11 papers
Proximity-Preserving Neural Subdivision
Hassan Ugail
Classical subdivision schemes are widely used because they are local, repeatable, and analytically tractable. A single stencil defines the entire refinement rule, and the behaviour…
Reliable Weyl Diagnostics for an Inhomogeneous Universe in Numerical Relativity
Hassan Ugail
The electric and magnetic parts of the Weyl tensor provide a geometric diagnostic for describing the local gravitational structure of an inhomogeneous universe, and they allow us t…
A Heisenberg Subdivision Scheme with Central Smoothness Loss
Hassan Ugail, Alfonso Carriazo
We introduce an interpolatory subdivision scheme for control polygons that take values in the three-dimensional Heisenberg group, the simplest noncommutative model geometry. The sc…
A Coherence Law for Trainability in Noisy Equivariant Quantum Neural Networks
Hassan Ugail, Newton Howard
Symmetry provides a quantum neural network structure, but on its own it does not keep the network trainable once noise is present. We ask which physical quantity decides whether th…
Geometric Phase-Space Structure in Cosmological Solutions of Einstein's Field Equations
Hassan Ugail
Einstein field equations allow cosmological dynamics to depart from the Friedmann-Lemaitre-Robertson-Walker (FLRW) idealisation in several physically different ways. Matter may bec…
Training Deep Visual Networks Beyond Loss and Accuracy Through a Dynamical Systems Approach
Hai La Quang, Hassan Ugail, Newton Howard +3
Deep visual recognition models are usually trained and evaluated using metrics such as loss and accuracy. While these measures show whether a model is improving, they reveal very l…