4 papers
Quaternionic Response Geometry for Proteins: Toward a Noncommutative Theory of Ordered Deformations
Xiaoting Chen, Chon-Fai Kam, Yu Li +6
Protein function may depend on both endpoint conformations and the ordered deformation histories by which they are reached. This distinction is relevant to allostery, conformationa…
Algebraic Representability as the Limiting Regime of Grokking: An Exactly Solvable Model with Holomorphic Activations
Chon-Fai Kam, Xavier Cadet, Miloud Bessafi +1
The paper analyzes two‑layer neural networks with holomorphic monomial activations (σ(z)=z^k) on modular arithmetic tasks, providing an exact algebraic condition for when a target…
Wavelet Variance Equipartition as a Threshold for World-Model Quality and Quantum Kernel TN-Simulability
Chon-Fai Kam, Xavier Cadet, Miloud Bessafi +1
While world models learn compact representations of complex environments, they lack a physics-grounded metric to assess the structural fidelity of their latent spaces. We identify…
WAN3DNS: Weak Adversarial Networks for Solving 3D Incompressible Navier-Stokes Equations
Wenran Li, Xavier Cadet, Miloud Bessafi +7
The 3D incompressible Navier-Stokes equations model essential fluid phenomena, including turbulence and aerodynamics, but are challenging to solve due to nonlinearity and limited s…