as deve…
Breaking certified defenses: Semantic adversarial examples with spoofed robustness certificatescs.LG
New attack tricks certifiably robust models into mislabeling images.
problem Defeating certified defenses against adversarial examples.
method Spoofed robustness certificates and large perturbations.
result Certifiably robust models can be fooled by large perturbations.
Over-parameterized neural networks generalize well in practice without any explicit regularization. Although it has not been proven yet, empirical evidence suggests that implicit regularization plays a crucial role in deep learning and prevents the network from overfitting. In this work, we introduce the gradient gap d…
In this paper we describe the local Ricci and Bianchi identities for an h-normal N-linear connection DΓ(N) on the dual 1-jet space J^{1*}(T,M). To reach this aim, we firstly give the expressions of the local distinguished (d-) adapted components of torsion and curvature tensors produced by DΓ(N), and then we analyze th…
Four-dimensional scanning transmission electron microscopy (4D-STEM) of local atomic diffraction patterns is emerging as a powerful technique for probing intricate details of atomic structure and atomic electric fields. However, efficient processing and interpretation of large volumes of data remain challenging, especi…
Finsler connection preserving the two-vector angle under the indicatrix-inhomogeneous treatmentmath.DG
The Finsler spaces in which the tangent Riemannian spaces are conformally flat prove to be characterized by the condition that the indicatrix is a space of constant curvature. In such spaces the Finslerian normalized two-vector angle can be explicated from the respective two-vector angle of the associated Riemannian sp…
Bayesian Entropy Neural Networks enforce constraints on deep learning predictions.
problem Deep learning models lack well-defined constraints in their outputs.
method Bayesian Entropy Neural Networks (BENN) using Maximum Entropy principles and the method of multipliers.
result BENN improves model robustness and reliability across various applications.
Prediction models in mobility and transportation maintenance systems have been dramatically improved through using machine learning methods. This paper proposes novel machine learning models for intelligent road inspection. The traditional road inspection systems based on the pavement condition index (PCI) are often as…
Transformer models are compared to curved spacetime in General Relativity.
problem Understanding the geometric structure of Transformer models.
method Geometric analogy to General Relativity, focusing on attention and curvature effects.
result Transformer token embeddings exhibit curvature, affecting their evolution over layers.
Mathematical model audits social media algorithms to prevent bias.
problem Algorithmic filtering can bias users' decisions and societal norms.
method Formalized mathematical framework for auditing social media algorithms.
result Data-driven statistical auditing procedure to regulate algorithmic bias.
Deep learning helps remove secondary -mode polarization to detect primordial gravitational waves.
problem Removing secondary -mode polarization from CMB data to detect primordial gravitational waves.
method Applied deep learning (ResUNet-CMB) to estimate and remove multiple sources of secondary -mode polarization.
result Deep learning can produce nearly optimal, unbiased estimates of the amplitude of primordial gravitational waves.