13 citations · 41 across the 26 of their papers we have counts for
9 papers · 1 filter
Okubo algebras and Exceptional Periodicity: tetracode gradings, root-lattice obstructions and Clifford cones
Alessio Marrani, Daniele Corradetti
The Okubo algebra brings together ternary gradings, integral root frames and rank-three geometry. We examine how these structures extend to the complex Exceptional Periodicity alge…
Closed-Form Noise Calibration Against Membership Inference for Random-Allocation DP-SGD
Murat Bilgehan Ertan, Marten van Dijk
DP-SGD protects training data by adding Gaussian noise to clipped gradients. The amount of noise is usually chosen by running a numerical privacy accountant inside a search. We stu…
Integral Orders for the Okubo Algebra and Idempotent Geometries of the Lattice
Daniele Corradetti, Alessio Marrani
We study the Coxeter-Dickson order as a common integral support for the octonionic, para-octonionic and compact real Okubo products. The three algebra structures have the sam…
Linguistic Holonomy and Statistical Watermarks: Inner Geometry of Meaning-Preserving Transformations
Daniele Corradetti
Statistical watermarks for language models live in the freedom of the signifier: they choose among tokens that are nearly equivalent in meaning, and they are therefore eroded by ex…
Integral Planes and Unit-Norm Polytopes
Daniele Corradetti
We introduce and study integral planes associated with crystallographic and non-crystallographic integral systems in real composition algebras. For an integral order $\Order$ in su…
Non-crystallographic systems of integers over composition algebras
Daniele Corradetti
In this work we revisit classical systems of integers inside the real normed division algebras from the point of view of finite norm shells and root systems. Building on the icosia…
Integral Shell Polytopes of Composition Algebras
Daniele Corradetti
Integral systems in real composition algebras give rise to finite metric configurations whose geometry is linked to both regular polytopes and root-systems. In this work we investi…
Integral elements of Okubo algebra and the E8-lattice
Daniele Corradetti
In this work we study the interplay between the Coxeter-Dickson -order, the para-octonions, and the real Okubo algebra. We first explain why a usual rotation presentation of…
Learning Hippo: Multi-attractor Dynamics and Stability Effects in a Biologically Detailed CA3 Extension of Hopfield Networks
Daniele Corradetti, Renato Corradetti
We present a biologically detailed extension of the classical Hopfield/Marr auto-associative memory model for CA3, implementing ten populations (two asymmetric pyramidal subtypes,…